The Mathematical Mythos
As mathematicians, we speak reverently of Koch curves and objects of the like.
"There exist," we say, "curves enclosing a finite area, yet which have an infinite
perimeter, such that a man driving along the curve, at any speed, no matter how quickly, is
never any measurable distance away from the point at which he started,"
and, in theory, in our heads and our hearts, we know this to be true.
But of course, it is only a well-woven story. No such curves demonstrably exist, in
the physical world. Indeed, no curves at all tangibly exist, but they only exist as abstraction.
What we have done is we have rigorously proven that something
is possible in an orderly fantasy-world; we have proven that a thing is logically conceivable, and
that follows from a set of axioms which we agree on ahead of time, but
really little more than that.
What we mean, is that in some perfect idealized storyteller's
universe such a thing is constructible.
Perhaps this little fiction will inspire us to create a
mathematics more useful to the practical person (this is a common defense for pure
mathematics,) and perhaps, we should hope, those axioms or abstractions which we are applying describe something of relevance to our
But I note that this is exactly the sense in how the ancients' faith in an old myth-story
was helpful in interpreting the universe around them. The abstractions are not the same,
and the rules of deduction are perhaps not explicitly laid out beforehand, but so long as human
beings think, these rules are present, for the scientist and the old myth-maker alike.
In mathematics, you see, we also have our hells and paradises of Infinity;
we are brought to infinite change in finite time on
the mad Elysian horse of Differential Equations, seeing any amount of work
done with infinitismal difficulty, and any thing accomplished with unbounded ease.
This is a mathematical mythos. Drink in its beauty, and learn to sing in its priestly language.
Accomplish anything with reason of thought, and understand the world
through its myths - through the abstractions.
The difference between modern theory and ancient myth is all, you see, a matter of where we start. Where some may see no room
for formulizing ideas, or generalization, or articulating notions precisely,
or definition of terms, another may come and resolve all of the chaos into
sense and order. Whether the realm is the realm of science and ignorance, or of harmony and dissonance, or of
angels and demons - what is it to us? In aiding us to understand
the world, in whatever aspect and in whatever words, they are the same.
So there is dangerously little difference between a great genius and
a great mystic.
We are all, you see, as scientists or poets or writers or programmers, not in the business of discovering truth, but better and better myths.
And knowing this, we should all work for the high laurel of the storyteller, that we might become better and more useful human beings.