School of Natural Sciences
By Freeman Dyson
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.
“Everything here is fraught with danger and excitement,” says Nima Arkani-Hamed, Professor in the School of Natural Sciences. With a broad sweep of his hand, he motions to the diagram he has drawn on the chalkboard in his office of the range of distance scales for known phenomena—from 10–33 cm, which is associated with quantum gravity and string theory, to 10+28 cm, which is the size of the universe.
“Why is the universe big, why is gravity so weak? You would think after 2,000 years of thinking about physics we would have good answers to questions like that. We have lousy answers to these questions,” says Arkani-Hamed. “Our current laws of nature—the Standard Model of particle physics—are perfectly consistent. No experiments contradict them, but they give such lousy answers to these questions that we think we are missing something very, very big.”
With the imminent start-up of the Large Hadron Collider (LHC), a particle accelerator that will collide protons together and allow us to probe the laws of nature down to distances of 10–17 cm, a billion times smaller than the atom, and ten times smaller than the tiniest distances we have probed to date, fundamental particle physics is on the threshold of a new era.
In the last decade, astronomical observations of several kinds, particularly of distant supernovae and the cosmic microwave background, also indicate the existence of what is known as dark energy, a uniform background field that is accelerating the expansion of the universe. The presence of dark energy suggests a fundamental gap in our current understanding of the basic forces of nature.
According to the standard cosmological model, dark matter comprises about 22 percent of the universe, while dark energy makes up 74 percent. “There is a few percent of residual dirt left over,” says Scott Tremaine, Richard Black Professor in the School of Natural Sciences, “and that is us and the stars, the galaxies, and everything we know.”
By Pia de Jong
That boy was the seven-year-old Freeman Dyson. He did not understand why his father had sent his remark to Punch. It was after all technically correct. What was so funny about it?
Dyson grew up to be a world-famous mathematician, physicist, astronomer, and an elegant writer. For sixty years, he has worked at the Institute for Advanced Study. On December 15, he will be ninety. An elfin man with pointed ears and mischievous blue eyes, he still walks faithfully to his office every morning, invariably dressed as the British boarding school boy he once was—with a tweed jacket and tie.
To celebrate Dyson’s ninetieth birthday, a conference was held in his honor at the Institute. He himself gave it the title “Dreams of Earth and Sky.” The speakers, also all chosen by him, were just as exciting as the Jules Verne books he devoured as a child—until he realized that they lived only in science fiction.
Thus, I find myself immersed in his fascinating world. I hear the English Astronomer Royal, Martin Rees, talk about alternative universes. I see a map of the nearest stars where extraterrestrial life might really exist. Magic formulas, the interior of the Earth, climate change, nuclear disarmament, life on Mars—ideas that are often as controversial as those of Dyson himself. But also with an equally infectious enthusiasm about everything there is to discover. If I were a child, Dyson would be my hero, and I would want to be an astronomer. Happily, there are many children in the audience.
By Siobhan Roberts
What lies beneath a structure with an unimaginable 196,883 dimensions?
In 1981, Freeman Dyson addressed a typically distinguished group of scholars gathered at the Institute for a colloquium, but speaking on a decidedly atypical subject: “Unfashionable Pursuits.”
The problems which we face as guardians of scientific progress are how to recognize the fruitful unfashionable idea, and how to support it.
To begin with, we may look around at the world of mathematics and see whether we can identify unfashionable ideas which might later emerge as essential building blocks for the physics of the twenty-first century.*
He surveyed the history of science, alighting eventually upon the monster group—an exquisitely symmetrical entity within the realm of group theory, the mathematical study of symmetry. For much of the twentieth century, mathematicians worked to classify “finite simple groups”—the equivalent of elementary particles, the building blocks of all groups. The classification project ultimately collected all of the finite simple groups into eighteen families and twenty-six exceptional outliers. The monster was the last and largest of these exceptional or “sporadic” groups.
In 2013, Freeman Dyson celebrated his ninetieth birthday and also marked his sixtieth year as a Professor at the Institute for Advanced Study, the longest tenure of any Faculty member in the Institute’s history. When Dyson first arrived as a Member in 1948, the Institute was less than twenty years old. “Dreams of Earth and Sky,” a conference and celebration conceived by Dyson’s colleagues in the School of Natural Sciences and held September 27–28, provided a perspective on his work and impact across the sciences and humanities. The program featured a range of talks on mathematics, physics, astronomy, and public affairs that reflect both the diversity of Dyson’s interests and his ability to open new dialogues.
The son of composer Sir George Dyson and Mildred Atkey, Dyson was born in Crowthorne, England, on December 15, 1923. He worked as a civilian scientist for the Royal Air Force in World War II, and graduated from Cambridge University in 1945 with a B.A. degree in mathematics. He went on to Cornell University as a graduate student in 1947 and worked with Hans Bethe and Richard Feynman. One of Dyson’s most notable contributions to science was the unification of the three versions of quantum electrodynamics invented by Feynman, Julian Schwinger, and Sin-Itiro Tomonaga. Dyson then worked on nuclear reactors, solid state physics, ferromagnetism, astrophysics, and biology, looking for problems where mathematics could be usefully applied. Author of numerous articles and books about science for the general public, he has also been heavily invested in human issues, from arms control and space travel to climate studies. Dyson once remarked that he was “obsessed with the future.” His keen observations and sense of wonder, which have inspired generations here at the Institute and beyond, are powerful testaments to the freedom provided by the Institute to follow one’s future, wherever it may lead.
By Juan Maldacena
Can the weird quantum mechanical property of entanglement give rise to wormholes connecting far away regions in space?
In 1935, Albert Einstein and collaborators wrote two papers at the Institute for Advanced Study. One was on quantum mechanics  and the other was on black holes . The paper on quantum mechanics is very famous and influential. It pointed out a feature of quantum mechanics that deeply troubled Einstein. The paper on black holes pointed out an interesting aspect of a black hole solution with no matter, where the solution looks like a wormhole connecting regions of spacetime that are far away. Though these papers seemed to be on two completely disconnected subjects, recent research has suggested that they are closely connected.
Einstein’s theory of general relativity tells us that spacetime is dynamical. Spacetime is similar to a rubber sheet that can be deformed by the presence of matter. A very drastic deformation of spacetime is the formation of a black hole. When there is a large amount of matter concentrated in a small enough region of space, this can collapse in an irreversible fashion. For example, if we filled a sphere the size of the solar system with air, it would collapse into a black hole. When a black hole forms, we can define an imaginary surface called “the horizon”; it separates the region of spacetime that can send signals to the exterior from the region that cannot. If an astronaut crosses the horizon, she can never come back out. She does not feel anything special as she crosses the horizon. However, once she crosses, she will be inevitably crushed by the force of gravity into a region called “the singularity” (Figure 1a).
The most detailed map of the infant universe to date was publicly released in March, showing relic radiation from the Big Bang, imprinted when the universe was just 380,000 years old. This was the first release of cosmological data from the Planck satellite, a mission of the European Space Agency that was initiated in 1996 and involved hundreds of scientists in over thirteen countries. In a lecture in May, Matias Zaldarriaga, Professor in the School of Natural Sciences, explained how theoretical models allowed the Planck team to determine the composition of the universe, map the seeds for the formation of structure, and confirm our broad understanding of the beginnings and evolution of the universe.
Our current understanding of the history of the universe began to take shape around the 1930s, after Edwin Hubble discovered that the universe was expanding. Since then, there have been great advances in understanding the composition of the universe and how it has evolved through cosmic history. According to the standard cosmology model, in the current phase in the history of the Big Bang, the universe began about fourteen billion years ago. Initially the universe was hot and dense with interacting particles. It has been conjectured that prior to this phase, the universe underwent a brief period of accelerated expansion known as inflation when quantum fluctuations, stretched to cosmologically large scales, became the seeds of the universe’s stars and galaxies.
By Hanno Rein
Pluto, the ninth planet in our solar system1 was discovered in 1930, the same year the Institute was founded. While the Institute hosted more than five thousand members in the following sixty-five years, not a single new planet was discovered during the same time.
Finally, in 1995, astronomers spotted an object they called 51 Pegasi b. It was the first discovery of a planet in over half a century. Not only that, it was also the first planet around a Sun-like star outside our own solar system. We now call these planets extrasolar planets, or in short, exoplanets.
As it turns out, 51 Pegasi b is a pretty weird object. It is almost as massive as Jupiter, but it orbits its host star in only four days. Jupiter, as a comparison, needs twelve years to go around the Sun once. Because 51 Pegasi b is very close to the star, its equilibrium temperature is very high. These types of planets are often referred to as “hot Jupiters.”
Since the first exoplanet was discovered, the technology has improved dramatically, and worldwide efforts by astronomers to detect exoplanets now yield a large number of planet detections each year. In 2011, 189 planets were discovered, approximately the number of visiting Members at the Institute every year. In 2012, 130 new planets were found. As of May 20 of this year, the total number of confirmed exoplanets was 892 in 691 different planetary systems.