3 20 453 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. For more information, and a schedule of upcoming lectures, please visit the <a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a>. Click on <a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&sort_field=Dublin+Core%2CDate&sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a> to view and sort all items in the collection. 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 Hyperlink A link, or reference, to another resource on the Internet. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data mp4 Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 00:50:06 URL https://youtu.be/aar1cdBheP0?si=G0wK-yy28X_O4amZ 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 <a href="https://youtu.be/aar1cdBheP0?si=G0wK-yy28X_O4amZ">Tragic Pharmacy: the "Noble" Lie and the Fall of Kallipolis</a> Description An account of the resource Video recording of a lecture delivered on November 3, 2023, by Kevin Kambo as part of the Formal Lecture Series. Professor Kambo describes his lecture: "In Plato's Republic, Socrates suggests that the best regime is doomed to fail. This failure is often attributed to inevitable errors in the rulers' eugenic calculations. I propose that the city's constitution must decline not because the eugenic calculations go wrong, but because the calculations have always been wrong, and this on account of congenital errors in the city's establishment. In this dramatic arc, from noble founding to destined fall, the reversal perhaps reveals the city to be a tragic figure. The Republic, then, would not be, as some read it, a prescription for authoritarianism or totalitarianism, but a reflection on political lies, human sacrifice, and the tragedy of politics." Professor Kambo is an Assistant Professor of Philosophy at the University of Dallas. Creator An entity primarily responsible for making the resource Kambo, Kevin 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 2023-11-03 Rights Information about rights held in and over the resource A signed permission form has been received stating: "I hereby grant St. John's College permission to: make a recording of my lecture, and retain copies for circulation and archival preservation at the St. John’s College Greenfield Library; make a recording of my lecture available online; make typescript copies of my lecture available for circulation and archival preservation at the St. John’s College Greenfield Library; make a copy of my typescript available online." Type The nature or genre of the resource moving image Format The file format, physical medium, or dimensions of the resource YouTube video Subject The topic of the resource Plato. Republic Utopias Political science--Philosophy Language A language of the resource English Identifier An unambiguous reference to the resource within a given context LEC_Kambo_Kevin_2023-11-03_ac Relation A related resource <a href="https://digitalarchives.sjc.edu/items/show/7991" title="Typescript">Typescript</a> Friday night lecture https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/1dab08a251433a029562e23bda745f23.mp4 400054e7d65b841388b983db9c7e6515 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. For more information, and a schedule of upcoming lectures, please visit the <a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a>. Click on <a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&sort_field=Dublin+Core%2CDate&sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a> to view and sort all items in the collection. 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 Moving Image A series of visual representations imparting an impression of motion when shown in succession. Examples include animations, movies, television programs, videos, zoetropes, or visual output from a simulation. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data mov Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 00:50:14 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 Ethics and Aesthetics of Sympathy in Sophocles' Philoctetes Description An account of the resource Video recording of a lecture delivered on October 11, 2024, by Dr. Ellwood Wiggins as part of the Formal Lecture Series. Professor Wiggins (SJC Annapolis, 1998) is an associate professor in the German department at the University of Washington, Seattle, where he teaches comparative literature and philosophy. He has also taught in Kentucky, Germany, and Russia. His teaching and research explore how people come to know one another and themselves, often exploring literary figures such as Odysseus or Philoctetes. Professor Wiggins describes his lecture: "The plot of Sophocles' Philoctetes turns on the experience of sympathy, which is often given credit for the moral education of Neoptolemus, Achilles' son. Yet is this emotion a reliable force for good? Sophocles' tragedy is a perfect proving ground to explore this question, and to test Aristotle's description of compassion in the Rhetoric." Creator An entity primarily responsible for making the resource Wiggins, Ellwood H., Jr. 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 2024-10-11 Rights Information about rights held in and over the resource A signed permission form has been received stating: "I hereby grant St. John's College permission to: make a recording of my lecture, and retain copies for circulation and archival preservation at the St. John’s College Greenfield Library; make a recording of my lecture available online; make typescript copies of my lecture available for circulation and archival preservation at the St. John’s College Greenfield Library; make a copy of my typescript available online." Type The nature or genre of the resource moving image Format The file format, physical medium, or dimensions of the resource mp4 Subject The topic of the resource Sophocles. Philoctetes Sympathy Language A language of the resource English Identifier An unambiguous reference to the resource within a given context LEC_Wiggins_Ellwood_2024-10-11_ac Alumni Friday night lecture https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/1c9f1744b49ca16735d6978e6266b6b6.mp4 f841c1639c0ffe4aea7da15167c18020 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. For more information, and a schedule of upcoming lectures, please visit the <a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a>. Click on <a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&sort_field=Dublin+Core%2CDate&sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a> to view and sort all items in the collection. 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 Moving Image A series of visual representations imparting an impression of motion when shown in succession. Examples include animations, movies, television programs, videos, zoetropes, or visual output from a simulation. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data mov Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 00:50:35 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 One and the Many in Psalm 42: Sicut Cervus Description An account of the resource Video recording of a lecture delivered on August 23, 2024, by Suzy Paalman as part of the Formal Lecture Series. Ms. Paalman offers the following description: The motet by Palestrina based on Psalm 42:1 is beloved at St. John's College. If one reads further into the Psalm than the first verse, one can find a return of the motif of water which first appears as "fontes aquarum" in Palestrina's Latin. These "flowing streams" return as tears, as a pouring out of the soul, as cataracts, and more. The "cervus" (deer) of the first verse never appears again explicitly. Instead, we take in images of people: a crowd of mockers, a throng of joyful worshippers, and more. Whereas adding bits of water together doesn't change the character of the water, gathering different people together can have great consequences for the individuals so gathered. The Psalmist wrestles with division and community in himself, in his surroundings, and with his God. What does he long for? Can we learn something about the longing of our own hearts by paying close attention to this Psalm? Ms. Paalman's lecture is the first formal lecture of the academic year. Previously referred to as the Dean's Lecture, this lecture is now called the Christopher B. Nelson Lecture. Creator An entity primarily responsible for making the resource Paalman, Susan R. 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 2024-08-23 Rights Information about rights held in and over the resource A signed permission form has been received stating: "I hereby grant St. John's College permission to: make a recording of my lecture, and retain copies for circulation and archival preservation at the St. John’s College Greenfield Library; make a recording of my lecture available online; make typescript copies of my lecture available for circulation and archival preservation at the St. John’s College Greenfield Library; make a copy of my typescript available online." Type The nature or genre of the resource moving image Format The file format, physical medium, or dimensions of the resource mp4 Subject The topic of the resource Palestrina, Giovanni Pierluigi da, 1525?-1594. Motets (1584 : Voices (4)). Sicut cervus Bible. Psalms, XLII Language A language of the resource English Identifier An unambiguous reference to the resource within a given context Lec Paalman Susan 2024-08-23_ac Deans Friday night lecture https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/f1483e8e62eb0076e8bb62c3d8ae3df4.mp4 7573930b275a0ee9d9bf5f317951061d 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. For more information, and a schedule of upcoming lectures, please visit the <a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a>. Click on <a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&sort_field=Dublin+Core%2CDate&sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a> to view and sort all items in the collection. 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 Moving Image A series of visual representations imparting an impression of motion when shown in succession. Examples include animations, movies, television programs, videos, zoetropes, or visual output from a simulation. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data mp4 Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 01:07:38 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 Phenomenology of Nature Description An account of the resource Video recording of a lecture delivered on September 20, 2024, by Ryan Shea as part of the Formal Lecture Series. Ryan Shea taught at Providence College for eight years, including courses in philosophy of science, environmental philosophy, and nature writing. His research weaves together ancient philosophical biology (especially Aristotle), the scientific revolution, phenomenology, German idealism, and Goethean qualitative science. His main project is to learn what it might look like to read the “book of nature” in a participatory, contemplative, phenomenological, and poetic fashion. Ryan Shea offers this description of his lecture: Edmund Husserl inaugurated the modern discipline of phenomenology with the rallying cry, "back to the 'things themselves'." And yet, when reading the works of phenomenologists, one might reasonably worry that we have bracketed the natural world, that we have left out precisely the "things themselves." This talk pursues two distinct, yet intertwined, questions. We begin with Socrates's central question (ti esti), "What is phenomenology?" This leads to our central concern, "How might we practice a phenomenology of nature?" The work of the poet, scientist, painter, and dramatist Johann Wolfgang von Goethe will serve as a guiding light. Creator An entity primarily responsible for making the resource Shea, Ryan 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 2024-09-20 Rights Information about rights held in and over the resource A signed permission form has been received stating: "I hereby grant St. John's College permission to: make a recording of my lecture, and retain copies for circulation and archival preservation at the St. John’s College Greenfield Library; make a recording of my lecture available online; make typescript copies of my lecture available for circulation and archival preservation at the St. John’s College Greenfield Library; make a copy of my typescript available online." Type The nature or genre of the resource moving image Format The file format, physical medium, or dimensions of the resource mp4 Subject The topic of the resource Phenomenology Nature Language A language of the resource English Identifier An unambiguous reference to the resource within a given context LEC_Shea_Ryan_2024-09-20_ac Friday night lecture https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/8b9c150192d6b7da8aad07234a5baa49.mp4 ea3433d8f3ad859a7d1646994230b977 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. For more information, and a schedule of upcoming lectures, please visit the <a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a>. Click on <a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&sort_field=Dublin+Core%2CDate&sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a> to view and sort all items in the collection. 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 Moving Image A series of visual representations imparting an impression of motion when shown in succession. Examples include animations, movies, television programs, videos, zoetropes, or visual output from a simulation. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data mp4 Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 00:51:36 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 Listen, Love, and Learn: The Formative Power of Singing without Paper Description An account of the resource Video recording of a lecture delivered on September 1, 2023, by Paul Vasile as part of the Formal Lecture Series. Mr. Vasile describes his lecture: "We'll explore practices of musicking rooted in the oral tradition and the ways they enrich and complexify how we interpret music from the page." Paul Vasile is a church musician, teacher, and composer who finds his greatest joy in collaborative and community-centered work. Creator An entity primarily responsible for making the resource Vasile, Paul 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 2023-09-01 Rights Information about rights held in and over the resource A signed permission form has been received stating, "I hereby grant St. John's College permission to: Make an audio recording of my lecture, and retain copies for circulation and archival preservation in the St. John's College Greenfield Library. Make an audio recording of my lecture available online." Type The nature or genre of the resource moving image Format The file format, physical medium, or dimensions of the resource mp4 Subject The topic of the resource Sight-singing Singing--Instruction and study Language A language of the resource English Identifier An unambiguous reference to the resource within a given context LEC_Vasile_Paul_2023-09-01_ac Friday night lecture https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/85496d1c24820397c03c46b8de9461e1.mp3 b63cb824cfbd08eee80904a9decd1b6c 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. For more information, and a schedule of upcoming lectures, please visit the <a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a>. Click on <a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&sort_field=Dublin+Core%2CDate&sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a> to view and sort all items in the collection. 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 minidisc Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 01:07:58 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 Political Foundations of Modernity Description An account of the resource Audio recording of a lecture delivered on January 24, 2003, by Henry Higuera as part of the Formal Lecture Series. Creator An entity primarily responsible for making the resource Higuera, Henry, 1954- 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 2003-01-24 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 Subject The topic of the resource Machiavelli, Niccolò, 1469-1527 Galilei, Galileo, 1564-1642 Descartes, René, 1596-1650 Bacon, Francis, 1561-1626 Science--Philosophy Science--Moral and ethical aspects Political science--Philosophy Language A language of the resource English Identifier An unambiguous reference to the resource within a given context MD-0020 Friday night lecture Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/6b56bcb73dc481fa0f85f15efef59305.mp4 896474d537ae373a4f360aa7ff57a9ac 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. For more information, and a schedule of upcoming lectures, please visit the <a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a>. Click on <a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&sort_field=Dublin+Core%2CDate&sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a> to view and sort all items in the collection. 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 Moving Image A series of visual representations imparting an impression of motion when shown in succession. Examples include animations, movies, television programs, videos, zoetropes, or visual output from a simulation. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data mp4 Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 01:15:20 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 Footnotes to Aristotle Description An account of the resource Video recording of a lecture delivered on September 13, 2024, by Graham Harman as part of the Formal Lecture Series. Professor Harman is an alum of the Annapolis campus of St. John's. He is currently a Distinguished Professor of Philosophy and the Liberal Arts Co-Ordinator at the Southern California Institute of Architecture, with teaching stops around the world focused on philosophical thinking, architecture, and art. He has repeatedly been included on ArtReview’s Power 100 list of the most influential figures in the contemporary art world. Dr. Harman gives the following description of his lecture: "The title of this lecture is a riff on Alfred North Whitehead's famous remark that Western philosophy can be considered as a series of footnotes to Plato. The lecture will interpret the difference between Aristotle's Physics and Metaphysics as a difference between the continuous and the discrete, and will seek to develop further Aristotle's notion of "contact" as how two things meet (thereby bridging the gap between the continuous and the discrete)." Creator An entity primarily responsible for making the resource Harman, Graham, 1968- 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 2024-09-13 Rights Information about rights held in and over the resource A signed permission form has been received stating, "I hereby grant St. John's College permission to: Make an audio recording of my lecture, and retain copies for circulation and archival preservation in the St. John's College Greenfield Library. Make an audio recording of my lecture available online. Make a typescript copy of my lecture available for circulation and archival preservation in the St. John's College Greenfield Library. Make a copy of my typescript available online." Type The nature or genre of the resource moving image Format The file format, physical medium, or dimensions of the resource mp4 Subject The topic of the resource Aristotle. Physics. Aristotle. Metaphysics. Philosophy Language A language of the resource English Identifier An unambiguous reference to the resource within a given context LEC_Harman_Graham_2024-09-13_ac Relation A related resource <a href="https://digitalarchives.sjc.edu/items/show/8021">Typescript</a> Alumni Friday night lecture https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/e188ef7223c15d8d3988569b2b9fd950.pdf cc6524226b152e5ea567b220e54df5dc PDF Text Text Music: The Representative Liberal Art Dean's Lecture, Friday, September 2, 1988 Wendy Allanbrook - Eva Brann I. fn General (Eva Brann) There is an old tradition concerning this, the first lecture of the new year of learning. It is supposed to be dedicated particularly to the freshmen among us. The others, upper-class students and tutors, are not supposed to mind if they hear things not entirely fresh to them. This is an occasion for talking straight and being explicit about what this community, which the freshmen r..ave newly entered, is like. Consider that phrase, "what St. John's is like." It is part of our pride and of our anxiety that this college is not like any other. And yet we intend it to be like something, namely as much as possible like the idea for teaching and learning it embodies, the Program. This program consists almost as much of what we staunchly don't do as of what we do do. So this lecture will be about the Program, about what is in it and what is not. But we have chosen to talk about the program by means of an example. It is what you will soon learn in your Greek tutorial to call a paradigm: how many things work. one pattern which indicates This paradigm is music. However, we want not only to tell but to demonstrate how things are intended to happen here. We hope that as this lecture proceeds it will show, practically, three things: First, that although the program is a firm course of learning, it is also full of live questions and problems which the faculty argues 1 �about. One such current concern is precisely the standing of music and its shadow effect, the absence of the visuai arts. Obviously the program that is will keep you very busy, but it is very likely to rouse in you an occasional interest in the program that isn't and might be. Let me inject a preachment here: Prepare to live a schizophrenic life ("Schizophrenic'' is a Greek word meaning splitminded). On the one hand trust the program to be a thoughtful and experience-laden guide to the studies of your next four years. other hand, hold everybody and everything responsible. On the Ask your tutors now and then--not so often as to become pests who wreck the daily process of learning--why you are doing what you are doing. them respond. Make And reserve the highest respect for those tutors who admit they have no pat answer and begin to think in front of and together with you. As the year goes on you will discover that there is a presence that haunts this campus. It is that of a man called Socrates who said that to carry on in life without asking questions about it is simply insupportable. He will be, as it were, egging you on. The second thing we want to show you is that it is possible to think together. We've all heard a lot of talk about "thinking for oneself," as if anyone could possibly think for us. The miracle is that we can think for ourselves together; it is that strange possibility which makes this school a community of learning.--By the way, I should say right now that such cooperation, too, will become questionable. You will read a text later on this year which will claim that although the friendship of like interests is a wonderful thing, to be totally happy is to be totally wrapped up in thought, 2 �absolutely self-sufficient. But the soul of this school is conversation, which is audible, cooperative thipking. study is not only allowed.--It is encouraged. And common In the question period we can talk--if you like--about the role of competition in this scheme. The third, dependent, effect we want to demonstrate is the really important one. It is that we can approach a subject on very different levels and with very different preparation. I will be talking about music in the widest sense. Mrs. Allanbrook will specify and make concrete some of my broad indications. Moreover, I am a, by now confirmed, amateur of music, while she has a lot of musical learning. My deficit will not, I hope, keep me from making some sense nor will her expertise keep her from reaching some fundamental questions. I am now getting closer to the topic, music, and it is precisely the matter of amateurism which brings me to it. college of amateurs. You have come to a All your tutors will have some expertise, but usually not in the classes in which they are guiding you. In those they will indeed be merely amateurs, which is just French for lovers-lovers of learning, of course. I will tell you what my expertise was, because it will be to the point later on. I was an archaeologist, which is to say, a kind of grass-roots art-historian. I got to sort out sherds of Greek pottery and to reconstruct the pictures on them, often revealing dramatic and sometimes deliciously scandalous goingson. Then I had to put a date to them, which takes close looking. But in music I am an amateur, and thereby hangs a tale important to the program. This program stands under the aegis of an activity called philosophy. In a few weeks you will have learned enough Greek 3 �to know that the word philosophy means "the love of wisdom." Now, the reason it is possible to put a whole school under this aegis is that to engage well in philosophy it is truly sufficient to love the enterprise, just as the first and last entrance requirement for this college is an ardent willingness to be here. There ~. sadly, some people who care very much about philosophical questions and are just not good at talking about them. But they are very rare. Philosophy requires disposition more than talent. It is otherwise with music. It is possible to love music with all one's soul, to live with it and by it and yet to have an uneducated ear, an ear that hears the effects without discerning the elements. Music has this enormous and mysterious power: Whereas one must be literate to love, say, a great novel, it is possible to be entirely enraptured by music and entirely illiterate iri it. It is because music can touch the soul by means of effects which are deeply rational and may yet remain stubbornly unapprehended that music is the hardest part of the Program to teach. Why, then, should it be a part of the Program at all? A good way to begin is with the name. Music is that which belongs to the Muses, nine ancient divinities.--If you transfer to Santa Fe sometime later on you will easily learn their names because the dorms are called after them. These goddesses are in charge of all kinds of human cultivation, epic, lyric, tragic, comic poetry, miming, dancing, even history. astronomy. The grandest of these is Urania, the muse of This fact will figure later on. daughters of Memory. All the Muses are the This fact yields a double inference: arts come to human beings by divine inspiration. 4 First, the And indeed, your �first and second seminar books begin, or very nearly begin, with the words: "Sing, Goddess. . . " and "Tell me, O Muse . . . " arts come to us through tradition or through memory. Note that a third possibility, the one most familiar to us is missing: arts are our own creation. Second, the that the That possibility was not added until the Renaissance, the start of modern times. In the beginning, then, music embraced all the arts. that will preoccupy you in the middle of human cultivation is seen to have two aspects. soul and gymnastics for the body. the place where you go naked. the year, In a book Plato's Republic There is music for the "Gymnasium" is a Greek word meaning So music is for the shapeliness of the soul, and gymnastics is for the candor of the body. However, it turns out in that book, there are even greater things than psychic and physical cultivation. These higher studies are those which later come to be called the liberal arts. They are higher because they do not just cultivate and shape you but because they put you into a relation with the way things are, or, as you will soon learn to say, with Being. One cultivates the arts for pleasure and self-development, but the liberal arts one pursues for the sake of truth. Incidentally, these arts are traditionally called "liberal'' for three reasons. First because they are taught to the free children of politically free parents, second because they liberate these youths from their dogmatic opinion, and third because they are done freely, without money-making in mind. If you look at our college seal you will find there a little ditty on this theme. They are called arts because they are elementary approaches to the elementary subject matters. Today there is much talk about skills vs. subject matter, process vs. product. 5 In the liberal arts there is �no such distinction: Studying the subject and learning the skill are almost completely one. Traditionally these arts, of which there are seven, have been divided into two sets. The lower, and basic, set of three is called the trivium or "three-way." speech: These trivial arts are the arts of grammar, logic, rhetoric. of "trivial" in this school is: Therefore the proper understanding of absolutely fundamental importance. The second set, the quadrivium, or "four-way," contains the arts of reason in nature. The Republic, the work I mentioned above, sets out what these are and how they are to be studied. The four arts-- they happen to be sciences, but sciences liberally learned happen in turn to be arts--are these: arithmetic, geometry, astronomy and a fourth I will mention in a moment. I need not tell you that you have come to a liberal arts college, indeed one of the few in the world where the liberal arts tradition is taken quite literally. Let me show you how much we mean it, how much your day will be dominated by these arts: Morning: Here is the schedule: Trivium, done in the Language Tutorial. Lower Quadrivium in the Mathematics tutorial. Late morning and early afternoon: Upper Quadrivium, done largely in the Laboratory. Late afternoon: Cultivation of the body, done largely in the Gymnasium. Evening: -Let me backtrack here. The Republic not only describes the quadrivium but tells how to study it, namely liberally, philosophically, not for practical purposes nor even as performances, but for the sake of 6 �reflection and insight. there is philosophy. Evening: Beyond the liberal arts and all through them So let me continue: Conversation about books that reflect on the nature of things, done in the Seminar. Night: Continued conversation. On Fridays, a Lecture. Possibly some sleep. And once a week you will come together to sing in Chorus. Now is the moment to come back to the topmost liberal art, in Plato's book, the one I had omitted just now. It is called harmony. The word itself means a fitting-together, a system, and in the narrower sense those fitted tonal structures out of which music is made. For these are a paradigmatic system. So we have come to music as the coping stone of the liberal arts. Why should this Greek author have put music, of all the arts, at the top, with and above the study of the heavens? reasons. I can think of four The first is complementary to the reason why the Greeks assigned a muse, the aforementioned Urania, to astronomy. It is that they thought that the stationary heavens, being organized on the model of a musical scale, were not only a rational but a beautiful system, as they said, a "cosmos," meaning an ornament. The second is that they thought that each moving planet (the Greek word planet means ''wanderer") in its orbit sounds forth a lovely note as it revolves and that all together these make a ravishing harmony. The third has to do with the fact I mentioned earlier on; that the conscious apprehension of music involves the study of number, as the production of musical instruments involves the study of geometry. Leibniz, a philosopher you will study as Juniors, says, that music is the soul's counting. One might say that it is also the ear's measuring. 7 Indeed as you will �d~s~over, there are certain ever-fascinating problems in mathematics to which we pay great attention, and which are spectacularly well exemplified in music. music. The whole quadrivium appears to be assembled in In fact, in a moment I shall claim that it coopts the trivium too. The fourth reason is closely bound to the third: Music is not only a kind of mathematics, but also a wonderfully peculiar kind. might call it "qualitative mathematics." Here is what I mean: One In number theory one does not, on the whole, want to say that some number relations are more agreeable than others. some, very definite, number relations They are called consonances. In music it turns out that ~more agreeable than others. Others make you shudder. For example, the tone that sits exactly between the two C's of our major scale, F# sounds so dreadful when sounded together with C that it is said to belong to the devil. Behind it there lies a simple but scandalous mathematical fact, the fact of so-called irrationality. I mean by qualitative mathematics. mathematics. That is what You could even call it miracle And that is also why we think that something is necessary for studying music that we expect for no other tutorial: some common prior experience. It is . for this reason that you will be going to Chorus in the year before the music tutorial--to have the specific common experience of this rational magic. But now I have committed a sin against logic. I have explained why music is the topmost liberal art without saying how this activity, so specially named after the goddesses of the cultivating arts, comes to be a liberal art at all. and ask rather: Let me attack this question in new terms Why is music traditionally a liberal art when the equally ingenious visual arts are not? 8 I can think of three answers-- �and a fourth, which is more a wonderful problem than an answer. First there is simply more hard music theory than there is art theory. There is, for instance, a physics of music as there has never been a physics of aesthetic color. There is, to be sure, a science of structured space which is analogous to the number theory of wellfi tted notes, namely perspective. But perspective came late into the visual arts and left soon.--It is not as n~cessary to painting as structured numbers are to music (though in fact we used to have in the Program a lovely sequence on perspective as a preliminary to the study of optics). I do not really know why there is more teachable theory of music than there are principles of visual arts. It must be something like the same reason why there are many respectable Sunday painters and very few bearable Sunday composers. Moreover, space has vastly more possibilities of being filled than does time, so that the spatial arts are correspondingly less easily developed from basic elements. This is one of those great questions which I leave dangling before you. Secondly, music has always been known to have a potent influence on bearing and character. You will read several books this year, the Republic among them, which will claim that music--and the dancing that goes with it--is crucial in the shaping of citizens. The ancients do not think, as we tend to do, that music primarily expresses our souls, but rather that it impresses them, stamps them with character. Imagine an unlikely event which will drive the point home: Suppose all children in our democracy were to learn to dance the minuet in kindergarten, to move every day for a year to a slow and stately music in modestly connected couples. Wouldn't America be a different 9 �country? I cannot think of any visual work that would have such an effect--if only because one can close one's eyes but not one's ears. There is also another reason why the visual arts do not impress themselves as directly on the soul as does music which I leave to last. I do, however, except architecture. • Architecture was, incidentally, the one visual art which was at certain times a candidate for being counted among the _liberal arts. Third, music has just the reverse relation to words than have the visual arts. We rightly wince just a little at those people who can't look at a painting in a museum until they have run to look at its title. But we think that is is a part of musical discernment to listen as carefully to the words of a Passion or an Opera as to the music. Pictures displace words, but words and music are meant to go together. Now thinking takes place in words. Consequently the meaning of music must be somehow closer to our thought than the meaning of a painting. How music and words have meaning separately and together is a confounding and enchanting question which you will hear more about tonight. Following my own advice to you earlier on, let me stop here to tell you forthrightly what I think about the presence of music and the absence of the visual arts from the . program. I think that the Greeks, who produced works of visual art, especially of sculpture and architecture, which once very palpably pierced my soul, had deep reasons for including music among the liberal arts while excluding these visual glories. And we in turn have good reason to stay with the liberal arts and, in preserving our integrity, to exclude something very wonderful--exclude it from the Program, I mean, of course, not from the campus. On the campus we should have, and do 10 �have, a lot of opportunities to do and see such art. But even in the Program itself there is sporadic room, for example, in Seminars, Lectures, Study Groups and Preceptorials on the visual arts. Particularly those Preceptorials, the small semi-elective study groups which you will join in your last two years,• are a good place for tutors to offer such studies. the following title: "Greek Temples, Gothic Cathedrals and Mid- Western Grain Elevators." of their own. preaching: I myself would like one day to offer These last have a certain utilitarian glory Here, incidentally, is the moment for yet another Come to the question period! For there you will hear with what passion and reason the contrary argument can be made. And there you yourselves can join in this perennial conversation. Finally, then, there is that fourth distinction between music and the visual arts which I have left to the last because it is the trickiest, most fascinating yet. representative. The visual arts are by and large They re-present , or imitate, a visible object. They convey a likeness, a similarity, an imitation, in such a way that one can find some sort of rough geometric relation--it is of the kind called projective--between, say, a portrait and its sitter or a landscape painting and its natural scene. It is the representative nature of the visual arts that accounts for · the effect I just mentioned, that these arts go to the soul less directly than does music: They require an intermediate recognition. I must tell you that the hottest and most crucial issue in modern esthetic theory is the "representationality" of all the arts in general and the imitative nature of painting in particular. There are people who claim that a cat in one painting and a cathedral in another are more like each 11 �other than a painted cat is like a live cat or a painted cathedral is like a stone cathedral. They think that imitation (or as you will soon learn to say, mimesis) is no factor in what makes a painting a painting. I mention this to show how fascinatingly extreme the arguments about representative art have become. Music, however, appears to have no such diverting problem; on the face of it, music hardly appears to be representational in the projectivai way of paintings. Take your favorite symphonic movement and ask yourself and your new roommate what it represents. surmise. It's an invitation to wild And yet music seems to show so much and mean so much. Here lies a captivating problem, and so begins the specific demonstration . Is music really in no way representational? We will see how we can think about particular pieces of music in the light of this large questions. I have talked about music as a liberal art, and now we will be drawn into its actual and specific pursuit. 12 �II. In Particular (Wendy Allanbrook) If I were again a student, seated in the audience tonight, the question I would be askingis "Why should one want to say that music is representational? Isn't it precisely its non-representational quality that gives music its glory?" This was surely my opinion when I was in college; I remember clearly the day I discovered a learn~d treatise that corroborated it, and spent hours in the stacks of the college library fiercely underlining pregnant passages. I have since lost my original copy of the treatise, a work by an eminent nineteenth-century music critic, Eduard Hanslick, entitled The Beautiful in Music, but I have no difficulty guessing the formulations that pleased me so: for instance, "The ideas which a composer expresses are mainly and primarily of a purely musical nature." [23] or "[Music's] nature is specifically musical .... [Its] beauty is not contingent upon nor in need of any subject introduced from without but ... it consists wholly of sounds artistically combined." [47] It is no longer clear why this notion of musical autonomy was so important to me then, against what heresy I was defending the sweet art. When, later on in my education, I came up against those who would argue the other way, I fought bitterly, and then fell. Often one becomes most passionately interested in pursuing the notions of which one once thought the opposite; I appear before you tonight with the enthusiasm of the converted. I shouldn't play quite so dumb, of course; there is an obvious enemy in question. For example, music that attempts a one-to-one correspondence with natural phenomena we often find ludicrous, and often indeed it is meant to be gently comic; there is something 13 �delightfully fey about those sixteenth-century madrigals that imitate cuckoos, and it is even more fun when, as was intended, you are singing them yourself. Another connection that gives musical repre- sentation a bad name is the one Hanslick seems principally to have been inveighing against: the noti~n of "self-expression," which leads to the vice of musical biography: in this passage Beethoven rails against his deafness, here Mozart mourns his father's passing. These claims are unsupportable, if only because so often our biographical expectations are frustrated. Mozart wrote some of his most sunny and popular music in the period just after the death of his father. Do we accuse him of lack of feeling on this account (some have), or dismiss the connection altogether? There seems to be a common agreement that music exists in another world than the fine arts and those that have to do with speech. One of your tutors, Mr. White, recently gave a lecture in which he discussed ways in which the fine arts and the poetic arts can be said to imitate. His point of departure was a well-known comparison, by the eighteenth-century German critic, G. E. Lessing, between a Greek statue and a passage in Vergil's Aeneid. Both depict the violent death of the Trojan priest Laokoon in the coils of a sea serpent, the one work in stone and the other in metrical speech. The statue, because it must choose only one moment in time for its representation, avoids the harrowing death cry of the priest and depicts a more restrained moment, prior to that of the greatest agony, in order not to become merely ugly or grotesque. The poetry, because it moves through time, can describe the terrible bellow of the priest, the desperate distortion of his features, because one by one it can leave 14 �them all behind. Music, too, is a temporal art, but can you imagine any way of making it the third in this comparison? no commonality at all. man? There seems to be Where do you make out the monster, where the How can we even specify what moment the composer has chosen? Unless the music is explained by a companion text--and this is really a special case--I see no way of talking about the three with the same analytic language. Unlike poems and paintings, the subject of a musical composition cannot be translated into a meaningful proposition. But what do we gain by severing all the connections the art bears to the human sphere? In fact, it was only in the nineteenth century that those who think about music decided to cast her thus adrift. And that came about largely as a development of that novel notion Miss Brann mentioned, that the arts are our own creation. If they are, it is not a giant step to the conviction that they are created anew by every artist, that every work is a personal statement of a private seeing--or hearing--that the audience is privileged to share. Music becomes pure feeling--the art of self-expression, the inner mysteriously made outer, and although this has its attractions, it is not an aesthetic that is supportable for long. No wonder Hanslick was in revolt; one begins to have some fellow-feeling for him. As a result of this legacy, modern philosophers make an extraordinarily vexed question of expression in music. That they use the word "expression'' is in itself indicative, for I suspect that were they to free themselves from the notion of feelings as the sole proper subject matter for music, they might not be so squeamish in their discussions. As one critic recently remarked, we go through 15 �such tortured arguments, and all we get is the freedom to attach the predicate ''sad" to the slow movement of a Beeth6ven Symphony. But other formulations had guided thinking about music for the previous millenia, formulations that more successfully made the connection between human beings and the art of shaping sound in time. Miss Brann mentioned the ancients' belief that music can impress our souls, give them shape. Aristotle, in remarks in the Politics about the importance of music to the education of a citizen, makes specific claims for the depictive qualities of music in its relation to the human soul: Rhythms and melodies especially contain to the true natures of anger and likenesses gentleness, and further of courage and temperance, and of all their opposites, this and of the other moral qualities is clear from its effects, for when we (and hear these things we are changed in our soul.) Aristotle's claim is that music makes "likenesses" of human passions and qualities, to which we naturally respond. Elsewhere, in the Poetics, he calls the poetic and musical arts all "modes of imitation" (mimesis in the Greek)--modes of imitation of human beings in act. Imitation is another degraded word today, for it implies origi- nals out there, of which the artist simply takes a copy, and it is more modern to consider the artist both the origin and the original. But if the original is the ways of human beings in the world, is the whole of God's cosmos, and there are infinitely many ways of taking that copy (I'll call these variations "style"), then the task of imitation seems not degraded, but endless, various, and noble. 16 �The crucial question then becomes, how do we make these musical copies? The answer lies in the qualitative mathematics of which Miss Brann spoke earlier. How does the soul count, the There are two principal ways, I would maintain: ~ measure? the way that number • shapes time--we call that rhythm--and the way that number informs pitch--it's harder to come up with a generic name for that. I hope not to be too provocatively simple when I say that in this counting only two numbers count, namely 2 and 3 (some Renaissance theorists counted to 6, and we could do that too, but for our purposes this evening it isn't necessary). I'll tell you briefly what those numbers mean, and then move to exemplify them. About rhythm I'll be most brief, for you probably know that the available rhythms reduce to counts of 2 and 3, or some combination thereof. Think of 2, or duple, as a march or simple alternation of left foot and right. 3, or triple, insert a hop on every left. With There are more elegant ways of adorning a walk to get a triple; the minuet Miss Brann mentioned goes to the count of 3. But more of this later. The 2's and 3's of pitch are rather more concealed, to the extent that we commonly call by the name "5" what really ought to be called "3." Yet the phenomena are sufficiently important and dazz- ling to have been credited to a discoverer, Pythagoras, and surrounded with their due mead of apochryphal stories about the circumstances of the discovery. The note we designate as 5 in the string of organized pitches we call a "scale" actually stands third in the order of generation. Take a string, and divide it in two equal parts. Pluck either half, and the resulting pitch will reduplicate the original, but higher--that interval we call the octave, which orders 17 �tonal space by its regular recurrence over the entire series of pitches. It puts the cap on our eight-note scale, which will sound all too familiar to anyone who has ever had a piano lesson: [Ex. 1] . Next in this soul's counting divide the string in thirds, and you have the fifth, so called from its position as number 5 in the ascending scale. It provides an intermediate resting-place in the / octave's span, dividing it almost, but not quite - (and this is crucial) in half. You'll recognize it from the sound of this perennial five-finger exercise: reverse: [Ex. 2]. By the way, the process works in if I want to divide a taut string into perfect halves, all I have to do is find the octave--our ear is indeed the measurer. While the octave is other, it is still somehow the same as our primal pitch, so the fifth is the first independent other; the octave is the encloser, the fifth the first enclosed. We will honor the order of experience by calling this pitch 5, and the interval it forms with our starting-place the fifth. Never forget, however, that it stands proudly third in order of generation, and that its generating number is 3. You will go more deeply into these miracles of embodied number in the music tutorial sophomore year, counting at least as far as 6, but for now this is all the theory you need to know. I shall try to put these various 2's and 3's to the work of imitation. ways. And I shall claim that they do this work in two important It's hard to find proper names for them; we've learned to be wary of the time-honored distinction between form and content in almost all its applications, and in a temporal art like music I think there is almost no defense for it. I find myself, however, stuck with modern names like "reference" and "process," or perhaps "reference" and "syntax" (I can't decide). 18 These duos take more explana- �tion, but they don't halt and freeze the persistent motion of the tones the way "form and content" do. If we wanted to be trendy, I could point out that we are on the cutting edge of modernity here, for our categories could be formalized into the modern pursuits of semiotics, or the study of signs, and narratology, which is nothing more than the study of beginnings, middles, and ends. Actually, that is - not such a bad description of what I want to talk about. I shall present you with three musical examples to illustrate these modes of imitation. In them the 2's and 3's of rhythm will intersect with the 2's and 3's of pitch to make dazzling imitative configurations. Given the embarassment of riches in music history, I can only be suggestive, not inclusive; I shall also be decidedly anti-chronological. I shall begin where those who know my preoccupations could well have predicted--with the music of Mozart. It was the music of Mozart that I most wanted, early on, to defend as pure, and precisely the same music I later found to be most delightfully contaminated with reflections of human activities. Furthermore, this particular work of Mozart's, the piano sonata .in F major, K. 332, a favorite example of mine, is precisely the kind of music the purists would argue is the most autonomous music your money can buy--instrumental music. Here there intrudes no voice uttering sounds that are signs of other presences, and thus forcing a translation to mundane can such music point beyond itself? porary with Mozart gives me~ning. How A French writer roughly contem- us a hint of how this might be: Michel Gui de Chabanon, actually an advocate of music's integrity, perhaps despite himself articulated one crucial way in which music can represent: Imitation in music is not truly sensed unless its 19 �object is music. imitate In songs one can warlike fanfares, melodies, etc. It hunting successfully airs, rustic is only a question of giving one song the character of another. Art, in that case, does not suffer violence. I'll translate this to our own purposes. Once music has a history, it can hardly fail to make reference to this past, - to provide its own vocabulary of expression. Miss Brann mentioned the educative value of minuets, and that is apposite here. Much of the art music you know, the music played in symphony halls and on good-music stations, pieces itself together from the more mundane music we use to accompany daily activities. The tempting world of human motion is out there to imitate, and some of our greatest composers have taken advantage of it. Love songs, lullabies, dances and marches, hymns, when are lifted from their usual environment and placed in the frame of a symphony or sonata, cannot help but point us back to the particular occasion that produced that humble popular gesture. One of the most prominent identifying characteristics of these gestures is rhythm. The music of the minuet, a noble dance, is there to assist the dancer in maintaining a noble posture--restraint, control, refinement. dignity. Practicing it, we may over time learn grace and Hearing it, we cannot help but think of these mobile vir- tues; our body strains to move with them. This smooth even count of three is character-building and character-evoking--truly "qualitative mathematics." To help you count that three, let me play a minuet part way into the first movement of the Mozart sonata. It comes at a crucial point in the piece, when a base has to be touched, a sense of arrival created--not home plate, but, to use a further spatial meta20 �phor, diagonally opposite. motion. Sense the dignity and tranquility of the When you hear what precedes it, you will feel it all the more by contrast: [Ex. 3]. This movement has a profusion of gestures; it might be described by the question "How many qualities has 3?" For it shows us 3 in many lights, often reminding me of one of those magic sugar eggs with the hole at one end, into which you look to marvel at the perfection of the detail observed in its miniature world. First we hear a singer, her breast swelling as she reaches for her high note. ber, this is all conveyed to us on the piano: [Ex. 4] Remem- She should continue, but instead her utterance is answered by two voices, not so clearly vocal anymore, one following the other at a brief interval and singing the same melody--imitative counterpoint is its proper name, and to Mozart's audience it had a rather old-fashioned ring-pompous and over-serious: [Ex. 5]. Another length, a simple unit of minuet, moves to the close, so that our first "sentence'' has three parts or clauses, of equal time but not necessarily equal weight. The next sentence is devoted to the rhythms of a hybrid minuet--a minuet crossed with hunting horns. We recognize the horns because the characteristic pitches of their calls in the field are imitated: [Ex. 6] . After a satisfying and discrete paragraph of this hunting minuet, the movement "turns on a dime" to a dark, passionate music often called "Storm and Stress," after the Romantic temper that affected it. Whole pieces were written in this style, but here it becomes just one affect among many. In its restlessness, however, it serves the subversive function of undermining home base, and moving us to that new place we must reach if we are to have any sense of 21 �having moved at all. And--as you have guessed--at the end of this so-called travelling music, we arrive at the well-shaped minuet you heard before: [Ex. 7]. The new arrival place marks the end of the beginning and the beginning of the middle, and quite naturally this new place is identified with 5 (3). The drama of the r~st of the piece will be the return to 1 via some cunningly shaped paths. The image of some sort of narrative does not seem to me to be far wrong, much more apt than the formalist analysis. Our delight in this imitation is the delight in the reflections of the many-wayed won- ders of a close and ordered world, disposed to form the crucial nodes of a well-wrought narration. What is peculiarly musical about it is that there is no real story in the sense we expect one, no proposition, no picture of Laocoon. Yet in this passage-through-time we sense an order, intuit a deep intent, and are deeply satisfied. This Mozart example is an example of imitation in the most direct and evocative fashion; I could show you many others. like to offer an example of a different sort: But now I would first off, vocal music (music with a text), sacred, not secular, and grand and special rather than playful and habitual. It is a piece those of you who have completed the music tutorial will know well, the culminating aria of Bach's St. Matthew Passion, "Mache dich, mein Herze, rein." It occurs after the Crucifixion, immediately following the moment when Joseph of Arimathea claims Jesus' body from Pontius Pilate. This scene follows the procedure of others in the Passion: a passage from the Gospel of Matthew narrating the scriptural event is set in the simplest speech song, and then commented on by an observer outside the time of the narrative, in verses by an eighteenth-century 22 �poet. The commentary itself usually has two parts--a discursive passage in a free declamatory style, sometimes called arioso, and a more summary, epigrammatic statement, set in the full panoply of . an aria, a closed musical form. This particular scene takes place in the evening, and the arioso text ponders the theological meaning of eventide: In the cool of the evening, Adam's fall was manifest. In the evening the Saviour casts him down. In the evening the dove returned, and brought the olive branch in its beak. o beautiful time! O Eventide! The covenant of peace is now made with God, for Jesus has completed his cross. His body comes to rest. Oh! dear soul, ask, go, and let the dead Jesus be given to you. O salutory, o precious keepsake! In this poetry the peace of the evening and the covenant of peace become one: Adam and Noah are fulfilled in Jesus, who has paid the most memorable price for the sins of all. Eventide becomes a sym- bol--and I think I use that difficult word correctly--for the peace of God that passes all understanding. Symbols are the theological way--the cross is paradigmatic--and the text of the Passion is suffused with them. So is the music, sometimes in an abstract and impalpable way, such as the reach up to B flat on the word "blood" (German Blut) in the scene of the Last Supper. Others, like the aria that follows this arioso, move us directly--musically--at the same time that they undergo this translation to a deeper Christian mean23 �ing. At the end of the arioso the singer (a male, a bass) addresses his own soul, telling it to go receive the dead Jesus, and then, in the most tender and moving aria in the Passion, enjoins his heart to prepare itself for the corning of Christ. Make yourself pure, my heart. I want to bury Jesus himself. The poetry of a second section, the music of which we will not examine, amplifies the symbolism: For he is henceforth to have his rest in me forever and ever. World, get out, let Jesus in! Bach suits actions to words. That's a conventional phrase most analysts like to fudge with, and given the text the composer has to set here, that must seem to you exactly what I am doing. not particularly fertile in musical ideas. The text is How do you draw a musical picture of a heart purifying itself? of a believer burying Jesus in himself (as the second part of the text suggests)? The task seems preposterous, perhaps even blasphemous. I'll suggest an absurdly simple answer. You write a cradle song, a lullaby. Cradle songs from time immemorial have used rhythmic 3's in groups of 2; that is, each 3 is a rock of the cradle, with the extra odd beat catching the pause of the cradle at the extreme of its swing, poised for return. These 3's are then grouped in 2's: the cradle rocks back and forth. Let's hear the instrumental introduction to the aria, to concentrate on the effect of the rhythm. Notice that the bass sets up the rhythm briefly before the melodic voices enter; th~ about it that the singer merely shares: [Ex. 24 motion has an eternality 8] . �Perhaps I should explain further why I find this device so wonderfully appropriate. On the surface it would seem to satisfy neither purification nor burial, the dual requirements of the text. But remember that the arioso text made death into sleep, an image that is important throughout the Passion. The believer--our last example was Joseph of Arimathea--holds the blessedly resting Jesus in his arms; this- male figure universalizes the pieta, the figure of the weeping mother holding Jesus in her arms after the descent from the cross. Mary holds a full-grown son who is beyond the solace of rocking, but the symbolic believer is allowed a maternal lullaby. It is thus, the aria argues, that believers should receive the Christ. In fact, the aria is an injunction to the believer to accept in full serenity the final agony of Christ as the bringer of peace to the world. Thus to bury Him is to rock Him to sleep with a mother's lullaby. There is some final musical detail I cannot omit describing before you actually hear the singer's voice. I have tried to show how Bach, in setting this seemingly unsuggestive piece of text, manages to explode it into deeper meaning using a musical gesture that becomes symbolic, moving the believer both physically and cognitively to a deeper Christianity. Strikingly, Bach sacrifices the text to the hypnosis of the eternal. Syntax, prosody, all those things that suggest human meanings in human time, are suspended, and even that element that makes musical syntax, the 5 (our 3), disappears to some extent. Musically the 1, the center of gravity, is instead held up on top, and a scale descends against it with each rock of the cradle: [Ex. 9]. The singer's line is wholly unvocal; it imitates a characteristic Baroque instrumental line where one instru25 �ment plays the parts of two, first high, then low. further apart so you can hear the two: [Ex. 10]. I'll split them A further distortion of our natural expectations is the actual setting of the text, rhythmically and melodically. "I want to bury Jesus myself"-- "Ich will Jesum selbst begraben"--"Ich will Je-- sum selbst begra-ben." Je- and gra- are stressed unnaturally by the move to a melodic peak on an offbeat: this extraordinarily awkward vocal line does violence to both melody and text in the service of the hypnotic cradle song. Singer, song, and syntax are dissolved in the cosmic lullaby that is the rocking of Jesus to the sleep of sin. All human history focusses on the descent from the cross; that moment of time must stand for eternity. When syntax must reassert itself, at the end of this musical section, we are wholly prepared for the vocal awkwardness on the final "begraben"--"bury"--the deep leap down from the 2 to the 1, the octave to the prime, precisely the kind of musical tone-painting we have grown to scorn this evening. Bach has habituated us in the course of this aria to music become meaning; we accept a musical barbarism as a convincing theological symbol: [Ex. 11] . There is other music I should have talked about, were there time, for example, the repertoire of many-voiced sacred Renaissance vocal compositions. There dance is absent, and composers eschew any obvious translation of textual images into musical ones. Yet the theorists of this music are most emphatic about its imitative quality. The object of imitation is nothing less than "wondrous Nature," as their prime spokesman, Gioseffo Zarlino, a sixteenth-century composer and writer, states. "Every composer ought to follow the beau26 �tiful order of nature, and he will be considered excellent in proportion to the resemblance of his procedures to those of nature." Zar- lino's "wondrous Nature" is a world informed by number, by our 2's and 3's. One of his cardinal principles is unity in variety, fol- lowing nature, which, he says "does not produce identical individuals in a species, but always somehow varied." "Numbers and proportion invite us to variety, for in them we do not find two similar proportions following one another." Here he is speaking about the harmonic proportion, a important number relation named after its embodiment in music. We have already heard the simplest form of that relation, in lowest whole numbers--the dovetailing of the 2 and the 3, or the octave and the fifth. [PLAY] · Harmodzein, the Greek word for the dovetailing of joints in carpentry (it also can mean to "set in order," or "govern," and also to "betroth") describes the way the octave and fifth lie harmoniously together, a concordance of dissimilar elements, giving their name to a number relation you will meet elsewhere in the program. To Zar~ino this relation comes closest of all musical relations to the sound of perfection, and so it must end every composition; for, in his words, "Perfection is characteristic of the end and not of the beginning of a thing." [EXAMPLE 8] A latet music that calls itself harmony (the examples we have been listening to this evening) will add another element to this dovetailing to fill it in, to make it less perfect and hence more sensuous (one eccentric modern theorist calls the fifth the "pre-sexual'' interval); this more homogeneous entity we call a "chord." But still the guiding relation remains the same--the harmonic proportion, the miraculous blending of the 2 and the 3. 27 �I have somewhat perversely tonight been giving you a music history in reverse, and it would be remiss of me not to add a postlude that takes it back to origins, so to speak. We have been dealing all evening with compounds--more than one line at a time--and now we will turn to simples. But only in the sense that we are no longer combining two pitches at a time; any implication that this one-line music is simple in the se-nse of "primitive" is wholly alien to my intention. I have heard it said of the repertoire of Gregorian chant that it is abstract, ethereal, above the world and its relations, out of time in its simple temporality. I don't believe that any example of this most human of arts can be like that, nor do I think that we endow it with any greater dignity or spirituality in so asserting. The goal is to let a sacred text speak out as simply and eloquently as possible, and again the 2's and 3's do the work. The text of the Latin hymn I have chosen, in unrhymed Latin verses, is from the Easter Mass, and it is a meditation on the miracle of the Resurrection. Let It reads, in part: Christians off er their thankful praises to the Paschal Victim. The Lamb hath ransomed the sheep: the sinless Christ reconcileth sinners to the Father .... Tell us, Mary; what did you see in your wayfaring? I saw the tomb of the living Christ, and the from the glory of Him rising .... We know that Christ has truly risen dead; have mercy on us, Victor King. Amen. At the center of this text is an act of human witness, at the conclu- 28 �sion one of human celebration. At no time does the chant call atten- tion to a particular phrase--it never makes "word pictures"--but the whole is animated with human pulses and human breaths. The rhythm of the poetry is primarily trochaic--a stress on the first, third, syllable, etc--and the musical rhythm by and large follows this grouping into 2's: "Victi~ paschali laudes irnrnolent Christi~ni." The 2's and 3's of pitch- order the ebb and flow of the melody. The octave is the limit of rest, the fifth (our 3, remember) the limit of tension. These seemingly narrow melodic limits set the theater for a narration without a story, for a dramatic mimesis of the condition of the human soul. When we hear the third phrase begin on the 5 and rise up to the octave above, our chests swell, our pulses race, at this brave effort against the center of gravity, the 1. On the return we compose ourselves, fold our hands, reflect, always in sympathy with the passion objectified in the music. We haven't here the histrionic swelling breast of the operatic soprano, but the effect is only dissimilar in its restraint. Above all chant is singing: is breath and how long one can hold it, the tightening of the vocal chords in order to attain a higher pitch: [Ex. 12] . posed this music is, and ordered, but inhuman it is not. Corn- For it is never without passion, if passion can be defined as the suffering or tolerating of the physical and emotional effects that devolve from the exertion of our human equipment. Hanslick, in his efforts to make mock of musical imitation, turns one memorable phrase that might seem in its sarcasm to put an end to the question altogether. "The animal to which music is most indebted," he says, "is not the nightingale but the sheep." 29 The song �of the sheep is, of course, that of the gut, the taut string, and we are being reminded to turn our attention away from frivolous thoughts of connections between music and nature to the sober practicalities of the making of pure musical sound. But, as I've tried to say tonight, I think his example contains in it the very image that is • his undoing, for it is the physics of the taut string that makes Aristotla say the There musical makes following~ seems to be tunings some also in the Politics: in us a sort of (harmoniai) and kinship rhythms, philosophers say that the soul to which is a tuning, others, that it possesses tuning. I submit that this music is an imitation of "wondrous Nature," our nature, as it uses musical number in the act of prayerful praise. further submit that very little music is not like this in some way, if we but look and listen. 30 I �., Allanbrook Example- t> ~ Example- 2 ~-a ,, ? 0 - -0- 0 0 t I. -e- 0 0 () 6 Ii II ea Exampl~s -e-· ~ ~0 l) 11 0 .g.. Examplt3 -· . " . A ~~- ? I a :oi).._ - r I ~' I I - Exanrple 4 C~n 1:::1:: 1:;; I Exampk 5 . -~ - I . -....... ~ I I --..-.. I I .....- .. - - Example Exan1ple 6 '~ r..r r . I 7 - - �Examplt 8 · ~Aria - (Chorus I) Exampl~ , 9 L A .... I ..... - I l m.2 --. ·, ., 1- I ' Example to m.2 ., II ~ m.3 .-. m.+ m.'1 �Examp~ II 00 Basso Cc:Jion• n B..~~~~~~~~~ Ma. - che dich,mein Her - ze, ben, _ ma-Che dicb,meinHeJ1.ze,rein,icb_ will Je- IWD selbat_ be- gra-ben, ich willJe-sum aelbst be- gra.-ben. �Example- 12 Victimae paschali laudes Sequence for the Solemn Mass of Easter Day .. I _. 7;· ~,i.~~..~~...~.~~,,~~.5.~.~~-~~·~·~.~~·~i-~.~-~11 5 Vic·ti·mae pa.·sch..li Lau·des •im·mo-lent Ch:i·sti • a·ni. -& • 4 • -- ~ • • 4 I • 0 • • • 4 • . .. .. II re-<on-ci ·Ii· a·Yit pec·c:a·to·res. • - • • • • It • - .. 2. A-gnus red··e·mit .c-Yes: Chri·stus in·no-cns Pa·tri J. Monet vi· ta du·eho con· ru · xe· re mi ·ran-do: dux Yi-tae mor-tu·us. re-gnat Yi·vus. 4.Dic S.An ~y .. • " no . bis . se . • " • . Ii ... Ma cos .. • •:=:; . ri . •• te - stes, • quid SU .·I f [6. • jl Cre • den • dum est 1. s..; · mua Qui • stum § ;a . Yi da . . 4 • 0 ma • gis 511r • iz • " Ii so • xis • se ""'* "w •a; • Ms • .. ~ re • sur • gen • tis: ·OS • . • vi . a? . Ye • stes. in et • • • • o:::Z =• pne·ce • det su .. • • . sti . um, di ri • • • • " glo • ri • am Yi • Yen • tis, et a Se-~ul·c:rum Oni • sti Sm- n= • xit Cui • stus spes me • a: &~ • d . in Ga· Ii · Lae • am. • ri ff mor ·tu Iii-;; • . ve . is • ii ra Ye . . " ci re: • Al - le • lu • ia. II �Victimae paschali 1. Victimae paschali laudes . laudes immolent Christiani. ~angs 1. Ta the Paschal Victim let Christians offer cf praise. 2. Agnus redemit oves: pe•=•=atares. 2. The Lamb has redeemed the sheep. reconciled sinners to the Father. 3. Mars et vita duelo conflixere miranda: regnat vi \ILts. 3. Death and life have en~aged in miraculous combat. of life is slain, <ye"t") liv.ing he reigns. 4. nob is Mari a.,. quid vidisti in via? Die vi vent.is, et gloriam vi di resLU-genti s: 4. Tell LlS, Mary, what YOLl saw on the way? I saw the sepul 1.:hre of the living Christ and the glory of his rising. Christus innocens Patri 5. Angelicas testes, sudarium; et vestes. mea: praecedet sues in Galilae~m. 5. Tt1e angel is risen. 6. i·= reconciliavit Sinless has Christ dux vitae mortuus, The leader Christi Sepulc:rum Surrexit Christus spes '"'i tni::s:;;e ·: ~~ th(;: ·= hr-cud and v·e·'5tur•::. Christ ;ny He will gc before his own into Galilee. C1'-edend1_tm est mag .l. s ·:;cJl i Mari ae ve1·-ac i qua1u .J1_1dae·~n..1m l · ;;:Jp~ ti_tt-b.::<.e fallac:i.• 6. Mary alone is more ta be deceitful crowd cf Jews. 7. S·=im1_:s Cl1ri ·: ;tum ·: ;urr···::?;: , mi st:ir· ere. -r I ~·~e know that Chr i ·;t has tr1_1l y r-i ·:;en f ram conqueror and king, have mercy en us. o believed th;? than vi ct;~r - the Je:ad. 1..\Ji pi::J •::f Bur-,dund\' Celeve~~h c~ntur y) � 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. For more information, and a schedule of upcoming lectures, please visit the <a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a>. Click on <a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&sort_field=Dublin+Core%2CDate&sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a> to view and sort all items in the collection. 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. 35 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 Music: The Representative Liberal Art Description An account of the resource Typescript of a lecture delivered on September 2, 1988, by Wye Allanbrook and Eva Brann as part of the Formal Lecture Series. Creator An entity primarily responsible for making the resource Brann, Eva T. H. Allanbrook, Wye Jamison 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 1988-09-02 Type The nature or genre of the resource text Format The file format, physical medium, or dimensions of the resource pdf Subject The topic of the resource Education, Humanistic Music Relation A related resource <a href="https://digitalarchives.sjc.edu/items/show/7970">Recording</a> Language A language of the resource English Identifier An unambiguous reference to the resource within a given context lec Allanbrook 1988-09-02 Deans Friday night lecture Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/ce0f82dc2f1d45c0048175d2f31da18f.mp3 58e3ccbff00e96ba0f7614ffe2920498 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. For more information, and a schedule of upcoming lectures, please visit the <a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a>. Click on <a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&sort_field=Dublin+Core%2CDate&sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a> to view and sort all items in the collection. 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. Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 01:14:02 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 Music: The Representative Liberal Art Description An account of the resource Audio recording of a lecture delivered on September 2, 1988, by Wye Allanbrook and Eva Brann as part of the Formal Lecture Series. Creator An entity primarily responsible for making the resource Brann, Eva T. H. Allanbrook, Wye Jamison 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 1988-09-02 Type The nature or genre of the resource sound Format The file format, physical medium, or dimensions of the resource mp3 Subject The topic of the resource Education, Humanistic Music Language A language of the resource English Identifier An unambiguous reference to the resource within a given context LEC_Allanbrook_Wye_1988-09-02_ac Relation A related resource <a href="https://digitalarchives.sjc.edu/items/show/7971">Typescript</a> Deans Friday night lecture Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/ce3a9ed332c90b715b71d14715c57c17.mp3 33745127913b97db28e96c3536e8231a 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. For more information, and a schedule of upcoming lectures, please visit the <a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a>. Click on <a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&sort_field=Dublin+Core%2CDate&sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a> to view and sort all items in the collection. 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.) 00:58:28 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 Leibniz's New Geometry Description An account of the resource Audio recording of a lecture delivered November 30, 2007, by Annapolis tutor Brendon Lasell as part of the Formal Lecture Series. Creator An entity primarily responsible for making the resource Lasell, Brendon 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 2007-11-30 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 Subject The topic of the resource Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716 Geometry--History Language A language of the resource English Identifier An unambiguous reference to the resource within a given context LEC_Lasell_Brendon_2007-11-30 Friday night lecture Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/8ecefb87d028b8d993d42f15beab8dab.pdf ae2f694b6263387e98b6f7ea35e47c3a PDF Text Text Leibniz’s New Geometry Brendon Lasell July 26, 2007 In February of 1682, Gottfried Wilhelm Leibniz published a paper giving the ratio between a circle and a circumscribed square. In fact, he claimed that (see diagram) when the circumscribed square BC is 1, then the circle is equal to 1 1 1 1 1 − + − + etc. 1 3 5 7 9 The announcement appeared in the second issue of a new journal, the Acta Eruditorum, the Acts of the Learned. The journal was intended to give learned men a way to announce their new discoveries, and it was the first such journal in Germany. Leibiniz’s paper does indeed present something new: nothing like the equality he gives had never been seen before. Leibniz’s paper thus serves to introduce readers to new mathematical knowledge. At the same time, the paper introduces its readers to its author. But the paper is only an introduction. A reader struck by the novelty of its claims would not be satisfied with what he can learn there about the new mathematics and its new author. The paper neither gives a argument for its main assertion, nor does it explain how the author came to it. Instead, he only gives an enunciation of a theorem, seen from several points of view. Intrigued by the mathematics, we may want to know something about the author who is boldly making such claims; but here too we are frustrated. The author only gives his initials, G. G. L., and if we investigate, we only find out that he is a relatively unknown court historian for a Duke in northern Germany. He is a new man among the learned just as his assertions are new in mathematical learning. In February of 1682 we cannot let what we think about Leibniz guide our thinking about Leibniz’s mathematics. Readers of Leibniz’s paper are thus left with no choice but to begin by looking at the enunciation of his new theorem from the points of view he gives us, neither looking ahead to a demonstration or analysis, nor looking back to an established body of work by the same author. Leibniz presents his new theorem above all from the point of view of tradition. His essays begins as follows: Geometers have always tried to investigate the proportions of curvilinear figures to rectilinear figures, but even now, after applying algebra, they still have not succeeded — at least with the methods they have published: for these problems cannot be reduced to 1 �algebraic equations, but they are beautifully useful, especially for reducing mechanics to pure geometry. Leibniz is doing what geometers have always done. He is trying to find the proportion of a curvilinear figure, the circle, to a rectilinear figure, a square. But geometers have not always succeeded at these tasks, even now in 1682, after they have learned from Descartes to apply algebra to solve geometric problems. Leibniz, however, succeeds at his task. Leibniz goes on to say more about the problems that geometers have solved, about their aims in solving these problems, and how his new solution satisfies these aims. Thus, when he gives us the proportion between a circle and a square, he asks us to look first of all not at circles or squares, or even at curvilinear and rectilinear figures in general, but rather at what geometers have always tried to do. His own work belongs not so much directly to geometry as to the history of geometry. It is a step forward in the progress of geometry. Now if we look at Leibniz’s new theorem as a solution to one of many problems that have been solved in the history of geometry, then it is natural to ask what light this new solution sheds on the process by which one comes to solve such problems in general. In an earlier letter where Leibniz presents the same theorem on the proportion between a circle and a square, he writes that “nothing is as important as seeing the origins of discoveries — they are worth more than the discoveries themselves in my opinion.” In a much later essay, he writes that seeing the origin of discoveries is important in that it helps “the art of discovering.” From the point of view of the art of discovery, geometry is not about circles or lines so much as about the general art of coming to new truths. When we look at Leibniz’s claim that the ratio of a circle to a circumscribed square is 1 1 1 1 1 − + − + etc., 1 3 5 7 9 we should then think first about the general art of finding proportions between curvilinear and rectilinear figures, and about the light this theorem sheds on that art. This is the point of view from which we will look at Leibniz’s mathematical work tonight. Starting from this new theorem about the ratio of a circle to circumscribed square, we will look at how Leibniz presents the art of discovery that is behind this theorem. We will begin by looking more closely at how Leibniz presents the tradition that his discovery about the circle belongs to, a tradition whose most prominent member is Archimedes, and how he breaks with that tradition. Next we shall broaden our scope to look at some of Leibniz’s later papers, where he presents more discoveries and lays out the method behind them. Here it becomes clear that Leibniz defines his new contribution to the art of discovery above all in opposition to Descartes. In particular, he introduces new objects into geometry that Descartes could not deal with, and a new way of representing these objects. Finally, we will return to the problem we started with and sketch how Leibniz’s new understanding of geometry leads him to discover the proportion between a circle and its circumscribed square. 2 �1 1.1 The tradition of the curved and the straight Archimedes Let us return to the opening sentence of Leibniz’s paper. There he writes that the problems of finding the proportions between curvilinear and recitlinear figures are “beautifully useful, especially for reducing mechanics to terms of pure geometry.” He continues, “Those who have looked more deeply into such things know this; few have done so, but they are among the most outstanding mathematicians.” The only example Leibniz gives of a “most outstanding mathematician” is Archimedes. Leibniz gives an example of a problem solved by Archimedes. Archimedes found the proportions between a cone, a sphere, and a cylinder constructed on the same circle. Here is a diagram. As Leibniz points out, Archimedes showed that given a circle AB, a sphere with the same diameter DC, touching the circle AB at the center C of AB, a cone ADB whose base is AB and whose vertex is D, and a cylinder ABF E whose base is AB and whose top EF touches the sphere DC at C, then the cone ADB is to the sphere DC as 1 is to 2, and the sphere DC is to the cylinder ABF E as 2 is to 3. Archimedes’ problem is an example of the kind of beautifully useful problem that Leibniz himself intends to solve. Why are these problems beautifully useful for Leibniz? It is easier to begin to see its beauty than its use. The beauty of the problem is first of all visible in the diagram itself. It is a simple diagram: only a few straight and curved lines traced on a sheet of paper. It is balanced perfectly between left and right. Again, as we go up and down the diagram there are repeated elements: the curved lines that are the circumferences of the circle at the top and bottom of the cylinder, along with the equator of the sphere. The straight vertical sides of the cylinder also add to our impression of vertical symmetry. Yet the vertical symmetry is not perfect. It is sharply broken by the straight diagonal sides of the cone, culminating in a point. The surface simplicity of the diagram is broken in other ways as well. Our imagination leads us beyond the simple plane surface of the drawing to a solid depth, and the sphere, cylinder, and cone then come to life and separate from each other. When we thus start to see the complexity behind the simplicity in the diagram, we begin to perceive its beauty. It is not merely simple, but rather gradually alludes to the complexity it is drawn out of. Our attention is drawn to the diagram because of its striking emptiness and stays with the diagram because its finitude offers little to distract us and its symmetry gives our attention a way to move without leaving the diagram, circling over its surface; yet as our attention is held fascinated by this surface it gradually opens up, leading us to into depths that were not at first seen. The theorem is, of course, more than simply a diagram. Archimedes proves that the cone is to the sphere is to the cylinder as 1 is to 2 is to 3. When we consider the statement of this theorem our attention is drawn away from the diagram to the simple numerical ratios of 1 to 2 to 3. The simplicity here is of a different kind. These numbers are not visible, and do not call on the 3 �imagination. While the cone, sphere, and cylinder are among the simplest things in geometry, 1, 2, and 3 are the simplest things in arithmetic. In contrast to the cone, sphere, and cylinder, these numbers are strikingly empty, and when we turn our attention to them there is little to hold it in place. The only movement we are led to follow is a movement onward: we go from 1 to 2 to 3 to 4, and continue to infinity. There is no natural circling of our attention back to where it began at 1. The simplicity of 1, 2, and 3 togther is thus not a beautiful simplicity. When Archimedes then identifies the simple geometric relations between the cone, sphere, and the cylinder together with the simple arithmetic relations between 1, 2, and 3, we are astonished. We would not expect these two very different kinds of relations to be identical. There is nothing about a sphere and a cylinder as they present themselves to our imagination that would suggest that they are to each other as the number 2 is to the number 3. But Archimedes can prove this. Step by step, in a long argument, he takes us to a point where we must admit the identity. This surprising identity, and its demonstration, are beautiful. They are beautiful not only because of the beauty of the diagram, but because as we follow the proof we move our attention back and forth between arithmetic and geometric simplicity, and unexpected depth gradually emerges. As the geometric diagram has a kind of beauty of its own, independent of any connection with arithmetic, what happens is primarily a beautification of arithmetic. By being linked to an elegant geometric configuration, the numbers 1, 2, and 3, which by themselves appear rather empty and uninteresting, acquire an unexpected depth. We can now see the relation between 2 and 3 in the relation between a sphere and a cylinder, and 2 and 3 thus become worth dwelling on and wondering at in a way they were not before. Following Leibniz’s lead, we have been looking how Archimedes discovery of the ratios between a cone, sphere, and cylinder is beautiful. Now to see this beauty well we would have to look not only at the enunciation of Archimedes’ theorem, but at its demonstration. Leibniz does not do this, and we do not have time to do it tonight. But I hope we have seen enough to glimpse something of the way Archimedes’ theorem spreads something of geometric beauty over arithmetic. Now Leibniz does not merely say that problems of finding proportions between curvilinear and recitlinear figures is beautiful, but that these problems are beautifully useful. But it is hard to see what is useful about Archimedes’ theorem. Once we know what the ratios between a cone, a sphere, and a cylinder are, there is nothing obvious we can go and do with this knowledge. Leibniz suggests that such problems are useful for “reducing mechanics to terms of pure geometry,” that is, for reducing the study of machines to terms of pure geometry. But this theorem hardly appears to lend itself to designing machines. We might turn to Archimedes other works in hope of finding some clue to the usefulness of the theorem Leibniz gives and others like it. But here again, we would be disappointed. It is true that some of the techniques Archimedes uses to find the ratio between a sphere and a cylinder do appear elsewhere in his mathematical works, and perhaps he even uses this ratio as a step in another 4 �argument. But there is, I believe, little in his mathematical works to indicate that he finds these kinds of problems useful. But Leibniz may not only be thinking of the extant writing of Archimedes. We know something of Archimedes not only through his writings, but also through the writings of historians. Here we are told that Archimedes was in fact a wonderful engineer. His mechanical ability plays a central role in one of the most striking episodes of the story of the rise of the Roman Empire. Archimedes built machines that were able to drive a powerful Roman army from his native city of Syracuse. The best telling of the story is in Plutarch’s life of Marcellus. It is worth spending a few minutes here to try to bring Plutarch’s telling of the story to life before us, so that we may see better how Leibniz’s invocation of Archimedes’ name may shed light on the tradition he is taking up in squaring the circle. Archimedes appears in Plutarch’s life of the Roman general Marcellus. Marcellus was involved in three great wars, stretching from his youth to his old age. The bulk of Plutarch’s life is concerned with the last of these three wars, a war between Rome and Carthage. These two great cities fought each other to decide who would be the dominant power in the known world. Rome, of course, eventually won, destroying Carthage completely about sixty years after Marcellus’ death. But during Marcellus’ lifetime the question was very much in doubt. Carthaginian armies were moving through Italy, threatening the city of Rome itself, and battles were also fought in Spain, Africa, and Greece. Not long after this war with Carthage had broken out, Marcellus was in charge of a Roman army in Sicily trying to defend Roman interests. Rome had come to rule Sicily in a war during Marcellus’ youth, but the new war with Carthage had emboldened some Sicilian cities to try to break free of Rome. Syracuse, the largest and wealthiest city in Sicily, was one of these cities. Just before Marcellus had arrived, a Syracusan general, Hippocrates, had “gratified the Carthaginians and acquired tyranny for himself by killing many Romans.” When the Roman army came to Syracuse Hippocrates, by spreading lies about Roman cruelty among the Syracusans, encouraged them to refuse to listen to Marcellus’ ambassadors. Marcellus than attacked by both land and sea. Marcellus was confident of his success, relying on the size and splendour of his preparation and on his own reputation. But to Archimedes and the machines of Archimedes all this was of no account. This man did not set out to make these as if they were worth being serious about; most of them were born as byproducts of geometry at play, after Hiero the king had become ambitious and had persuaded Archimedes to turn something of his art from mental things to bodily things, and by mixing its reason somehow or other through sense perception with use, to make this reason more manifest to the many. When the Roman army and fleet attack, Archimedes’ machines shot arrows, cast heavy rocks at them, inflicting heavy damage. When the Roman ships came up to the wall, the Syracusans used machines devised by Archimedes to 5 �grab hold of the ships with iron claws, lift them out of the water, and drop them again. The Romans quickly retreated in fear, giving up a direct assault, and settling into a siege that would last almost three years. Through Archimedes’ ingenuity alone the Syracusans had driven off Marcellus and the Roman army and fleet. Marcellus compares Archimedes to Briareus, a mythical hundred handed monster. According to Plutarch,“in reality, all the other Syracusans were a body for the preparations of Archimedes, while the soul moving and turning everything was one.” In driving off the Romans and preserving Syracusan freedom Archimedes has momentarily become a perfect tyrant over Syracuse. According to Plutarch’s description, it seems that Archimedes is not simply the ruling soul in Syracuse, but the only soul. Marcellus is right to find this situation both mythical and monstrous. Thus the geometry of Archimedes is wonderfully useful. It generates as a byproduct an amazing array of machines that are capable of repelling a mighty army. Even so, according to Plutarch, Archimedes held the art of making machines, mechanics, an art by which he had acquired a godlike reputation, in contempt: Archimedes possessed so great a spirit and depth of soul and such a great wealth of theorems that he chose to leave behind no writings about the things by which he had acquired the name and reputation of having the understanding of a god rather than of a man; instead, considering the business of mechanics and, in general, any art that grasps at what is useful, to be ignoble and base, he directed his love of honor to those things which have beauty and superfluity unmixed with necessity, things incomparable with everything else, and which furnish demonstration with a rivalry against matter, the latter bringing size and beauty, the former precision and enormous power; for it is not possible in geometry to grasp more difficult and weightier hypotheses in simpler and purer terms. Now remember that Leibniz, when speaking of the kind of problems Archimedes solved, calls them beatifully useful. They are both beautiful and useful. Earlier I tried to point to some of the ways Archimedes finding of the ratio between a sphere and a cylinder may be beautiful. We later turned to Plutarch’s life of Marcellus trying to find how Archimedes’ art might be useful. There we indeed see that Archimedes’ succeeds in turning pure geometry to mechanics, making his wonderful machines. But Leibniz not only attributes both beauty and use to Archimedes’ art, but says that the uses themselves are beautiful. In contrast, in Plutarch’s account, the mechanical uses of Archimedes’ geometry are contemptible in comparison with the pure beauty of geometry indifferent to use, to which alone he devoted his writings. Here then we begin to see a way in which Leibniz has broken from the tradition he sets before us. Leibniz suggests there is a harmony between beauty and use, while Archimedes (at least Plutarch’s Archimedes) turns away from use towards a pure beauty belonging to matter in a rivalry with demonstration. 6 �Before we finish with Archimedes, I should give the rest of Plutarch’s story. After being repelled by Archimedes’ machines, the Romans retreated, but they did not give up. They settled into a long siege, and after a few years found a way to take the city by strategem, without a frontal assault. When Marcellus had Syracuse in his power, he set his soldiers loose to plunder it. As the Roman army ran through the streets taking everything they could get their hands on, Archimedes was looking over a diagram, examining something by himself, and failed to notice that the city had been taken. A Roman soldier came up to Archimedes and ordered him to come with him. Archimedes did not want to go before he had finished his problem and established its demonstration. The Roman soldier became angry, drew his sword, and killed him. 1.2 Leibniz’s innovation Let us return now to Leibniz’s paper on the ratio of a circle to its circumscribed square. There, as we saw earlier, Archimedes appears as part of the geometric tradition of finding proportions between curved and straight things. After mentioning Archimedes and his theorem, Leibniz goes on to give a series of more modern proportions, found by nameless mathematicians, for other figures, and then turns to the unsolved problem of finding the ratio between a circle and a square. According to Leibniz, no one has yet been able to “bring the circle under laws such laws.” Others have found approximations, including first of all Archimedes, who showed that the ratio of a circle to a circumscribed square is greater than 21 to 28 and less than 22 to 28. But approximations are not what Leibniz is looking for; he is looking for an accurate expression. Now according to Leibniz, “many have not fully understood what they are looking for” when trying to find the quadrature of the circle, that is, the ratio between a circle and a circumscribed square. To clarify the what would count as a solution to the problem, Leibniz gives a classification of kinds of quadrature. A quadrature can either be done by calculation or by construction, and in either case it may be either accurate or not. There are therefore four different kinds of quadratures: accurate calculations, approximate calculations, accurate constructions, and nearly accurate constructions. No one has yet given an accurate calculation or construction for the quadrature of the circle, while Archimedes gave an approximate calculation, and others have given nearly accurate constructions. Leibniz claims his own quadrature is an accurate calculation. The simplest kind of accurate calculation would show that the ratio between the circle and the square is the same as the ratio between two whole numbers, just as Archimedes shows that the ratio between a sphere and a cylinder is the same as the ratio of 2 to 3. Leibniz calculation is not that simple. As we saw earlier, he shows that if the area of the square is 1, then the area of the circle will be 1 1 1 1 1 − + − + etc. 1 3 5 7 9 Leibniz goes on to explain that this means that in relation to the correct value for the area of the circle, 7 �1 1 1 1 1 1 1 will be − − − 1 3 1 3 1 3 + + 1 5 1 5 − 1 7 greater, yet with an error less than ...... less, .......................... ...... greater, .......................... ...... less, .......................... etc. 1 3 1 5 1 7 1 9 etc. Therefore the whole series contains all the approximations or values greater than or less than the correct one: for if it is continued far enough the error will be less than a given fraction, and thus also less than any given quantity. The whole series therefore expresses the exact value. And although we cannot express the sum of this series by one number, and the series may be produced indefinitely, nevertheless, because this series keeps to a single law of progression, we sufficiently perceive the whole with our minds. Here Leibniz has done something very bold. In looking at the table he gives, one might think he is only giving us more approximations. He gives us a series of expressions that each give an approximate value for the area of the circle. Each expression comes closer and closer than the last to being accurate, but none of them ever is accurate. And each expression is more complex than the last, so that we have to use long and complicated expressions to get a very accurate value for the area of the circle. If, for example, we wanted to find the area of 1 the circle with an error less than 100 , we would have to take the sum 1 1 1 1 1 − + − + ... − . 1 3 5 7 99 If we added and subtracted all 50 terms in this sum, we would get something equal to the correct value, plus or minus .01; we would therefore have a pretty accurate approximation of the correct value, up to two decimal places. If we wanted an approximation up to three decimal places, we could use a sum with 500 terms. Leibniz, however, sees more here than some rather laborious new ways to calculate an approximate value of the area of the circle. He sees a completely accurate calculation that gives the exact value of the area of the circle. This is the bold new leap Leibniz makes. To make it, he must see the series as giving a single value, rather than infinitely many values. This value cannot be contained in any individual sum of a finite number of terms; rather, it is contained in the “law of progression” that guides the whole series. This law tells us how to move from one sum to the next; it tells us, for example, how to move from the second sum, 1 1 − , 1 3 to the third, 1 1 1 − + , 1 3 5 8 �and then how to move from this sum to the fourth, 1 1 1 1 − + − . 1 3 5 7 The law of progession is the same at every step; no matter how far we go in the series, the way to move from one sum in the series to the next is the same. If anyone gives us a sum that occurs in the series, we can easily find the next sum by following the law. For Leibniz, we can therefore sufficiently perceive the whole series of sums, and it is thus just as good as a single number. Because the series gives us arbitrarily close approximations to the area of the circle, its value must be identical to the value of the area of the circle. Leibniz has thus given us a different kind of solution than we might have expected. When we first posed the problem, we were looking for a number that gives the area of the circle. But Leibniz tells us we did not understand the what we were really looking for: we were in fact looking for a law. Leibniz thus replaces numbers with laws. The primary mathematical object is a law. Now any law, in mathematics or otherwise, is universally obligatory. Everyone should obey the law. To obey the law, everyone must first understand what the law is. A law should therefore be something that is publicly declared and can be grasped by everyone . Accordingly, Leibniz introduces the law of progression of his series as a means by which we perceive the whole series. The law of progression is manifest to everyone. It becomes manifest here because Leibniz has presented it here in a table that makes us grasp it at a glance. By laying out the series of sums in a table, with neatly aligned rows and columns, we see just how we should move from one sum to the next, and how each new sum relates to the circle. The law of progression is captured in the visible relation between one row and the next. We thus grasp as well as we need to what is contained in the two “etc.”s at the bottom of the table, which contain the infinitely many unwritten sums and errors. Expressing the series of approximations in terms of words alone would not have been as effective as Leibniz’s table in making clear what the law behind the series is. In fact, any complicated mathematical truth is hard to grasp when expressed in words alone. We see this all the time in reading ancient mathematics. Even in the relatively simple propositions in Euclid, it is sometimes hard to understand what a proposition is about by reading the enunciation alone. Only after we see it set out in terms of a diagram does it become clear. The difficulty in understanding the bare enunciations becomes even greater in the more complicated works of Apollonius and Archimedes. Yet in all these authors there is a stubborn insistence on formulating everything in plain Greek, no matter how odd or unreadable the resulting sentences become. They do not resort to symbolic shorthands to try to make it easier for us to grasp the patterns behind what they are saying. In the resulting tension between the diagrams and the text in Greek mathematics we perhaps see the rivalry between matter and demonstration that Plutarch speaks of. The diagram is a kind of matter, lending beauty and size to the proposition, while the text is where the demonstration is found, providing power and precision. Each keeps jealously 9 �to its own domain, the diagram not trying to become a symbolic text, and the text not trying to become a picture. Leibniz collpses this tension. Text and diagram coalesce in a table expressing an underlying law. The strife of ancient mathematics disappears behind a new harmony. When Plutarch first introduces Archimedes, he writes that his machines are the result of King Hiero persuading him to turn something of his art from mental things to bodily things, and by mixing its reason somehow or other through sense perception with use, to make this reason more manifest to the many. When making his machines, Archimedes himself thus blurs the line between reason and sense perception in trying to make his geometry useful. He blurs this line in the interest of making his geometry manifest to the many, an interest that Leibniz shares. But as we saw earlier, Archimedes appears to hold the usefulness of his geometry in contempt. It is nothing compared to the beauty of the geometry on its own. For Leibniz, I believe, the beauty of geometry is not separable from its usefulness because he sees finding laws as its object. The theorems of a Leibnizian geometer reveal laws, and these laws are by their nature manifest to the many. These laws are naturally useful because they let us easily grasp powerful universal truths. It is only a bad geometer who fails to make himself perfectly clear, and only an idle pretence to suppose that there is some independent realm of pure theorems high above the understanding of the many. 2 Leibniz against Descartes In considering how Leibniz’s paper in February of 1682 is new, we have so far concentrated on how Leibniz’s solution moves beyond the work of Archimedes, the first geometer he names as belonging to the tradition of finding proportions between curvilinear and rectilinear figures. But this tradition has many later members, and Leibniz refers to their work as well. To be truly new, Leibniz’s solution has to go beyond not only Archimedes, but all previous modern mathematicians as well. Now in many places in his mathematical writings Leibniz gives the names of his important predecessors and describes their work, and it would be impossible here to give a complete picture of his understanding of the tradition leading up to him. But there is one mathematician with whom he contrasts himself more than any other: René Descartes. Descartes not only made important contributions to geometry that Leibniz depends upon, but also made some harmful errors that Leibniz tries to correct. In many of his published mathematical writings there are passages that point to these errors of Descartes. In this part of the lecture we will try to sketch how Leibniz saw himself as correcting the errors of Descartes. 10 �2.1 Descartes’ error Leibniz criticizes Descartes in a paper titled “On Finding the Dimensions of Figures” published in May of 1684, two years after his paper on the area of the circle. This paper sets forth a general method Leibniz uses to find the areas of figures. After briefly describing the method and some of the things it can do, he writes: I have many things of this kind by which Geometry is advanced immeasurably far beyond the boundaries set down by Viète and Descartes. For the ancients did not wish to use lines of higher degrees, and [they called] the solutions that were found by using them Mechanical. Descartes blames them for this and receives into Geometry all curves whose nature may be expressed by some Algebraic equation, that is, by an equation of a definite degree. He is right to do this; but there are infinitely many other curves that nevertheless can still be accurately described, and Descartes erred no less than the ancients when he excluded them from Geometry and called them Mechanical, evidently because he was unable to reduce them to equations and treat them by his rules. This is a criticism that Leibniz returns to again and a again in his mathematical papers. According to Leibniz, Descartes expanded the proper objects of geometry, including in it lines that the ancients rejected as mechanical. But Descartes himself does not go far enough. He introduces a new criterion for judging if a line is geometric, and his criterion is too narrow: he ends up rejecting some lines that are just as geometric as the ones he accepts. Leibniz tries to correct this error and include all lines that belong to geometry. As Mr. Burke puts it, there is an analogy: as Descartes is to the ancients, Leibniz is to Descartes. To understand better Leibniz’s criticism of Descartes, we will turn briefly to the text where Descartes makes the statements Leibniz is criticizing, the Geometry, which was published in 1637, about forty-five years before Leibniz’s first mathematical papers. There Descartes gives a way to simplify “all the problems of geometry,” by freely introducing “arithmetic terms into geometry, in order to make [himself] more intelligible.” He uses, for example, the term “multiplication” to describe finding a fourth proportional: if the line AB is a unit, and we have to “multiply” BD by BC, then Descartes simply constructs a fourth proportional BE for AB, BD, and BC, so that AB : BD :: BC : BE. BE is called the “product” of BD and BC. Descartes’ new arithmetic language enables him first to reduce all statements about geometry to statements about straight lines, but he quickly notes that “often one does not need to trace these lines on paper, and it suffices to designate them each by a single letter.” By designating geometric lines by letters and interpreting geometric relations in terms of arithmetic, he can use algebra to express geometric statements. For those of you who have not read the Geometry, I would say that the result is something like what you see in high school algebra, where geometric curves are expressed by equations using systems of coordinates. 11 �Descartes claims that his new method was unknown to the ancients, who seem to have been held back by their scruples about using arithmetic terms in geometry because they did not see with sufficient clarity the relation between these two subjects. To prove that his method is capable of going beyond the ancients, Descartes solves a problem that the ancients could not solve, the socalled locus problem of Pappus. We do not have time to go into much detail here, but in very general terms, this problem involves finding curves that satisfy certain conditions. We are given some properties of an unknown curve, and we have to find the curve that has these properties. The form of the problem is thus the same as that of countless other ancient geometric problems: for example, the problem of finding a square equal to a given polygon, or the problem of finding a mean proportional between two given lines. What is unusual about Pappus’ problem is that we do not know in advance what kind of curve line we are looking for. When we try to solve the problem, we may therefore want to understand what kind of curves line there are; that is, we may want to classify curved lines in general. But ancient geometry never deals with curved lines in general. It only gives us a handful of examples, such as the circle and the conic sections. Pappus gives us a case where these well known curves are solutions to his problem, but he does not have a way to describe the curved lines that solve his problem in more general cases. According to Descartes, even in the simple case where the solution is a conic section “he does not at all try to determine or describe this curved line, any more than he tries to explain the curves” that satisfy the problem in more complicated cases. Descartes claims he can do all this, determining and describing the solution in the simple case where Pappus only asserts what the solution is, and explaining the solution in more complicated cases. Now the key to Descartes’ general solution of the problem is a new understanding of what it means to find a curve. The ancients did not understand the nature of curved lines, and therefore excluded lines that properly belonged to geometry. Among the lines they excluded are precisely those that solve Pappus’ problem. By broadening what counts as a solution to the problem, Descartes is able to solve it. His solution is thus a model for the type of solution which Leibniz gives for the quadrature of the circle, where he broadens the definition of number to find an accurate value of the area of the circle. According to Descartes one should no more exclude the complex curves than the simpler curves, provided that one may imagine them to be described by a continuous movement, or by many successive movements each of which is entirely regulated by those which precede it. Descartes is thus able to include within geometry lines described in our imagination by all sorts of complicated machines, lines that the ancients would have rejected as mechanical. A little later Descartes gives a somewhat different formulation of which curves may be called geometric, identifying them with those curves whose points necessarily have a some relation to all the 12 �points of a straight line, a relation which may be expressed by some equation. In what follows, Descartes makes it clear that he is thinking of an algebraic equation, that is, an equation formed by adding, subtracting, multiplying and dividing known and unknown quantities; for example, y = x2 or x3 −2xy+1 = y 2 are both equations of geometric curves for Descartes. The equation of a curve determines what kind of kind of curve it is, and Descartes gives his solution to Pappus’ problem by using equations. It is this latter formulation of what counts as a geometric curve that Leibniz objects to. Leibniz sees no reason to limit ourselves to algebraic equations, since equations can express relations other than those that come from adding, subtracting, multiplying, and dividing known and unknown quantities. In addition to algebraic equations, Leibniz introduces new equations which he calls transcendent. These new equations are expressed in a new symbolism, which he calls a calculus. The curves corresponding to these equations are transcendent curves. They are the curves that Descartes mistakenly casts out of geometry. While Descartes was right to include all algebraic curves, and not just the few simple ones the ancients used, the circle and the conic sections, he was wrong to exclude transcendent curves. Just as by introducing algebraic curves Descartes can solve a problem the ancients could not, so also by introducing transcendent curves Leibniz can solve problems Descartes could not. 2.2 Leibniz’s new curves Leibniz at first only mentions the new calculus used for describing the new transcendent curves, without giving examples. It is only a few months later, in a paper titled “A New Method for Maxima and Minima, as well as for Tangents,” that he shows us the new calculus. By a “calculus” Leibniz seems to mean a symbolic system, that is, a collection of symbols and rules for manipulating them. Ordinary algebra is thus a kind of calculus for Leibniz. His new calculus is based on the old algebraic calculus, but it includes one new symbol, the letter d. Leibniz first introduces d using the diagram on your handout. We are given a straight line AX, called the axis, a curved line passing through V , a perpendicular V X from the curved line to the axis, called an ordinate and a tangent V B to the curved line. Leibniz takes an arbitrary straight line and calls it dx, and then defines dv to be the line such that dv : dx :: V X : BX. He calls dv the “difference of the vs.” Leibniz goes on to give the rules for manipulating this new symbol. For example, he writes that if y = xv, then dy = x dv + v dx. He does not demonstrate these rules when he first introduces them in the “New Method.” Instead, he gives some examples. As the full title of the paper suggests, the examples are concerned with finding maximum and minimum values of quantities, and with finding tangents to curves. 13 �Leibniz’s presentation of the new calculus is at first perplexing. He throws us into the middle of it without explaining why a new calculus is needed, what it is supposed to represent, or why it works the way it does. Instead, he gives us at least three ways to think about the new symbol d: 1. in terms of the proportion dv : dx :: V X : BX; 2. as something that represents “differences,” so that dv is the “difference of the vs;” 3. as a letter that is manipulated according to certain rules when combined with algebraic expressions. Of these three ways of thinking of d, I believe the second, in terms of differences, is the most fundamental. It can explain both the proportion Leibniz starts with, and the rules the new symbol must obey. Moreover, thinking of the new calculus in terms of differences most directly helps us understand why the new calculus helps us solve new geometric problems that Descartes’ algebraic calculus cannot. A few years earlier, in a letter to a friend, Leibniz writes of what he calls the “method of differences.” This method is based on the same method introduced in the “New Method”, but in the earlier letter Leibniz uses “differential figures.” According to Leibniz, a differential figure is one whose ”series of ordinates coincides with the series of differences from another series.” 1 The notion of a series of differences contains, I believe, the fundamental insight behind the new calculus. Consider again the figure in your handout. We could have taken any point V on the curved line and drawn an ordinate V X to get new values for both V X and AX, that is, for both v and x. There are therefore infinitely many possible ordinates for the curve through V . So far we have done nothing that the ancients did not do, as those of you who have read Apollonius know. But what Leibniz does that the ancients do not is consider these ordinates as a series; that is, he supposes that there is an ordered progression of ordinates, where every ordinate has an ordinate that immediately follows it. For Leibniz, after the ordinate V X there is a next ordinate V1 X1 . And immediately after V1 X1 there is another ordinate, and so on. These ordinates form an infinite series. It is in terms of this series that we can most easily see what Leibniz means by d: dv is the difference V1 X1 − V X between consecutive ordinates. Now Leibniz’s supposition is obviously absurd. There can be no next ordinate, because continuous magnitudes are infinitely divisible. Between any two points V and V1 there is always another point from which we can draw an ordinate, and therefore V1 X1 can never be the next ordinate. Leibniz is well aware of the absurdity, but it does not stop him. He is willing to embrace a way of thinking about geometry that he knows is false, in order to develop his new method. And this absurdity, this geometrical falsehood, is not something accidental to Leibniz’s new method. Leibniz indicates the centrality of thinking of differences of ordinates by the notation itself: dv is a shorthand for “the difference of the ordinates. As he develops his new calculus and its applications, 1 Letter to Tschirnhaus, p. 40 14 �both in the “New Method” and elsewhere, we see him again and again return to thinking in terms of series of ordinates and their differences. This thought is the engine that drives him to new discoveries, and we should try to follow Leibniz in embracing this way of thinking. We should resist the temptation to treat it straightaway as an error that needs to be corrected. But how can we embrace what looks like an elementary mistake? The idea of accepting false hypotheses in order to get at truth is not unknown in geometry. Every time we do a reductio proof we begin by setting down a false hypothesis. We then go through the proof, using this false hypothesis to derive in an orderly way other false statements until we come to something that is manifestly absurd. We then throw away the false hypothesis and embrace the contrary, true hypothesis once and for all. In Leibniz’s method, we also use the false hypothesis to derive in an orderly way other statements and finally end up with a true statement. But in Leibniz’s method, we do not throw away the false hypothesis when we are done. Leibniz’s method is not a reductio method, but in both methods we use false hypotheses in a carefully regulated way to come to true conclusions. The use of these hypotheses is bound by rules: they are not like Euclid’s definitions and common notions, or like the conclusions of demonstrated theorems, which we can freely introduce in whatever context we want. Rather, there are certain limited contexts in which reductio hypotheses or Leibniz’s hypothesis about the series of ordinates can be used. In both cases there are as it were laws to guide the way we incorporate false hypotheses in our arguments. Leibniz new geometry thus depends on new laws for the logic of geometry. To see more clearly what the laws are that guide Leibniz’s hypothesis about the series of ordinates, let us turn to a paper published a few months after the “New Method.” There Leibniz gives what he calls the “general principle” from which his method may may be deduced: that a curvilinear figure should be considered as equivalent to a polygon with infinitely many sides; it follows that whatever can be demonstrated about such a Polygon — whether in such a way that we pay no attention to the number of sides, or in such a way that it is more and more verified the greater number of sides we take, so that the error finally becomes less than any given number — can be declared to be true about the curve.2 To return to our diagram, if we draw a straight line between V and V1 , the points where consecutive ordinates meet the curve, and we do the same for every ordinate in the series, then we will get a polygon meeting the curve at the points V , V1 , etc. According to Leibniz, this polygon is equivalent to the curve through V . Now this polygon is not simply a single, fixed, polygon; it is a variable polygon that can have more and more sides. We can always take a greater number of sides. And when we prove something that is true about this variable polygon that becomes more and more true the more sides we take, 2 p. 62 15 �until it finally fails to be true by less than any given number, then we can say that it is true about the curve. This is the basic law that guides Leibniz’s use of the hypothesis that the curve is equivalent to a polygon. Here is a simple example. Suppose we are given a circle. According to Leibniz, we can assume this circle is a polygon with infinitely many sides. We can use this assumption to prove that the area of the circle is half the product of its perimeter and its radius. For if we take one of the triangles ACB making up the polygon, and drop a perpendicular DC from AB to the center C, then the area of the triangle is equal to half the product of AB and DC. If we sum up all the triangles in the polygon, we will see that the total area of the polygon is half the product of its perimeter and DC. This is true no matter how many sides the polygon has. Moreover, the more sides the polygon has, the closer DC comes to being equal to the radius AC. Therefore it becomes “more and more true” that the area of the polygon is equal to half the product of its perimeter and the radius of the circle. According to Leibniz’s principle, then, it follows that the area of the circle is half the product of its perimeter and its radius. There is a striking similarity between Leibniz’s treatment of a curve as equivalent to an infinitely sided polygon and his earlier treatment of an infinite series of numbers as equivalent to a number. Recall that as we take more and more terms in the infinite series 1 1 1 1 − + − + etc., 1 3 5 7 it comes closer and closer to the area of the circle. One could say that the equality between this series and the area of the circle becomes “more and more verified the greater number of terms we take, so that the error finally becomes less than any given number.” Leibniz argues that this series therefore expresses a single value that is equal to the area of the circle. Likewise, the infinite series of polygons that can be inscribed in a circle come closer and closer to the circle, and statements we make about these polygons that are “more and more verified the greater number of sides we take, so that the error finally becomes less than any given number” are in fact true about the circle. Leibniz therefore concludes that the circle is equivalent to a polygon with infinitely many sides. In the former case, Leibniz argued that we perceive the whole infinite series as one number because it keep to a single “law of progression.” The same argument would seem to apply in the case of the infinite polygon: we sufficiently perceive the whole infinite series of polygons as one figure because there is a law of progression that takes us from one polygon to the next. This law of progression is equivalent to the circle for Leibniz. Just as he earlier treated a law of progression as equivalent to a number, so here he treats a law of progression as equivalent to a geometric figure. We turned to Leibniz’s general principle to clarify the assumptions behind his introduction of the new calculus. The symbol d is supposed to mean differences of, when we make the assumption that there is an infinite series of ordinates. This assumption is obviously false. Yet it can be used to guide us to new truths when we use it legally. The laws that guide the use of the assumption depend on 16 �a general principle that curvilinear areas are equivalent to infinite polygons. An infinite polygon is in fact an infinite series of polygons, but it can be treated as a single polygon because this series obeys a single law. This law in effect becomes a mathematical object. There thus appear to be two kinds of new laws: the laws that guide the arguments using the new hypotheses, and the laws that become new geometric objects. But these laws are deeply entangled, and may in the end amount to only one law. The progression from one polygon to the next in the infinite series of polygons may be thought of as a series of steps in an argument. Or the special kind of argument that uses the new assumption may be absorbed within the object under consideration, so that Leibniz’s assumption is no longer false in the new geometry: if by speaking of the “series of ordinates” Leibniz simply means the law of progression for all finite series of ordinates, then there is no need to restrict the assumption to special arguments. It would be as true as any of Euclid’s postulates. Leibniz, fortunately, does dwell on these deep and difficult questions. Instead he simply introduces his new notation, tells us what the rules are, and moves on to solving problems. Consider again the diagram from the “New Method.” If we apply Leibniz’s general principle to the curve there, we can assume that there is a series of ordinates, so that V X and V1 X1 are consecutive ordinates, but only in the context of a certain kind of argument. We may treat the ordinates as if they form a finite series in order to prove statements about them that “are verified more and more” the more ordinates we take. Here is an example of the kind of argument we can make. Let V X and V1 X1 be consecutive ordinates of the curve through V . Then as we take more and more finely grained series of ordinates, the points V and V1 become closer and closer together, and the line through V and V1 becomes closer and closer to a tangent V B to the original curve. Therefore, according to Leibniz’s principle, the line through V and V1 is tangent to the curve. Leibniz gives his “general principle” in classical geometric terms, without any new symbols, and we have given our examples geometrically. But he is in fact following Descartes in trying to express the nature of curved lines with symbols. His new symbol d is precisely what is required to express as a curve symbolically as an infinite polygon. If we drop a perpendicular V T from V to V1 X1 , then V1 T will equal dv and V T will equal dx. If we are given dv and dx, we are given the infinitely small triangle V V1 T , and therefore the side V V1 of the polygon. Leibniz calls this triangle the characteristic triangle; it expresses the nature of the curve as an infinite polygon. To find dv and dx is to find the curve as an infinite polygon. As we saw earlier, Leibniz gives rules for finding dv in terms of dx, given the relationship between v and x. In other words, he gives rules for finding the curve as an infinite polygon, given the relationship between its ordinates and abscissas. Leibniz’s new calculus is a powerful new tool for solving geometric problems. Anything that can be expressed in terms of an infinite polygon can be expressed in terms of it. Since, as we saw earlier, both tangents and areas can be expressed in terms of an infinite polygon, they can also be expressed in terms of the calculus. Leibniz’s calculus can be used to square the circle, and Leibniz 17 �and those who came after him used his calculus to solve many new problems involving tangents and areas. The new calculus helps us solve these problems because it gives us a way of much more concisely expressing just the relevant relations for these kind of problems. More importantly, it gives us a way to express curves that we never would have been able to express before. Just as algebra let us write down equations for curves that we would never have had simple geometric expressions for, so Leibniz’s new calculus lets us write down equation for curves that would never have had simple algebraic expressions. These are the transcendent curves that he faults Descartes for excluding. They are the curves that can only be thought of as infinite polygons. 3 Conclusion Leibniz’s geometry is new because he has a new understanding of law in geometry. In contrast to Archimedes and the other ancients, Leibniz sees geometry as aiming at what is useful, and accordingly tries to find the most clear and concise way to express its underlying laws. With Descartes Leibniz shares the view that geometry aims at the useful and that one should try to introduce new symbols to make the underlying reasons as clear as possible. But in contrast with Descartes, Leibniz explicitly makes laws an object of geometry, and therefore is able to see a broader range of laws that might be clearly expressed by new symbols. Because Descartes was too attached to the symbols of algebra, he set up too narrow boundaries for what counts as a geometric curve. Descartes has no way to express the laws that curves give to the infinite polygons inscribed in them, and therefore rejects the transcendent curves that can only be expressed by these laws. In paper published in 1686, Leibniz offers some harsh criticism of Descartes and his followers. After giving a brief demonstration of an error Descartes made, Leibniz writes the following. Since nothing is simpler than our proof it is surprising that it did not occur to Descartes or the Cartesians, who are most learned men. But too much trust in genius led them astray: the former trusted his own genius, the latter another’s. For Descartes, having the usual vice of great men, finally became a little too confident. And I fear that not a few Cartesians are gradually beginning to imitate the many Peripatetics whom they mock; that is, I fear that they may be getting accustomed to consult the books of their teacher rather than right reason and the nature of things. Descartes’ text has become a dead authority to his followers. It is this dead authority that Leibniz frees himself from with his new geometry. Descartes’ geometry, like his physics, is prone to become rigid and lifeless, losing its connection to the original discoveries it made. The algebraic tools of Descartes’ geometry can come to seem too important on their own, and their function as 18 �expressing something is lost. Leibniz brings life back to geometry by once again letting its laws express themselves. 19 � 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. For more information, and a schedule of upcoming lectures, please visit the <a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a>. Click on <a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&sort_field=Dublin+Core%2CDate&sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a> to view and sort all items in the collection. 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 pdf Page numeration Number of pages in the original item. 19 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 Leibniz's New Geometry Description An account of the resource Typescript of a lecture delivered November 30, 2007, by Annapolis tutor Brendon Lasell as part of the Formal Lecture Series. Creator An entity primarily responsible for making the resource Lasell, Brendon 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 2007-11-30 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 Subject The topic of the resource Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716 Geometry--History Language A language of the resource English Identifier An unambiguous reference to the resource within a given context LEC_Lasell_Brendon_2007-11-30 Relation A related resource <a href="https://digitalarchives.sjc.edu/items/show/7968">Recording</a> Friday night lecture Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/2a14f15c8c401de9c4e7e9dfb41e6874.mp3 519988d94f8d86832489e267240ba0b5 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. For more information, and a schedule of upcoming lectures, please visit the <a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a>. Click on <a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&sort_field=Dublin+Core%2CDate&sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a> to view and sort all items in the collection. 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. Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 00:47:28 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 What Is a Book? Description An account of the resource Audio recording of a lecture delivered on August 30, 1991, by Eva Brann as part of the Formal Lecture Series. Creator An entity primarily responsible for making the resource Brann, Eva T. H. 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 1991-08-30 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 Subject The topic of the resource Books and reading Books Language A language of the resource English Identifier An unambiguous reference to the resource within a given context Tape 377 Deans Friday night lecture Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/919b797fbec913b540c0cbb393fe57a5.mp3 910da86aedefbdc513062b556798fb1d 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. For more information, and a schedule of upcoming lectures, please visit the <a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a>. Click on <a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&sort_field=Dublin+Core%2CDate&sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a> to view and sort all items in the collection. 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. Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 01:03:09 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 Perfections of Jane Austen Description An account of the resource Audio recording of a lecture delivered on January 31, 1975, by Eva Brann as part of the Formal Lecture Series. Creator An entity primarily responsible for making the resource Brann, Eva T. H. 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 1975-01-31 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 Subject The topic of the resource Austen, Jane, 1775-1817 English prose literature Language A language of the resource English Identifier An unambiguous reference to the resource within a given context Tape 262 Deans Friday night lecture Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/2ca40af5b4fbf2171fba64d5e88e7185.mp3 d5d8686a0624d3e4cb12dff3d7aa2031 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. For more information, and a schedule of upcoming lectures, please visit the <a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a>. Click on <a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&sort_field=Dublin+Core%2CDate&sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a> to view and sort all items in the collection. 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. Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 00:57:57 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 Plato's Theory of Ideas Description An account of the resource Audio recording of a lecture delivered on September 14, 1979, by Eva Brann as part of the Formal Lecture Series. The quality of the recording ranges from poor to very poor. Written versions of the lecture are available <a href="https://digitalarchives.sjc.edu/items/show/1239">in the Formal Lecture Series collection</a> and in the <a href="https://digitalarchives.sjc.edu/items/show/5146">St. John's Review (July 1980)</a>. Creator An entity primarily responsible for making the resource Brann, Eva T. H. 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 1979-09-14 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 Subject The topic of the resource Plato Philosophy, Ancient Language A language of the resource English Identifier An unambiguous reference to the resource within a given context Tape 445 Deans Friday night lecture Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/096998978c1ebc399778fba8572840d8.mp4 a1990f58ca45220f3a93dfb481d52fbd 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. For more information, and a schedule of upcoming lectures, please visit the <a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a>. Click on <a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&sort_field=Dublin+Core%2CDate&sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a> to view and sort all items in the collection. 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 Moving Image A series of visual representations imparting an impression of motion when shown in succession. Examples include animations, movies, television programs, videos, zoetropes, or visual output from a simulation. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data mp4 Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 00:00:00 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 The Science & Nature of Dogs: From Umwelt to Pet Description An account of the resource Video Recording of a lecture delivered on February 16, 2024, by Alexandra Horowitz as part of the Formal Lecture Series. Prof. Horowitz is the Senior Research Fellow in the Dog Cognition Lab at Barnard College in New York, and is also an Associate Professor in Psychology and English. Along with being a dog-cognition expert, she is the author of many academic journal articles and several books including, The Year of the Puppy – How Dogs Become Themselves (Viking, 2022) and Inside of a Dog: What Dogs See, Smell, and Know (Scribner’s, 2009). In addition to writing books, she hosts a podcast Off Leash on the Freakonomics Radio Network. This lecture is also part of the Steiner Lecture Series. The Andrew Steiner Memorial Lecture fund was created by the family and friends of Mr. Steiner, an alumnus (class of 1963) of St. John’s College, Annapolis. It was established to attract scholars from different disciplines and worlds, recognizing Andrew’s great intellectual versatility. Creator An entity primarily responsible for making the resource Horowitz, Alexandra 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 2024-02-16 Type The nature or genre of the resource moving image Format The file format, physical medium, or dimensions of the resource mp4 Subject The topic of the resource Dogs Cognition in animals Dogs--Psychology Language A language of the resource English Identifier An unambiguous reference to the resource within a given context LEC_Horowitz_Alexandra_2024-02-16_ac Rights Information about rights held in and over the resource A signed permission form has been received stating, "I hereby grant St. John's College permission to: Make an audio recording of my lecture, and retain copies for circulation and archival preservation in the St. John's College Greenfield Library. Make an audio recording of my lecture available online. Make a typescript copy of my lecture available for circulation and archival preservation in the St. John's College Greenfield Library. Make a copy of my typescript available online." Friday night lecture Steiner lecture https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/d873901677f671f74b082d6120d31dc3.mp3 0b9d2f17515c254ce8bd02453e1e2836 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. For more information, and a schedule of upcoming lectures, please visit the <a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a>. Click on <a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&sort_field=Dublin+Core%2CDate&sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a> to view and sort all items in the collection. 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. Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 01:03:51 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 Declaration of Independence Description An account of the resource Audio recording of a lecture delivered on April 30, 1976, by Eva Brann as part of the Formal Lecture Series. Creator An entity primarily responsible for making the resource Brann, Eva T. H. 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 1976-04-30 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 Subject The topic of the resource United States. Declaration of Independence Language A language of the resource English Identifier An unambiguous reference to the resource within a given context Tape 292 Deans Friday night lecture Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/1a97fb10e2121d3f43ebecbb1b9f880c.mp3 52cee81253de3cf4d78527d9f60c3b0c 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. For more information, and a schedule of upcoming lectures, please visit the <a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a>. Click on <a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&sort_field=Dublin+Core%2CDate&sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a> to view and sort all items in the collection. 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. Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 00:53:46 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 Universalisms Partially Applied: On Locke's and Kant's Racisms Description An account of the resource Audio recording of a lecture delivered on November 14, 2008, by Robert Bernasconi as part of the Formal Lecture Series. Creator An entity primarily responsible for making the resource Bernasconi, Robert 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 2008-11-14 Rights Information about rights held in and over the resource A signed permission form has been received stating, "I hereby grant St. John's College permission to tape the lecture that I shall give in Annapolis; make a recording of my lecture available online." Type The nature or genre of the resource sound Format The file format, physical medium, or dimensions of the resource mp3 Subject The topic of the resource Slave trade Race--Philosophy Race relations--Philosophy Locke, John, 1632-1704 Kant, Immanuel, 1724-1804 Language A language of the resource English Identifier An unambiguous reference to the resource within a given context LEC_Bernasconi_Robert_2008-11-14_ac Friday night lecture https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/32279ecd59b15a40cb0c6687d90564a3.mp3 ec91f70a7296b544e8d90d8976d5ec4f 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. For more information, and a schedule of upcoming lectures, please visit the <a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a>. Click on <a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&sort_field=Dublin+Core%2CDate&sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a> to view and sort all items in the collection. 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. Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 00:55:24 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 Francis Bacon and the Socratic Turn Description An account of the resource Audio recording of a lecture delivered on April 16, 1999, by Adam Schulman as part of the Formal Lecture Series. Creator An entity primarily responsible for making the resource Schulman, Adam 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 1999-04-16 Rights Information about rights held in and over the resource A signed permission form has been received granting St. John's College blanket permission to: "Make recordings of my lectures, speeches, and addresses available online. Make typescript copies of my lectures, speeches, and addresses available online." Type The nature or genre of the resource sound Format The file format, physical medium, or dimensions of the resource mp3 Subject The topic of the resource Bacon, Francis, 1561-1626 Language A language of the resource English Identifier An unambiguous reference to the resource within a given context LEC_Schulman_Adam_1999-04-16_ac Friday night lecture Tutors https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/7c8691672ab0013c653265ae04ca6fe6.mp3 64760d87e4c28f16c9b6f912200a9d8f 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. For more information, and a schedule of upcoming lectures, please visit the <a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a>. Click on <a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&sort_field=Dublin+Core%2CDate&sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a> to view and sort all items in the collection. 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 CD Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 01:00:47 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 Rousseau's Chemical Apprenticeship Description An account of the resource Audio recording of a lecture given on April 18, 2014, by Christopher Kelly as part of the Formal Lecture Series. Creator An entity primarily responsible for making the resource Kelly, Christopher, 1950- 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 2014-04-18 Rights Information about rights held in and over the resource The Greenfield Library has 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 Subject The topic of the resource Rousseau, Jean-Jacques, 1712-1778. Language A language of the resource English Identifier An unambiguous reference to the resource within a given context LEC_Kelly_Christopher_2014-04-18_ac Friday night lecture https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/1f498d8c95bd2a6649a37831bb522e52.mp4 682f0714cd84458f79f989ec4f8cdebf 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. For more information, and a schedule of upcoming lectures, please visit the <a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a>. Click on <a title="Formal Lecture Series" href="https://digitalarchives.sjc.edu/items/browse?collection=5&sort_field=Dublin+Core%2CDate&sort_dir=d">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a> to view and sort all items in the collection. 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 Moving Image A series of visual representations imparting an impression of motion when shown in succession. Examples include animations, movies, television programs, videos, zoetropes, or visual output from a simulation. Original Format The type of object, such as painting, sculpture, paper, photo, and additional data mp4 Duration Length of time involved (seconds, minutes, hours, days, class periods, etc.) 00:54:50 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 Being a Book Description An account of the resource Video recording of a lecture delivered on February 23, 2024, by Daniel Harrell as part of the Formal Lecture Series. Mr. Harrell describes his lecture: "When the so-called New Program was established at St. John’s College in 1937, conversation was to play no essential role—at least if you believe the first statement of the program, written by Scott Buchanan. Where you would expect the word 'conversation' you find 'instruction' instead, as in this brief description of the seminar: Meetings of seminar groups will occur twice a week with any additional meetings that special circumstances or difficulties may indicate. There will be two instructors in charge, and the instruction will make use of a wide range of devices from explication de texte to analysis of intellectual content and the dialectical treatment of critical opinion. When I read this description, I like to think that the importance of conversation to our endeavor emerged over time: a matter of discovery rather than dictate. Has something similar happened with the importance of books to our endeavor? We have always stated this importance in terms of what makes certain books great; but what makes them books, I have come to think, is even more central to our experience of reading them, discussing them, and learning from them. Perhaps there is no way to dictate by 'great' how we come to find ourselves in these books, just as there was no way to dictate by 'instruction' how we came to find ourselves in a conversation about these books. But what makes books books? What does it mean to be a book? This is the question of my lecture. And my hope—despite the St. John’s frame I use here—is that the lecture will be of interest to any reader of books, even if it fails, by my lights, to make full sense of a book." Creator An entity primarily responsible for making the resource Harrell, Daniel 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 2024-02-23 Rights Information about rights held in and over the resource A signed permission form has been received stating, "I hereby grant St. John's College permission to: Make a recording of my lecture, and retain copies for circulation and archival preservation in the St. John's College Greenfield Library. Make a recording of my lecture available online. Make a typescript copy of my lecture available for circulation and archival preservation in the St. John's College Greenfield Library. Make a copy of my typescript available online." Type The nature or genre of the resource moving image Format The file format, physical medium, or dimensions of the resource mp4 Subject The topic of the resource Books Definition (Philosophy) Meaning (Philosophy) St. John's College (Annapolis, Md.) Language A language of the resource English Identifier An unambiguous reference to the resource within a given context LEC_Harrell_Daniel_2024-02-23_ac Friday night lecture Tutors