path: root/neumann_weiner_review.otx

\chap Book Review: \booktitle{John von Neumann and Norbert Weiner: From Mathematics to the Technologies of Life and Death} (Steve J. Heims, The MIT Press)

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by David Finkelstein\par} 

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Childlike, greedy, flowering with mathematical beauty, they are heroic figures of twentieth century mathematics. This major dual biography treats of their mathematics, their Jewish roots, and the influence they exerted through the applications of their work, ranging widely through mathematics, physics, armaments, neuroscience, and philosophy. 

Why a dual biography? Perhaps because the crossings and partings of their lifelines show their individualities better than a single biography would. And certainly because Heims wants to contrast the two men to make his point. The book has an agenda. His narrative and his quotations from their works and conversations work towards that agenda. Again and again, to be blunt, Heims tells us that Wiener keeps the faith, von Neumann sells out.

This view comes as a shock to me. I too have made choices between Wiener and von Neumann, and when matters of science were involved I usually chose von Neumann. 

The first such decision occurred in my first year or two of college. The texts I found on quantum mechanics were sheer walls without fingerholds for my understanding, even after I learned from them how to solve elementary problems. After weeks of frustration I was overjoyed when I chanced on von Neumann's paper with Garrett Birkhoff, \essaytitle{The Logic of Quantum Mechanics,} where quantum evolution is ascribed---reduced, some would say; elevated, I felt---to an evolution in the laws of logic. Einstein drops one of Euclid's postulates. Bohr, says von Neumann, drops one of Boole's. Sitting in the high-ceilinged college library---long since razed and replaced---I formed a joyous surmise: perhaps my job was to explore the physics of these new logics. I resolved I would emulate Einstein's exploration of the physics of the new geometries. Armed with Langenscheidt's German-English dictionary, I fought slowly through the dense German of von Neumann's book on quantum mechanics, rejoicing whenever I arrived at a comprehensible paragraph. 

I saw Wiener at a distance and met his thinking more closely when I reached graduate school. Walter Harry Pius, his research associate and protégé, a figure in this book, lightened those heavy years for me more than any other faculty member. I met Pitts when I took his course in the mathematics of quantum theory. When he hit a snag on the blackboard, he would reach over the top of his head with his right hand and scratch his left temple as he puzzled. We walked miles along the Atlantic shore, he sampling the shellfish and explaining their functioning as we walked. Sometimes he cooked a dish for my wife and me in our one-room apartment on Beacon Street. Years later, not long before his death, I tracked him down to a dim cafe he frequented in Harvard Square, to thank him and re-establish contact. He sat alone reading, frail and withdrawn. Pitts did not remember me, and when I said my piece and left him to his book, he seemed relieved. I have not studied his neural nets in years but I still use his recipe for fried spinach. I wish Heims had captured his engaging personality.

Wiener thought differently about quantum theory than von Neumann. For Wiener, quantum jumps were like the dance of shining dust motes in a sunbeam that, I recall, held me for hours when I was a child, as I tried to catch a scintillation between thumb and slowly, slowly descending forefinger, always in vain. This dance is called Brownian motion. His probability methods worked for Brownian motion, and Wiener felt they would work for quantum jumps. The seeming randomness of Brownian motion is not basic but results from many variables hidden from our perception, particularly the atoms surrounding the dancers. Wiener was convinced the randomness of quantum theory too would result from hidden variables. 

Wiener's conviction must have been only strengthened by the viciously circular but widely quoted proof of von Neumann, that hidden variables could not account for quantum incompleteness. This famous proof is given in von Neumann's book on quantum theory, and shows that knowing as much as quantum theory allows about the past always leaves some (in fact most) questions about the future unanswered. It does not address the question that interested Wiener. What if one knew more than quantum theory allows? 

Acting on his conviction, Wiener buttonholed prominent physicists at MIT and forced them to consider hypothetical transgressions of the laws of quantum theory. They took these laws for granted, in the way a shoemaker takes his awl for granted, and Wiener kept them from their proper work. Desperate, they decided to sacrifice a maiden to the Minotaur. A physics graduate student might sate Wiener's appetite for physics and buy them peace. Clearly the transaction would benefit all involved, especially the graduate student. 

The possibility of working with the celebrated Wiener was tempting but I did not apply. Today I can say why more clearly. My inaction might be called a choice between Wiener and von Neumann, and has to do with quantum theory and the celebrated Einstein-Bohr dialogue. 

In their dialogue, Einstein and Bohr agree at the outset that quantum theory does not predict our future experiences from our past ones, and in that sense is \e{incomplete}, but disagree about whether such an incomplete theory may be the most informative that is possible, and in that sense may be \e{maximal}. Einstein, here playing the role of classical thinker, laments that the theory is poorer than nature. Bohr, the modern existentialist, is content that nature is richer than our theories. Einstein repeatedly attacks, Bohr successfully defends, the internal consistency of quantum theory.

I felt with Einstein and Wiener that quantum theory had to he replaced, but also that first, one had to grasp the new thing it brought into physics, and preserve that. Now the new thing about quantum theory is not incompleteness, its failure to make exact predictions. Classical Brownian motion shares that as Wiener noted. It is that while previous theories, including Einstein's relativity, dealt with uninvolved objectivity, quantum theory dealt with involvement. Incompleteness is only one aspect, a negative one, of involvement. This was expressed in various forms by Bohr (for whom the observation of a quantum phenomenon was part of the phenomenon observed), by Dirac (who formulated mathematically a generalized relativity principle for quantum theory, his transformation theory), and by von Neumann (whose expression was the most abstract and mathematically complete). Involvement leads to an extension of relativity from the categories of time and space to those of logic. The descriptors meaningful for a quantum system depend on its context in a way that is explicitly denied in classical Aristotelian logic. Einstein allowed for changes in our description of facts with changes in our relation to the system observed, but Bohr allowed for changes in the very totality of accessible facts. 

An artist walks around a model, tries one perspective, another, then returns to the first. Nothing seems to have changed. With each relation between artist and model goes a portrayal of the model. As soon as one artist leaves a perspective another can assume it. Many artists can use the same model, with little interference. Einstein's theory deals with this kind of objective relation between observer and observed. 

The next day the artist comes nearer, perhaps to study sheen and texture. One thing leads to another. In brief, the artist seduces and is seduced by the model. If we insist, we may say the artist has a new perspective, but it is better to say the two have become involved. This change of relation is not undone or shared as easily as a change in perspective. Quantum theory is a theory of involvement. 

Einstein never bought this extension of Einstein relativity by Bohr, from time and space to logic itself. Einstein never considered quantum jumps basic; he thought they were determined by a nonlinear unitary field theory, like catastrophes in the sense of mathematician Rene Thom. Wiener did not think quantum jumps were basic; he thought they were determined by hidden variables. 

But Heims sees it otherwise: He notes that Wiener described quantum theory dialectically, as a Hegelian synthesis of particle thesis and wave antithesis. He points out that von Neumann regarded the interface between the observer and his instruments as classical in its nature, so that the readings by the observer could be regarded as objective. 

Heims is accurate on both points and both are irrelevant. Dialectical materialism, curiously, is often linked with uncritical faith in absolutist theories like Newton's mechanics and Aristotle's logic. (See Engels on Newton's mechanics.) The philosopher who will pit his philosophy against the current physics is rare and rarely right. (But see Blake and Bergson on Newton's mechanics.) 

And the critical interface is not that between observer and instrument mentioned by Heims, who has misleadingly isolated part of von Neumann's discussion of measurement in terms of a tripartite observer $+$ instrument $+$ atom system. It is not \e{that} interface, which had better be classical, but the one between instrument and atom where quantum effects control. Von Neumann treated both interfaces correctly enough. 

We may prefer Wiener's ethics, but we should respect von Neumann's quantum theory. With all its defects (and Heims mentions the greatest: the assumed simultaneity of the measurement process, a discord with relativity) it has worked best for over half of a dynamic century, without any change at all. The latest speculations on the color and flavor of quarks still trim themselves to the Procrustean bed of von Neumann. It seems to me that Heims actually interchanges the attitudes to quantum theory of Wiener and von Neumann, when he finds Wiener radical and von Neumann conservative on that subject. 

Heims also considers von Neumann formalistic. He finds von Neumann cared less about the meaning of his axioms than about their mathematical form. This does not make sense to me. For example, von Neumann's axioms for set theory, and likewise his axioms for a cellular automation,\ednote{Automaton?} are ugly and clumsy, though seminal and famous, because in them he tried to express something that other mathematicians were not to take up for decades. In his set theory, dissatisfied with the static idea of the set, he attempted to take as basic instead the more processual idea of the transformation or mapping, at whatever cost in elegance of form. His abortive attempt prefigures the modern work in category algebra. Von Neumann never went to the operational meanings behind his symbols in the way characteristic, say, of the young Einstein; few ever do. Nevertheless, von Neumann exceeds the patience of most of his physicist readers in his treatments of epistemological questions of meaning and measurement. He left his personal mark on all the domains of applied mathematics, and became a master at the use of mathematics as a language with meaningful content. 

This makes his errors the more conspicuous. He as much as anyone introduced the concept of the collapsing state into quantum theory, and this concept is inconsistent with his own recognition that individual quantum systems have no state. There is a subtle trap---call it symbolatry for short---sometimes concealed by beautiful mathematics, the implicit and therefore incontrollable assumption that there is a natural isomorphism, emotionally an identity, between symbols and actuality. Sometimes as here von Neumann falls into this trap, as Heims notes. Pioneering has its hazards. It takes much longer to forget an old language than to learn a new one. 

The end of this dialogue is not yet in sight. There may well be a point of view that reconciles the discordant views of Einstein (and Wiener) with Bohr (and von Neumann). If we compare them with the assertions of quantum theory---not the objective ones of classical mechanics, but the self-referential ones, the hard line between the two kinds of theory begins to soften. 

Self-reference would be one of the major mathematical motifs of the century if no one but Gödel had played on it, but it permeates the mathematics of Wiener and von Neumann too, with a characteristic difference. For Wiener, self-reference took the form of self-regulation, for von Neumann, self-replication. Thus Wiener was led to invent cybernetics, a theory of communication, control and self-regulation in animal and machine, to make his actions and those of other scientists matters of conscience, and to decline power. Von Neumann, on the other hand, developed a theory of reproductive automata that foreshadows remarkably the actual genetic mechanism, assisted mightily with the automatic computations for nuclear bombs, and entered the circle of the power elite. The narrowness of his understanding and concern is measured by his statement (with Morgenstern) that \dq{the typical problems of economic behavior become strictly identical with the mathematical notions of suitable games of strategy}---another plunge into the same trap of symbolatry. 

Heims is concerned with mathematics and physics mainly as background to the actions of his people in and after World War II. (He calls that war a watershed, but surely he means a divide.) Wiener works at MIT on defense against air attack; von Neumann works at Los Alamos on the nuclear bomb. Both find their tasks require them to develop precisely the kind of mathematical structures they most love, integral differential equations for Wiener, logic systems for von Neumann. Wiener involves himself in protest against the Nagasaki massacre, considers never publishing again to avoid abuse of his work. Von Neumann separates himself even from the \journaltitle{Bulletin of Atomic Scientists,} a mildly anti-military voice, rejecting two invitations.

Von Neumann, with his middle-European Jewish origins, was alert to the danger of Hitler and Stalin before most of us, just as he was more conscious than most of us of the inadequacy of the computer as a model for the brain or the world, thanks to his involvement with such machines. I suppose that for him it would have been the greatest immorality not to arm the United States to the teeth. 

Heims regards von Neumann's haste to build bombs and super-bombs, computers and supercomputers, as another case of the widespread faith in the machine, the epidemic addiction to the technological fix. The trap of a superstitious belief in hardware---technolatry?---sits right beside the trap we have already noticed, which might be called a superstitious belief in software, and both wait for anyone who identifies the world with a computer, as the very analysis into hardware and software requires. 

Heims' agenda surfaces in the epilogue. Like Noah, he does not take the continued survival of civilization for granted. Perhaps he sees that all nations have access to nuclear explosives limited only by budget (and an occasional Israeli sortie); that today cities are held up for ransom as yesterday airplanes were, and tomorrow nations will be; that biological weapons are or will soon be less controllable,\ednote{In light of this surpisingly adept insight, I invite the reader to look into Critical Art Ensemble's study of germ (biological) warfare, \booktitle{Marching Plague}.} cheaper, more insidious, and deadlier than nuclear. Heims' main concern is how we are to survive this evolution of our technology of death. His agenda consists of actions for such survival. 

The Los Alamos team were as much slaves as masters of the nuclear genie. They could not keep him in his bottle forever, they could only help him out. Had only they exerted a wiser influence over the time and place of his dreadful emergence! Heims draws from their success and failure conclusions on how to fight against repetitions of that history. Action groups, a concern for wholeness, whistle-blowing---he pulls together many of the most hopeful developments of the last two decades. We are baby scorpions in a bottle and our stings are growing. If we survive long enough to escape our bottle, we must evolve into a community, and soon.

There is an element of irony in their deaths. The mathematician of self-regulation died of heart failure. The mathematician of self-replication died of cancer. From their lives Heins has made controversial and provocative ammunition for the movement for a viable world. He has deepened and shifted my perception of Wiener and von Neumann. He has made fresh the old dictum that intellect when divided front bean and soul and body breeds monsters.