Wednesday, November 4, 2015

Mathematics in Science Fiction

Are there any examples of science fiction in which math plays the central role?  Before examining that question, let me pose a simpler one: is mathematics a branch of the sciences, like physics or astronomy?

The answer is "no." Although mathematics and, for instance, theoretical physics, appear at first glance to be very similar, they couldn't be more different. In theoretical physics, the goal is to construct some sort of framework to explain how the universe works. It's inherently inductive -- we work from observations about the universe to produce an explanation that fits all of the facts. While this might include long stretches of deductive mathematics, at the end of the day, the only thing that matters is whether the theory explains the observations.

Mathematicians operate in exactly the opposite direction. They begin with a set of basic postulates (or, more accurately, the huge set of mathematical results that have been deduced from these postulates over the centuries) and use logical deduction to come up with new results. In real life, things aren't quite as "clean" as I'm suggesting here -- I suspect that mathematicians often use hunches and gut instincts, just like theoretical physicists, to try to guess new results and jump far ahead of what's currently known. But then they have to backtrack and prove everything deductively, or it doesn't "count" as mathematics.

One of the science encyclopedias in our house when I was growing up described mathematics as the "queen and servant of science," and I think that's a pretty apt description. (A little intellectual dumpster diving on Google now reveals that this was actually the title of a 1951 popular mathematics book by Eric Temple Bell). What's really mysterious is why mathematics, which seems to be a game played by mathematicians, describes the physical universe so well.  But I'll save that for a future post. On to science fiction!

Probably the most famous work of science fiction with a mathematical theme is "--And He Built a Crooked House--" by Robert Heinlein.  In this story, an architect builds a house in the shape of an unfolded tesseract (a four-dimensional cube), but an earthquake causes it to fold up into a true four-dimensional tesseract, with predictably bizarre results. And of course, there's the much older Flatland. I also know of a couple of short story anthologies with mathematical themes: Mathenauts (1987), and the older Fantasia Mathematica (1958), which includes the Heinlein story.

But in general, science fiction stories based on mathematics are few and far between.  (The existence of these special anthologies illustrates my point -- you'd never see an anthology about "physics in science fiction" or "astronomy in science fiction" -- that would include half the science fiction stories ever written!) There are many stories about mathematicians -- The Mind-Body Problem by Rebecca Goldstein is a classic example -- but those aren't science fiction.

I think that the nature of mathematics just doesn't lend itself very well to fictionalization. First, it's really hard to come up with speculative ideas in mathematics. Because math is deductive, it's more set in stone then anything in science. Once a mathematician proves something, it stays proved.  So it's conceivable (though unlikely) that we might someday evade relativity and develop faster-than-light travel.  But we're never going to discover that there are only a finite number of prime numbers, or that 2+2 = 5. Second, it's a lot harder to make mathematics both understandable and interesting to a non-expert reader. (Which is why I have tremendous respect for Martin Gardner). And if you can get around both of these problems, how do you apply a clever new idea in mathematics to people's lives to produce a story? It's just very, very difficult, and few writers have attempted it.

11 comments:

TheOFloinn said...

There was also "A Subway Called Moebius" in which the connectivity of the Boston subway system was increased just a wee bit too much.

Robert Scherrer said...

Great story! The author was apparently an astronomer of some note.

Kathy said...

I hesitate to toot's Asimov's horn, but the whole Foundation saga is based on a speculative idea in mathematics (which never even comes close to being explained, of course).

BTW, although he said he got the idea for the Foundation stories from reading Gibbon's "Decline and Fall of the Roman Empire," he also inserted elements of the French Revolution, right down the Encyclopaedia and a Committee for Public Safety

TheOFloinn said...

Actually, Imperial times were marked by the great Roman encyclopediasts: Macrobius, Pliny, et al. who wrote down (in highly abbreviated form) the knowledge gathered (mostly) by the Greeks.

Robert Scherrer said...

Actually, I would argue that the fundamental idea of the Foundation is that sociology/political science/economics could actually turn into real science. No danger of that happening any time soon....

Kathy said...

How would you classify Asimov's short story "The feeling of Power"? The premise is people have forgotten how to do basic arithmetic, until a humble technician rediscovers it.

The "new" science gets to be called "Graphitics" because it's written down on paper.

Robert Scherrer said...

I'd call it a story about mathematics - it's really science fiction about arithmetic! I once encountered a cashier who not only did not know how to do multiplication with pencil and paper, but didn't even believe that it was possible. Asimov was prescient.

Bobby B said...

A lot of stories by Greg Egan have mathematics as an underlying theme. Perhaps my favorites are "Unstable Orbits in the Space of Lies" and "Wang's Carpet's". Theodore Sturgeon also wrote a short story about a man having to figure out he's on a Mobius strip, "What Dead Men Tell".

Robert Scherrer said...

Greg Egan is one of my favorite authors, but you really do need a PhD in a technical field to fully appreciate his stories.

Allen jeley said...

nice

Allen jeley said...

Mathematics is great help in the since i read your project and its tell us how to use mathematics technique in since thanks for sharing thesis revision