Authors: Robert; Silverberg
It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knowledge… The most important questions of life are, for the most part, really only problems of probability.
, Théorie Analytique des Probabilités
Once a man learns to
he finds himself alone in the world with nothing but folly.
, A Separate Reality
We are born by accident into a purely random universe. Our lives are determined by entirely fortuitous combinations of genes. Whatever happens happens by chance. The concepts of cause and effect are fallacies. There are only
causes leading to
effects. Since nothing truly follows from anything else, we swim dictable, not even the events of the very next instant.
Do you believe that?
If you do, I pity you, because yours must be a bleak and terrifying and comfortless life.
I think I once believed something very much like the universe is a gigantic dice game, without purpose or pattern, into which we foolish mortals interpose the comforting notion of causality for the sake of supporting our precarious, fragile sanity. I think I once felt that in this random, capricious cosmos we’re lucky to survive from hour to hour, let alone from year to year, because at any moment, without warning or reason, the sun might go nova or the world turn into a great blob of petroleum jelly. Faith and good works are insufficient, indeed irrelevant; anything might befall anyone at any time; therefore live for the moment and take no heed of tomorrow, for it takes no heed of you.
A mighty cynical-sounding philosophy, and mighty adolescent-sounding, too. Adolescent cynicism is mainly a defense against fear. As I grew older I suppose I found the world less frightening, and I became less cynical. I regained some of the innocence of childhood and accepted, as any child accepts, the concept of causality. Push the baby and the baby falls down. Cause and effect. Let the begonia go a week without water and the begonia starts to shrivel. Cause and effect. Kick the football hard and it sails through the air. Cause and effect, cause and effect. The universe, I conceded, may be without purpose, but certainly not without pattern. Thus I took my first steps on the road that led me to my career and thence into politics and from there to the teachings of the all-seeing Martin Carvajal, that dark and tortured man who now rests in the peace he dreaded. It was Carvajal who brought me to the place in space and time I occupy on this day.
My name is Lew Nichols. I have light sandy hair, dark eyes, no significant identifying scars, and I stand exactly two meters tall. I was married—two-group—to Sundara Shastri. We had no children and now we are separated, no decree. My current age is not quite thirty-five years. I was born in New York City on 1 January 1966 at 0216 hours. Earlier that evening two simultaneous events of historic magnitude were recorded in New York: the inauguration of the glamorous and famous Mayor John Lindsay and the onset of the great, catastrophic first New York subway strike. Do you believe in simultaneity? I do. There’s no stochasticity without simultaneity, and no sanity either. If we try to see the universe as an aggregation of unrelated happenings, a sparkling pointillist canvas of noncausality, we’re lost.
My mother was due to deliver in mid-January, but I arrived two weeks ahead of time, most inconveniently for my parents, who had to get to the hospital in the small hours of New Year’s Eve in a city suddenly deprived of public transport. If their predictive techniques had been keener, they might have thought of renting a car that evening. If Mayor Lindsay had been using better predictive techniques, I suppose the poor bastard would have resigned at his own swearing-in and saved himself years of headaches.
Causality is a decent, honorable principle, but it doesn’t have all the answers. If we want to make sense of things, we have to move on beyond it. We have to recognize that many important phenomena refuse to be packed into neat casual packages but can be interpreted only by stochastic methods.
A system in which events occur according to a law of probability but aren’t individually determined in accordance with the principle of causality is a stochastic system. The daily rising of the sun isn’t a stochastic event; it’s inflexibly and invariably determined by the relative positions of the earth and the sun in the heavens, and once we understand the causal mechanism there’s no risk in predicting that the sun will rise tomorrow and the next day and the next. We can even predict the exact time of sunrise, and we don’t
know it in advance.
The tendency of water to flow downhill isn’t a stochastic event either; it’s a function of gravitational attraction, which we hold to be a constant. But there are many areas where causality fails us and stochasticity must come to our rescue.
For instance we’re unable to predict the movements of any one molecule in a liter of oxygen, but with some understanding of kinetic theory we can confidently anticipate the behavior of the whole liter. We have no way of foretelling when a particular uranium atom will undergo radioactive decay, but we can calculate quite accurately how many atoms in a block of U-235 will disintegrate in the next ten thousand years. We don’t know what the next spin of the roulette wheel will bring, but the house has a good idea of what its take is likely to be over the course of a long evening. All sorts of processes, however unpredictable they may seem on a minute-to-minute or case-by-case basis, are predictable by stochastic techniques.
According to the Oxford English Dictionary this word was coined in 1662 and is now
Don’t believe it. It’s the OED that’s
which gets less
every day. The word is from the Greek, originally meaning “target” or “point of aim,” from which the Greeks derived a word meaning “to aim at a mark,” and, by metaphorical extension, “to reflect, to think.” It came into English first as a fancy way of saying “pertaining to guesswork,” as in Whitefoot’s remark about Sir Thomas Browne in 1712: “Tho’ he were no prophet... yet in that faculty which comes nearest it, he excelled, i.e., the stochastick, wherein he was seldom’ mistaken, as to future events.”
In the immortal words of Ralph Cudworth (1617—1688), “There is need and use of this stochastical judging and opinion concerning truth and falsehood in human life.” Those whose way of life is truly governed by the stochastic philosophy are prudent and judicious, and tend never to generalize from a skimpy sample. As Jacques Bernoulli demonstrated early in the eighteenth century, an isolated event is no harbinger of anything, but the greater your sampling the more likely you are to guess the true distribution of phenomena within your sample.
So much for probability theory. I pass swiftly and uneasily over Poisson distributions, the Central Limit Theorem, the Kolmogorov axioms, Ehrenhai’t games, Markov chains, the Pascal triangle, and all the rest. I mean to spare you such mathematical convolutions. (“Let
be the probability of the happening of an event in a single trial, and let
be the number of times the event is observed to happen in
trials...”) My point is only that the pure stochastician teaches himself to observe what we at the Center for Stochastic Processes have come to call the Bernoulli Interval, a pause during which we ask ourselves.
Do I really have enough data to draw a valid conclusion?
I’m executive secretary of the Center, which was incorporated four months ago, in August, 2000. Carvajal’s money pays our expenses. For now we occupy a five-room house in a rural section of northern New Jersey, and I don’t care to be more specific about the location. Our aim is to find ways of reducing the Bernoulli Interval to zero: that is, to make guesses of ever-increasing accuracy on the basis of an ever-decreasing statistical sample, or, to put it another way, to move from probabilistic to absolute prediction, or, rephrasing it yet again, to replace guesswork with clairvoyance.
So we work toward post-stochastic abilities. What Carvajal taught me is that stochasticity isn’t the end of the line: it’s merely a phase, soon to pass, in our striving toward full revelation of the future, in our straggle to free ourselves from the tyranny of randomness. In the absolute universe all events can be regarded as absolutely deterministic, and if we can’t perceive the greater structures, it’s because our vision is faulty. If we had a real grasp of causality down to the molecular level, we wouldn’t need to rely on mathematical approximations, on statistics and probabilities, in making predictions. If our perceptions of cause and effect were only good enough, we’d be able to attain absolute knowledge of what is to come. We would make ourselves all-seeing. So Carvajal said. I believe he was right. You probably don’t. You tend to be skeptical about such things, don’t you? That’s all right. You’ll change your mind. I know you will.
Carvajal is dead now; lie died exactly when and as he knew he would. I am still here, and I think I know how I will die, too, but I’m not altogether sure of it, and in any case it doesn’t seem to matter to me the way it did to him. He never had the strength that was necessary to sustain his visions. He was just a burned-out little man with tired eyes and a drained smile, who had a gift that was too big for his soul, and it was the gift that killed him as much as anything. If I truly have inherited that gift, I hope I make a better job of living with it than he did.
Carvajal is dead, but I’m alive and will be for some time to come. All about me flutter the indistinct towers of the New York of twenty years hence, glittering in the pale light of mornings not yet born. I look at the dull porcelain bowl of the winter sky and see images of my own face, grown much older. So I am not about to vanish. I have a considerable future. I know that the future is a place as fixed and intransient and accessible as the past. Because I know this I’ve abandoned the wife I loved, given up the profession that was making me rich, and acquired the enmity of Paul Quinn, potentially the most dangerous man in the world, Quinn who will be elected President of the United States four years from now. I’m not afraid of Quinn personally. He won’t be able to harm me. He may harm democracy and free speech, but he won’t harm me. I feel guilty because I will have helped put Quinn in the White House, but at least I’ll share that guilt with you and you and you, with your blind mindless votes that you’ll live to wish you could call back. Never mind. We can survive Quinn. I’ll show the way. It will be my form of atonement. I can save you all from chaos, even now, even with Quinn astride the horizon and growing more huge every day.
I was into probabilities for seven years, professionally, before I ever heard of Martin Carvajal. My business from the spring of 1992 onward was projections. I can look at the acorn and see the stack of firewood: it’s a gift I have. For a fee, I would tell you whether I think particle chips will continue to be a growth industry, whether it’s a good idea to open a tattooing parlor in Topeka, whether the fad for bare scalps is going to last long enough to make it worthwhile for you to expand your San Jose depilatory factory. And the odds are I’d be right.