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Freeman Dyson, Professor Emeritus in the School of Natural Sciences, Is Always Full of Surprises (Page 1)

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Freeman Dyson, Professor Emeritus in the School of Natural Sciences, Is Always Full of Surprises (Page 1) BRUCE M.WHITE BRUCE Fall 2012 Fall (page 5), and curbing and 5), (page , Visitor in the School of Mathematics , trace the seal’s origins and influences— and origins seal’s the trace , (page (page 1), borders controlling by Professor Elizabeth Bernstein Elizabeth , Professor Emeritus in the School of School Historical in the Emeritus , Professor Mina Teicher Professor Emeritus in the School of Natural Sciences, is Irving Lavin Irving (page 8). Truth and Beauty and Truth Marilyn Aronberg Lavin Aronberg Marilyn Michael Michael van van Walt Praag Freeman Dyson, The Institute Letter Eugene Kontorovich (page 5), curtailing sex trafficking by Member Member by trafficking sex curtailing 5), (page At At the Institute, scholars and scientists seek truth and question claims of it. Mathematicians have Mathematics, observes The power and complexity of collectivity are further explored in articles about resolving intrastateresolvingaboutarticles in explored furthercollectivity are complexityof and power The among themthe finalcouplet of“Ode John on Keats’s a Grecian Urn”—and articulate why and how its elements and design embody the rare and very modern of mission the (page Institute 6). “The rad- ical nature of Flexner’s twinning of science and humanism with truth and beauty arose in part the fromradical nature of his concept for a ‘modern’ writesuniversity,” Irving Lavin, “by which he meant a university devoted exclusively to the pursuit of higher learning for its own sake and without regard to practical value.” re- often and proof elegant most the find to compelled mathematics, in beauty by motivated been long ferring to mathematics as a form of art, writes to (up term absolute an to beauty equating itself, beauty of mathematics the explores Teicher 1). (page the of ratio golden-section the in example, for seen, dependence) historical and geographical, cultural, a mosaic. in symmetries bodies possible human of and number rooms the or harmonious most always full of surprises (page 1). With William Press of the University of Texas, Dysonrecently found alwaysPressfullthesurprisesUniversityofof William (pageTexas, of 1).With doubt- for reasons his explains subtleDyson mathematicalanddeep a with gameDilemma, structure a strategiesused newPrisoner’s the for cooperation. of evolution the for model a as biologists population by ing therelevance theofmodel, which focuses exclusively individualon selection—the death indi-of viduals who make bad choices—and negates group selection in which the battle for survivalcollectively ratheris than individually. lost conflict by Professor Visiting Fassin Didier piracy by Member Studies, and his wife and colleague, and wife his and Studies, The need for an official Institute seal (above) was one of the first things that Abraham Flexner, found- Flexner, Abraham that things first the of one was (above) seal Institute official an for need The ing Director of the Institute, turned his attention to even before preliminary financial and practical issue, this were place. In in arrangements IAS Have you moved? Non-Profit Org. Please notify us of your change of address. U.S. Postage PAID Send changes to: Permit #49 Public Affairs, Institute for Advanced Study Princeton, NJ The Institute Letter Fall 2012 Einstein Drive, Princeton, NJ 08540 IAS or email [email protected] Robbert Dijkgraaf, Director Giles Constable Martin Rees and Leon Levy Professor Pierre Deligne David M. Rubenstein Freeman J. Dyson James J. Schiro Faculty Peter Goldreich Eric E. Schmidt Danielle S. Allen Phillip A. Griffiths William H. Sewell, Jr. Nima Arkani-Hamed Christian Habicht Harold T. Shapiro Yve-Alain Bois Robert P. Langlands James H. Simons Jean Bourgain Irving Lavin Peter Svennilson Angelos Chaniotis Arnold J. Levine Shelby White Patricia Crone Peter Paret Marina v.N. Whitman Nicola Di Cosmo Heinrich von Staden Brian F. Wruble Didier Fassin Michael Walzer Patrick J. Geary Morton White Trustees Emeriti Peter Goddard Richard B. Black Helmut Hofer Board of Trustees Martin A. Chooljian Sidney D. Drell Piet Hut Charles Simonyi Ralph E. Hansmann Jonathan Israel Chairman Helene L. Kaplan Stanislas Leibler Victoria B. Bjorklund Immanuel Kohn Robert MacPherson Curtis Callan David K.P. Li Juan Maldacena Cynthia Carroll Hamish Maxwell Peter Sarnak Neil A. Chriss Ronaldo H. Schmitz Joan Wallach Scott Robbert Dijkgraaf Michel L. Vaillaud Nathan Seiberg Mario Draghi Ladislaus von Hoffmann Thomas Spencer Roger W. Ferguson, Jr. James D. Wolfensohn Richard Taylor E. Robert Fernholz Chairman Emeritus Scott Tremaine Carmela Vircillo Franklin Vladimir Voevodsky Vartan Gregorian Institute for Advanced Study Avi Wigderson Benedict H. Gross Einstein Drive Edward Witten John S. Hendricks Princeton, New Jersey 08540 Matias Zaldarriaga Peter R. Kann (609) 734-8000 Bruce Kovner www.ias.edu Faculty Emeriti Spiro J. Latsis www.facebook.com/InstituteforAdvancedStudy Stephen L. Adler Martin L. Leibowitz www.twitter.com/the_IAS Enrico Bombieri Nancy S. MacMillan www.youtube.com/videosfromIAS Glen W. Bowersock David F. Marquardt Caroline Walker Bynum Nancy B. Peretsman The Institute Letter InstituteIAS for Advanced Study Fall 2012 The Prisoner’s Dilemma choice, either to remain silent or to say the other did it. The dilemma consists in the fact BY FREEMAN DYSON that each individually does better by testifying against the other, but they would collec- tively do better if they could both remain silent. When the game is played repeatedly by he Evolution of Cooperation is the the same two players, it is called “Iterated Prisoner’s Dilemma.” In the iterated game, each Ttitle of a book by Robert Axelrod. player does better in the short run by talking, but does better in the long run by remaining It was published by Basic Books in silent. The switch from short-term selfishness to long-term altruism is supposed to be a 1984, and became an instant classic. model for the evolution of cooperation in social animals such as ants and humans. It set the style in which modern sci- Mathematics is always full of surprises. The Prisoner’s Dilemma appears to be an entists think about biological evolu- absurdly simple game, but Axelrod collected an amazing variety of strategies for playing tion, reducing the complicated and it. He organized a tournament in which each of the strategies plays the iterated game messy drama of the real world to a against each of the others. The results of the tournament show that this game has a deep simple mathematical model that can and subtle mathematical structure. There is no optimum strategy. No matter what Bob be run on a computer. The model that does, Alice can do better if she has a “Theory of Mind,” reconstructing Bob’s mental Axelrod chose to describe evolution processes from her observation of his behavior. is called “The Prisoner’s Dilemma.” It William Press, Professor at the University of Texas at Austin, is the author of Numer- is a game for two players, Alice and ical Recipes, the cookbook for people who do serious scientific computing. He is the Julia Bob. They are supposed to be interro- Child of numerical cuisine. He recently invented a new class of Prisoner’s Dilemma gated separately by the police after strategies and tried them out numerically to see how they performed. He found that HERITAGE IMAGES/CORBIS Groups lacking cooperation are like dodoes, losing the they have committed a crime to- they behaved weirdly. They had a bad effect on his computer program, causing it to battle for survival collectively rather than individually. gether. Each independently has the (Continued on page 3) History and Peacemaking The Mathematics of Beauty BY MICHAEL VAN BY MINA TEICHER WALT VAN PRAAG t is known that mathematicians see uman beings have Ibeauty in mathematics. Many math- Hwaged war or engaged ematicians are motivated to find the in violent conflict with each most beautiful proof, and often they other since ancient times, an refer to mathematics as a form of art. observation that prompted a They are apt to say “What a beautiful Member at the Institute to theorem,” “Such an elegant proof.” In suggest in the course of a ca- this article, I will not elaborate on the sual conversation that surely beauty of mathematics, but rather the it was a waste of time and mathematics of beauty, i.e., the math- resources to try to prevent or ematics behind beauty, and how math- BUDDHIKA WEERASINGHE/STRINGER/REUTERS/CORBIS resolve armed conflicts, since ematical notions can be used to express War-displaced ethnic Tamil civilians wait for rations at a resettlement village in Batticaloa, Sri Lanka. there will always be others. beauty—the beauty of manmade cre- War, by any name,* does ations, as well as the beauty of nature. indeed seem to be a permanent feature of human society, as is disease for that matter. I will give four examples of beautiful We do not consider the efforts of physicians to cure patients or the research that goes objects and will discuss the mathematics into finding cures for illnesses a waste of time, despite this. Both phenomena, armed behind them. Can the beautiful object conflict and disease, change over time as circumstances change and as human beings be created as a solution of a mathemat- develop ways to prevent or cure some kinds of ills. A doctor treats a patient for that ical formula or question? Moreover, I patient’s sake without necessarily having an impact on the propensity of others to fall ill. shall explore the general question of GALLERIE DELL’ACCADEMIA, VENICE, ITALY Mediators and facilitators seek to help resolve conflicts to bring an end to the suffering whether visual experience and beauty Leonardo da Vinci’s Vitruvian Man, of those caught in their violence and destruction. Researchers in both fields hope to can be formulated with mathematical ca. 1487 contribute in a broader and perhaps more fundamental way to understanding and notions. addressing causes of these human ills and to finding new or improved remedies for them.
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