13 20 453 https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/fb3408aca935ffcd2a2ea3d941ee102b.pdf 77c1cc29af0d15782ccd897fcaf4506e PDF Text Text The College Aristotle's Definition of Motion by Joe Sachs Aristotle defines motion, by which he means change of any kind, as the actuality of a potentiality as such (or as movable, or as a potentiality-Physics 20la 10-11, 27-29, b4-5.) The definition is a conjunction of two terms which normally contradict each other, along with, in Greek, a qualifying clause which seems to make the contradiction inescapable. Yet St. Thomas Aquinas called it the only possible way to define motion by what is prior to and better known than motion. At the opposite extreme is the young Descartes, who in the first book he wmte announced that while everyone knows what motion is, no one understands Aristotle's definition of it. According to Descartes, "motion . . . is nothing more than the action by which any body passes from one place to another" (Principles II, 24). The use of the word "passes" makes this definition an obvious circle; Descartes might just as well have called motion the action by which a thing moves. But the important part of Descartes' definition is the words "nothing more than," by which he asserts that motion is susceptible of no definition which is not circular, as one might say "the color red is just the color red," to mean that the term is not reducible to some modification of . a wave, or analyzable in any other way. There must be ultimate terms of discourse, or there would be no definitions, and indeed no thought. The point is not that one cannot construct a non-circular definition of such a term, one claimed to be properly irreducible, but that one ought not to do so. The true atoms of discourse are those things which can be explained only by means of things less known than themselves. If motion is such an ultimate term, then to define it by means of anything but synonyms is willfully to choose to dwell in a realm of darkness, at the sacrifice of the understanding which is naturally ours in the form of "good sense" or ordinary common sense. Descartes' treatment of motion is explicitly anti- 12 Aristotelian and his definition of motion is deliberately circular. The Cartesian physics is rooted in a disagreement with Aristotle about what the best-known things are, and about where thought should take its beginnings. There is, however, a long tradition of interpretation and translation of Aristotle's definition of motion, beginning at least five hundred years before Descartes and dominating discussions of Aristotle today, which seeks to have things both ways. An unusually clear instance of this attitude is found in the following sentence from a medieval Arabic commentary: "Motion is a first entelechy of that which is in potentiality, insofar as it is in potentiality, and if you prefer you may say that it is a transition from potentiality to aotuali.ty ." You will recognize the first of these two statemen ts presented as equivalent as a translation of Aristotle's definition, and the second as a circular definition of the same type as that of Descartes. Motion is an entelechy; motion is a transition. The strangeness of the word "entelechy" masks the contradiction between these two claims. We must achieve an understanding of Aristotle's word entelecheia, the heart of his definition of motion, in order to see that what it says cannot be said just as well by such a word as "transition." The word entelecheia was invented by Aristotle, but never defined by him. It is at the heart not only of his definition of motion, but of all his thought. Its meaning is the most knowable in itself of all possible objects of the intellect. There is no starting point from which we can descend to put together the elements of its meaning. We can come to an understanding of entelecheia only by an ascent from what is intrinsically less knowable than it, indeed knowable only through it, but more known because more familiar to us. We have a number of resources by which to begin such an ascent, drawing upon the linguistic elements out of which Aristotle constructed the word, and upon the fact that he uses the word energeia as �January, 1976 a synonym, or all but a synonym, for entelecheia. The root of energeia is ergon-deed, work, or act-from which comes the adjective energon used in ordinary speech to mean active, busy, or at work. Energeia is formed by the addition of a noun ending to the adjective energon; we might construct the word at-work-ness from AngloSaxon roots to translate energeia into English, or use the more euphonius periphrastic expression, being-at-work. If we are careful to remember how we got there, we could alternatively use Latin roots to make the word "actuality" to translate energeia. The problem with this alternative is that the word "actuality" already belongs to the English language, and has a life of its own which seems to be at variance with the simple sense of being active. By the actuality of a thing, we mean not its being-in-action but its being what it is. For example, I recently saw a picture of a fish \vith an effective means of camouflage: it looks like a rock, but it is actually a fish. I don't seem to be talking about any activity when I attribute an actuality to that thing, completely at rest at the bottom of the ocean. But according to Aristotle, to be something always means to be at work in a certain wav. In the case of the fish at rest, its actualitv is the activity of metabolism, the work by which it is constantly transforming material from its environment into parts of itself and losing material from itself into its environment, the activity by which the fish maintains itself as a fish and as just the fish it is, and which ceases only when the fish ceases to be. Any static state which has any determinate character can only exist as the outcome of a continuous expenditure of effort, maintaining the state as it is. Thus even the rock, at rest next to the fish, is in activity: to be a rock is to strain to be at the center of the universe, and thus to be in motion unless constrained otherwise, as the rock in our example is constrained by the large quantity of earth already gathered around the center of the universe. A rock at rest at the center is at work maintaining its place, against the counter-tendency of all the earth to displace it. The center of the universe is determined only by the common innate activity of rocks and other kinds of earth. Nothing is which is not somehow in action, maintaining itself either as the whole it is or as a part of some whole. A rock is inorganic only when regarded in isolation from the uni- verse as a whole, which is an organized whole, just as blood considered by itself could not be called alive, yet is onlv blood insofar as it contributes to the maintenance of some organized bodv. No existing rock can fail to contribute to the hierarchical organization of the universe; I can therefore call any existing rock an actual rock. Energeia, then, always means the being-at-work of some definite, specific something; the rock cannot undergo metabolism, and once the fish does no more than fall to earth and remain there it is no longer a fish. The material and organization of a thing determine a specific capacity or potentiality for activity, with respect to which the corresponding activity has the character of an end. Aristotle says "the act is an end and the being-at-work is the act, and since energeia is named from the ergon it also extends to the being-at-an-end ( entelecheia)" (Metaphysics, 1050a, 21-23). The word entelecheia has a structure parallel to that of energeia. From the root word telos, meaning end, comes the adjective enteles, used in ordinary speech to mean complete, perfect, or full-grown. But while energeia, being-at-work, is made from the adjective meaning at work and a noun ending, entelecheia is made from the adjective meaning complete and the verb exein. Thus if we translate entclecheia as "completeness" or "perfection," the contribution the meaning of exein makes to the term is not evident. I would suggest that Aristotle uses exein for two reasons, which lead to the same conclusion: First, one of the common meanings of exein is "to be" in the sense of to remain, to stay, or to keep in some condition specified by a preceding adverb, as in the idioms kalos exei, "things are going well," or kakos exei, "things are going badly." It means "to be" in the sense of to continue to be. This is only one of several possible meanings of exein, but there is a second fact which makes it likelv that it is the meaning \Vhich would strike the ear of Greek-speaking person of Aristotle's time. There was then in ordinary use the word endelecheia, differing from Aristotle's word enteiecheia only by a delta in place of the tau. Endelecheia means continuity or persistence. As one would expect, there was a good deal of confusion in ancient times between the invented and undefined term entelecheia and the familiar word endelecheia. The use of the pun for the serious philosophic purpose of saying a 13 �The College at once two things for whose union the language has no word was a frequent literary device of Aristotle's teacher Plato. In this striking instance, Aristotle seems to have imitated the playful style of his teacher in constructing the most important term in his technical vocabulary. The addition of exein to enteles, through the joint action of the meaning of the suffix and the sound of the whole, superimposes upon the sense of "completeness" that of continuity. Entelecheia means continuing in a state of completeness, or being at an end which is of such a nature that it is only possible to be there by means of the continual expenditure of the effort required to stay there. Just as energeia extends to entelecheia because it is the activity which makes a thing what it is, entelecheia extends to energeia because it is the end or perfection which has being only in, through, and during activity. For the remainder of this talk, I shall use the word "actuality" to translate both energeia and entelecheia, and by actuality I shall mean just that area of overlap between being-atwork and being-at-an-end which expresses what it means to be something determinate. The words energeia and entelecheia have very different meanings, but function as synonyms because the world is such that things have identities, belong ,to species, aot for ends, and form material into enduring organized wholes. The word actuality as thus used is verv close in meaning to the word life, with the exception that it. is broader in meaning, carrying no necessary implication of mortality. We embarked on this quest for the meaning of entelecheia in order to decide whether the phrase "transition to actuality" could ever properly render it. The answer is now obviously "no." An actuality is something ongoing, but only the ongoing activity of maintaining a state of completeness or perfection already reached; the transition into such a state always lacks and progressively approaches the perfected character which an actuality always has. A dog is not a puppy: the one is, among other things, capable of generating puppies and giving protection, while the other is incapable of generation and in need of protection. We might have trouble deciding exactly when the puppy has ceased to be a puppy and become a dogcrt the age of one year, for example, it will probably be fully grown and capable of reproducing, but still awkward 1 1 14 in its movements and puppyish in its attitudes-but in any respect in which it has become a dog it has ceased to be a puppy. But om concern was to understand what motion is, and it is obviously the puppy which is in motion, since it is growing toward maturity, while the dog is not in motion in that respect, since its activity has ceased to produce change and become wholly directed toward self-maintenance. If the same thing cannot be in the same respect both an actuality and a transition to actuality, it is clearly the transition that motion is and the actuality that it isn't. Descartes is right and Aristotle is wrong. Of course it is possible that Aristotle meant what Descartes said, but simply used the wrong word, that he called motion an entelecheia three times, at the beginning, middle, and end of his explanation of what motion is, when he really meant not entelecheia but the transition or passage to entelecheia. This suggestion would be laughable if it were not what almost everyone who addresses the question today believes. Sir David Ross, certainly the most massively qualified authoritv on Aristotle of those who have lived in our century ;nd written in our language, the man who supervised the Oxford University Press's forty-five year project of translating all the works of Aristotle into English, in a commentanr on Aristotle's definition of motion, writes: "entelecheia ·must here mean 'actualization,' not 'actuality'; it is the passage to actuality that is kinesis" (Physics, text with commentary, London, 1936, p. 359). In another book, his commentary on the Metaphysics, Ross makes it clear that he regards the meaning entelecheia has in every use Aristotle makes of it everywhere but in the definition of motion as being not only other than but incompatible with the meaning "actualization." In view of that fact, Ross' decision that "entelecheia must here mean 'actualization' n is a desperate one, indicating a despair of understanding Aristotle out of his own mouth. It is not translation or interpretation but plastic surgery. Ross' full account of motion as actualization (Aristotle, New York, 1966, pp. 81-82) cites no passages from Aristotle, and no authorities, but patiently explains that motion is motion and cannot, therefore, be an actuality. There are authorities he could have cited, including Moses Maimonides, the twelfth century Jewish philosopher who sought to �January, 1976 reconcile Aristotle's philosophy with the Old Testament and Talmud, and who defined motion as "the transition from potentiality to actuality," and the most famous Aristotelian commentator of all time, Averroes, the twelfth century Spanish Moslem thinker, who called motion a passage from non-being to actuality and complete reality. In each case the circular definition is chosen in preference to the one which seems laden with contradictions. A circular statement, to the extent that it is circular, is at least not false, and can as a whole have some content: Descartes' definition amounts to saying "whatever motion is, it is possible only with respect to place," and that of Averroes, Maimonides, and Ross amounts to saying "whatever motion is, it results always in an actuality." An accurate rendering of Aristotle's definition would amount to saying (a) that motion is rest, and (b) that a potentiality, which must be, at a minimum, a privation of actuality, is at the same time that actuality of which it is the lack. There has been one major commentator ·on Aristotle who was prepared to take seriously and to make sense of both these claims. St. Thomas Aquinas, in his interpretation of Aristotle's definition of motion, (Commentary on Aristotle's Physics, London, 1963, pp. 136-137), observes two principles: ( 1) that Aristotle meant what he wrote, and (2) that what Aristotle wrote is worth the effort of understanding. Writing a century after Maimonides and Averroes, Thomas disposes of their approach to defining motion with few words: it is not Aristotle's definition and it is an error. A passage,, a transition, an actualization, an actualizing, or any of the more complex substantives to which translators have resorted which incorporate in some more or less disguised form some progressive sense united to the meaning of actuality, all have in common that they denote a kind of motion. It motion can be defined, then to rest content with explaining motion as a kind of motion is certainly to err; even if one is to reject Aristotle's definition on fundamental philosophical grounds, as Descartes was to do, the first step must be to see what it means. And Thomas explains clearly and simply a sense in which Aristotle's definition is both free of contradiction and genuinely a definition of motion. One must simply see that the growing puppy is a dog, that the half- formed lump of bronze on which the sculptor is working is a statue of Hermes, that the tepid water on the fire is hot; what it means to say that the puppy is growing, the bronze is being worked, or the water is being heated, is that each is not just the complex of characteristics it possesses right now; in each case, something that the thing is not yet, already belongs to it as that toward which it is, right now, ordered. To say that something is in motion is just to say that it is both what it is already and something else that it isn't yet. What else do we mean by saying that the puppy is growing, rather than remaining what it is, that the bronze under the sculptor's hand is in a different condition from the identically shaped lump of bronze he has discarded, or that the water is not just tepid but being heated? Motion is the mode in which the future belongs to the present, is the present absence of just those particular absent things which are about to be. Thomas discusses in detail the example of the water being heated. Assume it to have started cold, and to have been heated so far to room temperature. The heat it now has, which has replaced the potentiality it previously had to be just that hot, belongs to it in actuality. The capacity it has to be still hotter belongs to it in potentiality. To the extent that it is actually hot it has been moved; to the extent that it is not yet as hot as it is going to be, it is not yet moved. The motion is just the joint presence of potentiality and actuality with respect to same thing, in this case heat. A number of things need to be noted here. In Thomas' version of Aristotle's definition one can see the alternative to Descartes' approach to physics. Since Descartes regards motion as ultimate and given, his physics will give no account of motion itself, but describe the transient static configurations through which the moving things pass. By Thomas' account, motion is not ultimate but is a consequence of the way in which present states of things are ordered toward other actualities which do not belong to them. One could build on such an account a physics of forces, that is of those directed potentialities which cause a thing to move, to pass over from the actuality it possesses to another which it lacks but to which it is ordered. Motion will thus not have to be understood as the mysterious departure of things from 15 �The College rest, which alone can be described, but as the outcome of the action upon one another of divergent and conflicting innate tendencies of things. Rest will be the anomaly, since things will be understood as so constituted by nature as to pass over of themselves into certain states of activity, but states of rest will be explainable as dynamic states of balance among things with opposed tendencies. Leibniz, who criticized Descartes' physics and invented a science of dynamics, explicitly acknowledged his debt to Aristotle (see, e.g., Specimen Dynamicum), whose doctrine of entelecheia he regarded himself as restoring in a modified form. From Leibniz we derive our current notions of potential and kinetic energy, whose very names, pointing to the actuality which is potential and the actuality which is motion, preserve the Thomistic resolutions of the two paradoxes in Aristotle's definition of motion. But though the modern science of dynamics can be seen in germ in St. Thomas' discussion of motion, it can be seen also to reveal difficulties in Thomas' conclusions. According to Thomas, actuality and potentiality do not exclude one another but co-exist as motion. To the extent that an actuality is also a potentiality it is a motion, and to the extent that an actuality is a motion it is a potentiality. The two seeming contradictions cancel each other in the dynamic actualiity of the present state which is determined by its own future. But are not potential and kinetic energy two different things? The rock which I hold six feet above the ground has been actually moved identically to the rock which I have thrown six feet above the ground, and at .t hat distance each strains identically to fall to earth; but the one is falling and the other isn't. How can the description which is common to both, when one is moving and the other is at rest, be an account of what motion is? It seems that everything which Thomas says about the tepid water which is being heated can be said also of the tepid water which has been removed from the fire. Each is a coincidence of a certain actuality of heat with a further potentiality to the same heat. What does it mean to say that the water on the fire has, right now, an order to further heat which the water off the fire lacks? If we say that the fire is acting on the one and not on the other in such a way as to disturb its present state, 16 we have begged the question and returned to the position of presupposing motion to explain motion. Thomas' account of Aristotle's definition of motion, though immeasurably superior to that of Sir David Ross as interpretation, and far more sophisticated as an approach to and specification of the conditions an account of motion would have to meet, seems ultimately subject to the same circularity. Maimonides, Averroes, and Ross fail to say how motion differs from rest. Thomas fails to say how any given motion differs from a corresponding state of balanced tension, or of strain and conshaint. The strength of Thomas' in terpreta ti on of the definition of motion comes from his taking every word seriously. When Ross discusses Aristotle's definition, he gives no indication of whv the he toiouton, or "insofar as it is such," clause should have been included. By Thomas' account, motion is the actuality of any potentiality which is nevertheless still a potentiality. It is the actuality which has not cancelled its corresponding potentiality but exists along with it. Motion then is the actuality of any potentiality, insofar as it is still a potentiality. This is the formula which applies equally well to the dynamic state of rest and the dynamic state of motion. We shall try to advance our understanding by being still more careful about the meaning of the pronoun he. Thomas' account of the meaning of Aristotle's definition forces him to construe the grammar of the definition in such a way that the clause introduced by the dative singular feminine relative pronoun he has as its antecedent, in two cases, the neuter participle tou ontos, and in the third, the neuter substantive adjective tou dunatou. It is true that this particular feminine relative pronoun often had an adverbial sense to which its gender was irrelevant, but in the three statements of the definition of motion there is no verb but estin. If the clause is understood adverbially, then, the sentence must mean something like: if motion is a potentiality, it is the actuality of a potentiality. Whatever that might mean, it could at any rate not be a definition of motion. Thus the clause must be understood adjectivally, and Thomas must make the relative pronoun dependent upon a word with which it does not agree in gender. He makes the sentence say that motion is the actuality of the potentiality in which there �January, 1976 is yet potentiality. Reading the pronoun as dependent upon the feminine noun entelecheia with which it does agree, \Ve find the sentence saying that motion is the actuality as which it is a potentiality of the potentiality, or the actuality as a potentiality of the potentiality. This reading of ,t he definition implies that potentialities exist in two ways, that it is possible to be a potentiality, yet not be an actual potentiality. I said at the beginning of this talk that Aristotle's definition of motion was made by putting together two terms, actuality and potentiality, which normally contradict each other. Thomas resolved the contradiction by arguing that in every motion actuality and potentiality are mixed or blended, that ;the condition of becoming-hot of the water is just the simultaneous presence in the same water of some actuality of heat and some remaining potentiality of heat. I also said earlier that there was a qualifying clause in Aristotle's definition which seemed to intensify, rather than relieve, the contradiction. I was referring to the he toiouton, or he kineton, or he dunaton, which appears in each version of the definition, and which, being as I have claimed grammatically dependent on entelecheia, signifies something the very actuality of which is potentiality. The Thomistic blend of actuality and potentiality has the characteristic that, to the extent that it is actual it is not potential and to the extent that it is potential it is not actual; the hotter the water is, the less is it potentially hot, and the cooler it is, the less is it actually, the more potentially, hot. The most serious defect in Saint Thomas' interpretation of Aristotle's definition is that, like Ross' interpretation, it broadens, dilutes, cheapens, and trivializes the meaning of the word entelecheia. An immediate implication of the interpretations of both Thomas and Ross is that whatever happens to be the case right now is an entelecheia, as though being 3't 70 degrees Fahrenheit were an end determined by the nature of water, or as though something which is ·intrinsically so unS'table as the instantaneous position of an arrow in flight deserved to be described by the word which Aristotle everywhere else reserves for complex organized states which persist, which hold out in being against internal and external causes tending to destroy them. Aristotle's definition applies to any and every motion: the pencil falling to the floor, the \Vhite pages in the book turning yellow, the glue in the binding of the book being eaten by insects. Maimonides, Averroes, and Ross, who say that motion is always a transition or passage from potentiality to actuality, must call the being-on-the-floor of the pencil, the being-yellow of the pages, and the crumbled condition of the binding of the book actualities. Thomas, who says that motion is constituted at any moment by the joint presence of actuality and potentiality, is in a still worse position: he must call every position of the pencil on the way to the floor, every color of the pages on the way to being yellow, and every loss of a crumb from the binding an actuality. If these are actualities, then it is no wonder that philosophers such as Descartes rejected Aristotle's account of motion as a useless redundancy, saying no more than that whatever changes changes into that into which it changes. We know however that the things Aristotle called actualities are limited in number, and constitute the world in its ordered finitude rather than in its random particularity. The actuality of the adult horse is one, although horses are many and all different from each other. Books and pencils are not actualities at all, even though they are organized wholes, since their organizations are products of human art, and they maintain themselves not as books and pencils but only as earth. Even the organized content of a book, such as that of the first three chapters of Book Three of Aristotle's Physics, does not exist as an actuality, since it is only the new labor of each new reader that gives being to that content, in this case a very difficult labor. By this strict test, the only actualities in the world, that is the only things which, by their own innate tendencies, maintain themselves in being as organized wholes, seem to be the animals and plants, the ever-the-same orbits of the ever-moving planets, and the universe as a whole. But Aristotle has said that every motion is an entelecheia; if we choose not to trivialize the meaning of entelecheia to make it applicable to motion, we must deepen our understanding of motion to make it applicable to the meaning of entelecheia. In the Metaphysics, Aristotle argues that if there is a distinction between potentiality and actuality at all, there must be a distinction between two kinds of potentiality. 17 �The College The man with sight, but with his eyes closed, differs from the blind man, although neither is seeing. The first man has the capacity to see, which the second man lacks. There are then potentialities as well as actualities in the world. But when the first man opens his eyes, has he lost the capacity to see? Obviously not; while he is seeing, his capacity to see is no longer merely a potentiality, but is a potentiality which has been put to work. The potentiality to see exists sometimes as active or at work, and sometimes as inactive or latent. But this example seems to get us no closer to understanding motion, since seeing is just one of those activities which is not a motion. Let us consider, then, a man's capacity to walk across the room. When he is sitting or standing or lying still, his capacity to walk is latent, like the sight of the man with his eyes closed; that capacity nevertheless has real being, distinguishing the man in question from a man who is crippled to the extent of having lost all potentiality to walk. When the man is \valking across the room, his capacity to walk has been put to work. But while he is walking, what has happened to his capacity to be at the other side of the room, which was a]so latent before he began to walk? It too is a potentiality which has been put to work by the act of walking. Once he has reached the other side of the room . his potentiality to be there has been actualized in Ross' sense of the ·term, but while he is walking, his potentiality to be on the other side of the room is not merely latent, and is not yet cancelled by an actuality in the weak sense, the so-called actuality of being on that other side of the room; while he is walking his potentiality to be on the other side of the room is actual just as a potentiality. The actuality of the potentiality to be on the other side of the room, as just that potentiality, is nothing more nor less than the walking across the room. A similar analysis will apply to any motion whatever. The growth of the puppy is not the actualization of its potentiality to be a dog, but the actuality of that potentiality as a potentiality. The falling of the pencil is the actuality of its potentiality to be on the floor, in actuality as just that: as a potentiality to be on the floor. In each case the motion is just the potentiality qua actual and the actuality qua potential. And the sense we thus give to the word entelecheia is not at odds with its other uses: a mo- 18 tion is like an animal in that it remains completely and exactly what it is through time. l\'ly walking across the room is no more a motion as the last step is being taken than at any earlier point. Every motion is a complex whole, an enduring unity which organizes distinct parts, such as the various positions through which the falling pencil passes. As parts of the motion of ,the pencil, these positions, though distinct, function identically in the ordered continuity determined by the potentiality of the pencil to be on the floor. Things have being to the extent that they are or are part of determinate wholes, so that to be means to be something, and change has being because it always is or is part of some determinate potentiality, at work and manifest in the world as change. I shall close by considering the application of Aristotle's account of motion to two paradoxes famous in antiquity. Zeno argued in various ways that there is no motion. According to one of his arguments, the arrow in flight is always in some one place, therefore always at rest, and therefore never in motion. We can deduce from Aristotle's definition that Zeno has made the same error, technicallv called the fallacy of composition, as one who would argue that no animal is alive since its head, when cut off, is not alive, its blood, when drawn out, is not alive, its bones, when removed are not alive, and so on with each part in turn. The second paradox is one attributed to Heracleitus, and taken as proving that there is nothing but motion, that is, no identity, in the world. The saying goes that one cannot step into the same river twice. If the river flows, how can it continue to be itself? But the flux of the river, like the flight of the arrow, is an actuahty of just the kind Aristotle formulates in his definition of motion. The river is always the same, as a river, precisely because it is never the same as water. To be a river is to be the always identical actuality of the potentiality of water to be in the sea. 1 Joe Sachs graduated from St. John's in 1968; he took his M.A. degree at Pennsylvania State University after graduate studies at the New School for Social Research, New York; he was a teaching assistant at Penn State and became a tutor at St. John's in 1975. This is the text of an informal lecture delivered to the summer freshmen in Annapolis on July 6, 197 5. � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. 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Format The file format, physical medium, or dimensions of the resource pdf Creator An entity primarily responsible for making the resource Sachs, Joe, 1946- Friday night lecture Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/749f96e81365729aa65ad5e392f0a09e.pdf 2a23d863721e6f930fc3d6ee08acfa03 PDF Text Text ANTIGONE: ALL-RBSOURCBFUL/RBSOURCBLBSS Joe Sachs Fall, 1988 �This lecture has an ulterior purpose. It is a response to the growing chorus of voices one hears saying that Sophocles is too difficult for our sophomores to read. Now in some literal sense this is so obvious that it hardly needs saying. But some people take it to imply that we ought to stop reading Sophocles in the language tutorial, and this needs denying. My own opinion is that Sophocles is too difficult for us not to read: too good to miss, that is, and completely inaccessible unless one makes the effort to read his own words. That such an effort made with the minimwn of ·tools is already richly fruitful is one of the things I hope to show. To that end I promise that this lecture will be amateurish, in fact sophomoric. I have no doubt that I will make mistakes that could be corrected by anyone who has read all the scholarly literature on the subject. I have long ago made the choice that such correctness is not worth its price. The reading of Antigone presented here will rest on an elementary knowledge of Greek, an ignorance of its metrics, a lack of fastidiousness about syntax, and a heavy reliance on Liddell and Scott. I have had the luxury of being a sophomore more than once, but my heart is in that tutorial, and I will never graduate from it. Its very ineptitude prevents glibness, and requires a slow, stubborn questioning of every word. not a bad way to read. to do it can do it. With Sophocles that is It also has the merit that anyone who wants It would be a shame to listen to a lecture of this kind and not join in with it in the question period. �-2- Sophocles never stopped thinking about the Oedipus story. was in his nineties when he wrote Oedipus not live to see performed. Antigone. ~ He Colonus, which he did It was about 35 years earlier that he wrote The three Theban plays that we possess are not a trilogy nor in any sense parts of a whole. from different points of view. They are one story told three times I do not mean that Sophocles used various characters to give subjective colorings to the events, but that he himself saw the essence of the Oedipus story in three different acts of poetic concentration. I do not think he changed his mind from play to play about Oedipus or about what made his story important, though that would be difficult to show. I think he saw in the story the most important truths about human life, and kept opening windows into it so that the rest of us could see them too. But the Antigone seems to be far removed from the center of the Oedipus story. Oedipus is long departed when it begins. His two sons have tried and failed to share the kingship of Thebes, brought new misery on the city, and finally killed each other in battle. Creon, who succeeds them as king, and their sister Antigone respond to this catastrophe in incompatible ways, bringing on fresh catastrophe. And everyone knows that the heart of this play is the scene in which the two main characters step forth and debate the principles on which they have acted. The Antigone is a play about a disastrous moral collision, I one neither faced by nor caused by Oedipus, who is so far in the background that he might be any dead king who had both sons and daughters. This is a false picture of the play, but an almost inevitable first picture. More than other plays, the Antigone tempts us to single- �-3- sentence statements of moral or theme, and that sentence is always about the conflict between the laws of the city and the demands of private conscience, which listens to a higher law. I could quote such sentences from various commentators, but what would be the point? we can all say the same kinds of things ourselves, and probably have. Whatever else the play may be, it has within it a philosophic dialogue of undeniable clarity about a genuine and timeless dilemma. Sir Richard Jebb does not hesitate to conclude that the conflict of the play is not between people but between abstract principles, and that Creon and Antigone move us not as themselves but as vivid personifications of duty. I hope this formulation feels uncomfortable to you, but there is nothing !~possible about it. Poetry is not by its nature hostile to rationality, and part of the power of Sophocles' writing is undoubtedly an intellectual power. He might, in this one play, have made everything human and concrete an outer covering for an intellectual problem. There is a philosopher, Hegel, who saw the intellectual realm as a living drama enacted by the ideas themselves. that he loved the Antigone. It is no accident In his Phenomenology he sees the play as exhibiting the splitting in two of the ethical world, the destruction of ethical order by the emergence of an inner contradiction. and Creon are both right but also both wrong. Antigone Hegel says, "only in the downfall of both sides alike is absolute right accomplished, and the ethical substance as the negative power which engulfs both sides, that is, omnipotent and righteous Destiny, steps on the scene." (#472) In Hegel's account of the play everything accidental and individual falls away from the characters, even though individuality is itself �-4one of the things at issue. But Hegel writes with a depth worthy of Sophocles, and his approach to the play cannot be dismissed lightly. The only way to achieve a truer perspective on the play is to begin looking at its details, but it is worth noting first that there is another philosopher of the same stature as Hegel who seems to see the play in an opposite way. Aristotle, in his Rhetoric (III.xvi.9) criticizes the orators of his time for writing too exclusively from the intellect, making it impossible for them to discern or display moral character or purpose. He recommends that they follow, instead, the example of the Antigone. This is a wonderful passage, to which I will refer again. For the moment it defines a challenge for us: to see how what is peculiar to the Antigone is what is specifically moral, and does not stem from the intellect. The debate between Creon and Antigone takes place in daylight. It is important in many ways that the play begins in darkness. and her sister Ismene meet outside the city before sunrise. Antigone It is an intensely visual scene, but the pictures are in the imaginations of the two women. We begin where they do, trying to assimilate the horror of the previous day, and with Ismene at least, trying to see into another's inner visions. There are no formulated principles here, no light by which to see one's way. Ismene asks Antigone where she is in her thoughts Cline 42); what she sees c~early is that Antigone's thinking is spreading the darkness, like the purple dye emitted by a certain whelk to make the sea murky (20). This tiny example reveals the whole art of Sophocles, insofar as I can get hold of it. a translation may have Ismene saying 11 Where you seem to be pondering something," �-5- the word Sophocles has used for ponder is kalchainein, not an invented word, but not a very common one either, and one still heavily laden with its metaphoric origin. The root of the word is the name of the purple murex, a sea mollusc which clouds the water when it is threatened. Its secretion is the dye used by ancient kings for their royal purple. The animal itself was therefore valuable, and worth searching for through the murk. Thus its name came also to mean the searcher, as for example Kalchas, the seer in Book one of the Iliad. This is Sophoclean language: concrete, metaphoric, sensuous, and strong. We who do not speak his language must read whole entries in Liddell and Scott to hear what his characters are saying, and never be content to pick out one meaning that seems to fit the context. But there is still another favorite device of Sophocles in the line. Not only does Ismene say that Antigone is pondering, with a word that carries layers meaning gloom, royalty, and divine insight; she says it is clear so. ~deloun) that she is doing Sophocles loves to jam together words whose senses clash. "It is clear that you are in a murky soup of thoughts of royalty and divinity." The introduction of the word "clear" serves only to emphasize that nothing here is clear. I will note later some magnificent examples of this trick. It is in this scene in and about darkness that the themes of the play are introduced, and they are not law and conscience. line is Antigone's: Qkoinon sister, heart of Ismene. 11 The opening autadelphon Ismenes kara, "Shared self- The word autadelphos means prosaically full-sister daughter of the same mother as well as father, but this scene, like the whole play, is so full of the word autos and its compounds that �"."6- one must, in retrospect if not from the beginning, hear it as superimposing the meaning self on that of sister. Similarly, ~' meaning head, or very swnmit of what someone is, like our use of heart to mean someone's very core, carries the sense of Ismene's essential self. Antigone is saying "Ismene, what is most you yourself is also shared, is my self, so fully are we sisters." The two-sided question, what is shared? and what is oneself?, is the center of Sophocles' envisioning of the Oedipus story. Here, at the beginning of the play, the merging of two sisters into one self is a pathetic illusion. Before the end of the ninety-nine lines Antigone is telling Ismene she hates her. This moment when the sisters might be loving and comforting one another becomes a new division and separation, like that between their brothers. The image which dominates the whole play is the one which fills Ismene's imagination in this scene. She describes it twice. "We two were deprived of two brothers, dying on one day by a double hand." (13-14) And again, "two brothers, in the course of one day, self-slaying wretched ones, working out a corrunon doom with mutual hands." (55-57) It might be a great misfortune that each brother gave the other a fatal wound, but the special insight that makes this a nightmare vision for Ismene is contained, in the first telling, in the singular phrase, "a double hand," and in the second in the reflexive participle, "self-slaying." We are seeing a combat to the death fought with a mirror, so that the hand one lifts to strike the other moves backward to kill oneself. lifted his hand against his father, and destroyed himself. Oedipus Here that deed is doubled, as both Eteocles and Polyneices strike what seems �--7to be merely a brother, but for · each turns out to be himself. And now in front of us it begins to be quadrupled, as the sisters too begin tearing themselves apart. we see Oedipus. We look at Antigone, and through two mirrors And there is one more reflected reflection still to come. But why does Antigone's loving greeting of Ismene turn so quickly into a hate-filled parting? It is easy to blame Ismene. When Antigone tells what she intends, Ismene replies that those who are women, weak, and subjects must yield to those who are men, strong, and rulers. (58-64) In response to these arguments Antigone is splendid. In forbidding burial of Ployneices, Creon has crossed two boundaries that restrain legitimate rule, into the properly private (48) and into a realm where only the gods can be listened to (77). As for his masculine strength, that can be put to the test by anyone who does not fear death, and when Antigone looks at the image of herself dying for burying a loved brother, she calls it a beautiful thing (72). Ismene insists three times that the deed is impossible (79, 90, 92), but Antigone elegantly and succinctly tells her that there is only one way to know that. uses the future perfect: have stopped." (91) She "whenever I have no more strength, I shall In the Rhetoric, Aristotle tells us that Antigone acts not for the sake of what is useful or beneficial, but for the sake of the beautiful, out of goodness rather than prudence, and in the Ethics he tells us that the specific telos, or end, of virtue is the beautiful (III.vii). There is no question here, for example, of any superstitious fear that an unburied Polyneices will be denied �-aaccess to the other world, but only a clear sight that burying him is right, fitting, appropriate, and leaving him unburied deeply wrong, so that even the sacrifice of another life only makes the whole picture more beautiful. Antigone is a human being in the fullest sense, one courageous enough to do what needs to be done out of no practical calculation, for no reason other than that it is right. Her choice is beautiful, Sophocles' picture of her making it is beautiful, and she is beautiful. But she is also fierce. her father's fierceness (471). with her sister. The chorus will say she is fierce with In the first scene she is merciless But worst of all, she does not listen to Ismene. In the first line, she does not mean, I see you, Ismene, for what you are and take that into myself as part of me. you, Ismene, and see nothing but myself. She means, I look at The two can have a shared self only if Ismene is willing to become Antigone. If she does not feel the same feelings, Antigone rejects her as no true-born sister of hers (37-38). But Ismene is no coward, but in fact a true match for Antigone in firmness. If we listen to her we hear not a woman afraid to act, but one strong enough to endure anything, if she is convinced that any action will make things worse. (39-40) Ismene is frozen in horror before the image of her brothers, not because blood and death and loss are too painful for her to look upon, but because they brought it on themselves. In the speech in which Antigone only hears Ismene saying, let's act like weak women subjects, she in fact is saying much more, that is much more important. She asks Antigone to remember their father, not only dead but having died hated, shamed, and having brought �-9- it all on himself, and the mother who was to that father both mother and wife, the two names twisted like the noose with which she mutilated her own life. (49-54) Now their brothers have added more horror and shame, and Antigone wants to keep increasing it until they are all wiped out. To Antigone, all the deaths are the work of enemies, against whom the family must be defended. (9-10) But Ismene keeps hammering at the fact that everything their parents and brothers suffered was self-inflicted. In Ismene's view, she and Antigone have no enemies but themselves. What they need now is to forgive the beloved dead for their crimes, and be forgiven by them for taking no action. (65-67) Antigone's deafness to her sister makes Ismene all the more insistent, and Ismene's insistence makes Antigone all the more determined. Like the blows struck by their brothers, every attempt to persuade turns ,/ back on the sister who utters it as a new cause of her isolation. In the course of this first scene, the most important word in the play has been introduced and become increasingly prominent. word is philia. It means love which is not from desire, - That as~' nor for all human beings, as agape, nor between unequals, as st.i'Jrqe I but for those who are like oneself, of one's own kind. It therefore names both the love within a family and the friendly feeling among fellow-citizens. You have all read the sentence koina !!!, ton philon, the things of friends are common. Aristotle says in the Politics that the proper work of the lawmaker is to produce this feeling among all the citizens. (II.v.6-8) The confrontation between Antigone and Creon is not between conscience and law, but between philia and philia. �-10- This is part of the last of the mirror images of which I spoke. But the word has already come under strain between the two sisters. In Antigone's mouth philia means that which separates us from them, her immediate family from everyone else, all of whom are therefore enemies. It is after Ismene says that there is fault on the side of their family that Antigone begins to say she hates her (86}. Antigone's love is conditional, and those who do not earn it feel her hate. {93-94) Ismene's love is unconditional, no matter what Antigone says or does. (98-99) Antigone's .words are all about philia, and it is genuinely the motive of her deed, but she does not recognize its presence in front of her. This rejection of her sister's love is the worst error brought on by the darkness in which Antigone is moving, and she will pay for it. Creon, though he acts from calcuation and prudence, is looking to and acting for the sake of the same philia as is Antigone. her also, he has a clouded view of it. Like His understanding of the friendship that makes human community possible has an intellectual clarity, and his intentions are good, but he is acting quickly in a critical situation, and he makes a bad mistake. The Creon of this play is not the dishonest man he is in Oedipus at Colonus. Here he is a fitting antagonist for Antigone in the stubborn purity of his determination to do what is best. He has inherited the responsibility for a maimed and miserable city. Though his title to rule comes through blood-kinship to the ruling family, all of Thebes' long history of troubles has come from that same family. With the sunrise on this day, the instant he becomes king, he intends to cut off that family connection once and for all. �-11His inaugural address to the elders of his city is meant to .show them a genuinely new beginning and show himself as someone they can trust. They are to watch Polyneices suffer the ultimate violation, left as a piece of meat for dogs and birds.(205-6) They will see that to Creon this violator of the city is no nephew, but is nothing. (182-3) Creon's true decree is that all bonds of love and loyalty will henceforth begin with the city; no other bonds precede it, carry over into it, or carry any weight against it. (187-90) When one reflects that the ties within the Oedipus family are those of a blood-kinship flowing back into itself in a grotesque way, Creon's attempt to destroy all such ties is understandable. But as the words for same blood, xunaimon, and common blood, haima koinon, resound in his speech, we remember that Creon has a son and that his very name is blood. But Creon understands philia no better than blood-kinship, and no better that Antigone does. philia are identical. In fact the two misunderstandings of Just as Antigone has sisterly love before her in Ismene, Creon has the fellow-feeling of common citizenship before him in the chorus, and he is equally blind. The chorus, when Creon encounters it, is in the grip of a strong common emotion which he is preventing from flowing into action, and he doesn't even know it. For him the sunrise is his entry into kingship, but for the people of the city it is the moment they discover that the besieging Argive army has left in the night. Creon is full of his cleverness in having figured out a way to make them one people again, and does not see that they are already of one mind, one heart, and one motion, if he would just leave them alone, if not listen to them and join them. What the �-12chorus wants is to wipe out the war and the fear that have filled them, with a day and night of feasting, dancing, singing, and thankfulness to the gods. (148-54) Creon is telling them to prolong the horror by watching the desecration of Polyneices' corpse. Creon and Antigone are mirror images in many ways. Antigone's imagination in the first scene is dominated by a picture of enemies creeping up unseen on her friends. (9- 10) Creon likewise from his first scene keeps referring to a plot against him fueled by money. (221-2, 289-303, 1055) There is no smallest shred of evidence in the play that this plot exists anywhere but in his imagination. the need to act without delay because of these threats. acted, both are inflexible. Both feel And having Creon compares Antigone to the hardest iron, which most easily shatters, and to the wildest horse, most easily broken by a small bit (474-8), while Haimon compares Creon to a tree that does not bend in the wind, and .so is uprooted, and to one who keeps a sail too taut, and capsizes (712-17). But the fundamental identity between them is seen in the words which are compounds of autos. The Chorus tells Antigone that an autognotos orga, a self-willed temper, ' destroyed her (875), while Teiresias tells Creon that his authadia, self-pleasing or self-will, makes him guilty for his own bad luck (1028). The self-will 9f Antigone and Creon is the conviction each has of being the ·radical originator of his or her own deeds. This is the error of Oedipus. Oedipus left home to start life fresh, by his own doing. When he lifts his hand against his father, that is the outward, factual manifestation of his effort to cut off his own sources and be in the �-13- world without antecedents. the honor of her family. Likewise, Antigone must act alone to save she cannot run the risk of letting there be any love between her sister and herself which might dilute her resolution or divert her strength. The two of them might become a new being, and see the good in some way other than she sees it now. Creon as ruler has the whole world on his shoulders alone. And likewise He repeatedly uses compounds of the word kosmos when insisting that he can not in any slightest way allow himself to be ruled by a woman, a subject, or a child. (726-7, 734, 746) If the ruler is ruled there is anarchy (672), and the ordered world is destroyed (660, 677, 730). The meeting of Antigone with Creon is thus the confrontation of two powerful, isolated figures, doing battle for the sake of philia. Faced with each other, both are at their worst. to destroy each other, each destroys himself. In their determination The axis of the play seems to me to be the pair of lines 523 and 524. themselves. That is where they stake Creon has been arguing that the reverence, honor, and love shown to Eteocles must mean nothing if the same rites are accorded the enemy he lost his life fighting. Antigone has been replying with immovable certainty that what Eteocles and all the dead and the gods want is exactly what she has done. (505, cf. 89) They will never agree. Earlier, telling Creon in effect to shut up and get on with whatever he intends to do, Antigone has said you." (501) 11 my words were born displeasing Now, speaking her last words to him, she says, "I was born not to join in hating but to join in loving." Creon's last words back to her are, "Well since you are now on your way below, if one �-14must love, love them." Antigone's word symphilein, to join in loving, and Creon's word phileteon, one must love, are the nooses with which they hang themselves. disfigures it. Antigone's word is beautiful, but she herself Creon's word is a grotesque malformation with which not even he can live. Both Antigone and Creon are far gone in spite when they utter these words. Antigone is splendid in her courage, but she has been carrying a contradiction within her since the first scene, and it has now come to the surface. She has told Ismene that her love is conditional, and that Ismene has failed to earn it. But she has just explained with scorn that she cannot make a distinction between her brothers because her love is unconditional. Which is the truth? At this moment Ismene comes on stage, and all of Antigone's passionate coldness is turned upon her. Ismene had wanted nothing to do with the deed, but wants everything to do with the sister who must now suffer for it. All Ismene's words of desperate love for her sister are met by Antigone with irony and mockery. When Ismene finally screams, 11 Why do you torture me like this, when it does you no good?" (550), all the fight finally goes out of Antigone. what it is. 11 "In pain I am laughing at you, if laughing is Antigone makes no effort at reconciliation, but Ismene has stopped her runaway anger. The effect of this stopping is to turn Antigone inward, where she begins facing the death she has chosen. When she comes back onstage she will be a different Antigone from what we have seen of her so far. �-15When Antigone has been led away for now, Haimon enters to plead for her life. Just as Antigone's anger at Creon missed its mark and hit her sister, so now all Creon's rage at Antigone lands on his son. In accordance with his word phileteon, which says that love is a matter of impersonal necessity, to be arranged by prudent deliberation, Creon first explains to Haimon that when he thinks well about it he will see that this is not a woman he wants to love. (648-54) But Creon sees with fury that Haimon fights for, follows, and serves this woman in place of his father. (740, 746, 756) Creon knows how to handle proven and incipient treason at one stroke, as he has done with Polyneices and the city. "Bring her here at once," he says to the soldiers, and kill her in front of her bridegroom's eyes. (760-1) momentarily mad, but he has lost Haimon forever. Creon has gone He is hemorrhaging in front of us, and this wound will not close. With the device of Haimon's name, Sophocles shows us Creon in confrontation with his own blood. This was already true, more distantly, in his confrontation with his neice and desecration of the body of his nephew. And it is a truth implicit in the political principle by which he has chosen to rule, that only those human bonds will be recognized and honored that derive from the political one. From the beginning of his kingship, Creon has been doing violence to himself without knowing it. It must be emphasized that there is no intellectual contradiction here. Creon could live by his principle if he were a worse man, one whose cruelty was not a momentary mad impulse but a settled disposition, or if he were a man of firmer principle, like �-16- Brutus, the first consul of Rome, who killed his own sons for the sake of his city deliberately. But Creon is just an ordinarily good man, who considers his son and his wife part of himself. By his rules he has judged Polyneices simply an enemy, with no claim on him or on Thebes. But by sisterly love that has made Antigone a second enemy, and by erotic love, Haimon a third, and by a mother's love for the last of her children left alive, Creon's wife Eurydice a fourth. It is not money but love that has produced the plot against Creon, a widening circle of unruly, ungovernable loves from which he himself is not exempt. When he returns from seeing his son try to kill him and then kill himself, to discover that his wife has killed herself, Creon for the first time sees the truth: "I, I killed you, useless I" (1319-20), but also "I am dead" (1288), "I am no more than nothing" (1322). His own self lay outside him, in his wife and son, by way of bonds over which he had no control. He was not the source of the ordered hierarchy of Thebes, nor even the free origin of his own life, but part of a shared self, which he stabbed inward to the heart by striking outward. There are pictures in the play of lives better ordered. Haimon tells his father that he can listen to and respect a youth, a woman, and his subjects and be all the better a father, man, and king. (728-9, 737, 739, 741, 749) The chorus tells Creon that he and his son have spoken well doubly, mutually (725), even in disagreeing. This does not mean that these old men are too witless to make up their minds, but that they see the truth only in some yielding of both sides to each other. And the loveliest and most touching moment of the play is Ismene's second entrance. Antigone, wrapped up in herself, sees �-17only someone who would not act but wants to share the glory. (538-9, 542-3, 546-7) Creon, wrapped up in his mission to restore civil order, sees Ismene•s tears, and takes them for an involuntary confession of treason. (491-4) But the chorus, when they see her, break into a brief lyric passage, the only lines they speak in the play which are neither dialogue nor part of a full choral ode (526-30): And now before the gates here is Ismene, With sister-loving tears dropping down. A cloud above her· brows blood-red Stains her face, Wetting a beautiful cheek. Philadelpha, sister-loving, is here an adjective modifying tears. I remember, when I first read Antigone with a sophomore language class, asking how a feeling and its object can be attributed to drops of salt-water. A student named Ann Tive said simply, "They love her." Only the chorus speaks true words about Ismene, and they are loving words. Though the chorus itself speaks later of eros keeping watch on the cheek of a maiden, the love present here is not desire, not the remembered lust that moves of the old men of Troy whey they look at Helen. These men of Thebes have suffered a long time for the family," Oedipus, but they love this girl, and because they love her they can know her. Similarly, in the whole play it is only Ismene who speaks of Haimon with love. (572) This has confused centuries of editors so much that they often give the line to Antigone, though every manuscript gives it to Ismene, and it has tempted at least one modern reader to convict Isrnene of �-18/ desire for her sister's fiance. But Ismene and the chorus are examples of the philia that the play is all about. They can love people a step removed from them because they genuinely love those nearest them. One of the most striking images in the play is that of Teiresias, the blind seer. A great point is made of his being led by a boy. He enters with the words, "Lords of Thebes, we have come a common road, two seeing out of one. 11 (988-9) Thebes had lords, plural, not a dictator, because everyone must in some ways be led by others. Later he speaks of things "I learned from this boy ••• for to me he is a guide, as I to others. 11 (1012, 1014) Everyone who is unwilling to be led goes astray, misses the mark. Aristotle's famous word in the Poetics, hamartia, which somehow came to be misunderstood as a flaw, begins in archery and eventually becomes the New Testament word for sin. word error has perhaps the closest range of meaning. The English Teiresias tells Creon that erring is common to all human beings. (1023-4) That is why he shouldn't be afraid even now to change his course, but it is also why he should have known in the first place that Polyneices deserved burial. The city need not have joined in the honors, but there is no crime about which it can say, that criminal went so far astray that even in death he cannot be allowed to be recognized as human; we, the rest of us are the only ones safely within the human fold. being wrong does not make Antigone right. But Creon's Ismene's last speech to Antigone uses the same word, examartia, that Teiresias will use: 11 Surely the erring of us two is equal." (558) Why do all human beings err? The chorus, in the ode polla !2. deina (332-83), suggests that the very excellence itself which d~fines being �-19human is the source of error. "Wonders are many," "yet nothing stranger than a human being walks." the ode begins, To be human is to find a passage through anything, sea, wind, or earth, and to find a mechanism to overcome the power of anything, bird, beast, or fish, cold, sleet, or rain. The characteristic human epithet is pantoporos, all-resourseful, passing through every obstacle. Antigone has used the verb from the same root in the first scene to tell her sister, 11 I will find a way through, heaping up a tomb for a most loved brother." (80-1) But in one of those magnificent clashings I spoke of earlier, the chorus' word pantoporos collides with aporos, resourceless, helpless. (360) The meaning of aporos is immediately negated: comes upon nothing that is to be." "helpless he But the poetic effect of the line is the shock of hearing pantoporos aporos. In retrospect, or in reading, the words can be tamed, but the poet is writing for the ear, and Sophocles' words are wild. Pantoporos aporos cannot fail to confuse, to disturb. The choral odes are all hypnotic, and this one conveys a dreamlike sense that the very triumph of overcoming every obstacle is an achievement of helplessness. That is certainly a description that fits Creon. He becomes the helpless wreck he is at the end of the play precisely by mastering everyone, overcoming all opposition. In the antistrophe to the pantoporos aporos stanza the same position has the words hupsipolis apolis, supreme in the city/without a city. Supremacy destroys reciprocal relations, and destroys the community. But when the chorus ends the ode in dread of human greatness it is Antigone who appears before them. has told her amechanon ~, 11 Ismene you lust after impossibilities" (90), �-20and that she is determined perissa prassein, "to do extravagant things," things that go beyond. (68) It is primarily Antigone who displays the human excellence of refusing to accept any restraints to her will. Those restraints are outwardly Creon and his soldiers, but more importantly the inconvenient love and inconvenient otherness from herself of Ismene. Philia is the power that saves us from greatness, the acceptance of others into a wider self that can no longer say "I will not be stopped." But even though Antigone's defiance earned her death, she does not in the end go to her death defiant. She has one more scene, and in it she begins to return out of her isolation. The movement of the scene is difficult to understand, but full of truth. The chorus cries when it sees her being led to death, but conceals its tears in her presence. She asks the chorus for pity, but it gives her honor instead. She cries out that they are mocking her, and they rebuke her. In response to their rebuke, she begins telling painful and frightening truths about herself for the first time in the play. She has finally allowed someone to get close enough to break through her control. It happens harshly, violently, because she has fought so hard to make it impossible. As with her sister, Antigone has heaped contempt and scorn on the chorus to their faces. She was certain she knew what they thought, and that they kept silent like cowering dogs. It is her ugliest insult: "they tuck their mouths between their legs." (509) Then it was false, but now they do in fact conceal their honest feelings, because she has been so unapproachable. �-21Look at me, she says to them now, going to death solitary, unmarried, choosing to marry death. (806-16) They tell her what she seems to want to hear, You are glorious, autonomous, not a victim, but alone of mortals in choosing death. (817-22) She compares herself to Niobe, turned into rock, eternally weeping, and they say, Yes, you are godlike. (823-38) This is when she screams out that she is mocked. She wants not praise for her solitary courage, but pity for her loneliness, not the glory of Niobe but the pathos of her unending misery. her everything she is suffering is her own fault: They tell "You went out to the extreme edge of boldness, and crashed into the high seat of Justice." (853-4) But they inunediately soften their rebuke with the thought that maybe it is somehow her father's struggle that she is paying for. And now the lid that she has kept so firmly on her feelings is finally off. "You have touched my most painful worries," she says: parents monsters? horror? (857-66) Were my What in the world am I that was born out of such We see now why Antigone erupted into such violent hatred when Ismene suggested there was something wrong with their family. It was a hatred of her own uncertainties. Ismene was a self-sister, and Antigone was trying to expel . it from herself. Antigone's earlier certainty was a forcible effort of will in opposition to her uncertainty. Then she has said, "I know I am pleasing those whom it is most necessary for me to please." (89) truth: Now she tells the I nourish, that is, I work to keep alive, a hope that I will be received with love by father, mother, and brother. (897-9) is she nourishing that hope? How She has fed it by searching out the final, unassailable reason why she had to act as she did. These lines which �-22- we must now consider are much debated. Most editors and translators cut them out the play, or put them in brackets. three reasons for doing so: Sir Richard Jebb gives the lines are inconsistent with things Antigone has said earlier, illogical in themselves, and ungrammatical. Yet the lines are in all the manuscripts, and they are quoted by Aristotle. That the lines are inconsistent with her earlier appeals to divine law is true; she has changed now, and stopped pretending to be doing a duty. That the lines are illogical is exactly what Aristotle praises them for1 it is here that he says Antigone displays that she was acting not for any benefit but for the beautiful, not out of thought but out of goodness. That the grammar of the lines is strained is a sign that she is strained; this is understandable since she is facing death with all her private nightmares coming to the surface of her thoughts. In the Philoctetes, Sophocles has the main character go to pieces in front of us, with incoherent speeches and a long scream. And in the fourth line of this play, Antigone in her passion says there is nothing without doom that has not come to her, when what she means would have one less negative in it. What does she say that so disturbed Jebb and Fitzgerald and others? She says (904-20) that had it been a child or husband of hers lying dead on the field she would have left it to rot. she could always get another-husband, or bear another child, but with her parents dead, how could she ever get another brother? This is a repellent thought, and there is no reason to think for one second that it is true. Imagine trying to take a child of hers, living or dead, away from Antigone. �-23We have known her for only part of a day, but it is still ob' it would be easier to take a cub from a lioness or a grizzly ~t ,_;,.i,:; t\., Why does she il\~:k~ so ugly11~ falsei>. / · ? ~ .' I think it is an exa~ '· way of saying, I buried Polyneices for the sake of Polyneice! brother was irreplaceable, but love knows that every human bE irreplaceable. At the fringes of thought, Antigone finds an for what has no logic. must do. The immediate sight of love tells it When Antigone said it was not her nature to share j but symphilein, to join in loving, that was a smug debater's against Creon, and a lie made obvious by the presence of Isme Antigone now in her weakness and misery has made that claim t She has let go of everythi~g but love. The murky soup of div her family's blameless nobility, and the human joy of overcorr restraint have now ceased to cloud her sight. In her imagina she sees Polyneices as the only thing in the world that matte the claims on her from loving him as the only ones in the wox subject to conditions. The important thing about philia is that it is natural, We find ourselves in the world loving others who belong to us whom we belong. What we are is a result of whom and what we On the other hand, the defining characteristic of human being accept nothing natural as given but to be always overcoming e to our purposes or whims. of Creon. He says, 11 I am Antigone is glorious in her succes no~' she is the ~, 11 (484) if �-24get away with this, but he is already too late. even when they are at a standoff. She outshines him But she has announced that philia was the end for the sake of which she had broken all restraints. deed and its end were incompatible. had seen from the first. The That is the impossibility Ismene When Antigone returns before us on her way to die, she has collapsed under the weight of the contradictions in her soul. But she has made her final choice. It is love itself with its passivity and uncertainty that she has chosen, rather than the glory of being its champion. � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. 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Identifier An unambiguous reference to the resource within a given context lec Sachs 1988 Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Publisher An entity responsible for making the resource available St. John's College Language A language of the resource English Type The nature or genre of the resource text Rights Information about rights held in and over the resource St. John's College has been given permission to make this item available online. Format The file format, physical medium, or dimensions of the resource pdf Creator An entity primarily responsible for making the resource Sachs, Joe, 1946- Friday night lecture Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/3315871e022cd6ac5953e8da25db1041.pdf d08aa2db6bea57b02ad99a39d7a87b4f PDF Text Text The Battle of the Gods and the Giants Joe Sachs Spring, 1992 Dedicated to the memory of J. Winfree Smith �The difficulties that confront a reader of Aristotle's Physics begin with the title, and it is worth thinking about why. If you picked up for the first time a book that had the word mathematics in the title, and saw that it contained no algebraic equations, you might be surprised but you wouldn't be confused. You know that there is more than one kind of mathematics. You probably learned a lot of perfectly good arithmetic and geometry, perhaps even trigonometry, before you ever had to solve for an unknown. But when you pick up a book that claims to be about physics, and find no algebraic equations in it, you might wonder who is trying to kid you. Physics, after all, is the study of matter and energy, and these are only known through relations like "force equals mass times acceleration," or "the integral of force through distance is one-half the product of the mass and the square of the velocity." I have added nothing whatever to these two statements by saying them in words. I might have saved my breath by saying them in symbols, because the things I am talking about are not translatable into English, or any other language humans speak, but have their whole meaning within algebraic relations. But why should there be diverse kinds of mathematics, but only one thing that has a .right to be called physics, and why is physics the narrower of the two? These are not questions about how we use words, but about what we believe knowledge is, and what activities we recognize as instances of knowing. In the second Book of the Physics, just as also in the second Book of the Metaphysics, Aristotle has to explain why he is not going to treat his subject mathematically. His choice is not a matter of taste or preference, but a reasoned conclusion. We will consider his reasons in a few moments, but first let's think a bit about what mathematics is. You probably all know that in Greek ta mathemata are the leamable things, and therefore the understandable things. In some eminent way, mathematics is the place where understanding is achieved and displayed. But what is it that gives mathematics this special position? The seventeenth-century philosopher Descartes, in Part II of his Discourse on Method, gives an answer. Of all those who have ever sought for truth, he says, only the mathematicians have found any that was evident and certain, because only they have �2 constructed methodical demonstrations. Start with truths that are simple and evident, proceed step-by-step with inferences that are certain, and everything knowable, however remote and obscure it may seem to begin with, will eventually be trapped in a net of certainty. Knowledge is built like houses, streets, and cities, brick by brick, set parallel and at right angles, without choice, without flair, and without risk. How much of this Descartes really means is a question I can't help you with, and this is not going to be a lecture about Descartes. He has an ancient prototype, to whom I will soon turn. But if it is true that it is proof that makes mathematics what it is, what are we to say of the following example? In this century there was a mathematician named Ramanujan, who blossomed in India without benefit of an education. He was considered to have the highest mathematical genius and originality, but to have no idea of proof. How is such a thing possible? The connection between knowledge and mathematics is artfully presented in Plato's Theaetetus. It is with mathematicians that Socrates asks the question, what is knowledge? And with the same art, Plato indicates that the question about knowledge is bound up with the question of what it is that makes mathematics the eminent example of knowledge. The latter question is never formulated in the dialogue, but it is put in front of us dramatically, in the two people, Theaetetus and Theodorus. The student and teacher are both mathematicians, but there is a world of difference between them, and the unanswered question about knowledge is reflected in that difference. Theodorus once proved (147D) that if a square has an area of three square feet, its side is incommensurable in length with the foot. And he proved the same thing again about the square of five square feet, and again and again and again with six, seven, eight, ten, eleven, twelve, thirteen, fourteen, fifteen, and seventeen. This is a man who believes in proofs. If one proof is good, twelve are better, because certainty is achieved every time. Theodorus is a man who doesn't like controversy. His strongest expression of feeling in the dialogue comes when Socrates asks him (170D) whether people disagree with all his opinions. He swears an oath to Zeus, quotes Homer, and says that tens of thousands of �3 people always disagree with him, and surround him with troubles that are more than human beings can bear. In fact, in his younger days, Theodorus had turned away from philosophy and toward mathematics (165A). He says it was because philosophic talk consists of bare words, but what does he mean by bare? He shows immediately that he means that they are lacking in certainty; in one of his many refusals to take part in the discussion with Socrates, he says that he fears the shame of being overturned in argument. Mathematics is for Theodorus a haven of certainty. Because it has proofs, it is foolproof knowledge. But the picture of Theodorus at work proving things contains a contrasting picture of Theaetetus at work seeing something. Dissatisfied with an infinitely repeatable procedure, Theaetetus looks for and finds a single image by which he can see at glance whether any number of square feet will have a side that is incommensurable with the one-foot length: the image of the oblong rectangle. For any number, one need only see whether it can be produced by an equal times an equal; if it cannot, then as a square it will have a side that is neither any number of feet nor any fraction of a number. Theaetetus' proof of this is not given by Plato, but it appears in Euclid's proposition X,9. It is roughly this: one shows frrst that the squares on any two commensurable lines have areas in the same ratio as some pair of square numbers. Then if any square does not have a number of square feet equal to a square number, it cannot be on a side commensurable with the foot. As a proof, it is not very interesting. As an insight it is remarkable, and Socrates calls it "most beautiful" (148A). This might remind us that Theodorus began the dialogue by telling Socrates that Theaetetus is not beautiful, in fear that someone might suspect that he loved him, but is so far from being beautiful that he resembles Socrates. Theodorus fears that the integrity of his judgement would be compromised if what is known as true is also lovable as beautiful. Once one has noticed the picture Plato has drawn, it is unforgettable. What is the mathematician aiming at? Theodorus has found safety in certainty; Theaetetus stretches out to see the true in the beautiful. In the dialogue, Theaetetus repeatedly fails to see the image of knowing in his own seeing, but he is miles ahead of Theodorus, who must be prodded, �4 nagged, flattered, shamed, and roused to anger before he finally begins to take the risks that might lead to knowing. Mathematics is an example of knowing worthy of imitation not because it is so safe, but because it sees what it is thinking. In mathematics, things that are present to the intellect and understanding alone are present in such a way that the language of seeing must be used to descnbe it. I am sure you have all had the experience of learning a proof, but not seeing the conclusion. Was there ever a time after such an experience when you said, "Now I see"? If so, then you also see, now, what I mean. You see that in mathematics, a truth might be something that you not only think, not only understand, but encounter in the act of contemplation. The answer to the question, what is knowledge?, is never formulated in words in the Iheaetetus, but it is set in front of us, in pieces, to be seen. We are invited to recognize what knowledge is in such a way that by doing so we must enact it, engage in the act of knowing. Knowing resembles sense-perception in its immediacy, its first-hand, eyewitness character, but it cannot be sense-perception because the objects of the senses are fluctuating things that have no identity. Knowing must belong to some power of the soul other than sensing. But Theaetetus overshoots this other power when he calls it opinion. Socrates shows him that opinion is the residue that remains when thinking stops (190A). But the live thinking that permits the formation of an opinion might be the very activity of the soul that sees the evident intelligible things just as the eyes see the evident visual things. The last part of the dialogue, in which a logos is taken to mean an analysis into parts, keeps running into the difficulty than an intelligible whole must already be present as a whole before any analysis can be judged complete or correct. For example, in order to know that two times three is the same as four plus two, we must know six in some way that is independent of both analyses. In this humble example of knowing what six is, we can see the point that Theaetetus kept missing, just as he saw the point that Theodorus kept missing in his endless proofs about squares. On this way of looking at things, the glory of mathematics is not its procedure, and �5 certainly not its subject matter, but the fact that it makes the experience of contemplation readily available to us. The two authors with whom our math tutorial begins know this well. In I, 47, Euclid sets in front of us a construction in which almost everything that has preceded it is present in one image, and in Book XIII, in a five-fold image, he achieves the feat of bringing together most of the most striking things that have been shown in the previous twelve books. Ptolemy also constructs the Almagest to lead up to a high moment of seeing, in Book XII, in his common, composite diagram, which shows how, on either of two hypotheses, a ratio produces the appearances of planetary retrogradation. It goes without saying that the same picture reveals the causes of planetary progression, so that one image lays bare the intelligible heart of the cosmos. When Ptolemy speaks of contemplating the things that are always as they are, he does not mean bending the neck backwards at night. These three examples of objects of contemplation are not meant to be flashes of intuition, but are prepared for by long and disciplined work. But in them, what thinking has encountered successively in time reassembles itself in simultaneous presence. Active thinking still has to be going on, or the object will collapse, but it is not one-thing-after-another thinking. It is the kind of thinking we intend when we speak not of propositions but of theorems. What is proposed must be judged, and is at best adopted as a secure opinion, but a theorem is beheld. It belongs to the theater of the intellect. In Greek, this contemplative activity is called theoria. The examples I have given may make it seem that the theater of the intellect is the imagination, but this cannot be true. Just as the triangle drawn on the blackboard, on paper, or in the sand, serves only to direct the imagination to make a more adequate image, so the triangle in the imagination serves only to direct the intellect. Triangles are made of lines, and lines are breadthless, so anything we can see in the imagination cannot be the triangle about which we reason. But the picture in the imagination is a stepping-stone to seeing what is invisible. In the diagram of I, 47, the eye can follow an area between parallels to see it reappear in a different place and shape, yet as the same. The eye can do this because it is �6 informed by the intellect which has learned the elementary properties of parallel lines in Book I. But just as the intellect can inform the eye, in this case the eye of imagination, the eye can supply content to the intellect. The lines that form one construction, present all at once, mark out also one complex of interrelated properties of the triangle, on which the gaze of the intellect itself can rest. But does this mean that anything that is present in imagination can become content for the contemplation of the intellect? Aristotle says no. We might imagine that a human being is bigger than a city, or bigger than the universe, but nothing follows from that about what is true or even what is possible. This argument, at the end of Book III of the Physics, applies directly to the proof Lucretius gives of the infinity of the world. Lucretius asks what would happen to a javelin thrown outward from the supposed edge of the world, and his fantasy supplies an answer. But I could make a counter-fantasy that preserves the finitude of the world: the thrower swings his arm in a mighty arc, and the javelin flies backward toward the earth. The imagination is compatible with two pictures that are not compatible with each other. Either one can provide content for an opinion, but contemplation can only be directed at what is true. So there are things in the imagination that cannot become present in any way in the intellect. But suppose we ask the opposite question. Can everything that is in the intellect become present in imagination? It would seem that the highest, imageless kind of thinking must go beyond what the imagination is capable of, but Aristotle does not agree. In Book III, Chapter 8, of De Anima, Aristotle makes the surprising claims that whenever the intellect contemplates, it also beholds some image, and that, though the primary objects of the intellect are not themselves imaginable, they always have images. To understand what Aristotle is saying, one must distinguish the immediacy of contemplation from the successive making of connections. The kind of step-by-step thinking that we ordinarily do is obviously possible without images; we think, if all A is B, and all B is C, then all A must be C, and the necessity of the conclusion is only obscured by images. This kind of thinking is called �7 dianoia in Greek, and proceeds by assertions and denials, which Aristotle explicitly rules out in the passage we are considering. It is only nous, the contemplative intellect, that is guaranteed to be imbedded in images. But the necessity that every object of intellect have an image must have some cause. What can it be? I am sure that some of you are there ahead of me. After all, everyone knows that Aristotle rejected Plato's belief in separate forms, and taught that the universals that the intellect deals with are produced by th.e act of abstraction. If the universals came out of the sensible particulars in the fist place, then the images of those particulars would also be images of the corresponding abstractions. There is only one problem with this solution. Like most of the things that everyone knows about Aristotle, this one is not true. It is not even close. It is so spectacularly wrong that it blocks the understanding of anything Aristotle thought. It is not a tenable doctrine in the first place, as I will try to show. But worse than that, the belief that Aristotle held such a view makes the Physics a closed book, and that in turn deprives us of the most powerful alternative we might consider to the physics we are accustomed to. The idea of abstraction, as we use it and as we tend to impose it on Aristotle, abolishes the idea of nature. What, then, do we mean by abstraction? On the first day of your freshman math tutorial, when you or someone else said that points and lines are abstractions, what did you or she or he mean? In your Plato seminars, when people called justice and beauty abstractions, what did they mean? We do not need to examine the immense and diverse medieval and modern philosophic literature about the topic to be sure of certain things. An abstraction is a second-class citizen in the realm of beings. The first class citizen is whatever is not abstract but concrete. And what is concrete? Anything we can hold or touch is undeniable, genuine, and concrete. In Plato's Sophist, the Eleatic Stranger compares certain . people to the mythical giants who tried to pull everything down to the earth. (246A-B) These are people who aggressively insist that what is is always a body; when anyone says otherwise, they are contemptuous and won't listen. In the Theaetetus, Socrates has called �8 them the uninitiated, who believe that there is nothing except what they can clench in their hands (155E), but the word meaning uninitiated also means unsealed, leaky, or unsound, and suggests that the clenched fists of these hard-headed realists are really sieves, letting all sorts of things slip through. Socrates introduces these people as those who have not experienced wonder, and the Stranger places them among those whose way of talking is vague. They are comic characters, rigid in the way they hold their opinions but vague in the content of them, grasping things tightly while being slips through their fingers. Who are they? As Socrates tells Glaucon of the people in another strange image, they are like us. I suspect that there is one of these giants in every one of us, who is uncomfortable with the possibility that anything invisible or intangible could be anything at all. But it is so obvious that such things must somehow be something, that we take the shortest route to make ourselves comfortable again and call them abstractions. We make them up, and they are only in the mind. But to be so appealing to us, the word abstract must mean a little something, and our other uses of the verb mean things like to boil down, to remove, to extract. So here, in two sentences, we have already found a self-contradiction. Abstraction was supposed to make the objects of thought unmysterious by producing them. But whatever the process of abstraction is, it cannot have any product that is not already present beforehand. If we are abstracting from tangible bodies, then they must in the first place be made, in part, out of objects of thought. This is what I meant by saying that our usual idea of abstraction is not tenable. It makes the thinkable things unmysterious only by doing just the opposite to the visible things. It ends up claiming that our eyes see the invisible and our hands hold the intangible, because it tells us that when we think one of those invisible and intangible things, we have extracted it out of a body like a tooth. The idea of abstraction answers no question, but only goes around in a circle and gets dizzy. Anything it gives us, we already have; anything we don't already have, it can't give us. So what about the well-know fact that Aristotle said the forms are only abstractions? The Greek word aphairesis, which is translated as abstraction, is the ordinary word for �9 subtraction. It is used a few times in the Physics, and only in this ordinary sense. But the word does have our modem sense as well, and this is usually regarded as Aristotle's invention. This seems to me to be unlikely. I am aware of three places where Aristotle speaks of certain ideas as abstractions, and in two of the three he calls them the so-called abstractions. This use of the word is rare in Aristotle's works, and never, I repeat never, refers to anything but the objects of mathematics. In the Metaphysics (1061a 28ff.), Aristotle says that what the mathematician does is peel away (periairein) all the sensory attnbutes of things, and contemplate the quantities that remain. In De Anima he says that the intellect thinks these so-called abstractions, such as straightness, as separated things, even though they are not separated. (429b 18-19, 43 lb 16-18) In the Posterior Analytics he tells us what faculty these so-called abstractions actually depend on (81a 40-b 9), and I will return to this in a moment. In the Physics, Aristotle leaves out the word abstract, and simply uses the more revealing word separated. In Book II, Chapter 2, of the Physics, Aristotle says that the mathematician treats as separate what is not separate. This does not make his conclusions false. In fact, as Aristotle says in the Metaphysics (1078a 21-23), it is the best way to study anything. But they are not conclusions about nature. By separating the attributes of quantity and position from everything else, the mathematician loses nature, for three reasons. He leaves behind motion, material, and ends. Now you may not mind the loss of ends, and you may count it a gain to set aside the effects of material, such as friction, but the claim that mathematical abstraction gets rid of motion may seem puzzling. For Aristotle, though, this is the most emphatic reason for the unsuitability of a mathematical approach to nature. What does he mean? First of all, Aristotle does not banish mathematics from physics when it has something to offer. Optics, for example, can recombine what it has separated, using the mathematical line only as a temporary detour toward understanding a natural path. And several important arguments throughout the Physics are entirely about ratios. And the most important of the �10 branches of mathematics that Aristotle says surely belong to physics as well is astronomy, in which the whole point is to consider motions. But within mathematics, only one kind of motion is possible: change of position in a neutral, homogeneous, unlimited medium. We call it motion in space. According to Aristotle, such a thing never takes place in nature and never could. One might be tempted to think that pure spatial motion does not occur in the world, just because it is pure. The paths things follow are not exactly straight lines or parabolas, and the things that move are not points or spheres, but still, behind all the qualifications and complexities, there is something clear and simple that we can focus our attention on. Descartes says that the mathematician knows inotion better than anyone else (Le Monde, Ch. 7). Galileo tells us that the world is a book, written in mathematical characters; if we know how to read, we need not stare stupidly at marks on a page, but can grasp the meaning within. (The Assayer) And most wonderfully of all, Newton says that everyone knows what time, space, and motion are, but the vulgar--that's us--have a prejudice that such things bear some relation to sensible bodies. (Principia, scholium to definitions) These thinkers do not describe the world mathematically, they describe mathematics and say that it is the world. As their heirs, we now have not only the vulgar prejudices they attack: we have along with them a whole new array of sophisticated prejudices, at the center of which is the belief that we live and move in space. The idea of space is so firmly embedded in our thinking that it is hard to see that there is any alternative to it. According to Aristotle, though, space is an idea that arises only by self-deception. Since bodies are extended, we can think of the extension without at the same time thinking of the bodies. (211b 16-19, 212b 25-27) This is the separation or abstraction characteristic of mathematics, and Aristotle has no quarrel with it. But in order to get from mathematical extension to the idea of space, we have to pretend that what we abstracted was in the first place present in the world. We experience bodies, separate their extension from them, imagine it as space, and declare that it is the world. Now that we �11 have invented space, we are free to put things into it, in our imaginations, and set them moving along any path, at any speed that we please. Once we have replaced the world we live in with this invented world of space, this is in fact the only kind of motion possible, and we are apt to think that it really is all that motion could be. This is the fork in the road. If we can set this idea of motion in space aside for a while, we can enter Aristotle's Physics. If we cannot, we might as well set the book aside, for the central topic of Aristotle's Physics is motion, and he means what he says when he tells us the mathematician must leave motion behind. Change of place is one of the kinds of motion Aristotle considers, but change of place presupposes places, and there are no places in space. Spaces are all alike and are all together infinite. How do I know? I consult my imagination. That ought to give me a clue as to what kind of thing I am talking about. What Lucretius presents as a proof of the infinity of the world is in fact only a proof of the infinity of space, and I know in the same way that no part of space has any power or potency that would make it any more or less appropriate than any other for any inhabitant. But the things we encounter all have places. Trees don't grow in the air, human beings don't breathe in the sea, and stars don't circle underground. When things change place, we can't understand what is going on unless we know what kind of thing is moving, and whether it is going toward, away from, or through a place in which it can remain and sustain itself. The placeless realm of mathematical physics already makes the natural kinds to which things belong invisible. It is a de-natured realm. But the natures of things are not accessible to us through a simple turning to imagination. If we take Aristotle's road toward nature, on what power of knowing can we rely? I mentioned earlier that Aristotle does not say that we get at universal ideas by abstraction. The most important of those ideas, he says we get at by epagoge. This is usually translated as "induction," but that is misleading. We use that word to refer to the process of generalizing from many examples. In many places, Aristotle says unmistakably that one example is sufficient to give us the universal present in the particular (e.g. Posterior �12 Analytics 71a, 7-9, Physics 247b 5-7). Epagoge means "coming face-to-face with" something, and it belongs not to the dianoia, by which we make connections and figure things out, but to the nous, the contemplative intellect. The ultimate aim of the Physics is the contemplative knowledge of nature, and the inquiry depends all along on the presence of the contemplative faculty. Aristotle describes completed knowledge as a contemplative insight into ultimate things, combined with reasoned conclusions from them. His word for this is episteme, which comes to us through its Latin equivalent as science, and most commentators call the Physics a science, the science of moving things. Nothing could be further from the truth. Like all Aristotle's books, the Physics ascends toward the ultimate source of the appearances it studies. The ultimate source of natural motion is only uncovered in the last pages of the book. Aristotle calls this order of inquiry dialectical. It begins with experience, seeks to uncover its universal character, and reasons from effects to causes with the aim of bringing into presence that which makes its subject whole. It begins and ends in the faculty of nous, and consists in the progressive unfolding of its contemplative activity. If this road toward knowledge sounds familiar to you, there is a good reason. In the Meno, Socrates uses the myth or metaphor of recollection to describe how inquiry is possible. In Book VII, Chapter 3, of the Physics, Aristotle says straightforwardly that knowledge cannot come into being in us because it has always already been present in us all along. Our thinking becomes knowing when it calms down out of its native disorder. The physics familiar to us does violence to nature, by experiments to be sure, but more deeply and radically by turning natural things into mathematical ones. The act of abstraction cuts nature down to a size we can handle. Aristotle, on the contrary, says that we can let nature remain intact and still come to know it, because we are already in a living relation with it. We are finally in a position to see why the contemplative intellect always has images available to it. The object of nous has a name that will be familiar to you. Aristotle says it is the eidos. But he also says that nature is form. The nature of anything comes to it not �13 from its material but from the internal activity that forms it, and it is this same activity that is at work upon the human intellect whenever it contemplates. The content of contemplation is given to it by the activities that are always at work, forming the things in the world. That is why each single object of sense-perception has its universal character immediately present in it. The universal in question is the eidos at work, holding it together as the thing that it is. The intellect is present in every act of perception, and the imagination is available to every act of the intellect, because all three faculties are directed at the same being. Aristotle agrees with Plato that the forms of things are not abstract ideas, but are beings. They are not dependent on us, but rather everything that is is dependent on them. The great fact, evident everywhere around us, is the continual emergence and reemergence of things in accordance with kinds. Being is, first and last, living being. That is the meaning of Aristotle's claim that being is energeia, being-at-work, and always has the character of entelecheia, being-at-work-staying-itself. Everything that exists at all is or is part of some self-maintaining whole. Every living thing lives within the orderly and self-renewing whole that supplies its material needs, and everything that is not living has its nature within this organized cosmos. Does the rain fall so that crops may grow? (Bk. II, ch. 8) Not so that one man's crops may thrive while another man's wheat is spoiled on the threshing floor, but always, over and over, the waters that evaporate in the hot months return to earth in the cold months to sustain the earth not as a region of space but as a place in the cosmos appropriate to the life of plants and animals. When Aristotle says that nature acts for ends, he explains this by saying that the end is the form. Things have natures because they are formed into wholes. The claim is not that these natural wholes have purposes but that they are purposes. Every being is an end in itself, and the word telos, that we translate as end, means completion. When we try to judge Aristotle's claim that nature acts for ends, we tend to confuse ourselves in two ways. First, we imagine that it must mean something deliberates and has purposes. Second and worse, we begin with our mathematically conceived universe, and �14 can't find anything in it that looks like a directedness toward ends. But Aristotle indicates that it is just because ends are present in nature that a physicist cannot be a mathematician. We have seen that even change of place becomes impossible in mathematical space. But there are three other kinds of motion, from which the mathematician is even more hopelessly cut off, without which activity for the sake of ends would be impossible. Things in the world are born, develop, and grow. Genuine wholes, which are not random heaps, must be able to come into being, take on the qualities appropriate to their natures, and achieve a size at which they are complete. But mathematical objects can at most be combined, separated, and rearranged. If we have first committed ourselves to a view of the world as being extended lumps in a void, there is no way to get wholes or ends back into the world. That means in turn that the question of ends has to come first, before one permits any choice to be made that empties the world of possibilities. Why are we so likely to adopt the picture of the world that mathematical physics gives us, before even asking whether it requires us to give anything up? It is surely not a rational procedure to paint ourselves into a corner, and then ask whether there is someplace other than that corner that we really want to be. I think the answer to this question might emerge if we think about causes. The first thing Aristotle says in the Physics, which he says repeatedly in many other places as well, is that we do not know something until we know its cause. This may sound strange at first. I want to know one thing, and I am told that knowing it means knowing something else. But if I attach a predicate to a subject, I have at most made judgment or formed an opinion. If I can see through what, or on account of what, the predicate belongs to the subject, that third thing has given my thought a dimension of depth. But something stranger still happens when the new physics of the seventeenth century takes shape. Galileo tells us that investigating the causes of natural motions would be a waste of time. (Two New Sciences, NE p.202) Newton makes no hypotheses about the cause of the properties of gravitation, and says they would have no place in his science. (Principia, �15 general scholium) Descartes, as usual, gives us the clearest view of what is going on. He says that matter has no attributes that are not perfectly known to everyone. "You could not even pretend not to know it," he says. And, "you must necessarily conceive of it or you can never imagine anything." (Le Monde, Ch. 6) Suddenly the world needs no explanation. Everything in it is pre-explained. To exhibit any of the properties of mathematized matter is to see through it all the way to the bottom, because it is conceived as having no properties other than the ones that are being exhibited. We have already seen Aristotle's criticism of the idea of space. The extension of body is separated from body, and declared to exist by itself. The corresponding idea of matter depends upon it. It is filled space, the bearer of a few properties that are completely determined when they have been measured. Bodies, that had natures to begin with, were turned first into space and then into masses, and along the way the world became much easier to explain. Aristotle's approach to explanation is to let things be what they are, and inquire into the causes responsible for their being as they are. The alternative approach is to reduce the world to things that are so poor in properties and do so little that no explanation is required. In fact matter, understood as mass, doesn't do anything at all. It is the passive seat of motions that no more belong to it than do any other motions, or than to any other masses. It is not only Newton's first law, but all three of his laws that say that matter is inert. In his Opticks, Newton calls them passive laws of motion that all result from a force of inactivity. (Question 31) Aristotle says that being is being-at-work. Newton says that being is being so hard that nothing can cause it to change. Just as motion in space is not the same as change of place, matter conceived of as inert masses bears no relation to what Aristotle called hule or material. Nothing in the natural world is simply matter, but everything that is belongs to some living thing or to the organized whole of the cosmos. Everything is already formed in some way, and bursting with potency toward activity. Motion is understood by Aristotle always to be the result of the spilling over of the potentialities that belong to the material in any being. The opposite of �16 activity, passivity or inertia, is not present anywhere in Aristotle's account of things. Dunamis is nascent activity, striving to emerge, or dormant activity, awaiting its moment in the rhythm of life. From the standpoint of mathematical physics, such potentialities are occult qualities, and are not permitted to exist. The dream of this physics is to give back all the appearances of the world as determined by mere mechanism. Now the strangest fact is that this mechanistic approach to the world failed, and failed at the very moment that it was fully realized. The three laws of Newton's Principia embody and perfect the mechanistic picture of the world, but the Principia as a whole shows that the world does not fit into that picture. Masses are not just inert lumps that interact only when they happen to bump, but are sources of a mysterious gravitational pull, and the spaces between masses are not empty but in some way serve as the medium by which this attraction acts at a distance. The conception of matter and space produces a pleasing picture, in which the question, why?, need not ever be asked, but that picture does not account for any event. The inadequacy of the ideas of inert bodies and empty space surfaces again when light is shown to be wave motion, and then to be incapable of having any material medium for the waves to be in. Twentieth-century physics completes the destruction of the ideas that serve as its own foundation, when it shows that every particle of matter must also be an immaterial wave, and every wave must also be a particle. Not only can matter and space not give an account of anything, they cannot even hold on to the determinacy that makes them distinct from one another. What makes this failure of mechanistic explanation so strange is the fact that its failure doesn't seem to be regarded as a flaw. Mechanism continues as a dream, and as the guiding vision of an enterprise that keeps marching forward, producing ever more complex mathematical descriptions of events, and giving rise to ever more effective ways of controlling the world. It fails only as knowledge. The trouble is not that the mechanist account is incomplete. One cannot add a power of attraction to an inert mass, or tack a distribution of energies onto empty space. Things have to be conceived in the first place in �17 such a way that they might intelligibly be the bearers of such active states. But the whole point of the ideas of matter and space is that they be devoid of all hidden powers. Many true conclusions might follow from a set of false premisses, and one might be content to live with a certain number of loose ends, but the human desire to know will ultimately have its way. Some twentieth-century physicists have recognized the need to rethink the way the world is, from the bottom up. One has suggested that the true beings are potencies, of which particles and waves are only appearances. (Heisenberg) Another has suggested that the world is a seamless whole, in which nothing exists in isolation. (Bohm) A third has even studied Aristotle's definition of motion, in the hope that it might open some way out of the dead end of modern physics. (von Weizsacker) These issues are wide open. All that is agreed is that the physics of Galileo and Newton is "classical," which means untrue, and that current physics has found no way to articulate what it is talking about. One source of trouble may be that the world cannot be understood from the bottom up. It may be that physicists are looking for the right way to understand points, so that they can put them together and make lines. Everywhere on a line one can find a point, but only if the line is first given as a whole. The central ideas of Aristotle's physics are wholeness and continuity. In the first chapter of Book I, he argues that we have nowhere to begin an inquiry except with the wholes we encounter in experience. The task is not to replace them but to understand them. Throughout the Physics, the picture of the world is of living things in a cosmos, as opposed to matter in space. And no genuine whole can be understood by reducing it to its parts. How can it be understood? We have come back to the question of cause. Aristotle says that causes are of four kinds, and understanding anything requires knowing all four of its causes. But just as with the four kinds of motion, we have lost the meaning of three of the causes, and diminished the fourth beyond recognition. What we call the "efficient" cause makes some sense to us, because it corresponds to the transferences of �18 motion in a mechanical system. But Aristotle uses no word or phrase that could be translated as "efficient cause." The only cause external to a being that interests him is that which origi,nates motion. By efficient cause, we mean some motion earlier in time, that results in another motion by way of a push or a pull. But Aristotle argues at the beginning of Book VIII that there can be no first motion in time, but before any motion some prior one was necessary. These sequences of events are infinite, are casual only in a derivative and incidental way, and explain nothing. But there is another kind of sequence, not of events but of beings, not backward in time but upward in responsibility, that Aristotle says leads from any motion to its origin. He gives an example that is the same as that of a baseball flying off a bat. (256a 6-8) The origin of the motion is not the bat, but neither is it the hand or the arm, and it is certainly not the passage of an electron across a neural synapse. Only the human being as a whole can hit a baseball, and he does so as an origin of motion. The pitcher had to throw the ball first, but the batter does not re-act, as dead matter, but has to act, as a source with its own integrity, and can hold back from acting. The example illustrates two things that are at the heart of Aristotle's physics. First, the responsibility for any event has a place where it begins. Mechanical events form a homogeneous string of bumps and exchanges, but in the true, non-mathematical world, some events are incidental or instrumental, while others are causal because they are the sources of the rest. And second, the sources of motion are never themselves motions. (257b 9) Newton's third law says that motions are only caused by motions, but that means that the cause is always exactly the same kind of thing as the effect, and cannot provide an explanation of it. The corresponding principle in Aristotle's account is that where there is a motion, there is a being that is its origin. This means in turn that motion is never an explanation of anything, because it always leads back to something that is what it is not by motion but by activity. Mechanistic explanation starts at the bottom of things with inertia. Aristotelian explanation starts at the top of things with activity, energeia, being-at-work. �19 But being-at-work is what Aristotle says the form is, and the potency, or straining toward being-at-work is the way he characterizes material. Finally, the end, or telos, of a natural thing is so inseparable from its being-at-work that Aristotle fuses the two names into one: entelecheia, being-at-work-staying-itself. That is, the three causes other than the external source of motion work in just the same way that it does, except that they are all internal. The formal, material, and final causes are the what-it-is, of-what-it-is, and completeness-for-the-sake-of-which-it-is, which are responsible not only for motion but for any thing's being at all. If you have been thinking of them as a static blueprint, a heap of inert matter, and a distant, external purpose, you may be excused for wondering why they should be called causes. They are instead three ways of looking at the ceaseless working without which beings would indeed collapse into inertness. They are responsible for the motions which cannot be drawn on a blackboard, the birth, development, and growth to maturity of each being. More important still, the form, material, and end are responsible for the kind of rest into which the mature and complete being settles. This state of rest is not the cessation of motion, but the organization of motion into active equilibrium, the transformation of motion by which it is no longer change but just its opposite, stability. Aristotelian physics is not about how bodies fall and collide, but how bodies are. Mathematical physics tries to look behind the world, to a realm where being is simply given. Aristotle looks at the world and sees that in it being is always an achievement. The simplest examples of being as being-at-work are eating and breathing. But beings do not simply survive. All of them are at work in the lives they live, and in which alone they are complete. My dog, for example, lives in and for the chase. I have no sheep for her to herd, and squirrels and cats are not very co-operative, but rubber balls and plastic frisbees are adequate substitutes, because the ever-renewed chase is an end in itself. How do I know this? I think it is by the power of nous, applied in an attentive and patient looking in which what is important becomes foreground, and what is incidental recedes into the background. Her dunamis is apparent in the tense and concentrated stance characteristic of border �20 collies, her eidos is most evident in the swoop, capture, and return, and her telos is recognizable in the perfect fusion of desire and satisfaction in the same activity. There are physicists of an Aristotelian kind around us today. They are called ethologists or animal behaviorists. Their activity seems to me to be contemplative, since a life must take shape and unfold before them. Another kind of biologist seeks to reduce living things to the behavior of DNA molecules, to make their study finally a branch of mathematical physics. But while DNA is certainly part of the material basis of life, it doesn't explain anything. Two thousand years or so of breeding were involved in getting my dog her DNA, but only as a means to an end. All those breeders were looking at dogs at work. No account can begin with DNA. Even blue eyes can only be explained by someone who knows what eyes are and what blue is. Eyes live in the world and blue appears in the light, and no amount of inspection can find them in any molecule. One could imagine Theodorus contentedly working out genetic maps for species he had never seen, but Theaetetus would know something was missing. We deliberately stupefy ourselves when we first cut off from the living world all traces of wholeness and activity, then declare that they are not present because we cannot find them in the residue. We feel driven to conclude that life is only an offshoot of blind chance and necessity, because we have reduced our field of view to one in which nature cannot enter. The crowning irony is that the matter-and-space explanation at which molecular biology aims has already failed in physics itself. Still worse, many people are groping to recapture an idea of nature, only to be frustrated by a misguided respect for mathematical physics. Respect for living things is not a sentimental attachment, undercut by the way things really are, and the desire to see the natural world less disfigured by human encroachments is not a nostalgic longing for a lost way of life. The idea of natures as active causes is a live alternative to mathematical physics. A first step toward re-opening ourselves to the question of how things are would be to see the mathematical reduction of the world as something that limits and falsifies it. Looking at the world that way reveals a lot of �21 connections that help us manipulate things, but also conceals other things that might be at least equally important to us. Material might have an innate directedness toward certain complete wholes. Motion might be more than rearrangement of positions in a void. Aristotle's Physics could teach us how to keep our eyes open to possibilities. It might even convince us that it is possible to know something without destroying it. Things might be more, not less, than they first appear to be, with an interior depth of activity and an exterior richness of connections, just in being what they are. But most important of all, Aristotle might open our eyes to what knowing is. It is not a possession, but an activity. It is not a corporate activity of the human race, but yours alone, because no one can do it for you. Mathematics is one of its humbler manifestations, and all knowing is akin to mathematics in the sense that it is achieved when one beholds the way things are, together with its evidence, all at once in living thinking. But knowing is not limited to mathematics, or dependent on it. And it is not subject to progress, apart from the progression of each person's learning. As contributions to that kind of progress, the most recent books and pronouncements might be the most stale and barren, and Aristotle's Physics might have the inexhaustible freshness of nature itself. � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Description An account of the resource Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. Items include audio and video recordings and typescripts.<br /><br />For more information, and a schedule of upcoming lectures, please visit the <strong><a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a></strong>.  <br /><br />Click on <strong><a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&amp;sort_field=Dublin+Core%2CDate&amp;sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a></strong> to view and sort all items in the collection.<br /><br />A growing number of lecture recordings are also available on the St. John's College (Annapolis) Lectures podcast. Visit <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a> or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe. Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Title A name given to the resource St. John's College Formal Lecture Series—Annapolis Identifier An unambiguous reference to the resource within a given context formallectureseriesannapolis Text A resource consisting primarily of words for reading. Examples include books, letters, dissertations, poems, newspapers, articles, archives of mailing lists. Note that facsimiles or images of texts are still of the genre Text. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data paper Page numeration Number of pages in the original item. 22 pages Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Battle of the gods and giants Description An account of the resource Typescript of a lecture delivered on March 6, 1992 by Joe Sachs as part of the Formal Lecture Series. Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Date A point or period of time associated with an event in the lifecycle of the resource 1992-03-06 Rights Information about rights held in and over the resource St. John's College has been given permission to make this item available online. Type The nature or genre of the resource text Format The file format, physical medium, or dimensions of the resource pdf Relation A related resource <a title="Sound recording" href="http://digitalarchives.sjc.edu/items/show/3719">Sound recording</a> Language A language of the resource English Identifier An unambiguous reference to the resource within a given context lec Sachs 1992-03-06 Creator An entity primarily responsible for making the resource Sachs, Joe, 1946- Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/c794466c37e151964d2e24ddf789b5b1.mp3 6be998bab8b0c16846c27eaf822e5aa8 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Description An account of the resource Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. Items include audio and video recordings and typescripts.<br /><br />For more information, and a schedule of upcoming lectures, please visit the <strong><a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a></strong>.  <br /><br />Click on <strong><a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&amp;sort_field=Dublin+Core%2CDate&amp;sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a></strong> to view and sort all items in the collection.<br /><br />A growing number of lecture recordings are also available on the St. John's College (Annapolis) Lectures podcast. Visit <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a> or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe. Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Title A name given to the resource St. John's College Formal Lecture Series—Annapolis Identifier An unambiguous reference to the resource within a given context formallectureseriesannapolis Sound A resource primarily intended to be heard. Examples include a music playback file format, an audio compact disc, and recorded speech or sounds. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data audiotape (Tape 397) Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 00:57:00 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Battle of the Gods and Giants Description An account of the resource Audio recording of a lecture delivered on March 6, 1992, by Joe Sachs as part of the Formal Lecture Series. Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Date A point or period of time associated with an event in the lifecycle of the resource 1992-03-06 Rights Information about rights held in and over the resource St. John's College has been given permission to make this item available online. Type The nature or genre of the resource sound Format The file format, physical medium, or dimensions of the resource mp3 Relation A related resource <a title="Typescript" href="http://digitalarchives.sjc.edu/items/show/3720">Typescript</a> Language A language of the resource English Identifier An unambiguous reference to the resource within a given context lec Sachs 1992-03-06 Subject The topic of the resource Aristotle. Physics Creator An entity primarily responsible for making the resource Sachs, Joe, 1946- Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/f378473f91a906b6ad99498caa7c1f5a.pdf af5450e0b213d67aad6fd29e338f5c80 PDF Text Text God of Abrahalll, Isaac, and Jacob Joe Sachs One of the most difficult sentences in the Bible is in the fifth verse of the sixth chapter of Genesis: "And the Lord saw that ... every imagination of the thoughts of man's heart was only evil continually." In Biblical usage, the heart is the place and source of all thought and purpose. The inward life of the human creature is thus said to be only and unceasingly evil, poisoned by imagination. But it is just this capacity for inward and imaginative thought that distinguishes man from the other creatures. Every genuinely human action proceeds from choice, and choice is only possible when an array of possibilities is first represented in the imagination. The less active, flexible, and free the imagination is, the more constrained and slavish will be the action. So it is the very power that makes us what we are that is said to make us evil, and indeed to make us unworthy to live, since the text of Genesis continues: "And it repented the Lord that He had made man on the earth, and it grieved Him at His heart. And the Lord said, 'I will blot out man whom I have created from the face of the earth.'" In carrying out this purpose of His heart, God would be blotting out His own image. Should we say that the image had been defiled because the medium in which it was placed had become corrupt? I think it is worse than that. The power for which we are condemned is the image of God. The Bible does not say in what way we carry that image, but the phrase "image of God" is linked with Joe Sachs is a tutor at St. John's College in Annapolis. This is the text of a lecture given at St. John's in 1986, in October in Annapolis and in November in Santa Fe. It appears here by permission of The Great Ideas Today, a publication of the Great Books division of Encyclopedia Britannica, Inc. THE ST. JOHN'S REVIEW our dominion over the animals and with our being created male and female. Now some animals dominate others, simply by force, and man is certainly not unusual among the animals for being made male and female. But a dominion which is not merely violent, and a sexuality which is not just a matter of coupling in response to desire, are possible to human beings because we are capable of thoughtfulness for others and for one another. That thoughtfulness, which is imagination freely exercised for the sake of the good of another as well as of oneself, is thus the image of God. How is it that it can be not only evil, but only evil continually? It is easy to see that anything which depends on freedom can be misused. If not, it could not be properly used, freely. But why must the imagination always be misused? When the snake tells Eve that God is a liar, and is cheating her of good things because He wants to keep them to Himself, is she not free to say no to him? She is, but if she did so, it would be an answer based only on faith. She does not know that God's purposes are for her good. Where knowledge is lacking, imagination can always multiply possibilities. But why shift one's faith to the snake, and to the unknown benefits he promises? The snake is smart enough to give no reasons for distrusting God, and to give no content to his promises. "Your eyes shall be opened," he says, "and ye shall be as God, knowing good and evil." (3 .5) All the work of persuasion is left to Eve's own imagination. If we cannot say why the persuasion will necessarily succeed, I think at least we all know that it must. If it didn't, Eve would not be our ancestor, but belong to some other race. But the most telling display of the power of imagination comes after the fruit is eaten. The eyes of Adam and 11 �Eve are indeed opened, but to what? "They knew that they were naked." What is happening here? Whatever it is takes place only in the imaginations of Adam and Eve, and can be discerned only in the imagination of the reader. Just before this moment, Eve had implicated Adam in her act, and just after it, Adam will try to shift all the blame onto her. Adam and Eve had been ''one flesh," but now each has begun to treat the other as something to be used. The two look at each other, and neither likes the way it feels to be looked at in that way. Do you know that feeling-the feeling that comes when someone is looking at you with speculation? Adam and Eve cannot fail to know it, because each is experiencing it from both sides at the same time. Their response is the invention of clothes. They produce an imaginary safety, which is an outward sign of genuine inner barriers. Each has isolated himself by imagining how he might increase his own good at the expense of the other. It is to this new condition of solitary suspicion and distrust that their eyes are opened. Here the power of imagination has already gone out of control. Each of the two human beings has imagined the possibility of selling out the other, and as a consequence, each has imagined as well that the other is imagining the same thing. Imagined wrongs become genuine threats, and, with the making of clothes, what had been only inner begins to have outward effects. Some readers of Genesis say that the snake was right when he said that Adam and Eve would not die when they ate the forbidden fruit. Perhaps that is when they became mortal, these lawyer-like readers say, but God said ''in the day that thou eatest thereof thou shalt surely die," and we've got Him there. But God had also said that it is not good for man to be alone, and each human being has now begun considering that it might be better to be alone, to put his own good first and sacrifice the other to it. That possibility of separation immediately, and apparently uncontrollably, began becoming real. If Adam and Eve before that day had lived a life as one flesh, then surely on that day they did die: they died as one being and were re-born as two. Perhaps that is the way in which the imagination is only evil. The imagining of bad possibilities is an experience which cannot be erased; it makes us different and may make our lives worse. On the other hand, the imagining of good possibilities (for example, that God intends our good) seems to require effort to sustain, and to be always vulnerable to suspicion. The imagination is the source of both suspicion and faith, and it always makes suspicion the line of least resistance. The imagination is the image of God and the source of our freedom, but it is a freedom weighted toward isolation. It seems then that the power which is needed to make 12 life good tends by its own nature to make life bad. For example, my guess is that Abel was not a very interesting man, and not capable of much-that he was accepted for the little of which he was capable. It is his brother Cain, whose imagination leads to hurt feelings and murder, on whom God places a special mark of protection. Cain is cursed (is the first human being to be cursed), but his life is preserved, as presumably Abel's life could have been protected and preserved but wasn't. Throughout the Bible, it is the murderers, like Moses and David, and the thieves, like Jacob, on whom God's care is lavished. On the interpretation I am offering, the image of God is more fully present in Cain than in Abel, though also at greater risk of being perverted and destroyed. It is Cain who builds the first city, and it is his descendants who first make musical instruments and tools . But it is also Lamech, Cain's descendant in the fifth generation, whose song is preserved (4.23-4): "I have slain a man for wounding me, and a young man for bruising me; if Cain shall be avenged sevenfold, truly Lamech seventy and sevenfold." Can such a creature as man be saved from becoming what he thinks he wants to be? Command and punishment have been present since the first generation, but still the tormented murderer Cain has been succeeded by the self-satisfied and boastful murderer Lamech. It is another Lamech who is the father of Noah, but the first Lamech typifies the world God judges too far gone in violence and corruption to be allowed to endure. (6.11-13) Lamech not only kills, but glories in the slightness of the pretext for killing; he takes joy in multiplying in his imagination those whom he will kill for offenses which have not yet happened. By destroying others, he has built himself up into a mighty man of renown. (6.4) The human creature, left to itself, degenerates into this Cyclops-like being who boasts of being a law to himself. What does God give to the human creature to protect it from its own deadly inertia? The answer, I think, is threefold. God gives man a history, a covenant, and a Law, and the third cannot be understood apart from the first two. Some might think that the Law of Moses is simply a list of explicit prohibitions and commands meant to replace or at least hold back the imagination. On such an interpretation, the Jew need never make his own choices or risk his own judgment since everything he need ever do is spelled out in the hundreds of laws of the Torah. Now I hope to show that this is a misunderstanding of the Jewish Law, and in fact almost an inversion of it, but even if it were not, it would be no solution to the difficulty posed by the first six chapters of Genesis. If the faculty of imagination were beaten down in us, made powerless in our lives, the creation would be diminished, void of the image of God, and stunted at the �level of the things that creep on the earth. The Flood is not a curtailment of the creation but a renewal and affirmation of it. It is the beginning of history, and the occasion of the first covenant. God's first deed in the newly-washed world of Noah is to declare that He will never again destroy this world. This commitment on God's part is the covenant with N. ah. Although God also gives two laws to Noah and o his descendants, and although the word for covenant means a contract for which pledges are exchanged between two parties, it is of the utmost importance to see that God's promise is in no way conditional upon any performance or promise on man's part. The covenant is spelled out over nine verses (9. 9-17) as repetitious and emphatic as anything in the Bible. Mankind will never be destroyed under any circumstances. In order to see that this promise is not conditioned by man's observance of the law requiring capital punishment for murderers, one need only look at the reason given for the promise in chapter 8, verse 21. Mankind will forever be spared because ''the imagination of man's heart is evil from his youth." The reason for the covenant of universal forgiveness is identical to the reason given in the sixth chapter for universal condemnation and destruction. Human evil is pardoned, because it is in us from youth, that is, from before the time when we are responsible: it is our native condition. Whatever the purpose of the laws already given and to be given, they are not the price of the divine protection of human life. The rainbow is like the mark of Cain, placed now upon the whole human race . It says: this criminal has forfeited his right to live, but that life will be maintained by something stronger than his deserving. The sixth chapter of Genesis is often seen as the strongest evidence for the inconstancy of God in the Bible. He repents of the creation, reverses Himself, and destroys what He had made. Then in chapter 8, God reverses Himself again. Does the second reversal double the evidence of inconstancy? Or does it cancel it? The underlying reason for the perpetual pardon of mankind is the same as the underlying reason for its destruction. That is why the world after the Flood is not a new order of things, but an affirmation of the original creation. It is all right that the imagination of man's heart is evil; he was made that way. That is not the flaw that shows creation to be faulty, but part of the design . God's twice reversing Himself, on account of one unchanging reason, shows that neither He nor His relation to his creatures has undergone a change. Mankind after the Flood differs from mankind in Eden in only one way. He does not have a different heart; he has a history . It is possible to look at the God of the Bible as a bumbler, trying first one thing and then another in an effort THE ST. JOHN'S REVIEW to undo the unforeseen consequences of His past mistakes. But what if God's relationship with the human creature were fully formed from the beginning, but man, from his side, could only come into possession of that relationship by acquiring a history? God will send Abraham to a mountain to kill his son. Abraham will return with Isaac alive and unwounded, but for the rest of his life Abraham himself will have an unforgettable history. That episode is called a test or trial of Abraham (22.1), but for whose sake is he tested? An unconditional and irrevocable covenant has already been made with Abraham (12.1-3, 13.14-17, 15.18-20, 17.4-14), and its fulfillment depends upon the existence of Isaac. (17.19) Therefore God knows both that Abraham will pass the test and that he will not kill Isaac . Abraham is changed in order to become what God already knows him to be. The only difference after the test is that Abraham has come to know about himself some of what God already knew. History then is like a lens through which man can see himself and God. A human covenant is an attempt to determine an unknown and uncertain future by two parties who bind themselves mutually to bring it about. What then can be the meaning of a covenant between man and God? The first use of the word, for the covenant with Noah, is in a context which emphasizes the absence of the mutuality which is ordinarily the essence of all covenants. When the great covenant is made with Abraham, it is set out in the form of an exchange. In return for the promised land and a multitude of nations and blessings, Abraham must circumcise all the males of his household. (17.9-14) But the ritual of circumcision is not a return made to God, but a sign of the acceptance of His promise. If the circumcision fulfilled Abraham's side of the contract, it would make no sense for him to be put through the test of the sacrifice of Isaac, in which he is asked to destroy the possibility of the fulfillment of God's side of the bargain. When Abraham lifts the knife on the mountain in Moriah, he is abandoning any humanly intelligible role in bringing about the things promised him by God. My suggestion is that it is only at that moment that Abraham appropriates the covenant. That is the moment when he knows that he did not enter into the relationship with God simply for the sake of the things God would give him, since in asking for Isaac's life, God is saying in effect "Give back everything I have given you and any possibility of ever getting any more of it." God already knew that Abraham's side of the covenant was nothing but his believing it (15.6): "Abraham believed in the Lord, and He counted it to him for righteousness." After the test on the mountain Abraham knew those same things about himself: both how strongly he believed and that his belief was the only thing he had to offer God. 13 �The change of his name from Abram to Abraham is an indication that the man with whom the covenant is made does not yet exist when the covenant is first announced. Abraham cannot see who God is or what God is asking of him until his own life has unfolded sufficiently. Inthat way, divine covenant is inseparable from human history. And that is why the covenant of forgiveness with Noah can only be made with a human race that knows of the destruction in the Flood and of the violence and corruption that preceded it. Noah and his descendants possess a world which does not differ from the one given to Adam and Eve, but to Noah's generation that world is seen refracted through its history. The world after the Flood can be seen as a possession that could have been lost, that almost was lost and was only spared by the free choice of its creator. But how does that differ from a world that might not have been made, and only came into being by the free act of creation? It differs only in being more fully known for what it is. It is with the knowers, the inheritors of a history, that God first makes a covenant. Similarly, Isaac is no different after Abraham's ordeal on the mountain, but to Abraham he must have become more precious as a son who could have been lost, but was spared by the free act of God. But Isaac was already a miraculous son, given to Abraham and Sarah when they were far beyond the natural capacity for child-bearing. Again, Abraham's history only makes Isaac more fully known for the free gift he is, the Abraham has come to know this truth with excruciating vividness. It has been pointed out to many of us by Mr. Littleton that the word love occurs first in the Bible when Abraham is commanded to kill his son: "Take now thy son, thine only son, whom thou lovest." (22.2) Perhaps the creation, or the bringing to sight, of human love also occurs first in the giving and re-giving of Isaac with a joy and a pain beyond any in the power of nature. The covenant that promises that the world will endure is made with a generation that knows not to take the world for granted, and the covenant that promises the blessing of descendants is made with an Abraham who knows not to take a child for granted. Those with whom covenants are made have been given the chance to know themselves and the things they have as creations of a creator. That, I think, is always the meaning of covenant in the Bible: the discovery and acknowledgment of createdness. This meaning of covenant is best exemplified in the history of Jacob. As with so many of the things we have looked at, this point is revealed by first seeming to be its opposite. The covenant between God and Jacob is first made at Beth-el, when Jacob is on his way east toward the home of his uncle, in the land from which Abraham had departed. It is worth listening to every word of it. 14 God speaks to Jacob in a dream, saying (28.13-15), "I am the Lord, the God of Abraham thy father, and the God of Isaac. The land whereon thou liest, to thee will I give it and to thy seed. And thy seed shall be as the dust of the earth, and thou shalt spread abroad to the west, and to the east, and to the north, and to the south. And in thee and in thy seed shall all the families of the earth be blessed. And behold, I am with thee, and will keep thee withersoever thou goest, and will bring thee back into this land; for I will not leave thee, until I have done that which I have spoken to thee of." Jacob awoke, and "vowed a vow, saying," (vv . 20-22) "If God will be with me, and will keep me in this way that I go, and will give me bread to eat, and raiment to put on, so that I come back to my father's house in peace, then shall the Lord be my God, and this stone, which I have set up for a pillar, shall be God's house; and of all that Thou shalt give me I will surely give the tenth unto Thee." Here, surely, is a man of imagination. Where Abraham believed, Jacob spells out terms and conditions. Where Abraham did just what he was told to do, Jacob offers extra inducements, to hold God to his bargain. It is not the case that Abraham never bargained with God. There is the obvious instance of the dialogue over Sodom and Gomorrah (18.17-33), in which Abraham artfully drives down to ten the number of righteous people needed to save his nephew's life. And there is a less obvious moment when Abraham, having laughed at the thought that his ninety-year-old wife and hundred-yearold self would produce another child, tries to talk God into substituting Ishmael for the promised son. (17.18) Indeed, in his defense of Sodom, Abraham challenges God to His face, asking "Shall not the Judge of all the earth do justly?" Like Adam, Cain, Moses, and David, Abraham does not submit to God without a struggle. But what we see in Jacob at Beth-el is something utterly unlike any such challenge or struggle. Open conflict seems to bring men closer to God, but Jacob holds himself apart. Though he is afraid at Beth-el, he is cool with God, and keeps his wits about him in an effort to protect himself from any fraud on God's part. And Jacob has reason to be cautious. God speaks to him about his seed, while Jacob is running for his life; God makes promises about all the families of the earth, when Jacob doesn't know if he can ever see his own family again. Abraham had also been at Beth-el (12.8), but heading west, toward God's promise. Jacob is there heading east, running away from the mess he has made of his life. The covenant has been announced to him, and Jacob has vowed a vow, but at this point in his life, the covenant with Jacob has not yet come into being. The turning point in Jacob's life does not occur when he is at Beth-el, but seven years, one month, and one day SPRING 19& �later, on the morning after his wedding. What God's appearing to him did not accomplish, Laban's deception of him does. Jacob had been successful at extortion, with his brother, fraud, with his father, and petty legalism, with God. Now, for the first time and all at once, he is a victim of all three at the hands of his uncle. The most surprising thing, to one who has followed the story of Jacob to this point, is that he lets himself be taken advantage of. The moment when he does so is like the moment when Adam and Eve look at each other and make clothes, in that the Biblical text gives us not one word about what fills that moment, or about what causes the next thing that happens to come out of it. The crucial event again takes place only in the imagination of the character, and again can only be discerned by the imagination of the reader. We have to back up a bit, to try to see the context of that moment whole. Jacob begins life with a brother who is older than he, stronger, and preferred by their father. Against these disadvantages are set the facts that Jacob is cleverer than Esau, preferred by their mother, and unhampered in the pursuit of his own advantage by any respect for justice. We first hear him speak when he gives voice to an inspiration that shows the quality of his imagination. (25.31,33) Esau has, from birth, the rights of the first-born, but Jacob has at this moment food, and his brother is very hungry. Why not extort the former by withholding the latter?, thinks the man who will be so artful at drawing up a covenant. If Esau wants food badly enough right now, let him first swear away his birthright forever. Esau agrees, and Jacob discovers that even the weaker can be a successful bully. Jacob now has everything his brother was entitled to by law and custom, and lacks only what his father has the power to give by free choice out of love. His mother Rebekah thinks of a way for him to steal even that, and Jacob is quick-witted enough to carry it off. Just as his brother's hunger offered an opportunity for advantage-taking to an imaginative man, his father's blindness can now be the making of Jacob. He can set out in the world with everything, except trust. There is only one moment in the swindling of his father for which Jacob is unprovided by his mother. (27.20) When Isaac asks how he had found venison so quickly, · Jacob immediately has an answer: the Lord your God helped me. This is a remarkable answer, seizing upon Isaac's trust in God as another weapon against him, along with his blindness, and quietly urging him to get on with the blessing, since so far this Lord is only Isaac's God. The story of Jacob's first theft, of Esau' s birthright, ends with the sentence, "So Esau despised his birthright." (25.34) This means, one presumes, that Esau thought so little of the birthright that it was worth no more to him than a bowl of lentil soup. There is no way to absolve THE ST. JOHN'S REVIEW Jacob from injustice in the exchange, since it is not an Esau free from duress who agrees to it, but one in whom hunger is used for torment by a brother's cruelty. Still, the magnitude of the crime is lessened if the loss was not very important to Esau. But in the case of this second theft the same argument would have to work the opposite way. It is Isaac's caring so much about the blessing in God' s covenant that Jacob uses to strengthen his hold over his blind father. The story of Jacob's second theft could fittingly end, "So Jacob despised his father." It is easy to despise Isaac, or to overlook him altogether. He is present at what is perhaps the most sublime moment in the Bible, but as a child and at the wrong end of a knife. In the trial of Abraham, Isaac in no way acts . In the first episode in which Isaac attempts to act, his efforts are useless. (26.1-12) In a time of famine, Isaac goes to the king of the Philistines, attempting to protect himself by calling his wife his sister. If some Philistine wanted Rebekah, and knew her to be married, he might kill her husband. But Abraham has been there before Isaac, and used the same deception with the same king. Abimelech had been in danger on account of Sarah (Ch.20), and now avoids trouble by protecting Isaac, who gets what he wants in spite of his utter ineffectuality, because of the memory of his father. At this same time God renews the covenant with Isaac, but says He is doing so for Abraham's sake. (26.5,24) A brief series of wanderings and troubles then ends at Beersheba, which Isaac so names to signify that he has found water and a place to rest only by good fortune . (26.32-3) And that is the whole story of Isaac's life, up to the crowning humiliation in his old age at the hands of his wife and his son Jacob . There was a time when I wondered at the expression, God of Abraham, Isaac, and Jacob. Why does the ordinariness and incompetence of Isaac merit a pla<;:e equal to those of his father and son in the naming of God? It was Mr. Littleton who pointed me in the direction of an answer. What does Isaac do when he discovers that he has been fooled and betrayed? He blesses Jacob again, this time deliberately and voluntarily . (28.3-4) If I am correct that there is a moment in the life of each of the patriarchs when he makes the covenant his own, it must be this moment of forgiveness in which Isaac does so. Isaac's one free and effective act in the account we are given of him is an acknowledgement that he cannot act at his own caprice. Esau is his first born and the son he loves, but he will not be the heir of God's promise. To some extent, Isaac undoes Jacob' s crimes by saying yes to their result. Acting now from knowledge and choice, Isaac gives Jacob what Jacob had first stolen from him. But the pardon is not complete, because Esau does not participate in it, and he is the one of those wronged by Jacob. Esau in fact feels that nothing will satisfy him but killing 15 �Jacob, and goes so far as to hope for Isaac's death, to let him feel free to do the killing. (27 .41) Even in his murderous rage, Esau has more respect for his father's feelings than Jacob ever had. Jacob passes through Beth-el and travels to his uncle's home far to the east near what is now Iraq, to escape his brother. His mother thinks it will only take a few days for Esau to forget what Jacob has done to him. (27.44-5) Jacob does not share her optimism, for after a month with his uncle he proposes that he spend another seven years working for him as the price of marrying Laban's daughter Rachel, with whom Jacob is already in love. (29.18) Why does Jacob make this offer? He is certainly a man who knows how to get important things cheaply. He got his brother's birthright for a bowl of soup and his father's blessing for a lie, and he offered God absolutely nothing until God should first give him everything he wanted: a safe and comfortable journey and return home. Now he freely offers seven years of work for a woman he already desires. Can it be that he is simply trying to make certain of outlasting Esau's anger? That can't be the whole reason, since he could be spending that same time as Rachel's husband. I suspect that Jacob is offering those seven years more to himself than to Laban, that he wants a long time to forget about looking out for himself, to submerge himself in work, out of which he might emerge as a better man to begin a life with Rachel. I think this is not as far-fetched an interpretation as it might at first seem. When Jacob first comes into the presence of Rachel and Laban he weeps tears of relief and gratitude (29.11-13), and this is after a journey of five hundred miles or more in which, perhaps for the first time in his life, Jacob must have known deprivation, fear, and uncertainty. Just as Tolstoy's Pierre found no true freedom with the largest private fortune in Russia and the best education available in Europe until he had discovered in prison what a human being is, so too may Jacob's journey have been the beginning of his growing up. But the best evidence that Jacob's servitude was a freely chosen penance is the way he acts when it is over. We have finally returned to Laban's deception of Jacob, and Jacob's un-deception the morning after. We have now to try to enter Jacob's imagination when, having discovered that he married and slept with Leah, he confronts Laban. (29.25-6) "What is this that thou has done unto me? did not I serve with thee for Rachel? wherefore then hast thou beguiled me?" are the questions that come tumbling from Jacob's mouth. Listen to Laban's cool reply, and try to hear in it what Jacob must be hearing. "It is not so done in our place, to give the younger before the first-born." Do you hear it? To a Jacob who was still the shallow and unfeeling thief of his younger days, this would be a lame excuse and nothing more. To a Jacob 16 whose thoughts are full of the wrong he has done his older brother in his own place, Laban's words must be like a knife that stabs him to the heart. Does Laban know what Jacob has done at home? Do his words mean, "I have not injured you but given you exact justice for your crimes"? It is certainly possible that in all that time word might have come to Laban from some traveller or servant or Jacob himself of what Jacob had done. But it does not matter. Even if Laban does not know fully what he is doing, it is done with exquisite accuracy. A marriage with Laban's undesirable daughter has been extorted from Jacob, as Esau's birthright from him; the consumation of that marriage has been achieved by disguise and fraud, as the first giving of Isaac's blessing was achieved; and Jacob has been outwitted in his contract, as he sought to outwit God at Beth-el with codicils and loopholes. In the face of this triple humiliation, our resourceful Jacobaccepts it. He takes it, as we say, like a man. In this moment of passivity and failure Jacob is for the first time as much a. man as his father was. I have called this moment the turning point in Jacob's life. It is not, however, the occasion of a life-long sacrifice, since the customs of the time permit Jacob a second wife, and he marries Rachel only a week later. Nor is it the occasion of a complete change of Jacob's character, since he eventually comforts himself with a lot of petty cheating of Laban. (30.25-32.3) Thirdly, it is not the moment when Jacob appropriates the divine convenant; that is an unmistakable event thirteen years later. The moment when Jacob stands before Laban and hears his mockery is the first time we see Jacob swallow his pride. Jacob has already acknowledged his fault, according to our reading of the story, but he now accepts that the working off of that fault will not be a matter of his own private arrangements with himself, .a nswerable to no one else. When Laban says, in effect, "You can have Rachel too, but I'll take seven more years," we hear only, "And Jacob did so." (29.28) Like his father and grandfather before him, Jacob has begun to accept that it is not he who directs his own life, and to be wiling to live on terms other than his own. Jacob sets out for home after spending twenty years with Laban, seven for Leah, as it turned out, seven more for Rachel, and six more to earn livestock and servants. (31.41) Near the River Jordan he camps at Peniel, having sent half his followers to another encampment, while he waits to meet Esau, and perhaps to be killed. The second thing Jacob does at Peniel is to send a succession of messengers carrying gifts to Esau; the first and third things he does there are the interesting ones. Taken together, they replace the covenant at Beth-el, of Jacob's eastward journey. This time it is Jacob who initiates the encounter, and again we will listen to all his words, as he prays SPRING 1986 �(32.10-13): "O God of my father Abraham, and God of my father Isaac, 0 Lord, who saidst unto me: Return unto thy country, and to thy kindred, and I will do thee good; I am not worthy of all the mercies, and of all the truth, which Thou hast shown unto Thy servant; for with my staff I passed over this Jordan; and now I am become two camps. Deliver me, I pray Thee, from the hand of my brother, from the hand of Esau; for I fear him lest he come and smite me, the mother with the children. And Thou saidst: I will surely do thee good, and make thy seed as the sand of the sea, which cannot be numbered for multitude. " Jacob's prayer at Peniel is certainly self-regarding, selfserving, and self-seeking. The important thing about it is that it is a prayer. Jacob reminds God of His promise, but does not claim to have made any exchange for it or promise to make an_y return for it. He speaks now as one who has nothing to offer but his need. When Jacob says he is unworthy of the mercy and truth he has received, he is using a way of speaking fairly common in the Bible, ·the Oriental courtesy of self-abasement. It is not a way of speaking we have ever heard from Jacob, though, and in this case I think he means exactly what he says. There is much good in his life, two wives, eleven children, and great wealth, and it is all sheer blessing, and not his own doing. There is also more than enough bad in his life, enough to cost him his life and perhaps the massacre of all his family and dependents, and that is his doing and just what he deserves. There is none of the spelling out of obligations of the covenant at Beth-el, but only a giving voice to the conviction that he himself cannot provide himself the minimum conditions of carrying on a life. Having sent his prayer to God, and presents to his brother, Jacob that night sends away his family and everyone and everything else with him, and spends the night alone. (32.23-5) But when Jacob isolates himself, he is not alone. We are told, abruptly and mysteriously, "there wrestled a man with him until the breaking of the day.'' Abraham struggled with God face-to-face over Sodom and over Ishmael, and something similar occurs with Adam, Cain, Moses, and David. It is in the strange and beautiful episode of Jacob's wrestling that the meaning of all such struggles becomes accessible. I am not talking about symbolism, but about how and to what end the wrestling match takes place. Let us first simply look at what happens in that struggle at Peniel. We know that the wrestling match goes on all night, that Jacob continues despite a serious injury, either a sprained thigh muscle or a dislocated hip, that his adversary is called a man in the narration but is taken by Jacob himself to be God, and that Jacob is striving not to throw or pin this adversary or in any way get the bet- THE ST. JOHN'S REVIEW ter of Him, but only to remain in His embrace. Jacob fights in order that he not be let go, except with a blessing. If the wrestling match is taken together with Jacob's prayer, it provides further evidence that Jacob's honest opinion is that all the good in his life comes only from God, and that if he stands on his own merit, he deserves to be killed by his brother. And this finally is the full meaning of the Biblical covenant: It is the bargain one can make only out of utter clarity that he has nothing to bargain with. The fierceness of Jacob's struggle reflects the knowledge he has gained of the desperation of a life without God. Anything he could hope for without God, he has learned that he doesn't want. And this moment is Jacob's full and final appropriation of the covenant, his . explicit acknowledgement of his createdness, his essential and inescapable dependence upon a creator. The meaning of the moment is recognized by the change of Jacob's name to Israel, he who strives with God. And Jacob becomes Israel also in the sense that none of his progeny will be excluded from the covenant: he is the blessed nation promised to his grandfather and father. In this way, Jacob's wrestling is the completion of creation: the separation of light from darkness, land from water, family from family, and brother from brother comes to an end after thirty-two chapters of Genesis. If Jacob's wrestling is the culmination of the history of creation, it must somehow address the troublesome sentence with which we began: "And the Lord saw that . .. every imagination of the thoughts of man's heart was only evil continually." That sentence was interpreted to mean that the instrument of human freedom has an inherent inertia toward making its worst suspicions come true by actions intended to guard against them. The history of mankind before the Flood was summarized as a motion from the self-tormenting murderer Cain to the self-congratulating mass murderer Lamech. The three Hebrew patriarchs do not have purified hearts; what they have are ordeals which lead to self-knowledge as created beings, and trust in a· divine promise of prosperity and a rest from troubles, but not for themselves. It is natural for all human beings to want something for themselves, in the present. Esau asks his father if he does not have a little blessing left over for him (27.36); Lot, escaping from Sodom, asks God if he can't stay in a city, just a little one (19.20); and Abraham meets the first explicit account of the covenant with a request that a little something be done for Ishmael (17.18). But none of the patriarchs is given anything out of the ordinary in his own lifetime, except an invitation to trust God. The history of mankind after the Flood, up to the coming into being of the nation Israel, is a return to self-torment, but relieved by a promise of peace for future generations. The covenant does not transform the conditions of human life, 17 �but it presents itself as a step toward such a transformation. Jacob's life after he becomes Israel is still full of trouble. He has a life, because Esau does forgive him (33.4), but he himself seems to have learned nothing from his conflict with his brother. Like his father before him, Jacob openly loves one of his sons most, and brings about hatred in his house. (37.1-4) As a result he loses that son, and then the son second dearest to him. When he is reunited with them in Egypt, he is brought before the Pharaoh, who asks him, "How many are the days of the years of thy life?" Jacob replies, "The days of the years of my sojournings are a hundred and thirty years; few and evil have been the days of the years of my life, and they have not attained unto the days of the years of the life of my fathers in the days of their sojournings." (47.8-9) Why does Jacob talk this way? Is he a bitter man at the end of his life? Does he feel that God's promise has been a deception? His words in the following chapter make it clear that this is not his attitude toward his life. When Jacob is on his deathbed, he hugs and kisses his grandchildren and says to Joseph, "I had not thought to see thy face; and lo, God hath let me see thy children also." (48.11) Jacob does not lack gratitude. Pharaoh seems to look at him though as an aged man specially favored by fortune. I think what Jacob is saying to him is: I am no one special. I am an ordinary man. Others have lived longer. If I am distinguished in any way it is in the same way as my father and grandfather, in not having had a life at all in the settled sense, but a never-ending wandering. Did Jacob receive the things he insisted upon at Bethel? He certainly did not starve or freeze to death, he got back to Beersheba, and he was not attacked. In deeper ways, though, he got both more and less than he asked for. Safety is too weak a word to describe what Jacob gained when he looked on Esau's forgiving face and said it was like seeing the face of God. (33.10) On the other hand, home is too strong a word for a place Jacob had to leave in his old age, not only for food but for release from the anxiety about his children with which his last years were troubled; and I doubt that Jacob would have been much comforted to know that the Egyptians gave him a royal funeral. (50.2-3) For Jacob, home and security remained only promises for a distant generation, while the joys of his life always came unexpectedly, with the intensity of gifts that one cannot take for granted. And what became of the imagination of Jacob's youth, in which he set himself against everyone and everything else in the world? It seems to have been not overcome or crushed, but fed by the knowledge he gained from experience and promises he was given by God. The Jacob who warns Pharaoh against envying him is not a man 18 in whom imagination has died. It is in his imagination that Jacob judges his life as one that has never come to rest. That is a long way, though, from the time when that same imagination sought to find its rest by defeating and outwitting everyone else. Jacob's imagination looks at the past through his history and at the future through the divine convenant, and finds an in-between, human kind of rest in the acceptance of troubles as worth enduring. The Law of Moses incorporates Jacob's understanding of his life. The Jew is commanded to recite, every year when the harvest comes, the words "a wandering Aramean was my father." (Deuteronomy 26.5) A land flowing with milk and honey is never to be taken for granted, but to be looked on as achieved through a history of struggle. But is the land the completion of the promise made to Abraham, Isaac, and Jacob? Why is the promised land not a new Eden, and just as likely to be lost? Is memory strong enough to outweigh the corrupting tendency of imagination simply by evoking the history and the covenant? I will argue that the life of the wandering Aramean, the Syrian nomad, is transposed from the outer to the inner human realm by means of the Law itself. I once listened to a learned man explain that the Jewish Law contained nothing spiritual, that it concerned itself exclusively with external possessions and outward acts. This man went so far as to claim that the Hebrew word translated "covet" in the tenth commandment means instead ''obtain by magic,'' but I cannot recall that he had anything at all to say about the command in Leviticus to love your neighbor as yourself. (19.18,33-4) His purpose was to show the inferiority of Judaism to Christianity, but I have also heard more than one rabbi explain that the superiority of Judaism consists precisely in its concentration on the outer things under a man's control, rather than on the inner and involuntary things. It seems to me, though, that the regulation of outward life in the Jewish Law is always for the sake of its significance for inward life. The keynote of the whole Law is sounded in the command to the hearer to talk about the law all the time, whenever one is free from necessary business. (Deuteronomy 6.6-7) It is not a Law to be memorized, but one to be interpreted. It does not bring the life of moral struggle to an end, but stimulates that life. Most of what the Law has to give is not on its surface, but evident only to the imagination, through the activity of interpretation. The ultimate Biblical response to the corruption of human life by imagination is the giving of the Law, not to replace the imagination but to feed it with strong meat. Now some of you may be thinking, that sounds good, and there are some good things in the Law of Moses, but isn't much of the Law unenlightened and even barbaric? For example, doesn't that Law approve of slavery? The SPRING 1986 �Law does not forbid slavery, and certainly recognizes its existence, but as far as I can determine, every mention of slavery in the five books of Moses deals with the freeing of slaves. The most extensive ordinances deal with Jewish slaves, who must be set free after six years of work (Ex. 21, Deut. 15), liberally furnished with livestock, grain, and wine (D 15.13-14). Most remarkable is that the slave owner is commanded not only to free the slave, but not to do so grudgingly. (D 15.18) Further, any slave, Jewish or otherwise, is exempt from the famous law of retaliation, an eye for an eye, a tooth for a tooth. This is true in one way in the Code of Hammurabi, a Babylonian king contemporary with Abraham: there the eye or tooth of a slave is worth less than that of a man, but requires a payment of money to the slave's owner. (Laws 196-201) Presumably the slave's owner is free to knock out eyes and teeth as long as the slave has eyes and teeth to knock out. But in the Law of Moses, the slave's eye or tooth is worth his freedom: a slave owner who strikes his slave must set him free for the eye's sake, or for the tooth's ·sake. (E 21.26-7) And every fiftieth year is a jubilee year in which all slaves must be set free. (Lev. 25.54) Slavery in the Bible, then, is a limited institution, with laws made to mitigate its harshness. But we have yet to consider the most interesting of those limitations, the law concerning runaway slaves. Again, for the sake of contrast, we mention the Code of Hammurabi, under which anyone harboring a runaway slave was to be killed. (Law 16) In our enlightened times, this was not a capital offense, but still the United States Constitution required that anyone held to forced labor in one state had to be returned from any other state. (Art. 4, Sec. 2) And in the nineteenth century, Congress passed a law under which a federal judge was paid twice as much when he found an accused person to be a runaway slave as when he let him go. The law preventing slaves from running away follows simply from the logic of the institution of slavery itself. If someone can choose with his feet not to be a slave, and the law does not compel him to return, he is no slave in the first place. A law permitting a slave to escape his servitude is bad law and bad logic. Listen to the Biblical law on the subject: "Thou shalt not deliver unto his master a bondsman that is escaped from his master unto thee; he shall dwell with thee, in the midst of thee, in the place which he shall choose within one of thy gates, where it li.keth him best; thou shalt not wrong him." (D 23.16-17) Any slave who doesn't want to be a slave, and who can run away, is no longer a slave, but is protected by the law. Is not the very institution of slavery undermined by this little restriction? Why then does the Law not explicitly forbid slavery? What is the attitude toward slavery implicit in the Law? Think about it, as the sixth chapter of Deuteronomy requires. THE ST. JOHN'S REVIEW The logic of slavery, that leads to the duty of returning a runaway slave, is the same as the logic of war, that leads to conscription. If war is right and the nation is at war, individuals cannot be permitted to refrain from fighting by their own choice. If we are at all on the right track in understanding the Law, then, we should expect to find military conscription absent or even forbidden, and this is just what we do find. There is one law in Deuteronomy that forbids a man to go into battle during his first year of marriage, and commands him to stay home and make his wife happy. (24.6) Mr. O'Grady used to comment that this law has no provision for cases when there are not enough soldiers left. It is unconditional in choosing the happiness of a young bride as a higher end than victory in battle. Let us listen to the general law governing the conduct of battle (D 20.5-8): "The officers shall speak unto the people, saying: 'What man is there that hath built a new house and hath not dedicated it? let him go and return to his house, lest he die in the battle, and another man dedicate it. And what man is there that hath planted a vineyard, and hath not used the fruit thereof? let him go and return unto his house, lest he die in the battle, and another man use the fruit thereof. And what man is there that hath betrothed a wife, and hath not taken her? let him go and return unto his house, lest he die in battle, and another man take her.' And the officers shall speak further unto the people, and they shall say: ' What man is there that is fearful and faint-hearted? let him go and return unto his house, lest his brethren's heart melt as his heart."' Not only a new wife, but also a fiancee, a new house, and a new vineyard have higher claims on a man than does any battle, but again there is one further restriction that seems to undermine the whole institution of war. Under the Jewish Law, no one can be a soldier if he doesn't want to. The Bible is full of bloody warfare, and even glorifies it, and in certain special cases forbids humane treatment of the enemy. (D.20.16-18) These things can be defended, but are still disturbing to most of us. But anyone who was thus disturbed in his heart in Biblical times would, under the Law, be automatically exempt from fighting. Under such a law, the Vietnam war probably could not have been fought, but there is no such calculation in the Bible. Does the Bible teach the rightness of war? In the third place, let us consider usury, the lending of money at interest. The Bible in no way restricts this practice, so long as the borrower is not a Jew or a resident alien. (D 15.3, 6; 23.21) From a fellow Jew, no form of interest in goods or money in any amount may ever be taken. (D 23.20) Usury is permissible in foreign commerce, but never to be part of the life of one's own community. Within the community one may lend, and accept a pledge as collateral for repayment, but with three restrictions: a mill or millstone may never be taken as a 19 �pledge, since without it a man may not tum his crop into bread (D 24.6); if the pledge is a garment, the lender must return it to the borrower every night, since he may have no other covering to sleep under (D 24.12-13; E 22.25-6); and under no circumstances is the lender to go into the borrower's house to choose the article to be taken in pledge, but he must wait outside and take what he is given (D 24.10-11). The necessity to borrow from one's neighbor must, under the Law, have no cost in money or goods, in hardships the lender might be unable to foresee, or even in embarrassment. But the most remarkable provision for the borrower is a law requiring that all debts be cancelled every seven years. (D 15.1-11) Here is what the Law says to the lender: "If there be among you a needy man, one of thy brethren, within any of thy gates, in thy land which the Lord thy God giveth thee, thou shalt not harden thy heart, nor shut thy hand from thy needy brother; but thou shalt surely open thy hand unto him, and shalt surely lend him sufficient for his need in that which he wanteth. Beware that there be not a base thought in thy heart, saying: 'The seventh year, the year of release, is at hand; ' and thine eye be evil against thy needy brother, and thou give him nought; ... Thou shalt surely give him, and thy heart shall not be grieved when thou givest unto him." This law is not only for the protection of the poor; it seems even more strongly concerned with protecting the rich man against his own feelings. Perhaps one might say of all three, slavery, war, and usury, that they are all right, so long as one does not think that they are all right. A fourth institution provided for in Deuteronomy is monarchy. (17.14-20) For about a thousand years from the time of the patriarchs, Israel has no king, but the Law foresees a desire for one when the people reach the promised land. The Law authorizes a king, so long as he does not multiply for himself horses, wives, or gold and silver, if he copies out the Torah for himself and reads it all his life. He is to be a king without pride over his subjects, regarding himself primarily as a subject of God. Does the Law sanction monarchy, or make it impossible? The last institution I will ask you to consider is private property. You will not be surprised to hear that in the Bible it is neither forbidden nor simply approved, but is a qualified legal right. A tenth of every year's income must be set aside, in part for celebration, and in part for the use of priests, strangers, widows, and orphans. (D 14.22-29) But the amount from which the tenth is taken is not everything that grows in a man's fields . When one harvests grain, olives, or grapes, one may not glean his fields. (D 24.19-22) Something must always be left behind for the needy. And at any time of year, anyone may enter the vineyard of another and eat his fill, so long as he carries nothing away, and may take away from another man's cornfield everything he can pluck with his hand. 20 (23.25-6) We must conclude that the produce of a man's own land belongs to him, as long as he doesn't take all of it or use all that he takes, and that it belongs also to everyone else, as long as they do not abuse that right. At this point, I think it is safe to conclude that the effect of the Jewish Law is not to settle the questions of the moral life, but to unsettle them. This does not mean that the Law is vague about how people should act, or leaves loopholes for the clever to escape its requirements, or even, God forbid, fosters a belief that morality is only relative. On the contrary, the Law is so clear about where obligations begin and end that it reveals an unmistakable two-sideness in anything that purports to be the principle or end of human life. Some discussions of morals and politics are doctrinaire, deducing actions rigidly from formal principles. The Bible exhibits a treatment of human things of another kind, a kind which one finds also in Plato's dialogues and Aristotle's Ethics. This non-formal approach requires the exercise of judgment, the drawing of lines, and the balancing of conflicting goods. It is the opposite of irrational, but it does not restrict itself to conclusions accessible in the understanding by logic; its proper instrument is the imagination. When we hear in a political or moral discussion, as we do every day, that some conclusion follows because otherwise, "where do you draw the line?" the speaker is doing no more than confess the inadequacy of his imagination to the topic before him. The formalistic approach to human things is always an evasion of everything that matters to us. On the contrary, the Law of Moses is full of everything human, including war, slavery, and every gradation of political and economic oppression. Its purpose is not to wipe out these evils-that could only be accomplished by wiping out us, their authors-but to provide ammunition for a never-ending struggle against them. Jacob's wanderings in the Syrian desert were for him and for his descendants the primary characteristic of his life. It was the promise of rest in the divine covenant that made such a life acceptable. But the covenant is not a literal promise of earthly peace and prosperity. Moses knew this when he said both "there will be no poor amo'ng you . . . if only you will obey the voice of the Lord your God, '' and also "the poor will never cease out of the land." (D 15.4-5,11) The purpose of the Law, as of the covenant, is to prevent a coming to rest in the wrong place. This is not to say that the Law cannot be obeyed, but that there is no such thing as a completion of such obedience. The more one succeeds in obeying it, the more this Law opens the imagination to the more that still needs to be done. This is not an infinite process that makes all striving futile, but one that makes striving ever more effective. Such striving toward an end reflects the strife, in any thoughtful human being, of the imagination with itself. SPRING 1986 � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Description An account of the resource Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. Items include audio and video recordings and typescripts.<br /><br />For more information, and a schedule of upcoming lectures, please visit the <strong><a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a></strong>.  <br /><br />Click on <strong><a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&amp;sort_field=Dublin+Core%2CDate&amp;sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a></strong> to view and sort all items in the collection.<br /><br />A growing number of lecture recordings are also available on the St. John's College (Annapolis) Lectures podcast. Visit <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a> or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe. Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Title A name given to the resource St. John's College Formal Lecture Series—Annapolis Identifier An unambiguous reference to the resource within a given context formallectureseriesannapolis Text A resource consisting primarily of words for reading. Examples include books, letters, dissertations, poems, newspapers, articles, archives of mailing lists. Note that facsimiles or images of texts are still of the genre Text. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data paper Page numeration Number of pages in the original item. 10 pages Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource God of Abraham, Isaac, and Jacob Description An account of the resource Typescript of a lecture delivered on October 24, 1986 by Joe Sachs as part of the Formal Lecture Series. Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Date A point or period of time associated with an event in the lifecycle of the resource 1986-10-24 Rights Information about rights held in and over the resource St. John's College has been given permission to make this item available online. Type The nature or genre of the resource text Format The file format, physical medium, or dimensions of the resource pdf Relation A related resource <a title="Sound recording" href="http://digitalarchives.sjc.edu/items/show/3717">Sound recording</a> Language A language of the resource English Identifier An unambiguous reference to the resource within a given context lec Sachs 1986-10 Creator An entity primarily responsible for making the resource Sachs, Joe, 1946- Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/6f7633ae70bc649f910df4dd1af3414b.mp3 388f372d6746616aff28db958d68ca2d Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Description An account of the resource Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. Items include audio and video recordings and typescripts.<br /><br />For more information, and a schedule of upcoming lectures, please visit the <strong><a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a></strong>.  <br /><br />Click on <strong><a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&amp;sort_field=Dublin+Core%2CDate&amp;sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a></strong> to view and sort all items in the collection.<br /><br />A growing number of lecture recordings are also available on the St. John's College (Annapolis) Lectures podcast. Visit <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a> or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe. Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Title A name given to the resource St. John's College Formal Lecture Series—Annapolis Identifier An unambiguous reference to the resource within a given context formallectureseriesannapolis Sound A resource primarily intended to be heard. Examples include a music playback file format, an audio compact disc, and recorded speech or sounds. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data audiotape (Tape 519) Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 01:04:08 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource God of Abraham, Isaac, and Jacob Description An account of the resource Audio recording of a lecture delivered on October 24, 1986 by Joe Sachs as part of the Formal Lecture Series. Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Date A point or period of time associated with an event in the lifecycle of the resource 1986-10-24 Rights Information about rights held in and over the resource St. John's College has been given permission to make this item available online. Type The nature or genre of the resource sound Format The file format, physical medium, or dimensions of the resource mp3 Relation A related resource <a title="Typescript" href="http://digitalarchives.sjc.edu/items/show/3718">Typescript</a> Language A language of the resource English Identifier An unambiguous reference to the resource within a given context lec Sachs 1986-10-24 Creator An entity primarily responsible for making the resource Sachs, Joe, 1946- Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/67f8f6000ddbefff7561e6cfd3d6cf23.pdf 54879a3983a90785acab44f734fccb9b PDF Text Text ST. JoHN's CoLLEGE LECrURE SERIES- rg82 JoE SAcHs a lecture given in Annapolis September 17, 1982 �The Parable of Don Quixote D n the twenty-fifth chapter of the first part of Don Quixote, the for­ tunes and spirits of the book's hero are at their lowest. He has been bruised and laughed at, and has lost part of an ear and most of his teeth. He has mistaken an inn for a castle, whores for maidens, and windmills and sheep for enemies. His intervention in the affairs of others has led a servant boy to be beaten worse than before, and has set loose on Spain an entire column of convicts who have made him and Sancho the first of their new victims. Even the simple-hearted Sancho has lost his trust in his master. " 'God alive, Sir Knight of the Mournful Countenance,' said San­ cho, 'I cannot bear in patience some of the things that your Grace says! Listening to you, I come to think that all you have told me about deeds of chivalry . . . is but wind and lies, all buggery or humbuggery, or whatever you choose to call it. When anyone hears your Grace .. ., what is he to think except that such a one is out of his mind?' " Shortly Don Quixote will be left alone, sunk in gloom, in the Sierra Moreno, the Dark Mountains. He had entered that lonely place partly out of fear of the police, a fear which could influence him because of his disappointment over the behavior of those he thought he was helping. But even at such a time, Don Quixote has an answer for his squire. " 'Look, Sancho,' said Don Quixote, 'by that same God I swear that you have less sense than any squire in the world ever had. How is it possi­ ble for you to have accompanied me all this time without coming to perceive that all the things that have to do with knights-errant appear to be mad, foolish, and chimerical, and everything happens backwards?' " It is Don Quixote's standard evasion when things go wrong or he is proved wrong: we are enchanted. Our senses are not to be trusted, and things are not as they seem. In this case he is driven to claim that everything is ex­ actly the opposite of the way it seems, and he is right. The remainder of Part one, after Don Quixote enters "the Sierra Moreno, is the long unfolding of a series of happy endings of stories yet to be made known to us, and which come to pass without any effort on Don Quixote's part. His last action in Part one is the freeing of the convicts in Chapter twenty-two, with thirty chapters remaining. Yet none of the good that is done in those thirty chapters could have happened were it not for the earlier deeds of Don Quixote. And the happy endings do not come St. Johns Lecture Series 1 �about by some comic reversal of Don Quixote's intentions. They grow out of his deeds directly in the spirit of those deeds, by a Quixotic contagion. Finally, it is not the case that Don Quixote's actions are justified only by unforeseen consequences, but each of his acts is, for those who have eyes to see it, good in itself, and exactly the opposite of the way it seems. Pairs of contrasting opposites in Don Quixote are often remarked. The book combines the conventions of romantic fiction with all the ugly, smelly facts of real life. Of the two main characters, one is tall, thin, energetic, and spiritual, the other short, fat, lazy, and corporeal. The main character acts like a lunatic but speaks like the wisest of men. But the most important contrast in the book is less often noticed. It is that bet­ ween the story the narrator understands himself to be telling and th� one he tells, and it points the way to the underlying distinction on which the book is built: the distinction between fact and truth. Cervantes puts between himself and his story a historian who comes from a nation known for lying (1.9,11.3), a translator, and perhaps one or more other people; it is the sort of matter about which Cervantes is not a very careful bookkeeper. But there is one consistent voice which presents to us all the episodes in the book, including those which precede the beginning of Cid Hamete Benengeli's manuscript and those for which, as Sancho notes with awe, there was no human witness. The narrator through whom we know all that we know of Don Quixote tells us that when his character decided to become a knight he looked around for a make-believe beloved just as he looked for a sword and helmet; but the same narrator gives a careful reader all the information he needs to see that Alonso Quixano has been secretly and hopelessly in love with Al­ donza Lorenzo for twelve years (1.1,1.25). The narrator mocks Don Quix­ ote's speech about the Golden Age as nonsense which only occurs to him by an association with acorns (1.11), but the goatherds to whom it is ad­ dressed are moved by Don Quixote's eloquent respect for their way of life, and repay him with all the gifts in their power. When Don Quixote defends Marcela (1.14), the beautiful girl who chooses not to marry anyone, the narrator tells us that he is playing at defending a damsel in distress, but anyone who listens to what he says will hear him give the reason for which he became Don Quixote: that beauty demands a response from us, an effort not to possess it but to be worthy of it. Cervantes writes in the guise of someone who nf'ver sees the things that matter amid events he describes in meticulous detail. In belittling his hero, Cerv antes belittles himself, and it is lett to u� to discover whether we are cut to the measure of that same littleness. It is a simple rhetorical trick that Cervantes plays, gently manipulating his readers by appealing to our vanity, our pleasure in feeling superior to the stupid narrator by seeing things to which his coarse sight does not penetrate. A most generous author, we are dealing with, who allows us for the most part to indulge in superior laughter at the crazy knight and the gullible squire, and still to have someone to look down on when we see those characters more deeply and truly. The narrator's misunderstandings begin practically on the first page of 2 The Parable of Don Quixote �this book, when he tells us that the gentieman about whom he is writing has gone crazy. It is certainly the most widely held opinion among those who meet Don Quixote, but there are three exceptions. In Part two, three sensible people come to know him and come to other conclusions about his sanity. Don Diego de Miranda, the gentleman in the green greatcoat, decides that Don Quixote is "a crazy sane man and an insane one on the verge of sanity." (11.17) And later, at an inn, which he takes for an inn, when he is on his way to Saragossa, Don Quixote meets Don Juan and Don Jeronimo, who are finally unable "to make up their minds as to just where they were to place him in the vague realm between sound sense and madness." (II .59) It is no accident that this pair of judgments is made available to us, for together they mean that the categories mad and sane break down when applied to Don Quixote. He must be said to belong to both, or to neither. He is unlike other men, but the distinction between the mad and the sane does not illuminate that difference. The truly illuminating distinction is given to us by Don Quixote himself, whose judgment is always the most trustworthy in the book. When the gentleman in green is worrying about what to make of his com­ panion, Don Quixote guesses his thoughts, and breaks in on them in a kindly way. He forgives his friend for thinking him foolish and mad, and does his best to explain why he does what he does. "Even as it is easier for the prodigal to become a generous man than it is for the miser, so is it easier for the foolhardy to become truly brave than it is for the coward to attain valor. And in this matter of adventures, you may believe me, Senor Don Diego, it is better to lose by a card too many than a card too few." Prodigality, we shall see as we go on, is one of the most important words in the book. When Don Quixote appears ridiculous, which is most of the time, it is not for lack of wits but for his deliberate choice to be pro­ digal. With what is he prodigal? With money, of course, but with all the things that constitute himself. When, in his fiftieth year, Alonzo Quixano became Don Quixote, it was not because his brain dried up but because he judged his safe and settled life to be a miserly one, a dried-up life. From that time on he ceased to hoard his capacities to act, to befriend, and to benefit. He gives his reason for doing so again and again in a single word, the most important word in the book: gratitude. As he says to one of the shepherdesses in Part two, "My profession is nothing other than showing gratitude." (11.58) Gratitude is the reciprocal response to grace. In his discourse on arms and letters (1. 37), Don Quixote explains that the highest achievement of human letters and learning is distributive justice. He has chosen instead the higher calling of the soldier, which aims at bestowing the grace of peace. The middle-aged Alonzo Quixano decided to stop liv­ ing a life which received grace but returned none. In Part two, Don Quixote asserts that the greatest sin is not pride but ingratitude. This has already been shown in Part one. The whole of Don Quixote is a parable, and its first part contains two parables-within-a­ parable. The captive's story is constructed as the parable of the prodigal father; ingratitude is revealed in the parable of the curious impertinent. While Don Quixote sleeps in the inn to which he is taken from the Sierra St. Johns Lecture Series 3 �Moreno, his companions read aloud a story about a man who is curious about the wrong things. His name is Anselmo. Let us listen to him describe his complaint to his friend Lotario (1.33). "You may think, my friend, that in return for the favors God has shown me by giving me such parents as mine and bestowing upon me with no stinting hand what are commonly known as the gifts of nature as well as those of fortune, I should never be able to thank Him enough, not to speak of what He has done for me by giving me you as a friend and Camila for my wife . . . Yet with all these advantages . . . I lead the most empty and fretful existence of any man in this universe . . . The thing that so tortures me is the desire to know whether or not my wife Camila is as good and perfect as I think she is, for this is a truth that I cannot accept until the quality of her virtue is prov.ed to me in the same manner that fire brings out the purity of gold. For it is my opinion, my friend, that a woman is virtuous only in the degree to which she is tempted and resists temptation. " Can you hear why he is called Anselmo? I will remind you of the words of Saint Anselm in the first chapter of the Proslogium. "Lord, thou art my God, and thou art my Lord, and never have I seen thee. It is thou that hast made me, and hast made me anew, and hast bestowed upon me all the blessings I enjoy; and yet I do not know thee. Finally, I was created to see thee, and not yet have I done that for which I was made. "0 wretched lot of man, when he hath lost that for which he was made!. . . We suffer want in unhappiness, and feel a miserable longing, and alas!We remain empty . . . I wished to smile in the joy of my mind, and I am compelled to frown by the sorrow of my heart. Gladness was hoped for, and lol a source of frequent sighs!" Anselm puts an end to the torment in his soul by finding a proof of the existence of God, but Anselmo, who also cannot enjoy blessings which rest only on faith, when he seeks proof of Camila's love, destroys his own life and those of everyone around him. Anselmo insists that Lotario try to seduce Camila, and try again and again while Anselmo keeps himself absent from her. Since no human quality is infinite, and since every time Camila resists temptation Anselmo causes it to be increased, and since he himself is never present to his wife to help her be his wife, Anselmo finally achieves the only result that can come from his actions. He makes Camila unfaithful. He does not prove her unfaithful, because she was not so until he made her so. A wife's love is not a neutral fact to be ascertained by experiment, but a living thing sustained in part by the husband's faith in it. When Anselmo decides that .his faith is an insufficient foundation for his marriage, he loses it, because there is no foundation other than faith for a marriage to rest on. And it is important (Cervantes underlines the importance by breaking the story off) that the marriage continues for a while on a foundation of deceit. The deception does not last because Camila's maid joins in it, and the chain of corruption inevitably lengthens until it pulls all of them down. Anselmo's curiosity is impertinent or misplaced because a wife's love The Parable of Don Quixote �calls not for curiosity but for gratitude. In his inability to appreciate the wife he has, Anselmo removes himself from her, so that she has no hus­ band and he has no wife. The subsequent infidelity and deaths only turn into fact the truth that was already present in Anselmo's lack of faith. Don Quixote's village priest pronounces the story implausible (1.35), proving, for one of the innumerable times in the book, that he does not know how to read a story. Every marriage is founded on faith alone, but it is the unlikely and ima�inary story of Anselmo that reveals that truth. And once one has gotten hold of the truth behind the implausible facts, one sees that it is a truth about more than just marriages. At that point Cervantes' story comes into its own as a parable. The story of the curious impertinent illuminates the larger story of Don Quixote, but the characters in the one do not stand for characters in the other. That is not the nature of a parable. The myths Socrates tells in Plato's dialogues are intended to be interpreted, to be destroyed as stories and transformed into their philosophical content. They have no use but to invite interpretation. The allegory Dante tells in the Divine Comedy is always speaking of two or more things at once. The principal story holds together as itself, but its principal meaning depends upon the recognition of allegorical counterparts. A parable differs from both. Its content is not intended to refer to anything but itself. It is told because someone who understands it will be in a position to think about some other subject which is the teller's chief concern, and because anyone who cannot understand it would not be able to get anything out of any direct talk about that matter of chief concern. The parable draws on things close to one's experience, to prepare the imagination to deal with things less familiar. The parable of the curious impertinent reveals that there are things in the world which are invisible except to the eyes of faith, things which gen­ uinely exist but can be destroyed if they are not believed in. In an impor­ tant exchange immediately preceding the reading of the story of the curious impertinent, the priest declares that there never were knights­ errant in the world. The innkeeper replies that he knows there are none now, but that they surely lived in those days. Sancho worries that one of them might be right, but makes up his mind to wait and see. If there is a knight errant in the world, only Sancho will have his eyes open to see him. Don Quixote's first encounter, the first time he leaves home, is with two whores at an inn (1. 2). He sees gracious ladies, and addresses them with courtesy. Their first response is coarse and cruel laughter. If. the scene ended like that, we would have to agree with the narrator that Don Quixote suffers from delusions and sees not what is in front of him but what he wants to see. But something happens while no one is looking, and when we return from the stables with the innkeeper, we find the young women treating Don Quixote with kindness and bearing themselves with modesty. They have become the gracious ladies that no one, including themselves, except Don Quixote, saw them as. It is a very small and very important event, even if it has no lasting effect on the women's lives. For a short time at least, they were not the sluts they had thought themselves to St. ]ohn 's Lecture Series 5 �be, but free beings, capable of accepting and returning courtesy. Their graciousness was nowhere to be seen until Don Quixote's faith and their works brought it into being, but he saw it while it was still nothing but possibility. Do you see the com1ection with Anselmo? He doubted the virtue his wife had, and thereby destroyed it. Don Quixote believes in the virtues the two women do not have, and thereby brings them into being. Anselmo withdraws himself from his wife. Don Quixote involves himself with total strangers. Anselmo does not know how to love the woman he is in love with. Don Quixote may have the secret of loving everyone in the world. But Don Quixote's subsequent acts of charity, with the boy Andres and with the convicts, seem to be not mad but naive, a mockery of the very notion of doing good. When he prevents Andres from being beaten, and leaves his master on his honor to pay the boy his just wages, the result is the worst beating Andres has had in his life, and the loss of his job. When Andres tells him what has happened, and curses him for it, Don Quixote is deeply troubled. When he frees the convicts, it is Don Quixote who is beaten, by the very men he tried to help, and robbed of everything he car­ ries and wears. It is that episode which sends him into the mountains, where, for a time, he is not himself. For the narrator, there is nothing troubling about these results. They merely confirm what every grown-up in the world except Don Quixote already knows. For Don Quixote they are severe tests of his faith in people, but tests which he survives, and rightly. Don Quixote has benefitted Andres by forcing an end to a situation in which the boy regarded himself as someone who could be beaten at the whim of another, so long as the beating was not too bad. Like the two whores, Andres had taken himself at the valuation of others. They started to be taken for ladies. Andres is angry at being forced to be a man. We see him last on the road to Seville. We do not know what will become of him there, but we know that it will be what he makes of himself. Andres had accepted and made the best of a slavish role into which he was born and in which he was remaining by inertia. From Don Quixote he suffered the painful gift of his freedom With the convicts, Don Quixote worries that some might be innocent, convicted only because they were poor and without friends. Others he sees to be guilty, but of no very serious crimes. But his motive for freeing them does not depend on the facts about them. Don Quixote is outraged that, whatever they have done, the king should make slaves of them. Don Quixote believes in punishment; he spends much of the book dealing it out. But he does not believe in punishment that precludes forgiveness. The king's justice rests on the ultimate in impertinent curiosity: on the question whether a man shall be allowed to continue to be a man or shall be created a slave. The convicts had not used their freedom well, but they had it not on human sufferance but by God's grace. Don Quixote does not find a solution to the problem of human ingratitude, but he does prevent its multiplication, and hence rights a wrong. 6 The Parable of Don Quixote �The two craziest of Don Quixote's deeds in Part one seem not ex­ plicable as acts of faith or charity, because they do not involve other peo­ ple. They are his attacks on the windmills and the sheep. There is a clue to the meaning of these episodes in Part two, when Don Quixote tells San­ cho, "In confronting giants, it is the sin of pride that we slay. " (11. 8) I suspect that, in attacking both the windmills and the sheep, Don Quixote was ineffectually, but literally, confronting giants- private companies of great wealth which, under royal patent, were exploiting the land of Spain on a gigantic and unheard-of scale. One windmill is sufficient to knock Don Quixote off his horse, but it is a clump of thirty or forty of them at which he charges in anger. And it is not a flock or herd of sheep at which he charges, but a vast assemblage of them to which his word army is ap­ propriate. There must be something wrong with the unbounded commer­ cial development that is beginning to change the face of Spain, because it is founded on pride. On the other hand, every deed of Don Quixote rests on faith in the Gospels. It should be becoming clear in what way the story of Don Quixote is itself a parable. At this point I have just about made good my claim that Don Quixote's actions in Part one are all understandable and good. I have not mentioned several encounters in which he gives and receives lumps and bruises. The most serious injury he causes is a broken leg, to an arrogant young priest who speaks rudely and treats him as though he were nothing. (1.19) Until he is in pain and unable to move, Alonso Lopez is too wrapped up in himself to recognize Don Quixott:: as another like himself to whom elementary courtesy is due. And as soon as Don Quixote sees that the man needs help, he .is quick to give it. Alonso Lopez has learned his own impor­ tance from his theological education, but he has not learned who his neighbor is. If he is capable of learning such a lesson at all, both the anger and the kindness of the crazy knight could teach it to him. Don Quixote is meddlesome, but his meddling always takes the form of pertinent curiosity. Though he talks often of the privileges of rank, he acts always as though every human being deserves honor. He is entitled to teach manners to a priest, to insist that the king accord even a criminal minimal recognition as a member of his own species, to require a master to treat his servant with respect, to make that servant and prostitutes aware of their own dignity, and even to strike a few blows at gigantic faceless companies which do their business in indifference to what they do to the world they share with ordinary people. Don Quixote earns the right to interfere with everyone by recognizing every human life as a claim upon himself. His curiosity is pertinent because when the test comes he always acts as though the good of another pertains to him. And we are en­ titled to wonder if, in Don Quixote, we are witnessing a man who loves his neighbor as himself. When Don Quixote enters the Sierra Moreno he is far from believing that he has done anything worthwhile, but his influence is already present in the world and working its own effects. He himself is miserable and alone. He spends his time imitating the penance of Amadis of Gaul, an episode noteworthy because it makes one realize that nowhere else in the St. Johns Lecture Series 7 �book does he imitate anyone. Only in this brief, dark retirement from the world does Don Quixote ever try to remember something a knight in a book did in order to mimic it. Ordinarily he is the opposite of an imitator, the most original of men, in the sense that his deeds originate in himself out of the true array of possibilities before him. It is the rest of us, who judge and act out of habit, custom, and inertia, who are the imitators. The enchantment of which Don Quixote speaks is primarily the siren song of habit which prevents us from truly encountering the things and people before us. We take them for what everyone else always takes them for. In a chapter which Cervantes calls "one of the most important in the entire history" (11.6), Don Quixote's niece tells him to act like what he is, a man who is old, sick, and poor. In the Sierra Moreno, that is just how he acts. When Sancho returns to him in the mountains, he finds his master thinner than ever, jaundiced, fainting from hunger, and sighing for Dulcinea. But when he tries to speak to him of his beloved, Don Quixote will only say that he is not worthy of her grace (1.29). When his priest, for a joke, says he has heard of a mad sinner who will undoubtedly be damned for setting free some galley slaves, Don Quixote hangs his head in silent humiliation. It is his wonderful friendship with Sancho that brings him back to himself. Here is the colloquy which brings him out of his melancholy and restores his sanity. (1.30) " 'Faith, Senor Licentiate,' (said Sancho,) 'the one who performed that deed was my master. Not that I didn't warn him beforehand and ad­ vise him to look what he was doing, it being a sin to free them, for they were all of them the greatest rogues that ever were.' 'Blockhead!' cried Don Quixote upon hearing this. 'It is not the business of knights-errant to stop and ascertain as to whether the afflicted and oppressed whom they encounter going along the road in chains like that are in such straits by reason of their own crimes or as a result of misfortunes that they have suffered. The only thing that does concern them is to aid those individuals as persons in distress, with an eye to their sufferings and not to their villainies. I chanced to meet with a rosary, or string, of poor wretches and merely did for them what my religion demands of me. As for the rest, that is no affair of mine. And whoever thinks ill of it- saving the dignity of your holy office and your respected person, Senor Licentiate- I will simply say that he knows little of the laws of chivalry and lies like an ill-begotten son of a whore. All of which I will make plain to him, to the fullest extent, with my sword.' " Soon Don Quixote is drawing Sancho ahead of the others they are travelling with, to question him in insatiable detail about Dulcinea. As always, Sancho's disloyalty has strengthened Don Quixote's faith, and Don Quixote's healing anger at his squire has strengthened Sancho's devo­ tion to his master. Those two are then wholly themselves, while those riding along behind them have, without knowing it, become new beings in Don Quixote's image. Dorotea, who has been seduced and deserted by the nobleman Don Fernando, who has run away from home and twice trusted men who then tried to rape her, who has ended up in the Sierra Moreno in despair, is 8 The Parable of Don Quixote �now in the company of three new knights-errant. Don Quixote's curate and barber, who, contemptuous of his behavior but concerned for his welfare. have come hunting for their friend to hring him home. have found themselves distracted by Dorotea's distress, and each has sworn himself to her service (1.28,29). Cardenio, who has also been misused by Don Fernando, and had run away to the Sierra Moreno to escape his troubles and all human society, has regained his sanity and hopes, and sworn that Don Fernando will either marry Dorotea or fight him. Two men for whom the idea of chivalry is matter only for mockery, but who are in the Sierra Moreno on account of Don Quixote, and two despairing victims, who are brought out of their solitude by Don Quixote's friends, are now a band united by mutual faith, by the giving and receiving of charity, and by the hope that life may still hold some unlooked-for good for a young woman in distress. The four of them connive at an elaborate pretense of knight-errantry to patronize Don Quixote, while none of them notices that they are living the actuality of it. For the remainder of Part one, Don Quixote sleeps, listens, holds back from disputes to be a peacemaker, allows himself to be carried homeward in a cage, and, after one abortive attempt in the last chapter to return to knight-errantry, chooses the prudent course of returning home to await more propitious times. He, the most active of men, is for the most part content with his return to passivity. We are never told why directly, but Cervantes shows us why through the Captive's story, which is Cervantes' parable of the prodigal father. Luke's story of the prodigal son begins with a young man's heedless­ ness of others, the Captive's story with his father's heedlessness of self. Each leads to the premature distribution of an estate. The prodigal father, worried that he will waste what he has, sells his lands, divides the proceeds among his sons, and sends them out into the world. One pursues trade, and becomes wealthy; a second pursues letters, and eventually becomes a judge. The Captive, in the image of his father, becomes a knight. After twenty-two years the family is reunited, the father's faith justified, the wealth he denied himself multiplied, the sons whose presence he sacrificed returnecl to him freely out of love. But this sum­ mary of the story leaves out the most important character in it, the Moorish maiden Zoraida. When the prodigal father lets go of his property and his sons, he cannot know that a stranger is waiting in the world whom only his deed will save. Of the many quixotic characters in Don Quixote, the most quixotic of them all is the Moorish princess Zoraida, who cannot take any pleasure from wealth, a loving father, or the society of her own people, because in her childhood she heard stories of the Virgin Mary from a Christian slave. She gives up everything to go with the Christian knight to a country where the Virgin Mary is worshipped. Upbringing, language, heritage, custom, and ritual do not produce faith in Zoraida; the inspiration of the imagination by stories does. The prodigality of the Captive's father, and of the Captive himself, who returns most of his inheritance and embarks on a soldier's life, make possible her rescue from a country not hospitable St. Johns Lecture Series 9 �to her spirit. The band of knights-errant descended from Don Quixote, and already enlarged, gives her that reception to a Christian country of which she has dreamed. Between Don Quixote's return to the inn and the Captive's arrival there, four more lives have been saved from unhappiness. Don Fernando, who arrived breathing threats and murder at Luscinda, who betrayed him after he had betrayed Cardenio and Dorotea for her sake, has relented and amended his life, making it possible for Cardenio and Luscinda to marry, and returning himself to Dorotea. Don Fernando's conversion is brought about by the unanimous and whole-hearted urging of the group in the inn, which includes the curate and barber, now in­ volved in the lives of others by the same pertinent curiosity that took Don Quixote away from his home. As Zoraida was waiting in the world for the liberating act of the prodigal father, so, it turns out, was Dorotea, lost, alone, and in danger in the Sierra Moreno, waiting for the liberating, in­ fectious generosity of Don Quixote. She acknowledges as much, when finally abandoning all pretense with Don Quixote, she says to him, "I am convinced that had it not been for you, sir, I should never have had the good fortune that is now mine, and in this I speak the veriest truth, as most of these worthy folk who are present can testify." (1.37) The long chain of entangled lives which extends to the Captive's brother's teen­ aged daughter and her boyfriend, which is linked in mutual generosity to realize the highest possibilities of each, which is the exact inverse of the chain of corruption extending from Anselmo, owes its existence to Don Quixote. In the parable surrounding the parable, he is the prodigal father. Don Quixote, having chosen not to hoard the grace his own life con­ tained, made it available in unpredictable ways to people unknown to him. Contributing also to that transmission is, of course, an immense ele­ ment of coincidence, as, one after another, nine people who are in various ways making one another unhappy arrive at the same place. But perhaps coincidence is one of those categories under which things appear to our enchanted sight as other than they are. Cardenio and Dorotea are both in the Sierra Moreno because it is the place of despair, but they are not there together until Don Quixote's friends bring them together. Until that time, the latent truth that their interests coincide cannot become a fact, and that is why they are in despair. The coincidence of their connection with each other only has consequences in the world when the utterly disinterested curate and barber chose to make their cares coincide with those of two strangers. Similarly, the Captive and his brother might have spent the night at the same inn without knowing it, had Don Quixote's friends not been there to ask each for his story, and to involve themselves in those articles. If the truth of coincidence is that all lives coincide, then the fact of coincidence ceases to be surprising. Arrival at the inn where the steadily multiplying good will begotten by Don Quixote works its effects is for Don Fernando "like attaining Heaven itself, where all the misadven­ tures of earth are at an end. " (1.36) In contrast to Don Fernando's way of 10 The Parable of Don Quixok �recognizing the truth behind the facts, Don Quixote's taking the same inn for a castle is modest understatement. I have said that Don Quixote does not do anything in Part one after he frees the convicts. He is present in the subsequent deeds as the Captive's father is present in the lives of his sons, in just the measure that they are independent of him. But it is now necessary for me to qualify what I've said, because Don Quixote, for a brief moment in Chapter forty-five, does something important. He leads an army. He leads it in a conflict in which no one is hurt because he quickly puts a stop to the fighting. But it is an episode in which, while nothing happens, the participants reveal them­ selves for what they are. It is thus like those Platonic dialogues which Mr. Klein has called ethological mimes. Before describing the episode I will mention two others of the same kind from earlier in this book. In Chapter four, during that first brief sally in which the whole truth of Don Quixote can be read, he encounters some Toledo merchants on the�r way to buy silk. For a moment they stand opposed, Don Quixote commanding them to swear that Dulcinea is the most beautiful woman in the world, one of the merchants insisting that they be shown her, or at least her portrait, before being required to commit themselves. In anger, thoroughly provoked by the rude joke-; of one of the merchants. Don Quixote lowers his lance and charges. As happens as often as not with Rocinante, his horse stumbles, and he is a loser without combat. But Don Quixote on the ground, beaten by servants, with the merchants on their horses, laughing in a slightly embarassed way, is just the enchanted ap­ pearance, the merely factual outcome of the episode. The truth of it is one man understanding that the beauty that is worth declaring and defending is the beauty that is invisible, while a group of others think of the beauty of a beloved woman as they do of the quality of a sample of silk. It is the soul of a knight and the soul of a merchant that are set before us. In Chapter twenty, Don Quixote and Sancho run afoul of another phase of the textile industry, the sounds of the hammers of a fulling mill. I am disregarding Don Quixote's advice in speaking of it. "I do not deny," he says, "that what happened to us has its comical aspects; but it is best not to tell the story, for not everyone is wise enough to see the point of the thing." The point of the thing is that Don Quixote is truly brave, because he is brave in the dark. The fact of the matter is that he, like Sancho, spent a night in terror of something that could not harm them, and had to endure Sancho's laughter in the morning. But does one who fears in the night have the right to mock in the daylight? Night will always come again, and will hold terrors, and Don Quixote has proved that he can face them with courage. The revelation of courage does not· require a solemn occasion; for those with eyes to see, it is compatible with events that are ridiculous. In Chapter forty-five, as in the flaring of a match or a lightening-bolt, there is the briefest of military engagements: the battle over Mambrino's helmet. The battle has no outcome because Don Quixote does not allow it to. The point of the thing is the drawing of a line between the two sides, St. Johns Lecture Series 11 �and the revealing of the genuine willingness of each to fight. There is no issue present worth fighting over, as Don Quixote says. But there is the ut­ most importance in discovering for what one is willing to fight. On one side is an army of police, peasants, and servants, fighting in defense of the proposition that a barber's basin is a barber's basin and belongs by right to the barber. On the other side is an army of caballeros, Don Luis, Don Fer­ nando, the Judge, and their natural and rightful leader, Don Quixote. One combatant seems to be on the wrong side, for Sancho Panza fights with the knights. But Sancho is no longer the cowardly peasant of twenty­ five chapters earlier. Just five pages before the battle begins, Don Quixote has noted that Sancho has become a true man, and deserves to be dubbed a knight (1.44). The knights fight to defend the proposition that honor ex­ ists wherever one stakes one's honor, even in the homeliest of objects. Don Quixote's dignity elevates the barber's basin, just as his love elevates Dulcinea above the sight of merchants and his courage elevates a fuller's mill beyond the comprehension of a coward. For the only time in the book, Don Quixote has an army to lead, and the one thing he does with it, the instant it comes into being, is disband it. The battle he fights is against the automatic taking of the things in the world at their lowest valuation, and it is both won and lost as soon as the sides are drawn. Don Quixote has learned to see the possibilities which do not appear and the truths which facts never disclose by reading books of knight­ errantry. Cervantes, of course, claims that he wrote Don Quixote to com­ bat the harmful effects of such books. But what, exactly, are those harm­ ful effects? Four chapters of the text are devoted to a mammoth debate on the subject (1.47-50). The curate, of course, contributes his characteristic argument that such books foster mistaken notions among the uneducated about the facts of the past. People might even be moved by accounts of miracles which never happened. But a new character, more elevated in the hierarchy of the Church, a canon of Toledo, is introduced to carry the principal responsibility for exposing the evils of the books which have cor­ rupted Don Quixote. It is not right, the canon argues, that amusement ever be entirely separated from instruction, and not possible that pleasure could come from books that depict unlikely events in an episodic presentation and a crude style. The canon knows that the books of knight-errantry violate all these rules of good writing, because he has begun reading practically all of them that have ever been printed. In fact, he has enjoyed reading every one of them, but has always caught himself in time to remind himself that they are worthless, and incapable of affording true pleasure. He has never allowed himself to finish reading one. He once tried writing one himself, which observed all the rules of good writing, but he left it unfinished when he realized that most people wouldn't like it. Now the canon is an honest man, and if he were to hear his opinions presented as briefly as this and all in one place, he would find himself as peculiar as he finds Don Quixote. Spread over twenty pages, and supported with abundant ex­ amples, his discourse is in fact very impressive. Don Quixote, of course, mops the floor with him, but listen to the sur12 The Parable of Don Quixote �prising way he does it. "Do you mean to tell me that those books that . . . read with general enjoyment and praised by young and old alike, by rich and poor, the learned and the ignorant, the gentry and the plain people-in brief, by all sorts of persons of every condition and walk in life- do you mean to tell me that they are but lies? Do they not have every appearance of being true? " Don Quixote does not say that the books are good, but that they are true. What is true about them? They are in touch with the deepest springs of our common humanity. There are incessant references in the book to the truthfulness of histories, by which everyone else means some sort of authoritative assurance of a matching-up with a dead and inaccessible past. Only Don Quixote sees that a more important truth lies in what matches up with the buried longings and unrealized possibilities in all of us. Cervantes' discourse remains parabolic, but it is time for our own to become direct. The effect, harmful or otherwise, of books of knight­ errantry, is not the subject of chief concern. The canon, showing the monstrous improbabilities the romances ask us to swallow, mentions a seventeen-year-old boy killing a giant, an army of a million men defeated because the book's hero is on the other side, and a tower full of knights miraculouslv sC'attered all over the f'arth. and C'oncl u des that hooks full of . such things have no place in a Christian state. Is it not clear that the canon is talking of one th in g while Cervantes is thinking of another, and that the name of that other is the Bible? The canon tells Don Quixote to t urn to the Book of Judges if he wants to read about knightly exploits, attributing its superiority to its accuracy. But even if the story of Samson and Delilah is more factual than that of Amadis of Gaul, does the worth of the Bible depend on its quota of facts? In the first chapter of Part two, Don Quixote gives a lesson in how to read, which is wasted on his audience of the curate and the barber. He says, "the truth is so clear that I can almost assure you that I saw with my own eyes Amadis of Gaul." Is Don Quixote talking about amusement? About instruction? Those two categories do not exhaust the purposes of writing, and it is only because the canon thinks they do that he is so con­ fused about his own experiences with books. Stories that affect us set our imaginations to work. That activity can disclose ourselves to us, what we care about, what we fear, what we long for. The combination of disclosure and stimulation may, as it does with Don Quixote, inspire ac­ tion. Even when it doesn't, it may enrich the interior realm from which thought and action can be nourished. It is not possible for a work of fic­ tion to relieve boredom for a time, and then vanish as though it had not been. Because the work of our imaginations is an indispensable partner in the presentation to us of a work of fiction, reading or listening to one is always an experience which must leave some mark. Under the word fic­ tion I include history, if it is formed into stories. It follows, then, that stories cannot be received by us passively or iden­ tically. And finally, it follows that the Bible cannot be what it is, mostly stories, and be understood for the many by a learned few who would con­ trol the rightness of beliefs. In our vulnerability to stories, we are all alike, St. John i l«ture Series 13 �and the canon cannot rise above his own humanity. In our response to stories, where the possibility of faith lies, we are independent and free, and the canon cannot rise above us. Cervantes' book is a parable of faith, written at the time of an Inquisition. You may have noticed that I have not had much to say about Part two, and you must realize by now that I am not going to. In fact, I have used Part two as though it were Cervantes' commentary on Part one. It is more than that. In it, Cervantes magnifies Don Quixote's mistakes, failures, doubts, and miseries, so that we will be willing to let him die. We are left alone at the end of Part two, in a way that we are not at the end of Part one. We have only ourselves to rely on, and no longer Don Quixote, to assimilate and come to terms with our encounter with him. If we are to carry away anything of importance from that encounter, it must survive a passage through his inexplicable abandonment of everything he believed. But Cervantes is too good a storyteller to make even half a book entirely painful to his best and most trusting readers. He gives as compensation for our ordeal Sancho Panza, for Part two is Sancho's book. With the many ways in which Don Quixote and Sancho are obvious opposites, one is apt not to notice how much they are alike. Each has left home and submitted himself to adventure and the workings of pro­ vidence, Don Quixote because he longs to be acknowledged and accepted by Dulcinea, Sancho because he longs for an island, where he would be an important man, see his children honored, and not have to do any work. Within their enormous sameness, their differences make their friendship the most stable of self-maintaining communities. When they pull against each other it is always for the sake of the same goal, that grace without which a life, whether devoted to honor or to pleasure, is incomplete. In the course of his companionship, his fights, and his reconciliations with Don Quixote, Sancho acquires habits which will sustain his quixotic long­ ings after he has lost his friend. . He has progressively become brave enough to fight in defense of his master (1.24), alongside his master (1.45), and finally in rebellion from his master (II.60). He has likewise absorbed enough ofhis master's wisdom that he is able, on his own in charge of his inland island, to resolve a paradox that would defeat Bertrand Russell (Il.51). But most important of all, association with Don Quixote has liberated Sancho's imagination. What Sancho sees from the flying horse Clavileno has nothing to do with knight-errantry, since his imagination has been differently nourished than has Don Quixote's. A mustard seed from the Gospels, some garbled astronomy, and memories of his boyhood as a goatherd combine in San­ cho's visions (II.41). With the eyes of an imagination thoroughly his own, set free in him by Don Quixote, Sancho sees that his longing is for no ear­ thly island (II.42). As Don Quixote is a lover of honor, so is Sancho a lover of pleasure, with sufficient imagination. always. to be grateful and never to be satisfied. 14 The Parable of Don Quixole � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Description An account of the resource Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. Items include audio and video recordings and typescripts.<br /><br />For more information, and a schedule of upcoming lectures, please visit the <strong><a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a></strong>.  <br /><br />Click on <strong><a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&amp;sort_field=Dublin+Core%2CDate&amp;sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a></strong> to view and sort all items in the collection.<br /><br />A growing number of lecture recordings are also available on the St. John's College (Annapolis) Lectures podcast. Visit <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a> or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe. Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Title A name given to the resource St. John's College Formal Lecture Series—Annapolis Identifier An unambiguous reference to the resource within a given context formallectureseriesannapolis Text A resource consisting primarily of words for reading. Examples include books, letters, dissertations, poems, newspapers, articles, archives of mailing lists. Note that facsimiles or images of texts are still of the genre Text. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data paper Page numeration Number of pages in the original item. 15 pages Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource The parable of Don Quixote Description An account of the resource Typescript of a lecture delivered on September 17, 1982 by Joe Sachs as part of the Formal Lecture Series. Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Date A point or period of time associated with an event in the lifecycle of the resource 1982-09-17 Rights Information about rights held in and over the resource St. John's College has been given permission to make this item available online. Type The nature or genre of the resource text Format The file format, physical medium, or dimensions of the resource pdf Relation A related resource <a title="Sound recording" href="http://digitalarchives.sjc.edu/items/show/3715">Sound recording</a> Language A language of the resource English Identifier An unambiguous reference to the resource within a given context lec Sachs 1982-09-17 Creator An entity primarily responsible for making the resource Sachs, Joe, 1946- Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/fe390b517fad0ca74769f889599e685c.mp3 8bbbc72ed90b989c30db05ab87ac4fef Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Description An account of the resource Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. Items include audio and video recordings and typescripts.<br /><br />For more information, and a schedule of upcoming lectures, please visit the <strong><a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a></strong>.  <br /><br />Click on <strong><a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&amp;sort_field=Dublin+Core%2CDate&amp;sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a></strong> to view and sort all items in the collection.<br /><br />A growing number of lecture recordings are also available on the St. John's College (Annapolis) Lectures podcast. Visit <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a> or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe. Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Title A name given to the resource St. John's College Formal Lecture Series—Annapolis Identifier An unambiguous reference to the resource within a given context formallectureseriesannapolis Sound A resource primarily intended to be heard. Examples include a music playback file format, an audio compact disc, and recorded speech or sounds. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data audiotape Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 00:47:05 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource The Parable of Don Quixote Description An account of the resource Audio recording of a lecture delivered on September 17, 1982, by Joe Sachs as part of the Formal Lecture Series. The tape cuts off part of the lecture. The missing section begins on page 12 of the lecture typescript, at the end of the first sentence in the paragraph that begins "It is not right," and is missing page 13 and most of page 14. The tape ends with, "As Don Quixote is a lover of honor," which is the last sentence of the lecture. Creator An entity primarily responsible for making the resource Sachs, Joe, 1946- Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Date A point or period of time associated with an event in the lifecycle of the resource 1982-09-17 Rights Information about rights held in and over the resource St. John's College has been given permission to make this item available online. Type The nature or genre of the resource sound Format The file format, physical medium, or dimensions of the resource mp3 Language A language of the resource English Identifier An unambiguous reference to the resource within a given context LEC_Sachs_Joe_1982-09-17_ac Relation A related resource <a title="Typescript" href="http://digitalarchives.sjc.edu/items/show/3716">Typescript</a> Subject The topic of the resource Cervantes Saavedra, Miguel de, 1547-1616. Don Quixote Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/abf8d3a833817fa6e4ca33d97641f296.mp3 0c6de2ed6e62258cfbb1082214339128 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Description An account of the resource Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. Items include audio and video recordings and typescripts.<br /><br />For more information, and a schedule of upcoming lectures, please visit the <strong><a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a></strong>.  <br /><br />Click on <strong><a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&amp;sort_field=Dublin+Core%2CDate&amp;sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a></strong> to view and sort all items in the collection.<br /><br />A growing number of lecture recordings are also available on the St. John's College (Annapolis) Lectures podcast. Visit <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a> or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe. Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Title A name given to the resource St. John's College Formal Lecture Series—Annapolis Identifier An unambiguous reference to the resource within a given context formallectureseriesannapolis Sound A resource primarily intended to be heard. Examples include a music playback file format, an audio compact disc, and recorded speech or sounds. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data audiotape (Tape 52, Vol. 2) Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 01:02:26 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource The beginning of the St. John's program Description An account of the resource Audio recording of part two of a lecture delivered in July 1972 by Stringfellow Barr entitled "The beginning of the St. John's program". Creator An entity primarily responsible for making the resource Barr, Stringfellow, 1897-1982 Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Date A point or period of time associated with an event in the lifecycle of the resource 1972-07 Rights Information about rights held in and over the resource St. John's College has been given permission to make this item available online. Type The nature or genre of the resource sound Format The file format, physical medium, or dimensions of the resource mp3 Relation A related resource <a title="Part One" href="http://digitalarchives.sjc.edu/items/show/3713">Part One</a> <a title="Photographs" href="http://digitalarchives.sjc.edu/search?query=%2B%22The+Beginning+of+the+St.+John%27s+Program%22&amp;query_type=boolean&amp;record_types%5B%5D=Item&amp;submit_search=Search">Photographs from the lecture</a> Language A language of the resource English https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/0ff4e11f50a4c8136675f252f3d28f8b.mp3 81aa8f11a197d4cc9124dfdbf841c807 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Description An account of the resource Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. Items include audio and video recordings and typescripts.<br /><br />For more information, and a schedule of upcoming lectures, please visit the <strong><a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a></strong>.  <br /><br />Click on <strong><a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&amp;sort_field=Dublin+Core%2CDate&amp;sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a></strong> to view and sort all items in the collection.<br /><br />A growing number of lecture recordings are also available on the St. John's College (Annapolis) Lectures podcast. Visit <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a> or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe. Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Title A name given to the resource St. John's College Formal Lecture Series—Annapolis Identifier An unambiguous reference to the resource within a given context formallectureseriesannapolis Sound A resource primarily intended to be heard. Examples include a music playback file format, an audio compact disc, and recorded speech or sounds. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data audiotape (Tape 52, Vol. 1) Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 01:31:12 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource The beginning of the St. John's program Description An account of the resource Audio recording of part one of a lecture delivered in July 1972 by Stringfellow Barr entitled "The beginning of the St. John's program". Creator An entity primarily responsible for making the resource Barr, Stringfellow, 1897-1982 Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Date A point or period of time associated with an event in the lifecycle of the resource 1972-07 Rights Information about rights held in and over the resource St. John's College has been given permission to make this item available online. Type The nature or genre of the resource sound Format The file format, physical medium, or dimensions of the resource mp3 Relation A related resource <a title="Part Two" href="http://digitalarchives.sjc.edu/items/show/3714">Part Two</a> <a title="Photographs" href="http://digitalarchives.sjc.edu/search?query=%2B%22The+Beginning+of+the+St.+John%27s+Program%22&amp;query_type=boolean&amp;record_types%5B%5D=Item&amp;submit_search=Search">Photographs from the lecture</a> Language A language of the resource English Identifier An unambiguous reference to the resource within a given context lec Barr 1972-07 (part 1) https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/a715ac5c895949d67ad8e9052c322938.mp3 d0ee594456840281f563f2772ece653d Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Description An account of the resource Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. Items include audio and video recordings and typescripts.<br /><br />For more information, and a schedule of upcoming lectures, please visit the <strong><a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a></strong>.  <br /><br />Click on <strong><a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&amp;sort_field=Dublin+Core%2CDate&amp;sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a></strong> to view and sort all items in the collection.<br /><br />A growing number of lecture recordings are also available on the St. John's College (Annapolis) Lectures podcast. Visit <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a> or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe. Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Title A name given to the resource St. John's College Formal Lecture Series—Annapolis Identifier An unambiguous reference to the resource within a given context formallectureseriesannapolis Sound A resource primarily intended to be heard. Examples include a music playback file format, an audio compact disc, and recorded speech or sounds. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data audiotape (Tape270) Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource <em>Homo loquens</em><span> from a biological standpoint</span> Description An account of the resource Audio recording of a lecture given on September 19, 1975 by Curtis Wilson as part of the Formal Lecture Series. Creator An entity primarily responsible for making the resource Wilson, Curtis Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Date A point or period of time associated with an event in the lifecycle of the resource 1975-09-19 Rights Information about rights held in and over the resource St. John's College has been given permission to make this item available online. Type The nature or genre of the resource sound Format The file format, physical medium, or dimensions of the resource mp3 Language A language of the resource English Identifier An unambiguous reference to the resource within a given context lec Wilson 1975-09-19 Relation A related resource <a title="Typescript" href="http://digitalarchives.sjc.edu/items/show/3652">Typescript</a> Deans Friday night lecture Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/af5ebc6ba49b6d9d7eedc31ac7ace1a8.mp3 3cf19b84ee8890349f3d5091a33aa94b Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Description An account of the resource Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. Items include audio and video recordings and typescripts.<br /><br />For more information, and a schedule of upcoming lectures, please visit the <strong><a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a></strong>.  <br /><br />Click on <strong><a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&amp;sort_field=Dublin+Core%2CDate&amp;sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a></strong> to view and sort all items in the collection.<br /><br />A growing number of lecture recordings are also available on the St. John's College (Annapolis) Lectures podcast. Visit <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a> or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe. Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Title A name given to the resource St. John's College Formal Lecture Series—Annapolis Identifier An unambiguous reference to the resource within a given context formallectureseriesannapolis Sound A resource primarily intended to be heard. Examples include a music playback file format, an audio compact disc, and recorded speech or sounds. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data audiotape (Tape 218) Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 01:16:50 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource On the discovery of deductive science Description An account of the resource Audio recording of a lecture given on September 14, 1973 by Curtis Wilson as part of the Formal Lecture Series. Creator An entity primarily responsible for making the resource Wilson, Curtis Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Date A point or period of time associated with an event in the lifecycle of the resource 1973-09-14 Rights Information about rights held in and over the resource St. John's College has been given permission to make this item available online. Type The nature or genre of the resource sound Format The file format, physical medium, or dimensions of the resource mp3 Relation A related resource <a title="Typescript" href="http://digitalarchives.sjc.edu/items/show/3651">Typescript</a> Language A language of the resource English Identifier An unambiguous reference to the resource within a given context lec Wilson 1973-09-14 Deans Friday night lecture Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/990af6e012bacecfba691ecd37b02cea.mp3 1f57fec1ed71fdc024ee515130830a8e Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Description An account of the resource Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. Items include audio and video recordings and typescripts.<br /><br />For more information, and a schedule of upcoming lectures, please visit the <strong><a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a></strong>.  <br /><br />Click on <strong><a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&amp;sort_field=Dublin+Core%2CDate&amp;sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a></strong> to view and sort all items in the collection.<br /><br />A growing number of lecture recordings are also available on the St. John's College (Annapolis) Lectures podcast. Visit <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a> or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe. Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Title A name given to the resource St. John's College Formal Lecture Series—Annapolis Identifier An unambiguous reference to the resource within a given context formallectureseriesannapolis Sound A resource primarily intended to be heard. Examples include a music playback file format, an audio compact disc, and recorded speech or sounds. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data audiotape (Tape 227) Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 01:11:29 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Kepler and the Mode of Vision Description An account of the resource Audio recording of a lecture delivered on September 13, 1974 by Curtis Wilson as part of the Formal Lecture Series. Creator An entity primarily responsible for making the resource Wilson, Curtis Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Date A point or period of time associated with an event in the lifecycle of the resource 1974-09-13 Rights Information about rights held in and over the resource St. John's College has been given permission to make this item available online. Type The nature or genre of the resource sound Format The file format, physical medium, or dimensions of the resource mp3 Language A language of the resource English Identifier An unambiguous reference to the resource within a given context lec Wilson 1974-09-13 Subject The topic of the resource Kepler, Johannes, 1571-1630 Deans Friday night lecture Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/57bd401ecb5e95375d5d97eab312f2a2.mp3 f021c3a3de9d142fde8eca6613b5dae4 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Description An account of the resource Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. Items include audio and video recordings and typescripts.<br /><br />For more information, and a schedule of upcoming lectures, please visit the <strong><a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a></strong>.  <br /><br />Click on <strong><a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&amp;sort_field=Dublin+Core%2CDate&amp;sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a></strong> to view and sort all items in the collection.<br /><br />A growing number of lecture recordings are also available on the St. John's College (Annapolis) Lectures podcast. Visit <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a> or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe. Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Title A name given to the resource St. John's College Formal Lecture Series—Annapolis Identifier An unambiguous reference to the resource within a given context formallectureseriesannapolis Sound A resource primarily intended to be heard. Examples include a music playback file format, an audio compact disc, and recorded speech or sounds. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data audiotape (Tape 236) Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 01:07:21 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Dynamical Chaos: Some Implications of a Recent Discovery Description An account of the resource Audio recording of a lecture delivered on October 7, 1994, by Curtis Wilson as part of the Formal Lecture Series. Creator An entity primarily responsible for making the resource Wilson, Curtis Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Date A point or period of time associated with an event in the lifecycle of the resource 1994-10-17 Rights Information about rights held in and over the resource St. John's College has been given permission to make this item available online. Type The nature or genre of the resource sound Format The file format, physical medium, or dimensions of the resource mp3 Relation A related resource <a title="Typescript" href="http://digitalarchives.sjc.edu/items/show/3654">Typescript</a> Language A language of the resource English Identifier An unambiguous reference to the resource within a given context LEC_Wilson_Curtis_1994-10-07_ac Subject The topic of the resource Chaotic behavior in systems Deans Friday night lecture Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/6616019e126b4f036f43a1ff9ec6fcce.mp3 8b507e967ea692c11e88b40c93120812 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Description An account of the resource Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. Items include audio and video recordings and typescripts.<br /><br />For more information, and a schedule of upcoming lectures, please visit the <strong><a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a></strong>.  <br /><br />Click on <strong><a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&amp;sort_field=Dublin+Core%2CDate&amp;sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a></strong> to view and sort all items in the collection.<br /><br />A growing number of lecture recordings are also available on the St. John's College (Annapolis) Lectures podcast. Visit <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a> or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe. Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Title A name given to the resource St. John's College Formal Lecture Series—Annapolis Identifier An unambiguous reference to the resource within a given context formallectureseriesannapolis Sound A resource primarily intended to be heard. Examples include a music playback file format, an audio compact disc, and recorded speech or sounds. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data audiocassette Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 01:14:18 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Galileo Agonistes Description An account of the resource Audio recording of a lecture delivered on October 1, 1999, by Curtis Wilson as part of the Formal Lecture Series. Creator An entity primarily responsible for making the resource Wilson, Curtis Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Date A point or period of time associated with an event in the lifecycle of the resource 1999-10-01 Rights Information about rights held in and over the resource St. John's College has been given permission to make this item available online. Type The nature or genre of the resource sound Format The file format, physical medium, or dimensions of the resource mp3 Relation A related resource <a title="Typescript" href="http://digitalarchives.sjc.edu/items/show/3655">Typescript</a> Language A language of the resource English Identifier An unambiguous reference to the resource within a given context LEC_Wilson_Curtis_1999-10-01_ac Subject The topic of the resource Galilei, Galileo, 1564-1642 Deans Friday night lecture Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/a375f74c6a153cfb0a78dccf2f6a545d.pdf 7dd9121990a30d2212936b9ce385e5c3 PDF Text Text l Curtis Wilson Galileo Agonistes My topic this evening is one that 50 years ago I had aspirations of delvmg into, then got lured away from, and now once more seek to come to terms with. Galileo in life was a combative controversialist, and ever since he has been a subject of controversy. My talk will be an interpretation. I shall first review what I think can be said about Gahleo's discovery of the iaw of free fall, taking care not to inject post-Galillean physics into the Galilean moment - a source of frequent errors. Then I shall speak of Galileo's struggle to keep the Church from condemning heliocentric astronomy, the failure of that struggle, and his trial before the Inquisition . My subject, I must warn you, requires attention to details. God, or the devil, is in the details .. I start with the old story in old textbooks about how the whole fabric of Aristotle's cosmology and physics came tumbling down one day in 1589, when Galileo, aged 25, newly appointed mathematics instructor at the University of Pisa, before professors and students assenlbled, dropped two cannonballs of different sizes from the Leaning Tower of Pisa. A simultaneous thud, we're told, heralded the birth of a new, experimental physics. Alas, this account omits crucial details. The original story was told by Viviani, Galileo's last pupil, who likely had it from his old teacher. The experiment, says Viviani, was designed, to show !Exhibit A:Jl that the speeds of mobile bodies of the same material [my emphasis] but of uneqiial weight, moving through the same medium, are not in the ratio of their absolute weights, as Aristotle claimed, but they move with equal speed ... ; and neither do the �2 speeds of" given mobile body. moving through diverse mediums. have the inverse ratio of the resistances, or densities of these mediums ... The import of these details emerges from a treatise on motion Galileo was writing in 1589.2 Consider first the second point. According to Aristotle's PhysicS, a given body falls in different mediums v.1th speeds that are inversely as the resistances of those mediums.3 If the resistance were absent, Aristotle says, the speed of the falling body would be infinite. Exhibit B: Aristotle's Rule of Speeds in Different Mediums Let VA• Vs be the body's speeds in mediums A and B; and let RA• Ra be the resistances in those mediums. Then according to Aristotle Suppose RA - 0. Then the ratio RB : RA becomes infinite, and so must VA: Vs. Therefore VA - oo, which is impossible. Aristotle concludes that a medium must be present: the void can't exist . . Galileo in his early treatise rejects Aristotle's proportion. A piece of wood falls in air With a certain speed, call it unit speed. Galileo identifies the ,. resistance in Aristotle's proportion with density. Let the density of air be unit density, and let the density of water be 4 (800 would be more like it, but I use . Galileo's numbers). Then by Aristotle's rule, the piece of wood should fall in water With a speed of one-fourth. But it doesn't fall; it rises and floats. Galileo thinks the speed of fall or rise varies as the difference between the density of the body and the density of the medium. Whence this idea? It smacks of Archimedes. In fact, Galileo has written a little book on the famous crown problem. He knows the principle of buoyancy: �3 a body immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid. That principle is irreconcilable with Aristotle's doctrine of heaviness and lightness. According to Aristotle, heavy bodies, by their heaviness, fall toward the center of the universe; light bodies, by their lightness, recede from that center. Heaviness and lightness are the fundamental qualities of the sublunary elements in Aristotle's world. Galileo in 1589 still assumed, with Aristotle, that the center of heavy things is the center of the world. But as an Archimedean, he has had to conclude that there is no such thing as lightness; all bodies are heavy, but some are more dense than others. A body goes up or down depending on whether its density is less or greater than the density of the medium. Galileo, however, is an Archimedean with an Aristotelian question. Archimedes did not deal With motion; force for him was static force , force balanced by another force. Galileo, like Artstotle, wants to know the cause of the speed of falling bodies. Aristotle had stated that the downward motion of a mass of gold or lead is quicker in proportion to its size, its weight. 4 If greater heaviness is greater downward tendency; mustn't the heavier body fall faster? Well, Galileo has learned it can't be so. Of two pieces of the same material, suppose the heavier fell faster. Tie them together. The combination must fall more slowly than its heavier part,. since it is held back by the lighter part.5 But this combination constitutes a heavier body, so it ought to fall faster. Aristotle's idea contradicts itself. Galileo concludes that every body of a gtven material, in a gtven medium, has a speed of fall or rise determined by the difference in density between the �4 body and the medium. The greater the difference in density, the greater the body's speed. What Galileo at this time called the body's natural speed of fall could be determined if the medium were entirely removed, but this, he believed, was not physically possible. Is all this right? No. For one thing, Galilee is speaking of a natural .· speed, not an acceleration of fall. The adjective natural here expresses an Artstotelian notion: a body moves naturally if the arche of its motion is internal to it, not imposed from without. Galileo at the end of his life will still be using this term .. natural" as though in the Artstotelian . ense, but it will s have become for him a question.6 What about the acceleration? Galileo in 1589 considers it to be not natural but adventitious. It occurs, of.course, whenever a body starts falling from rest; to reach the speed determined by its density and that of the medium, it must pass through all lesser degrees of speed. To explain this, Galileo supposes that an impetus was originally impressed on the body to raise it up: .... when it is let fall, this impetus diminishes at its own rate, the way the heat impressed on a piece of iron diminishes when the iron is separated from the fire that was the heat's source. As the impetus diminishes, the body picks up speed; and when all the impetus is gone, it moves uniformly. This theory is scarcely testable. It looks like an intellectual trap. Where did Galileo get it? - for it is unlikely he invented the whole thing. He had entered the University of Pisa in 1581, aiming at a medical career. In 1585 he dropped out Without a degree. disgusted by his professors' standpat Aristotelianism. Mathematics had caught his fancy - Euclid and �5 Archimedes. Natural philosophers, he said, should do as mathematicians do; deducing consequences from defmitlons and axioms.7 He was out to become a university rnatheniatician. How gain the requisite reputation? He published the book about Archimedes' buoyancy principle I mentioned earller. He devised mathematical derivations, and sent them about for critique. In 1587 he visited Christopher Clavius, mathematics professor at the Collegio Romano, the Jesuit college in Rome. The Jesuits were then a new and innovative force in education. They had recently debated among themselves whether mathematics was precisely applicable to the world, and Clavius had taken the affirmative, arguing that astronomy, music, optics, mechanics scientiae mediae, "middle sciences," the school.men haQ. called them - applied exactly. Many of Galileo's early MSS, we now know, echo lectures given at -, the .COllegto Romano.s Galileo was specializing in mechanics, astronomy, and the critique of Aristotle's physics. The exact route whereby Galileo acquired his early doctrines on motion remains unclear. A Venetian named Benedelti had held similar doctrines, but Galileo apparently didn't know his work at first hand.9 In 1589 Galileo obtained his first post, at Pisa; it paid pitifully little. When his father died 1n 1591, he became the family breadwinner. With support from Clavius and others he obtained a better-paying professorship at the University of Padua. There he remained from 1592 to 1610. A hopeful thing in Galileo's early work on natural motion was his attempt to verify his theory on inclined planes, where the motion is slower, more easily measurable. From the principle of the lever he had derived the rule �6 for equilibriu1n of weights on diversely inclined planes. Exhibit C: Equilibration of Weie;hts on Inclined Planes W1 • lying on CA, and cvnnected with the vertically hanging weight W2. is in equilibrium with W2 if, and only if, W1: W2 :: CA: CB.IO The larger weight W 1 is sustained on the incline by the smaller weight W2 hanging vertically, because the downward tendency of W 1 is reduced by the constraint on its direction . .To the downward tendency as reduced by the constraint in direction, Galileo gave the name momento. In going from statics to kinetics, Galileo n1akes an Aristotelian mistake: he assumes that, not the acceleration, but the speed produced is proportional to the static force or momento. There should follow a certain ratio of the times down diversely inclined planes. but experiment disconfirms it. For a while at least. Galileo ex.plained the disconfirmation as due 1.o accidental causes. To get out of this trap, Galileo needed to focus on acceleration, and then by experiment to discover the rule - famou~as Galileo's discovery - that the distances traversed are as the squares of the times. Galileo had made this discovery, it appears, by October, 1604"' On that date, in a letter to his friend Paolo Sarpi in Venice, he wrote as follows: Exhibit D: Galileo's Letter to Sarpi. October 1604 Thinking over the questions about motion, in which, to demonstrate the accidents observed by me, I have been lacking a totally indubitable principle that I could take as axiom, I am reduced to a proposition which has much that is natural and evident about it; and this being supposed, I demonstrate the rest, that is, that the spaces traversed in natural motion [are as the squares of the times], and consequently the spaces traversed �7 in equal times are as the odd numbers starting with unity... And the _ principle is this: ' that the mobile body goes increasing its speed in proportion to its distance from its starting point ... Please consider it and tell me your opinion.11 For his demonstration, Galileo has onl_y an outline of the steps, as we learn from a separate manuscript: 12 Exhibit E: Galileo's fol. 128. I suppose (and perhaps I shall be able to demonstrate it) that the heavy body falling naturally goes continually increasing its speed in proportion to its distance from its starting-point .... The speed with which the moving body has come from A to D is compounded c of all the degrees of velocity it has had at all the points of the line AD, and the speed with which it has passed aver AC is compouaded of all the degrees of velocity it has had at all the points of the D 1---~ line AC. Therefore, the speed with which [the body] has passed the line AD has to the speed with which ft has passed the line AC the ratio fof the square on DA to the square on CA]. The line AB represents distances traversed in falling. Lines at right angles to AB represent degrees of speed, increasing in proportion to the distance fallen through. A "degree of velocity" (grado di vel~ita) is a punctual speed, a speed at a point; it doesn't endure. Galileo speaks of compounding these punctual gradi di velocita to find the ratio of the speeds with which different distances are traversed. The degrees of speed thus compounded, he is saying, are measured by trtangles; so the speeds with which AD and AC are traversed are as the ., . triangles ADH and ACG. These are similar, and hence to one another as the squares on the corresponding sides. From this result, Galileo needs to get to what he knows experimentally, that the distances from the begmnL.'1.g of motion are as the squares of the �8 times. The steps he proposes for this derivation are wrong - careless blunders. No mathematically legitimate steps lead from the composition of punctual degrees of speed varying as distance, to the variation of distance with the squares of the times. Galileo himself, 4 or 5 years later, in 1608 or 1609, proved that the supposition of Exhibit E won't do. His argument goes as follows. Suppose AC is half AD . AD contains an infinity of points, and so does AC. At each point of AD, and at each point of AC, there is a punctual speed. The punctual speeds in the one distance can be put in one-to-one correspondence with the punctual speeds in the other, in such a way that each punctual speed in AD is twice the corresponding punctual speed in AC . Galileo infers that AD, the double distance, would be traversed in the same time as AC, its first half. But then the rest of AD would have to be traversed instantaneously, which is impossible. The argument, I believe, is valid. A motion starting from rest, with its speed varying as distance traversed, is impossible. ~ Suppose, however, that the line AB in Exhibit E represented time. Then the two compounded sums of degrees of velocity would be given by the two triangles ACG and ADH, and these triangles are as the squares of AC and AD, that is, as the squares of the times. If the areas of the triangles were proportional to distance traversed, we would have the result that Galileo has found expertmenW}y. Eventually, in his Dialogue on the Two Principal World Systems, of 1632, Galileo will cany through just this derivation, in which an infinity of instantaneous speeds are compounded over time, and represented in a diagrcµn �9 as areas, and it is stated that for these areas to be as the distances traversed is ben ragionevole e probabile, very reasonable and probable. I 3 A plausible proof but, Galileo recognizes, peculiar. It involves the very strange notion of instantaneous speed - a speed that doesrft have any duration, and so no distance is traversed by it - and it involves the adding up an actual infinity of such speeds. The serious application to the world of this questionable concept and procedure was unprecedented. To return to 1604: Galileo at that time was unwilling to let AB represent time. Empirical evidence, he thought, showed that the speed offall increases as distance. In the MS from which I've been quoting, he says that this principle appears to him molto naturale. and agrees v.:1-th our experience with instruments that operate by percussion: the magnitude of the effect is as the distance from which the body falls. He is thinking, for instance, of pile drivers. He has tested the principle, dropping weights on a stretched bowstring. The impact pulls the bowstring downward into a V-shape. If the weight is let fall from the double ~ height, the Vis deeper. These two V-shapes can be reproduced statically by hanging weights on the bowstring; the two weights that produce the two Vs are as 1:2. Galileo assumes that the effect is proportional to speed, and so concludes that speed is proportional to distance of fall. This is a mistake. How did Galileo correct himself? The scholars of this century have argued over whether Galileo was basically an experimentalist, or a desk mathematician.14 He was both. In the case of the motion of natural fall it was by experiment that he emerged from error. The key experiment is a highly sophisticated, indeed a masterly expertment.15 �10 Galileo arrived at the correct variation of speed in free fall only in 1608 I or 1609, 20 years after the Leaning Tower demonstration. This discovery presupposed the prior discovery of the parabolic trajectory of projectiles. He clinched both discoveries using the apparatus diagrammed in Exhibit F. Exhibit F: Apparatus for testin2 parabolic traf ectory and law of free fall ___________ _l AB = grooved inclined plane of height H; BC = grooved curve leading to horizontal projection at C; CF= path of projectile when falling through height hand .advancing through distance D. Suppose, first, that the inclination of,;the inclined plane is fixed, and that the ball in repeated rolls is started each time from the same point A at height H, measured from the table-top on which the inclined plane rests. Then on reaching C it will be projected horizontally, always With the same horizontal speed so long as the initial conditions are unchanged. It will fall in a curve. What curve? Suppose that the height h can be adjusted, by raising or lowering the horizontal board onto which the ball falls. Then it becomes possible to accumulate a series of paired values of D and h, all of them pertaining to the same curve. Galileo suspected it was a semi-parabola with vertex at C . In that �11 case h must vary as 02. There is evidence that Galileo carried out thiS test. The semi-parabolic result is exactly what we would expect if h increases as the square of the time, while D increases linearly with the time. HaVing con.firmed the parabolic shape, Galileo turns the expertment around, and uses the parabolic shape to examine the speeds achieved in fall through different heights H along the inclined plane. The distances D turn out to vary as the square root of H . The relevant calculations are given in some detail in Exhibit G: Essential details of folio 116v * 1000 ... .....,. HO<l 100 ·.: · ' ' J 1 w'UIOOOO I I 1121 I uoo 117% 800 f.CIO 1l.JIO tJO• 1tl1 '0 10 22 " TM[ ""ST CAS[ S"°"1.0 I< 0' "fllfHC! '"°'" lOO 121 ~: io ----1llll 2101 10 10 1100 300 HHOO ~ .,,lo 220. ~ , l 2 • 10 :~ ~ ../1711MOO • ••. lO<I . ''000 l . ·. ·.- lOO eoo ..• .. --..J.ll2 ••• . XX) . : "~:~ .. .. .. 2133 140000 <··--2Ul ~. _ •.•.; lOO 100 1'"'TOI" 1000 100 ?'ii'i lOO 100000 Vl70e•oo .... •O" ::: �12 The genius pf this experiment is that it avoids measurtng time, so much more difficult for Galileo than for us, and it gives a direct measure of instantaneous speed in descent along an inclined plane; the final speed in the descent is turned by the curved groove BC into a uniform horizontal speed proportional to the distance D; and then D proves to be as the square root of H. In sum.m.ary, Galileo's twenty-year struggle was brought to a successful conclusion by a combination of mathematical reasoning and sophisticated experimentation. A few years later, in a letter to his former student Benedetto Castelli, Galileo wrote: Nature is inexorable and immutable, and she does not care at all whether or not her recondite reasons and modes of operation are revealed to human understanding ... 16 I take that to express his sense of how formidable an opponent Nature is, in the contest that consists in trying to understand her. The remainder of this lecture is about the middle phase of Galileo's life, beginning in July 1609 with his getting newS" of a spyglass constructed in Flanders, and ending with the publication of his Dialogue on the Two Chief World Systems in 1632, then his trial by the Inquisition the following year, and his condemnation for heresy in June 1633. · In July 1609 Galileo built his own first telescope. In August he built a . better one, and by December he had a 20-power instrument, which he turned on the Moon. He saw mountains that cast shadows. From the lengths of the shadows he reckoned the approximate heights of the mountains in units of terrestrial distance . The Moon reflected sunlight, not as a polished mirror does, �13 but as do sand, dirt, and rock; it looked rather Earth-like. Maybe plants could grow on it. Better dirt, Galileo thought, than jasper or diamond. His report was met \Vith incredulity. The lµnar mountains, Christopher Clavius opined, were illusions of Galileo's telescope. On getting a better telescope, Clavius had to admit the appearances were as Galileo stated, but he wanted the Moon to be smooth, spherical and crystalline. Couldn't Galileo's mountains, he asked, be differences in density? To such suggestions Galileo had this reply: ... if we still want to let anyone imagine whatever he pleases, and if someone says that the Moon is spherically surrounded by transparent invisible crystal, then I shall willingly grant this provided that With equal courtesy it is permitted me to say that thiS crystal has on its outer surface a great number of enormous mountains, thirty times as high as terrestrial ones, which, being of diaphanous substance, cannot be seen by us ... The only fault here is that it is neither demonstrat~d nor demonstrable. I? In Januruy .1610 Galileo discovered four small stars accompanying Jupiter. They appeared as if situated on a strrught line passing through the planet and at rtght angles to the line of sight. In successive hours and on successive nights they individually changed their distances from Jupiter, passing from the east to the west of it and back again. By early 1611 Galileo was able to assign frurly accurate orbital periods about Jupiter to all four, assuming uniform circular motion. Thus, contrary to Aristotle, the Earth was not the only body about which celestial bodies move in circular motion. �14 Galileo called these stars Medicean after the ruling family of Tuscany, and so wangled for himself a position as "mathematician and philosopher to the Grand Duke of Tuscany". He could return to his native Florence. Late in 1610 Venus was far enough from the Sun for telescopic observation, and Galileo found that it had phases like the Moon's. It had been considered self-luminous, but the phases were evidence that it shone by reflected sunlight. Galileo found Venus's diameter to vary over time by a factor of about 6; it was largest when Venus is a crescent, and smallest when it appears as a circular disk. Hence its orbit surrounded the Sun. By similar observations of Mars, he found this planet when 90° from the Sun to be gibbous, that is, not fully round; its diameter also varted by a factor of about 5, being largest when the planet was in opposition to the Sun. The Martian orbit · therefore surrounded the Sun, and the Earth as well. Continued improvement of his tables for the Jovian satellites led Galileo to a new discovezy in July 1612. Comparing an observation With his tables, he realized that one of the satellites, the outennost of the four, had been eclipsed, passing into the shadow cast behind Jupiter by the Sun. He found that, if he took the mid-points of the satellite eclipses for epochs or starting-times, his tables became more accurate. The satellites were moving more uniformly with respect to the line from the Sun through Jupiter than with respect to the line from the Earth through Jupiter. The heliocentrist would expect this. It iS also what would be expected under the semi-heliocentric arrangement, where the Earth remains at rest, the other planets go round the Sun, and the Sun circles the Earth: the so-called Tychonic system.18 �15 Su.nspots were observed from 1610 onwards. A German Jesuit, Christoph Scheiner, writing under the pseudonym Apelles, put forward the idea that they were planets, hence compatible With celestial immutability. Galileo, citing his own careful observations and measurements, destroyed this hypothesis With merciless sarcasm. The spots moved round the Sun with changes in shape and mutual distances which implied they were on or very close to the Sun's surface. The Sun must be rotating, with a period of about 25 days, about an. axis through its center. The spots could be seen coming to be, coalescing, separating, ceasing to be. The Sun was a mutable body. Following these telescopic discoveries, Galileo becanie for the first time a public proponent of Copernicanism. In his student days, he had opposed this doctr1ne, listing tlie standard dynamical objections against it: bodies let drop from a height would not fall vertically to the ground, and so on. His early De Motu shows that by 1590 he had studied Ptolemy's Almngest and Copernicus's RevolutiDns with care. In a late revision of the De Motu, he introduced the idea that a spherical body at the center of heaV:y things, if set rotating, would continue·to rotate without the need for an internal or external mover. I 9 Such a motion he called neutral, distinguishing it thus, both from the natural downward motion of a heavy body, where th~re is an internal arche, and from a forced motion where there is an external mover. A consequence, though Galileo does not mention it, is that the daily apparent westward rotation of the stellar sphere could be accounted for by supposing the Earth to be rotating eastward about its polar axis. Galileo also considered as neutral the motion of a ball rolling on a polished horizontal surface concentrtc With the Earth's center; the �16 smallest force would set it moving, and it would then move forever unless impeded.20 An extension of this was that a body dropped from a tower on a rotating Earth, since it shares the tower's motion, would fall to the tower's base. The standard dynamical objections to the Earth's diurnal rotaton, Ga.lileo now realized, were without basis. In 1597 Kepler sent Galileo a copy of his first book, The Cosmographic Mystery, which was outspokenly Copernican. Galileo in responding stated that he had held the Copernican view for some years, but had refrained from defending this position publicly, intimidated by the fortune of our teacher Copernicus, who though he will be of immortal fame to some, is yet by an infinite number (for such is the multitude of fools) laughed at and rejected.21 By 1613, Galileo's telescopic discovertes had shown Ptolemaic astronomy to be untenable. The semi-heliocentric arrangement, on the other hand, might still seem an option: it gave much of the economy of the Copernican system, without putting the Earth in motion. Galileo could refute arguments against the Earth's motion; what arguments did he have for its motion? He was averse to the wildly speculative theological symbolism that made Kepler a Copernican.22 For the Earth's motion, he wanted terrestrial evidence. And already, in the 1590s, he thought he had found it: in the tides. This is a vexed topic. Why, people ask, was Galileo so stupid as to propose a tidal theory that doesn't agree With Newton's? Galileo, of course, died 11 months before Newton was born, so couldn't leaITI from him. But what these people fail to realize is how much wrong guessing, by intelligent men, �17 went on ~fore a correct understanding of tides emerged. Galileo's theory, incidentally, was right in a respect in which Newton missed the mark.23 First, however, what was Galileo's mistake? In his dialogue of 1632, he says, Of all great men who have philosophized on such a puzzling effect of nature [the tides], I am more surprised about Kepler than about anyone else; although he had a free and penetrating intellect and grasped the motions attributed to the Earth, he lent his ear to the dominion of the Moon over the water, to occult properties, and to similar childish ideas.24 In Galileo's view, attractions, sympathies, antipathies, were unscientific notions. He wanted mechanical explanations, preferaqly such as could be embodied in an actual model of brass, wood, water, and so on. Among l 7thcentury thinkers, he was not alone in thus restricting himself. Among Galileo's contemporaries who attributed the tides to the Moon's attraction, none could account for there being two tides per day. The Moon crosses our meridian once eveiy 25 hours, But, in Galileo's Venice as in our Chesapeake Bay, two high tides occur in that interval. So far as I know, the first to show why this should be so was Newton. What counts is differential attraction. When the Moon is on our mertdian, it attracts the nearby waters more strongly than the Earth's center, and the Earth's · enter more strongly. c than the waters on the opposite side of the Earth. So when there is a high tide for us, there should be a high tide on the opposite side of the Earth as well. Another difficulty is that high tide occurs, not when the Moon is overhead, but hours later; the delay varies from place to place. Why? �18 An obseivation that especially interested Galileo was this . In Venice, at the head of the Adriatic, the difference between high and low tide was about 6 feet, whereas at Dubrovnik, close to where the Adriatic opens into the Mediterranean, it was only a few inches. How explain that? CD.lileo's theory had two main parts. The first of these is wrong, but not for the reasons usually given. Galileo supposes that, because the Earth has two motions, the diurnal rotation and the Exhibit H annual motion, the waters of the ocean are B alternately accelerated and decelerated with a periodicity of one day. See Exhibit H, where the smaller circle is the Earth, the larger ······F ····················E-····················· i········ ·· circle the Earth's annual orbit. At B, that is, at midnight, the diurnal and annual motions add G together; at D, that is, at noon, the diurnal motion subtracts from the annual; at intermediate places the Earth's surface speed has intermediate values. This variation in surface speed, Galileo says, disturbs the waters; they slosh back and forth in their ocean basins, seeking to return to equilibrium. Does such a disturbance really occur? From a Newtonian point of view, Galileo's account is inadequate. Two accelerative fields are being combined. The combination would produce a disturbance, if the law of gravity were any other than an inverse-square law; a terin from the inverse-square law cancels it out. This, to be sure, was not understood by Galileo or Newton or anybody till recently. Critics had better beware, but yes, Galileo was wrong. �19 But i;lOW, suppose the disturbance occurred. According to the second part of Galileo's theory-, the resulting pendulum-like motion will have a characteristic pertod, determined by the size and shape of the basin. It will vary, Galileo says, as the length of the basin, and inversely as its depth. Actually, the period varies as the square-root of the length, but Galileo's second point, about the depth variation, is non-intuitive; presumably he discovered it by experiment. Apparently, by experiments with water in long basins, he observed that the water in the middle does not rise and fall, but moves back and forth, while the water at either end of the basin moves up and down. It was thus that he explamed to himself the difference in the heights of the tides in Venice and Dubrovnik. The study of the characteristic frequencies of ocean basins is a central feature of present-day tidal theory. The initial disturbance is caused, not as Galileo supposed, but by the gravitational attractions of the Moon and Sun. Newton knew that the shapes of ocean basins had something io do with the tides, but he lacked the mathematics for tre1.ting the problem. The first to give a correct mathematical formulation of the pendulum-like component of tidal motion was Laplace, a centuiy after Newton. Let these remarks suffice as to what is wrong and right about Galileo's theory ofthe tides. Galileo's campaign for heliocentrism roused the biblical fundamentalists . In December of 1613, the Medicis invited Castelli, professor of mathematics in Pisa. to dinner. The Grand Duchess Christina pressed him to defend the compatibility of heliocentrism .with the miracle reported in Chapter 10 of the �20 Book of Joshua, where Joshua says in the sight of Israel, "Sun, stand thou still." Castelli reported the evening's discussion to Galileo, who responded with a long letter on the same theme. The letter was copied and circulated widely. On December 21, 1614, Tomrnaso Caccini, a young firebrand of a Dominican, preached a sermon in Florence's Santa Marta Novella, denouncing ·the Galileists and all mathematicians as practitioners of diabolical arts and enemies of true religion. On the following February 7 Niccolo Lorin!, a pious elderly Dominican, sent to the Inquisition in Rome a copy of Galileo's letter to Castelli, here and there altered maliciously, to be examined for heretical content. Meanwhile Galileo had expanded the letter into a longer letter to the Grand Duchess Christina. Scripture, Galileo quotes a churchman as saying, tells how to go to heaven, not how heaven goes. It has to do with faith and morals, not with the make-up of the natural world. It is addressed to uneducated folk, and must speak their language. For the sake of theological consistency, some of its statements must be interpreted metaphorically: God does not literally stretch forth a hand, or have a backside, or get angry. As for implicit or explicit assertions in Scripture about the natural world, Galileo took his cue from Augustine's treatise, On the literal interpretation of Genesis. If natural philosophers have established a fact by observation or strict demonstration, their conclusion must take precedence over the literal interpretation of Scripture. And, Galileo went on to insist, the Church should remain uncommitted on matters where the fact has not yet been, but might be thus established. Such a matter, he urged, was the Copernican hypothesis . �21 Two ieomments. Galileo here assumed that faith and natural philosophy do not and cannot conflict. This seemed to him obvious. For us today, it can be a more difficult question. Secondly, Galileo identified strict science with truths established by observation or by demonstration.25 By observation, for instance, he had established that the Moon is mountainous. The propositions of Euclid had been established by demonstration from premisses which he took to be indubitable. In the case of the Copernican hypothesis, he knew of no indubitable premisses from which it could be derived. Thus in arguing from the tides, Galileo argued exsuppositione, presupposing the Earth's motion. The explanation could become an established truth only if all possible alternatives were disproved. In his Dialogue of 1632 Galileo has Salviati say: "We have established the impossibility of explaining the motions observed in the tides while simultaneously maintaining the immobility of the containing vessel. "26 That is a claim to have excluded the alternatives. Evidently Galileo underestimated the difficulty of doing that. ""Exclusion of all alternatives, in any ultimate sense, is probably impossible. But the point I want to make is that Galileo did not articulate a practicable methodology for the new science. In December 1615, against the advice of the Tuscan ambassador, Galileo went to Rome to try to clear his name of the suspicion of heresy and to campaign against the suppression of the Copernican theory. He was an ardent campaigner. One Roman witness reported in January 1616: He discourses often amid fift~en or twenty guests who make hot assaults upon him, now in one house, now in another. �22 , Monday... he achieved wonderful feats; and what I like most was that, before answering the opposing reasons, he amplified them and fortified them himself With new grounds which appeared invincible, so that, in demolishing them subsequently, he made his oppo!!ents look all the more ridiculous.2 7 His efforts were to no avail. On 24 February 1616, theological consultants appointed by the Holy Office to assess Galileo's Copernicanism reported to the Pope as follows (Exhibit J:) Propositions to be assessed: (1) The Sun is the center of the world and completely devoid of local I motion. Assessment: All said that this proposition is foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture, according to the literal meaning of the words and according to the common interpretation and understanding of the Holy Fathers and the doctors of theology. (2) The Earth is not the center of the world, nor motionless~ but moves as a whole and also with diurnal motion. Assessment: All said that this proposition receives the same judgment in philosophy and that in regard to theological truth it is at least erroneous in faith.28 On the following day, 25 February, (see Exhibit K:) His Holiness [the Pope) ordered the most illustrious Lord Cardinal Bellarmine to call Galileo before himself and warn him to abandon these �23 opinions; illld if he should refuse to obey, the Father Commissary, in the presence of a notary and witnesses, is to issue him an injunction to abstain completely from teaching or defending this doctrine and opinion or from discussing it; and further, if he should not acquiesce, he is to be imprisoned.2 9 On 26 Februruy, (see Exhibit L:) At the palace of... the said Most Illustrious Lord Cardinal Bellarmine, ... and in the presence of the Reverend Father Michelangelo Segizzi, ... , Commissary of the Holy Office, having summoned the above-mentioned Galileo before himself, the same Most Illustrious Lord Cardinal warned Galileo that the above-mentioned opinion was erro~eous and that he should abandon it; and thereafter, indeed immediately, ... , the aforesaid Father Commissary, in the name of His Holiness the Pope and the whole Congregation of the Holy Office, ordered and enjoined the said Galileo, who was himself still present, to abandon completely the above-mentioned opinion that the Sun stands still at the center of the world and the Earth moves, and henceforth not to hold, teach, or defend it in any way whatever, either orally or in writing, otherwise the Holy Office would start proceedings against him. The same Galileo acquiesced in this injunction and promised to obey~3o According to the Pope's command, please recall, an injunction was to be imposed only if Galileo refused to obey the initial order to abandon his erroneous opinions. There is no evidence that Galileo refused, so the injunction would appear to be illegal. Another suspicious circum st ance is that �24 it is not signed, as injunctions usually were. Is the document a forgery, as some scholars have supposed? Or does its remaining unsigned mean that Bellarmine and Segizzi were at loggerheads? Bellannine was chief theological adviser to the Pope, and a Jesuit; Segizzi, head of the Inquisition, was a Dominican. The Dominicans had for centuries had charge, not only of the Inquisition, but of all questions relating to theological orthodoxy. Segizzi can have been jealous of Bellarrnine, or suspected him of leniency in the Galileo matter. Bellarmine may have refused to sign the document, or told Galileo to ignore it as illegal. We do not know. The rumor circulated that Galileo had been forced to abjure, that is, to renounce under oath his Copernicanisrn, and had been given salutary penances. In May Galileo asked, and received from Bellannine, a certificate denying theis rumor. It asserted (Exhibit M) that he has only been notified of the declaration made by the Holy Father and published by the Sacred Congregation of the Index, whose content is that the doctrine attributed to Copernicus ... is contrary to Holy Scripture and therefore cannot be defended or held .... I This certificate was signed by Bellarmine and given to Galileo. To say with Bellarmine that the Copernican doctrine could not be defended or held, was not t6 say with Segizzi that it could not be taught or discussed in any way . whatever. In the schools, heretical doctrines were commonly discussed, even debated, in order that they might be understood. In 1623 Maffeo Barbalini, an educated Florentine and a friend and admirer of Galileo, became Pope Urban VIII. The event was hailed as the dawn �25 of a new, liberal-minded regime. In the spring of 1624 Galileo went to Rome, and obtained the pope's permission to write a dialogue on the two systems of the world, Ptolemaic and Copernican, geostatlc and geokinetic. Urban did not fear that Copernicanism would be proven true. Though we might be unable to ~ account for the tides except on the geokinetic theory, God, be;ng omnipotent, could bring them about in a different way. Galileo, Urban ordered, should feature this argument in his dialogue. In non-theological language, it says that our explanations are always hypothetical. An ambiguity, let me say, lurks in this word "hypothesis." Its accepted meaning, in Galileo's day, was instrumentalist. A hypothesis was a likely stocy, useful for prediction, but Without further claim to truth. It was mere hypothesis. Much astronomical theory in that day cannot be viewed otherWise. But a hypothesis can have a different meaning, which I shall call fallibilist. The fallibilist does not know the ultimate truth of his hypothesis, but he pursues it as possibly revealing a piece of the system of the world. In support of this hope, or faith, he looks to the logical economy of the hypothesis, its aesthetic aptness, the reach of its pragmatic success. I suspect that to Galileo the initial appeal of the Copernican arrangement was a fallibilist appeal. But in Galileo's basic, Aristotelian conception of science, science consisted of empirical facts together with necessary demonstrations. Such a conception was inadequate to the needs of the new science. Well, Galileo set about wrtting his dialogue. He was now 60. For 20 years arthritic attacks had kept him in bed for days at a time; progress was slow. The MS was at last completed toward the end of 1629. It included a new argument �27 accounted for except on a geokinetic theory. Argument exsuppositi.one, with the alternatives dismissed .. The third interlocutor, Sagredo, is the eager listener, intent on SaJViati's argument, anticipating its conclusions, objecting in order to elicit clartfication. A keen observer of natural effects, he is excited by the explanatory possibilities of the heliocentric hypothesis. Mustn't Galileo have shared this openness to learning that he describes so charmingly in Sagredo? From the beginning, unfavorable comments about the Dialogue circulated in Rome. And now the injunction of 1616 was brought forth from the Inquisition archives, and the Pope was infonned of its content. Just at this juncture, in the spring of 1632, Urban VIII was facing an international crisis of gigantic proportions. For 8 years he had pursued balance-of-power politics in alliance with Cardinal Richilieu in France, and in accommodation of the Protestants in Germany. Now Gustavus Adolphus, the Swedish Protestant general, had invaded Bavaria, the center ofGerman Catholicism, and had sacked the Jesuit Colleges there. Urban had~to realign the papacy with the Spanish Hapsburgs. Meanwhile. the Spanish cardinals were charging Urban with leniency in the fight against heresy; he was threatened with impeachment unless he took a more forceful stand.31 To the pope 1 thus pressured, Galileo's failure to inform him of the injunction was treachery in his own backyard. He was outraged. In the summer of 1632, sales of Galileo's Dial.ague were stopped in the papal states, and all copies were confiscated. A specially appointed cornm.1ss.ioQ examined the book and concluded that Galileo had Violated the injunction. �28 The Tuscq.n government, of which Galileo was an employee, attempted to forestall a trial, without success. The first interrogation took place on 12 April 1633. Asked about the events in 1616, Galileo stated that he had been given an oral warning by Cardinal Bellannine that the Earth's motion could neither be held nor defended, but only discussed hypothetically. He denied having received a special injunction prohibiting him from discussing this motion in any way whatsoever; as evidence for this, he produced Bellarmine's certificate. He denied that his Dialogue held or defended the Earth's motion; rather, it showed that the arguments for it were not conclusive. Bellarmine and Segizzi were dead; Galileo was the sole survivmg Witness of the events of26 February 1616. The strongest charge, of disobedience to a papally imposed injunction, was fatally weakened. But, Urban insisted, a sentence there must be. In a prtvate conference, Maculano. now Commissary of the Holy Office and chief judge in the trial, persuaded Galileo to plead guilty to a lesser charge, promising in return a light sentence. Galileo re-read his Dialogue, and deposed as follows on 30 AprtI (see Exhibit N): I freely confess that [my book} appeared to me in several places to be written in such a way that a reader, not aware of my intention, would have had reason to form the opinion that the arguments for the false side, which I intended to confute, were so stated as to be capable of convincing because Q\,theii: strength, rather than being easy to answer .... s2 Galileo's excuse for having given this impression was that he was more desirous of gloi:y than was suitable; he wanted to appear clever: �29 My error then was, and I freely confess it, one of vain ambition, pure ignorance, and inadvertence.33 In confessing to ambition and a desire to appear clever, Galileo, I believe, was honest. He was a proud man, product of a Florentine tradition of gentility, culture, and independent thought that went back to the 15th century, before the age of despotism and excessive bowing and scraping. But had he really intended to make the arguments for Copernicanism appear weak, as he claimed? That claim was disingenuous. What else could he have said? In his letter to the Grand Duchess Christina he had written (see Exhibit 0): ... to command that the very professors. of astronomy themselves see to the refutation of their own observations and proofs as mere fallacies and sophisms is to enjoin something that lies beyond any possibility of accomplishment ..• .Before this could be done they would have to be taught how to make one mental faculty command,. another, and the inferior powers the superior, so that the imagination and the will might be forced to believe the opposite of what the intellect understands.34 The Pope was not satisfied. He ordered that Galileo be interrogated under the formal threat of torture in order to determine his intention, a standard procedure. Whatever the outcome, he was to abjure publicly, to be held under arrest at the Inquisition's pleasure, and his book was to be banned. On 21 June the interrogation was carried out, Galileo maintaining the innoce11Qe Qf �30 his intention. On the following day he was read the sentence, and he recited the formal abjuration. So Gallieo lost the battle. His writings were instrumental in winning the war. Not, to be sure, in the papal states, where natural science sputtered to a stop, but elsewhere in Europe, where Galileo's Dialogue appeared in Latin and in English, and his last work, The Two New Sciences, also appeared. The problems of inertial motion that GaWeo had posed within a pre-inertial framework were solved Within an inertial framework by Huygens, Newton, and others. Newton, who had read the Dial.ogue, says that Galileo discovered the law of free fall and the parabolic path of projectiles by applying Newton's first two laws of motion: an impossible feat of anachronism, but science was hastening on and leaving its history behind. In articulating his Rules of Philosophizing, Newton quoted a line from the Dialogue that Galileo had given in Latin and attrtbuted to Aristotle:jrustra .fit per plura quod potestfieri per pauctora ("in vain is that done with many that can be accomplished with fewer").35 It was a ""slogan enjoining logical economy. To Galileo, logical economy was a hopeful clue to hidden system. By late 1684, Newton, applying the slogan, had reached the result that the solar system's center of gravity was not at the Sun's center but near it. He had, he claimed, "'proved the Copernican system aprioii." It was more than a determined sceptic would grant. But the hypothesis was showing its power, prepartng for a pragmatic success that would leave its rtvals in the shade. The science that Galileo initiated by showmg that we can be in motion without knowing it has flourtshed. Generalized and formalized in successive steps by Newton, by �31 Lagrange, 'by Einstein, its fruitfulness has not yet been exhausted. Notes 1. Fram Viviani's Racconto istorico della vita di Galileo Galilei, as quoted by E.A. Moody, "Galileo and Avempace," Joumaljor the History of Ideas, XII (1951), p.167 n.8. 2. I.E. Drabkin and Stillman Drake, Gallileo Galilei On Motion and On Mechanics (University of Wisconsin Press, 1960), 3-131. 3. Aristotle, Physics N, ch.8, 215a24-216a20. 4. De Caelo, 309bl4-16. 5. "Artstotle," says Galileo, "makes this sanie assumption in his solution of the 24th Mechanical Problem." See Pseudo-Aristotle, MechanicalProblems, 855b3436. 6. Galileo Galilei, Two New Sciences (tr. Stillman Drake; Univ. of Wisconsin · Press, 1974), pp.158-59 (Ed. Naz., VIII, p.202). 7. In his early treatise on motion (see Galileo Galilei On Motion and On Mechanics, University of Wisconsin Press, 1960, p .50), Galileo says: �32 The method that we shall follow in this treatise will be always to make what is said depend on what was said before, and, if possible, never to assume as true that which requires proof. My teachers of mathematics taught me this method. But it is not adhered to sufficiently by certain philosophers who frequently, when they expound the elements of physics, make assurnptions that are the same as those handed down in [Aristotle's] books On the &ml or those On the Heaven, and even in the Metaphysics. And not only this, but even in expounding logic itself they continually repeat things that were set forth in the last books of Aristotle. That is, in teaching their pupils the very first subjects they assume that the pupils know eveiything, and they pass on to them their teaching, not on the basis of things that the pupils know, but on the basis of what is completely unknown and unheard of. The result is that those who learn in this way never know anything by its causes, but merely have opinions based on belief, that is, because this is what Artstotle said. And few of them inqutre whether what Aristotle said is true. 8. William A. Wallace, Galileo and his Sources: the Heritage qfthe Collegio Romano in Galileo's Science (Princeton, N.J.: Prtnceton University Press, 1984-) 9. See Stillman Drake & I.E. Drabkin, Mechanics in Sixteenth-Century Italy (University of Wisconsin Press, 1969), pp.204-206. �33 10. See Galjleo Galilei On Motion and On Mechanics, 173-75. 11. Le Ope re di Galileo Galllet, X, 115. 12. Ibid., VI!!, 373-4. 13. Galileo , Dialogue Concerning the Two Chief World Systems (tr. Stillman Drake; University of California Press, 1962), p.229; Ed. Naz., VII, pp.255-56. 14. Alexandre Koyre was a prominent proponent of the platonist Galileo; see his Etudes Galileennes (Paris: Hermann, 1939); Metaphysics and Measurement (Harvard, 1968), Chapters I-IV. Thomas Settle showed in 1961 that Galileo's inclined plane expertment could be performed With remarkable precision, using only means that would have been available to Galileo: see Thomas B . Settle, "'An Experiment in the History of Science," Science, Vol.133 (1961), 19-23. Next, Stillman Drake took up the empiricist lheme, and in 1973 published an article in Scientific American (May, 1973, pp.85-92) on "Galileo's Discovery of the Law of Free Fall." Unfortunately his enthusiasm and imagination got out of hand, and his reconstruction here (as in some other cases) cannot be sustained. 15. I am chiefly dependent here on R.H. Naylor, "Galileo's Theory of Projectile Motion," Isis 71 (1980) , 550-70, and David K. Hill, "Dissecting Trajectories," lsiS 79 (1988), 646-68. �34 16. Quoted from Maurice A. Finocchiaro, The Galileo Affair: a Documentary History (University of California Press, 1989), p.50. 17. Stillman Drake, Galileo at Work (Chicago: University of Chicago Press, 1978), pp.168-69. 18. Stillman Drake , Galileo: Pioneer Scientist (University of Toronto Press, 1990), pp.145-55, mistakenly characterizes this as compelling evidence for the Earth's annual motion about the Sun. 19. See GalUeo Galllel On Motion and On Mechanics, pp. 72-74; Stillman Drake, "The Evolution of De Motu," Isis 67 (1976), 245 20. Galileo Galilei On Motion and On Mechanics, 171. 21. Galileo, Opere (Ed.Naz.), Vol.IO, p .68. 22. Like Kepler, however, Galileo entertained the idea, "as not entirely unphilosophical," that the motion of the planets had its cause in the rotating Sun; see his "Letter to the Grand Duchess Christina" in Stillman Drake (tr.), Discoveries and Opinions of Galileo (Doubleday Anchor Books, 1957), pp.212-13 . 23. I am indebted here to a recent study by Paolo Palmieri, "Re-examining �35 Galileo's Tpeory of Tides," Archlvefor History of Exact Sciences, Vol.53 (1998), 223-375. 24. :rv1aurice A. Finocchiaro, GaJ.ileo on the World Systems (University of Cal1foµi1a Press. 1997), 304; Galileo, Dialogue Concerning the Two Chief World Systems (tr. Stillman Drake}, 462. 25. See Ernan McMullin, "The Conception of Science in Galileo's Work," in Robert E. Butts and Joseph C. Pitt (eds.), New Perspectives on Galileo (D. Reidel Publishing Co., 1978), pp.209-57. 26. Finocchiaro, tr., Galileo on the V./orld Systems, 288. 27. See Giorgio Di Santillana, The Crime of Galileo, pp.112-13. 28. Maurice A. Finocchiaro, The Galileo AjJa7r: A Documentary History, 146. 29. Ibid., 147. 30. Ibid., 147-48. 31. See Pietro Redondl, Galileo Heretic (tr. Raymond Rosenthal; Princeton University Press, 1987), pp.228-33. Redondi's larger thesis that there was a hidden agenda in the Galileo trial, pertaining to Galileo's atomism and its �36 relation to the Eucharist, has not been accepted by other scholars. 32. Finocchiaro, op.cit., p.278. 33. Ibid. 34. Stillman Drake, Discoveries and Opinions Q[Galileo, 193. 35. Galileo, Dialogue Concerning the Two Chief World Systems {tr. Stilln1an Drake, University of California Press, 1962), 123. �Addend um to p. 11: the calculations of folio l l 6v. Upper Middle: H 1 = 600, H 2 = 300, D22 = 800 x 800. DI -' ~ 800 • 800 • 600 300 Lower Left: H 1 D = 800 • 800 • 800 ) 300 I Upper = 800, H2 = ,,/ 12BOOOO = I 131 = 300, D22 = 800 x 800. = ,,/ l70666fJ R_ight: H 1 = 828, H 2 = 300, D 2 2 I soo • 800 • 828 '"/ 300 = 1306 = 800 x 800. = ,,/ 1766400 = 1329 Lower Middle with numbers to Right: H 1 D, = ; v soo •soo • 1000 300 = ,,/2133333 = = 1000, H 2 = 300, D 2 2 = 800 x800. 1460 �Handout for "Galileo Agonistes" Exhibit A: {Galileo's demonstration at the Leaning Tower of Pisa was designed to show] that the speeds of mobile bodies of the same material [emphasis added] but of unequal weight, moving through the same medium, are not in the ratio of their absolute weights, as Aristotle claimed, but they move with equal speed•.• ; and neither do the speeds of a given mobile body, moving through diverse mediums, have the inverse ratio of the resistances, or densities of these mediums ... (From Viviani's Racconto tstorlco della vtta di Galileo Galilet, as translated by E.A.Moody, "Galileo andAvempace," Joumalforthe History of Ideas, XII (1951), p.167n.8] Exhibit B: Aristotle's Rule of Speeds in Different Mediums Let VA• V8 be the body's speeds in mediums A and B; and let RA, R 8 be the resistances in those mediums. Then according to Aristotle V A:Ve :: Re:RA. Suppose RA - 0. Then the ratio Ra:RAbecomes infinite, and so must VA:V8 • Therefore VA - eo, which is impossible. [Cf. Aristotle, Physics, 215a29-216a8.] Exhibit C: Equilibration ofWei®ts on Inclined Planes W 1 , lying on CA, and connected with the vertically hanging weight W2 , is in equilibrium with W 2 if, and only if, W1 : W2 :: CA: CB. [See Galileo, OnMechanlcs f..\ (tr.Stillman Drake; University of Wisconsin Press, 1960), 173-75.] Exhibit D: Galileo's Letter to Sarpi, October 1604 Thinking over the questions about motion, in which, to demonstrate the accidents observed by me. I have been .Jacking a totally indubitable principle that I could take as axiom, I am reduced to a proposition which has much that is natural and evident about it; and this being supposed. I demonstrate the rest, that is, that the spaces traversed in natural motion are as the squares of the times. and consequently the spaces traversed in equal times ~e as the odd numbers starting with unity... And the principle is this: that the mobile body goes increasing its speed in proportion to its distance from its starting point... Please consf dcr it and tell me your opinion. B �Exhibit G: Essential details of folio l 16v [From David K. Hill. "Dissecting Trajectories," Isis 79( 1988), 646-68; p.663.1 1100 100 I I 3 I .. UIOOOO ·~·· : - l•IO •o , 1321 1172 1330 1301 10 22 ISOO 1131 .., IOO 'llOll THI flllST CAH SHOIJU) 11 Dl,,llllNCI 300 121 ~ 30 2201 JOO HUOO 10 10 1100 ~ · ·30 10 220I 100 i""'iZ'i ~' .J111uoo 300 1•ooo'l 300 IOO . ___JgQ .. , JIU ::=-·,300•~ _ _ __ .'.- 300 JIU 100 1000 _JM JUI 300 100000 1"T"Oi "'701•00 11•0 120 ,-;-s vUUIOO ..... ...... ...... Exhibit H: "Acceleration" in Galileo's theory of the tides .AFGI =Earth's annual orbit BCDL = the Earth B -- -·- ..r··-, . c·· G �Exhibit M: Bellarmine's Certificate of 26 May 1616 We. Robert Cardinal Bellannine. have heard that Sig. Galileo Galilei Is being slandered or alleged to have abjured In our hands and also to have been given salutary penances for this. Having been sought about the truth or the matter. we say that the abovementioned Galileo has not abjured in our hands, or in the hands of others here in Rome, or anywhere else that we know, any opinion or doctrine of his; nor has he received any penances, salutary or otherwise. On the contrary, he had only been notified of the declaration made by the Holy Father and published by the Sacred Congregation of the Index, whose content is that the doctrine attributed to Copericus (that the Earth moves around the Sun and the Sun stands at tbe center of th~ tv1>rlf'J ~thout moving from cast to west) is contrary to Holy Scripture and therefore cannot be defended or held. In witness whereof we have written and signed this with our own hands, on this 26th day os May 1616. [Finocchiaro. op.cit., 153) Exhibit N: Galileo's confession I freely confess that [my book] appeared to me in several places to be written in such a way that a reader, not aware of my intention, would have had reason to form the opinion that the arguments for the false side, which I intended to confute, were so stated as to be capable oC convincing because of their strength~ rather than being easy to answer .... My error then was, and I freely confess it, one or ¥.ii.ii Ci.ilib1tl<m, pure ignorance, and inadvertence. [Finocchiaro, op.cit., 278 J Exhibit 0: From the letter to the Grand Duchess Christina: ... to command that the very professors or astronomy them.selves see to the refutation of their own observations and proofs as mere fallacies and sophisms is to enjoin something that lies beyond any possibility or accompllshm.eut .... Defore this could be done they would have to be taught haw to make one mental faculty command aaothec, &Id the inferiot powers the superior, so that the imagination and the will might be forced to believe the opposite of what the intellect understands. (Stillman Drake, Discoveriesand Opinions of Galileo, p.278) � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. 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Type The nature or genre of the resource text Format The file format, physical medium, or dimensions of the resource pdf Language A language of the resource English Identifier An unambiguous reference to the resource within a given context lec Wilson 1999-10-01 Relation A related resource <a title="Sound recording" href="http://digitalarchives.sjc.edu/items/show/3666">Sound recording</a> Deans Friday night lecture Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/7ec97439251554bf03cf696c54146279.pdf c7cc897d5704aa0c9cc7922fd62d2e5f PDF Text Text 1 Dynamical Chaos: Some Implications of a Recent Discovery Curtis Wilson My subject is a peculiar behavior of dynamical systems that has come to be recognized only during the last thirty years. In 1975 James Yorke christened this behavior chaos - perhaps a misnomer. Chaos is a Greek word that has no plural. Since Hesiod it has meant the nether abyss, the first state of the universe, or total disorder. The dynamical behavior that James Yorke called chaos is order and apparent randomness intertwined. A dynamical system is - what? How about this? - a set of entities that interact so as to undergo a development. The entities could be planets or billiard balls; maybe cardiac muscle fibers or neurons. Maybe even bidders on the New York Stock Exchange; but let that go. In my illustrations this evening, the components will be chunks of matter, unbesouled. To understand why dynamical chaos was recognized only recently takes a bit of mathematical background. Mathematically, . dynamical systems are represented by differential equations. Differential equations are distinguished by containing instantaneous rates of change, velocities, say, or accelerations. Now empirically you can't measure an instantaneous rate of change, but only changes over f_init~ differential equation, therefore, intervals of time . A is a hypothesis. To verify the hypothesis you must first §Olve the equation, or integrate it. That means, you must somehow .eliminate the rate or rates of change, and obtain the value of the dependent variable - which is �2 what you are interested in - as · a function of th~ independent variable, which is usually time. Thus you will have a relation you can check empirically. Procedures for solving a good many differential equations were worked out in the 17th and 18th centuries. The solutions turn on what is called the fundamental theorem of the calculus, discovered by Newton and Leibniz. The procedures, like the differential equations, assume that time is continuous. Not all differential equations are thus soluble "analytically," as we say. It may be impossible to disentangle the dependent variable from its rate of change, or, if there is more than one dependent variable, to disentangle these variables from one another. Then you can't arrive at a formula giving each variable as a function of the time. All linear differential equation s are soluble. In these equations, the dependent variables and their rates of change occur only to the first power, and don't multiply one another. An equation in just two variables occurring only to the first power can be graphed as a straight line; hence the name linear. But there are non-linear differential equations, in .which some of the dependent variables, or their rates of change, are raised to powers, or multiply one another. Some of these equations are analytically insoluble. In fact, most dynamical systems in the world can be modeled accurately only by non-linear differential equations, most of which are insoluble. It is dynamical systems modeled by such �3 differential equations, non-linear and insoluble, that exhibit the behavior that James Yorke called chaos. Here a small change in the independent variable can produce a sudden large change in a dependent variable. Such phenomena, we're told, nature; for instance, flourish in in the dripping of a faucet. How can insoluble differential equations be studied? The chief way is by what is called numerical integration. This differs from the analytical integration I previously spoke of, which relies on the fundamental theorem of the calculus. In numerical integration the independent variable is not varied continuously; instead, it is increased by finite jumps. Starting with certain initial values of the variables, numerical integration assumes that the initial rate of change remains constant for some small, finite interval, say a second, and on that assumption computes the values of all the variables at the end of the second. Then with the new values it goes on to compute the values of all the variables at the end of the second interval. And so on . The procedure is not strictly accurate. But if the intervals are made small enough, of what is going on; it can even, it can give a good idea in many cases, be made to yield predictions as accurate as the observations. The first large-scale numerical integration ever performed was carried out in 1758, to compute the return date of Halley's Comet. It took 6 months' work by three people, morning, noon, and night. Their final prediction was a month off, and even then they were lucky, because their computation contained some partially �4 compensating errors. Recognition of the chaos named by James Yorke came only in the decades since 1960, with the development of highspeed electronic computers that could carry out numerical integrations no one had previously thought practical. I am going now to illustrate this kind of dynamical chaos, and to talk about some of its characteristics. My interest in this subject arose because for some years I have been pursuing the question of how planetary astronomy became a precise predictive science, and since 1980 it has become apparent that planetary astronomy involves James Yorke's chaos. This chaos limits predictibility. Philosophers, I suspect, should learn about it. New perspectives open up if we recognize how widespread it is. More on this later. I begin with the simple pendulum. It consists of a heavy bob, suspended by a weightless, inextensible thread - mathematical physicists love to invoke such things. If we draw the bob aside and let it go~ it oscillates back and forth. On one side of the handout, I have derived its equation of motion, and shown it to be nonlinear. I'll repeat the argument now. We measure e, the departure of the thread from the vertical, in radians, defined as arc-length divided by radius. So the arclength will be given by the radius-arm, or length of the thread, here l, times 0. In the science of dynamics as founded by Galileo and Newton, we are interested in accelerations, that is, rates of change of velocity; velocity itself being a rate of change of \ \ �5 position. Acceleration is thus a rate of change of a rate of change. In our case, we are interested in the acceleration of the bob, hence of its position as measured by the arc 1·0. But 1 is a constant; so the acceleration we are interested in is 1 times the acceleration of 0, which I write as theta with two over-dots, 0. The reason the bob accelerates is that it is pulled downward by gravity. The acceleration of gravity at a given spot on the Earth is a constant, which we call g . But the bob can't go straight down, with the acceleration g, because it is suspended by the thread. To find ho w much of g accelerates the bob along its path, we " resolve" g into components , one in line with the thread - this component merely tenses the thread - and the other component at right angles, along the path. In the handout I explain that the latter component is g·sin 0. Our equation is then e-ll·sin0, - 1 where, remember, the double over-dot means acceleration, radians per second per second . I say that this equation is nonlinear. Sin 0 ls given by an infinite series - I won't prove this, please take it on faith: e - e3 3! + e5 5! If only the first term were present , we would have a linear equation. But there are higher powers, going on forever. Now it turns out that this nonlinear equation is soluble. I �6 won't write down the solution, which is somewhat complicated. It implies that the pendulum is not isochronous: wider-angled swings take a little longer. Galileo, gazing at the suspended lamps in the Cathedral of Pisa, guessed the pendulum was isochronous, and wanted so much to believe this, that he never made the simple experiments that would have shown the assumption false. Of course, the simple pendulum is approximately isochronous, for small-angled swings. Suppose that 0 is 6°, about 1/10 of a radian . In the series expansion for the sine, if the first term is 1/10, the second term is 1/6000 . We can choose to ignore it, along with all the higher terms . That is called linearizing the equation. Mathematical physicists have been doing it for nearly 300 years, in order to obtain neat, soluble equations. The hope is always that the linearized equations give good enough approximations. And so they do, when the system is close enough to a stable equilibrium. Suppose, then, we limit our simple pendulum to swings of 6° or less . The effects of nonlinearity will be present, but tiny. And now let us introduce a perturbation. When the word perturbation is used, we mean that there is some motion we can regard as fundamental, and some other disturbing motion that is superimposed . The Earth's motion is controlled primarily by the gravitational action of the Sun, but it is perturbed detectably by the Moon, Venus, Jupiter, Saturn, and so on. Suppose the point of suspension of our pendulum is put into a small oscillation, in the very plane in which we first set the �7 bob to oscillating . We could use a crank mechanism for this. Let the amplitude of this perturbing motion be a small fraction of the length of the pendulum. Let the period of the forcing motion be one we can vary; call it T. And suppose we set T to be somewhere near the period of our linearized simple pendulum, which I shall call To. To is given by a formula some of you have learned, 2 n: times the square root of 1 over g. T; =- :ur -- -- fy . f The equation of motion for the new set-up, which I won't write down , is not soluble analytically; it won't yield a formula for 0 as a function of time. But a numerical integration can be carried out . John Miles of UCSD did this in 1984, to determine the position of the bob each time the perturbing motion reaches the righthand end of its range . Starting from below T0 , he increased the period T of the perturbing motion. At a certain point, the motion of the bob, in its original direction of motion, which I ' ll call the x-direction, became unstable . But meanwhile there were two possible motions that were stable motions that included a sideways component, a y-component. The motion of the bob made a gradual transition to one or the other of these stable motions. When T = 0.9924 T0 , the position of the bob each time the perturbing motion comes to the righthand limit of its excursion moves in this figure (Figure 1) . You probably want to know what the whole motion of the bob is . It is in a slowly rotating ellipse wi th slowly varying a xes . But let me focus solely on the position of the bob each time �4y/} 0 ·2.~ -2.~ 0 0 4x/i T = 0.9924 To �8 the perturbing motion reaches the righthand end of its range. If Tis 1.0150 T0 , our point moves in a doubled curve (Figure 2); what is called a bifurcation has occurred. A small quantitative change has produced a sharp qualitative change. Let the period be increased so that Tis 1.0213 T0 (Figure 3); another bifurcation has occurred. A cascade of further bifurcations occurs, as T is increased. When we reach T = 1.0225 T 0 (Figure 4), the figure appears smudged, with many paths close together. The pattern, if accumulated over a long enough time, appears to be symmetric with respect to the x-axis, although the bob may spend substantial intervals in either the top or bottom half of this pattern, transferring from one to the other at seemingly random times. Random is - what? The word comes from old French randir, to run or gallop; the French knight, having donned his armor, and drunk certain flagons of wine, was hoisted by crane onto his horse and galloped about the field, doing random mayhem. The Anglo-Saxon, by contrast, wore bearskin, drank mead, and on the battlefield went berserk, a word meaning bearskin. To define random mathematically, is something else again. Perhaps we can say what it is not. If our pattern were two or more periodic motions superimposed, it would be what is called quasiperiodic; if the periodic motions were incommensurable, there would be no exact repetitions, but the motion would not be random or chaotic. But our motion doesn't look quasi-periodic, with those sudden shifts from one part of the pattern to another. Let's turn to an actual physical experiment. Al Toft, �4y/~ 0 -2.s----~--------------------------._J 2.~ 0 -z., 4x/_,f T = 1. 0150 T 0 �z.~ 4y/J. 0 -2.~------------__.-----------~~ 2.S 0 .. z., 4x/ _e T = 1. 021J To �4y/J. 0 -~5'----~~~~---A~~~~~~-- .. ,~ Z.5 0 4x/J T = 1.0225 T0 �9 assisted by Otto Friedrich - machinist and carpenter for the laboratory - made this pair of double pendulums in tandem, in accordance with a description given in the American Journal of Physics in 1992. Each double pendulum consists of an upper and lower part, turning on bearings, so that the friction is small. Each part of each double pendulum, both the upper and the lower, has its own natural period for small-angle oscillations. The situation for the lower pendulum is similar to that of the perturbed simple pendulum I previously described. But now the perturber (the upper part) is itself significantly perturbed; we have what is called feedback, circular causation. The two double pendulums are identical twins. They are mounted together on a sturdy support, so that neither will influence the other. If I start one of them in an oscillation, the other does not pick up the motion. If I start both together in a small oscillation, they play together nicely. Now let's try a large initial displacement. The pendulums don't stay together. Nor, if we try the experiment over again, does either do exactly what it did the first time. I hope this surprises you. Before trying to account for it, let's see how we might show quantitatively that the repetition isn't exact. We could use a rigidly mounted electromagnet to hold the pendulum in a fixed initial position, to the side. Suppose the switch releasing the pendulum started a stroboscopic flash camera, that took photos every 25th of a second. On each exposure we could measure the angular deviations from the vertical of the upper and �10 lower parts. Then we could proceed to compare different trials. This has actually been done. In explaining this, I shall introduce a bit of the relevant mathematics. Take a look, for just a moment, at the differential equations of the double pendulum (Figure 5). On the lefthand .. side, on top, you see 0,, the angular acceleration of 0,, which is the deviation of the upper pendulum from the vertical. And .. below, on the lefthand side of the second equation, you see 0 2 , the angular acceleration of 0 2 , the deviation of the lower pendulum from the vertical. On the righthand sides you see a number of constants: g, and 1 2 , the lengths of the two parts of the pendulum; µ, 1, the ratio of their masses. Also involved are sines and cosines of the two angles, and also of their difference, . ~0; these are . variables. And two more variables are 0, (over-dot) and 0 2 (overdot), the momentary angular velocities of the upper and lower parts of the pendulum. Both 0, thus depend on four variables, .. (double-dot) and 0 2 (double-dot) e, and 621 . e, . (dot) and 82 {dot). The two equations a r e not soluble; we can't get separate formulas for the two angles, as functions of time. But our system at any moment depends on the four variables 0,, 0 2 , . . 0,, and 0 2 • In the 1830s William Rowan Hamilton proposed representing the evolution of such a system in a hyperspace, with a number of dimensions equal to the number of variables on which the state of the system depends. Then a point in this space would correspond to a momentary state of the system, and a succession of points, �......... ~ <l .......... ·- c: ,,..,... ( /) ......... ~ <l .......... (/) 8 ,....._ o~ - ,..... ,,..,... ....... + ,..-.... ......... ~ MN <l od';) ~ No~ <l '--' '-' M N (/) (/) 0 0 0 0 I I. ..:;, ~ ~ c: c: ·- ·- V'J ..._,., ~ V'J ~ \\ II ~~ :~ - ,.... �11 or trajectory, would show how the system develops. The space is called phase space. In our case, the space is 4-dimensional, and you can't visualize it. You can nevertheless conceive it without contradiction. In the 1890s Henri Poincare undertook to study insoluble, nonlinear differential equations, by examining the ensemble of possible trajectories in phase space. In our case, let's consider a few trial runs with our double pendulum, say four, and compare the points in phase space at the successive moments when the photographs are taken. For a given moment, the points in the four different trials will not be the same. There will be a "distance'' between any two of them, and we can get numbers for these distances, using the 4-dimensional analogue of the Pythagorean theorem; that is, we take the square root of the sum of the squares of the components. In this figure (Figure 6), the experimental separations are plotted for the first half second. The solid line was obtained by numerical integration of the differential equations, using two slightly different sets of initial conditions. The separations increase on the whole. That the separations have downswings at certain places is due to the fact that, at the end of each swing, when the lower pendulum is starting down again, it pulls down on the upper pendulum, and this is a relatively stable situation. A statistical study of these numbers shows that, on the average, the separation increases geometrically. Suppose the initial separation between two trajectories in phase space is ~x 0 • Then the separation at time t is �100 . ' 10 ~rltion brtween rruls 1and3 ~trials 2 .1nd 3 • o x 0.0 0.1 01 ~~hon ~ 0 o - stp.au1tion ~ration~ tri.lls 1 and 4 trids 2 and 4 ~pu11tion ~ttn trUls J and 4 s.ep.aration bnwttn n~l h'Ub OJ 0.4 05 0.6 Time (seconds) f'ig. 9. Experimental results from typical initial condition; bold curve is IWDerical result. �12 "x t - - &x0 ·eH - U I where e is a constant greater than 1, and A is a positive constant, called Lyapunov's exponent, after the Russian who first discussed its import. The separation doesn't just increase by the same additive increment in each unit of time, but gets multiplied by the same factor, so that the increase is exponential. Of course, our data is only for the first half second. Strictly speaking, A should be determined as a limit as t goes to infinity. But you can't get funding for experiments that long. The chaos is apparent, but is it real? H6w explain it? First, however, what does a positive A do to prediction? Recently it has been shown that the long-term orbital evolutions of the inner planets, Mercury, Venus, Earth, and Mars, are characterized by positive Lyapunov exponents. For instance, certain perturbations of the Earth are in near-resonance with its annual motion, in close analogy with the case of our perturbed simple pendulum; and the same kind of chaos results. Now we never know, with infinite precision, where a planet is. By numerical integration it has been shown that initial uncertainties for the Earth increase by a factor of 3 every 5 million years. An initial error of 15 meters produces an error of 1.5 million kilometers after 100 million years. Yes, we'll all be dead, but my concern is a theoretical one, about the nature of our knowledge. Can we understand a little better what this chaos is, and whence it comes? Back to phase space and another of Poincar~'s new �13 techniques. Here (Figure 7) is the 4-dimensional phase space of our double pendulum, somehow represented in a pseudo-diagram; q 1 and q 2 are the coordinates, in our case angles, and p 1 and Pa are the corresponding momenta, products of velocity and mass. The presentation of the equations of dynamics in terms of the p's and q's is due, once more, Hamiltonian, to William Rowan Hamilton. H, called the is the energy of the system, expressed in terms of the p's and q's. We'll assume for the present argument that His a constant: H In the pseudo-diagram H is represented as a surface; but it is really a hypersurface in 4-dimensional space; the pseudovisualization is only to help you identify the terms I am using. The constancy of H will allow us to express Pa as a function of p,, q 1 , and q 2 : p 2 = p 2 (p 1 , q 1 , q 2 ) . We can thus consider the projection of any possible trajectory in the 4-dimensional phasespace onto a 3-dimensional volume. That projection will contain all the information that the 4-dimensional trajectory contained. The reduction in the number of dimensions brings us back to something visualizable. Poincare carried the process a step further. If the trajectory is bounded - doesn't go off to infinity - then its projection in the 3-dimensional space will intersect some plane in that space repeatedly, say the plane qa = 0 (Figure 8). Such a plane is called a Poincare surface of section. What sort of pattern will the intersections make? In the 1960s two astronomers, Henon and Heiles, were �H = canst ��14 studying a nonlinear differential equation intended to model the motion of a star around a galaxy. They used numerical integration to find successive intersections of the star's trajectory with a Poincare surface of section. When the energy of the system was relatively small, the intersections - lay on certain distinct curves (Figure 9). With an increase in energy, the pattern became this (Figure 10). There were still islands where , for certain initial conditions, the trajectory remained on nice curves; but other trajectories proved to be chaotic, giving seemingly randomly placed intersections. When the energy was increased still further, the islands disappeared (Figure 11). The motion is deterministic; that is, given the state of the system at any moment, the equation of motion determines its state at the moments that follow. The initial conditions determine a position and a velocity, and the equation of motion then determines an acceleration . Given position, velocity, and acceleration, there is only one way to go. But the resulting pattern looks crazy. Again I ask, How should we understand that? Consider a plane of section with the dimensions p and q; suppose the successive points of section are confined to the unit square (Figure 12). A theorem in Hamiltonian dynamics says that, if the energy of a dynamic system remains constant, the volume occupied by the allowed trajectories is also constant. But in truly chaotic dynamics, the trajectory never returns to the same point, or even to any identifiable curve . The volume of allowable paths gets dispersed, mixed up with bubbles of the unallowable . �....... ...:· ... ; ... ,... /. l • f ! •. I ( ·-- ..... .. ...... . ... .. -....... .· ...· I i• . . i -..·.+:.·.·. . '··... ,·'* I " \ ·~ ~' .... ' .. .. ' '\ \ \ 'I I I ··.:. ,. \ . . . '.. . .. .. .. ,, I .....~.: .. ,, , , '. ... . ...·' ·. ··..... \ ... . ·, . . . .-- ... .. ·\ .. .. ·.·. le , , ·.· ' ' ... ... .. ,,. I I ., Results for E =.04167 �./ -. .· .·· ...·· ,..·/ .. ,. \" // fI /. .- .. \ . .. . .... ~. ! . .:.·1 \: \ ../ \ \ ... --. ... I ..... . . • . ...·. ·.. ·. .: I \ \ \ ~-\ r··.. \\ . \. ==' -~ ·.· > . ···.,·, ··.. . .· -- ·... . ......~ . . ... ·.:.. .. .. ... --: .- -.:..; ·. . ······ .......'-··.•, I '•• : •......• • - -t ' I I ,: 0 • .... • .. ·· ..·· Results for E = .125 �. ·. . /.,./';/::..'·...·..~. r.·. .. .. . ... : ... . ;·... •! :• .... . I; .. •... -...• .. .,.. ' .. ~ .. . I .; • ·.· . \~ . ' .. . ., . .• ;·• -!A ; .... ·· . .. ·.. .. .... . ·:~:·\. ..'•. .·~ .\ :- . .. , .·.:. \ I . .- . . . .. . ·~~ ... • •:,,.r • .·· ·~. ~· '•. ·.. ··.~... .. -..... . . .. ~• :· .. . .,· .. ·.. .. ,: . ..:i "'.. . :: ' ..· / .. ... '· , ....... > .' ·. ~ ·.· ..: . • .. , :: .,. ·.·· '4 ~-·· .....·· · . I ! .... '\• :-· Results for E = .16667 �~/ �15 Some Russian mathematicians have sought to describe this mixing, using a cocktail shaker, rum and cola. Sorry, we're stuck with their noxious example. Initially, separate. After a few shakes, the rum and cola are if we imagine the cola as divided up into moderately small cells, we find some rum in each cell. Later, the subdivision can be made finer and finer, with each cell containing some rum. This is called a mixing transformation. Some dynamical systems have been proved to evolve in this way, for instance a gas consisting of spherical elastic molecules. Nearby possible trajectories necessarily spread apart, defocuss . But, because their energy is finite, they don't go off to infinity, but get folded back into the same space. The rule is Stretch and Fold. It may be characteristic of chaotic dynamics generally. For illustration, I shall present a particular mixing transformation, called the Baker's Transformation (Figure 13). You'll find a description of it on the other side of the handout. Let the square, as if it were dough, be first squashed down into a rectangle twice as long and half as high; then let the right half of it be set atop the left half. We get back a square. What happens to a point (p,q) within the square? Both p and q are numbers between 0 and 1. By the squashing, all p's are doubled; but then, by the operation of placing the right half atop the left half of the rectangle, the p's that became greater than 1 are reduced again, by subtraction of the unit 1, to numbers between 0 and 1. We can write this: p As for the q's, ~ 2p (mod 1). if our q was in the left half of the ��16 original square, it is simply halved: q ~ q/2 . If it was in the right half, after halving it we add 1/2: q ~ q/2 + 1/2. It will be helpful to think about p and q as written in binary notation, so that each p and q will be written as, first, a zero, followed by a binary point ~replacing our decimal point), followed in turn by a string of zeros and ones, infinitely long . All numbers between 0 and 1 can be written thus. 0.1 means 1/2, 0.01 means 1/4, 0.001 means 1/8, and so on. We use powers of 2 instead of powers of 10. Let our initial p and q be : p = 0 . P1P~PJ . .. q I = 0 . q lqiqJ .. . I where the letters with subscripts are zeros and ones . Now a neat thing about binary notation is that multiplying by 2 just amounts to shifting the binary point to the right, while dividing by 2 just amounts to shifting it to the left . If our initial point was in the left half of the square, then p 1 was 0, and after the squashing, the transformed p will be 0 · PiPJP4 · · · But the same result holds if our initial point was in the right half of the square, for then p 1 was 1, and after the binary point is moved to the right, 1 must be subtracted. In successive transformations p will become O.p4P s P~ ·· ., and so on. What about the q's? If our original point was in the left half of the square, 0. Oq,q~q 3 then we want the halved value of q, which is • • •• I have moved the binary point to the left one place. If our �17 original point was in the right half of the square, then q first gets halved, but we must add 1/2 when the right half of the rectangle is put atop the left half. Now, in this case p, was 1, which in the first binary place after the binary point, means 1/2. So the transformed q can be written O. p 1 q 1 q,q 3 • ••• Actually, this works for q's in the left half of the original square as well, for there p 1 was 0. A little reflection will show you that the succession of transformed q's will be 0. p,q,q, ... , 0. p 3 p,p,q,q, ... , and so on. As the successive pairs of transformed p's and q's emerge, the important digits, the digits up front, come from ever farther to the right in the original coordinate p. Initially, they looked insignificant . Yet however far to the right they were originally, they become crucial as the returns continue. The sensitivity to initial conditions is infinite. There is one more thing I want to say about the p's and q's. You perhaps know that if, after any place in the sequence of digits representing a number between zero and 1, we get a repeating pattern, going on indefinitely, then the number is expressible as a simple fraction. You can write it down exactly, without taking an infinite time to do so. There are other numbers, like; like J2/2, that you can compute to as many places as you there is an algorithm, a computational procedure, for doing so. There are even algorithms for computing ~/4, which is neither expressible as a fraction, nor even as the root of an algebraic equation. �18 All these are known as computable numbers. The algorithms for computing them can all be expressed with a finite number of mathematical symbols. The algorithm may involve some kind of infinite recursion or iteration; but this can be indicated with a single symbol, meaning, "keep doin~ it over again." So all the algorithms can be written in what we can call an alphabet, with a finite number of symbols; and we can then alphabetize them, list them in an order so that none will be left out , if we keep on going . Thus they are denumerable . Therefore computable numbers form a denumerable set. It is, however, an infinite set; every integer, for instance, has a square root, so there are an infinity of them. But there is a proof, Georg Cantor's famous diagonal proof, showing that the numbers between 0 and 1 are infinitely more numerous than a denumerable set. It follows that there are infinitely more incomputable numbers than computable ones. Our chaotic trajectories have landed us in the midst of this jungle of incomputable numbers . Suppose, though it is empirically impossible, that we knew our initial p and q exactly . The differential equation for the motion is not soluble; our only resource is numerical integration, for which we turn to a high-powered computer . The computer, however high-powered, cannot give us the chaotic trajectory precisely. That is because it is a finite-state machine. It cannot accept a number expressed by an infinite number of digits; it automatically rounds it off . With our p's and q's undergoing a mixing transformation, the rounding, after a �19 while, will be disastrous; we will lose essential information. Whether the p or the q, at some later stage in the succession of transformations, starts with a 0 or a 1 will be as uncertain as the toss of a coin. Let me now, by way of conclusion, state some thoughts as to the import of nonlinear dynamics. 1. According to Laplace, writing in 1812 (and I quote), An intelligence that knew, for a given instant, all the forces by which nature is animated, and the respective situation of all the beings that compose it, if it were vast enough to subject these data to analysis, would embrace in a single formula the motions of the largest bodies of the universe and of the smallest atom; nothing would be uncertain to it, and the future, like the past, would be present to its eyes. The human mind, in the perfection that it has been able to achieve in astronomy, presents a pale image of this intelligence. Laplace is expressing a universal determinism, which he equates with predictibility. Such a determinism, presenting the world as a closed causal network, has of ten been taken as a dogma of science; but its universalism appears to make the activity of the scientist unintelligible. Voltaire swallowed the doctrine whole: everything [he wrote] is governed by immutable laws ... everything is prearranged ... everything is a necessary effect . ... There are some people who, frightened by this �20 truth, allow half of it ... There are, they say, events which are necessary and others which are not. It would be strange if a part of what happens had to happen and another part did not .... I necessarily must have the passion to write this, and you must have the passion to condemn me; we are both equally foolish, both toys in the hand of destiny. Your nature is to do ill, mine is to love truth, and to publish it in spite of you. Post-Newtonians, impressed by the success of the new dynamics, did not consider that the new methods might prove limited in scope. The success of this dynamics was a success in solving linearized differential equations. The world was taken to be an integrable system, each variable being finally expressible as a function of time, independent of the others. So the world would be made up of non-interacting Leibnizian monads, each experiencing its own private cinema, the harmony between them divinely preestablished. This view, I say, was mistaken, because the differential equations required to model processes in the real world are mostly nonlinear, and most nonlinear differential equations are insoluble. It is from insoluble, nonlinear differential equations that dynamical chaos arises. Here determinism and predictibility part company; Laplace's demon, to do what he required of it, would need to compute with incomputable numbers. Successive approximations, which are the human way, wouldn't suffice. �21 I have spoken so far as if of a closed dynamic system, insulated from the rest of the universe. But mixing systems such as I have described are hypersensitive to initial conditions, and therefore hypersensitive to tiny perturbations. The flash of an electron in a distant star may affect our mixing system. The intelligence that Laplace imagined, however vast, being yet discursive, will suffer from overload. If there is a God that knows the future, it is by means inscrutable to human reason. 2. I want now to go beyond chaos. There is more to nonlinear science than chaos. As we have seen, the chaos we have been concerned with is not simply disorder; it is approached in an orderly way; it is describable in a coherent way. Can nonlinear dynamics lead to more interesting sorts of order? In fact, in dissipative systems far from equilibrium, new and surprising kinds of order arise. Some of these are described in a book by Prigogine and Stengers entitled Order out of Chaos. Example. The Benard instability is due to a vertical temperature gradient set up in a horizontal liquid layer. The 1.... I I t f lower surface is heated to a given temperature, higher than that --1 of the upper surface. Thus a permanent heat flux arises, from bottom to top, and for a low temperature gradient, this occurs by heat conduction alone, while the liquid remains at rest. But when the imposed gradient of temperature reaches a certain threshold ~ value, a convection involving the coherent motion of ensembles of molecules is produced. Millions of molecules move coherently, forming convection cells of a characteristic size. At higher Iv �22 temperature gradients there occur periodic fluctuations in temperature and in the spatial arrangement of the cells; finally there is turbulent chaos, which, again, is not without its order. Similar kinds of order arise in dissipative chemical systems. With reactants entering and products leaving, the system may organize itself spatially, or may come to act like a chemical clock, beating rhythmically. Such coherent behaviors on the macroscopic level do not appear to be reducible to the dynamics of atoms and molecules. We have what may be called emergence. 3. According to a fairly broad consensus among scientists today, living things are among the entities that have so emerged. We are, in some sense of the word "are," stardust. Living things are complex, dissipative structures, to some extent selfregulat ing, but maintained ultimately by the flux of energy from the Sun. If the geological time-scale is represented as a 30-day month, then life appeared in the oceans by the 4th day, but became abundant only on the 27th. The first land plants and the first vertebrates appeared on the 28th day; most of human culture appeared only in the last 30 seconds. All this, at least up to the last 30 seconds, is understandable in terms of evolution by random variation and differential reproductive success. Living things are not only embedded in the surrounding geological world, but by their activities they have altered that world; at an early stage, for instance, ancient relatives of present-day algae produced the oxygen of the atmosphere. In various degrees, living things have a circumscribed autonomy; it �23 is wider for those with homeostasis of the blood, wider still for those that can reason before reacting. These are beings with desires, aims, purposes. The world-lines of such semi-autonomous entities, with their separate agendas, may intersect. A man goes to the agora, in the case imagined by Aristotle, and meets someone who owes him money. N~ith~r planned this encounter; it is by chance. Species migrate or spread, encounter one another, interact, find new ecological niches. A world evolving through chance-like encounters, new entities emerge in time, in which including intelligent beings, is unintelligible if, with Leibniz or Voltaire or Laplace, we take that world to be an integrable system. In an integrable system, the mere reversal of velocities sends time backwards. There is no essential distinction between future and past. The smoke can go down the chimney and reconstitute the firewood. Why can it not? In the middle of the 19th century the law of entropy was discovered: in any closed system, a certain mathematical function tends to a maximum, and there is thus a forward direction to time, diametrically opposed to the backward direction. This law is of everyday use in physics and chemistry, to predict the outcome of experiments. But it contradicts dynamics, if the world of dynamics is an integrable system. Physicists like Boltzmann sought to derive the law of entropy from dynamics; irreversibility from reversibility. By the 1890s it was clear that it couldn't be done; a statistical or probabilistic assumption, distinct from the dynamics, was �24 necessary. Chance had to be assumed to be real. This is an empirical assumption, warranted by experience. Probability theory, at its core, is an empirical science, which assumes the future to be different from the past. Also toward the end of the 19th century, the American philosopher C.S. Peirce suggested that the dissipative tendencies of entropy could be balanced by the concentrative effects of chance. Chance can have an integrative role, in the emergence of new entities like us. Thus dissipative processes intertwine with integrative ones. Nowhere is this more the case than in the activity most distinctive of humans, that of learning and communicating. It is not possible without a functioning brain, dependent on a flux of energy; the reactions involved are dissipative and therefore irreversible. When we learn a Greek paradigm, we change the physiology of the brain. We learn not as beings detached and separate from the world, but as parts of it, by engaging in activities of exploration, hypothesis, construction, testing. Here there is an interplay between chance and reason. And this is especially true in learning about nature: such learning requires that we enter into a dialogue with nature. Thus I think that Einstein, when he sought a vision of the world from totally outside it, and denied the reality of time, was mistaken. The perspective I am suggesting leads to a new respect for nature, of which we are not the overlords but in which we are both embedded and emergent. In this perspective, there are no �25 guarantees; we live in a chancy world. Nevertheless, a_qualified hope is rational. Human knowledge increases, not always steadily, sometimes by surprising zigzags or even reversals; but the trend is unmistakably incremental. It is not a deductive chain. It is a rope, no single strand of which is, by itself, of incorrigible strength; but different strands, by pulling against one another, constitute a fabric stronger than any of its parts. In this lecture I have sought to signalize a mistake into which dynamicists and philosophers of the past three centuries fell, imagining the world to be an integrable system. The biological perspective I have been sketching can be a corrective. Our survival depends on recognizing and respecting our own complexity and that of the nature in which we are both embedded and emergent. According to rabbinical commentary, the first word of Genesis, Berechit, means not "In the beginning,", but "In a beginning." Twenty-six attempts, say the rabbis, preceded the present Genesis; all ended in failure. Holway sheyaanod, exclaimed God as he created the world: "Let's hope that this time it works." � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Description An account of the resource Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. 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Original Format The type of object, such as painting, sculpture, paper, photo, and additional data paper Page numeration Number of pages in the original item. 38 pages Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Dynamical Chaos: Some Implications of a Recent Discovery Description An account of the resource Typescript of a lecture delivered on October 7, 1994, by Curtis Wilson as part of the Formal Lecture Series. Creator An entity primarily responsible for making the resource Wilson, Curtis Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Date A point or period of time associated with an event in the lifecycle of the resource 1994-10-07 Rights Information about rights held in and over the resource St. John's College has been given permission to make this item available online. Type The nature or genre of the resource text Format The file format, physical medium, or dimensions of the resource pdf Language A language of the resource English Identifier An unambiguous reference to the resource within a given context lec Wilson 1994-10-07 Relation A related resource <a title="Sound recording" href="http://digitalarchives.sjc.edu/items/show/3667">Sound recording</a> Subject The topic of the resource Chaotic behavior in systems Deans Friday night lecture Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/6d99d1fd78293c9f087e4d115903549e.pdf df5feafbf57724224be37971ccc7b036 PDF Text Text On RnoWfng Ho ond 1U1oWin~ Wboi [urtt·s A. Wilson �ON KNOWING HOW AND KNOWING WHAT Curtis A. Wilson My lecture this evening concerns the relation between making and knowing; between skill or craft or art--the Greeks called it techne--and contemplative knowledge; between knowing how and knowing what. I begin by attempting to sketch, roughly, three different, successive ways in which this relation has been lived or thought about . First, a primitive stage, paleolithic, pre-agricultural. Certain relics of it, both living and non-living, have persisted into our ti.me and world. Among the relics are, first of all, skeletal remains and tools, implements. Primitive humans were tool-makers. It was an amateur French geologist and antiquary , Boucher de Perthes, who in the 1840's and 50's first began to identify the chipped flint tools of the Old Stone Age, and to defend them for what they were before his disbelieving contemporaries. Then , since the 1920's, evidence has accumulated that humans were toolmakers even before they were human , that is , before they assumed the physical form of present-day Homo sapiens . It was not the brain that came first, but upright posture and the hand . When the hominid precursors of the hlUllan race came down out of the trees and walked upright upon the plains, they thereby freed their fingers and opposable thumbs for new uses, for the making and deployment of tools , weapons, utensils. The australopithecines of South Africa, with only 500 cubic centimeters of brain, no more than a chimpanzee or gorilla, were already walking erect and using stone implements. The more recently discovered remains of Homo habilis, "handy man", as his discoverers named him, show a brain of 800 cc , still not the normal size for Homo sapiens , which is 1200 to 1500 cc; but Homo habilis is already, 3 and 3/4 million years ago according to Mary Leakey ' s r ecent find, an upright -walking tool-maker. The available evidence thus goes to show that the freeing of the hands for tool- making and tool-use preceded most human evolutionary brain enlargement . It looks as though the cerebral enlargement and the increasingly skillful use of the hands went together, the two developments reinforcing each other and yielding evolutionary advantage to the brainiest and handiest who were, so we can plausibly guess, the same . The stone-age humans, then, came provided with the bodily and psychic equipment for seeing , grasping , and handling objects . We can guess that they were provided also with an exceptional capacity for learning. Coordination of hand and eye in handling objects , ability to learn new ways--these were what made possible the use of sticks and stones as extensions of human limbs . But probably we are thinking so far only of individual capacities ; the true acquisition of a kind of tool by a group of hominids or humans implies that the making and using of it can be taught and learned , and so transmitted by tradition. There would have to be a continuing society, capable of transmitting traditi on. And this is exactly what the archeological �2 record reveals--continuity of traditions of tool production , lasting through millenia, with but minor c~anges. Tool production was socially controlled. The implements of each type are practically identical in any given culture, over long periods and large areas. The hand-axes of figure 1, for instance, were shaped by a fairly elaborate process of chipping , a process that would take any one of us a pretty long time to learn . The hand-axe is believed to have been a general purpose tool, used.mainly for cutting and scraping, as in skinning game. It seems to have been the predominant tool in the equipment of the early Stone-Age hunters. Its production and use started in southern Africa about a half million yearsago , and then spread northward through Africa and Asia Minor and Europe over a period of several hundred thousand years, with only minor variations and improvements in technique. Hand-axes dug up at sites as wide ly separated as the Cape of Good Hope and London are indistinguishable except for their being made of different types of rock. The traditional character of Stone-Age craft is also represented by the paintings made by Upper Paleol i thic man in a hundred caves or so of southern France and northern Spain (figures 2 and 3). These were started about 30,000 years ago and were kept up for 20,000 years, with increasing refinement and detail and t:i:ueness to what is seen . The paintings were painted, of course , by lamplight and from memory. The ordering of the paintings within the caves--bison, horses, and oxen in the central chambers; deer, manunoth, and ibex in outer areas ; rhinoceros, lion, and bear in the farthest recesses--seems to be fairly constant, suggesting tradition-controlled practices. Among the paintings are occasional drawings of men dressed in the skins, horns , and tails of various animals, much in the manner of the medicine men or shamans in North American Indian tribes. This suggests a connection between the paintings and ritual magic, perhaps the preparation for the hunt. But p rehistoric skeletons and artifacts reveal very little indeed as to how the primitive looked out upon his world, and viewed his own role within it . There is another kind of evidence, the whole set of observations of ethnologists on pre-literate, stone-age peoples surviving into the present or recent past. To what extent these peoples have remained untouched by civilizations, past or present , may be uncertain, but certain characteristics appear to be common . The human communities are small, going to several hundred at most; within them , everyone knows everyone else. They are selfcontained economically. There are no fUll-time specialists; even the job of shaman is a part-time one; for everyone must help with the task of food getting. The wanen, to be sure , have different roles from the men, seedgathering, for instance , instead of hunting. The members intermarry and have. a strong sense of solidarity. They think their own ways better than those of others. The Bakouris in central Brazil, for instance, have one and the same word for "we", "our", and "good", and another for "not we", "bad" , "unhealthy" • Men and womer. within the group are s ef~n as persons, not �3 as parts of mechanical operations . Groupings of people depend on status and role, not on mere practical usefulness. However pressing or demanding the business of survival, the focus is not on mere individual survival, but on the kinship unit, the personal nexus that joins human being, society, and nature in an endless round of birth, growth, decay, and rebirth . The central meaning of things lies in the linking of the deceased to the living and the yet unborn . The moral and sacred order predominates over the merely technical . The useful arts , with all the know-how they involve, are not isolated as merely useful or artful, but like an intense sport or dance or ceremony , form part of the sacred round . As for knowledge, theory conceived as aiming at universal validity , it is absent . There is nothing for it to be of. There is no concept of a nature within which things happen according to regular, impersonal, cause-and-effect sequences . Natural events are interpreted as part of the communal life. Nature is though of as replete with spirits, acting by social norms which can be violated only at risk of retribution . The reg u lar ity of occurr ences remains in the background, does not become a theme . The primitive human is alerted only if the event is a misfortune, or otherwise emotionally priv ileged ; and then he traces it to an evil spell, or the enmity of a spirit , or a neglected ritual . But even here there is n o rule-like r egulari ty to follow in the interpretation . Everything is particular: this tree , this river , this animal, this man, this spirit. And spirits are capricious . A person may indeed attempt to exercise spiritual power ov er spirits ; if he succeeds , he is a shaman, that is , a technician of the spirit . But woe to him who , having gained status as a shaman, fails in confrontation with another shaman t o win the contest in the exercise of shamanistic power ; shame , e x ile , possible insanity await him. The shaman's power i s not founded in stable wisdom ; its exercise is a risky affair. Meanwhile , primitive consciousness is filled with knowledge, knowledge connected always in the most intimate way with know-how; knowledge in the mode of acquaintance with kinds of thing , kinds of material, kinds of processhow to coax fire into the hearth , how to use tension and twist to send the arrow hurtling through the air , and so on . Things, materials, and processes are silently recognized in their generic characters, and these recognitions form the tacit background for all the activities of everyday life . But the theoretical knower, he who would bring these things forward out of their tacitness into lucidity and articulation, has not yet appeared . Second phase . This begins with the invention of agriculture. Knowledge and utilization of the reproductive cycle of plants brings a new kind of independence of external nature, a new set of possibilities and problems . Human life ceases to be parasitic upon the animals and plants that nature happens to provide . Foresight and planning must now extend through one annual cycle to the next . New and quite different techniques replace the old: the sowing of seed, hoeing, reaping, threshing, storing, grinding, baking, brewing . Permanent settlements become possible; people now live in villages. Within a relatively short span of time, considering �4 the hundreds of thousands of years that paleolithic tribes had wandered the earth, within a very few thousand years; between8000and 3000 B.C., the agricultural revolution passes into the urban revolution. In the river valleys of the Tigris and Euphrates, the Nile, and the Indus, that which we call civilization first emerges. Civilization means, in the first place, a number of things added to society: a marketplace, writing, a city, public control of irrigation, public works. Different civilizations develop away from the forms of folk society in different ways, but in all, there are certain features distinguishing them from primitive, folk conmunities. Kinship ceases to be the basis for the organization of society, and is replaced by residence. In other words, the state has come to be. As villages ball up into towns, and towns into cities, the members of society come face to face with diversity of beliefs and customs. Personal relations are replaced by impersonal, economic, utilitarian ones . Crafts become full-time occupations, often engaged in under conditions of lowly servitude . The old moral orders may persist in greater or lesser degree, but they necessarily suffer in the midst of recognized diversity. The conmon result is a state cult that draws int o itself various elements of the old cults, in the effort to gain general acquiescence. Already there are those who are taking in hand the management of the moral order; these are the priests . Probably also there are scribes , those who master the calculative and notational skills required for the construction projects of the state and for the keeping of records. In brief, a literate elite has come to be, which separates itself from the world of the rural farmer and the town craftsman. The separation has been said to be fatal to science. But the literate elite, narrow-minded and self-serving though it often may be, has the functi on of maintaining the lore of mathematics and astronomy and the calendar. In Babylonia, between the 6th and 3rd century B.C., the sophistication of mathematical procedure and the accuracy of astronomical prediction became astounding. Still, this was not science in our sense. Egyptian and Babylonian mathematics had nothing to do with ideas, or, in particular, with the idea of nature. At least in the west, this idea of an immanent order in the universe, independent of any arbitrary will, was first clearly articulated by certain wise men, legislators and merchant princes of the 7th and 6th centuries in the canmercial republics that the Greeks established along the coast of Asia Minor. It is worth noting that these wise men express themselves in the language of the administration of justice and of commercial or monetary exchange. Anaximander puts it thus: That from which all things are born is also the cause of their coming to an end, as is meet, f or they pay reparations and atonement to each other for their mutual injustice in the order of time. And a century later Heracleitus is saying: All things may be reduced to fire, and fire to all things, just as all goods may be turned into gold and gold into all goods. �5 The second part of the statement refers to coinage, which was invented about 610 B.C. in Lydia. So human processes and artifacts are used to express the nature of nature. It is a man fran Ionia, too, who first challenges the popular and Homeric notion that the arts were given to men by the gods from the beginning. "The gods," says Xenophanes, "did not reveal to man all things from the beginning, but men through their own search find in the course of time that which i s better." And Anaxagoras says: it is because man has hands that he became wiser than the brutes. Later on, the pre-history of the human race becomes a theme for the Sophists. Among the Greek thinkers generally , beginning with the Ionian philosophers and continuing down to Aristotle, the theories differ in detail and emphasis, but in all of them the past is viewed as the history of the progressive humanization of the animal man through the invention of the arts. Now of all the Greek discussions of the arts, the one tnat will have the most influence in later times, and against which the initiators of modern science will stage their revolt, is the Aristotelian account. According to Aristotle, art imitates or completes nature . This formula undoubtedly has more than one meaning and application. One way in which the arts complete nature is in giving rise to leisure, which frees humans for what Aristotle regards as their highest function, the pursuit of knowledge or science. Aristotle says: As more arts were invented, and some were directed to the necessities of life, others to recreation, the inventors of the latter were natur ally always regarded as wiser than the inventors of the former, because their branches of knowledge did not aim at utility. Hence when all such inventions were already established, the sciences which do not aim at giving pleasure or at the necessities of life were discovered, and first in the places where men first began to have leisure. But how does art imitate nature? is as follows . I think the fundamental meaning Things come to be, Aristotle says (and he is quoting a common view), either by nature or art or chance. Chance is an incidental cause; it means that something comes to be that could have come to be by design, but it occurred in fact by accident. Nature and art, on the other hand, are similar to one another, and unlike chance, in that each of them acts for an end. That nature acts for an end is most obvious, Aristotle says, in animals other than man: they make things neither by art nor after inquiry or deliveration. Wherefore people discuss whether it is by intelligence or by some other faculty that these �6 creatures work,--spiders, ants, and the like. By gradual advance in this direction we come to see clearly that in plants too that is produced which is conducive to the end ••• If then it is both by nature and for an end that the swallow makes its nest and the spider its web, and plants grow leaves for the sake of the fruit and send their roots down (not up) for the sake of nourishment, it is plain than this kind of cause is operative in ~hings which come to be and are by nature. Both art and nature act for the sake of an end , but they differ in that nature is an internal principle of motion or change, in that in which it acts, whereas art r esides essentially in a subject distinct from the material on which it acts. Art is characterized by a form or idea which is present in the soul of an intelligent being and is used to direct his activity; and this form is the form of the artifact or artful result that the artist or artificer aims to realize in the material. The arts are thus principles of change belonging to an exterior agent, like the idea of health in the physician which causes outside of itself the physical health in the patient . Nature is also a form, but is internal to the natural thing; it is like the doctor doctoring himself. The tree grows by an internal principle, the house is built by the external agency of the builder. Now art is closer and more familiar to us than nature, for it is that by which we act on the world around us . It therefore serves Aristotle as a precious intermediary for the explanation of what nature is. Nature is less easily knowable to us than art, yet it is knowable--so Aristotle claims. To know the nature of a thing, according to Aristotle, we must grasp the what of it, its being-what-it-is. We can do this, he says, by means of the definition. Through the verbal formula of the definition the intellect knows, has present to it, the what of a class of things, say swallows, spiders, or trees. This is undemonstrable but nevertheless graspable knowledge, for according to Aristotle, there are forms in things which are knowable. The knowing of them constitutes the starting point for all further knowledge claiming universal validity. Third phase. The founders of modern science rejected Aristotle's claim, and along with it they rejected the notion of art as imitating nature . They begin, on the contrary, with the assertion that, as between the products of nature and the products of art, there is .!!£essential difference. As Francis Bacon puts it, "men ought ... to be firmly persuaded that the artificial does not differ from the natural in form or essence . •. " Knowledge canes to be identified with making , cognition with construction. "We know the true causes only of those things that we can build with our own hands or intellect," says Mersenne in the 1620's . "To men is granted knowledge only of things whose generation depends upon their own judgement," says Hobbes in the 1640's. Meanwhile, there is a reappraisal of the practices, operations, and know-how of the arts called mechanical. Says Galileo: �7 I think that antiquity had very good reason to enumerate the first inventors of the noble arts among the gods, seeing that the cormnon intellects have so little curiosity .... The application to great invention moved by small hints, and the thinking that under a ••• childish appearance admirable arts may be hidden is not the part of a trivial but of a super-human spirit. In the new way of looking at things, it is the machine which serves as the model of what can be understood and explained. What is a machine? That may not be so easy to say. The word "machine", derives from the Greek m~chane, which means a contrivance for doing something, an expedient, or a remedy against ills. In antiquity the word in both Greek and Latin came to be applied particularly to devices for lifting weights , levers, pulleys, and the like. Also , in Lucretius' poem, the word machina is applied to the enti re world in the phrase machina mundi, and this phrase reappears in Christian writers of the middle ages, with perhaps the connotation that the world is something made. But the machine that chiefly served as model and inspiration in the new science of the 17th century was a particular machine, invented sc;me three centuries before: the weight-driven or mechanical clock. Kepler,who in 1604 first introduced detailed mechanism into the theory of the heavens, wrote at the time: At one time I believed that the cause that moved the planets was a soul .•. I now affirm that the machine of the universe is similar not to a divine animated being, but to a clock •.• and in it all the various movements depend upon a simple active material force , in the same manner that all the movements of the clock are due to the moving we ight. A few years later, Descartes extends the metaphor to nature as a whole. There is no difference (he says) between the machines built by artisans and the diverse bodies that nature alone composes except the following: the effects of the machine depend solely upon the action of pipes or springs and other instruments which for the reason that they must have some proportion to the hands of those who build them are always so big that their figures and their motions appear visible, whereas the pipes or springs that produce natural effects are generally too small to be perceived by our senses. It was on the analogy of clocks and mills that Descartes proposed to account for the functioning of all animals as well as the functioning of the human body. Controversy over Descartes' view of animals as machines provoked one controversialist to insist that "every Cartesian, in order to be consistent, should therefore affirm, with the same seriousness with which he affirms it with respect .to beasts, that the other human beings who coexist with him in the world are machines." The claim that human beings are simply machines, and not in need of the immaterial rational �8 souls with which Descartes had still seen fit to endow them, is at length asserted gleefully in the 1740's by Lamettrie, who concludes that life is solely for pleasure, becomes enormously corpulent and dies of indigestion at the court of Frederick the Great. But it is an altogether serious claim that Jacques Monod makes, in his recent book Chance and Necessity, when he affirms that all living things are chemical machines. In this pronouncement, I take him to be espousing the vast program of research that is molecular genetics. I now turn to the consideration of certain machines. I shall try to make evident what makes them tick, what principles are involved . Later I shall return to the relation between knowing how and knowing what. I beqin with the so-called mechanical clock , the great paradigm of the 17th century revolutionaries of science. Instruments for keeping track of the daily passage of time have been known since very ancient times: wax candles and hemp ropes, certain lengths of which were supposed to burn in a definite time; sundials; sand-clocks; and especially water-clocks, which were in use in early Egyptian civilization and which from Alexandrian times, the third century B.C., onward, often assumed very elaborate forms, with special jackwork actuating puppetry to mark the passage of the hours. But the clock called mechanical was invented about A.D. 1300. See figure 4. What you see here is an alarm clock of about 1400 frc:m a monastery It rings the bell at settable times, and since the hand around the face in 16 hours , which is exactly the length of the winter night in Nuremberg, the presumption is that it was used the sexton, so that he might in turn call the monks to read their offices. in Nuremberg. travels longes t to wake nightly Before going to the heart of the mechanism, let me say a few words about the gearing, which transmits measured amounts of rotational motion from one part of the apparatus to another. There is nothing novel about gear wheels in A.D. 1300. Gearing was used in the windmill, (see figur e 5) , to change from a vertical plane of rotation to a horizontal plane of rotation; the windmill of this type was invented in the late 12th century, the earlies t sure date for one being 1185, in Yorkshire . Twelve centuries earlier, similar gearing was already being used in water wheels (see figure 6) , invented apparently in the first century B.C. But even more elaborate gearing was being made as early as the 3rd century B.C., by Archimedes and others, for calendrical computing machines and planetar ia . In 1900 the sunken wreck of a Roman ship was found in the Aegean Sea by sponge divers; it has been dated to about 80 B.C. It contained, along with a lot of statuary, presumably destined for sale to the upper fluffy duff of Rome and other Italian cities, a peculiar mechanism of iron, badly rusted (see figure 7). Only in 1972, with the aid of x-radiography, was sense made of it; its gear ratios, it turns out, are based on astronomical constants well-known in antiquity. It is a calendrical cc:mputer, which was turned �9 by hand, in order to find out where the sun, moon, and planets would be at giv en times . Similar types of gearing must have been used in a mechanism described by Cicero . He writes: ••. Whe n Ar chi me de s fastened on a g lobe the movements of moon, sun, and five wandering stars , he , j ust like P l a t o' s God who bu ilt the world in the Timaeus , made one r e v olution of the s ph e r e control several movements utterly unlike i n s l owness and swiftness. Now if in this wor ld of ours phenome na c annot take place without th e act of God, neither could Archimedes have reproduced the same movements upon a g l obe wi thout divine genius . There is enough evide nc e to suggest a long traditicn of geared calendar work and planetaria, starting with Arch imedes and his contemporaries, transmitted through Islam to the West, and c ulminating in a number of clockdriven planetaria constructed in the midd l e of the 14th century in Europe. As far as the gear-work is concerned, the c lock seems to come into being fully-fledged as a "fallen angel from the world of astronomy". The gear-work is one source of the clock, deriving from the heavens, but it still needs a terrestrial heart. By this I intend that which makes it, literally, tick. Look once more at figure 4. On the left hand, at the top, you see a bell; our word "clock" comes from the French word "cloche" meaning bell. Below the bel l , and slightly to the left, you see a wheel shaped something like a crown, and therefore called a crown wheel. Around its axle is wound a cord, which goes to a weight that you cannot see. Suspended by a string in front of the crown wheel is a vertical rod, called the verge, and at the top of it is rigidly attached a bell clapper. The way thi s bell-ringing mechanism works will be clearer in a moment. Now this bell-ringing apparatus, it seems, was first used just by itself. You released a catch, the weight began to fall, the crown wheel to turn, and the bell to be hammered by the clapper at the top of the verge. out of one motion, the releasing of the catch, you got several motions, the bell rung several times: a helpful gadget for a sleepy or lazy bell-ringer. But on the right you see another crown wheel, with another verge suspended in front of it, and atop the verge, a horizontal bar with weights on it, called the foliot, meaning "crazy dancer ". The invention of the weight-driven clock consisted in seeing that the mechanism of the bellringing gadget, here on the left, could be used for a quite different purpose, to solve the problem of making a clock go by means of a weight. What is that prob lem? In 1271 Robert the Englishman wrote: "clockmakers are trying to make a wheel that will accomplish a comp lete revo lution each day, but they cannot quite pe rfect their work." The difficulty was that the weight as it falls tends to accelerate, and so to make the clock go faster and faster . One could of course use a brake or some form of friction to keep the weight fall i ng at a constant rate, but very qui ckly the rubbing surfaces would wear smooth , so tha t the speed of the clock �10 . would increase. The invented solution was what is called an escapement: in the case of the 14th century clock, it is a verge and foliot escapement . We shall see best how it works by turning to a simplified diagram ; see figure 8. Here the gear work has been eliminated for simplicity's sake, and the crown wheel has been replaced by a wheel with projecting pegs ; both may be called 'scape or escape wheels . The previous picture did not show clearly the pallets or little plates that project from the verge .above and below, in such a way as to mesh with the indentations i n the ' scape wheel . Now suppo se the ' scape wheel moving in the di r ection of t he arrow. The peg at t he top of t he wheel is j u s t striki ng the upper p a llet. The motion of the wheel , and hence of the descending weigh t , is momentari l y c h eck e d by t he inertia of the system composed o f verge , foliot , and the weight s o n the f ol i ot . Then the driv i n g weight slowly acce l e r ates this system till the peg has pus h e d the t op p al l e t out o f the wa y, and has set the verge and foliot swinging c ounterclockwise as seen from abo ve. For a brief moment the driving weight can fal l freely. But now the swing of the verge and foliot brings the bottom pallet between the pegs of the scape wheel; notice that the bottom pallet proje c ts from the verge in a different direction, something over 90° away from the direction of the top pallet . Almost immediately, the peg at the bottom of the wheel strikes the lower pallet. Now this peg at the bottom of the wheel has to be moving in the opposite direction from the peg at the top of the wheel, just because of the way wheels are. Hence the counterclockwise swing of verge and foliot is stopped, and the fall of the driving weight slowed again, until the verge and foliot are slowly accelerated into a clockwise rotation. Thus the fall of the driving weight is repeatedly interrupted by being compelled regularly to reverse the motion of the verge and foliot with weights. This is an instance of what is nowadays called negative feedback: a process produces an effect that slows down and thus regulates that very process. By means of it, the average overall motion of the weight, and hence of th e clock, is rendere d uniform. So originated th e weight-drive n clock, throug h the invention of the escapement, which is literally what make s the clock tick. And this clock, suddenly, toward the midd l e of the 14th c entury, s e ized t he imagination of the burghers and princes of Eur ope. Towns vied wi t h towns t o have in church or townhal l the mos t elaborate set o f p l anets whe el ing , cocks crowing, angels trump eting, and apos t le s, k i ngs , and p r ophets ma rching and counterrnarchi ng to the ho urly b oomi n g of th e b e l ls . And also i n th e middle of t h e 1 4th century , Nicole Oresme , schoolman , bishop , adv iser to the kin g of France , first enunciated the metaphor of the universe, or at least the supra-lunar part of it, as a vast mechanical clock--a metaphor that would later be e x tended to the whole world and become a metaphysics. The fascination was with the mechanical marvel of the thing, with automatic, rhythmically self-acting machinery. Earlier I evaded the problem �11 of defining the word machine. We need distinctions here, and with the invention of the clock , the automatic machine which is no longer a tool in the sense of a prosthetic instrument or extension of human limbs, I suggest we would do well to confine the term machine to devices that store energy , then release it in determinate ways, under various constraints and feedback mechanisms, so that particular purposes are accomplished. I should note that this term energy achieved its pres ent-day sense only a litt le over 100 years ago; I shall come back to the problem of its meaning. By the constraints the stored energy is compelled to bring about certain determinate motions, either desired in themselves , as in the clock, or for the work they can accomplish. The criterion of a good machine is completeness of constraint: the parts of the machine should so connect as to eliminate all but the desired motions. By this criterion, the 14th century clock was not very good , and in fact it needed a little old lady in a black smock to re-set it every day. The v erge and foliot escapement in particular , must be criticized because its swing is stopped only by an impact between the pallets and the teeth of the crown wheel, and every such impact brings with it a recoil- - a source of extr a friction, wear and tear, inaccuracy . Moreover, the swing of the verge and foliot has no proper period of its own; its temporal span depends simply on the successive impulses that it receives, which are unlikely to be exactly equal. Improvements came . From the 14th century onwards, the craft of clockrnaking begins to flourish, to develop into skille d instrume nt-making, a craft ca:nbining mathematical know-how wi th expertness at the lathe and gear-cutting machine . The clockmakers and their offspring, the instrument-makers , will have a very great deal to do with the scientific and indus trial r e volutions of the 17th, 18th, and 19th centuries. Already in t he 16th century they were producing tiny spring-actuated watches. But the difficulty about the verge and foliot escapement is met only in the 17th century, with two new inventions. The first of these inventions i s Galileo ' s and Huygens' replacement of the foliot by the pendulum; see figure 9 . The verge is shown at the top of the drawing; it is now horizontal, at right angles to the pendulum to which it is rigidly attached . The advantage of the pendulum is that it has an almost constant, natural period of swing ; the period approaches more nearly to constancy as the amplitude of swing is diminished. This clock is much more accurate than a verge and foliot clock, but unfortunately the verge with its pallets required a 40° swing to clear the teeth of the crown wheel, and with so l arge a swing, slight differences in amplitude make for noticeable differences in period. The second invention reduces the angle of swing; see figure 10. This i s the anchor escapement, invented apparently by Wm. Clement about 1670. Only part of the 'scape wheel is shown here. The bent lever above carries the pallets, and rotates from side to side on an axle that is rigidly atta8hed to the pendulum's fulcrum. The arc of swing has now been reduced to 3 or 4°. With this improvement, and continued refinement of all �12 moving metal parts to reduce recoil and friction, 18th century clocks could be made that deviated from their average rate by no more than 1/10 second per day. Reduction of friction , elimination of impact and recoil, achievement of thesmoothest working and greatest efficiency--these are machineshop matters. But the concern with them, we shall see, leads to important conclusions : that the universe is not an eternal clock, and that change, not locomotion, is fundamental . This brings me to the second machine I shall examine, the steam engine. · The first practically successful steam engine was built by a provincial iron-monger, Thomas Newcomen , between 1702 and 1712. There had been various previou s efforts to use the expansive force of steam, some of them going back to Hellenistic times . The trouble with these devices was that they did not develop much power . And this they did not do b e cause the metallurgy was not available to make boilers and pipe joints that would hold steam at high pressure . A successful steam e n gine built around 1700 had to us e low pressure steam . The solution was , to use it in conjunction with the weight of the atmosphere , which had been discovered by Torricelli and Pascal a half century before. We do not know how Newcornen came by his ideas , but in any case, his engine was an atmospheric engine . See figure 11. This is the 1712 version of Newcomen ' s engine , hooked up for pumping water fran a mine, the main u se to which his engine was put .Below on the right is the boiler, just beneath the piston cylinder . When steam is admitted to the cylinder, the piston rises to the top, mainly because of the weight of the pump rod hanging from the other end of the rocking beam. Next, the connection between boiler and cylinder is closed, and cold water is sprayed into the cylinder , condensing the steam and so producing a partial vacuum . This allows the atmospheric pressure , acting on top of the piston , to force it back to the bottan of the cylinder, and so raise the pump rod. Then the next cycle is started by the admission of more steam. Notice that the force stroke is altogether due to the atmosphere ; the steam pressure never rises much above one atmosphere of pressure . The working of these engines is said to have been accompanied by an extraordinary amount of wheezing, sighing , creaking, and bumping. They were compared, of course, to living things . They were dreadfully inefficient . By minor improvements, the thermal efficiency was approximately doubled by the 1770's, bringing it up to what we would now calculate as being about 1%. More important improvements in efficiency were made by James Watt, during the last quarter of the century . As instrument maker to the University of Glasgow, he was asked in 1763 to repair a small model of a Newcomen engine, and was astonished by the huge quantities of steam required to make it work. Much steam was consumed just in heating up the cylinder , �13 after it had been cooled down in the steam-condensation phase of the cycle . It would be an e c onomy if t h e cylinder could be maintained always as h ot as t h e ste am ent e ring i t . " The means of accomplishing this did not immed iate ly p r esent itse lf," W t s a ys ; "but early i n 1765 it occur red at to me that, if a communi c ati on were open ed between a cylinder containin g s team, and a nothe r v e s sel wh i c h was e x hausted o f a i r and oth e r f l u ids , the s te am, as an elas tic f l uid, would imme diate ly rush into the emp ty v e sse l .... " Thi s wa s the i nvent ion o f the s eparate condenser. See fi g ure 12. On the right is the b oile r C; E i s t he p i s t o n cylinde r, which i~ enclosed i n a s team jacke t; d own b elow it i s the separa te c ondenser F, and beside it, the vacuum pump H which is operated by a rod and chain connecte d to the rocking beam. When the p iston i s a t the top of its stroke, the exhaust valve to the conde n ser open s , and steam begins to be drawn from the cylinder into the condenser. Steam at about atmospheric pressure is simultaneously admitted to the cylinder above the piston, forcing the piston downward; the advantage o f using steam rather than atmospheric air is that the cylinder stays hot. When the piston reaches the lower end of its stroke, the exhaust valve to the condenser is closed, the inlet valve that admits steam above the piston is also closed , and a valve is opened which allows steam to flow from the cylinder above the pis t on , through a pipe which is to the left of the cylinder, to the cylinder below the piston . The pressure on the two sides of the piston is thus equalized , and th e piston rises, being pulled up to the top by the weight of the pump rod . The separate condenser led to about a three-fold improvement in efficiency . Watt ' s further improvements were aimed not at efficiency but at making the steam engine a n effective replacement for the wa ter wheel, in delivering rotary power to factory equipment . See figure 13. I shal l not describe this engine, except to point out that it had to deliver power in both halves of its cycle, and so be double-acting , and this required that the piston rod be rigidly connected to the rocking beam, and at the same time , that it be kept moving in a straight line--no mean problem to solve , but Watt solved it by the invention of what i s called a parallel-motion linkage, and thereby initiated a whole branch of mathematical study. The large flywheel you see at the right helps by its rotational inertia to keep up a smooth delivery of power. Above t he flywheel, to the left of its center , you see the centrifugal governor, whose speed of rotation is made to regulate the amount of steam entering the cylinder~­ anothe r in s tance, like the clock e s c apement, of negative feedback. What about steam engines for railway locomotives and steam boats ? Engines for these purposes would have to be less massive than the Watt engine; but if they were to be a good deal smaller and still develop the req uired power, they would have to us e high-pressure steam. Watt had always opposed the high-pre ssure engine, on the grounds that it was unsafe; and so high-p r e ssure e ngines did not s tart to appear until after 180 0, when Watt' s various patents lapse d. The new engines were unsafe; life on the Mi s sissippi and indeed the e ntire history of steam powe r frcm �14 1800 to 1850 was punctuated by appalling explosions. The new engines were also three and more times more efficient than any earlier engines . A variety of experiments were now undertaken to discover what the most efficient engine would be like. On what did efficiency depend? Was there a limit? If so, how could it be approached or attained? These questions receive their first general answer in a small book published in 1824 under the title Reflections on the Motive Power of Fire. The author was a young man of 29 named Sadi Carnot . The thinking in this book was deeply influenced by the thinking in another book by another Carn ot , Lazare Carnot, famous for his role in the military and political history of France during the 1790's, and also Sadi's father. In 1782, Lazare Carnot had written a b ook entitled Essay on Machines in Ge n eral . In the preface he states: One of the most interesting prope rties of machines, which, I believe, has not yet been remarked . .. is that in orde r to make them produce the greatest possible effect, there must necessarily be no percussion, that is to say, that movement should alway s change by insensible degrees. This , of course, i s an ideal condition which is impossible to attain in practice, and can only be approached. The principle is nevertheless important. It acc ounts, for instance , for the superior efficiency of an overshot waterwheel as compared with an undershot water wheel . In the overshot wheel , the water d rops into a bucket at the top of the wheel , and then acts on the whee l simply by i ts weight, rather than by its motion . In the undersho t whee l, the water gains speed by descending along the stre am bed, then impacts against the blades at the bottom of the wheel; but a good deal of the possible effect, about half , is lost in the eddies and turbulent motion of the water . Lazare Carnot had a formula for what was being lost; he called it live force--it was what we now call kinetic energy. And he shows that, in an ideal machine in which all friction, impact, and brusque motion is avoided, all the kine tic e nergy that is used up can appear as what we now call "work", measured by we ight raised through a distance; he uses neither of the terms "work" or ''energy", whose strict modern usage dates from the 1850's, but he has the ideas. Now the way in which Carnot the younger at first makes use of the elder Carnot's work is as follows. Heat, thought Sadi Carnot , is like water, in that just as water tends of itself to flow downhill , so heat tends of itself to flow from the hotter to the colder body. And just as the waterwhe el utilizes the live force of the descending water to do work, so, thought Sadi Carnot, the thermal machine does work by making use of the descending heat. Now the conditions for the maximum generation of power from the water wheel were that the water should enter the machine without turbulence and leave with velocity. Similarly, Carnot reasoned , the thermal engine would achieve its maximum effect if all the heat trans- �15 ferred from hot body to cold body had the effect of changing the volume of the gas or steam in the cylinder, and hence causing the piston to move; none of the heat should be permitted to follow its natural propensity of simply flowing frcm hot body to cold body without further effect. How could this condition be met? See figure 14, which shows what Carnot imagined . Let there be a volume v of gas or steam in a cylinder , its pressure being represented 1 in the diagram by the height of the point A. Also, let the cylinder be in thermal contact with a reservoir of heat, such as a steam jacket that can be maint ained at a constant temperature 8 ; and suppose the cylinder to be 1 at a temperature only infinitesimally less than 0 . Heat will then flow 1 frcm the heat reservoir into the cylinder; the gas will expand ; and the piston will move outward . It will move very slowly , of course, because the transfer of heat will be very slow , since the temperature difference between reservoir and cylinder is only infinitesimal. Never mind; we are concerned not with speed but with thermal efficiency, with getting the most for our expenditure on fuel; and while it may take several millenia for the locomotive to progress from here to Glen Burnie, we are in no hurry, of course, and can do a bit of extra thinkin g in the interim. What I have been describing is the isothermal expansion indicated in the diagram by the line from A to B. It is the most efficient of all ways of getting work from heat, so why not use it, letting the gas expand for e v er? Of cours e , we would need an infinit ely long cylinder, which is an inconvenience . Also, we had better note that as the gas in the cylinder e xpands , its pressure falls, in accordance with a well-known law called .Ebyle ' s law ; the falling pressure is indicated in the diagram by the falling of the curve AB from left to righ t . By-and-by the pressure of the gas will have fallen to the level of atmospheric pressure, and then the p iston will stop . So this won't do; what we need, clearly , is a series o f processes in which the system is brought back to its initial state ; that is, we n eed a cycle, so that the isothermal expansion can be started over again. What about simply compressing the gas isothermally, back from B to its initial state A? This won 't do, either , because we should have to do just as much work in compressing it as it had originally performed in its expansion . Those of you familiar with plots of pressure against volume of a fluid know that the area under such a curve represents work performed; and of course the area under the curve AB, namely V ABV , is just the same 2 as the area under BA, the same curve traversed in t~e opposite direction. We need to return the gas to its initial state by a less costly route. The solution to the problem is called a Carnot cycle. Here is the way of it. Stop the isothermal expansion at B , while the pressure of the gas is still above atmospheric; remove the cylinder from contact with the. heat reservoir at temperature 0 , and immediately insulate it thermally, so that no heat can pass in or out} then let the gas expand further. Because �16 heat is not allowed to pass in or out, this further expansion, from B to C, is called an adiabatic process. Note that the adiabatic curve is much steeper than the isothermal curve; this means that the temperature is dropping as well as the pressure. Let there be a cold r eservoir, containing, say, ice and water at temperature 8 , and let the adiabatic 2 e xpansion continue until the gas almost reaches this lower temperature, or is infinitesimally above it. Next place the cylinder in contact with this cold reservoir, and compress the gas from C to D. During the isothermal compression from C to D, we are having to do work on the gas , and heat is flowing out of the cylinder into the reservoir . However , we do less work than we would have to have done t o compress the gas at the higher temperature. Finally, compress the gas adiabatically from D to A, so that its temperature rises to the original temperature 0 , and its pressure and 1 volume assume the original v alues indi cated by Ehe point A . We are now ready to begin a new cycle . What have we gained? A ce rtain amount o f heat has been taken from the hot reservoir; call it Q . A certain net amount of work h as been done 1 by the engine, say, in raising a weight ; call it W. W i s the difference between the work the expanding gas does, represented by the area v ~cv 3 1 and the work done~ the gas in compressing it , namely v AQCV ; e viden~ly 3 1 the net work is r epresented by the area of the curvilinear quadrilateral ABCD. For an expenditure of coal or oil or wood yielding the heat Q , we have 1 gained the work W. And Carnot asserts that no thermal engine working between_ the same two reservoirs at temperatures a and 8 could be more 1 2 efficient. Carnot p roves this assertion, but before showing how he does so I wish to correct an error that his argument contains , one which follows from the analogy of the waterwheel . He assumes that all the heat Q that 1 enters the cy l inder during the isothermal expansion from A to B also leaves the cylinder during the isothermal compression from C to D; he assumes , in other words, that Q is equal to what I have labelled Q . Actually, 1 2 the energy to do the work W is extracted from the heat Q , and so W is equal to Q minus Q . This conclusion , or its equivalent , was reached 2 1 simultaneously by more than a dozen Europeans thinking and experimenting independently during the 1830's and '40's ; Sadi Carnot himself reached it before his early death in 1831 . Natural philosophers were pushed to it both by a conviction in the unity of nature, and by a variety of observed instances of what we would now call transformations of energy . What is this energy that is being transtormed? All that can be said, I believe, is that it is something capable of doing work, capable of raising weight through a distance, and as such capable of being treated quantitatively . There is no single mathematical formula for it. But the postulate that there is this entity called energy which is conserved in all the transformations of nature has come to be basic in all scientific accounting, all our dealings with nature, all scientific thought about the economy of nature. It is called the first law of thermodynamics. �17 Now for the proof, appropriately corrected, of Carnot's theorem, see figure 15. The efficiency of Carnot's engine is given by W/Q , where we can measure work and heat in the same units of energy. Let there be, if possible, a more efficient engine, working between the same heat reservoirs, and let it produce the same amount of work W while extracting from the hot reservoir a smaller amount of heat, Q 1 .Then its efficiency 1 will be Y/' = W/Q ~ where Q 1 is less than Q , so ~hat Y)' is greater than 1 this more efficient engine to run the Carnot engine 1 1 Y)· Now let us use in reverse , which we can do, since all the processes that go on in the Carnot engine are reversible. Run in reverse, the Carnot engine becomes a refrigerator; a net amount of work W is put into it; it extracts heat Q from the cold reservoir and rejects the larger amount of heat Q to 2 1 the hot reservoir. And to run the Carnot engine in reverse, we can use the work W produced by the new and supposedly more efficient engine, which I have labelled l in the diagram . Coupling these two engines together in this way, we obtain a rather peculiar device. There is no net input or output of work. Heat , in amount equal to Q -Q ', is extracted from the 1 1 cold re servoir and r ejected to the hot reservoir. That is all. This result does not violate the first law of therrnodynmanics. Yet surely, Carnot and the physi cists who followed him judged, it is impossible ; heat of itself does not flow up a temperature gradient. And therefore Clausius and Kelvin in the 1850's formulated a law, the second law of thermodynamics, of whi ch this result would be the violati on . As Clausius put it: '1 = It is impossible to cons truct a device that, operating in a cycle , will p roduce no effect other than the transfer of heat fran a cooler to a hotter body. Let me n ow try to formulate the main implications of this law and of the reasonings that accompany it . First , as we can see from the diagram of the Carnot cycle , it is never possible to convert any quantity of heat completely into work, without further effect ; some of the heat must always be ejected to a colder reservoir. This means that, even in an ideal heat engine, the efficiency is always less than 100%. I mention in passing that the efficiency depends on the temperatures of the two heat reservoirs, and is improved by raising the temperature of the hot reservoir and lowering that of the cold reservoir. This accounts in part for the superior efficiency of the high pressure steam engine, which provides a higher difference in temperature between the boiler and the atmosphere . Secondly , the Carnot engine represents an ideal limit; no actual engine can reach that limit, or come close to it. The temperature difference between reservoir and cylinder cannot be made infinitesmial. The adiabatic containers never insulate perfectly. Always some of the heat follows its natural propensity and flows from the hotter to the colder bodies without causing any motion of the piston, without doing any work. This means that if a heat engine does some work, raising a weight, say, and if we then undertake to have the weight fall and the engine run in reverse as a �18 refrigerator or heat pump, in an effort to restore the exact initial conditions from which we started, we will not succeed except by investing extra energy in the process. In this sense, the processes that go on in the heat engine are irreversible. Thirdly, by a series of particular arguments dealing with each kind of process encountered in the world, chemical, electrical, nuclear, and so on, it results that all natural processes are irreversible, in the sense just explained. In each case, some heat is dissipated, and the reversal of the process would require that we extract this heat and convert it completely into work done, say into the lifting of a weight , without any further effects ensuing . But this would violate the second law of thermodynamics . Each process, then, has a natural direction , towards a more stable configuration or state. To be sure, any given process may be run in the reverse direction, by making special arrangernents , but these always involve the irreversible expenditure of available energy . If we consider all the changes that occur in the surroundings as a result of any process, then the second law assures us that of the total energy with which we began , some will hav e became unavailable for the production of useful work . As a measure of the transformation of free into unavailable energy , the physicists use a quantity called entropy , which increases as the transformation proceeds . I f in any natural process we consider all the energy exchanges involved , we find that the net result is an increase in entropy. By computing the c h anges in entropy in any process , we can determine its natural direction , which is the direction of entropic increase . From any o n e moment , then, to any later moment , the world changes irreversibly . Perhaps we are in some sense aware of this, just in b eing aware of being alive ; but it is a different matter to assert it as a fundamental fact o f natural science . A number of physicists during the 19th century felt the 2nd law of thermodynamics to be disturbing, and attempted to reduce it to mechanics , that is , to derive it from mechanics . But this cannot be done, for the simple reason that the equations of mechanics are indifferent as to whether time runs backwards or forwards, and therefore irreversibility is not derivable from them . What the physicists in fact did was to construct a kind of analogue to thermodynamics , called statistical mechanics. It turns out to be quite as irreducibly and fundamentally statistical as it is mechanical. The kind of statistics used must be chosen so as to fit the system studied, and lead to the known empirical consequences that thermodynamics predicts. In any case , the second law remains, as Eddington called it, "time's arrow", signifying not hCM fast change will occur, but the overall direction in which it will irrevocably go, toward configurations that we may call more stable . Thermodynamically, then, the world changes irreversibly; but in special circumstances, it appears that it does so in ways that especially interest us. Let there be, for instance, a sun, radiating energy unremittingly into the unfillable sink of outer space. But in its flow from hot to cold, let some of the energy pass by way of an earth, an assemblage of �19 certain chemicals, a temporary trap for the energy in its inevitable entropic descent. In such case, Morowitz has recently argued, with high probability the improbable happens; that is, order arises--symmetry, cyclical transformation, process that has a shape and pattern. Matter which left to itself, in the dark, without a sun to shine upon it, remains inanimate, random, chaotic, now under the surge of solar energy is transformed into an ordered dance of living forms. Are they forms that we will recognize, feel convivial with, if it comes to be the point of our being introduced? Or is life as we know it a very unique thing, perhaps a species of some more inclusive genus, but nevertheless a quite distinct species? The question is very speculative, but if one examines the delicate balance of conditions our earth has~enjoyed up to now, and if one considers the extent to which chance e vents, events that were not determined mechanistically to happen, have entered irreversibly into biological evolution , then the likelihood that human-like beings exist elsewhere in the universe looks small, nothing worth gambling on. Living systems could have employed righthanded proteins, instead of left-handed ones, and perhaps that would have made little difference. But the evolution of the human brain, into which thousands of irreversible events have entered, has happened only once that we know of; and the alternative possibilities seem countless. A conclusion on which I expect us therefore to agree is that life-stuff as we know it, and the biosphere within which and with which it evolves, are to be cherished as our proper heritage . And thermodynamics, wearing the human smudge and sharing the human smell , is the .economic science that must guide us in the management of this our household, warning us of the irreversible character of our transactions with nature, the finitude of the resources upon which we draw, the ineluctable price of degradation of energy that must be paid for every maintenance or achievement of order or form or value. I have been engaged in what can have seemed a long digression from my original theme , but I think I am not too far from my starting point ; something that also happens with random walkers . Modern science in its inception, I have said, set up for itself the program of science as construction, the sublimation of our age-old capacities for lifting, heaving, pushing, pulling, taking apart, rearranging. Perhaps there is something inescapable about our imagining that program as carried to completion-the completed description of the world and of ourselves as an assemblage of spatially and temporally located, deterministically interacting parts-a machine. Yet surely the resu lt is bizarre, a bad metaphysical dream, a world of bare fact from which problems and persons, learning and knowing and valuing are absent. If asked to argue against this image on the basis of scientific results, I should say that there are no doubt certain bridges over which the effects of molecular happenings--the deterministic ones and also (please remember!) the chanceful ones--move into our world of sweet and bitter, hot and cold, painful and pleasurable, clumsy and skillful. And I should propose that if chance has acted in the development of the biosphere, it must also be active in the normal functioning of the living body and can be expected to lead to its most significant effects in the functioning of �20 the human b r ain . Long ago Epicuros , knowing t hat otherwise knowing and willing were imposs i b le , p ostulated an alt ernative t o necessity in the swerve of the atoms . Th e pr esent- day version of tha t alt e r nativ e i n physics allows us to s peculate how de cisions and de l ibe rations u tili z e (but do not consti tut e !) t he chance -li ke for king of t he causality of eleme nta ry events, how morally and logi c al l y a ch an ce of a l t e rnative s equence can b e come s i gnificant in allowing us to wi l l yes or no, to give way to or to "stand up to t emptation". Of cours e I do not know this; i t is sp e cu l a t ion. Less s pe cul a tive ly, I wou ld re - di r ect your a tte ntion from the constructed, or what is assume d t o be constructed , to the constructi ng , that is, the practice of skills that is everywhe re entwined in the activity of science. Now these skills involve , to begin with, the us e o f our body and of tools. our own body is the only t hing in the world that we never normally experience as an ob j e ct; we experi ence it rather in terms of the world to which we are attending from our body . It is by making this intelligent use of our body that we fe e l it t o b e our body, and not simply an object. When we adopt a tool for use, we transform it from an object into a sentient extension of our body. Suppose, for instance, we are using a probe to explore a dark cavern. If we are using it f or the first time, we feel its impact against our fingers and palm ; but as we become accustomed to its use, our awareness of its imp act on the hand is transformed into a sense of its point touching the objects we are exploring. We become aware of the feelings in our hand in terms of their meaning located at the tip of the probe or stick to which we are attending. We attend from the feelings in our hand to their meaning at the tip of the probe. So, in the exercise of this and other skills, the re is a tacit background of perception and rule-following, and a focal awarene ss directed to an object. Similarly, in the vocal exp ression of a thought, I rely on an ability to produce syllabic sounds, on an acquaintance with vocabulary and a grammatical skill in stringing words together to form sentence s , but all of this muscular and linguistic know-how is tac it and subsidiary to the meaning that I am attempting to convey . All thought contains components-rules that are being followe d, pe r cept ions , dispositions to act or respond-on which we depend but of which we are not focally aware . Thought dwells in these components as if they we r e p arts o f our body. Thinking is not only of something, though it is always and necessarily that; it is also fraught with the roots from which i t springs. Like a muscular skill, it has a from-to character. So do we keep expanding our body into the world, by assimilating to it sets of particulars which we inte rgrate into comprehensive entities. So do we form, intellectually and practically, an interpreted universe pop ulated by entitie s, the p articulars of which we have interiorized for the sake of comprehending their meaning in the shape of the wholes to which they belong. �21 So do we recognize a problem, Meno's paradox to the contrary notwithstanding; to recognize a problem is to recognize that something is present though hidden; it is to have an intimation of the coherence of hitherto uncomprehended particulars. So also do we come to recognize a person, in a gesture or in the performance of a skill . Indeed, we cannot recognize a skill unless we understand that we are faced with a coordinated performance, and proceed to pick out the features that are es sential to it, the action that is at work within it . So we get to know the intimate parts of a skill and the powers of the person behind it . Finally , what about objectivity, objective science in the view I am taking? I should answer, first, that we stand on no platform, from which a strictly detached knowing is possible. The zero-point of our history is not accessible to us; even as knowers, we are subject to irreversible time. But standing within our world, the world that has come to be for us , we can once more entertain, following the example of certain Ionians, the idea of knowing as universally valid, true knowledge as a ideal , limiting notice. This will be a moment of suspension of practical acti vity. It will be a moment of wonder, in which there emerges the idea of the essentialwhatness of things, their being . To entertain the idea of such knowing is to enter consciously a tradition that i s embodied but dormant with in u s ; it is to accept, not a model, but an unfinished and unfinishable task. To seek to uncover the original meaning of this idea is an essential step toward the discovery of what we are. �?'". 3in. 2 0 Acheulian hand-axes from Furze Platt nror l\1aiclcnhcocl. P'IGTTRE l �FI"r .. RE 2s Cave P~intinp The red deer, below, frequentl y painted on the walls of Lascaux, was probably one of the principal food sources of the inhabitants of the area. Now restricted to mountainous and forested regions of Europe and Asia, this deer species--of wh ich the North American elk is a variety-formerly inhabited diverse environments. �P'!GPRE '.5: Cave Paintin!" of Wild Ox or Auroch• �P'T'1T'RE 4: 2:arl:v ~othic Alarm Glock, c. 1400, from Crurch of St. Sebaldu1 in Nuremb~rg [ - '\) --__/ , .I i ' �II ~IGURE (th• diagr.'" h 5: Po1t Windmill of th• 16th century) 'fl'IGURE 6 Roman mill with gean: after Vitruvius. �FFitTRB 7s Calendrical "'rearing from Calendar Macrine, 1st century B.C. �l'!":TTRS' 8 I 3irnpl if'ied ~f verge and f TJiagram e1cap oliot ement !'FF'RE 9 Combinetion of pendulums ~ith pall•t• int verge and Galil ro~ueed ~p e o en1 Huv gen• "J . , v �!1'Ilf11 RE' 10: ~nchor E1cgp1m1nt with n•ndulum introduced by William 8l•~snt �P'I'JPRE 11: Newcomen 1 1 Atmo1oheric Engine of 171 < .. , .. ,· .... _ Ch :a tn Pl u ~ M in( "pump rod Jl'l'"'.TTRJ? 1 ?: \'fatt Single-Acting Enl!'ine with Sen~rate Condenser 1I 'od Cylinder �., I ?'I·'!l'RE' 13: Watt I Rotqtive I c.nf!in• ~ T)ou b 1•-Actin~ ' - �W PRE 14 : The C!!rno t C:vc l e r e, \ \ \ A v, vl- v~ Vo w~ 7 - e L l.' /'1 Q, - Q.,_ f ..( cit n c '7 = 1 ~ E ~ ct>, - Q, - Q.,_ Q, - I- Q'l. c:O I �"'..,.·1' .R:;:' ' 15• 8 arn ot ' s Tl- sorem Q, I R l O a. I == Q, - W Q~::. Q, - w / Co Id w <?., ? ::. ) I Q II Net ~ e4.1- Q, Net :. Ato.. t kl <_ Q e x1v-o. c ft l I fv-c~ - (Q,' - w) c/ e I 1°vt vt J. <P, - £?,I t;; Co J,J reStY VO I ..... lV, - Q,' hot r'f'S~r Vol..- � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Description An account of the resource Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. 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Visit <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a> or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe. Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Title A name given to the resource St. John's College Formal Lecture Series—Annapolis Identifier An unambiguous reference to the resource within a given context formallectureseriesannapolis Text A resource consisting primarily of words for reading. Examples include books, letters, dissertations, poems, newspapers, articles, archives of mailing lists. Note that facsimiles or images of texts are still of the genre Text. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data paper Page numeration Number of pages in the original item. 34 pages Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource On knowing how and knowing what Description An account of the resource Typescript of a lecture delivered on September 17, 1976 by Curtis Wilson as part of the Formal Lecture Series. Creator An entity primarily responsible for making the resource Wilson, Curtis Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Date A point or period of time associated with an event in the lifecycle of the resource 1976-09-17 Rights Information about rights held in and over the resource St. John's College has been given permission to make this item available online. Type The nature or genre of the resource text Format The file format, physical medium, or dimensions of the resource pdf Relation A related resource <a title="Sound recording" href="http://digitalarchives.sjc.edu/items/show/282">Sound recording</a> Language A language of the resource English Identifier An unambiguous reference to the resource within a given context lec Wilson 1976-09-17 Deans Friday night lecture Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/a9b539a566e0b95815f9b30a80814537.pdf 84276775799eb9abd7c750189822464c PDF Text Text HOMO . LOQUENS FROM A BIOLOGICJl.L STANDPOINT by Curtis Wilson St. John's College Annapolis, 1"..aryland Septeil'ber, 1975 �The words homo loquens, in the title I announced for this lecture, mean speaking man, man the speaking one. As a designation for the human species, homo loquens perhaps has an advantage over the official zoological designation, homo s~piens, man the sapient, wise, discerning one, the one who savours the essences of things. The human capacity for loquaciousness is somewhat more obviously verifiable. But what has that capacity to do with things biological? This is a complicated and problematic topic. Forgive me if I first approach it by slow stages, then attempt a gingerly step when the going becomes treacherous~ I wish to begin with a small technical matter, an aspect of the physiology of speech-production. Respiratory patterns in different species of air-breathing vertebrates differ in many details. Different species have special regulatory systems, adapted to special behavior patterns. There is the panting of dogs, specially adapted for cooling; birds, during flight have the unique ability to increase their intake of oxygen a hundredfold; the sperm whale can go without breathing or dive for 90 minutes, the beaver for 15, man for about 2 1/2; and so on. All these differences are species-specific. In a human being, the respiratory patterns during quiet breathing and during speech are remarkably different (see Table I). The volume of air inhaled, as shown in the first item of the table, increases by a factor of 3 or 4 during speech. The time of inspiration, as compared with the time for a complete cycle of inspiration plus expiration, decreases by a factor of 3. The number of breaths per minute tends to decrease drastically. Expiration, which is smooth during speechless breathing, is periodically interrupted during speech, with a build-up of pressure under the glottis; it is during expiration that all normal human vocalization occurs. The patterns of electrical activity in expiratory and inspiratory muscles differ radically during quiet breathing and during speech. Both chest and abdominal musculature are utilized in breathing, but during speech the abdominal musculature is less involved, and its contractions are no longer fully synchronized with those of the chest musculature. In quiet breathing, one breathes primarily through the nose; during speech, primarily through the mouth. More than you wanted to know, I'm sure. My point was to show that breathing undergoes marked changes during speech. And remarkably, humans can tolerate these modifications for almost unlimited periods of time without experiencing respiratory distress; witness fillibusters in the U. s. Senate. Think now of other voluntary departures from normal breathing patterns. If we deliberately decide to breathe at some arbitrary rate, say, faster than ordinary -- please do not try it here -- we quickly experience the symptoms of hyperventilation: light-headedness, giddiness, and so on. Similar phenomena may occur when one is learning to play a wind instrument or during singing instruction; training in proper breathing is requisite for these undertakings. By contrast, talking a blue streak for hours on end comes naturally to many a three-year-old. The conclusion must be that there are sensitive controlling mechanisms that regulate ventilation in an autonomous way during speech. More generally, it is evident that we are endowed with special anatomical and physiological adaptations that �-2- enable us to sustain speech for hours, on exhaled air. Do we speak the way we do because we happen to possess these special adaptations, or did these adaptations develop during evolution in response to the pressures of natural selection or the charms of sexual selection? I think there is no way of answering these questions; it is difficult enough when one can refer to skeletons, which fossilize; behavioral traits do not. But whatever the answer, there is still this further question, whether the genetic programming for speech extends beyond the mere provision of vocal apparatus? Might it not, in addition, determine the make-up and structure of language in a more detailed and intimate fashion? Such a question runs counter to views that are widely held. Is not language, after you have the voice to __ pronounce it with, fundamentally a psychological and cultural fact, to which biological explanations would be largely irrelevant? Do not languages consist of arbitrary conventions, made up in the way we make up the rules of games? Wittgenstein speaks of language as a word-game, thereby likening it to tennis or poker. Is it not apparent that the conventions of any particular language, like the rules of :tennis o::-: poker, are transmitted from generation to generation by means of imitation, training, teaching and learning? Are not these the important facts about language, the facts that reveal to us its nature? Until recently, students of linguistics and psychology have tended uniformly to answer these questions in the affirmative. To many, the extraordinary diversity of human tongues has seemed argument enough against any assumption of linguistic universals, that is, characteristics of language imagined to be rooted in human nature. The reductio ad absurdurn often mentioned is the attempt of the Egyptian king Psammetichos to determine the original human language. As reported by Herodotus, Psammetichos caused two children to be raised in such a way that they would neither hear nor overhear human speech, the attendants being instructed meanwhile to listen out for their first word. The report was, that is was Persian. The experiment is said to have been repeated in the 13th century by Frederick II, Holy Roman Emperor, and again around 1500 by James IV of Scotland, who was hoping that the children would speak Hebrew, and thereby establish a biblical linec:_ge for Scotland. No result was reported. Stress on the arbitrariness of language has been enhanced by a coalition between linguistics and behaviorist psychology. Behaviorist psychology is led, by its premisses, to the view that language is merely an arbitrary use to which the human constitution, anatomical and physiological, can be put, just as a tool can be put to many arbitrary uses by its manipulator. A recent account that views language in this way is the book Verbal Behavior by B. F. Skinner. Along with other behaviorist scientists, Skinner holds that all learning can be explained by a few principles which operate in all vertebrates and many invertebrates. The process is called operant conditioning. Learning the meaning of a word, Skinner holds, is like a rat's learning to press a bar which will cause a buzzer to sound, announcing "food pellets soon to come". Learning grammar, likewise, is supposed to be like learning that event A is followed by event B, which is in turn followed by event c. Many an animal can be trained to acquire associations �-3- of this kind. Skinner would hold that there is nothing involved in the acquisition of language _that is not involved in learning of this kind. Unquestionably, we would be mistaken to deny the importance or the power of the conditioned reflex, either in language acquisition or in other learning. The experimental psychologists have recently announced that even the visceral organs can be taught to do various things, on given signals, with rewards provided immediately afterward to reinforce the action. We are told that rats, with the reward held out of another shot of electrical juice in a certain center of the brain, have been taught to alter their blood pressures or brain waves, or dilate the blood vessels in one ear more than those in the other. Similar achievements in operant conditioning are held out as a bright future hope for humans. What rich experiences in self-operation are not in store for us? On the other hand, the successes of this technology do not necessarily tell us much about the character of what it is that is being conditioned. The behaviorist treats the organism as a black box; he controls the inputs and records the outputs; what goes on in the box is not, as he claims, an appropriate concern of his. He cites the similar situation in quantum physics. In the case of quantum phenomena, the physicist cannot successfully describe what is there when he is not looking, not using probes that interact with whatever it is. But, _ between the situation in quantum physics and the situation in the study of animal behavior, there is this difference. Animal behavior goes on, observably so, · even when the animals are not being experimented on. May it not be important to try to observe this behavior, before we .set out to change it, as we can, so frighteningly, do? Those who study the behavior of animals in their natural habitats nowadays have a special name for their study, Ethology. Long hours of patient observation, much of it during the last 50 years, have demonstrated how intricate, how unexpectedly adaptive, how downright peculiar, are the patterns of behavior specific to particular species of animals. Many of the patterns function as communication: the elaborate courtship rituals of birds, the less elaborate ones of butterflies and certain _ ish; the way in which two dabbling ducks, on meeting, lower their f bills into the water and pretend to drink, as an indication of nonagressiveness; and so on. Among these behaviors, there is one tha.t has been called truly symbolic. That is . the dance of the honeybee, the symbolism of which was first recognized and deciphered by Karl von Frisch in the 1940's. Let me describe it briefly (see Figure I) • The dance that a forager bee performs in the dark hive gives, by a special symbolism, the distance and direction of the food source she has found. If, for the Austrian variety of bee, the food source. is less than 80 meters away, she performs a round dance, running rapidly arouna in a circle, first to the left, then to the right. This in effect says to the hive bees: "Fly out .from the hive; close by in the neighborhood is food to be fetched." �-4If, on the other hand, the food source is more than 80 meters away, the forager will use the tail-wagging dance. The rhythm of the dance tells the distance: the closer the source, the more figure-of-eight cycles of the dance , per minute. The tail-wagging part of the dance, shown by the middle wavy line in the diagram, tells the direction, in accordance with a curious rule. On the vertical honeycomb_ in the hive, the direction up means towards the sun, and the direction down means away from the sun. If the tail-wagging run points 60° left of straight up, the food source is 60° to the left of the sun, and so on. Directions with respect to the sun have been transposed into directions with respect to gravity, the directions are reported with errors of less than 30. This same dance is used in the springtime when half the bees move out of the hive and form a swarm, seeking a new nesting place. Scout bees fly out in all directions, then return and dance to announce the location they have hit on. It is important, of course, that the selected spot be protected from winter, winds, and rough weather, and that there be abundant feeding nearby. The surprizing thing is that not just one nesting place is announced, but several at the same time. The dancing and the coming and going can continue for days. By their dances the bees engage in mutual persuasion, inciting one another to inspect this site or that site. The better the site, the longer and more vigorously the the returning bee dances. The process continues until all the scout bees are dancing in the same direction and at the same rate. Then the swarm arises and departs for the homesite it has thus decided upon. Mistaken decisions are few. The dance human language the language a depends solely of the honeybee is symbolic in a genetically determined way. That is not genetically determined in the same way is easy to show: child learns, whether Swahili, Cantonese, Urdu, or any other, on the language of those by whom he is brought up. · The vocabulary of a human language is not genetically fixed. However, I do not believe that the discussion of the biological foundations of language can properly end at this point. My reasons for saying this are two. In the first place, there are certain features of human speech which are not found in the natural corrnnunication systems of animals, but which are found universally in all known human languages, present or past. The existence of these features is, at the very least, consonant with the possibility that there is a genetic foundation underlying human speech. The facts appear to be most easily accounted for by assuming that there is such a foundation, , forcing human speech to be of a certain basic type. Secondly, this same assumption receives support from the study of primary language acquisition in children. It is not that Psammetichos was right, or that children if left to themselves would commence to speak proto-IndoEuropean or any language resembling adult human language. All genetically determined traits depend for their appearance to a greater or lesser degree, on features of the environment. The genes or genetic factors do not of themselves determine an �-sbody parts or physiological or behavioral traits. Rather, they determine developmental processes, which nonnally succeed one another in a determinate way, but can be profoundly affected by environmental influence. These facts point to the possibility that genetically determined traits might appear only in the course of maturation, and then only in response to specific influences from outside the organism. Ethologists inform us of many instances of speciesspecific, genetically based behavior that emerge only in this way. An example is imprinting. Thomas More described it in his .Utopia. Chicks or ducklings or goslings, a few hours or days after hatching, enter a critical period. Whatever object they first encounter during this period, within certain limits of size, and moving within appropriate limits of speed, they begin to follow, and continue to follow through childhood. The object followed can be, and usually is, the mother; but it can also be an ethologist like Konrad Korenz on his hands and knees, or something stuffed at the end of a stick. Failure to. develop imprinted responses during infancy may cause behavioral abnormalities in the adult bird -- abnormalities that cannot be corrected by later training.· Imprinting is only one of many known species-specific characteristics or behaviors that appear in the course of development, in response to what are sometimes called "releasers", environmental stimuli of specified kinds. It will be my contention that important features of human linguistic capacity are of this kind. After discussing these two points, I shall conclude with certain reflections on what they might mean. I begin, then, with three features of human speech that do not appear to be found in the natural communication systems of animals (see Table II) : 1. Phonematization 2. Concatenation 3. · Granunar What is meant by phonematization? The vocalizations heard in the human languages of the world are always within fairly narrow limits of the total range of sounds that humans can produce. We are able to imitate, for instance, the vocalizations of mammals and birds with considerable accuracy, given a little training, but such direct imitations never seem to be incorporated in the vocabularies of human languages. In all human languages, the meaningful units, words, or more strictly speaking, morphemes, are divisible into successive, shorter, meaningless sounds called phonemes. Morphemes are the smallest meaningful units into which an utterance can be .divided. A morpheme can be a single word such as "water"; it can be more than one word as in "spick and span"; and it can be less than a single word, as in the "er" in "whiter", which turns the adjective "white" into a comparative. Phonemes are the meaningless sounds into which morphemes can be di.v ided. A phoneme is not, strictly speaking, a single sound, but rather a small class of sounds; it can be defined as the smallest �-6distinctive unit functioning within the sound system of a language to make a difference. Refinements aside, the central fact I wish to convey is this: in all languages, morphemes are constituted by sequences of phonemes. This is a fact that the inventors of the alphabet were probably about the first to come to understand. The fact could have been different. One can imagine a language in which the symbol for a cat was a sound resembling a miaow; in which size was represented by loudness, color by vowel quality, and hunger by a strident roar. Morphemes in such a language would not be analyzable into phonemes. All human languages are phonematized, but each language uses a somewhat different set of phonemes, in each case a small set. Parrots and mynah birds excel other animals in the imitation of human speech, but i t is doubtful that they speak in phonemes. The matter could be put to a test. A parrot that had heard only Portuguese, and had acquired a good repertory of Portuguese words and phrases, could be transferred into an environment where he would hear only English, and have the opportunity of repeating English exclamatory remarks. If these remarks emerged with a Portuguese accent, the n it would be clear that the parrot had learned Portuguese phonemes, which he proceeded to use in the vocalization of English words. In the opposite case, we would conclude that the parrot had the capacity to imitate sounds accurately, but had not acquired the habit of using phonemes for the production of speech. In the human child, speech by the same test would turn out to be phonematized. The second general characteristic of human speech I have listed is concatenation. Human utterances seldom consist of single morphemes in isolation; in no human speech-community are utterances restricted to single morphemes; in all languages, morphemes are ordinarily strung together into sequences. To be sure, the peoples of many, perhaps most cultures, are less garrulous than we; they use language only in certain circumstances and only somewhat sparingly, while we talk a good deal of the time. It is nevertheless true that humans in all speech-communities concatenate morphemes. The third property presupposes concatenation; it is the property of grammatical or syntactical structure. By "structure" I am going to mean a set of relations that can . be diagrammed. In no language are morphemes strung together in purely random order. Native speakers of a language normally agree in rejecting certain utterances as ungrammatical, and in recognizing certain other utterances as grammatical. According to Noam Chomsky, for instance, the sentence "colorless green ideas sleep furiously" is grammatical, though meaningless or nearly so; the concatenation ... furiously sleep ideas green colorless", the same words in revers e order, is ungrammatical. The one concatenation admits of a syntactical diagram, the other does not. �-7It is generally assumed in linguistics that the grammar of a language is completely describable by means of a finite and in fact small set of formal rules. For no natural language has such a description been achieved as yet, otherwise one could program a computer to utter the grammatical sentences in the language. Apparently the mechanism involved in the grammar of a natural language is complex. I shall return to this topic again; the point now is just the W1iversality of grammar -- a relatively complex kind of system -- as a feature of human languages. All three properties I have described are, so far as the available evidence indicates, without cultural histories. Phonematization, concatenation, grammatical structure, are features of all known human language, past or present. And although languages are always in process of change, it is not the case that these changes follow a general pattern from a stage that can be called primitive to one that can be called advanced. No known classification or analysis of human languages provides any basis for a theory of the development of language from aphonemic, non-grammatical, or simple imitative beginnings. These facts are consonant with the hypothesis that there is a genetic foundation underlying human speech, forcing it to be of a certain basic type, and in particular, to have the features I have just described. In support of this hypothesis, I take up now the development of language in the child. The first sound a child makes is to cry. Immanuel Kant says the birth cry has not the tone of lamentation, but of indignation and of aroused wrath; presumably because [the child] wants to move, and feels his inability to do so as a fetter that deprives him ·o f his freedom. More recently a psychoanalyst has written of the birthcry: It is an expression of the infant's overwhelming sense of ir.feriority on thus suddenly being confronted by reality, without ever having had to deal with its problems. In view of the anatomical immaturity of the human brain at birth, these adult interpretations are rather surprizing. No doubt the infant in being born undergoes a rude shock. But crying is a mechanism with a number of importan~ functions; one of the earliest is clearing fluid out of the middle ear, so that .the child can begin to hear. The mechanism is ready to operate at birth, and the infant puts it to work. The sound made in crying changes slightly during childhood, but otherwise does not mature or change during one's life. Crying is not a first step in the development that leads to articulate speech; it involves no articulation; the infant simply blows his horn without operating the keys. A quite distinct sort of vocalization begins at about the 6th or 8th week after birth: little cooing sounds that appear to be elicited by a specific stimulus, a nodding object resembling a face in the baby's visual field. A �-8clown's face painted on cardboard, laughing or crying, will do for a while. The response is first smiling, then cooing. After about 13 weeks it is necessary that the face be a familiar one to elicit the smiling and cooing. During cooing, some articulatory organs are moving, in particular the tongue. The cooing sounds, although tending to be vowel-like, are not identical with any actual speech sounds. Gradually they become differentiated. At 6 months they include vocalic and consonantal components, like /p/ and /b/. Cooing develops int.o babbling resembling one-syllable utterances, for instance /ma/, /mu/, /da/, /di/. However, the babbling sounds are still not those of adult speech. The first strictly linguistic feature to emerge in a child's vocalizations is contour of intonation. Before the sound sequences have determinable meaning or definite phonemic structure, they come out with the recognizable intonation of .questions, exclamations, or affirmations. Linguistic development begins not with the putting together of individual components, but rather with a whole tonal pattern. Later, this whole becomes differentiated into component parts. Differentiation of phonemes is only approximate at first and has to be progressively refined. The child is gradually gaining control of the dozen or so adjustments in the vocal organs that are required for adult speech. By 12 months he is replicating syllables, as in "mamma" and "dada". By 18 months he will normally have a repertory of three to 50 recognizable words. I have described this development as though mothers were not trying to teach, but of course they normally are. It is nevertheless a striking fact that these stages emerge in different cultures in the same sequence and at very nearly the same ages, and in fairly strict correlation with other motor achievements. Detailed studies have been made of speech acquisition among the Zuni of New Mexico, the Dani of Dutch New Guinea, the Bororo in central Brazil, and children in urban U.S.A.; in all cases, intonation patterns become distinct at about the time that graspin9 between thumb and fingers develops; the first words .appear at about.the time that walking is accomplished; and by the time the child is able to jump, tiptoe, and walk backward, he is talking a blue stre:i.k. Among children born deaf, the development from cooing through spontaneous babbling to well-articulated speech-sounds occurs as with normal children, but of course the development cannot continue onward into the stage at which adult words are learned through hearing. Among the mentally retarded, these developments are chronologically delayed, but take place with the same correlation between various motor achievements. Given the variety of envirorunental conditions in these several cases, it seems plausible to attribute the emergence of linguistic habits largely to maturational changes within the growing child, rather than to particular training procedures. The specific neurophysiological correlates of speech are l .i ttle known, but that there are such correlates and that they mature as speech develops is supported by much evidence. The human brain at birth has only 24% of its adult weight; by contrast, the chimpanzee starts life with a brain that already weighs 60% of its adult value. The human brain takes longer to mature, and �-9- more happens as it matures, including principally a large increase in the number of neuronal connections. A large part of the discernible anatomical maturation takes place in the first two years; the process appears to be complete by about 14 years of age. By this time the neurophysical basis of linguistic capacity has become localized in one of the two cerebral hemispheres, usually the left. If by this time a first language has not been learned, no language will ever be learned. Speech defects due to injuries to the brain that occur before the final lateralization of the speech-function are usually overcome; but if the injury comes after lateralization, the speech defect will be permanent. Capacity for speech does not correlate uniformly with size of brain. There is a condition known as nanocephalic dwarfism, in which humans appear reduced to fairy-tale size; adult individuals attain a maximum height of between two and threefeet (see Table III). Nanocephalic dwarfs differ from other dwarfs in preserving the skeletal and other bodily proportions of normal adults. Brain weight in these dwarfs barely exceeds that of a normal newborn infant. The brain weight of the nanocephalic dwarf, given in the middle row, is only a little over a third of that of a 2 1/2 year old boy, but the ratio of body weight to brain weight is equal to that of a 13 1/2 year old boy. These dwarfs show some retardation in intellectual growth, and often do not surpass a mental age-level of ~ or 6 years. But all of them acquire the rudiments of language, including speaking and understanding; they speaJc grarm:natically, and can manufacture sentences which are not mere repetitions of sentences they have heard. The appropriate conclusion appears to be that the ability to acquire language depends, not on any purely quantitative factor, but on specific modes of organization of human neurophysiology. One further point concerning the neurophysiological basis of language. The main evidence here is provided by aphasias (aphasia= a +~ava1, not+ to speak). These are failu~es in production or comprehension of language, resulting from injuries to the brain. And this evidence argues, for one thing, against regarding language ability as being encoded simply in a spatial layout of some kind, say a network of associations in the cerebral cortex. Subcortical areas are involved, as well as cortex. The aphasias most frequently involve, not disruption of associations, but rather disruption of temporal order, affecting either phonemes in the production of words, as in spoonerisms, or words and phrases in the production of sentences. The patient is unable to control properly the tempcral ordering of these units, and as a consequence they tumble into the production line uninhibited by higher syntactic principles. In general, the sympton is lack of availability of the right thing at the right time. Language is through-and-through an affair of temporal patterns and sequences. The neurophysiological organization required for this cannot be simply that of associations. In the making of speech-sounds, for instance, certain muscles have to contract, the efferent nerve fibers innervating these muscles are of different lengths and diameters, and as a consequence the times required for a �-10- nerve inpulse to go from brain to muscle differ for different muscles. Hence the nerve im.pulses for the production of a single phoneme must be fired off from the brain at different times, and the sequences of impulses for successive phonemes must overlap in complex ways. In the simplest sequential order of · events, it thus appears that events are selected, not in response to immediately prior events, but in accordance with a hierarchic plan that integrates the requirments for periods of time of several seconds' duration. All this patterning in time is thought to depend on a physiological rhythm of about 6 cyles per second, in relation to which other events are timed. Arrangements of this complexity do not come about by learning. The evidence here, as well as the observations I have already described as to the way voice-sounds develop in children, points to the existence of an innate mechanism for the production of phonemes, one which is activated by a specific input, the appearance of the human face, and which matures in stages. Could anything similar be argued for competence in syntax, the ability to understand and produce grarn.~atical sentences? Here you will undoubtedly be more doubtful, for surely the grammars of different languages are different. Please recall that the sets of phonemes used in different languages are also somewhat different. The universality of phonematization is compatible with different languages employing different. subsets of the humanly possible phonemes. The claim for universa~ity of grammar must be of similar kind. The grammars of human languages are not of just any imaginable kind of ordered concatenation of morphemes. Rather, they derive from a certain subclass of the imaginable orders, a subclass involving phrase structure and what has been called "deep structure". The production of grarrnnatical sentences turns out to pose requirements similar to those necessary for the temporal ordering of phonemes; a serial order in which one element determines the next is insufficient; there has to be hierarchical organization, in which elements connected with one a,.,other are separated temporally in the production line. Let me return now to the description of stages in the primary acquisition of language by a child. At about the end of the first year of life, the child normally utters his first unmistakeable word. For a number of months, while the child is building up a repertory of about 50 words, he utters only single-word utterances. He frequently hears sentences like "Here is your milk", "Shall daddy take you by-by?", and so on, but he will neither join together any two words he knows nor can he be induced to do so on request. Does he lack the memory or the vocalizing power to produce a two-word utterance? The evidence is against these suppositions. Then, roughly between 18 and 24 months, he suddenly and spontaneously begins to join words into two-element phrases: . "up baby", "baby highchair", "push car", and so on. What explains the shift? An important observation at the one-word stage is that these single words are given the intonations or pitch-contours of declarative, interrogative, or �-11- hortatory sentences. The single-word utterances seem to function in meaning in the same way as sentences will function later cm: "Doggie" might mean, for instance, "There is a dog". When the two-word construction "push car" appears, it is not just two single-word utterances spoken in a certain order. As single-word utterances, both "push" and "car" would have primary stresses and terminal intonation contours. But when they are two words programmed as a single utterance, the primary stress and higher pitch come on "car"; and the unity of the whole is indicated by the absence of a terminal pitch contour between the words and the presence of such a contour at the end of the sequence. What appears to be happening is that the child is by stages increasing his span, his ability to plan or program longer utterances. Grammar is already present in embryo. Further development will be a process of successive increases in span or integration, on the one hand, and progressive differentiation of the parts of utterances on the other. Imitation plays a role in this process, but it is seldom mere parroting. In Table IV I have listed some imitations actually produced by two children, whom I shall call Adam and Eve; both were about two years old. First note that the imitations preserve the word orderof the model, even when not preserving all·the words. This is not a logical necessity; it is conceivable that the child might reverse or scramble the order; that he does not suggests that he is processing the utterance as a whole. A second fact to notice is that, when the models increase in length, the child's imitation is a reduction, and that the selection of words is not random. The words retained are generally nouns, verbs, and less often adjectives: words sometimes called "contentives", because they have semantic content; their main grammatical function lies in their capacity to refer to things. The forms omitted are what linguists call "functors", their grammatical functions being more obvious than their semantic content. The omission of the functors leads to a kind of telegraphic language, such as one uses in wiring home: "Car broken down; wallet stolen; send money American Express Baghdad". In the child's telegraphic utterances, how will the appropriate functors come to be introduced? While the child engages in imitating, with reductions, the utterances of the mother, the mother frequently imitates, with expansion, the utterances of the child (see Table V). The mother's expansions, you will note, preserve the word order of the child's sentences, she acts as if the child meant everything he said, and more, and it is the "more" that her additions articulate. She adds functors. The functors have meaning, but it is meaning that accrues to them in context rather than in isolation. The functors tell the time of the action, whether it is ongoing or completed; they inform us of possession, and of relations such as are indicated by prepositions like in; on, ~' down; they distinguish between a particular instance of a class as in "the highchair", and an arbitrary instance of a class, as in "a sandwich"; and so on. �-12How or to what extent these adult expansions of the child's utterances help the child to learn grammatical usage is uncertain. It has been found that inunediate imitations by the child of just uttered adult sentences are less frequently well-formed than spontaneously produced utterances. The view that progress toward adult norms arises merely from practice in overt imitation of adult sentences is clearly wrong. The child rather appears to be elaborating his own grammar, making use of adult models, but constantly analogizing to produce new and often mistaken words or forms. Take pluralization (see Table VI) . In English there are a few irregular plurals, as of mouse, foot, man. The child normally regularizes these plurals: mouses, foots, mans. Instead of foot vs. foots, some children give feet for the singular, feets for the plural. One does not get an initial fluctuation between foot and feet, such as one would expect if only imitation of adult forms were a _ work. t Most English plurals are regular and follow certain formal rules. Thus we have mat vs. mats, but ~atch vs. matches. Words ending in sibilants, such as match, hors e , b o x, add a vowe l before the..§_ of the plural. Children have difficulty with pluralizing these words, and tend at first to use th e singular form for both singular and plural. Sometime s a child will analogize in such a way as to remove the sibilant, substituting for instance, for box vs. boxes, the singularplural pair bok vs. boks. Then at some point the ch~ld produces the regular plural of a sibilant word, say, boxes. Frequently when this happens he may abandon temporarily the regular plural for non-sibilant words, so that one gets foot vs. footses. What is happening? Overlaid on the child's systematic analogic forms, there is a gradual accumulation of successful imitations which do not fit the child's system. Eventually these result in a change in the system, often with errors due to over-generalizing. Consider also the past tense inflection, which in English bears considerable similarity to the plural inflection (see Table VI again). There are regular forms like walk-walked, and irregular ones like go-went. Among the regular verbs, the form of the past d e pends on the final phoneme of the simple verb: so we have pack-packed and pat-patted. In the case of past-tense inflection in contrast with pluralization, however, the most fre q uently used forms are irregular, and the curious fact is that the child often starts regularizing these forms before having been heard to produce any other past-tense forms. Thus goed, doed, corned appear among the first past-tense forms produced. The analogizing tendency is evidently very strong. · The occurrence of certain kinds of errors on the level of word construction thus reveals the child's effort t.o induce regularities from the speech he is exposed to. When a child says, "I buyed a fire car for a grillion dollars," he is not imitating in any strict sense of the term; he is constructing in accordance with rules, rules which in adult English, are in part mistaken. At every stage, the child's linguistic competence extends beyond the sum total of the sentences he has heard. He is able to unders tand and construct sentences �-13- which he cannot have heard before, but which are well-formed in terms of general rules that ar·e implicit in the sentences he has heard. Somehow, genius that he is, he induces from the speech to which he is exposed a latent structure of rules. For the rest of his life, he will be spinning out the implications of this latent structure. By way of illustration of this inductive process, and .of a fur~her stage in the achievement of grarrunatical competence, let me indicate some aspects of the development of the noun phrase in children's speech (see Table VII). A noun phrase con~.ists of a noun plus modifiers of some kind, which together can be used in all the syntactic positions in which a single noun can be used: alone to name or request something, or in a sentence as subject, object, or predicate nominative. The table at the top gives a number of noun phrases uttered by Adam or Eve at about two years of age. Each noun phrase consists of one word from a small class of modifiers, M, followed by one word from the large class of nouns, N. The rule for generating these noun phrases is given below in symbols: NP · is generated by M plus N. The class M does not correspond to any single syntactic class in adult English; it includes indefinite and definite articles, a possessive pronoun, a demonstrative adjective, a quantifier, a cardinal number, and some descriptive adjectives. In adult English these words are of different syntactic classes because they have very different privileges of occurrence in sentences. For the children, the words appear to belong to a single class because of their common privilege of occurrence before nouns; the lack of distinction leads to ungranunatical combinations, which are marked in the table by an asterisk. Thus the indefinite article should be used only with a · comrnon count noun in the singular, as in "a coat"; we do not say "a celery", "a Becky", "a hands". The numeral two we use only with count nouns in the plural; hence we do not say "two sock". The word "more" we use before mass nouns in the singular, as in "more coffee", and before count nouns in the plural, as in "more nuts"; we would not say "more nut". To· avoid the errors, it is necessary not only that the privileges of occurrence of words of the class M be differentiated, but also that nouns be subdivided into singular and plural, common and proper, count nouns and mass nouns. Sixteen weeks after Time I, at Time II, Adam and Eve were beginning to make some of these differentiations; articles and demonstrative pronouns were now distinguished from other mewbers of the class M. Articles now always appeared before descriptive or possessive adjectives, and demonstrative pronouns before articles or other modifiers. Twenty-six weeks after Time I, the privileges of occurrence had become much more finely differentiated. Adam was distinguishing descriptive adjectives and possessive pronouns, as well as articles and demonstrative · pronouns, from the ' residual class M; Eve's classification was even more complicated, though she was a bit younger. Also, nouns were being differentiated by both children: proper nouns were clearly distinct from common nouns; for Eve, count nouns were distinct from mass nouns. �-14Simultaneously with these differentiations, further integrations were occurring: the noun phrases were beginning to occur as constituents in longer sentences; the permissible combinations of modifiers and nouns were assuming the combination privileges enjoyed by nouns in isolation. Thus the noun phrase, for Adam and Eve, was coming to have a psychological unity such as it has for adults. This was indicated by instances in which a noun phrase was fitted between parts of a separable verb, as in "put the red hat on". It was also indicated by substitution of pronouns for noun phrases in sentences, often at first with the pronoun being followed by the noun phrase for which it was to substitute, as in "mommy get it my ladder", or "I miss it cowboy boot". Whether any theory of learning at present known can account for this sequence of differentiations and integrations is doubtful. The process is more reminiscent of the development of an embryo than it is of the simple acquisition of conditioned reflexes or associations. What is achieved is an open-ended competence to comprehend sentences never before heard, in terms of a hierarchical structure, that embeds structures within structures. To illustrate, let me use, not a child's sentence, but an example that Chomsky excerpts from the Port Royal Grammar of 1660 (see Figure II). The sentence is: "Invisible God created the visible world". The sentence may be diagrammed as shown in the figure; Chomsky calls these diagrams phrase markers. There is a phrase marker for what he calls surface structure; this has the function of determining the phonetic shape and intonational contour of the sentence. And there is a phrase marker for what he calls deep structure; this shows how prior predications are embedded in the sentence, and determine its meaning. Are formal structures like the one indicated by this diagram really operative when linguistic competence is being exercised? There are a number of indications that this is so. One indication is the extent to which the understanding of language involves resolution of ambiguities, or disambiguation as it is sometimes massively put. Consider the sentence "They are boring ' student~" (see Figure III) . This has two different interpretations, which are represented by the diagrams on the screen. In interpretation A, the word "boring" is linked with the word "students"; the students are thus characterized as boring. In interpretation B, the word "boring" is linked with the word "are", which thus becomes the auxiliary verb in the present progressive tense of the verb "to bore", it is the students who are being bored, by certain other persons designated by "'.:he pronoun "they", but otherwise mercifully unidentified. In an actual conversation, the context of meaning would have led us to apply, as quick as a thought or perhaps more quickly, the correct phrase marker to the interpretation of the sequence of uttered sounds. Other examples show how deep structures are essential to understanding (see Table VIII). Consider the two sentences: John is eager to please John is easy to please. �-15- These sentences have the same surface structure. But a moment's thought shows that the word "John" has two very diffe·r ent roles to play in the two sentences. John in the first sentence is the person who is doing the pleasing; in the second sentence he is the person who is being pleased. John is the underlying subject in the first case, and the underlying object in the second case. Deep structure or grammar is involved in understanding the difference in meaning of the two sentences. An opposite sort of case occurs when the surface granunars of two sentences are different, although the meaning is essentially the same. Consider this sentence in the active mode: "Recently seventeen elephants trampled on my summer home". Now consider the following sentence in the passive mode: "My summer wa.s trampled -on recently by seventeen elephants." A native speaker of English feels that these sentences are related,that they have the same or very similar meanings. Yet their surface structures are very different. Recognition that both sentences are describing the same event presupposes that speaker anJ. hearer refer them both to a single deep structure embodyin~ the single meaning. Something similar happens in recognition of similarity between visual patterns, where there is no point-to-point correspondence between them. Now all of this is unlikely to . seem astonishing, for it is' very familiar, You and I, like the bourgeois gentilhomme, have been speaking and listening to more or less grammatical prose for a long time now. People living at the seashore are said to grow so accustomed to the murmur of the waves that they never hear it. Aspects of things that could be important to us may be hidden by their familiarity. The point I have been seeking to make is one that is due to Noam Chomsky, a linguist I have been depending on more than once this evening. The grammaticality of human languages involves properties that are in no sense necessary properties of a . system that would fulfill the functions of human communication. A grammar, for instance, in which statements would be generated · word-by-word, from left to right, so to speak, so that any given morpheme would determine the possible classes of morphemes that might follow it, is a kind of grammar that might have been used, but was not. Instead, human speech involves dependencies between non-adjacent elements, as in .the sentence "A.Tlyone who says that is lying", where there is a dependency between the subject noun "anyone" and the predicate phrase "is lying". All operations in human languages, transforming, for instance, an active into a passive sentence, or a declarative into an interrogative sentence, operate on and take account of phrase structure. Example: we form the1nterrogative of the English.sentence, "Little Mary lived in Princeton",. by introducing an auxiliary to the verb ("Little Mary did live in Princeton"), then inverting the order of the auxiliary and the noun-phrase which is the subject, to get "Did Li.ttle Mary live in Princeton?" It would be entirely possible to form interrogatives in a different way independently of phrase structure. There is no apriori reason why human languages should make use exclusively of structure-dependent operations. It is Chomsky's conclusion that such reliance on structure-dependent operations must be predetermined for the language learner by a restrictive initial schematism of some sort, given genetically, and directing the child's attempts to acquire linguistic competence. �-16Put differently, one does not so much teach a first language, as provide a thread along which linguistic competence develops of its own accord, by processes more like maturation than learning. The Chomskian analysis requires that we take one more step. The fact that deep structures figure in the understanding and use of language shows that grammar and meaning necessarily interpenetrate. The child's grammatical competence matures only along with semantic competence, the organization of what can be talked about in nameable categories and hierarchies of categories. This process, like the development of grammatical competence, involves successive differentiations. Sensory data are first grouped into as yet global classes of gross patterns, and then subsequently differentiated into more specific patterns. The infant who is given' a word su.ch as "daddy", and has the task of finding the category labelled by this word, does not start out with the working hypothesis that a specific, concrete object, say his father, uniquely bears this name. Rather, the word initially appe ars to be u s ed as the labe l of a general and open category, corresponding to the adult category of people or men. Infra-hwnan animals are taught with difficulty, if at all, to make the generalizations involved in naming, whereas children fall in with the ways of names automatically. Name s, other than proper names, refer to ope n and flexibl e c l a s ses, which are subj e ct to e xte nsion and differentiation in the ~ourse of languag e usage. Catego rization and naming involve relations between categories; nothing ever resides in a single term; ~ means nothing without £ and probably ~ and ~; £ means nothing without .5:.. and c and d. Children go about assimilating the relations that are embodied in language, not me rely imitatively, but in an active, inventive, and critical way. They are full of impossible questions: "How did the sky happen? How did the sun happen? like a lamp? Who makes bugs?" Why is the moon so much At first, they are ultra-literal in their reactions to idioms and metaphors. When grandmother said that winter was coming soon, the grandchildren laughed and wanted to know: "Do you mean that winter has legs?" And when a lady said "I'm dying to hear that concert", the child's sarcastic response was, 11'Then why don't you die?" Sometimes reconciliation of adult requirements requires genius. Chukovsky reports that a four-year-old Muscovite, influe nced both by an atheist father and by a grandmother of orthodox faith, was overheard to tell her playmate: "There is a god, but, of course, I do not believe in him." The active analogizing and generalizing of 4- and 5-year olds is discernible in the odd questions they can put: "What is a knife -- the fork's husband?" "Isn't it wonderful? I drink milk, water, tea, and cocoa, but out of me pours only tea." "What does blue look like from behind?" �-17For a certain period, there is a special, heightened sensitivity to the strangeness of words and their meanings; by age 5 or 6 this talent begins to fade, and by 7 or 8 all traces of it have disappeared. The need has passed; the basic principles of the child's native language have been mastered. What is it that has in fact been gained? We say, knowledge of a language. But what is a language, my language? Thoughtfully considered, this is a wellnigh impossible question, because a language is .not a simple object, existing by itself and capable of being grasped in its totality. It exists in the linguistic competence of its users; it is what Aristotle would call an actuality of the second kind, like the soul, or like knowing how to swim when you are not swirruning. Through it I constitute myself a first-person singular subject, by using this short word "I", which everyone uses, and which in each seems to refer to something different, yet the same. And through it I am brought into relation with others -- the ubiquitous "you" -- and with the public thing that is there for both you and me, a treasury of knowledge and value transmitted through and embedded in language. We hear language spoken of as "living language", and there is evidence enough to make it more than a metaphor. Language reproduces itself from generation to generation, remaining relatively constant, yet with small mutations, enough in fact to account for-its growing and evolving, leaving vestiges and fossils behind, and undergoing speciation as a result· of migrations,, like Darwin's finches on the Galapagos Islands. A change here provokes an adjustment there, for the whole is a complex of relations, mediating between a world and human organisms that are a part of it. The way a word is used this year is, in biological lingo, its phenotype; the deep and more abiding sense in it is its genotype. It is we, of course, who are accomplishing all this; but we do not know how we accomplish it. It is mostly a collective, autonomic kind of doing, like the building activities of ants and termites, or the decision-making of bees. It takes generation after generation, but we are part of it whenever and however we utter words or follow them in the sentences th.at we hear or read, whether lazily or intently, whether with habitual acceptance or active inquiry. Always the words are found for us, and fitted with meanings for us, by agents in the brain over which we exercise no direct control. We can either float with the stream, sometimes a muddy tide of slang and jargon and cliche, or struggle cross stream or upstream. Sometimes we can, sensing the possible presence of a meaning, attempt a raid on the inarticulate; we can launch ourselves into speech, discovering what it is that we mean as we proceed. We "articulate"; the word once meant division into small joints, then, by an effortless transition, the speaking of sentences. There are unexpected qutcomes. We may find that our utterance is ungrarrunatical or illogical; or we may discover that the connection of ideas leads in directions we had not previously considered. In any case, phonetic, syntactical, and semantic structures are being actualized in time, without our quite knowing how. Yet we can strive after that lucidity and precision which, when achieved, make language seem transparent to what there is. �-18I have already been carried beyond the two propositions I set out to defend, and in doing so, I have moved into a region of ambiguity. The question as to what is determined by nature, independently ofus, and what is man-made, is an ancient and disturbing question, embedded in old etymologies and myths. (See Table IX). In more than one language, the word "man" is derived from "earth". So it is in Hebrew: Adam, "man", comes from the word for "ground". As shown in the upper diagram, the IndoEuropean root for "earth" gives us "man" and "human" as well as "humus". The notion here is that of the autochthonous origin of humans, their origination from the earth itself; it is a notion found in early cultures all over the world. An implication would seem to be that man is like a plant in his naturalness. On the other hand, as shown in the lower diagram, the IndoEuropean root "wiros", "man" or "the strong one", leads not only to virile but, staggeringly, to world, suggesting that man makes himself and his world. The dicho~omy, the tension, emerges in the Theban cycle of myths (see Table X). Following a suggestion of Levi-Strauss, I am listing elements of it in chronological order from left to right and from the top downward, but in columns, to show the repetition of similar elements. Cadmus is sent off to seek his sister; he kills a dragon, a chthonic monster, that will not permit men to live, and sews the teeth of the dragon in the earth; from the teeth sprout up armed men who kill one another, all except five who become the ancestors of the Thebans. In column I are listed events of the myth in which blood relations seem to be given too much importance. In colu..~n II are listed murders of brothers by brother, of a father by a son: here blood relations are brutally disregarded. Column I is thus opposed to column II. In column III, chthonic monsters that were killing off humans are themselves killed by men; we can interpret this as a denial of the autochthonous origin of man, an assertion that man has now become selfsufficient, himself responsible for his continued existence. In column IV .a re listed the meanings of the names of the Labdacidae, including Oedipus; the etymologies all indicate difficulty in walking or in standing upright. In myths throughout the world, this difficulty in walking or standing is characteristic of the creature that has just emerged out of the earth; the names given in column IV thus constitute an assertion of the autochthonous oYigin of man. Column IV contradicts column III, just as column I contradicts column II. The myth de?ls with a difficulty of one sort, not by resolving it, but by juxtaposing it to another, parallel type of opposition. Neither man's rootedness in nature nor his transcendence of nature is unproblematic: The study of language and its acquisition by children indicates that our language has genet~c foundations or roots. These, however, have their fruition only under appropriate conditions, only through culture. Man is by nature a cultural animal. He does not fabricate his linguistic culture out of whole cloth. On the one hand, it becomes conceivable that a universal grammar and semantics might be formulated, describing the species-specific features and presuppositions that characterize human linguistic behavior universally. On the other hand, nature's gift of language brings with it an apparent freedom from deterministic necessity not previously present. Most of our sentences are quite new; it is �-lguncommon for one sentence to come out the same as another, though the thoughts be 1;.he same. Our utterances are free of the control of detectible stimuli. The number of patterns underlying the normal use of language, according to Chomsky, is orders of magnitude greater than the seconds in a lifetime, and so cannot have been acquired simply by conditioning. While the laws of generation of sentences remain fixed and invariant, the specific manner in which they are applied remains unspecified, open to choice. The application can be appropriate. Articulate, structurally organized signals can be raised to an expression of thought. Achievement here is subject to change and old laws, and it depends on a sensitivity to old meanings as well as new possibilities. It requires both strength and submission. �TABLE I Respiratory Adaptation in Speech Breathing Quietly During Speech 3 3 Tidal volume ·soo-600cm Time of inspiration Time of inspiration + expiration about 0.4 about 0.13 Breaths per minute 18-20 4-20 Expiration Continuous & unimpede d Periodically interrupted, with increase in subglottal pressure Electrical activity in expiratory muscles Nil or very low Nil or very low at start of phonation; then increases rapidly and continues active to end of expiration Electrical activity in inspiratory muscles Active in inspiration & nil during expiration Active in inspiration & in expiration till expiratory muscles become active Musculatures involved Chest & abdominal, closely synchronized Mainly chest; slight de synchronization between chest and abdominal muscles Airways Primarily nasal Primarily oral 1500-2400cm �FIGURE I ROUND DANCE ..,.,,,. / ,.... - --- / ' I l~ 1 "'-; /"'- - t / -/~: --./...: .- .--..:_ '\ '\\ "" './,, ~ \ I I I I 1 \ I I \ I I ~ ' / ' / / / ~.,.......::....- .....:.. ......... ........ . . TAIL-WAGGING DANCE -· - -..... . . ..,&'" , . lrn/ ...._ .-.,. • /?' ,,--. \ / ..-. ~ / r 'l~ -k::;~/ ' ' \. ...~~}~\. I ~ ' ) ' \ (.... ( \ ' I / ~ \ t t ' \ \ · J,- '~ ) . l I 1 \ \.. '- --....-- _.,,. / I l d ' I ' I I / -...... __. _.,,.,,.. / �TABLE II Species-specific Features of Human Speech 1. Phonematization "Morphemes": the smallest meaningful units into which an utterance can be divided. Examples: water spick and span "er" in "whiter", "taller", etc. "Phoneme": the smallest distinctive unit of sound functioning within the sound system of a language to make a difference. Examples: /p/ vs. /b/ /t/ vs. /d/ Phonematization: all morphemes in all natural human languages are divisible into phonemes. single morphemes are strung together into sequences, rather than being used in isolation. 2. Concatenation: 3. Grammar or Syntactical Structure: in no human language are morphemes strung together in purely random order. Examples (Chomsky) : Grammatical: furiously" Ungrammatical: colorless" "colorless green ideas sleep "furiously sleep ideas green �TABLE III Comparative Weights of Brain and Body in Humans, Including Nanocephalic Dwarf, Chimpanzees, and Monkeys Body Wt. (kg) Brain Wt. (kg) Human (male) 2-1/2 13-1/2 1.100 12.3 yes Human (male) 13-1/2 45 1.350 34 yes Human (male) 18 64 1.350 47 yes INanocephalic dwarf 12 13-1/2 0. 400 34 ye_s_u_ Chimp (male) 3 12-1/2 ·o.4oo 34 no 47 0.450 104 no 0.090 40 no I Chimp (female) adult Rhesus monkey adult 3-1/2 Ratio (Bcdy : Brain) Speech Acquisition Age I �TABLE IV Imitations by Adam and Eve, Two years of Age Model Utterance (parent) Child's Imitation Tank car Tank car Wait a minute Wait Daddy's brief case Daddy brief case Fraser will be unhappy Fraser unhappy He '.s going out He go out That's an old-time train Old-time train It's not the same dog as Pepper Dog Pepper No, you can't write on Mr. Cramer's shoe Write Cromer shoe a minute Contentives Nouns: Daddy, Fraser, Pepper, Cromer; tank car, minute, brief case, train, dog,shoe V~rbs: wait, go, write Adjectives: unhappy, old-time Functors: the possessive inflection 's the modal auxiliary will the progressive inflection -ing the contraction of the auxiliary verb is the preposition on the articles the and an the modal auxiliary can �TABLE V Adult Expansions of Child Pronouncements Utterances of Child Mother's Expansions (Additions circled) Baby highchair BabyE in the ) highchair Mommy eggnog Mommy(£ad herleggnog Eve lunch Eve~ having1lunch Monuny sandwich Mommy Sat wall ~sandwich ~sa~wall Throw Daddy Throw\it t~ Daddy Pick glove Pick(!he'j glove &J �TABLE VI Plural Inflection Regularization of irregular fonns: Singular vs. Plural mouse mouses foot foots feet feets man mans or: Words ending in sibilants First Stage: (as well as horse, match, judge, etc.) treated as both singular and plural ~ox bok vs. boks, in analogy with normal Possible Second Stage: "s" pluralization, replaces box vs. boxes Third Stage: after box vs. boxes is produced, then we also get foot vs. footses, hand vs. handses Past Tense Inflection goed corned / come went ~came buyed doed do --------- ~did / buy"-.... ~bought �TABLE VII TIME I: Noun Phrases with Generative Rule A coat That Adam Big boot *A celery That knee Poor man *A Becky More coffee Little top *A hands *More nut The top · *Two sock Dirty knee My Monuny · Two shoes My stool *Two tinker toy NP ~ M + N M a, big, dirty, little, more, my, poor, that, the, two N Adam, Becky, boot, coat, coffee, knee, man, Monuny, nut, sock, stool, tinker toy, top, etc. TIME II: A. Subdivision of Modifier class with Generative Rules Privileges peculiar to articles Obtained Not Obtained A blue flower *Blue a flower A nice nap *Nice a nap *A your car *Your a car *A my pencil *My a pencil Rule: B. NP -7. Art + M + N (Not: NP --7 M + art + N) Privileges peculiar to demonstrative pronouns Not Obtained Obtained *That a horse *A that horse *That a blue flower *A that blue flower * Blue a that flower Rule: NP --7 Dem + Art + M + N *Ungrammatical in adult English �FIGURE II Chomskian Phrase Markers "Surface Structure" Sentence (S) ~ Subject (Noun Phrase) Predicate /~ /~ Noun . . Adjective t .Invisible t God Verb Object \ the visible world created "Deep Structure" Sentence (S) ·~ 1~ Predicate Subject /\ God /~ Object Verb S /l~ Subject J, God Copula J is Pred . Adj. -} invisible J Created l~ S //~ Subject Copula Pred. the world J.. the world "' . is \. Adj. visible �FIGURE III "They are boring Students ... : Two Interpretations Interpretation A Sentence Predicate , Subject ~ Nominative Predicate j I Verb I I Adjective Copula Pronoun students boring are They \ J I j ~Noun Interpretation B Sentence /~ Predicate subject I~ verb Pronoun j They Object I~ Progressive Aux j are \ boring \ Noun \ students �TABLE VIII Evidence For "Deep" Structure Surface structures the same, deep structure different: John is eager to please. { John is easy to please. Surface structures different, Recently seventeen elephants trampled on my summer house. deep structures the same: My summer home was recently trampled on by seventeen elephants. Visual patterns recognized as similar, although no point-to-point correspondence exists between them. -- -7 ~- �TABLE IX Some Etymologies _/7 gum an (Germanic) dhghem ------------~----------.-:.-gumen ' (IndoEuropean) (Old English) = "earth" = "man" homo, humanitas · (Latin) humus (Latin) ="mould", "ground" chthon (Greek) = "earth" human (English) humus (English) chthonic ----,...autochthonous (English) = "fromthe earth itself" = . "of the earth" vir---(Latin) = "man" --->- virile {English) wiros (IndoEuropean) = "man" we.r (Germanic, Old English) ="man", "the~ strong one" ~ weorold ~ world (AngloSaxon) (English) = "age of man", "world" alt, old (AngloSaxon) = "age" �TABLE X I Blood relations overemphasized II IV III Blood relations underemphasized Chthonic monsters that would not permit men to live are slain by men Difficulties in walking straight and standing upright Cadmus seeks his sister Europa, ravished by Zeus Cadmus kills the dragon The Spa rti (the sown dragon's teeth) kill one another Labdacus (Laius's father) = "lame" Laius (Oedipus' s father) = "left-sided" Oedipus kills his father, Laius Oedipus kills the Sphinx Oedipus "swollen-foot" Oedipus marries his mother, Jocasta Eteocles and Polyneices, brothers, kill one another Antigone buries her brother, Polyneices, despite prohibition Column I Column II .. Column IV Column III �Bibliography (In the preparation of this lecture I made use of the following books: the book by E. H. Lenneberg, as well as the book edited by him, was particularly useful.) Benveniste, Emile, Problems in General Linguisitcs (Coral Gables, Fla.: University of Miami Press, 1971) ., Chomsky, Noam, Aspects of the Theory of Syntax (Cambridge, Mass.: M.I.T. Press, 1965) -------------, Cartesian Linguistics (New York: ------------- Language and Mind (New York: Harper & Row, 1966) Harcourt, Brace, and World, 1968) CrYstal, David, Linguistics (Penguin, 1971) Frisch, Karl von, The Dance Langua ge and Orientation of Bees (Cambridge, Mass. Belknap Press of Harvard, 1967) Goldstein, Kurt, Language and Language Disturbances (New York, 1948) Lenneberg, E. H., The Biological Foundations for Language (New York: & Sons, 1967) John Wiley Lenneberg, E. H. (ed.), New Directions in the Study of Language (Cambridge, Mass.: M. I. T. Press, 1966) Lindauer, Martin, Communication Among Social Bees (New York: Lyons, John, Noam Chomsky (New York: Atheneum, 1967) Viking Press, 1970) Saussure, Ferdinand de, Course in General Linguistics (ed. Bally & Sechehaye; tr. Baskin; New York: 1959) Skinner, B. F., Verbal Behavior (New York: Appleton-Century-Crofts, 1957) � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Description An account of the resource Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. 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Type The nature or genre of the resource text Format The file format, physical medium, or dimensions of the resource pdf Language A language of the resource English Identifier An unambiguous reference to the resource within a given context lec Wilson 1975-09-12 Relation A related resource <a title="Sound recording" href="http://digitalarchives.sjc.edu/items/show/3670">Sound recording</a> Deans Friday night lecture Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/28fc0ef83421bc48ced180ef9592f166.pdf 4752df1c50794c0b6c8b320b1782ea68 PDF Text Text On The Dis coverv of Deciucti ve Seier ,._:y A Lecture Given at S t. John ' ::; C llege o n September l ; , 1973 by Curtis Wilson �On the Discovery of Jeductive Science How did the notion of deductive science--science based on defi r itio~s. postulates_, and axioms, science consisting of a sequence of proposi tior:s. each of which is deduced, either from previously deduced propositions, or from the definitions, post ulates, and axioms initially set out--how did this notion first come to be thought of. and then realized? For there seems to have been a partic ul ar moment in whic h this idea was first conceived; so far as we can tell, it di d not meke its appeara nce at differe nt times e nd places, independently . conception? Can we leer ;: a nythi ng about t he or igina_:_ I am going to pursue this question. altho ugn es you wi~l at once realize, it is not the sort of questio n that is likely to receive a non-conjectural a nswer. The grou - d ~ere hes been worked into a deep and slippery mud by the trampling feet of conte nding scholars; merA non-c lassi cists or not yet classicists like mvselt are liable to stLmble over the m oulde ri ng carcasses of de funct t heories, not yet dece ntly interreu Certai n questions of historica l fact that are materia l to this discussior I am able to answer only conj ectural ly . At the sa m e time, I wish to affirm that my primar y ai m is not to esta bl i sh historical facts, nor vat to hypothesize possible ca uses for those facts, but rather to locate the mea ning of facts that, it seemed to me , come nearest to bei ng relieble . I went to be gin by sayi ng somethi ng a bout pre-Greek mathematics. The oldest m athematical documents know n from a ny place on t his earth are Egy ptian papyr i stemming from the Middle Kingdom, 2000- lR OO B. C., and clay ta blets dug out of the sa~ds of Mesopota mia, and stemming from abo ut 1800-1 600 E. C. lll lL\11 n I I I 1n 1111n 1 n -=:i. <=>-<2>1 I I I I I In © ~ . Inc::> \.i.) I I I I I !l'\f\~ll I I I ,.g<:::vr-21111,;r~r"""""~ 1111~AA11-.c.~ 111 iMll_ ~; u__._1- I I I I 1111> IC:? rc:7 @ I I I i""ri =~11 ~ I "C/ n @ #Jil'i= c:AI!i 1 ii I I I I 1nnn $ ~ ---1111n~ I I I R=:>"1111g1111(\IC:;? 1111 i~~:: :n8g;+r~IA1 I I I 111 c!!!!:ol 11lvrl I In Cl.. II l t' 11 I I 1111(\ 1 ~ 1 �In figure I you see a transcription from a papyrus now in Moscow, showing the computation of the volume of a truncated pyramid with square base and top. The base is four cubits on a side, the top two cubits on a side, and the height or distance between base and top is six cubits. The text says: "Add together this 16 with this 8 and this 4. ;T6 is the area of the base, 4 the area of the top, and 8 the product of the side of the base by the side of the top~~ ~e heighi7; you get 2. You get 28 . Multiply 28 by 2. Compute one-third of 6 You get 56 . Behold: it is 56. You have found right." Now the result is right. if you were building pyramids; It is something you might want to know but by the time of the Middle Kingdom the Egyptians had ceased building pyramids , enjoyable though that occupation seems to have been, as we gather from the inscriptions of rival work gangs. It is not clear that there was any immediate practical reason for anyone in the Middle Kingdom to know the rule for computing the volume of a truncated pyramid. in the first place . But the real puzzle is how this rule was discovered It is a complicated rule , and there is no plausible empirical way of arri ving at it by, say , weighing certain objects; therefore reasoning was involved . But on the other hand, the Egyptian mathematicians would not fall back on algebraic transformations in the modern manner , since their mathematics dealt e xplicitly only with particular numbers . There are a number of hypotheses as to how the Egyptians' procedure could have been arrived at, the most plausible , I think , involving a slicing of the pyramid into parts. Let us take another example. "A square and a second square whose side is 2 have together an area of 100. Cf. + 4 of the first square, Show me how to calculate this . '' note that Egyptian fractions , with one exception , are unit fractions , fractions we would write with 1 as numerator. They are written by putting a line above the number we call the denominator. The exception was 2/3, written by putting two of these lines above the numeral 3. Now for the solutionj] "Take a square of side 1, and take 2 + 4 (3/4) of 1 as the side of the other square. "Multiply 2 + i by itself; this gives ~ + 16. "Hence, if the side of one of the areas is taken to be 1, and that of the other is 2 + 4, then the addition of the areas gives 1 2 + 2 + I6 . �"Take the sQuare root of this; it is l + 4. "Take the square root of the given number 100; "How many times is l + 4 contained in 10? it is 10. Answer B.. " The two squares then have sides 8 x l = 8 and 8 x t = 6, the sum of their squares being 100. Now Egyptian mathematics has certain general characteristics . Firs t, Egyptian m thematics, whatever it is dealing with--areas, volumes , a numbers of bricks or loeves of bread or jugs of beer--is always a matter of numerical calculation . integers and fractions. The mathema tician is a computer who uses both Second, there are no explicit proofs whatever, but reasonings have to have been emp l oyed in the solution of problems. Fi nally , whil e the pr oblems prese nted in the papyri seldom appear to be actua l practical pr ob le ms , they give the ge neral impression of being the sor t of proble ms tha t a n instruct or migh t think up for his s t udents, in order to pre pare them for solvin g pr actical problems. Instructors seldom s ucc eed i n be ing strictly pra c ti cal, but the Egyptian ones appear to have unde rstood their a ctivity as occurring within the horizon of the practical . A istotle claimed tha t the mathematical arts had been founded in Egypt , r beca use there the pries t ly cla ss wa s allowed leisure; but this is i ncor rec "' The Eg yp tia n ca l c ul a tive art was the possession not of a priestly cla s s , bu t of scr ibes who ha d practical functions in the state, and among wh om there wa s rivalry. So we find one scribe ridiculing another: "You come to m to inquire conce r ni ng the rations for the sol die r s, e and you say ' r e ckon it out. 1 You a r e deserting you:r office I •••. I caus e you t o be abashed when I bring you a commend of your l or d, you who e r e his Roya l Sc r i be . A bu i lding ramp is to be constructed , 730 cubits long , SS cubits wide, SS cubits high at its summit •• •• The quantity of bricks needed for it is asked of the generals, a nd the scribes are all asked t ogether , without one of them knowing a nything. They all put their trust in you •• • • Behold your name is famous • • • Answer us how many bricks are needed for it?" It seems likely, then, that the mathematical papyri were textbooks used in the school for scribes. �In Babylonia, the m hematical texts appear to have been produced at by • similar class of scribes. proofs ere entirely absent; The texts give problems with their solutions; t he procedures are always numerica l . the problems practical problems? example from the time of Once again, yes and no. Hammurabi ~ Are Here is an 1700 B. C.: "I have multiplied length and width, th us obtaining the area. Then to the area I added the excess of the length over t he width. The total res ult i s 183 . with the result 27. I omit the solutio n. eq ua tion. I have also added the length a nd width, Required: length, widt h, and area." For us it would involve t he solutio n of a quadratic This Babylonia n pro bl e m does not strike me a s a practical probl e m, or a near neighbo r to one . Th e adding of a length to a n area seems to me decidedly impractical, per haps e ven nonsensical . a bit haywi re: This is ma the m atics gone a pedagog ue might inve nt it to bemuse his pupils, a lways understa nding , of course, that ~alculating is a good th ing. Babylonia n mathemat i cs, however, is a go od deal more powerful t he n Egyptian mathema ti cs . Whe n the Babylo nian scri be wrote: 'f2 = lj 24,51,1 0 (I em using the I ndian numerals in place of t he Ba bylon ian), he m nt ea 1 + 24 60 10 51 + 602 + 603 This is the Babylo nian approximation to the sq uare root of 2, or diagonal of a square of unit side. The Babylonians definitely knew a nd used t he proposit i on we call t he theore m of Pythagoras, which is i nvol ved in getti ng thi s approximation, but nowhere do any of the c lay tablets that have bee n decip hered give a proof of this or any othe r t heorem . The approximation, which is pr obably t he result of a series of successively closer approximations, is good to one-millionth . Ptolemy will still be using i t, ha ving a cquire d it probab l y indirectly from the Ba bylo nians, when he computes his ta ble of chords in the second century A. O. Now if we turn to other civilizations besides the Eg y~tia n and the Babylonia n , but still uninfluenced by Greek thought-- the civilization of the Yellow River valley , say, or Maye~ civllization- - I think we shall once agai n find e computational art, often highly developed , but not explicit deductions . You may on occas ion find the contrary asserted. Joseph Needham in his Science a nd Civilization in China gives a passage from a Chinese mathematical text which perhaps origi nated as early as t he 4th century B. C. . it is accompanied by a diagram which he labels "proof of the Pythagoras Theorem" (Fig ure 2 ·, P. 5). 4 �I quote from the text: "Of old, Chou Kung addressed Sheng Kao, saying, "I have heard that the Grand Prefect L'.Ihat is Sheng K~ is versed i n the art of numbering . May I ve nture to inquire how Fu-Hai anciently established the decrees of the celestial sphere? ••• I should like to ask you what was the origin of these numbers? ~ the course of his reply Sheng Kao say!!i/ " Lat us cut a rectangle diagonally, and make the width 3 units, and the length 4 units. 5 units l ong. The diago nal between the corners will t hen be Now after drawin~ a square on this diagonal, circumscribe it by hal f rectangles like that which has been lsft outside, so as to form a square plate. Thus the outer half recta ngles of width 3, l ength 4, and diagonal 5, together make two recta ng les ~ total area then the remai nder L'.Ihat is, of the square of area This is called ' pil i ng up the rectangles. 4.27 .££7; is of area 25. 1 "The methods used by Vu the Great in governing the world were derived from these numbers ••• He who understands t he earth is a wise m n, and he who unde rsta nds the heavens is a sage. a derived fro m a straig ht line. rig ht angle . Knowledge is The straig ht line is derived from the And the comb i natio n of t he r ight angle with numbers is what guides and r ules the ten thousand things. "Chou Kung exclaimed, ' Excel lent indeed!'" Nothing here, I would u rge~ theore m of Pythagoras, so-called. has really been proven, certainly not the Needha m hes shown in overwhelm ing detail that be twee n the 5th century B.C. and the 15th century A. O. no people on earth exercised more tech nical ingenuity then the Chinese. 5 Lo~ in advance �of the West, they possessed caste i r on, en escapement c lock, the navigational compass, gunp0111der, printi ng by movable type, the segmental arch bridge. But as for deductive science, the Chinese would not encounter it until the Jesuits came to China in the late 16t h ce ntury, bringing the textbooks of their fellow J esuit, Christopher Cla vius. It is e cur i ous fact that, for some centuries thereafter, Chinese students reciting their Eu clidean theorem out of Clevius would finish not with our Q.E. D. but wit h the Chinese word for "nail." Apparently they were citing their a uth ori ty ~ "c la vus 11 being the Latin word for " nai l." It is conceivable t hat some day, in the investigatio n of early civilizations un i nflue nced by Greece, evide nce wi ll turn up for the existence of some pieces of ded uctive mathemat i cs. On t he basis of what is known today , the prospects for s uch a find are di m. Ded uctive mathemat ics is a rare bird, which first settled, so far as we k n ow~ How did it happen 9 in Greece. Whet did it mea n tha t it ha ppe ned? Seeking a n answer, I t ur n to a doc ume nt of late a ntiquity, a comme ntary on t he first book of Euclid's Elements written by Proc lus in the middle of the 5th century A. O. Proclus was a member of the Pl atonic Academy i n Athens during the last ce ntury of its 900-yeer existence. The comme ntary i ncludes e kind of catalog ue of ancient geome ters which is based on an earlier history of geometry, now lost, by Eudemus, a disciple of Aristotle writi ng in the late 4th century B.C. The acco unt begi ns by sa ying that geome t ry was first discovered among the Egyptia ns , and originated in the remeasuri ng of their lands necessitated by the a nnua l floodi ng of the Ni le. Prac l us then proceeds as fol lows: Thales, having travelled in Egypt, first i ntroduced this theory into Hallas . H discovered ma ny things himse lf , and pai nted t he road to e the pri nciples of ma ny others, to those who came after hi m, attacking some questions in a m ore ge neral way, and others i n a way more depe nde nt on sense perceptio n. Gfter me ntioning the names of two other a nc i e nt geometers, Proc lus co n ti nues~ After t hese, Pythagoras tra nsformed t he phi losophy of t his (geometry) into a schem of liberal education. e He surveyed its princi ples from the highest on down, and investigated its t he ore ms s e parately fro m matter end intellectually. He it was who discovered the doc trine of irrationals �and the constr uction of the cosmic figures. A little farther on we read~ . . . .· . . Hippocrates of Chics, who invented the method of squaring lunules (crescents formed from arcs of circles) and Theodorus of Cyrene became eminent in geometry. For Hippocrates wrote a book on elements, the first of whom we have any recbrd who did so. With respect to Procl us says. Hi~pocrates A ffagment of of Chics, there is no reason to doubt what Hippocrat~s' work on lunules still exists, end i t shows a high level of .r igor • . ThusHippocrates may very will have writte n a book on the ele ments of geometry . Thus, at the time Hippocrates was teaching geometry in Athen s, around 430 B. C., the process of tur ning geometry into a ded uctive science :was in all probability well advanced. Thales, who was active abo ut a ce nt ury and a half before Hippocrates of Chios, is a much more shadowy figure , end it is unclear interpret what Procl us says about him . ho~ we should Proclus attributes to Thales the discovery a nd proof of five propositions: (1) A circle is bisected by any diameter. (2) V ertical a ngles of intersecting straight lines are equal. (3) The ba se a ng les of an isosceles triangle are equal. (4) Two triangles s uch that two a ngl es a nd the included side of one are equal to two a ngles a nd the i ncl ud ed side of t he other, are themselves eq ual . (5) The a ngl e at the periphery of a semicircle is right. Now these are general , theoretical propositions, theorems, propositions to be contemplated rather than mere rules for sol utio n of problems. The e nunciatio n of the m may therefore mark a decisive step in the emergence of theoretical scie nce. But how were they proved? The usual guess is that it was by superpositio n, the visual showing that one figure or part of a fig ure would coi ncide with a nother . If this is right, the n it is unlikely t hat we have here the notion of a logically co nstructed theory which begins with expressly enunciated premises and advances step by s tep. need not have e nunc i ated any premises explicitly. to the principles, es Proc lus says; TI:lales He pointed the road the extent to which he laid out principles is totally unclear. As for Pythagoras, . who~.e books have been devote. in recent times d to showi ng that the encie'n t eccol..ints . of his mathematical exploits are 7 �unworthy of trust. 2 These accounts stem from members of the Platonic Academy from the 4th century and later, men who saw in t'ie 6th-century oythegoras a forerunner of Plato, and who tended to attribute to him discoveries that had been made later on i n the Pythagorean tradition. Pythagoras cannot have known all the five cosmic figures, because two of them, the octahedron and the icosahedron, were first discovered by Theaetetus, a contemporary of Plato . evidence that lines. Pythegor~ s Contrary to what Proclus says, there is no good knew anything abo ut the doctrine of irrational The old verse quoted by Plutarch, according to which Pythagoras, on making a certain geometrical discovery, sacrificed an ox, cannot be true, because it is well attested that Pythagoras was a vegetarian, who believed in transmigretior, of souls end was opposed to the killing of What we can be fairly sure of, with regard to Pythagoras, aside animals. of course from his having had a golden thigh, is that he had made the flight to the Beyond end had become the leader of a cul t, a medicine men, a shaman. He can well heve taught that odd numbers ere ma le, even numbers female; that five is the marriage number; 1, 2, 3, end 4. that ten is perfect, being the sum of Somewhat similar beliefs have been found ell over the world, in connecti on with rituals end creation myths, and have not led to ded uc tive mathematics. Pythagoras' thought see m to have been cosmogonic, s concerned with t he coming-to-be of our world out of somethi ng prior e nd more f undamental. There is no trustworthy evide nce that Pythagoras ever carried out an $xplicit proof. On the other hand, the transformation in the character of mathematics that Proclus attributes to Pythagoras may well have bee n brought about by Pythegoreahs . tradi tion; The old accounts ~peak of a split within the Pythagorea n the Mathematikoi, those who wished to discuss &ild teach openly the mathematicel disciplines, separated off from the secret cult, the Akousmetikoi , the hearers of the sacred end secret sayings. Reliable 4th-century so_ urces ep_eek of the eri th.rneticel studies of the 5th-century Pythagoreans. Ar istotle says that the so-celled Pythag oreans were the first to deal with mathamete, mathematical disciplines. According to the Epinomis, a dialogue written either by Plato or a follower of Plato, the first and primary disciplines o.r me theme of the Pythagoreans was eri thmetic. Now it is possible to make a plausible recanstruction of some 8 �of this early Pythagorean arithmetic. When this is done, we find ourselves before a piece of deductive science, quite possibly the earlies~ thst ever was; and it is a science in which the principles are explicit, anr in which the theorems are, to use Proclus' terms, investigated independently of matter and intBllectually. The reconstruction necessarily starts from Euclid's text, which appears 1o be : to a certain extent, a compilation from earlier texts which it drove we ~now o~t of circulation, and which are now wholly lost, so that of them only from certain references by Aristotle or Plato or other ancient eJthors. The reconstruction proceeds by a kind of literary archaeology. Flourishings s.c. Thales fl or. 585 Pythagoras flor. 550 B.C . Parmenides flor. 475 B.C. Hippocrates of Chios flor. 430 B.C. Archytas of Tarentum flor. 400 B.C. Theaetetus c. 415-369 B.C. '"llato c. 428-348 B.C. ristotle A 384-322 B.C. Euclid flor. 300 B.C. Permi t me t o give here a set of not very reliable dates. Flourishin~ was something Greeks did as a rule at age 40, j ust as they often died at 80, to suit the taste f or symmetry of a certain 2nd-century B.C . chronographer named Apollodorus. Euclid wrote about 300 B.C. There are good gr ounds to believe that a good deal of geometry had been organized as Ei deducti ve science by the time of Hippocrates of Chics, about 430 B.C.; end there are plausibilities in assuming that portions of arithmetic had been organized deductively even earlier. In discussing this development, I shell went to refer to Parmenides, who lived in the first half of the 5th century; to Archytas of Tarentum, a Pythagorean end friend of Plato living around the tur n of the 5th end 4th centuries; and to Theaetetus, another friend of Plato, who died es a result of battle wounds in 369 s.c., and was ona of the greet mathematicians of antiquity, being the author, in ell probability, of nearly ell of books X end XIII of Euclid's Elements. 9 �In 1936, Dakar Becker pointed out a number of peculiar facts concerning Propositions 21-34 of Book IX of Euclid. These theorene are for the m9et pert so obvious that it is herd to imagine why anyone would be eo fussy es to want them proved. "If as many even numbers as we please be added together, the whole is even." Certainly. "If from an even number an even number be subtracted, th,., remainder will be ever.." Who will doubt it? The proofs, with one exception, do not depend on any previous theorems in Euclid's Elements: tney depend rather on certain definitions given et the start of Book VII, the first of the arithmetical books . exceptio n, IX .32, depends on IX.13. The one Bu t Bec ker sus pects the proof as we now have it to be Euclid 's eme nda tion of the origina l proof; that IX.32 follows quite stra igh tforwardl y fro m IX .3 1 . he s hows Th us Proposit i ons IX.21 to IX.34 can be a self-s uf ficient set of prop osi tions depe nde nt only on certain defi ni tio ns. Moreover, with one cur ious except ion , no thi ng else in Euclid 's Elements depe nds on t he s e propositio ns. The exceptio n is the last propositio n of Book IX . whi ch moder n editors dele te as no t being integral to Book X. It i s the ancient proof of the incom rnens urability of the side and diagonal of the square, a nd what i t depends on is t he doctri ne of the even and the odd, a nd more specifically ~ Propositio ns 32-34 of Book IX. Becker believed that, origi na l ly, before i ncorpora ti on i n Euclid's Eleme nts, the doctrine of the eve n a nd the odd had led to another co nseque nce, the traces of which have bee n left i n Euclid. Propositio ns 21-34 of Book IX are followed by two fi nal propositions , 35 and 36 ; 35 is used for the proof of 36, and 36 shows how to construct a perfect number--perheps all perfect numbers, but t hat I believe is not yet known. Euclid 's proofs for these two propositions depend on propositions in Book VII having to do with ratios of numbers. Becker shows that 35 a nd 36 can be proved on the bas i s of the immediately precedi ng propositions of Book IX, independe ntly of any reference to ratios. Thus Becker's c onj ecture is that, long before Euclid, there existed a treatise on the even a nd t he odd, includi ng Propositio ns 21-36 of Book IX and t he lest proposition of Bo ok X; t hat out of piety Euclid or some ancient editor added this treatise to the Elemen ts, then, in an effort to integrate this addition with the whole, changed sona of the proofs, making use of propositio ns on numerical ratios from Book VII . This hypothesis et least accounts for the pec ul iarit ies of Book IX that I have cited. J (1 �- That s uch a doctri ne of the even and the odd already existed in the 5th century is supported by the fact that Plato defines arithmetic as the doctrine of the even and the odd, and refers to this doctrine as a familiar discipline. Following Be cker, Van der Wee rde n has argued that most of Book VII of Euclid had also been worked out in the 5th century. One of his arguments is that Archytes of Tarentum, in a work on musical theory written about 400 B. C., depends on propositions found in Book VIII , a nd these propositions depend in turn on propositions in Book VII . Now since Ar chytas is punctilious in working out the mos t trivial syllogisms, it is extremely unlikely that he me rely ass umed the propoeitio ns he needed; be already proved. he must have known theffi', to On the other ha nd, if the propositions of Bo ok VII existed in any form in Archytas' time, then Van der W aerde n concludes that t hey must have bee n i n almost exactly their preeent for m and thus in apple-pie order; for Book VII is worked out with gree t care and !n such a strictly logical fashion that no step c:e n be removed withodt', the whole collapsi ng. There are other cl ues that lea d Va n der W aerden to believe t hat most of Book VII was complete be fore Hippocrates of Chios wrote in lunules . Two pieces of ded uct i ve arit hmet i c, then, along with fUppocrates 1 quadra t ure of l unules, constit ute th e available presumpt ive evide nce for the character of 5th-century de ducti ve m ett.rMtics. Ca n we learn a nything fro m them, which m ht throw light on t he question of what it meant for ig them to come to be? I want to ta ke up, first, t he demonstratio ns , then, the premises on whic h t hey are based . Every Euclidea n propositio n e nds wit h th e ste r eot yped f ormula , ~¥ l~1. JeC.taf<.., m ning : the very thing that it was necessar y to s how. ea The i nfinitive h e re,dEt~C\"(., seems to he ve had the origi nal mea ni ng of s howi ng vis ually. Thus in Pl ato's dialog ue Cr a tylus Socrates says: "Ca n I not step up to a men a nd se y to him , ' This is your portrait~ a nd show him perhaps his own likeness or, perhaps, that of a womanr And by 'show' (bK~~) ! mean,-· br!~ before the se nse of sight. "(430 Early geometry must have been primarily a kind of visual showing, the pointi ng out of a symmetry, or the poseibility of the coincidence of two figures, superposition. But in Euclid's text every effort is made to red uce the dependence on s uperposition to a minimum . Thus we co m E w s uspect that there was pre•nt a kind of anti-illustrative, anti-empirical 11 8 ) �tendency in mathematics, as it was being transformed into deductive science. Thie same tendency is detectible in arithmetic as we ll as geometry. Pythagorean arithmetica l doctrines seem to have been originally worked out and taught with the aid of calc ulating pebbles. There is a frag ment of the comic poet Epicharmus, writte n proba bly before 500 B.C ., that r uns as followa: "~hen there is e n eve n number present, or, for all I care, en odd number, and someone wants to add a pebble or to take one away , do you think that the number remai ns uncha nged?" "Not me!" "W ell, the n, look at people: one grows, a nother one perhaps gets shorter, and they are co nstantly s ubj ect to c ha nge. Bu t whatever is changeable in charac ter and does not re ma i n the same, that is certainly different fro m what is c hanged. You and I are also differe nt people f rom what we were yesterday, a nd we will still be different i n the f ut ure, so that by the s ame argument we are never the same." Presumably the sl y rogue goes on to arg ue that he need not pay the debt he contracted the day before . ristotle, too, speaks of t he Pythagorean ·pebble fig ur es, t he tria ngles , A squares, and rectangles formed of pebbles with which the Pythagoreans ta ught arithmetica l truths. W can easily see how t he y could have satisfied e themselves, with their pebble figures, of the propositio ns co ncer ni ng the even end the odd. Take Proposition IX.30: if an odd number is t he divisor of an even number, the n this sa m odd number is also the divisor of half e the even number . 0( I . , ... •• •• ••• y • 1• I •• • /3 , eve n number i ••• The nu mber will be a rectangular numbe r, with our odd number , the divisor, represented by the pebbles for ming one of the sides. But the number as a whole is even, hence divisible in half, es by the vertical line. W see e at once, then, that our odd number is a side of the hal f rectangle, hence a divisor of the half. The proof of this proposition in Euclid is qui te different. ere not represented by points, but rather by lines. The numbers W know that A e rchytas repreaente numbers in this way, by lines, as a matter of course, and 12 �presumably, therefore, this . mode of representation had become before his time, that is, already in the 5th century. ~ow co~ventic - ~ . by looki no a: a line which represents a number, one cannot tell whether the number i s even or odd, since any line can be halved: consequently, Euclid's visual representation of the numbers does not help us at all to see wh~ the proposition is true. A pebble configuration could only represent visuall ; a particular number ; the new representation has the advantage of generality , but it also has the disadvantage that it forces one to look for an entirelv new proof. The ne w proof that ~uclid gives 0s involves the famous reduction to the absurd, or indirect demonstratio r.. that the odd number Ct(", The important step is to show the divisor, measures the even number~ an even number of times, or in other words, that the quotient, i:::uclid's argument runs as follows: possible, let it be so. Now C( I SS '/ that multipl ,,,in g y taker at the start to be odd , and an odd number y y , is not odd , for if 8 . end makes multipl yi~ g yie ld s onl y an odd number , as Euclid has oreviouslv showr. would be odd, which is impossible at t he start to be even. 1 !x~ if V~To V i s even. ' }, 0( was an odd numbe r Therefore it because it was take;r Thus the anti-illustrative tendency brings with it the reductio ad abs urdum proof . It is s urpris ing how many red uct io proofs occur in t he arithmetical treatises that , accordi ng to Becker a nd Ve n der Wa erde n , stem from the 5th-ce ntury D ythegoreans. In propositions 21-36 of Book !X there are s ix s uch proofs. or eight if we accept Becker's 35 and 3E. reconstr ~ ctions of 32, Tn the first theore ms of Book VII there ere 15 s uch proofs . Moreover, t he proof of the incommens urability of the side and diagonal of the souare is also a reductio, and in this case we have to do with a truth whi c h is altogether non-vis uali za bl e. Let m pause to review e the strategy ot that proof. oe)e relatively prime, therefore not both even. 2 2 2 0( = 2 f> • The refore 0( is even, Therefore is even. ~ Therefore ~2 = Therefore~ an even numb~r . =an even rumt~r. f{(J ~Va, To V �Suppose, if possible, that the side and diagonal of a square .!!:.!. colTllHtnaurable. Then there would be a length that measured both, and also a largest such length. ~ times, and the side Now 0( and /3 Lat this largest such length measure the diagonal f, times, where 0( and fJ are integers or whole numbers. cannot both be even, for otherwise our unit length could have been doubled, and the numbers helved, contrary to the assumption that the unit length was the largest possible; must be odd. so at least one of the numbers The sequence of the proof then shows that both must be even, or as Aristotle says in referring to this proof, that the same number must be both even and odd. The only alternative left is to relinquish the original assumption that commensurable. 0( and f3 exist, or that s i de a nd di agonal are In this demonstration human reason exhibits a rather astonishing power, the power to discover whet eyesight could never in any way disclose. This discovery would e ncourage the a nti-ill ustrative tendency, a nd t he reco urse to indirect proofs. It also implies that geometry cannot be subsumed under arithmetic, a nd needs therefore to be built up as en independent science in its own right. But the releva nt point at this moment is that the emergence of ded uctive scie nce appears to be connected with this anti-ill ustrative tende ncy, a nd with the closelyconnected introduction of reductio proofs. What about the principles or premises of Pythagorean arithmetic? I have already mentioned that t he premises of the doctri ne of the eve n end the odd are to be found amo ng the definitio ns of Eucl id 's Book VII , and only there. The same thing goes for the doctrine concerning divisi- bility and proportionality found in Book VII itself. And fundamentally, ell the definitions of Book VII rest on the first two definitio ns , the definition of number--a number is a multitude composed of unit s or monads-and then the definition of monad : monad is that according to which each of the things that are, each of the beings, is called one. definitions do, above all, is to whole numbers . li~it the following what these discussio~ to Comparing this Greek arithmetical theory with Egyptian and Babylonian numerical work, we see that the Greek theory is s harply distinguished by its careful avoidance of fractions; and the first definition, whatever else it is doing, is expressing this prohibition against fractions, this insistence on the indivisibility of the one or unit. This insistence 1119S already traditional in Plato 's time. 14 �In the Republic Socrates speaks of "the teaching concerning the one ·• ( ( \. 1t 7rFf<- I /e C/ le &v f<~ l')<rr~ ), end explains whet he means by it, I quote: ••• You er g doubtless aware that experts in this study, if anyone to c ut up the 'one' in argument, laugh at him and refuse atte~pts to allow it ; but if you mince it up, they multiply , always on guard lest the one should appear to be not one but a multiplicity of parts ••• Suppose now ••• someone were to ask them, "My good friends, whet numbers ere these you are talking about, in which the one is s uch as you post ulate, each unit equal to every other without the slig htest differe nce end admitting no division into perts?" do you think wo ul d be their answer? What This, I think---that they are speaki ng of units which can only be co nceived by thought, a nd which it is not possible to deal with i n a ny other way, ~hy Socrates' expla natio n tells us had to be i nsisted upon ; the indivisibility of" the one if t he one were divisible, then (t would be a multiplicity of parts, hence many, not one. t hat the one is In other words, the though t divisi ble is self-contradictory. Thus the insistence on the indivisibility of the one, which is Eu clidean and also, accordi ng to Plato ' s Socrates i n the Republic, pre- Platonic, is the concl usion of an indirect demonstratio n, a reduction to the abs urd. I have not yet taken up the pr inciples used i n early ded uctive geome try, but let me recapit ulate whet I have said, and consi der wha t it s uggests. The earliest ded uctive sc i e nce, as far as we ca n tell , wa ~ the arithmetical theory of the so- ca lled Pythagoreans of the 5th ce ntur · Their scie nce dif f ers fro m all earlier ma t hematics, first , in exhibiti ng e n a nti-empi rical tende ncy, whic h sough t to eliminate mere visual showing . as wit h the pebble fig ures ; second ly, in m aking use of indirect demonstretior· or proof of som ething by red uct ion of its opposi t e to absurdity : thirdly, in i ns isti ng upon the indivisibility of the one, on the ground that admissio n of its divisibility would co ntradict the very meaning of t he word "one . " N these feat ures cell to mind certai n lines that remain of ow a poem written early in the 5th century, the poem by Pa rme nides of Elea : end to no other author of this time can these features be related , try to sa1 some words about the poem of Parmenides. Only fragments of it remain. controversial. Their interpretation is thoroughly There is widespread assurance that, whatever it was that p:; �Parmenides meant, he was wrong. On the other hand, it will be little conteatad, I believe, if I say that Parmenides was the founder of Dialectic. Aristotle says that Zeno of Elaa, Parmenides' pupil, was the founder dialectic; of but I think that may be because Zeno wrote out arguments in prose, whereas Parmenides wrote a poem in epic verse, while dialectic has essentially nothing to do with verse. I believe there is also rather general agreement that Parmenides, in composi ng his poem, was responding to, and attacking, earlier cosmogonies, which sought to derive all the variety and diversity of the world out of some underlying stuff, understood to be the real stuff of the world. The poet begins by describing his journey in a chariot, drawn by that know the way, end escorted by the Daughters of the Sun . mar~s arrive, high in the sky, before the gates of Nigh t a nd Day. They The Sun Maidens persuade t he Goddess Justice to ope n the gates, a nd Permenides is welcomed by the goddess who takes his hand and ass ures him that it is right end just that he, a mortal, should have take n this road. H must now learn e both the unshaken heart of well-rounded truth, a nd the un r el iable beliefs of mortals. The goddess describes three ways of i nquir y: (~dr() and cannot not be; attenda nt of Truth;" rily not be; first, "That it i s, .. this is the way of Pers uasion, f or s he is the second, "That it is not (OU!f. E;o't'"<./) , and must necessa- this I tell you is a way of t ota l ignorance;" "That it is, e nd it is not , t he same a nd not the same; third, this is the wa y t hat ignorant mortals wander, bemused." An initial difficulty t hat we face i s t hat , altho ugh t he pronoun "it" is not expressed in Greek, we can hardly resist t he impress ion that there is something that is being talked abo ut, a nd we s houl d like t o know what it is . The next fragme nts may be helpful . "It is the same th ing that ca n be thought and ca n be." ''b.lhat ca n be spoken of and thought must be; for it is possible for it to be , but it is not possible for nothing to be. These things I bid thee ponder . " In a preliminary a nd s uperfi cial way I think I can conclude that the subject of the verb €0"'C~Y is: that which is intended in thought, what we call the object of thought. argument: that which thought intends 16 The goddess is presenting an ~ exist; but nothing ca nnot exist; �therefore thac which thought intends cannot be nothing; hence it must exist. The syllogism holds, I believe, although at that point in time logic had not been i nvented. But whet does it meen? way is cannot be entertained in thought. it is intentional in character . That which in no Thought always is of somethi ng , Hence I must accept the Gedde s ~ ' rejection of the seco nd way, or non-way, of inouiry . But the Goddess means somethi ng more. Some of this "more" emerges es she proceeds to dispose of t he third wey of inquiry. This '.: che way whereo n, she says, mortals who know no thi ng wa nder two-headed; guides the wa ndering thought in thei r breasts; both deaf perplexity they are borne a t ong, e nd blind, bemused, es undiscer ning hordes, who have decided to believe that it is , and it is not, t he same and not the sa m , and e for whom there is a way of a ll things that t ur ns back upon itself . says the goddess, "shall this be proved: "Never," are not, ere; that things tha t but do tho u hold beck thy thought from this way of inq uiry, nor let cust om t hat comes of much experie nce force t hee to cast alo ng this way a n aimless eye a nd a noise-cl utte red ear and tongue , but judge t hrough logos (t hrough reasoning ) t he hard-hitti ng re futat io· I have uttered. " "It is necessery,"adds the Goddess,"to say and to think t hat Be ing is . " Now i n one way , t his is ell simple and unde ni.l!!ble. Whe n I entertai n a n idea, when I use e word to sig ni fy some idea, I inte nd what I affi of es a consta nt, invaria ble. t~inki ~ g N ever mind that my thought, m intending y of what I a m t hinking ab out, is a s hifting a nd not ver y co nt r ollaoi e process. What i s t hought e nd named is i ntended as having a certain fixity . Ot he rwi se, as A totle puts it , to seek tr uth wou l d be to ris follow flyi ng game. W wo uld be reduced to t he level of Crat ylus, wn0 e did not think it ri ght to say a nyt hing , a nd instead only moved hi s f inger, a nd who criticized H erecleitus for s a ying that it is imposs ible to step t wice into the same river, for he, Cretylus, said t ha t one could not do it eve n once. On one level , the words of the Goddess are simply telling u~ whet t he prereq ui sites e nd necessities are for speech and thought that will be free of contradictio n. Per~e ni des' poe m is the ear li est docume- preserved fro m the past whic h speaks explicitly of the logical necess i L1es of thought . �V.t the diecouree of the Goddeee ie more strange end frightening, or ineane, or ee Whitehead might say, important, then I have bean making it out to be. The Goddess is not concerned with just anything that might be thought; Being. aha is concarned--she aeys so again and again--with What is all this silly talk about Being? Being to do but be? What else is there for "It is necessary," says the Goddess,"to eay and to think that Being is." Is it? Then is it necessary t:.o say and to think that rain rains, that thunder thunders, or that lightening lightenings, and are not these parallel caaee? to this question. I shall litter come back, vary briefly, It is just here that the poem becomes exasperating end impossible, prompting Aristotle to eay more than once: false, and the conclusions do not follow. the premises are From the fact that Being just ia, the Goddess proceeds to conclude that Being is precisely One, and contain• no plurality, no multiplicity or differentiation within it, and no motio n. In particular, a nd to A ristotle's great disgust, the Elastics claim to have discovered the self-contradictory character of motion. It is Zeno, Parmenides 1 pupil, who formulates this discovery ir the most memorable wa y. The flyi ng arrow is in every insta nt exactl y where it is, is et rest in the space equal to itself, and since this is true of every moment of its fli ght , it is a lways at res t , it does not move. N ever mind the mortal wound we thi nk it ca n i nflict; this does not answer the argument, it does not tell us how m otion can be consistently thought. The ques tio n is not whether Ze no is wrong but how. being debated in th~ It is still philosophical journals. In the case of Parmenides, a more insistent ques t ion is what he can have meant by his poem. There is a second part to it, called the W of ay Seeming or Opinion, of which 40 lines remain, and this speaks of the coming-to-Iba of the uisible things of our ordinary world out of Fire end Night. Di d Parme nides intend the Way of Op inion to have a ny validity at all, or only to present the bemused and e rring beliefs of mortals~ Plutarch remarks that P•rmanide~ has taken away neither fire nor water nor rocks nor precipices, nor yet cities ••• for he has written very largely of tl!\e.aarth, heaven, su n, moon end stars, end hes spoken of the generation of men. Treditione credit Parmenides with having given laws to the city of Elea , and with having bean the firet to aay that the Earth is round, that the 18 �Moon shines by reflected light, and that the m orning star is identical with the evening star--momentous diecoveries every one of the m. But such actions and discoveries do not seem easily compatible with the teeching about Being that the goddess has set forth, with such emphasis, such imperial absolutism. no place in it for huma~ The heart of well-rounded truth appears to have law , for the earth's rotundity and its conical shadow, for Venus and her i.rregularities, or for Parrnenides or you or me . The speech of the Godde~s is never~heless as I have said, dialectic takes its start. sophists begins. fateful. With Parmenides, The age of those called Gne of the earliest of them, Protagoras, is clearly reacting to Parmenides whe n he makes his famous statement : man, he says, is the measure of all things, of the things that are, that they ere, and of the things that are not, that they are not. Who but Parmenides had raised these questions about Being and not-Being? Protagoras has concluded that the Parmenidean standard of truth, that is, freedom from contradiction , is unreachable; thought, he thi nks , inevitably involves contradiction. Therefore he t urns to sense-experience, end asserts his right to say that the same thing ca n et one time be, a nd et another tinE not be , according es he, Protagoras, holds it to be or not to be. In Protagoras' time and later, there will be other objectors with other form ulati ons, rejecting the speech of the Parmenidean Goddess in othe r ways. argues, first, that nothing is; known; Gorgies, for insta nce, second, that if anything is, it cannot be third, that if anythi ng is end can be known, it ca nn ot be expressed i n speech. Among the Permenideen sequels, I want to suggest, was deductive arithmetic. For according to A ristotle, Parmenides was the first to speak of the Dre accordi ng to logos, according to definition; end arithmetic seems to have become deductive just when the Pythagoreans set out to fou nd the doctrine of the even end the odd on the definition of the One, on its essential indivisibility, end proceeded in Pa rmenidean style to formulate proofs which relie d no longer on visualization but rather on non-contradiction of the logos . Of course--ar,d this is a crucial qual ificetion--no ari thmeticien could follow the teaching of the Par,menideen Godd$SS strictly. W hen the deductive eri th.metician took his start from the indivisibility of the One, ha was proceeding in accordance with e Parmenidean neceaeity of thought. 19 W hen he �went on to multiply the O . in order that ne, violating the Permenicle~ W of Truth. ey arithm~tic might be, he was Permenidean-wise, how could there be many ones, each exactly the eeme ea every other, and yet each retaining its identity to the extent of remaining separate from the others? The way in which these many ones can be, or ere in being, is e question not for arithmetic, but for meta-arithmetic, but apparently the arithmeticians recognized that their discipline depended on the question about being. The Euclidean definition of Monas, One, reads: Mona s is that in accordance with which each of the beings is celled one. A plurality of beings--what they are rema ins unclear--is here presupposed. Ae for geometry, the violations of the Permenidean logos that are necessary in order for it to becom.e deductive are m ore The drastic~ definitions of point and line with which Euclid begins Book I were no doubt modelled on the definitions of One and N umber, but there is a world of difference between the cases. ~ithout is The definitions tell us that e point parts, that a line is without breadth, but we cannot go on to derive any geometrical propositio n from these rattier problematic de nials . It was the questionable character of the geometrical things that led Protagoras to reject the possibility of geometry altogether: does not touch e straight pole in one point only; impossible, Q.E.D. a wheel, he said, therefore geometry is But even if the geometrical definitions are granted, thPy do not provide a s ufficient bas is for the organi zation of geometry as a deductive sc i ence. At the beg i nning of Euclid's Elements three kinds of principles ere set out. ('/ ofo~ First, definitions or .,,, ... third, common notions or KO<V<lit. second, postulates or E:.VVO<~. argued that the term }(.oe,vo,l l11vrx.O(<. and therefore not due to Euclid. may 111&11 have been ~!~crrcl'; ; ) ,, ~("ttYrcy'; About a century ago, it wes had to be of late Stoic origin, Wes the:r:e an ear lier Greek term? rt this is the term that Proclus constently uaae instead of Not~ /v~cqc.. , end it may heve been the term in front of him in his Euclidean text. ueae ' ~" ~1'bv~r~f~ Instead of ~t. for definitions, Proclus commonly this usage is found earlier in Archimedes, end earlier still i n Plato's Republic, wher.e the odd end the even, end the various kinds ' of figures end angles are said to be tr.a.tad in the sciences that deal with them es Jir.fitf<Y&S and ~~J'µ q'71( • All thi-ee of these terms, m fJttYErte, , ~tr{µ ty'7"tY , were connected at one time with the practice of dialectic. �The t er m o{c,7.J!A-~T~, post ulates, comes fro m t he ver b C(~T{w, to req uire, to ask. " W never, " Procl us tells us, "the stateme nt is unk nown and neverhe theless is take n as tr ue wi th out th e stude nt's conced i ng it, t he n, A ristotle J/ says, we cal l it a n C{ l TY)f'ACX:·" J whic h ca n al s o mea n to require, to ask; dialogues. I , / The ter m ~cwf(~o(comes f rom ~ww, it is ofte n so used i n the Platonic To be s ure, Pr oclus sa ys of the axioms th8 t they are deemed by everybody to be t ,- us a nd no one disputes them. I beli eve t hJ.s statement reflects a n A totelia n and post- Aris t ote l ian usage . ris Aristotle himself refers to the ear lier, dialec tical usage whe n he says: br,~ l dW is used of a propositio n which the ques tio ner hope s the questioned perso n wil l concede. ( / A for the term UTro()e<ret.<:, , there is perhaps litt le nee d to mention its s dialectical use . At a certa i n po int i n Plato's Repub lic, Socrates speaks of the principle. of non-contradictio n, the presuma bly unshakeabl e principle according to whic h it is not possible for the same thi ng at the same time in the same respect and same rela tion to suffer, be, or do opposite things . And having e nuncia ted the principle, he says, "Let us proceed on the hypothes is that this is so, with the understandi ng t hat, if it ever appear otherwise, everything that res ult s from the assumpt ion s hal l be invalidated .'' (43~a) And as even the not-so-dialectical A ristot l e recognizes, this princi ple can only be esta blished cont r oversially. tha t is to s ay , dialectically, agai nst e n adversary who offers to say some thing . M general point is a s imple one. y The first bo ok of the ele m nts of e geometry of whi c h we have record was writte n i n the middle of t he fifth ce ntu ry, by Hi ppocrates of Chios. An a nti -vis ua l , anti-ill ustrative tend e ncy t hat had first emerged, so far as I know, in Parmenidea n dia l ectic, is a l read y prese nt i n the geometrica l proofs of Hippocrates of Chios that have come dow n to us , a. g .proofs of i nequalities t ha t would be obvious to visual inspection. The fact that at an early stege the ter m adopted for the s premises of geometry were t erms of dialectic, terms referri ng to assumptio ns or concessions that do not entirely lose their provisional character but are req uired i n order that a discussion m ight proceed, reinforces the impression that the transformation of geometry into a deductive science was carried out i n a context determined by the practice of dialectic. 21 �It is also important to realize hare that the premises of geometry had to ba concessions: propositions needed to derive whet not only geometers but even surveyors and carpenters knew, yet propositions which violated, in the most obvious way, the canons of the Parmenideen logos. Two things equal to the same thing, Euclid tells us, are equal to each other. But whet is equality but sameness, and how can three things that ere exactly the same be three? How, moreover, are we to perform the absolutely impossible feats that the c/t1t(1'40fT~ require--to draw a straight line from point to point, to extend a line, to describe a circle? by Socrates in the Republic: Pert of the paradox here is described "The science (of geometry)," he says, "is in direct contradiction to the language spoken by its practitioners. epe.ak in a ludicrous way, although they cannot help it; They for they speak as if they were doing somethi ng and as if all their words were directed towards action. For all their talk is of squaring and applying and addi ng and the like, whereas the entire discipline is directed towards knowledge." (527a-b) It is probably this peculiar mixture that Timaeus is referring to when he speaks of geometry es apprehending whet it deals with by a bastard kind of reasoning. I should like to conclude with a short summary of and comment on whet I have been saying, followed by a brief epilogue . Deductive scie nce appears to have been first discovered by a few Greeks ; so far as I know, this discovery remained unique . into oblivion during certain times; Knowledge of it fell et whatever later times the possibility of deductive science has been recognized, the recognition hes come through the . recovery of Gr~ek ' deductive science. What did the original discovery involve, what did it mean, for those who made it? have sought to examine. That is tha question I From a plausible reconstruction of Pythagorean deductive arithmetic, I am led to conclude that the essential moves were a~ay (1) the turning from visualization and taking recourse in logos; (2) the application of a negative test, the method of indirect proof or reduction to the absurd. Now these two steps ere diel•ctical steps, they ere the steps of the method thet Socrates in the Phl!edo own: describes as hie "I was afraid," ha says, "that my soul might be blinded altogether if I looked at things with my eyes or tried to apprehand them only by the help of the senses. And I thought I hmd better hsve recourse to th• loqos •• •• Thie wee the method I adopted. I first assumed some principle, W'hich I 22 �judged to be the strongest, and then I affirmed as true whatever seemed t o agree wi th t his, and that which disagreed I regarded as untrue. " But i n all the features that Socrates mentions, Socratic method is essentially Eleatic, Parmenidea n dialectic. The search for the sources of Pythagorean deductive arithmetic thus l eads us back to Parme nides, or to someone else , who lived abo ut t he same time , and whose uttera nces had the same effec t . What was so special . so pecul ia r, abo ut the discourse of the Parme nidea n Goddess, that it coul d pre cip i ta t e what foll owed? "Thinki ng a nd the thought that it is," the sa me . says t he Goddess, "are one a nd For yo u will no t fin d thought apart from t hat which is •• ; for there i s a nd s hal l be no other besides wha t is, s ince D t iny has fettered es it so a3 to be whoJe and immovabl e ." " It is necessary to say a nd to th i nk . " the Goddess adds,"that Bei ng is." These words are spoke n r.ot E,y Parmenides but to Pa r menides . H is being e called upon to s ay a nd to thin k, and the saying and thi nki ng are not separated , al tho ugh t he order ir, which the f _,oddess names them is worth not ici ng , being the opposite of t hat which we m oder ns te nd to ch oos e. bet ter remind ourselves , is Greek t hin ki ng ; meant: The thinking , we ha d the verb is to perceive by the e yes , to observe, to notice . !J2!irl, which once I t is not to conceive, to analyze . to grasp, to attack i n our thinking. And that which Parmenides i s asked to say and to notice, what will it do for him to say e nd to notice it ? The sente nce, "Be i ng is ," does indeed offer nothing to grasp, nothing to conceptual ize, nothing to attack i n our thinking, nothing to analy ze. Excep t -- there is a twoness there. verb, essentially, of course, the same word . present , and there is its prese nce. There is the noun and the Yet, there is that which is To say and to notice not onl y whet is prese nt but its prese nce is to be arrested in front of someth ing . to be , at least a little bit, asto nished. us . I t is to respec t what li es before It is to think appropriately, as bef its the m atter. Greek t hought ceased aski ng: It is At some point O of whet do the many things come to be? ut and began to ask i nstead: W hat is the Being of that which is in front of us? Ti to on is the Greek: what is t he bei ng ? implicit the so-called laws of logic : In this question, there are A is A, A is not not- A. scie nce, I em propos ing, takes it start here. Deductive W het seems to have been importa nt, for these beginnings, was not answering the questio n but purs ui ng it. Even Aristotle, fro m whom we have received more answers than questions , nevertheless says: 23 �~oth formerly and now and forever it remains something to be sought and something forever darting awsy: Ti to on ? Suppose, if you will, that the account I propose is something like J1e truth. Then deductive science came to be and perhaps still comes to be aa a result both of a logos from beyond the gates of Night and Day, and of the fracturing of Being and of the Motion going on in the Realm of Fire and Night. Or can deductive science proceed on its own way, simply leaving behind whet triggered its coming-to-be? It has sometimes attempted to do to become, for instance, purely formal, with the specification of this ~ every element end every rule of operation, and the exclusi on of every bit of explicit or implicit ontology, with the intent of i nsuring log ical completeness and consistency . The effort has led t o ma ny refinements; but the odd result of modern metamathematica l study is t hat t he eff ort cannot succeed in its original intention. l'lathemati cs does no t succeed in being completely in itself and for itself . I t s t r iumph lies not in isolated grandeur , but in coping as best it ca n with necessities that appear . Deductive mathemati cs , no t quite a c e ntury afte r coming to be , underwent a crisis with r espec t to its foundations . ~ Jrability can well have been early i~ The discovery of incomme n- the 5th centur y. It impl ies, rather 1 ibviously one would think , the falsity of the old Pythago r ea n do ctr ine that 1 11 !2 is number , whatev e r that doctrine may have meant. But i f t he d i scovery ,,1as early, an important c onsequence of i t was s omewha t slow in be ing real i zed . ~ -he teaching concerning ratios of magnitudes was origina l ly con ce ived in 1a numerical fashion: fou r magnitudes a re proportional when the first is the same part, parts or multiple of the second t hat the third is of the fourth. That definition is still being used by Hippo crates of Chi os. Archytas, around 400 B. C., is saying that logistic , the doc t r ine of r atios of numbers, has the highest rank among the arts . and in particular it is superior to geometry, "since it can treat more clearly then the latter whatever it will." Archytas thus fails to notice that the fact of incommen- s urability sets a new task for mathematics , the formulation of a new definition of proportionality, one which will apply to megnitudes that rney be incommensurable. 24 �The problem is solved by the early fourth century, possibly by Theaetetus; at least he is the first we knOliln to have used the new definition, and he did so extensively. The new definition of same ratio or proportionality ls not the one embodied in Euclid, the definition due to Eudoxus, but a precursor of the latter, one which we can argue Euclid excised from Book X es it came down to him from Theeetetus. The manner At the beginning of Book VII of of the new definition is worth noting. Euclid , a method is given of determining the greateat common divisor of two numbers ; it has come to be called the Euclidean algorithm. What is the greatest common divisor of 65 , 39? 65 39 26 39 26 13 But 13 measures 25. Ans: 13 is g.c.d. (65,39) . The lesser of the two numbers is subtracted from the greater until a yet smaller number remains . This smaller remainder is subtracted from the preceding subtrahend in the same manne r, and so one continues, obtaining a series of decreasing remainders , until one arrives at a remainder that measures the preceding remainder . 1 .1 the case shown, this number is 13, which is the greatest common divisor of 65 and 39. This same procedure of successi ve, in-tur n, subtractions--lts Greek name was antanairesis---can be applied to megnitudee, in order to determine their common measure . But suppose t hey are incommens urable; then the subtractions would go on forever, without any remainder being found that measured the preceding remainder. A particular such ~ituetion is shown in the following diag ra m, which showg the side and diegonel of a square: A EB (aymmetry) CD DE (isoecelee rt. 6. ) CD = CE = AB (or CB) - CD (or EB) AC - AB And ao on ad infinitum. c 8 E 25 �f iret the aide is subtracted from the diagonal, leaving CD; then subtracted from the side CB t111ice, and so on; CD is I will not go into. the .proof of incommanaurability hare, 111hich necessarily involves a reduction to the absurd; but one can get a hint from the diagram as to why the process would be infinite. procaaa of antanairasis would ~o pair of original magnitudes. The subtract two times frorn rel1)8inder three times from remainder n. Nevertheless, this infinite on in e determinate way, for e given n~ remainder, for example, might .!:!::.!.; and remainder n-1 might subtract The two and three, along with the corres- ponding numbers for all the other subtractions, would characterize and define the antanairesis as a whole. definition of same ratio: Then same antanairesis could be the a first magnitude wo uld have to a second magnitude the same ratio as a third to a fourth if the first and second magnitude had the same antanairesis as the third end the fourth. With this definition, it ie possible to prove, for example, that rectangles under the same height are to one another as their bases, because one sees that the antanairesis 111ill go on in the same way with the rectangles as with the bases, even though the antanairesis be infinite. There are other mathematical exploits of Theaetetus, embodied in booka X and XIII, and they are of a kind with the formulation of the definition of proportionality that I have just described . Using theoreme about numbers in new ways , Theaetetue succeeds in rendering what was inexpressible expressible . Such achievement, I would suggest, should be put down under the rub r ic of Pa~cal's esprit de finesse , rather than under his esprit de geome trie, the geometrical turn of m nd, which Pascal i so berates for i t s blindness to t he pro blem of the principle s. The Pythagorea n mathe nia t a, arithmetic , geom tr y, a nd the rest, are not libe r a l e arts merely or pr ima ril y i n being deduct ive , i n proceeding s t e pwi s e i n accordance wi th ce rtain r ules . essential relation to tb_e Their liberali t y, it seems t o me, ha s an a~reness not merely of logical necessity , but of that necessity with which they ere designed to cope : we are free men when we ere aware of tha-t ne.e.essi ty and can begin to cope with it. liberal arts become f ully Hber~+ _ only The as we turn to11JBrd the problem of the principles, toward the rMtr.ix of necessity in which those principles ere embedded, toward the question of being from which those arts take their riae. 26 �Notes l. (p. 1) This lecture owes everything, or nearly everythl~g. t~ ' number of studies by historians of mathematics, parti~~1~:'.;; 0. Becker, "Die Leh re vom Geraden und Ungeraden im n0Tc: nr. Rue:. der euklidischen Elemente,'' uellen und Studien zur Gesc~1ch~Q der Mathematik ••• , Abt. B, Band 3 193 , 125-1 5; B. :., va!1 der Waerden, "Die Ari thmetik der Pythagoreer, '' Mathematische Annalen, !20, (1947-1949), pp. 127-153, and Science AwaJcening (Ne~ Y~~k: Oxford Univ. Press, 1971): G. Vlastos, "Zeno of Elea" in .i::nclyclopedia of Philosophy, VIII, 370; O. Neugebauer, The ~xact Sciences in Antiquity, 2d ed., 1957; and above all articles by Arpad Szabo: "Zur Geschichte der Dialektek des Denkens, 11 in Acta Antigua Academiae Scientiarum Hungaricae, II (1954), 17-62, and "The Transformation of Mathematics into Deductive Science and the Beginnings of its Foundation on Definitions and Axioms," in Scripta Mathematica, 27 (1964), 28-48 and 113-139. For the Proclue text I depended on Procli Diadochi in Primum Euclidis Elementorum Commentarii (ed. Friedlein, Teubner, 1873) and the recent translation by the late Glenn H. Morrow, A Commentary on the First Book of Euclid's Elements (Princeton, 1970). In the section on Parmenides there may be recognized a certain inspiration, much diluted, of Martin Heidegger~s What is Called ~hinking? (tr. Wieck & Graz, New York: Harper & Row , 1954). ?. In particu1ar, see Walter Burkert , Lore and Science in Ancient ~lthagoreanism. 27 � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Description An account of the resource Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. 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Visit <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a> or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe. Contributor An entity responsible for making contributions to the resource St. John's College Greenfield Library Title A name given to the resource St. John's College Formal Lecture Series—Annapolis Identifier An unambiguous reference to the resource within a given context formallectureseriesannapolis Text A resource consisting primarily of words for reading. Examples include books, letters, dissertations, poems, newspapers, articles, archives of mailing lists. Note that facsimiles or images of texts are still of the genre Text. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data paper Page numeration Number of pages in the original item. 28 pages Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource On the Discovery of Deductive Science Description An account of the resource Typescript of a lecture given on September 14, 1973, by Curtis Wilson as part of the Formal Lecture Series. <br /><br />The lecture was also published in <a href="https://digitalarchives.sjc.edu/items/show/487">The College, volume XXXI, number 2 (January 1980), pages 21-31</a>. Creator An entity primarily responsible for making the resource Wilson, Curtis Publisher An entity responsible for making the resource available St. John's College Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Annapolis, MD Date A point or period of time associated with an event in the lifecycle of the resource 1973-09-14 Rights Information about rights held in and over the resource St. John's College has been given permission to make this item available online. Type The nature or genre of the resource text Format The file format, physical medium, or dimensions of the resource pdf Language A language of the resource English Identifier An unambiguous reference to the resource within a given context lec Wilson 1973-09-14 Relation A related resource <a title="Sound recording" href="http://digitalarchives.sjc.edu/items/show/3669">Sound recording</a> Subject The topic of the resource Science--Methodology Deans Friday night lecture Tutors