The Parthenon and Liberal Education

Michael Weinman, Geoff Lehman

Description

The Parthenon and Liberal Education seeks to restore the study of mathematics to its original place of prominence in the liberal arts. To build this case, Geoff Lehman and Michael Weinman turn to Philolaus, a near contemporary of Socrates. The authors demonstrate the influence of his work involving number theory, astronomy, and harmonics on Plato's Republic and Timaeus, and outline its resonance with the program of study in the early Academy and with the architecture of the Parthenon. Lehman and Weinman argue that the Parthenon can be seen as the foremost embodiment of the practical working through of mathematical knowledge in its time, serving as a mediator between the early reception of Ancient Near-Eastern mathematical ideas and their integration into Greek thought as a form of liberal education, as the latter came to be defined by Plato and his followers. With its Doric architecture characterized by symmetria (commensurability) and harmonia (harmony; joining together), concepts explored contemporaneously by Philolaus, the Parthenon engages dialectical thought in ways that are of enduring relevance for the project of liberal education.
List of Illustrations
Acknowledgements

Introduction: Thinking the Parthenon and Liberal Arts Education Together

Part I. Plato on Dialectic and the Problem-Based Study of Mathematics

1. Dialectic and the Mathematical Arts in Republic (9.587b–588a): Philolaus’s Scale and the Final Bout between the Just and Unjust Souls

2. Dialectic and the Mathematical Arts in Timaeus (35b–36c): Philolaus’s Scale in the Construction of the World-Soul

3. Platonic Dialectic, Pythagorean Harmonics, and Liberal Arts Education

Part II. Harmonia and Symmetria of the Parthenon

4. The Parthenon and the Musical Scale

5. The Corner Problem

6. Refinements and the Question of Dialectic

Afterword

Appendix A
Pythagorean Musical Ratios

Appendix B
Principal Measurements of the Parthenon

Appendix C
Elements of the Doric Order

Appendix D
Ground Plan of the Parthenon

Appendix E
Glossary of Technical Terms

Notes
Works Cited
Index

Sujets

• Philosophie
• Philosophie antique
• Sciences formelles
• Histoire des mathématiques
• History of art
• Philosophy
• History of architecture
• Philosophy of mathematics
• Mathematics
• History of mathematics
• Ancient philosophy
• Science
• Architecture

Informations

• Publié par: State University of New York Press
• Date de parution: 01 mars 2018
• Nombre de lectures: 0
• EAN13: 9781438468433
• Langue: English

Extrait

T HE P ARTHENON
AND
L IBERAL E DUCATION
SUNY series in Ancient Greek Philosophy

Anthony Preus, editor
T HE P ARTHENON
AND
L IBERAL E DUCATION
G EOFF L EHMAN M ICHAEL W EINMAN
Cover art: Façade and North Colonnade of the Parthenon on the Acropolis, Athens , daguerreotype, 1842, Joseph-Philibert Girault de Prangey (French, 1804–1892).
Published by State University of New York Press, Albany
© 2018 State University of New York
All rights reserved
Printed in the United States of America
No part of this book may be used or reproduced in any manner whatsoever without written permission. No part of this book may be stored in a retrieval system or transmitted in any form or by any means including electronic, electrostatic, magnetic tape, mechanical, photocopying, recording, or otherwise without the prior permission in writing of the publisher.
For information, contact State University of New York Press, Albany, NY
www.sunypress.edu
Library of Congress Cataloging-in-Publication Data
Names: Lehman, Geoff, 1971– author.
Title: The Parthenon and liberal education / Geoff Lehman and Michael Weinman.
Description: Albany, NY : State University of New York, 2018. | Series: SUNY series in ancient Greek philosophy | Includes bibliographical references and index.
Identifiers: LCCN 2017013762 (print) | LCCN 2017059383 (ebook) | ISBN 9781438468433 (ebook) | ISBN 9781438468419 (hardcover : alk. paper)
Subjects: LCSH: Philolaus, of Croton, approximately 470 B.C.– | Mathematics—History. | Plato. | Philosophy, Ancient. | Parthenon (Athens, Greece)
Classification: LCC B235.P44 (ebook) | LCC B235.P44 L44 2018 (print) | DDC 182/.2—dc23
LC record available at https://lccn.loc.gov/2017013762
10 9 8 7 6 5 4 3 2 1
Contents
L IST OF I LLUSTRATIONS
A CKNOWLEDGEMENTS
I NTRODUCTION
Thinking the Parthenon and Liberal Arts Education Together
P ART I
Plato on Dialectic and the Problem-Based Study of Mathematics
C HAPTER 1
Dialectic and the Mathematical Arts in Republic (9.587b–588a): Philolaus’s Scale and the Final Bout between the Just and Unjust Souls
C HAPTER 2
Dialectic and the Mathematical Arts in Timaeus (35b–36c): Philolaus’s Scale in the Construction of the World-Soul
C HAPTER 3
Platonic Dialectic, Pythagorean Harmonics, and Liberal Arts Education
P ART II
Harmonia and Symmetria of the Parthenon
C HAPTER 4
The Parthenon and the Musical Scale
C HAPTER 5
The Corner Problem
C HAPTER 6
Refinements and the Question of Dialectic
A FTERWORD
A PPENDIX A
Pythagorean Musical Ratios
A PPENDIX B
Principal Measurements of the Parthenon
A PPENDIX C
Elements of the Doric Order
A PPENDIX D
Ground Plan of the Parthenon
A PPENDIX E
Glossary of Technical Terms
N OTES
W ORKS C ITED
I NDEX
Illustrations
Figures 4.1 The Parthenon, Athens (447–432 BCE): view from the northwest 4.2 The Parthenon: view from the southeast 4.3 Model of the Acropolis as it looked around 400 BCE (Royal Ontario Museum, Toronto) 4.4 Ground plan of the Acropolis in the fifth century 4.5 The Parthenon: column capital and entablature, west façade 4.6 Battle of a Lapith and a Centaur: metope from the south flank of the Parthenon 4.7 Diagram of the Doric order as it appears in the Parthenon 4.8 Diagram of the Ionic order 4.9 Erechtheion, Athens (421–406 BCE): Capital and architrave from the east façade 4.10 The Temple of Athena, Paestum (late sixth century BCE): view from the southwest 4.11 The Temple of Hera Lacinia, Akragas (begun ca. 460 BCE): view from the southeast 4.12 The Temple of Hera Lacinia, Akragas: ground plan 4.13 The Temple of Concord, Akragas (begun ca. 440 BCE): view from the southeast 4.14 The Temple of Zeus, Olympia (begun ca. 457–56 BCE): east façade elevation 4.15 The Temple of Zeus, Olympia: ground plan 4.16 The Temple of Poseidon (or Hera II), Paestum (begun ca. 460 BCE): west façade 4.17 The Temple of Aphaia, Aegina (ca. 490s BCE): view from the southeast 4.18 Photograph of Le Corbusier on the Acropolis, September 1911 4.19 The Parthenon: interior of the south peristyle 4.20 The Parthenon: view of the southwest corner 4.21 The Parthenon: west façade 4.22 The Parthenon: ground plan 4.23 The Parthenon: section, showing the Doric and Ionic orders of the interior 4.24 Parthenon replica, Nashville (begun 1920s): interior of the naos 4.25 Figures K, L, and M from the Parthenon’s east pediment 4.26 Figure M (Aphrodite?) from the Parthenon’s east pediment, detail 5.1 The Parthenon: northeast corner 5.2 The Parthenon: entablature, northwest corner 5.3 The Brandenburg Gate, Berlin (1788–1791): entablature, northwest corner 5.4 The Parthenon: east façade, south side of the entablature 5.5 The Parthenon: east façade 5.6 The Parthenon: east façade, north side of the entablature 5.7 Doryphoros , ancient Roman copy in marble of a bronze original of ca. 450–440 BCE by Polykleitos 5.8 The Temple at Segesta (420s BCE): view from the southeast 5.9 The Temple at Segesta: view from the southwest corner, showing curvature 6.1 The Parthenon: view from the northeast corner, showing curvature 6.2 The Parthenon, west façade, Ionic frieze: beginning of the Panathenaic procession (?) 6.3 Diagram of the column inclinations of the Parthenon 6.4 Joseph-Philibert Girault de Prangey, Façade and North Colonnade of the Parthenon on the Acropolis, Athens , daguerreotype, 1842 6.5 The Parthenon, west façade: detail showing Doric capitals and Ionic frieze with Doric guttae underneath 6.6a and 6.6b Jacques Carrey, drawings of the south and north sides of the east pediment of the Parthenon, 1674 (Paris, Bibliothèque Nationale) 6.7a and 6.7b Jacques Carrey, drawings of the north and south sides of the west pediment of the Parthenon, 1674 (Paris, Bibliothèque Nationale) 6.8 The Parthenon, Ionic frieze, depicting the Panathenaic procession (?): south side, bulls being led to sacrifice 6.9 The Parthenon, Ionic frieze, depicting the Panathenaic procession (?): east side, central scene (ritual with the peplos of Athena, or sacrifice of the daughters of Erechtheus and Praxithea?)
Acknowledgments
E very book is the work of more than one person. The truth of this claim is self-evident when, like this one, the book is signed by two people. There are many others, however, without whose efforts these words would not have seen the light of day, and it is a privilege and a pleasure to express our gratitude to them.
First and foremost, we are indebted to Robert Hahn and Anthony Preuss, whose interest and belief in our attempt to harmonize discourses not often pursued in concert has inspired and challenged us to live up to the standard of the SUNY series in Ancient Greek Philosophy. We also thank those friends, colleagues, students, and former students whose careful and considerate reading of parts of this book have improved its expression and helped us avoid numerous missteps. Claudia Baracchi, David Hayes, Dmitri Nikulin, Bill Pastille, and Gregory Recco merit special mention in this regard. Linda Eggert, Oumaïma Gannouni, and Lindsay Parkhowell, our peerless student assistants at Bard College Berlin during various stages of the research and writing this project demanded, have more than earned our enduring gratitude for their efforts.
The origins of the book, in many ways, lie in an interdisciplinary core course we taught together, with other colleagues, at Bard College Berlin, Plato’s Republic and Its Interlocutors, and we would like to thank the students and colleagues with whom we worked in the course’s various incarnations over the years. Also, much of the foundation for this book was laid in our design and execution of an international conference, Pythagorean Harmonics from Philolaus to Leibniz, held at Bard College Berlin (then ECLA of Bard) in October 2013. We are grateful to the conference participants, the college, its leadership (Dean Catherine Toal and then-Rector Thomas Rommel), our colleagues at the college who worked so hard to make the event a success, and all who attended. We are likewise indebted to David McNeill, Jon Mikalson, Dmitri Nikulin, and Michalis Sialaros for inviting us to present our work, and to the audiences at the University of Essex, the New School for Social Research, the University of Virginia, and University College London for helpful and challenging responses.
Robert Hannah and Vassilis Petrakis, our (initially anonymous) reviewers for SUNY Press, made essential suggestions in the review and revision process. Indeed, their responses modified the overall structure of the book and we made countless reformulations of expression and of content because of their responses. Andrew Kenyon, Ryan Morris, and Anne Valentine at SUNY Press have been ideal partners as we bring this book to completion. Their insights into materializing our intellectual labor and their professionalism have been invaluable.
Geoff Lehman would like to thank his parents, John and Elizabeth, and his sister, Julie, for their continuing support and encouragement. He also would like to thank David Rosand, who was his main support in the study of art over the years, and with whom he often discussed, among countless other topics, the Art Humanities course at Columbia University, where he first began thinking about the Parthenon.
Michael Weinman would like to acknowledge the unflagging and invaluable support he receives from Irit Dekel, a source of intellectual energy, an honest critic, and a life mate who is truly without parallel or shared measure.
Needless to say, with all the thanks we owe to so many people, we alone are responsible for whatever faults remain.
Introduction
Thinking the Parthenon and Liberal Arts Education Together
M ICHAEL W EINMAN AND G EOFF L EHMAN
T his work is simultaneously expansive and narrow in its scope. It is expansive in that it takes up three objects that would generally be thought to diverge widely: (1) the early history of Greek mathematics; (2) Plato’s Republic and Timaeus , in convers