Randomness
Our very brains revolt at the idea of randomness. We have
evolved as a species to become exquisite pattern-finders — long before the
advent of science, we figured out that a salmon-colored sky heralds a dangerous
storm, or that a baby's flushed face likely means a difficult night ahead. Our
minds automatically try to place data in a framework that allows us to make
sense of our observations and use them to understand events and predict them.
Randomness is so difficult to grasp because it works against our
pattern-finding instincts. It tells us that sometimes there is no pattern to be
found. As a result, randomness is fundamental limit to our intuition; it says
that there are processes that we can't predict fully. It's a concept that we
have a hard time accepting even though it is an essential part of the way the
cosmos works. Without an understanding of randomness, we are stuck in a
perfectly predictable universe that simply doesn't exist outside of our own
heads.
I would argue that only once we understand three dicta — three
laws of randomness — can we break out of our primitive insistence on
predictability and appreciate the universe for what it is rather than what we
want it to be.
The First Law of Randomness: There is such a thing as
randomness.
We use all kinds of mechanisms to avoid confronting randomness.
We talk about karma, in a cosmic equalization that ties seemingly unconnected
events together. We believe in runs of luck, both good and ill, and that bad
things happen in threes. We argue that we are influenced by the stars, by the
phases of the moon, and by the motion of the planets in the heavens. When we get
cancer, we automatically assume that something — or someone — is to blame.
But many events are not fully predictable or explicable.
Disasters happen randomly, to good people as well as to bad ones, to
star-crossed individuals as well as those who have a favorable planetary
alignment. Sometimes you can make a good guess about the future, but randomness
can confound even the most solid predictions — don't be surprised when you're
outlived by the overweight, cigar-smoking, speed-fiend motorcyclist down the
block.
What's more, random events can mimic non-random ones. Even the
most sophisticated scientists can have difficulty telling the difference between
a real effect and a random fluke. Randomness can make placebos seem like miracle
cures, harmless compounds appear to be deadly poisons, and can even create
subatomic particles out of nothing.
The Second Law of Randomness: Some events are impossible to
predict.
If you walk into a Las Vegas casino and observe the crowd
gathered around the craps table, you'll probably see someone who thinks he's on
a lucky streak. Because he's won several rolls in a row, his brain tells him
that he's going to keep winning, so he keeps gambling. You'll probably also see
someone who's been losing. The loser's brain, like the winner's, tells him to
keep gambling. Since he's been losing for so long, he thinks he's due for a
stroke of luck; he won't walk away from the table for fear of missing out.
Contrary to what our brains are telling us, there's no mystical
force that imbues a winner with a streak of luck, nor is there a cosmic sense of
justice that ensures that a loser's luck will turn around. The universe doesn't
care one whit whether you've been winning or losing; each roll of the dice is
just like every other.
No matter how much effort you put into observing how the dice
have been behaving or how meticulously you have been watching for people who
seem to have luck on their side, you get absolutely no information about what
the next roll of a fair die will be. The outcome of a die roll is entirely
independent of its history. And, as a result, any scheme to gain some sort of
advantage by observing the table will be doomed to fail. Events like these —
independent, purely random events — defy any attempts to find a pattern because
there is none to be found.
Randomness provides an absolute block against human ingenuity;
it means that our logic, our science, our capacity for reason can only penetrate
so far in predicting the behavior of cosmos. Whatever methods you try, whatever
theory you create, whatever logic you use to predict the next roll of a fair
die, there's always a 5/6 chance you are wrong. Always.
The Third Law of Randomness: Random events behave
predictably in aggregate even if they're not predictable individually
Randomness is daunting; it sets limits where even the most
sophisticated theories can not go, shielding elements of nature from even our
most determined inquiries. Nevertheless, to say that something is random is not
equivalent to saying that we can't understand it. Far from it.
Randomness follows its own set of rules — rules that make the
behavior of a random process understandable and predictable.
These rules state that even though a single random event might
be completely unpredictable, a collection of independent random events is
extremely predictable — and the larger the number of events, the more
predictable they become. The law of large numbers is a mathematical theorem that
dictates that repeated, independent random events converge with pinpoint
accuracy upon a predictable average behavior. Another powerful mathematical
tool, the central limit theorem, tells you exactly how far off that average a
given collection of events is likely to be. With these tools, no matter how
chaotic, how strange a random behavior might be in the short run, we can turn
that behavior into stable, accurate predictions in the long run.
The rules of randomness are so powerful that they have given
physics some of its most sacrosanct and immutable laws. Though the atoms in a
box full of gas are moving at random, their collective behavior is described by
a simple set of deterministic equations. Even the laws of thermodynamics derive
their power from the predictability of large numbers of random events; they are
indisputable only because the rules of randomness are so absolute.
Paradoxically, the unpredictable behavior of random events has
given us the predictions that we are most confident in.
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