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gwillen comments on Harry Potter and the Methods of Rationality discussion thread, February 2015, chapter 109 - Less Wrong
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Depends on what kind of time travel and what kind of universe. Heck, even classical newtonian real-valued physics is not computable (but is computable to arbitrary precision). If the information content of the universe is finite (like, it is a grid of finite many cells, each of them could be in only finite many states, and time is discrete as well), then time travel is computable - you just have to store the information for the past 6 hours and brute-force consistent stable loops.