our bodies. He would undoubtedly have been just as intrigued by the in-
tricate way we are all connected to the real line. If a real number is se-
lected at random, it is almost certain that the digits of that number tell
the complete stories of every human being who has ever lived, or will ever
live, and each story is told infinitely often.
The ideal random penny, whose f lips can be viewed as the binary digits
of a number that is normal in every base, turns out to be not just a tool for
deciding who should kick off and who should receive in the Super Bowl,
but an oracle of more-than-Delphic stature. It answers every question that
could ever be answered, if only we knew how to read the tea leaves. But of
course, we never will.
Tumbling Dice: Why We Can’t Know What the Universe Knows
Earlier in the chapter, we asked whether the roll of a die was unpredictable;
after all, if the universe knows what is going to happen, why can’t we? In the
latter portion of the twentieth century, a new branch of mathematics
emerged. Chaos theory, as it was to be called, emerged as it was discovered
that unpredictable phenomena come in two f lavors: inherently unpredicta-
ble phenomena, and phenomena that are unpredictable because we cannot
obtain sufficient information. Inherently unpredictable phenomena exist
only in an idealized sense—the f lips of an ideal random penny correspond
to the binary digits of a number that is normal in every base, but such a
number does not correspond to any quantity that can actually be measured.
The phenomenon of chaos, as it appears in both mathematics and phys-
ics, is a specific type of deterministic behavior. Unlike random phenom-
ena, which are completely unpredictable, chaotic phenomena are in
theory predictable. The mathematical laws underlying the phenomena
are deterministic; the relevant equations have solutions, and the present
and past completely determine the future. The problem is not that the
laws themselves result in unpredictable phenomena, it is that we cannot
predict the phenomena because of information underload. Unlike quan-
tum mechanics, where we cannot know the value of parameters because
those values do not exist, we cannot (as yet) know the value of parameters
because it is impossible for us to gather the requisite information.
Now You’re Baking with Chaos
The dictionary defines chaos as “a state of extreme confusion and disor-
der.” The recent profusion of restaurant-based reality shows and movies
portray the kitchen in such a fashion—harried chefs screaming at wait-
176 How Math Explains the World