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 onesided, 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.
As a rule, chroniclers become extremely honest when they feel that what they have to say about themselves is of monumental importance. I, on the contrary, with the premise of honesty arrive at the complete immaterialness of my person; that is, I am forced into an insufferable garrulity simply because I lack the ability to tell where the statistical caprice of personality composition leaves off and the rule of the behavior of the species begins.
In various fields one can acquire knowledge that is real, or the kind only that provides spiritual comfort, and the two need not agree. The differentiation of these two types of knowledge in anthropology borders on the impossible. If we know nothing so well as ourselves, it is surely for this reason: that we constantly renew our demand for nonexistent knowledge, i.e., information as to what created man, while ruling out in advance, without realizing it, the possibility of the union of pure accident with the most profound necessity.