Quote of the Week

… the corpus of mathematics does resemble a biological entity which can only survive as a whole and would perish if separated into disjoint pieces.

Alain Connes

7 Responses so far »

  1. 1

    Doug said,

    Hi Kea,

    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

  2. 2

    Kea said,

    giving a verbal description of pursuit-evasion games [PEG]

    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.

  3. 3

    nige said,

    Surely mathematics is already separated into lots of pieces, called specializations. If Alain Connes claims that every mathematician knows the whole of mathematics and that disciplines within mathematics are as interdependent as you’re claiming, that’s very impressive!

    (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.

  4. 4

    Doug said,

    Hi Kea and nige,

    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.

  5. 5

    CarlBrannen said,

    I think that Connes’ statement on mathematics is more applicable to physics. Mathematicians are fermions, they can get along just fine without each other. Physicists are bosons that stick together in a biological manner.

  6. 6

    Mahndisa S. Rigmaiden said,

    06 10 07

    Hey guys:
    What is the difference between physics and mathematics anyway?

  7. 7

    Kea said,

    Hi Mahndisa! Good to see you. I agree with your sentiment, but in the context of M theory one should probably be careful to differentiate between the mathematical reality of the cosmos and the practising of mathematics by internal observers doing physical research.


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