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 sai
d 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.
I once wrote a program for an experiment of one of my friends. The idea was to simulate, in a computer, families of neutral beings; they would be homeostats, cognizant of their "environment" but possessing, initially, no "emotional" or "ethical" qualities. These beings multiplied—only in the machine, of course, therefore in a way that a layman would call "arithmetically"—and after a few dozen "generations" there continually appeared, over and over again, in each of the "specimens," a characteristic that made no sense at all to us, a sort of equivalent of "aggression." After many painstaking but fruitless checking calculations, my friend, at his wit's end—really grasping at straws—began examining the most trivial circumstances of the experiment; and then it turned out that a certain relay had reacted to the changes of humidity in the air, and thus those changes had become the hidden producer of the deviation.
I cannot help thinking of that experiment as I write, for is it not possible that social evolution lifted us from the Animal Kingdom in an exponential curve—when we were fundamentally unprepared for the ascent? The socialization reaction began when the human atoms had barely given evidence of their first cohesiveness. Those atoms were a material strictly biological, a material made and prepared to satisfy typically biological criteria, but that sudden movement, that upward shove, seized us and carried us off into the space of civilization. How could such a start not have bound onto that biological material accidental convergences, much as a probe that, lowered to the ocean floor, scoops up from it, along with the desired object, debris and chance pieces of junk? I recall the damp relay in the sophisticated computer. And the process that engendered us—why, pray, must it have been in every respect perfect? Yet neither we nor our philosophers dare consider the idea that the finality and singularity of the existence of our species do not at all imply a perfection under whose aegis the species originated—just as such perfection is not present at the cradle of any individual.
It is a curious thing that the marks of our imperfection, which identify the species, have never been, not by any faith, recognized for what they simply are, that is, the results of uncertain processes; on the contrary, practically all religions agree in the conviction that man's imperfection is the result of a demiurgic clash between two antagonistic perfections, each of which has damaged the other. The Light collided with the Dark, and man arose: thus runs their formula. My conception sounds ill-natured only if it is wrong—but we do not know that it is wrong. The friend whom I mentioned caricatured it; he said that according to Hogarth humanity is a hunchback who, in ignorance of the fact that it is possible not to be hunchbacked, for thousands of years has sought an indication of a Higher Necessity in his hump, because he will accept any theory but the one that says that his deformity is purely accidental, that no one bestowed it upon him as part of a master plan, that it serves absolutely no purpose, for the thing was determined by the twists and turns of anthropogenesis.
But I intended to speak about myself, not about the species. I do not know where it came from or what caused it, but even now, after all these years, I find within myself that malice, as vigorous as ever, because the energies of our most primitive impulses never age. Do I shock? Over many decades now, I have acted like a rectification column, producing a distillate composed of the pile of my articles as well as of the articles occasioned by them—hagiography. If you say that you are not interested in the inner workings of the apparatus which I unnecessarily bring out into the light, note that I, in the purity of the nourishment I have vouchsafed you, see the indelible signs of all my secrets.
Mathematics for me was no Arcadia; it was, rather, a court of last resort, a church that I entered, unbelieving, because it offered sanctuary. My principal metamathematical work has been called destructive, and not without reason. It was no accident that I called into question, irreversibly, the foundations of mathematical deduction and the concept of the analytic in logic. I turned the tools of statistics against these basic notions—until at last they crumbled. I could not be a devil underground and an angel in the light of day. I created, yes, but on ruins, and Yowitt is right: I took away more truths than I ever gave.
For this negative balance the epoch was held to account, not I; because I had followed in the steps of Russell and Gödel—after the former had discovered the cracks in the foundation of the Crystal Palace, and after the latter had shaken it. It was said that I had acted in the spirit of the time. Well, of course. But an emerald triangle does not cease to be an emerald triangle when it becomes a human eye—in an arranged mosaic.
More than once I have wondered what would have become of me had I been born within any one of the four thousand cultures we call primitive, which preceded ours in that gulf of eighty thousand years that our lack of imagination contracts to the foreground, the foyer, of history proper. In some of them I would no doubt have languished; but in others, who knows, I might have found greater personal fulfillment, as one visited, as one creating new rites, new magic, thanks to the talent I brought into the world, that of combining elements. Perhaps, in the absence of a restraining curb, which in our culture is the relativism of every conceptual entity, I could have consecrated, with no trouble, orgies of havoc and debauchery, because in those ancient societies they practiced the custom of a temporary, periodic suspension of daily law, by dissolving their culture (it was the bedrock, the Constant, the Absolute of their lives, and yet, remarkably, they knew that even the Absolute required holes!) in order to give vent to the festering mass of excesses that could not be fitted into any codified system, and of which only a portion found expression in war masks and family masquerades, under the bit and bridle of morality.
They were sensible, rational, those severings of societal bonds and rules, the group madness, the pandemonium liberated, heightened by the narcotics of rhythm and poison. It was the opening of a safety valve, out of which poured the factor of destruction; through this particular invention barbarity was adapted to man. But the principle of a crime from which one could retire, of a reversible madness, of gaps rhythmically repeated in the social fabric, has been done away with, and now all those forces must go in harness, work treadmills, play roles that are too tight for them and always ill-suited. So they corrode everything quotidian; they hide in every place; for nowhere is it permitted them to emerge from anonymity. Each of us is, from childhood, fastened to some publicly allowed piece of himself, the part that was selected a
nd schooled, and that has gained the consensus omnium; and now he cultivates that fragment, polishes it, perfects it, breathes on it alone, that it may develop as well as possible; and each of us, being a part, pretends to be a whole—like a stump that claims it is a limb.
As far back as I can remember, no ethics ever took root in my sensitivity. Cold-bloodedly I built myself an artificial ethics. But I needed to find a reason to do this, because setting up rules in a desert is like taking Communion without faith. I am not saying that I planned out my life in as theoretical a manner as I present it here. Nor did I attach axioms to my behavior—retroactively. I proceeded always in the same way, at first unawares; the motivations I later guessed.
Had I considered myself a person who was basically good, I would have been quite unable to understand evil. I would have believed that people perpetrated it always with premeditation—that is, that they did what they had resolved to do—because I would have found no other source of vileness within my personal experience. But I had better knowledge; I was aware of my own inclinations, as well as of my blamelessness for them—blamelessness because I was, after all, the way I was to begin with, and no one had ever consulted me in the matter.
Now, for one slave to strangle another slave to satisfy the forces implanted in both; for one blamelessness to torture another if there existed any chance whatever to resist such a compulsion—to me this was an offense against reason. We are given to ourselves and it is fruitless for us to question what is given, but if there should open up the minutest chance to oppose the Way Things Are—how can one not seize it? Only such decisions and such actions are our exclusive human property, as is the possibility, also, of suicide. This is the sector of freedom where our unasked-for inheritance meets with contempt.
Please do not tell me I contradict myself—the self who saw in the Stone Age a time of dreams come true. Knowledge is irreversible; one cannot go back into the darkness of sweet ignorance. In that time I would have had no knowledge and would have been unable to obtain it. One must make use of the knowledge one possesses. I know that Chance fashioned us, put us together as we are—and what, am I to follow submissively all the directives drawn blindly in that endless lottery?
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