when we look back, I think it’s going to become clear that computation is by far the most important idea that’s emerged in the past century.
How do we tell if something has a purpose, anyway? Well, even in everyday situations, it may not be terribly easy. When we see some complicated object, what is functional about it? What is ornamental? What is ceremonial? Think about Stonehenge. Or think about early handprint cave paintings. It seems like the only way to tell if these things have purposes is to have some kind of historical, cultural connection to them. I mean, if you find a flint from the Stone Age, and it’s been chipped away, was it a Stone Age tool built for a purpose, or just some stone with random chippings on it?
what I’ve concluded is that actually the mathematics we have today is really just a historical accident: the direct generalization of the arithmetic and geometry that happened to be used in ancient Babylon. So it’s just history that makes the particular axiom systems we’re using seem meaningful to us.
here’s a way we might imagine figuring out if something was created for a purpose or not. We figure out a purpose that can be ascribed to its behavior. And then we ask whether the construction of the thing is somehow minimal for achieving that purpose. Or whether instead the thing has all sorts of extraneous stuff that’s irrelevant to this purpose.
maybe you can think of radio and cellphone transmissions. Those have historically had lots of regularity—but actually they’re beginning to approach the technology optimization point I mentioned before—doing more compression and so on, and being spread spectrum, and starting just to look random.
There’s no abstract computational way to distinguish the lump of material that has us encoded in its behavior from one that’s just an ordinary lump of material, doing its ordinary physics. It’s sort of humbling. After all that development of our civilization, and of our technology, we end up being patterns of behavior that are not fundamentally different from patterns of behavior produced by physics all over the universe.
Mathematica does symbolic integrals, for example, better than any human. Of course, it doesn’t use human methods. It just blasts through to the answer using fancy math. And that means, for example, that when Wolfram|Alpha shows the steps for doing an integral it’s really a fake: it’s something that was reverse engineered from the answer, and specifically set up to be human understandable.
let’s say you ask it to solve a physics problem. Well, thinking in sort of classic AI style you might think: it should solve the problem by human-like reasoning, by figuring out how this object affects that object in this way, and so on. But that’s kind of medieval. It’s kind of like old-fashioned natural philosophy. But 300 years ago we had Newton and friends, who brought mathematics into natural philosophy. And gave us ways to in a sense use math to blast through to the answer to physics problems, without any human-like reasoning.
It’d surely fail a Turing test—it knows far too much, and can figure far too much out.
a lot of good human composers seem to come to the WolframTones site to get “creative inspiration”—from a computer.
here’s the funny thing: our times, these years, are the first times in history when a decent fraction of everything that happens is recorded.