0) So, cool — Wolfram is hypothesizing our universe is a bunch of discrete relations defining a hypergraph, and it works via graph rewriting rules
https://writings.stephenwolfram.com/2020/04/finally-we-may-have-a-path-to-the-fundamental-theory-of-physics-and-its-beautiful/
…http://writings.stephenwolfram.comwritings.stephenwolfram.com 

1) Pretty funky for those of us working on AGI designs (like OpenCog) based on hypergraph knowledge stores in which cognitive processes are implemented as hypergraph rewrite rules… #opencog

2) I think Wolfram is largely in the right direction, though I also think that in some key respects he’s less far along than Ben Dribus was in 2013 in “On the Axioms of Causal Set Theory” https://arxiv.org/abs/1311.2148 

3) “This paper offers suggested improvements to the causal sets program in discrete gravity, which treats spacetime geometry as an emergent manifestation of causal structure at the fundamental scale….” (Dribus) — really a masterwork

4) Dribus showed that all the structure of modern unified physics is there in various structures defined over hypergraphs, and gave an abstract graph version of Schrodinger's Eq, including Feynman sums over spacetime continua as in loop quantum gravity (spacetime foam) etc.

5) HOWEVER, neither Dribus nor Wolfram nor anyone else has quite gotten these frameworks to distinguish between the 8 zillion variants of unified physics that can be formulated in this sort of abstract framework...

6) So at this point, these are very promising alternative frameworks for exploring and formulating physics theories, but haven't yet been used to deliver concrete theoretical progress w/ specific predictive value

7) But — the use of the same math formalism for mind and physics is intriguing esp. in the light of the relation btw observer and observed in QM... it suggests one can formalize the inter-creation of mind and reality at a fundamental level using hypergraph rewriting.

8) Maybe we can use hypergraph rewriting as a formalism for what I’ve called “Euryphysics” — the study of the hypothetical broader macro-cosmos in which our physical universe, and our consciousness, both bounce around among other forms and patterns http://journals.sfu.ca/jnonlocality/index.php/jnonlocality/article/view/65

9) One place Wolfram's intuition is markedly distinct from that of Dribus and others active in this area (and me) is that Wolfram strongly suspects there is a simple deterministic hypergraph-rewrite rule underlying our multiverse (serving as the generator basically).

10) It's quite possible that this sort of hypergraph-rewriting multiverse framework is correct, but the multiversal hypergraph has extremely high algorithmic information content... rather than having some simple deterministic generating function.

11) It may work more like: the generating hypergraph-rewrite rules of the multiverse are sampled from some amplitude-distribution over possible rewrite-rule-sets.

12) In which case we should be looking for the amplitude-distribution (e.g. the rating function for what quantifies the nice-ness of a rewrite rule or rule-set) rather than for the single magic rewrite-rule or rule-set.

13) Now Wolfram does say "But what if there wasn’t just one rule that could be used? What if all conceivable rules could be used? What if every updating event could just use any possible rule?"

14) And he argues that it doesn't matter what deterministic generating rule is chosen, as it's equivalent to a frame of reference in physics: "Basically it’s saying that any (computation universal) rule will do—if we’re prepared to craft the appropriate description language.”

15) But I think having one rule is different than using different stochastically selected rules each time an event happens. My point is: Wolfram thinks our multiverse has finite (and very small) algorithmic information, I am skeptical...

16) I would say the multiverse description language must be a probabilistic programming language based on infinite-order probabilities manipulated via paraconsistent logic, right?

17) Which Curry-Howard will map into cross-universal gradual typing, in which the “introduction” of types for otherwise-untyped expressions occurs equally forward and backward in time in accordance w/ quantum temporality --

19) Or as my long-time AI collaborator Nil Geisweiller said when seeing Wolfram’s stuff: * OpenCog 42.0 *

20) Now the program that generates and runs all programs has a pretty small algorithmic information (Schmidhuber’s multiverse!). But this program generates all computable multiverses not just ours — so that the choice of ours is the thing whose complexity needs evaluating

21) What if the amplitude distribution from which the generating hypergraph rewrite rules of the multiverse are chosen is a trans-Turing oracle? (I think I need to put that on a T-shirt!!) Yeah... OpenCog 42.0 ...