The Mathematician, the
Writer,
the Ant, and the Fish
By Scott Warner
© 2006,
Scott Warner
I'm not saying writing and math are the
same. No, they are obviously different. Writing is inspiration and talent;
math is operands and operators. Writing sets the butterfly of one's mind
loose across a meadow. Math pins the butterfly to graph paper. Writing is
also a complex problem of a kind mathematicians have been trying to solve
for years.
How can this be?
Language, the writer's tool, can be
deliciously ambiguous as it builds into complex dreamscapes or cascades into
nuance. It may be at once beautiful and blunt, subtle and salient. It's hard
to imagine anything that makes us more human.
Mathematical symbols are measurable,
quantifiable, and the lingua universale to talk with all those
annoyingly silent extraterrestrials for precisely the opposite reason: they
are abstractions outside our experience, as though dug up at Olduvai.
Everyone understands them, and everyone agrees.
Well, not everyone. Go figure.
Some mathematicians believe that the
"unambiguous" structures we've chosen to model reality are, in fact, as
human as language. Even worse, much of what we think is absolute about
mathematics isn't, more than enough to frustrate any would-be cosmic gossip.
The boundaries between the two professions
are, to coin a phrase, muddy.
In complexity theory, a branch of
mathematics that tries to find order in chaos, a problem is "P-complete" if
it can be solved in a finite number of steps. Harder problems take more
steps, the hallmark of arithmetic. Computers are very good at solving them.
Indeed, they are designed so.
The real world, naturally, doesn't contain
many P-complete problems.
Consider a traveling salesman trying to
find the quickest route through a city to spend the most time with each
client. There isn't an algorithm that solves his problem. There's no way to
know how many steps or even how best to reach the answer. The only sure way
is to test all routes.
The traveling salesman and dozens like it
are called NP-complete (non-deterministic, polynomial time). These are
problems not in P that can't be solved in a predictable number of
steps.
Why can't a computer just generate all
possible solutions? None of us would live that long, for starters. And some
mathematicians aren't quite sure that P and NP are different.
Computer scientists have written programs
that move through the "search space" of these problems to find a good
solution the way an ant forages for food or the way that schools of fish
change direction. For not only do ants and fish work within the NP-complete
systems of the real world, they do so without thinking at all.
What does this have to do with writing?
Here's what we know about NP-complete
problems:
-
A solution doesn't come quick and easy – formulas
don't work.
-
A solution for one problem won't work exactly the
same way for another.
-
It's impossible to know how long it will take to
reach a solution.
Substitute "final draft" for "solution" and
"written" for "solved," and you'll see my point. The act of writing is like
solving an NP-complete problem, because there are many ways to express an
idea well. And no writer knows exactly how long that will take.
Can mathematicians teach a writer anything?
At first thought, no. A draft evolves as it
is written and isn't sitting forever in a virtual slush pile waiting to be
discovered. A mathematician (I'm guessing, because I'm not one) might say
that the problem's search space is dynamic.
Writing is akin to our traveling salesman
problem with streets and clients constantly moving. While one can't imagine
any computer solving it, we humans manage just fine. I suppose it's why true
artificial intelligence is elusive.
Still, general approaches to solving
NP-complete problems might help (translation in parentheses):
-
Algorithmic approaches don't work.
(There are no formulas for plots.)
-
Rules of thumb that generate possible
solutions are applied using a general strategy. (A "trial and error"
approach works best.)
-
A "fit test" is crucial to discard
suboptimal solutions. (Edit with a critical eye.)
-
There isn't any way to know if a
solution will be found quickly. (Writing is rewriting.)
NP-complete problems show that sets of
rules apply differently depending on the circumstances. This is also true of
writing. The complexity of the task defines boundaries, whether we call it a
heuristic search space or a novel's ending.
A writer who spends an hour searching for a
word or phrase on a hunch only to discard it a day later may be thrust in a
completely new direction. Writing, it seems, is as much journey as
destination. And therein is the main difference.
I'll keep watching the bookstores for the
next best seller written by a computer, just in case.
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