John Carlos Baez (npub1nf4…nqe4) thanks for the TLDR of their mapping, now I don't need to filter the paper for that info.
Greg Egan (npub12cu…d38p) The fun thing is that in this system one can calculate the system at arbitrary future times (you're also right that there are no shortcuts, but that is inevitably encoded in the word "computation"). However, this goes besides the point of undecidability, and this is i.m.o. the crux about all the misunderstandings. It is not "undecidable" to calculate the trajectory (and its less clear what that even is supposed to mean). Its the decission problem, whether the trajectory has or doesn't have a certain property, which is undecidable.
And in this phrasing the undecidability is suddenly not-surprising-at-all even to the lay person: If the property can take arbitrarily long to realize (like an arbitrarily long periodic path), how should we ever decide that we have waited sufficiently arbitrarily long to tell...
That said, I find that sentence about "undecidable trajectories" in the papers abstract borderline misleading (and yet I totally understand that its sexy to write). And I find the debate about undecidability in general often covered in a bit too much of miracle cloths.
papalex
npub1w8…9a0pl
2025-12-23 22:28:39 UTC
in reply to nevent1q…5g86
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"content": "nostr:npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4 thanks for the TLDR of their mapping, now I don't need to filter the paper for that info. \n\nnostr:npub12cuzzqzv8e8y7na77a9zv47mx2v6pec60qs5h7takzmv5p0mw0fsmgd38p The fun thing is that in this system one can calculate the system at arbitrary future times (you're also right that there are no shortcuts, but that is inevitably encoded in the word \"computation\"). However, this goes besides the point of undecidability, and this is i.m.o. the crux about all the misunderstandings. It is not \"undecidable\" to calculate the trajectory (and its less clear what that even is supposed to mean). Its the decission problem, whether the trajectory has or doesn't have a certain property, which is undecidable. \nAnd in this phrasing the undecidability is suddenly not-surprising-at-all even to the lay person: If the property can take arbitrarily long to realize (like an arbitrarily long periodic path), how should we ever decide that we have waited sufficiently arbitrarily long to tell... \n\nThat said, I find that sentence about \"undecidable trajectories\" in the papers abstract borderline misleading (and yet I totally understand that its sexy to write). And I find the debate about undecidability in general often covered in a bit too much of miracle cloths.",
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