Sleeping Beauty, centered world models, and why 1/3 is the right credence
jessi_cata · x · 2026-10-17
A long-form thread dissecting the Sleeping Beauty Problem: a coin is flipped Sunday without revealing the result; if tails, your Monday memory is wiped, so on waking you can't tell Monday from Tuesday. Is the probability of heads 1/2 or 1/3?
- The author sides with 1/3: Heads+Monday, Tails+Monday, and Tails+Tuesday waking scenarios are equally likely; halfers insist Sunday's objective odds shouldn't shift with memory loss.
- The deeper question is whether indexical events like "it's Monday" can carry probabilities at all — probability as objective physical chance vs. Bayesian subjective credence. The author argues beliefs about your own time and place are testable and legitimate, formalized as a centered world model: a description of the universe plus which point in it is "here and now," like knowing which player you are in a multiplayer game.
- The author sketches connections across anthropics, decision theory, reinforcement learning, and consciousness, while admitting the full formal story isn't done yet.
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