Hello, my name is Spencer Hargiss, I'm new here. I just remembered an idea I had when learning about the Wolfram Physics project, and it still seems exciting to me. It lacks mathematical rigor, but might be useful. And I thought, hey, why not share?
The idea is that maybe the universe isn’t a graph, but is a self-replicating pattern of information within a graph. I’m going to try to make an argument for why it’s worth taking this possibility seriously. The possibility could change our ideas about what kind of graph we are looking for, and alter basic assumptions about how the graphs relate to quantum mechanics. And in any case, it's a delicious idea and great brain-candy, so it's probably worth chewing on as food for thought.
The inflationary universe, in most theories I’ve heard of, expanded unbelievably fast… within a truly microscopic period of time it became so large that nobody really knows how big it is. Yet, right after that things settled down, and now it’s expanding at a measurable, accelerating, but pretty modest rate. That’s a massive discrepancy. It reminds me of the difference between the strength of the gravitational force and the other forces, the difference in magnitude is so large. It screams for an explanation.
Let’s say the graph tends to expand at some sort of rate, let’s say every step the number of nodes doubles. If a step corresponds to the Planck length or something like that, that’s going to be a really unbelievable expansion rate. Every second the universe would get 2^10^44 something times bigger… that’s just a crude non-rigorous ballpark estimate. The point is it might account for the blistering rate of expansion in the early universe. That might suggest, when figuring out what hyper graph rule we’re looking for, we should look for a rapidly expanding rule like that. If the Universe is based on cellular automata like rules and has that kind of Oomph, the oomph must emerge from the rule itself.
But then what happened? Why is the universe not expanding at that rate if it's driven by a rule which tends to do that? I'm sure there's lots of explanations out there already in the community, and I wouldn't doubt someone's already considered the one I'm going to propose.
The idea is that the universe is not simply the graph, but a self-replicating pattern inside the graph. Kind of like a cellular automation on a strand of DNA… the pattern is a 1D pattern, but it replicates into a higher dimensional space. You could imagine DNA that doesn’t copy exactly but instead follows a rule, like a classic cellular automata rule. Each time it’s copied, time advances one step on the DNA. Any creatures that exist in this DNA automation universe would experience themselves as occupying a 1D universe which is changing in size relatively slowly, even as the pattern really grows geometrically. If they looked really closely at things they might find evidence of the copying process which could clue them in.
Similarly, you can imagine a rapidly expanding graph being the agar or substrate in which a 3D pattern—the universe—is replicating itself, and evolving according to a 3D rule which is distinct from the graph rule. The graph itself could be 3D (each node on average connecting to 6 others, or whatever), but it's likely to have more dimensions than the pattern. The process of replication could be much simpler than the process for biological organisms, since it exists on a much simpler level and doesn't have metabolism or competition to deal with. This idea could range from a weak version where copying information is simply what this graph rule does from the start, or a strong version where the copying process evolved through a messy drawn out process of natural selection, in which the 'natural laws' we know are the product of evolution and adaptation seeking to maximize the rate of replication. Remember that the graph evolves so rapidly and is so large that if the emergence of a replicator is even possible at that level, it would come about much more quickly and inevitably than with biological life.
This way we could still imagine that the graph has a rapidly expanding rule, and also explain our slowly expanding universe.
I could say a lot more, but all of this is completely conceptual rather than mathematical, I'm going to treat this post as a seed which I hope might sprout into a real hypothesis in a more methodical mind than my own.
Thanks for reading! Anyone who has any questions, comments, or objections: please let me know.