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devas comments on Causal Universes - Less Wrong
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this is my first time approaching a meditation, and I've actually only now decided to de-lurk and interact with the website.
One way to enumerate them would be, as CCC has just pointed out, with integers where irrationality denotes acausal worlds and rationality denotes causal worlds.
This however doesn't leaves space for Stranger Things; I suppose we could use the alphabet for that. 1 If, however, and like I think, you mean enumerate as "order in which the simulation for universes can be run" then all universes would have a natural number assigned to them, and they could be arranged in order of complexity; this would mean our own universe would be fairly early in the numbering, if causal universes are indeed simpler than acausal ones, if I've understood things correctly.
This would mean we'd have a big gradient of "universes which I can run with a program" followed by a gradient of "universes which I can find by sifting through all possible states with an algorithm" and weirder stuff elsewhere (it's weird; thus it's magic, and I don't know how it works; thus it can be simpler or more complex because I don't know how it works).
In the end, the difference between causal and acausal universes is that one asks you only the starting state, while the other discriminates between all states and binds them together.
AAAAANNNNNNNND I've lost sight of the original question. Dammit.
It would be nice if there was some topology where the causal worlds were dense in the acausal ones.
Unfortunately, this strikes me as unlikely.
Why would that be nice?
Yes, and I forgot to put it in.
Wait, causal worlds are dense IN acausal ones?
Is that a typo, and you meant "causal worlds were denser than acausal ones" or did I just lose a whole swath of conversation?
I mean the class of causal worlds be dense in the class of worlds, where worlds consists of causal and acausal worlds. The same way we understand a lot of things in functional analysis: prove the result for the countable case, prove that taking compactifications/completions preserves the property, and then you have it for all separable spaces.
Well, I admit that I had originally considered that Stranger Things would most likely be either causal or acausal; I can't really imagine anything that's neither, given that the words are direct opposites.
In the case of a Stranger Thing that's strange enough that I can't imagine it, we could always fall back on the non-real complex numbers, which are neither rational nor irrational (and are numerous enough to make real numbers look trivial by comparison).