Hey guys:

What is the difference between physics and mathematics anyway?

There may be a mathematical unification through economics which might be liberally interpreted as a continuous transformation of quanta transactions.

The quanta may be monetary, biologic, energy, etc.

This [mathematics of game theory] has been a rich field for economists and engineers, the latter using applied physical mathematics.

]]>(Read that ‘very impressive’ in a sarcastic tone of voice, please.)

However, I’m just a disbeliever because I’ve some experience of how groupthink damages freedom and creativity in physics. Maybe, because maths isn’t full of petty dictators, it benefits more from things like social networks and interactions, without groupthink leading to mass insanity as in physics areas like string theory.

]]>Thanks, Doug. And I suppose my interpretation sits somewhere between your biological one and a purely mathematical one. Someday we will get Games in there, when surreal numbers and zeta functions find their place in higher categorical number theory.

Re the article itself: it’s simply beyond belief how Connes moves about the whole of mathematics, from zeta functions to Langlands to Motives to KK theory to NCG to physics. I cannot imagine ever understanding more than a tiny fraction of the definitions in these subjects, let alone calculating in them.

]]>I tend to agree with the AC quote of this thread.

However, one of your oldest companions adds an interpretive twist.

AC, from my perspective, is giving a verbal description of pursuit-evasion games [PEG] with an equilibrium condition of “stable strategy” to “… survive as a whole …” whether as multiple entities playing in markets, biology, mechanics, etc.

References:

New:

Evolution and the Theory of Games: John Maynard Smith, Evolutionarily Stable Strategy

http://en.wikipedia.org/wiki/Evolution_and_the_Theory_of_Games

Evolutionary Game Theory: 2. Two Approaches to Evolutionary Game Theory

… first approach, consider the problem of the Hawk-Dove game, analyzed by Maynard Smith and Price in “The Logic of Animal Conflict … [PEG] …

… second approach, consider the well-known Prisoner’s Dilemma.

http://plato.stanford.edu/entries/game-evolutionary/

Vidal, Shakernia, Kim, Shim and Sastry, “Probabilistic Pursuit-Evasion Games: Theory, Implementation and Experimental Evaluation”, IEEE. Transactions on Robotics and Automation, 2002, looking at local-max and global-max.

http://cis.jhu.edu/~rvidal/publications/tra01-final.pdf

Old:

Tamer Basar and Geert Jan Olsder, “Dynamic Noncooperative Game Theory (Classics in Applied Mathematics)”, [SCIAM], textbook

Bernd Heidergott, Geert Jan Olsder and Jacob van der Woude, “Max Plus at Work: Modeling and Analysis of Synchronized Systems: A Course on Max-Plus Algebra and Its Applications (Princeton Series in Applied Mathematics) “ textbook

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