successful, primarily in areas offering easy quantification of the relevant
parameters. However, just because it is easy to quantify the relevant pa-
rameters does not guarantee success; almost all the major stock market
crashes have been characterized by an utter inability on the part of the
major prognosticators to predict them. Possibly, some future Hari Selden
may glimpse the multidimensional geometrical structures in whose
shapes are written the portents of the future, but I think it more likely
that some future Kenneth Arrow may discover that even though those
geometrical structures may exist, there is no way for us to determine
what they are.
In the Footsteps of Aquinas
Some of the greatest minds in history have endeavored mightily, as did
Saint Thomas Aquinas, to prove the existence of a deity; and some equally
great minds have endeavored just as mightily to prove that a deity cannot
exist. These proofs have one thing in common. They have utterly failed to
convince the other side.
It is hard to imagine a proof on any subject that would elicit greater in-
terest on the part of the public. Such a proof would answer, one way or
another, one of the most profound questions that has ever been asked. It
is also likely that the appearance of such a proof would generate a fire-
storm of controversy as to its validity. It is unlikely that such a proof
would be a simple one, as most of the simple lines of proof have been ex-
hausted centuries ago.
I’ve seen several of these proofs employing dubious hypotheses and/or
dubious logic, although I have yet to see any proofs on either side employ-
ing purely mathematical reasoning, with numbers, shapes, tables, or any
of the other concepts of mathematics. Possibly the easiest is the one that
argues for the nonexistence of God via the following paradoxical construc-
tion: If God exists, he or she must be all-powerful, so can God make a
stone so heavy that he or she cannot lift it? If he or she cannot make such
a stone, then he or she cannot be all-powerful. If he or she can make such
a stone, then the fact that he or she cannot lift it provides evidence that he
or she cannot be all-powerful.
There is a limit even to the all-powerful, and overcoming such a paradox
is one of them. One might with equal validity argue that the inability to
duplicate the cube using compass and straightedge proves the nonexist-
ence of God.
In fairness, a rebuttal should be given for one of the classic arguments
given for the existence of God; the “first cause” argument. It is argued
244 How Math Explains the World