His Master's Voice (2 page)

An autobiography that begins by listing cowardice, malice, and pride as the foundations of one's psyche entails, from the deterministic point of view, a logical error. If one says that everything in us is predetermined, then predetermined also must have been my resistance to my inner meanness, and the difference between me and other, better people is then reduced to nothing but a variation in the localized source of the behavior. What those better people did voluntarily, at little cost, for they but followed their own natural inclination, I practiced in opposition to mine—hence, as it were, artificially. Yet since it was I who dictated conduct to myself, I was, in the overall balance—in this formulation—nevertheless predestined to be as good as gold. Like Demosthenes with the pebbles in his stammering mouth, I put iron deep in my soul, to straighten it.

But it is precisely in this equalizing that determinism reveals its absurdity. A phonograph record of angelic singing is not an iota better morally than one that reproduces, when played, a scream of murder. According to determinism, he who desired and was able to be better was no more or less fated beforehand than he who desired but was unable, or than he who did not even attempt to desire. This is a false image, for the sound of battle played on a record is not an actual battle. Knowing what it cost me, I can say that my struggle to be good was no semblance. Determinism simply deals with something altogether different; the forces that operate according to the calculus of physics have nothing whatever to do with the matter—just as a crime is not made innocent by its translation into the language of amplitudes of atomic probabilities.

About one thing Yowitt is definitely right: I always sought difficulty. Opportunities for me to give free rein to my natural malice I usually forwent, as too easy. It may sound strange, or even nonsensical, but I did not suppress my inclination to evil with my eyes fixed on the Good as a higher value; rather, I suppressed it for the precise reason that I felt so powerfully its presence in me. What counted for me was the calculus of resistance, which had nothing in common with the arithmetic of morality. Therefore I really cannot say what would have become of me had the principal trait of my nature been the inclination to do only good. As usual, reasoning that attempts to picture ourselves in a form other than what is given breaks the rules of logic and must quickly founder.

Once only did I not eschew evil; that memory is connected with the protracted and horrible death of my mother. I loved her, yet at the same time I followed with an unusually keen and avid attention the process of her destruction in the illness. I was nine then. She, the personification of tranquillity, of strength, of a composure almost sovereign, lay in a lingering agony, an agony prolonged by the doctors. I, at her side in the darkened bedroom filled with the stink of medicine, still kept a grip on myself; but when I left her, as soon as I had shut the door behind me and found myself alone, I stuck out my tongue joyfully in the direction of her bed, and, that being insufficient, ran to my room and breathlessly jumped up and down in front of the mirror, fists clenched, making faces and giggling with delight. With delight? I understood perfectly that my mother was dying; since that morning I had fallen into despair, and the despair was as real as my stifled giggling. I remember how the giggling frightened me, yet at the same time it took me beyond everything I had known, and in that transgression there was a dazzling revelation.

That night, lying alone, I tried to comprehend what had taken place; unable to do this, I worked up a befitting pity for myself and my mother, and tears flowed until I fell asleep. I considered these tears to be an expiation; but then, later, the whole thing repeated itself, when I overheard the doctors conveying worse and worse news to my father. I dared not go up to my room; deliberately I sought the company of others. Thus the first person I ever shrank from was myself.

After my mother's death I gave myself up to a child's despair that was untroubled by any qualms. The fascination ended with her last breath. With her died my anxiety. This incident is so confusing that I can only offer a hypothesis. I had witnessed the fall of the Absolute—it had been shown to be an illusion—and witnessed a shameful, obscene struggle, because in it Perfection had come apart like the most miserable rag. This was the trampling of life's Order, and although people above me supplied the repertoire of that Order with special evasions even for so dismal an occasion, these additions failed to fit what had happened. One cannot, with dignity, with grace, howl in pain—any more than one can in ecstasy. In the messiness of loss I sensed a truth. Perhaps I saw, in that which disrupted, the stronger side, and so sided with that side, because it had the upper hand.

My hidden laughter had no connection with the actual suffering of my mother. I only feared that suffering; it was the unavoidable concomitant of the expiring—that I could understand, and I would have delivered her from the pain had I been able. I desired neither her suffering nor her death. At a real murderer I would have thrown myself with tears and pleas, like any child, but since there was none, I could only absorb the cruel treachery of the blow. Her body, bloated, turned into a monstrous, mocking caricature of itself, and it writhed in that mockery. I had only one choice: either to be destroyed with her or to jeer at her. As a coward, then, I chose the laughter of betrayal.

I cannot say whether it really was this way. The first paroxysm of giggling seized me at the sight of the destruction; perhaps the experience would have skipped me had my mother met her end in a fashion more aesthetic, like quietly falling asleep, a form that is much favored by people. It was not like that, however, and, forced to believe my own eyes, I proved defenseless. In earlier times a chorus of hired mourners, brought in quickly, would have drowned out the groans of my mother. But the decline of tradition has reduced magical measures to the level of hairdressing, because the undertaker—and I overheard this—suggested to my father the various facial expressions into which her frozen grimace could be reworked. My father left the room then, and for a brief moment I felt a tremor of solidarity, because I understood him. Later I thought of that mortal agony many times.

The idea of my laughter as a betrayal seems incomplete. Betrayal is the result of conscious decision, but what causes us to be drawn to destruction? What black hope, in destruction, beckons man? Its utter inutility rules out any rational explanation. This hunger has been suppressed in vain by numerous civilizations. It is as irrevocably a part of us as two-leggedness. To him who seeks a reason but cannot abide any hypothesis of a design, whether in the form of Providence or of the Diabolical, there remains only the rationalist's substitute for demonology—statistics. Thus it is from a darkened room filled with the smell of corruption that the trail leads to my mathematical anthropogenesis. With the formulae of stochastics I strove to undo the evil spell. But this, too, is only conjecture, therefore a self-defensive reflex of the mind.

I know that what I am writing here could be, with slight shifts in emphasis, turned to my favor—and that some future biographer will try to do this. He will show that with intellect I conquered my character, achieved a great victory, but defamed myself out of a desire to do penance. Such labor follows in the steps of Freud, who has become the Ptolemy of psychology, for now, with him, anyone can explain human phenomena, raising epicycles upon epicycles: that construction speaks to us, because it is aesthetic. He converted the pastoral model into one that was grotesque, unaware that he remained a prisoner of aesthetics. It was as if the purpose had been to replace the opera, in anthropology, with tragicomedy.

Let my posthumous biographer not trouble himself. I require no apologia; all my effort was born of curiosity, untouched by any feeling of guilt. I wanted to understand—only to understand, nothing more. For the disinterestedness of evil is the only support, in man, for the theological argument; theology answers the question where does a quality come from that has its origin neither in nature nor in culture. A mind immersed totally in the human experience, and therefore anthropocentric, might finally agree with the image of Creation as a somewhat sick joke.

It is an attractive idea, that of a Creator who merely amused Himself, but here we enter into a vicious circle: we imagine Him sadistic not because He made us that way, but because we are ourselves that way. Meanwhile the utter insignificance and smallness of man vis-à-vis the Universe, of which science informs us, makes the Manichean myth a concept so primitive as to be trivial. I will put it in another way: if a creation were to take place—which personally I cannot conceive—then the level of knowledge that it would require would be of such an order that there would be no place in it for silly jokes. Because—and this really is the whole credo of my faith—nothing like the wisdom of
evil
is possible. My reason tells me that a creator cannot be a petty scoundrel, a conjurer who toys ironically with what he has brought into being. What we hold to be the result of a malign intervention could only make sense as an ordinary miscalculation, as an error, but now we find ourselves in the realm of nonexistent theologies—that is, theologies of fallible gods. But the domain of their constructional practices is nothing other than the field of my lifework, i.e, statistics.

Every child unwittingly makes the discoveries from which have sprung the worlds of Gibbs and Boltzmann, because to a child reality appears as a multitude of possibilities, where each can be taken separately and developed so easily that it seems almost spontaneous. A child is surrounded by a great many virtual worlds; completely alien to him is the cosmos of Pascal, a rigid corpse with even, clocklike movements. The ossified order of maturity later destroys that primal richness. If this picture of childhood seems one-sided, for example, in that the child owes his inner freedom to ignorance and not choice—well, but every picture is one-sided. With the demise of imagination I inherited its residue, a kind of permanent disagreement with reality, more like an anger, though, than a rejection. My laughter had already been a denial, and a more effective kind, perhaps, than suicide. I acknowledge it, at the age of sixty-two; and the mathematics was only a later consequence of this attitude. Mathematics was my second desertion.

I speak metaphorically—but hear me out. I had betrayed my dying mother, betrayed all people, opting, with the laughter, for a thing of power greater than theirs, however hideous it was, because I saw no other way out. Later I would learn that this enemy of ours—which was everything, which had built its nest in us as well—I could also betray, at least to a certain extent, because mathematics is independent of the world.

Time showed me that I had been doubly mistaken. Genuinely to opt for death, against life, and for mathematics, against the world, is not possible. The only true option is one's own annihilation. Whatever we do, we do in life; and, as experience has demonstrated, neither is mathematics the perfect retreat, because its habitation is language. That informational plant has its roots in the world and in us. This comparison has always been with me, even before I was able to put it into the language of a proof.

In mathematics I searched for what I had valued in childhood, the multiplicity of worlds, which broke contact with the imposed world, but so gently that it was as if the latter had been stripped of its force—a force that lay within us as well, yet was hidden enough for us to forget its presence. Later, like every mathematician, I learned to my surprise how unpredictable and incredibly adaptable is that activity, which at first resembles a game. One enters into it proudly; without apologies and unequivocally one shuts out the world; with arbitrary propositions that rival, in their uncontestableness, Creation, one performs a definitive closure; this is to separate us from the vortex in which we are forced to live.

And lo, that denial, that most radical break, leads us precisely to the heart of things, and the flight turns out to have been an attainment, the desertion—an appreciation, and the break—a reconciliation. We make the discovery, then, that our escape was apparent only, since we have returned to the very thing we sought to flee. The enemy metamorphoses into an ally; we are purified; the world gives us to understand, silently, that only by means of it may we conquer it. Thus our fear is tamed and turns to joy, in that special refuge whose deepest interiors intersect the surface of the only world.

Mathematics never reveals man to the degree, never expresses him in the way, that any other field of human endeavor does: the extent of the negation of man's corporeal self that mathematics achieves cannot be compared with anything. Whoever is interested in this subject I refer to my articles. Here I will say only that the world injected its patterns into human language at the very inception of that language; mathematics sleeps in every utterance, and can only be discovered, never invented.

What constitutes its crown may not be cut free from its roots, because it arose not in the course of the three hundred or eight hundred years of civilized history, but through the millennia of linguistic evolution: at the loci of man's encounter with his environment, from the time of tribes and rivers. Language is wiser than the mind of any one of us, just as the body is wiser than the discernment of any of its units as it moves, self-aware and many-faceted, through the current of the life process. The inheritance of both evolutions, of living matter and of the matter of informational speech, has not yet been exhausted, but already we dream of stepping beyond the boundaries of both. These words of mine may make poor philosophizing, but that cannot be said of my proofs of the linguistic genesis of mathematical concepts, of the fact, in other words, that those concepts arose neither from the enumerability of things nor from the cleverness of reason.

The factors that contributed to my becoming a mathematician are complex, no doubt, but one major factor was talent, without which I could have accomplished in my profession no more than could a hunchback in a championship track-and-field competition. I do not know whether the factors that had to do with my character, rather than with my talent, played a role in the account I intend to give—but I should not rule out the possibility, for the importance of the affair itself is such that neither natural modesty nor pride ought to be considered.