middle-aged male driver with one accident in the past five years who
wants to insure his 2005 Honda Civic. I sometimes have to bite my lip
when contemplating my auto insurance bill, especially in view of the fact
that there is a teenage driver in the family. Balancing this is the realiza-
tion of how different my life would be (if I even had a life to live) had not
merchants gathered in coffeehouses in the seventeenth century in order
to share jointly the cost of voyages of exploration and commerce. In a
sense, aided by the increased accuracy in risk assessment resulting from
developments in probability and statistics, we are still doing that today.
Random Is As Random Does
Part of the reason for the success of mathematics is that a mathematician
generally knows what other mathematicians are talking about, which is
not something you can say about just any field. If you ask mathemati-
cians to define a term such as group, you are going to get virtually identi-
cal definitions from all of them, but if you ask psychologists to define
love, you will probably get several variations that depend upon the school
of psychological thought to which the respondent adheres.
The shared vocabulary of mathematics is not necessarily esoteric. Most
people have just as good a take on some ideas as do mathematicians. If
you were to ask John Q. Public for a definition of the word random, he
would probably say something like “unpredictable.” Somewhat surpris-
ingly, the mathematical definition of the term random variable goes out-
side the realm of mathematics into the real world for its definition; a
“random variable” is a mathematical function that assigns numbers to
the outcomes of random experiments, which is a procedure (such as roll-
ing a die or f lipping a coin) in which the outcome of the procedure cannot
be determined in advance. Mathematicians use the term nondeterminis-
tic, which sounds a lot more erudite than unpredictable—but both words
basically boil down to the same thing. Deterministic means that future
events depend on present and past ones in a predictable way. Nondeter-
ministic events are ones that cannot be so predicted.
But is rolling a die or f lipping a coin truly random, in the sense that it
is absolutely unpredictable? If one rolls a die, the initial force on the die is
known, the topography over which the die is traveling is known, and
the laws of physics are the only ones in play, might it not be possible, in
theory anyway, to predict the outcome? Obviously, this is a tremendously
complicated problem, but the potential gain for gamblers in the world’s
casinos makes this a tempting problem to solve. In the middle of the
twentieth century, a gambler spent years developing a method of throw-
170 How Math Explains the World