Back when I used do theoretical physics for a living, I must admit I didn’t think much about trying to find a fundamental theory; I was more concerned about what we could figure out based on the theories we had. I thought maybe we’d be able to have a possible model for the first seconds of the universe, but we’d spend years trying to see whether it might actually connect to the physics we see today. It’s basically making us a very simple “piece of space”. We remain technologically trapped while the climate worsens and our resources dwindle. Is casual invariance just associativity? The only way to keep the foliation consistent in the multiway graph above is to have it progressively expand over time. Here’s another rule: {{x, y, z}, {u, y, v}} → {{w, z, x}, {z, w, u}, {x, y, w}}. We started understanding how quantum mechanics works. Maybe one day we will have built up familiar ways of talking about the concepts that are involved. In other words, even though we have done a different sequence of updates, the outcome is the same. But even if the size of the hypergraph is always increasing, that doesn’t mean we’d necessarily notice. But, OK, even though geodesics were originally defined for continuous space (actually, as the name suggests, for paths on the surface of the Earth), one can also have them in graphs (and hypergraphs). So, OK, what might we see in the universe today that would reflect what happened extremely early in its history? But in quantum mechanics the formalism involves any particular system doing lots of different things “in parallel”, with us just seeing samples—ultimately with certain probabilities—of these possibilities. In other words, the observer is saying “that’s the state I consider the system to be in, and I’m sticking to it”. And in our models they’re not—even though, as we’ll see, relativity comes out just fine. To answer that, we have to talk about what physics is supposed to be about, and more broadly, what science is for. Yes, there are different possible paths of history. We can ask about other strange phenomena from general relativity. I soon realized that if that was going to be the case, we’d in effect have to go underneath space and time and basically everything we know. And while it might seem like a detail here, it actually turns out that it’s at the core of why relativity works, why there’s a meaningful objective reality in quantum mechanics, and a host of other core features of fundamental physics. So far, I’ve read half of this, will read the other when I get time. We need to work through a lot of complicated computation, mathematics and physics. There’s no absolute way for the observer to “know what’s going on in the universe”; all they ever experience is a series of updating events, that may happen to be affected by updating events occurring elsewhere in the universe. At least relative to the particles we currently know, such particles would have few hypergraph elements in them—so I’m referring to them as “oligons” (after the Greek word ὀλιγος for “few”). But the process of measuring dimension shows an example of how we can start making “physics-connectable” statements about the behavior of our rules. The additional massive benefit of the digital physics approach has over others is that it constrains the set of possible physical models. Yet applying this rule over and over again produces something that looks really complicated. In a typical case we can think of different reference frames in rulial space as corresponding to different description languages in which an observer can describe their experience of the universe. But in our models there’s in a sense too much emergence for this to work. But, OK, so what rules should we consider? But when we think about how “space is maintained” it’s basically through all sorts of seemingly random updating events in the hypergraph. As I mentioned earlier, there’s potentially a big problem here with computational irreducibility. [10] In order for the model to present these features, it must exhibit the Church-Rosser property (or "causal invariance" as Wolfram terms it).