A Beautiful Math
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15. Colin Camerer, interview in Pasadena, Calif., March 12, 2004.
16. David J. Buller, "Evolutionary Psychology: The Emperor's New Paradigm," Trends in Cognitive Sciences, 9 (June 2005): 277–283.
17. Not surprisingly, evolutionary psychologists have reacted negatively to Buller's criticisms, contending that he distorts the evidence he cites. You can find some of their counterarguments online at http://www.psych.ucsb.edu/research/cep/buller.htm.
18. Ira Black, remarks at the annual meeting of the Society for Neuroscience, Orlando, Florida, November 3, 2002. Black died in early 2006.
19. Steven Quartz and Terrence Sejnowski, Liars, Lovers, and Heroes, William Morrow, New York, 2002, pp. 41, 46.
20. E.J. Chesler, S.G. Wilson, W.R. Lariviere, S.L. Rodriguez-Zas, and J.S. Mogil, "Identification and Ranking of Genetic and Laboratory Environment Factors Influencing a Behavioral Trait, Thermal Nociception, via Computational Analysis of a Large Data Archive," Neuroscience and Biobehavioral Reviews, 26 (2002): 907.
21. Colin Camerer, interview in Pasadena, March 12, 2004.
QUETELET'S STATISTICS AND MAXWELL'S MOLECULES
1. Isaac Asimov, Foundation and Empire, Ballantine Books, New York, 1983 (1952), p. 1.
2. Ibid., p. 112.
3. Philip Ball, "The Physical Modelling of Society: A Historical Perspective," Physica A, 314 (2002): 1.
4. Ibid., p. 7.
5. Pierre Simon Laplace, A Philosophical Essay on Probabilities, Dover, New York, 1996 (1814), p. 4.
6. Gauss was not, however, the first to devise the curve that bears his name. The French mathematician Abraham de Moivre (1667–1754) initially developed the idea in the 1730s.
7. See Frank H. Hankins, "Adolphe Quetelet as Statistician," Studies in History, Economics and Public Law, 31 (1908): 33, 18.
8. Adolphe Quetelet, Sur L'Homme et le developpement de ses facultes, ou essai de physique sociale. The philosopher Auguste Comte also coined the term "social physics" about the same time, and had his own ideas about developing a science of society. See Roger Smith, The Norton History of the Human Sciences, Norton, New York, 1997, Chapter 12.
9. Adolphe Quetelet, Preface to Treatise on Man (1842 English edition), p. 7. Available online at http://www.maps.jcu.edu.au/course/hist/stats/quet/quetpref.htm.
10. Ibid., p. 9.
11. Ibid., p. 17.
12. Ibid., p. 14.
13. Ibid., p. 12.
14. Stephen G. Brush, "Introduction," in Stephen G. Brush, ed., Kinetic Theory, Vol. I, The Nature of Gases and Heat, Pergamon Press, Oxford, 1965, p. 8.
15. Henry Thomas Buckle, History of Civilization in England, quoted in Ball, "Physical Modelling of Society," p. 10.
16. Ibid., Chapter 3, "Method Employed by Metaphysicians," pp. 119–120. Available online at http://www.perceptions.couk.com/buckle1.html.
17. Ibid., p. 120. Note also that he allowed "experiments so delicate as to isolate the phenomena," but said that could never be done with a single mind, which was always influenced by others, so that such isolation is really not possible.
18. Ibid., excerpt. Available online at http://www.d.umn.edu/~revans/PPHandouts/buckle.htm.
19. Ibid.
20. Quoted in P.M. Harman, The Natural Philosophy of James Clerk Maxwell, Cambridge University Press, Cambridge, 1998, p. 131.
21. James Clerk Maxwell, "Does the Progress of Physical Science Tend to Give Any Advantage to the Opinion of Necessity (or Determinism) over that of the Contingency of Events and the Freedom of the Will?" Reprinted in Lewis Campbell and William Garnett, The Life of James Clerk Maxwell, Macmillan and Co., London, 1882, p. 211.
22. Ignoring things like whether your opponent has a weak backhand.
BACON'S LINKS
1. www.imdb.com. There are additional actors in the database who cannot be linked to Bacon because they appeared either alone or with no other actors who had appeared in any other movies including actors connected to the mainstream acting community.
2. Similar network math was developed by Anatol Rapoport, who is better known, of course, as a game theorist.
3. Duncan Watts and Steven Strogatz, "Collective Dynamics of ‘Small-World' Networks," Nature, 393 (June 4, 1998): 440–442.
4. Steven Strogatz, interview in Quincy, Mass., May 17, 2004.
5. These three examples were chosen because of the availability of full data on their connections; at that time, C. elegans was the only example of a nervecell network that had been completely mapped (with 302 nerve cells), the Internet Movie Data Base provided information for actor-movie links, and the power grid diagram was on public record.
6. Watts and Strogatz, "Collective Dynamics," p. 441.
7. In fact, here's a news bulletin: Oracle of Bacon hasn't updated its list yet, but as of this writing its database shows that Hopper has now surpassed Rod Steiger as the most connected actor, with an average of 2.711 steps to get to another actor versus Steiger's 2.712. Of course, these numbers continue to change as new movies are made.
8. Réka Albert and Albert-László Barabási, "Emergence of Scaling in Random Networks," Science, 286 (15 October 1999): 509.
9. Jennifer Chayes, interview in Redmond, Wash., January 7, 2003.
10. Thomas Pfeiffer and Stefan Schuster, "Game-Theoretical Approaches to Studying the Evolution of Biochemical Systems," Trends in Biochemical Sciences, 30 (January 2005): 20.
11. Ibid., pp. 23–24.
12. Suppose the drivers of two cars are caught on opposite sides of a snow-drift, both wanting to get through to go home but neither wild about shoveling snow. The "cooperator" would get out of the car and shovel through the snowdrift, while the "defector" would stay warm inside the car. If both defect, no snow gets shoveled and neither gets to go home, so they both lose. If they both shovel, they get to go home with half the work required of one shoveling alone. But if one shovels the whole thing, the other gets to go home for free. Game theory math shows that each driver's best move depends on the other's: If the other guy defects, your best move is to cooperate; if the other guy cooperates, your best move is to defect. This game is mathematically the same as the hawk-dove game in evolutionary game theory.
13. F.C. Santos and J.M. Pacheco, "Scale-Free Networks Provide a Unifying Framework for the Emergence of Cooperation," Physical Review Letters, 95 (August 26, 2005). A subsequent paper by Zhi-Xi Wu and colleagues at Lanzhou University in China questions whether it is the scale-free nature of the network that is really responsible for this difference, but that's an issue for further network/game theory research. See Zhi-Xi Wu et al., "Does the Scale-Free Topology Favor the Emergence of Cooperation?" http://arxiv.org/abs/physics/0508220, Version 2, September 1, 2005.
14. Holger Ebel and Stefan Bornholdt, "Evolutionary Games and the Emergence of Complex Networks," http://arxiv.org/abs/cond-mat/0211666, November 28, 2002.
ASIMOV'S VISION
1. In Sylvia Nasar's book A Beautiful Mind, she suggests that Asimov's Foundation might have been inspired by the Rand Corporation, where Nash worked on game theory in the early 1950s. But Asimov's novel Foundation, appearing in 1951, was in fact a compilation of short stories that had begun to appear before the Rand Corporation was created in 1948. The first Foundation story appeared in 1942.
2. Serge Galam, "Sociophysics: A Personal Testimony," Physica A, 336 (2004): 50.
3. The term "econophysics" was coined by Boston University physicist H. Eugene Stanley.
4. Serge Galam, "Contrarian Deterministic Effect: The ‘Hung Elections Scenario,'" http://arxiv.org/abs/cond-mat/0307404, July 16, 2003.
5. James Clerk Maxwell, "Illustrations of the Dynamical Theory of Gases," Philosophical Magazine (1860). Reprinted in Brush, Kinetic Theory, p. 150.
6. An important point about statistical physics is that different microstates can correspond to indistinguishable macrostates. Various possible distributions of molecular speeds, for instance, can produce identical average velocities. That is one of the reasons why statistical mechani
cs is so successful. Even though it makes statistical predictions, in many cases the overwhelming number of possible microstates produce similar macrostates, so the prediction of that particular macrostate has a high probability of being accurate.
7. Katarzyna Sznajd-Weron, "Sznajd Model and Its Applications," http:// arxiv.org/abs/physics/0503239, March 31, 2005.
8. Peter Dodds and Duncan Watts, "Unusual Behavior in a Generalized Model of Contagion," Physical Review Letters, 92 (May 28, 2004).
9. Steven Strogatz, interview in Quincy, Mass., May 17, 2004.
10. Colin Camerer, Behavioral Game Theory, Princeton University Press, Princeton, N.J., 2003, p. 465.
11. Damien Challet and Yi-Cheng Zhang, "Emergence of Cooperation and Organization in an Evolutionary Game," Physica A, 246 (1997): 407–428.
12. Jenna Bednar and Scott Page, "Can Game(s) Theory Explain Culture? The Emergence of Cultural Behavior Within Multiple Games," Santa Fe Institute Working Paper 04-12-039, December 20, 2004, p. 2.
13. Ibid.
14. Ibid.
15. Ibid., pp. 2–3.
16. Doyne Farmer, Eric Smith, and Martin Shubik, "Is Economics the Next Physical Science?" Physics Today, 58 (September 2005): 37.
MEYER'S PENNY
1. David Meyer, interview in La Jolla, Calif., August 6, 2003.
2. You can find more on this explanation for the quantum penny game in Chiu Fan Lee and Neil F. Johnson, "Let the Quantum Games Begin," Physics World, October 2002.
3. David A. Meyer, "Quantum Strategies," Physical Review Letters, 82 (February 1, 1999): 1052–1055.
4. David Meyer, interview in La Jolla, Calif., August 6, 2003.
5. Lan Zhou and Le-Man Kuang, "Proposal for Optically Realizing a Quantum Game," Physics Letters A, 315 (2003): 426–430.
6. This is a key point. You cannot use entanglement to send faster-than-light messages, because you need some other channel of communication to learn the measurement of the other particle.
7. Adrian P. Flitney and Derek Abbott, "Introduction to Quantum Game Theory," http://arxiv.org/abs/quant-ph/0208069, Version 2, November 19, 2002, p. 2.
8. Kay-Yut Chen, Tad Hogg, and Raymond Beausoleil, "A Practical Quantum Mechanism for the Public Goods Game," http://arXiv.org/abs/quant-ph/0301013, January 6, 2003, p. 1.
9. Azhar Iqbal, "Impact of Entanglement on the Game-Theoretical Concept of Evolutionary Stability," http://arXiv.org/abs/quant-ph/0508152, August 21, 2005.
PASCAL'S WAGER
1. E.T. Bell, Men of Mathematics, Simon & Schuster, New York, 1937, p. 73.
2. Blaise Pascal, Pensées. Trans. W.F. Trotter, Section III. Available online at http://textfiles.com/etext/NONFICTION/pascal-pensees-569.txt.
3. Laplace, a later pioneer of probability theory, did not find Pascal's argument very convincing. Mathematically it reduces to the suggestion that faith in a God that exists promises an infinite number of happy lives. However small the probability that God exists, multiplying it by infinity gives an infinite answer. Laplace asserts that the promise of infinite happiness is an exaggeration, literally "beyond all limits." "This exaggeration itself enfeebles the probability of their testimony to the point of rendering it infinitely small or zero," Laplace comments. Working out the math, he finds that multiplying the infinite happiness by the infinitely small probability cancels out the infinite happiness, "which destroys the argument of Pascal." See Laplace, Philosophical Essay, pp. 121–122.
4. David H. Wolpert, "Information Theory—The Bridge Connecting Bounded Rational Game Theory and Statistical Physics," http://arxiv.org/abs/cond-mat/0402508, February 19, 2004.
5. David Wolpert, interview in Quincy, Mass., May 18, 2004.
6. Wolpert, "Information Theory," pp. 1, 2.
7. E.T. Jaynes, "Information Theory and Statistical Mechanics," Physical Review, 106 (May 15, 1957): 620–630.
8. If you're flipping a coin, of course, the two possibilities (heads and tails) would appear to be equally probable (although you might want to examine the coin to make sure it wasn't weighted in some odd way). In that case, the equal probability assumption seems warranted. But it's not so obviously a good assumption in other cases. I remember a situation many years ago when a media furor was created over a shadow on Mars that looked a little bit like a face. Some scientists actually managed to get a paper published contending that the shadow's features were not random but actually appeared to have been constructed to look like a face! I argued against putting the picture on the front page of the paper, insisting that the probability of its being a real face (or a representation of a face) was minuscule. But a deputy managing editor replied that either it was or it wasn't, so the odds were 50-50! I hoped he was kidding, but decided it would be wiser not to ask.
9. Jaynes, "Information Theory," pp. 620, 621.
10. This is, of course, the basis for teachers grading on a "curve," the bell-shaped curve or Gaussian distribution that represents equal probability of all the microstates.
11. David Wolpert, interview at NASA Ames Research Center, July 18, 2005.
12. Ibid.
13. Another decision-theory system was worked out by the statistician Abraham Wald, but the story of the similarities and differences between Wald's and Savage's approaches goes far beyond the scope of this discussion. If you're interested, you might want to consult a paper exploring some of these issues: Nicola Giocoli, "Savage vs. Wald: Was Bayesian Decision Theory the Only Available Alternative for Postwar Economics?" Available online at http://www.unipa.it/aispe/papers/Giocoli.doc.
14. David Wolpert, interview at NASA Ames Research Center, July 18, 2005.
15. Strictly speaking, it's not the temperature of an individual, it's the temperature that the external scientist assigns to the individual, Wolpert points out. Just like in statistical physics, the temperature is a measure of what the external scientists infer concerning the molecules in a room (since a single molecule doesn't have any particular temperature—temperature is a property of the distribution of velocities of a set of molecules).
16. Wolpert, interview at NASA Ames, July 18, 2005.
EPILOGUE
1. Orson Scott Card, Ender's Game, TOR, New York, 1991, p. 125. Thanks to my niece Marguerite Shaffer for calling Ender's Game to my attention.
2. Ibid. p. 238.
3. Joshua Greene, interview in San Francisco, Calif., April 17, 2004.
* * *
Index
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This strategy retains the full value of the academic Index, and presents the relative positions and distribution of Index references within this book. The Index Page Numbers are hyperlink pointers and have no relationship to the Mobipocket Reader soft-generated page numbers.
A
A Beautiful Mind (Nasar), vi, 2, 54, 246
A Few Good Men (film), 144, 145
Abbott, Derek, 193
Aché (Paraguay), 116–117
Adventures of Sherlock Holmes, 34
Age of Reason, 9, 12
Agricultural policy, 16
Al Qaeda, v
Albert, Réka, 156, 157, 160
Alexander, Richard, 86
AltaVista, 158