Lazette Gifford
Publisher & Editor


The Mathematician, the Writer,
the Ant, and the Fish

By Scott Warner
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.