WARNING: the following contains references to mathematics and may involve actual instances of calculus.
During Magic 101, my one (required) semester of college physics, the professor assured me and my fellow history and lit majors that there was no such thing as calculus in the real world.
For the most part, that works for me. But every now and then something reminds me that I’m only seeing part of the universe. Take yesterday, for example, when I read Stephen Wolfram’s blog post on “Computational Knowledge and the Future of Pure Mathematics”. Stephen is hands-down the most brilliant person I’ve ever met, and arguably one of the smartest people on the planet. (Caltech PhD at age twenty, he was the youngest recipient of the MacArthur “genius” fellowship in 1981.)
In addition to being the creative force motivating Mathematica, one of the premier computational software tools out there, Stephen is also one of the best writers I’ve ever encountered. Of course, his essay is (literally) mostly Greek to me, but his clean, elegant prose is also uniquely accessible to math-less luddites and former English majors everywhere.
Math, especially pure math, says Stephen, is essentially a way of using a language to tell a story. But his description of that might also be the most perfect description of the writing process I’ve ever seen.
I’ve been doing language design now for 35 years—and it’s the hardest intellectual activity I know. It requires a curious mixture of clear thinking, aesthetics and pragmatic judgement. And it involves always seeking the deepest possible understanding, and trying to do the broadest unification—to come up in the end with the cleanest and “most obvious” primitives to represent things.
He has other points to make, of course. I liked his consideration of whether math, especially pure mathematics, is science or art. “If it’s science, then being able to make more theorems faster is surely good. But if it’s art, that’s really not the point. If doing pure mathematics is like creating a painting, automation is going to be largely counterproductive—because the core of the activity is in a sense a form of human expression.”
And as a side note for sci-fi and fantasy writers (not to mention fans of Star Trek and Dr. Who), he even asks about the trope of the computer “…going off and doing math by itself”. Wolfram speculates, “I would expect that in time the computer will be able not only to identify new structures, but also name them, and start building stories about them. Of course, it is for humans to decide whether they care about where the computer is going, but the basic character of what it does will, I suspect, be largely indistinguishable from many forms of human pure mathematics.”
So… okay, then. It sounds like I don’t need to worry about HAL, the murderous computer from 2001: A Space Odyssey, telling me, “I can see you’re really upset about this. I honestly think you ought to sit down calmly, take a stress pill, and think things over.” Instead I’m reminded of one of my favorite classic sci-fi stories, “The Last Question”, which involves a computer designed to consider entropy and the eventual end of the universe. Even after all human consciousness has died out and space and time no longer exist, the computer whirs on, assembling and considering data until finally answering the question nobody is left to ask. The last line of The Last Question is “LET THERE BE LIGHT!” And there was light—”. (Asimov, Isaac. The Last Question. Science Fiction Quarterly. November 1956)