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Systems that exhibit quantum behavior and functional completeness

Posted 4 months ago
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I'm pretty new to the Wolfram Physics project and my interest is that of an amateur, so apologies in advance if this is a naive question, or if it not formulated in the most precise way:

I've been interested in distributed ledgers, specifically those using directed acyclic graphs rather than blockchain, which shows some interesting behavior that resemble the quantum properties that come out of the causal hypergraph. Basically, causally possible but mutually conflicting updates to the ledger state can emerge in the data structure, but observations of the ledger state force the network to converge around one or the other causal path.

At the same time, I've noticed that the data structure exhibits functional completeness - you can build NOR gates out of the certain message structures and start to model arbitrary computational logic. This got me thinking that if you had an update rule (or rules), that exhibited functional completeness (I'm not sure how to define this exactly), would that not imply that you could build any other rule out of it? And therefor it would be a "universal" rule from which any of the the properties of our physical reality could emerge.

POSTED BY: B R
Answer
3 Replies

You are welcome. If you want, have a look at this post that I wrote today, inspired by your question.

Posted 4 months ago

Thanks! I just came across this idea of rulial space in another post just before seeing this and realized it may be indeed the idea I was trying to express, although in a much clearer form. Thanks for the feedback and the link.

POSTED BY: B R
Answer

I am not sure, but I think that you are referring to something similar to what Wolfram says when he talks about rules that "emulate" other rules (Exploring Rulial Space). I think that it could indeed be possible that all the computationally complete rules are actually equivalent and that we (computationally bounded observers) are not able to tell exactly what rule is being applied.

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