November 3, 2011
How simple would you imagine the underlying rule for the universe could be? How many lines of code would you guess, roughly what range?
Here’s a way to think about that. If you start enumerating possible universes, you can—the best representation I’ve found for what I think is a reasonable way to get at this is using networks, transformation rules for networks, so you can represent that as code in Mathematica or something. And each of these transformation rules is probably two, three, four lines long, something like that. But what’s perhaps a better measure is to ask, If you start enumerating possible rules for the universe, how many rules are you looking at before you find one that’s plausible? If you look at the first 10 rules and start enumerating rules—there are probably different way to enumerate them; it doesn’t matter that much which different scheme you use, because the way combinatorics works, the different schemes don’t give you vastly different numbers—once you start enumerating, the first few you look at are completely, obviously not our universe: no notion of time, different parts of space are disconnected, all kinds of pathologies that are pretty obviously not our universe. The thing that I thought would be the case is that one would have to look through billions of different candidate universes before you find ones that aren’t obviously not our universe. One of the things I discovered a few years ago is that that is not the case. Even within the first thousand conceivable candidate universes, there are already rules, already cases, candidate universes, whose behavior is complicated and you can’t tell that it isn’t our universe. Can’t prove that it is our universe, but you can’t tell that it isn’t our universe.
So what typically happens is you’ll start one of these things off and it will bubble around, and you’ll follow it until it has—well, when I was last doing it, it was maybe around 10 billion underlying nodes—and then it’s off and running and bubbling around, and you say, Is it our universe or is it not our universe? Well, this is where computational irreducibility bites you, because you ran it up to 10 billion nodes, but that’s still 10-to-the-minus-58th second of the evolution of our universe, and it’s really hard to tell at that point whether this thing that’s bubbling around is going to end up having electrons and protons and god knows what else in it. That’s where there’s a whole depth of technology that effectively has to recapitulate—effectively what one’s doing is some version of natural science, because you’ve got this universe that you’re studying, it’s in your computer, it’s bubbling around, and then you have to kind of deduce what are the natural laws for that. What are the effective natural laws for that universe. You know what the underlying laws are because you put them in, but you have to say, well, what are the effective laws that come out and how do they compare to the effective laws we’ve discovered in physics? And so what I’m saying is that even in the first thousand candidate universes, there are already ones that might be our universe. And in fact, it could be that one of the ones that’s sitting on my computer, that it is our universe, we just don’t know it yet. That’s the difficulty in making that connection between what we know now from physics and what we can see in this candidate universe. It’s not where one’s in a situation and saying, Oh my gosh, there’s no way that rules this simple can produce the kind of richness that we need to be our universe. We’re in a different situation where rules this simple can create incredibly rich and complicated behavior; we just can’t tell exactly what that behavior is.
For me, it’s sort of an interesting thing, because in modern science—post-Copernican science—one’s led to think in this kind of humble Copernican way where there can’t be anything special about us somehow. At some point, we thought we were the center of the universe, and that turned out not true at all. But now when it comes to our whole universe, we can imagine there is an infinite set of candidate universes. So the thing that seems wrong from a Copernican tradition is this: Why should our universe be one of the simple ones? You might say, Why isn’t it just some random universe out there?