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These general "multicomputational processes" are well known in computer science as nondeterministic transition systems, or coalgebras for the powerset functor. And in that setting there is a lot of work that has been done about the kinds of logical statement that can be said about their evolution -- such as whether a given proposition about the states may always or eventually hold; this is coalgebraic modal logic. As usual, Wolfram does not mention this prior work.

One thing that I have often thought though is that the mathematical sciences could do with more cross-pollination with coalgebra.


Wow, thank you.

So I adhere to the Schützenberger view of automata theory, that the way to explain a semester's finite automata theory to a math major in twenty minutes is via rational power series on noncommuting variables. Change the semiring from true/false to probabilities and one gets hidden Markov chain theory.

So how do nondeterministic transition systems fit into this picture? I'm guessing that the connection should blow my mind with a new way to see power series?


I'd love to see both an answer to your question, and also your twenty minute explanation written up, if you haven't already!


I have no idea what all of this means, but would like to share a GPT-4 discussion that might illuminate your request.

https://chat.openai.com/share/6a76cdcc-a303-4717-885c-519951...


I have one of their machines (a StarBook that I am typing this on), and it is excellent. It probably helps to have a $9m seed round -- certainly it means Framework can do much more marketing (including such as the Steam Deck stunt) and hire more people -- and I'm sure it's easier to raise those funds from the US, but it is clearly not necessary. I hope that Star Labs does well enough that they are able to expand, raise funding if they wish, and compete with better capitalized companies.


I am typing this on their latest StarBook. It's a great machine. As for durability, it has an aluminium body and seems sturdily built. I expect it to last a good few years.


would you be able to share a video or blog review of this thing ?


In fact, the compositional structure underlying that of predictive coding [0,1] is abstractly the same as that underlying backprop [2]. (Disclaimer: [0,1] are my own papers; I'm working on a more precise and extensive version of [1] right now!)

[0] https://arxiv.org/abs/2006.01631 [1] https://arxiv.org/abs/2101.10483 [2] https://arxiv.org/abs/1711.10455


Hurry and publish before I have manuscripts ready applying these results.


Hey, Eli :-)

I'm working on it; I'll send you an e-mail. Things quickly turned out to be more general than I realized last year.


That would make sense. The whole ACT/categorical cybernetics community has been working out how massively general optics are :-).


I found this, which seems to be a build of Okular for Windows: https://chocolatey.org/packages/okular

(I haven't tested it -- happy Okular Linux user here. It was linked from the site you linked, though.)


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