Wolfram’s Physics Project is a very interesting one and its recent evolution fascinates me. I think that the recent discovery of the ruliad is a good progress in the project. However, there is something I don’t understand:
According to Wolfram’s writing about the ruliad (The Concept of the Ruliad—Stephen Wolfram Writings), there is only one ruliad which contains all possible formal systems. I understand why there should be only one ruliad as it would contain all possible computational rules by definition. However, I can imagine a formal system or abstract situation where somehow there could be multiple rulial spaces or “ruliads”. So, at the end, wouldn’t it be possible that there could be other ruliads (for computational systems, I’m not talking about other possible “ruliads” containing hypercomputation)?
It’s about computational equivalence, different computational rules can have the same rule signature, being computationally equivalent, which can be seen as the same rule. In my opinion.
And couldn’t there be different computational rules with different rule signatures somehow, so that their respective “ruliads” would be different in some way or another?
I went to review the technical document Wolfram-ModelsForPhysics.pdf, and for the “formal system where could be multiple rulial spaces”, I didn’t see that. Well, I am not deep in Rulliad but below is how I think. And please forget about my previous “Computational Equivalence”, I mistook that concept.
Yes, “Rulliad contains all possible computational rules”, but do you remember that hypergraph? Rulliad contains rules only about edges on nodes: nodes that have no inner attributes, nodes that are only distinguishible by their connections in the directed (multi) graph
so rules are about how those edges change, regardless of nodes themselves. There may be different sets of rules with different input/output edge groups, but by difinition Rulliad includes all of them, I didn’t see where the other Rulliad are.
By the way, I don’t know why but I have a one day cool down after I post or reply, so I didn’t reply until now.