The two-player Iterated Prisoner’s Dilemma game is a model for both sentient and evolutionary behaviors, especially including the emergence of cooperation. It is generally assumed that there exists ...no simple ultimatum strategy whereby one player can enforce a unilateral claim to an unfair share of rewards. Here, we show that such strategies unexpectedly do exist. In particular, a player X who is witting of these strategies can (i) deterministically set her opponent Y’s score, independently of his strategy or response, or (ii) enforce an extortionate linear relation between her and his scores. Against such a player, an evolutionary player’s best response is to accede to the extortion. Only a player with a theory of mind about his opponent can do better, in which case Iterated Prisoner’s Dilemma is an Ultimatum Game.
The physical sciences have alternated between revolutions driven by new ideas and explorations driven by new tools.
Thomas Kuhn was a theoretical physicist before he became a historian. He saw the ...history of science through the eyes of a theorist. He gave us an accurate view of events in the world of ideas. His favorite word, “paradigm,” means a system of ideas that dominate the science of a particular place and time. A scientific revolution is a discontinuous shift from one paradigm to another. The shift happens suddenly because new ideas explode with a barrage of new insights and new questions that push old ideas into oblivion. I remember the joy of reading Kuhn's book,
The Structure of Scientific Revolutions
, when it first appeared in 1962. It made sense of the relativity and quantum revolutions that had happened just before the theoretical physicists of my generation were born. Those were revolutions led by deep thinkers—Einstein and Heisenberg and Schrödinger and Dirac—who guessed nature's secrets by dreaming dreams of mathematical beauty. Their new paradigms were created out of abstract ideas. In those revolutionary years from 1900 to 1930, ideas led the way to understanding.
Renowned physicist and mathematician Freeman Dyson is famous for his work in quantum mechanics, nuclear weapons policy and bold visions for the future of humanity. In the 1940s, he was responsible ...for demonstrating the equivalence of the two formulations of quantum electrodynamics - Richard Feynman's diagrammatic path integral formulation and the variational methods developed by Julian Schwinger and Sin-Itiro Tomonoga - showing the mathematical consistency of QED.This invaluable volume comprises the legendary lectures on quantum electrodynamics first given by Dyson at Cornell University in 1951. The late theorist Edwin Thompson Jaynes once remarked, "For a generation of physicists they were the happy medium: clearer and better motivated than Feynman, and getting to the point faster than Schwinger".This edition has been printed on the 60th anniversary of the Cornell lectures, and includes a foreword by science historian David Kaiser, as well as notes from Dyson's lectures at the Les Houches Summer School of Theoretical Physics in 1954. The Les Houches lectures, described as a supplement to the original Cornell notes, provide a more detailed look at field theory, a careful and rigorous derivation of Fermi's Golden Rule, and a masterful treatment of renormalization and Ward's Identity.Future generations of physicists are bound to read these lectures with pleasure, benefiting from the lucid style that is so characteristic of Dyson's exposition.
On the Distribution of the spt-Crank Andrews, George; Dyson, Freeman; Rhoades, Robert
Mathematics (Basel),
09/2013, Letnik:
1, Številka:
3
Journal Article
Recenzirano
Odprti dostop
Andrews, Garvan and Liang introduced the spt-crank for vector partitions. We conjecture that for any n the sequence { N S (m , n) } m is unimodal, where N S (m , n) is the number of S-partitions of ...size n with crank m weight by the spt-crank. We relate this conjecture to a distributional result concerning the usual rank and crank of unrestricted partitions. This leads to a heuristic that suggests the conjecture is true and allows us to asymptotically establish the conjecture. Additionally, we give an asymptotic study for the distribution of the spt-crank statistic. Finally, we give some speculations about a definition for the spt-crank in terms of “marked” partitions. A “marked” partition is an unrestricted integer partition where each part is marked with a multiplicity number. It remains an interesting and apparently challenging problem to interpret the spt-crank in terms of ordinary integer partitions.
How did life on earth originate? Did replication or metabolism come first in the history of life? In this book, Freeman Dyson examines these questions and discusses the two main theories that try to ...explain how naturally occurring chemicals could organize themselves into living creatures. The majority view is that life began with replicating molecules, the precursors of modern genes. The minority belief is that random populations of molecules evolved metabolic activities before exact replication existed. Dyson analyzes both of these theories with reference to recent important discoveries by geologists and chemists. His main aim is to stimulate experiments that could help to decide which theory is correct. This second edition covers the enormous advances that have been made in biology and geology in the past and the impact they have had on our ideas about how life began. It is a clearly-written, fascinating book that will appeal to anyone interested in the origins of life.
Lehmer’s Interesting Series Dyson, Freeman J; Frankel, Norman E; Glasser, M Lawrence
The American mathematical monthly,
02/2013, Letnik:
120, Številka:
2
Journal Article
Recenzirano
The series
\documentclass{article} \pagestyle{empty}\begin{document} $S_k(z) = \sum_{m=1}^{\infty} \leftC^{2m}_{m}\right^{-1} m^k z^m$ \end{document}
is evaluated in a nonrecursive and closed ...process. It can be analytically continued beyond its domain of convergence
\documentclass{article} \pagestyle{empty}\begin{document} $|z|<4$ \end{document}
whenk= 0, 1, 2, …. From this we provide a firm basis for Lehmer’s observation that π emerges from the limiting behavior ofSk
(2) ask→ ∞.
Here is the definitive new edition of the hugely popular collection of Einstein quotations that has sold tens of thousands of copies worldwide and been translated into twenty-five languages.
A gravitational machine is defined as an arrangement of gravitating masses from which useful energy can be extracted. It is shown that such machines may exist if the masses are of normal astronomical ...size. A simple example of a gravitational machine, consisting of a double star with smaller masses orbiting around it, is described. It is shown that an efficient gravitational machine will also be an emitter of gravitational radiation. The emitted radiation sets a limit on the possible performance of gravitational machines, and also provides us with a possible means for detecting such machines if they exist.
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