Sean Carroll has just interviewed physicist and mathematician Stephen Wolfram. It’s a long interview and I’ve not finished it. I’m only 45 minutes in to an interview that rand to 2 hours and 39 minutes. For what it’s worth, I bought Wolfram’s A New Kind of Science when it came out, read around in it, found some interesting things. Wolfram, as I’m sure you know, is a controversial figure.
Anyhow, here’s six things I highlighted in the interview. I’m not going to attempt to explain how we got to the first point, and then how from there to the second, and so forth. I’m just presenting these things.
As usual, there’s more at the link.
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1. Beneath pre-existing notions of space and time
0:09:48.9 Stephen Wolfram: Right. Yeah, that’s right. I never thought that cellular automata would be relevant to fundamental physics. I mean, other people were sort of saying “Cellular automata are going to solve fundamental physics!” And I was like, “No, please don’t say that. That’s just not going to work.” And cellular automata are very minimal models, once you have a ;xed notion of space and time. And they’ve been extremely fertile models for huge numbers of different kinds of things, from road trakc aow, to chemical catalysis, to leaf growth, to all kinds of different things.
0:10:21.0 SW: But they assume a pre-existing notion of space and time, and so in thinking about physics I had realized ages ago that we really need to go underneath the notions of space and time that we’re familiar with and see how to build those up from something more fundamental. And so sort of the real starting point of our project is to think about just these... They’re just... Space is made of something, that has not been sort of in the tradition of physics, and the tradition of mathematics as well, that’s not really been a thing that people think about. Space just is something in which things are placed at certain positions and so on. [...]
0:12:40.1 Sean Carroll: So what I have in mind is a bunch of dots, nodes that are connected by lines to form some kind of graph, and do I imagine that the dots, the nodes, are they labeled? Are there different kinds of dots or is there just an Ur-dotness that they all share?
0:12:58.9 SW: It’s an Ur-dot, that’s just... They’re all identical. The only thing about them is they are... Two dots are either identical or they’re not identical. That is, there’s a particular dot or there’s another dot, and so the only thing about them is kind of their identity, so to speak. They don’t have colors, they don’t have positions, they just know “I’m this dot and not that other dot.” [...]
0:13:47.3 SW: That’s the idea. So, there are many pieces to that setup. For example, one thing is, all there is is these kind of atoms of space and connections. There’s nothing in space, there’s nothing... It’s not like you then say, “We’ve got space, now let’s put an electron in space.” If you want an electron, you have to make it out of space, so to speak. You have to make it from features of that pattern of connections between the atoms of space. So that’s kind of... That’s sort of the base story of what is the data structure of the universe, what is the universe sort of made of, and that’s the idea, it’s made of these discrete elements and relations between those elements, which we can think of as being kind of lines joining them.
2. Open to the public
0:15:47.9 SC: And I like the fact that you just used the word hypergraph, because I like to share the jargon with the audience so they can go look it up, because especially, I should note, you... I don’t want to talk too much about style and procedure here, ’cause there’s far too much physics to talk about, but you did announce this project with a website and a call to participate. If people want to dig into the details, what is the URL they should be going to?
0:16:15.0 SW: Wolframphysics.org.
0:16:17.0 SC: There you go. And people can ;nd out what the details are and do their own calculations, so that’s...
0:16:22.2 SW: The other thing we’ve done kind of in terms of the public, which has been really a big success, is we’ve live-streamed a lot of our internal working meetings, and we’ve... All the notes from this project are all posted on the web, basically the day after they’re made, typically, and that’s... And it’s been really interesting, because a lot of people who are... A lot of professional physicists have gotten involved but also a lot of people who are, for example, involved in computer kinds of things and understand sometimes more of some of our jargon than the physicists would understand, have also gotten involved. And it’s really been an interesting process to sort of do science live and in public, so to speak.
3. Computational equivalence, computational reducibility – FUNDAMENTAL STUFF
0:24:57.0 SW: So in other words, what that’s saying is you might think you start off with an incredibly trivial program that only does trivial computations, as you make the program a little bit more complicated it would gradually do more and more sophisticated computations, and as you make a really, really, really complicated program, it would do really, really complicated computations. But the somewhat surprising claim of the principle of computational equivalence is that’s not true. Once you get above some very low threshold, you’re immediately at the max, you’re immediately doing computations that are as sophisticated as anything. And that principle has many implications, and probably the most important for, immediately, for physics is this phenomenon I call computational irreducibility.
0:25:40.2 SC: That was the next one. So go ahead and say that, yeah.
0:25:43.7 SW: Right, so the question there is, if you are running a program, can you tell what it will do. One way you can tell what it will do is you just run every step, just like the program would run itself. But another thing you can do is say, I’m much smarter than that program, I can jump ahead and it’s going to run for a million steps but I can jump to the end and say the answer is going to be 42, or something.
0:26:08.2 SW: And so one of the ideas of the exact sciences, the mathematical sciences, for a long time has been sort of a sign of doing wonderful things is that you can jump ahead like that, you can readily predict where will the planets be at some time in the future and so on. So that’s what I call computational reducibility, the ability to reduce the computational effort necessary to and the answer to jump ahead. So the claim is actually, there are lots of systems that are computationally irreducible, in the sense the only way to ;nd out what they’ll do is just to run every step, or in effect just to observe what the system does.
0:26:47.9 SW: And the reason that happens is because of the principle of computational equivalence. Because if you think you’re the observer, you’re the predictor, you are a computational system as well, and the question is, how do you as a computational system compete with the system you’re trying to predict. So if it was the case that you could really be smarter than the system you’re trying to predict, then yes, you could potentially jump ahead, but what the principle of computational equivalence says is, no, actually that won’t be that way. You will be exactly computationally equivalent to the system you’re trying to predict. And so the system you’re trying to predict, its behavior will seem to you sort of irreducibly complicated. So that’s one of its implications.
4. It takes a few steps to get from next to nothing to the floor of our universe
0:31:12.8 SC: I’ll take all the reasons for optimism I can get, I’m all on board with that. So good, so with those in mind, let’s go back to the physics that you’re actually constructing here. We have a hypergraph, we have some rules for updating it, now, should I read the speci;c... Is the idea that there is a speci;c correct rule for our universe and that rule basically is the fundamental laws of physics?
0:31:35.5 SW: Okay. So this is where things get a little bit more complicated. So, I think that it is probably the case that there will be a rule that we’ll be able to hold up and say, with this rule, we can reproduce what we observe in physics. Now, footnote, which is a really interesting footnote, I think. You might say, why did we get this rule and not another rule? It seems very... Particularly if the rule is simple, that’s like Copernicus was wrong, so to speak. There isn’t nothing special about us, we got the simple universe, so to speak, or we got the universe with the simple rule, not the universe with the, to us, incredibly complicated-seeming rule.
0:32:15.2 SW: So the thing that is then very surprising is that... And this is... We probably have to go a few more steps before we can really, really dig into this properly, is the idea that actually you can think of the universe as running all possible rules. And we as observers of the universe are essentially exist in a particular... In a sense- reference frame, in a particular position in rulial space, as we call it, that essentially gives us a particular sampling of this sort of universe of all possible universes. And that particular sampling is given our way of parsing what happens in the universe, that is something that we could attribute to a particular underlying rule, but actually, we can also think of it as just a slice of this kind of universe of all possible universes.
5. The 2nd law of thermodynamics and being computationally bounded
0:35:23.6 SW: Intelligent observers? No. Observers with... So the question is, what is the right idealization of a human observer? So I’ll give you a couple that seem to be enough, okay? So one important one is we’re computationally bounded. We don’t get to observe... So let’s take the gas molecule example again. If you... You have this gas, it’s got a bunch of molecules bouncing around, if you’re a sophisticated-enough observer you can see every single molecule, you can work out all the collisions, and in particular, that will allow you... So, a big principle in statistical mechanics is the second law of thermodynamics, which says typically the sort of... Typically things get more random as the molecules bounce around in a gas.
0:36:06.6 SW: But if we are not computationally-bounded observers and we can figure out what all these trajectories of all these molecules are, we don’t get the second law of thermodynamics. As non-computationally bounded observers, the second law of thermodynamics simply isn’t true. And that same idea of a computationally-bounded observer is necessary, I think, for us to believe that space has a continuous structure, and various other things about the universe. So that’s kind of step one.
0:36:34.9 SC: So we’re not Laplace’s demon.
0:36:37.5 SW: What’s that, sorry? 0:36:38.0 SC: We’re not Laplace’s demon.
[Side note on the anthropic principle]
0:40:56.7 SW: I think you raised the anthropic principle. And, to me, the anthropic principle is sort of a story of lack of imagination, so to speak. Because it’s saying the only way that we can have life, intelligence, consciousness, whatever, is the particular way we’ve seen it. And one of the consequences of this principle of computational equivalence is that actually something like intelligence is ubiquitous.
0:44:40.2 SW: Oh, yeah, yeah. Right. The sequence of updates, the hypergraph together with all its updates is supposed to be spacetime. And one of the things that is interesting and non-trivial here is most traditional views of physics have thought of space and time as being the same kind of thing. In this model they’re really not.
0:45:00.0 SC: Sure.
0:45:00.0 SW: Space is the extent of the spatial hypergraph. Time is the computational process of updating this hypergraph. So time is the progression of a computation. Space is just, oh, you follow these connections in the hypergraph. And so that makes it not at all obvious that you’re going to get things like relativity out of the model, because one is breaking apart the traditional connection between space and time.