The Quantum Pontiff

ACM Classic Books

Via Michael Nielsen’s friendfeed, I am led to ACM Classic Books Series. If you’ve got ACM subscription access, some of the book are even in electronic form. Cool. I love the introduction to “The Computer and the Brain” by John von Neumann:

Since I am neither a neurologist nor a psychiatrist, but a mathematician, the work that follows requires some explanation and justification. It is an approach toward the understanding of the nervous system from the mathematician’s point of view. However, this statement must immediately be qualified in both of its essential parts.

I feel like I need to use an intro like this everytime I submit a paper to a computer science conference.


  1. #1 John Sidles
    December 5, 2008

    Thanks for this post, Dave!

    After the stress of finishing (yet another) proposal … few things in life are as deeply satisfying as laying in bed … eating cake frosting from a can … and reading the Quantum Pontiff!

    The linked-to Preface to von Neumann’s book, which was written by Klara von Neumann after his death, was too poignant for comfortable reading, though.

    From my perspective, von Neumann’s work exemplifies the radical style of science, which seeks not only to conceive new theorems and discover new physical laws, but also to construct narratives that make sense of those theorems and laws.

    That von Neumann would knowingly devote the last months of his life to constructing such a narrative—while suffering from end-stage metastatic osteosarcoma, which is among the most painful of all fatal diseases—is a tribute both to von Neumann’s commitment and to the power of narrative as a binding agent for mathematics and science.

    It would have made me feel happier … a little less out of von Neumann’s league … if Klara’s preface had concluded “and Johnny wrote the whole thing in bed, in the early morning hours, while eating cake frosting from a can.”

  2. #2 David
    December 5, 2008

    I feel like I need to use an intro like this everytime I submit a paper to a computer science conference.

    Since I am neither a computer nor a scientist …

    I read “Who Got Einstein’s Office” a couple of years ago. It’s a history of the IAS. Of all the people in that book, I wish I could have a day with Johnny.

  3. #3 Jonathan Vos Post
    December 6, 2008

    When I search on “von neumann” in my own gmail, I uncover lots. But this one might be right for this blog (see item 12 below).

    My coauthor prof. Philip V. Fellman emails me:

    “‘The why of the applicability of Statistical Physics to
    Economics’ by Esteban Guevara Hidalgo. To me this
    looks like just a fancified, highly annoted and
    referenced version of the quantum sillines off Jim
    Hazy et al. I found the characterization of the Nash
    equilibrium particularly inaccurate and inapt making
    me seriously doubt if this guy has any slightest clue
    about the real NE or has even read Nash’s dissertation
    (unfortunately, I always think that is the only
    reasonable starting point for research on the Nash

    “Also, I had not previously known that either
    altruism or a ‘Collective welfare principle’ were
    elements of qm or qft. Let me know what you think
    after you have a chance to look at this.”

    “I came across this because I was trying to figure
    out whether a business article that one of my doctoral
    students Sharon Mertz (research director at Gartner,
    the big software analysis firm), and my colleague Nick
    Nugent and I did at ICCS 7 belongs in the arXiv or
    should be left to more purely business publications.”

    So I replied:

    I don’t believe Esteban Guevara Hidalgo either.

    (1) The thin air of Quito, Ecuador has given him anoxia.

    (2) How silly to START with Econophysics, as if it is given that this is a validly founded discipline.

    (3) “Could economics and statistical physics be correlated?” as if they are both random, and one only wonders if they are independent or not.

    (4) Fluctuations, economic earthquakes, and turbulence all mentioned on p.1 as if equivalent. Begs the question, cubed.

    (5) Invokes entropy with out specifying WHICH entropy.

    (6) p.2: “In this paper we try to obtain a deeper relationship between quantum mechanics and game theory…” Deeper than whose theories? Are the experts all more shallow than the Quester of Quito?

    (7) “An ESS [Evolutionarily Stable Strategy] is also a Nash
    equilibrium since is [sic] the best reply to itself..” Huh?

    (8) “Quantum games have proposed a new point of view…” And my Monopoly board and chess table have made some good suggestions, too.

    (9) He does not BEGIN to indicate the alternative models available of Natural Selection (p.3) and I don’t think he knows why he picked the one he did, nor how it works. Santa Fe Institute folks are not so naive.

    (10) On the other hand, looking for a [Peter] Lax representation of the replicator dynamics is a good idea. Lax went to Stuyvesant High School, long before me, by the way.

    (11) table 1, p.3, gets to the heart of his “theory.” The
    correspondances are far less exact than he pretends. It’s what he wants to be true.

    (12) Then he invokes Saint Schrodinger and Saint von Neumann, with no clue as to the *-algebras that von Neumann invented to generalize QM, and what we’ve learned about them especially in the last 15 years.

    (13) table 2 and table 3 “Although both systems are different, both are analogous and thus exactly equivalents.” Huh? This is where I’d find a refutation, if I were more awake.

    (14) “Through these relationships, we could describe classic, evolutionary, and quantum games, and also the biological systems…” We could, could we? But we do not. Proof by desire.

    (15) p.5: Shannon. Boltzman, von Neumann: gentlemen, I suppose you’re wondering why I called you here today.

    (16) Chaotic dynamics go through 3 stages. Huh?

    (17) Now he brings in the “referee” with no explanation of how the referee can be entangled with a player, or player with player, or multiple referees. Deep stuff swept under the rug.

    (18) “We can made [sic] certain ‘measurement’, experiment or ‘trick’ to determine which the state of the player is.” Then invokes Sanov [cf. "A Quantum Version of Sanov's Theorem", Bjelaković, Igor; Deuschel, Jean-Dominique; Kr�ger, Tyll; Seiler, Ruedi; Siegmund-Schultze, Rainer; Szkoła, Arleta, Communications in Mathematical Physics, Volume 260, Issue 3, pp.659-671]
    Abstract: We present a quantum version of Sanov’s theorem focussing on a hypothesis testing aspect of the theorem: There exists a sequence of typical subspaces for a given set Ψ of stationary quantum product states asymptotically separating them from another fixed stationary product
    state. Analogously to the classical case, the separating rate on a logarithmic scale is equal to the infimum of the quantum relative entropy with respect to the quantum reference state over the set Ψ.
    While in the classical case the separating subsets can be chosen universally, in the sense that they depend only on the chosen set of i.i.d. processes, in the quantum case the choice of the separating subspaces depends additionally on the reference state.

    (19) p.6 I don’t see where he gets the Collective Welfare Principle, as I don’t believe his thermodynamics, nor do I buy his description of this as “tacit rules” and then uses semantically loaded political vocabulary.

    (20) p.6 “Quantum Mechnics could be a much more general theory that [sic] we had thought…. must be… must be… must be….” Oh, yeah?

    (21) p.7 “It is important to remember that we are dealing with very general and unspecific terms, definitions and concepts like state, game and system.” His job is to make these definitions specific, and not make vague analogies disguised with falsely specific equations.

    (22) Temperature is in here again, never convincingly the first time. Admits he doesn’t know what it means in this context.

    (23) “Entropy can be defined… different contrains [sic]. See (5), above.

    (24) His “conclusions” merely reiterate his unsubtantiated claims.

    “By analyzing the relationships between a socioeconomical system modeled through evolutionary game theory and a physical system modeled through quantum mechanics we show how although both systems are described through two theories apparently different both are analogous and thus exactly equivalents. The extensions of quantum mechanics to
    statistical physics and information theory let us use some of their definitions for the best understanding of the behavior of economics and biology. The quantum analogue of the replicator dynamics is the von Neumann equation. A system in where all its members are in Nash equilibrium is equivalent to a system in a maximum entropy state.
    Nature is a game in where its players compete for a common welfare and the equilibrium of the system that they are members. They act as a whole besides individuals like they obey a rule in where they prefer to work for the welfare of the collective besides the individual welfare.”

    (25) The final flare of crackpottery comes in the last sentence:
    “Also, we could maybe understand nature like a game in where its players compete for a common welfare and the equilibrium of the system that they are members.” Wooo!

    Let me first give [an excerpt from] a Huxley essay from 139 years ago, that greatly moved me as a child, which says so much more than this dubious arXiv paper…

    The excerpt that grabbed me as a child:

    “The chess board is the world, the pieces the phenomena of the universe, the rules of the game are what we call the laws of nature. The player on the other side is hidden from us. All we know is that his play is always fair, just and patient. But, also, that he never overlooks a mistake or makes the smallest allowance for ignorance.”
    Professor Huxley’s Hidden Chess Player
    by R. H. Hutton
    The Spectator; January 11, 1868