
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'tguess it, weknow 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.
Stochastic.According to the Oxford English Dictionary this word was coined in 1662 and is nowrare or
obs. Don't believe it. It's the OED that'sobs., notstochastic, which gets lessobs. 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, Ehrenhaft games, Markov chains, the Pascal triangle, and all the rest.
I mean to spare you such mathematical convolutions. ("Letp be the probability of the happening of an
event in a single trial, and lets be the number of times the event is observed to happen inn 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
struggle 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