Ask A Genius 1303: Cellular Automata, Discrete vs. Continuous Models, and Algorithmic Information Theory
Author(s): Rick Rosner and Scott Douglas Jacobsen
Publication (Outlet/Website): Ask A Genius
Publication Date (yyyy/mm/dd): 2025/03/03
Scott Douglas Jacobsen: Did you want to do any science stuff? Cellular automata is a discrete, rather than continuous, computational model dealing with grids of cells. In this case, these four-dimensional cells evolve based on rules. This is based on Stephen Wolfram’s book A New Kind of Science. He argues that simple rules can generate complex systems and suggests that this could model the universe.
So, my first two questions are: Where do the rules come from, and are they the right rules?
Rosner: I would say to be concise, but not the right rules. Not the right rules.
Jacobsen: Right.
Rosner: You can set up rules that generate complexity, but just because you can do that doesn’t mean those are the rules governing the universe. I think the rules for the universe stem from what can exist by being non-contradictory at a fundamental level.
You could dig deeper into that foundation and find more levels to explore. But Wolfram’s rules rest on an underlying structure—the grid, the computational framework—built on more fundamental layers of abstraction.
If he’s using a three-dimensional… I mean, if you’re going to have a three-dimensional—
Jacobsen: Oops.
Rosner: Shit. Hold on. Earthquake. Hold on. I’ve got to check in with Carole.
Jacobsen: Hello?
Rosner: Earthquake. Let me talk to Carole. I’ll be back in a second. I’m going to jump to—
[Earthquake gap]
Jacobsen: I checked it out. Was that a 3.1?
Rosner: 3.9 is what I’m seeing.
Jacobsen: Is it done?
Rosner: Yeah. But when I was looking around, I saw that Southern California has had quite a few quakes in the last 48 hours. This was the first one we felt.
Jacobsen: We had one over here recently too.
Rosner: Well, you’re along the same fault line, right? I don’t know what we were talking about. Do you just want to continue tomorrow?
Jacobsen: We were getting towards the physics. What were we talking about—cellular automata?
Rosner: Yeah.
Jacobsen: Here’s my follow-up question: Do you think it’s legitimate for Wolfram to jump to a discrete model rather than remaining agnostic about discrete versus continuous?
Rosner: I don’t know. I’ve been giving you a lot of “I don’t know” lately. People like to point out that quantum events are, well, events. Which means they’re things that happen—discrete occurrences. Take an atom, for example. When a quantum event occurs, the atom is in one state and then in another.
You’ve got an electron in one state, and then suddenly, it’s in a different state. It doesn’t gently drift from a more energetic state to a lower one—it jumps. That’s a discrete event rather than a continuous transition. So, that suggests that discrete events form the universe’s fundamental structure.
At the same time, plenty of things in the universe operate in a non-discrete, or at least an implicitly non-discrete manner—basically, everything. But take a photon, for instance. A photon can be detected leaving an atom. You can’t detect the photon itself leaving but can detect the atom’s state changing.
And then, you can detect that photon again at some later point in space and time. That implies that the photon traversed space in a continuous way. Even though if you actually detect it mid-flight, you interfere with it, and it’s no longer the same photon that was originally emitted.
However, I read somewhere that there are ways to detect photons without capturing them. But anyway—even if you can’t track a photon between its origin and destination, it still bears the earmarks of having travelled continuously. The classic example is the two-slit experiment. Or even more, if you put a barrier between the emission point and its destination, the photon won’t arrive.
It has to try—the space has to be unencumbered along its path. So, objects travelling continuously suggest that not everything is discrete. Though, again, you could make a counterargument that a photon and its trajectory could be characterized in some system with a discrete set of variables. But the counter to that is: sure, you can do that, but it does not sound very easy. You could argue that the universe operates in the simplest way possible, and that means accommodating both discrete events and objects that appear to travel continuously.
Now, you could push back and ask, “Do they really travel continuously?” Because if you zoom into small enough distances, space becomes foamy and lacks true continuity. But again, the counterargument is that adding layers of complexity doesn’t necessarily make the model better—it just makes it messier. So, I guess I’m on a team that “any system built entirely on discrete events is probably not the best model.” Did I say “discontinuous?” Yeah. A system built entirely on discrete, discontinuous events might not be the most natural way to describe reality.
Jacobsen: What about the idea that the universe isn’t information per se, but more of a giant computational process? It doesn’t necessarily have to incorporate data or bits as we understand them, but rather, the fundamental process is computation, flipping the relationship between information and computation.
Rosner: The universe is highly emergent in what it can do—it almost operates in a “by any means necessary” way, like a Malcolm X principle applied to physics. It seems that the brain, for example, does a lot of combinatorial coding when it processes and transmits information. That’s an efficient way of minimizing the amount of data needed to represent information. If that even makes sense. But simultaneously, the brain is an evolved system—it doesn’t just rely on one method. It processes and retains information through whatever means works best. It takes every possible shortcut that hundreds of millions of years of evolution have stumbled upon. So, if you tried to model a brain using only combinatorial coding, you’d probably create something less efficient than an actual brain.
Similarly, if you tried to model the universe as constrained to only one type of information processing, you’d probably end up with a less efficient model than the actual universe. Like the brain, the universe seems to leverage every mechanism at its disposal to process and store information.
I need to grab some juice for my eyes—drying up here. Also, I forgot what the original question was. It was like, “Is the universe just an information processor?” So, I didn’t answer that.
Jacobsen: What about Gregory Chaitin’s work in algorithmic information theory (AIT)? The idea that the complexity of a system can be described in terms of the shortest possible algorithm needed to represent it? AIT uses information content to analyze physical systems, meaning that the complexity of a system can be characterized by the brevity of the algorithm that describes it.
Rosner: Is that… what? I don’t know. This is the first I’ve heard of it—I haven’t read anything about it. But it reminds me of something.
Okay, so Ramanujan—I think that’s his name—ends up in the hospital. Hardy, the mathematician, comes to visit him. Hardy says, “How was your trip?” And Ramanujan replies, “Fine, I rode over in a taxi with a very uninteresting number—1729.”
And Ramanujan says, “I beg to differ. That’s a very interesting number. The smallest number can be expressed as the sum of two cubes in two different ways.” Which, to people who get off on that kind of thing, is basically arithmetic porn.
But this brings us back to algorithmic simplicity, where you have many paradoxes about the simplest way to describe a system. For instance, you tried to identify the first “uninteresting” number. It’s not zero because zero has all sorts of special mathematical properties. One isn’t uninteresting either—it’s the multiplicative identity. Two are interesting because they are the smallest prime and the only even prime. Three is the first odd prime, so it’s interesting. Four is the first perfect square.
Then maybe you reach a number like 17 and say, “Okay, that’s the first uninteresting number.” But I could respond, “No, that makes 17 interesting because it’s the first uninteresting number.” So now it’s no longer uninteresting. The paradox is that you can’t define an uninteresting number without making it interesting by defining it that way.
And funnily enough, 17 actually shows up in a lot of comedy punchlines or in places where people need a random-seeming number. People unfamiliar with number theory will often pick 17 because it appears arbitrary. Two feels too fundamental. Twelve is a dozen, which is too familiar. Thirteen is unlucky. Fourteen is a fortnight or a stone if you’re in Britain. Eventually, you get to 17, which seems like a random, unspecial number—so it gets used often.
So, anyway, I don’t fully buy into algorithmic information theory without hearing a more detailed explanation. But we can cover that tomorrow.
Jacobsen: All right. Be safe.
Rosner: Okay.
Jacobsen: I’ll see you later.
Rosner: Bye.
Jacobsen: Okay.
Rosner: Bye.
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