Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: If a tree falls on Sleeping Beauty... , published by ata on the AI Alignment Forum. Several months ago, we had an interesting discussion about the Sleeping Beauty problem, which runs as follows: Sleeping Beauty volunteers to undergo the following experiment. On Sunday she is given a drug that sends her to sleep. A fair coin is then tossed just once in the course of the experiment to determine which experimental procedure is undertaken. If the coin comes up heads, Beauty is awakened and interviewed on Monday, and then the experiment ends. If the coin comes up tails, she is awakened and interviewed on Monday, given a second dose of the sleeping drug, and awakened and interviewed again on Tuesday. The experiment then ends on Tuesday, without flipping the coin again. The sleeping drug induces a mild amnesia, so that she cannot remember any previous awakenings during the course of the experiment (if any). During the experiment, she has no access to anything that would give a clue as to the day of the week. However, she knows all the details of the experiment. Each interview consists of one question, “What is your credence now for the proposition that our coin landed heads?” In the end, the fact that there were so many reasonable-sounding arguments for both sides, and so much disagreement about a simple-sounding problem among above-average rationalists, should have set off major alarm bells. Yet only a few people pointed this out; most commenters, including me, followed the silly strategy of trying to answer the question, and I did so even after I noticed that my intuition could see both answers as being right depending on which way I looked at it, which in retrospect would have been a perfect time to say “I notice that I am confused” and backtrack a bit. And on reflection, considering my confusion rather than trying to consider the question on its own terms, it seems to me that the problem (as it’s normally stated) is completely a tree-falling-in-the-forest problem: a debate about the normatively “correct” degree of credence which only seemed like an issue because any conclusions about what Sleeping Beauty “should” believe weren’t paying their rent, were disconnected from any expectation of feedback from reality about how right they were. It may seem either implausible or alarming that as fundamental a concept as probability can be the subject of such debates, but remember that the “If a tree falls in the forest.” argument only comes up because the understanding of “sound” as “vibrations in the air” and “auditory processing in a brain” coincide often enough that most people other than philosophers have better things to do than argue about which is more correct. Likewise, in situations that we actually encounter in real life where we must reason or act on incomplete information, long-run frequency is generally about the same as optimal decision-theoretic weighting. If you’re given the question “If you have a bag containing a white marble and two black marbles, and another bag containing two white marbles and a black marble, and you pick a bag at random and pick a marble out of it at random and it’s white, what’s the probability that you chose the second bag?” then you can just answer it as given, without worrying about specifying a payoff structure, because no matter how you reformulate it in terms of bets and payoffs, if your decision-theoretic reasoning talks about probabilities at all then there’s only going to be one sane probability you can put into it. You can assume that answers to non-esoteric probability problems will be able to pay their rent if they are called upon to do so, and so you can do plenty within pure probability theory long before you need your reasoning to generate any decisions. But when you start getting into problems where there may be multiple co...