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Additional articles from new and past issues of the Institute Letter will continue to be posted over time and as they become available.
Ancient History: The Director's Cut––Oliver Stone at the Institute for Advanced Study
By Angelos Chaniotis
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From left: Nathanael Andrade, Angelos Chaniotis, Oliver Stone, Gary Leva, and Yannis Hamilakis discuss historiography in the context of cinema. Photo by Bentley Drezer |
The study of cinematic representations of ancient history is one of the most rapidly rising fields of classical scholarship. As an important part of the modern reception of classical antiquity, movies inspired by Greek and Roman myth and history are discussed in academic courses, conferences, textbooks, handbooks, and doctoral theses. Such discussions involve more than a quest for mistakes—a sometimes quite entertaining enterprise. They confront classicists and ancient historians with profound questions concerning their profession: What part does the remote past play in our lives? How do modern treatments of the past reflect contemporary questions and anxieties? How is memory of the past continually constructed, deconstructed, and reconstructed?
My father worked in the movie industry in the 1950s and 60s as a producer and leaseholder of one of Greece’s largest movie theaters. This may have been the impetus for me to become a cinephile. However, my fascination with the representation of history on the big screen is part of my interest in how memory is shaped. Many Members of the School of Historical Studies, past and present, share this interest. Adele Reinhartz (Member, 2011–12) is the author of Scripture on the Silver Screen (Westminster John Knox Press, 2003) and Jesus of Hollywood (Oxford University Press, 2007); among current Members, the archaeologist Yannis Hamilakis studies the place of the past in modern Mediterranean societies and their media; the ancient historian Nathanael Andrade incorporates movies into undergraduate teaching; and the historian of Latin America Jeff Gould directs historical documentaries.
The Prisoner's Dilemma
By Freeman Dyson
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Groups lacking cooperation are like dodoes, losing the battle for survival collectively rather than individually. |
The Evolution of Cooperation is the title of a book by Robert Axelrod. It was published by Basic Books in 1984, and became an instant classic. It set the style in which modern scientists think about biological evolution, reducing the complicated and messy drama of the real world to a simple mathematical model that can be run on a computer. The model that Axelrod chose to describe evolution is called “The Prisoner’s Dilemma.” It is a game for two players, Alice and Bob. They are supposed to be interrogated separately by the police after they have committed a crime together. Each independently has the choice, either to remain silent or to say the other did it. The dilemma consists in the fact that each individually does better by testifying against the other, but they would collectively do better if they could both remain silent. When the game is played repeatedly by the same two players, it is called Iterated Prisoner’s Dilemma. In the iterated game, each player does better in the short run by talking, but does better in the long run by remaining silent. The switch from short-term selfishness to long-term altruism is supposed to be a model for the evolution of cooperation in social animals such as ants and humans.
Mathematics is always full of surprises. The Prisoner’s Dilemma appears to be an absurdly simple game, but Axelrod collected an amazing variety of strategies for playing it. He organized a tournament in which each of the strategies plays the iterated game against each of the others. The results of the tournament show that this game has a deep and subtle mathematical structure. There is no optimum strategy. No matter what Bob does, Alice can do better if she has a “Theory of Mind,” reconstructing Bob’s mental processes from her observation of his behavior.
History and Peacemaking
By Michael van Walt van Praag
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War-displaced ethnic Tamil civilians wait for rations at a resettlement village in Batticaloa, Sri Lanka. |
Human beings have waged war or engaged in violent conflict with each other since ancient times, an observation that prompted a Member at the Institute to suggest in the course of a casual conversation that surely it was a waste of time and resources to try to prevent or resolve armed conflicts, since there will always be others.
War, by any name,* does indeed seem to be a permanent feature of human society, as is disease for that matter. We do not consider the efforts of physicians to cure patients or the research that goes into finding cures for illnesses a waste of time, despite this. Both phenomena, armed conflict and disease, change over time as circumstances change and as human beings develop ways to prevent or cure some kinds of ills. A doctor treats a patient for that patient’s sake without necessarily having an impact on the propensity of others to fall ill. Mediators and facilitators seek to help resolve conflicts to bring an end to the suffering of those caught in their violence and destruction. Researchers in both fields hope to contribute in a broader and perhaps more fundamental way to understanding and addressing causes of these human ills and to finding new or improved remedies for them.
The Mathematics of Beauty
By Mina Teicher
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Leonardo da Vinci’s Vitruvian Man, ca. 1487 |
It is known that mathematicians see beauty in mathematics. Many mathematicians are motivated to find the most beautiful proof, and often they refer to mathematics as a form of art. They are apt to say “What a beautiful theorem,” “Such an elegant proof.” In this article, I will not elaborate on the beauty of mathematics, but rather the mathematics of beauty, i.e., the mathematics behind beauty, and how mathematical notions can be used to express beauty—the beauty of manmade creations, as well as the beauty of nature.
I will give four examples of beautiful objects and will discuss the mathematics behind them. Can the beautiful object be created as a solution of a mathematical formula or question? Moreover, I shall explore the general question of whether visual experience and beauty can be formulated with mathematical notions.
I will start with a classical example from architecture dating back to the Renaissance, move to mosaic art, then to crystals in nature, then to an example from my line of research on braids, and conclude with the essence of visual experience.
The shape of a perfect room was defined by the architects of the Renaissance to be a rectangular-shaped room that has a certain ratio among its walls—they called it the “golden section.” A rectangular room with the golden-section ratio also has the property that the ratio between the sum of the lengths of its two walls (the longer one and the shorter one) to the length of its longer wall is also the golden section, 1 plus the square root of 5 over 2. Architects today still believe that the most harmonious rooms have a golden-section ratio. This number appears in many mathematical phenomena and constructions (e.g., the limit of the Fibonacci sequence). Leonardo da Vinci observed the golden section in well-proportioned human bodies and faces—
in Western culture and in some other civilizations the golden-section ratio of a well-proportioned human body resides between the upper part (above the navel) and the lower part (below the navel).
Life on Other Planets
By David S. Spiegel
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Sighting a deer outside of Fuld Hall; how long did Earth have to wait before life "walked into sight"? |
Until a couple of decades ago, the only planets we knew existed were the nine in our Solar System. In the last twenty-five years, we’ve lost one of the local ones (Pluto, now classified as a “minor planet”) and gained about three thousand candidate planets around other stars, dubbed exoplanets. The new field of exoplanetary science is perhaps the fastest growing subfield of astrophysics, and will remain a core discipline for the forseeable future.
The fact that any biology beyond Earth seems likely to live on such a planet is among the many reasons why the study of exoplanets is so compelling. In short, planets are not merely astrophysical objects but also (at least some of them) potential abodes.
The highly successful Kepler mission involves a satellite with a sensitive telescope/camera that stares at a patch of sky in the direction of the constellation Cygnus. The goal of the mission is to find what fraction of Sun-like stars have Earth-sized planets with a similar Earth-Sun separation (about 150 million kilometers, or the distance light travels in eight minutes).