You arguments are interesting, but I find myself still believing that no single-probability answer is really quite right for the problem.
When you tell me that we select a random marble from a bag, I know what that means. When you tell me that I will either awaken twice, or just once, and we can select a random “awakening”, then yes, somehow of the three awakenings we draw on the tree the answer is 1⁄3. But two of those awakenings occur sequentially, while one is mutually exclusive with the two.
From the perspective of beauty herself all of those awakenings are, in some sense, indistinguishable from one another—they entail (or may entail) identical subjective experiences. If someone came along and said that in such cases you have you use Bose statistics [1], then I would feel like they were wrong—but I would not be able to definitively tell them they were. Maybe identical states of mind (from memory wipes, or human copying machines or other Anthropic stuff) need to be treated Bose-like.
[1] Bose statistics occur in quantum physics where combinatorials come up. An excellent way of thinking of them is given in the book “The beginning of Infinity” by David Deutch: given a bag of beads, when one bead is removed, we can ask “what is the probability that this specific bead will be removed” in a sensible way. However, if your (electronic) bank balance reads $100, and you spend $1 on your card, it just doesn’t make sense to ask “what is the probability that the dollar removed is the first dollar in my account?”. The account is just a quantity that is incremented down. With quantum particles it turns out (experimentally) that the different end states occur with probabilities as if we had one field (like an electric bank account) for each distinguishable type of particle. In the limit where all the particles are distinguishable (each bank account reads either 0 or 1) then the statistics returns to normal. https://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_statistics This is one reason why people often like to talk about quantum fields instead of particles—the fields act like ledgers that increment up and down, not like collections of marbles.
Saying that when you spend $1 on card “it removes a random dollar from the account” is not even wrong, it is in entirely the wrong frame. Similarly, if I am going into a copying machine that will produce many identical copies of me, then saying “after the copying, I will be a random one of those people” is also (arguably) not even wrong, but in the wrong frame. How much do these things change if, instead of asking “just before” copying or going to sleep we ask just after waking up or stepping out of the copy machine?
Well yes, I didn’t really expect that this post on its own will be persuasive enough. But I hope it gave you enough curiosity not to entirely dismiss the idea, that the solution may be possible and search for it with deeper analysis of a problem isn’t just a fool’s erand.
Let’s see how my next two posts are going to change your beliefs about the matter.
I am interested to see your deeper analysis. To clarify, I am not saying “there is nothing more interesting to discuss on sleeping beauty and anthropic stuff”, my take is more that when you do your deeper analysis you should be open to the idea that maybe the question is confused, underspecified or otherwise in need of refining.
You arguments are interesting, but I find myself still believing that no single-probability answer is really quite right for the problem.
When you tell me that we select a random marble from a bag, I know what that means. When you tell me that I will either awaken twice, or just once, and we can select a random “awakening”, then yes, somehow of the three awakenings we draw on the tree the answer is 1⁄3. But two of those awakenings occur sequentially, while one is mutually exclusive with the two.
From the perspective of beauty herself all of those awakenings are, in some sense, indistinguishable from one another—they entail (or may entail) identical subjective experiences. If someone came along and said that in such cases you have you use Bose statistics [1], then I would feel like they were wrong—but I would not be able to definitively tell them they were. Maybe identical states of mind (from memory wipes, or human copying machines or other Anthropic stuff) need to be treated Bose-like.
[1] Bose statistics occur in quantum physics where combinatorials come up. An excellent way of thinking of them is given in the book “The beginning of Infinity” by David Deutch: given a bag of beads, when one bead is removed, we can ask “what is the probability that this specific bead will be removed” in a sensible way. However, if your (electronic) bank balance reads $100, and you spend $1 on your card, it just doesn’t make sense to ask “what is the probability that the dollar removed is the first dollar in my account?”. The account is just a quantity that is incremented down. With quantum particles it turns out (experimentally) that the different end states occur with probabilities as if we had one field (like an electric bank account) for each distinguishable type of particle. In the limit where all the particles are distinguishable (each bank account reads either 0 or 1) then the statistics returns to normal. https://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_statistics This is one reason why people often like to talk about quantum fields instead of particles—the fields act like ledgers that increment up and down, not like collections of marbles.
Saying that when you spend $1 on card “it removes a random dollar from the account” is not even wrong, it is in entirely the wrong frame. Similarly, if I am going into a copying machine that will produce many identical copies of me, then saying “after the copying, I will be a random one of those people” is also (arguably) not even wrong, but in the wrong frame. How much do these things change if, instead of asking “just before” copying or going to sleep we ask just after waking up or stepping out of the copy machine?
Well yes, I didn’t really expect that this post on its own will be persuasive enough. But I hope it gave you enough curiosity not to entirely dismiss the idea, that the solution may be possible and search for it with deeper analysis of a problem isn’t just a fool’s erand.
Let’s see how my next two posts are going to change your beliefs about the matter.
I am interested to see your deeper analysis. To clarify, I am not saying “there is nothing more interesting to discuss on sleeping beauty and anthropic stuff”, my take is more that when you do your deeper analysis you should be open to the idea that maybe the question is confused, underspecified or otherwise in need of refining.