Table Of Content

he isual ind II T V M Michele Emmer edited by The Visual Mind II leonardo Roger F. Malina, series editor The Visual Mind, edited by Michele Emmer, 1993 Leonardo Almanac, edited by Craig Harris, 1994 Designing Information Technology, Richard Coyne, 1995 Immersed in Technology: Art and Virtual Environments, edited by Mary Anne Moser with Douglas MacLeod, 1996 Technoromanticism: Digital Narrative, Holism, and the Romance of the Real, Richard Coyne, 1999 Art and Innovation: The Xerox PARC Artist-in-Residence Program, edited by Craig Harris, 1999 The Digital Dialectic: New Essays on New Media, edited by Peter Lunenfeld, 1999 The Robot in the Garden: Telerobotics and Telepistemology in the Age of the Internet, edited by Ken Goldberg, 2000 The Language of New Media, Lev Manovich, 2000 Metal and Flesh: The Evolution of Man: Technology Takes Over, Ollivier Dyens, 2001 Uncanny Networks: Dialogues with the Virtual Intelligentsia, Geert Lovink, 2002 Information Arts: Intersections of Art, Science, and Technology, Stephen Wilson, 2002 Virtual Art: From Illusion to Immersion, Oliver Grau, 2003 Women, Art, and Technology, edited by Judy Malloy, 2003 Protocol: How Control Exists after Decentralization, Alexander R. Galloway, 2004 At a Distance:Precursors to Art and Activism on the Internet, edited by Annmarie Chandler and Norie Neumark, 2005 The Visual Mind II, edited by Michele Emmer, 2005 CODE: Collaborative Ownership and the Digital Economy, edited by Rishab Aiyer Ghosh, 2005 From Technological to Virtual Art, Frank Popper, 2005 The Visual Mind II edited by Michele Emmer The MIT Press Cambridge,Massachusetts London,England © 2005 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. MIT Press books may be purchased at special quantity discounts for business or sales promotional use. For information, please email special_sales@mitpress. mit.edu or write to Special Sales Department, The MIT Press, 5 Cambridge Center, Cambridge, MA 02142. This book was set in Bell Gothic and Garamond by SNP Best-set Typesetter Ltd., Hong Kong and was printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data The visual mind II / edited by Michele Emmer. p. cm. — (Leonardo) Includes bibliographical references and index. ISBN 0-262-05076-5 (hc : alk. paper) 1. Art—Mathematics. 2. Geometry. 3. Aesthetics. I. Title: Visual mind 2. II. Title: Visual mind two. III. Emmer, Michele. IV. Leonardo (Series) (Cambridge, Mass.) N72.M3V58 2005 701¢.5—dc22 2004057850 To Valeria Max Bill Fred Almgren H. S. M. Coxeter Contents introduction Michele Emmer xi Section 1 Mathematics and Aesthetics 1 1 the phenomenology of mathematical beauty Gian-Carlo Rota 3 2 mathematical beauty and the evolution of the standards of mathematical proof James W. McAllister 15 3 aesthetics for computers, or how to measure harmony Jaroslav Neˇsetˇril 35 4 visual mathematics: mathematics and art Michele Emmer 59 Section 2 Geometry and Art 91 5 life through art Carmen Bonell 95 6 john robinson’s symbolic sculptures: knots and mathematics Ronald Brown 125 7 geometries of curvature and their aesthetics Brent Collins 141 8 poetry in curves: the guggenheim museum in bilbao Giuseppa Di Cristina 159 9 eightfold way: the sculpture Helaman Ferguson with Claire Ferguson 187 10 the geometric aesthetic George W. Hart 215 11 art and the age of the sciences Charles Perry 235 12 some aspects of the use of geometry in my artistic work Sylvie Pic 253 Section 3 Mathematics and Art 269 13 local/global in mathematics and painting CapiCorralesRodrigáñezwithanAppendixbyLauraTedeschini-Lalli 273 14 visual knots: concerning geometry and visuality in the work of marcel duchamp Manuel Corrada 309 15 lunda symmetry: where geometry meets art Paulus Gerdes 335 16 four-dimensional space or space-time? the emergence of the cubism-relativity myth in new york in the 1940s Linda Dalrymple Henderson 349 17 “reverse perspective”: historical fallacies and an alternative view Clemena Antonova and Martin Kemp 399 18 four-dimensional projection: art and reality Tony Robbin 433 19 rational design versus artistic intuition in stained- glass art Tomás García Salgado 449 Section 4 Geometry,Computer Graphics,and Art 469 20 dynamics, chaos, and design Michael Field 473 21 paul klee on computer: biomathematical models help us understand his work Roberto Giunti 495 22 parameterized sculpture families Carlo H. Séquin 527 23 the aesthetic value of optimal geometry John M. Sullivan 547 Contents viii Section 5 Mathematics,Visualization,and Cinema 565 24 mathematics and cinema Michele Emmer 569 25 some organizing principles Peter Greenaway 601 26 ﬁgures and characters in the great book of nature Jean-Marc Lévy-Leblond 623 27 circle packings and the sacred lotus Tibor Tarnai and Koji Miyazaki 647 28 meander mazes on polysphericons Anthony Phillips 667 contributors 685 name index 689 subject index 697 Contents ix