Aren't these multiway systems essentially what we see with ambiguous grammars that yield parse forests rather than parse trees? The "forest" here is a forked parallel computation started upon encountering any ambiguous rewrite.
One application of these might be to resolve the meaning of probabilities under the many-worlds interpretation of quantum mechanics. When an interaction takes place, a number of worlds are created for each possible outcome, but it was never clear how to formally derive the probability of finding yourself in any given world (the Born rule).
Under the section titled "Observers, Reference Frames and Emergent Laws" in this article, you can see some branches merging again in that first graph, so perhaps the probabilities of the Born rule are due to parallel computations that merge in this way, ie. the probability you'd find yourself in the BBBB world rather than the AA world at step 3 of the computation is 2/3 vs. 1/3, respectively. If rules generate recurring patterns as shown there, these might show up as stable probabilities in aggregate.
> Aren't these multiway systems essentially what we see with ambiguous grammars...
Yes.
> One application of these might be to resolve the meaning of probabilities under the many-worlds interpretation...
There's some ways to go before we Hilbert spaces, operator algebras, and the like, but yes, the idea would be that some path counting procedure would be used to derive the Born rule. It would be great to bridge with Carroll's self-locating uncertainty paper [0]
> Under the section titled "Observers, Reference Frames and Emergent Laws" in this article, you can see some branches merging again in that first graph, so perhaps the probabilities of the Born rule are due to parallel computations that merge in this way...
One application of these might be to resolve the meaning of probabilities under the many-worlds interpretation of quantum mechanics. When an interaction takes place, a number of worlds are created for each possible outcome, but it was never clear how to formally derive the probability of finding yourself in any given world (the Born rule).
Under the section titled "Observers, Reference Frames and Emergent Laws" in this article, you can see some branches merging again in that first graph, so perhaps the probabilities of the Born rule are due to parallel computations that merge in this way, ie. the probability you'd find yourself in the BBBB world rather than the AA world at step 3 of the computation is 2/3 vs. 1/3, respectively. If rules generate recurring patterns as shown there, these might show up as stable probabilities in aggregate.