⚗️alchemist⚗️ (npub1pt6…6mf6) yes, I agree with this. and more specifically I would say math is a somewhat easier planning problem that arbitrary planning because logic gives a way of purely *syntactically* representing the *semantics* of... I'm not sure there's a word for this, but, maybe, "bundles of paths through time"?
if you consider GOFAI-style planners, like STRIPS and PDDL, the reason they do their search through manipulation of symbolic statements rather than direct world states a la MCTS, is precisely because they want to group various paths through configuration space into bundles that can be treated as a whole. if you think of the monoid action on world-configuration-space defined by the agent's actions, then the symbolic representation is implementing a kind of homomorphism into a monoid action over term rewriting systems, that in some sense "compresses it". what's unique about math is that since math is already term-rewriting, you can do this "for free" and more importantly, it actually works robustly without the lossyness that GOFAI planning would be subject to
nemesis :blackhole: /
npub10z…xyg26
2024-01-19 18:30:13
in reply to nevent1q…3un8
Author Public Key
npub10zrcn8lufu6f5yvpv0llqy5rr82kg2wld432jan9fz83rsnxnzws2xyg26Seen on
wss://relay.nostr.bandPublished at
2024-01-19 18:30:13Event JSON
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"content": "nostr:npub1pt6l3a97fvywrxdlr7j0q8j2klwntng35c40cuhj2xmsxmz696uqfr6mf6 yes, I agree with this. and more specifically I would say math is a somewhat easier planning problem that arbitrary planning because logic gives a way of purely *syntactically* representing the *semantics* of... I'm not sure there's a word for this, but, maybe, \"bundles of paths through time\"?\n\nif you consider GOFAI-style planners, like STRIPS and PDDL, the reason they do their search through manipulation of symbolic statements rather than direct world states a la MCTS, is precisely because they want to group various paths through configuration space into bundles that can be treated as a whole. if you think of the monoid action on world-configuration-space defined by the agent's actions, then the symbolic representation is implementing a kind of homomorphism into a monoid action over term rewriting systems, that in some sense \"compresses it\". what's unique about math is that since math is already term-rewriting, you can do this \"for free\" and more importantly, it actually works robustly without the lossyness that GOFAI planning would be subject to",
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