A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature

Capa
National Academies Press, 21/09/2006 - 272 páginas

Millions have seen the movie and thousands have read the book but few have fully appreciated the mathematics developed by John Nash's beautiful mind. Today Nash's beautiful math has become a universal language for research in the social sciences and has infiltrated the realms of evolutionary biology, neuroscience, and even quantum physics. John Nash won the 1994 Nobel Prize in economics for pioneering research published in the 1950s on a new branch of mathematics known as game theory. At the time of Nash's early work, game theory was briefly popular among some mathematicians and Cold War analysts. But it remained obscure until the 1970s when evolutionary biologists began applying it to their work. In the 1980s economists began to embrace game theory. Since then it has found an ever expanding repertoire of applications among a wide range of scientific disciplines. Today neuroscientists peer into game players' brains, anthropologists play games with people from primitive cultures, biologists use games to explain the evolution of human language, and mathematicians exploit games to better understand social networks. A common thread connecting much of this research is its relevance to the ancient quest for a science of human social behavior, or a Code of Nature, in the spirit of the fictional science of psychohistory described in the famous Foundation novels by the late Isaac Asimov. In A Beautiful Math, acclaimed science writer Tom Siegfried describes how game theory links the life sciences, social sciences, and physical sciences in a way that may bring Asimov's dream closer to reality.

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Índice

Introduction
1
1 Smiths HandSearching for the Code of Nature
11
2 Von Neumanns GamesGame theorys origins
27
3 Nashs EquilibriumGame theorys foundation
51
4 Smiths StrategiesEvolution altruism and cooperation
73
5 Freuds DreamGames and the brain
93
6 Seldons SolutionGame theory culture and human nature
110
7 Quetelets Statistics and Maxwells MoleculesStatistics and society statistics and physics
126
9 Asimovs VisionPsychohistory or sociophysics?
164
10 Meyers PennyQuantum fun and games
182
11 Pascals WagerGames probability information and ignorance
197
Epilogue
217
AppendixCalculating a Nash Equilibrium
225
Further Reading
230
Notes
233
Index
249

8 Bacons LinksNetworks society and games
144

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