This is also interesting if you imagine that you and your other copies don’t all have the same memories—instead, each person remembers how many times they’ve been copied. So the first copy never remembers getting copied, and then the second copy remembers getting copied once, etc. Now the probabilities are no longer so obvious, because the only straightforward probability is the 50% probability the two most recent yous have that they’re the other one—everyone else is distinguishable. The “probability” is instead some measure of caring, or personal identity transfer (to the extent that one believes that there is some kind of identity-fluid that obeys locality and conservation when getting transferred around).
There’s a standard way to elicit practical ‘probabilities’ via bets in these situations: play for charity (with independent bets). In order to have something to bet about, let’s turn the memories back off, and ask people to bet on whether they’re the original (perhaps you have a tattoo on the back of your neck that doesn’t get copied), betting with their favorite charity’s money. At what odds should they make these bets—when does the charity start making money if your decision procedure says to bet? It’s at 1:N odds, not 1:2^N odds.
Again, we should contrast this with the case where you have some family heirloom in a box, and whenever you’re duplicated you put the box at random in the room of one of your two causal descendants. If only the original gets duplicated 100 times, the box really is in the first copy’s room with 50% probability and in the original’s room with 1 in 2^100 probability. So if personal identity behaves like physical stuff that gets passed on to your duple descendants, changing how you make copies changes the distribution of the stuff.
Another variation might be to Sleeping Beautify this problem—change the duplication into memory erasure. This makes more sense if we use the variation where you remember how many times you’ve been copied. Suppose the scientists who perfected the memory erasure pill used on Sleeping Beauty are now working on a selective memory restoration pill. Every day, your memories of the last 24 hours will be erased. But every two days, the scientists will flip a coin—if heads, restore your memory from one day ago, if tails, restore your memory from two days ago. In this way, every two days your memories advance by one day.
This procedure doesn’t seem, to me, to change any relevant probability about the situation. On each day, you know that you have a 50% chance of being the one with the causal descendant. So becoming the “oldest” means winning a series of coin flips. But as I noted above, in addition to probability, this problem is asking us about the measure of caring, or hypothetical identity-fluid, and the memory erasure version totally changes our intuitions about how that gets sloshed around.
“This is also interesting if you imagine that you and your other copies don’t all have the same memories—instead, each person remembers how many times they’ve been copied”—I didn’t assume that all of the copies have the same memories; just that all copies have a real or false memory of the first copy. Everyone is distinguishable except for the original and the latest copy, but how does it break this analysis? (Actually I realised that I was less clear on this than I could have been, so I edited the post)
For each split, if you are really experiencing this event you have a 50% chance of being the original and 50% of being the latest clone. However, regardless of how many clones remember the event, there is only a 2/n chance of actually experiencing the splitting as either the original or the new clone and so splitting this 50⁄50 gives a 1/n chance of being either.
Probability according to who? Who is making a prediction that can be either true or false, and their state of information leads them to assign this probability?
For example, suppose I get cloned twice, once today and once tomorrow, with no loss of memories or awareness. The only special thing about the cloning device is that it won’t copy the tattoo I have on the back of my neck. Right after I get cloned today, I will think there’s a 50⁄50 chance I have the tattoo. Then maybe I’ll go home and check in the mirror and my P(tattoo) will go close to 0 or 100%. Then tomorrow, the person with the tattoo will go get cloned again—thus learning that they have the tattoo even if they forgot to check in the mirror. Meanwhile, the person with no tattoo sits outside in the waiting room. After this second cloning, the person in the waiting room still knows they don’t have the tattoo, while the two people who just got cloned think they have a 50% chance of having the tattoo.
At no point in this story does anyone think they have either a 1⁄3 or 1⁄4 chance of having the tattoo.
“After this second cloning, the person in the waiting room still knows they don’t have the tattoo, while the two people who just got cloned think they have a 50% chance of having the tattoo”—What’s the setup? If it is known that the person with the tattoo is always the one being cloned, the first person in the waiting room can deduce that they don’t have the tattoo when the second person walks into it. So it is only the most recent clone who has a 50⁄50 chance of having the tattoo, unless I’m misunderstanding the problem?
Yes—what you’re calling “the original,” I’m calling “the person with the tattoo” (I’m choosing to use slightly different language because the notion of originalness does not quite carve reality at the joints). So, as in R Wallace’s thought experiment, the person with the tattoo is the person getting cloned over and over.
One might claim that there is a further probability in this situation—the probability you should assign before the whole process starts, that you will in some sense “end up as the person with the tattoo.” But I think this is based on a mistake. Rhetorically: If you don’t end up as the person with the tattoo, then who does? A faerie changeling? There is clearly a 100% chance that the person with the tattoo is you.
Regarding the bet with charity—the only reason the bet with charity (as I mentioned in the case where none of you have any memories that indicate which copy you might be) a 1/N result rather than a 1⁄1 result is because all copies of you have to make the bet, and therefore the copies with no tattoo pay off money. If, the day before the cloning, you bet someone that you could show up tomorrow tattoo and all—well, you could do that 100% of the time.
As I mentioned above, it’s perfectly valid to have a degree of caring about future copies, or a degree of personal identification. But the naive view that “you” are like a soul that is passed on randomly in case of cloning is mistaken, and so is the notion of “probability of being the original” that comes from it.
This is also interesting if you imagine that you and your other copies don’t all have the same memories—instead, each person remembers how many times they’ve been copied. So the first copy never remembers getting copied, and then the second copy remembers getting copied once, etc. Now the probabilities are no longer so obvious, because the only straightforward probability is the 50% probability the two most recent yous have that they’re the other one—everyone else is distinguishable. The “probability” is instead some measure of caring, or personal identity transfer (to the extent that one believes that there is some kind of identity-fluid that obeys locality and conservation when getting transferred around).
There’s a standard way to elicit practical ‘probabilities’ via bets in these situations: play for charity (with independent bets). In order to have something to bet about, let’s turn the memories back off, and ask people to bet on whether they’re the original (perhaps you have a tattoo on the back of your neck that doesn’t get copied), betting with their favorite charity’s money. At what odds should they make these bets—when does the charity start making money if your decision procedure says to bet? It’s at 1:N odds, not 1:2^N odds.
Again, we should contrast this with the case where you have some family heirloom in a box, and whenever you’re duplicated you put the box at random in the room of one of your two causal descendants. If only the original gets duplicated 100 times, the box really is in the first copy’s room with 50% probability and in the original’s room with 1 in 2^100 probability. So if personal identity behaves like physical stuff that gets passed on to your duple descendants, changing how you make copies changes the distribution of the stuff.
Another variation might be to Sleeping Beautify this problem—change the duplication into memory erasure. This makes more sense if we use the variation where you remember how many times you’ve been copied. Suppose the scientists who perfected the memory erasure pill used on Sleeping Beauty are now working on a selective memory restoration pill. Every day, your memories of the last 24 hours will be erased. But every two days, the scientists will flip a coin—if heads, restore your memory from one day ago, if tails, restore your memory from two days ago. In this way, every two days your memories advance by one day.
This procedure doesn’t seem, to me, to change any relevant probability about the situation. On each day, you know that you have a 50% chance of being the one with the causal descendant. So becoming the “oldest” means winning a series of coin flips. But as I noted above, in addition to probability, this problem is asking us about the measure of caring, or hypothetical identity-fluid, and the memory erasure version totally changes our intuitions about how that gets sloshed around.
“This is also interesting if you imagine that you and your other copies don’t all have the same memories—instead, each person remembers how many times they’ve been copied”—I didn’t assume that all of the copies have the same memories; just that all copies have a real or false memory of the first copy. Everyone is distinguishable except for the original and the latest copy, but how does it break this analysis? (Actually I realised that I was less clear on this than I could have been, so I edited the post)
For each split, if you are really experiencing this event you have a 50% chance of being the original and 50% of being the latest clone. However, regardless of how many clones remember the event, there is only a 2/n chance of actually experiencing the splitting as either the original or the new clone and so splitting this 50⁄50 gives a 1/n chance of being either.
Probability according to who? Who is making a prediction that can be either true or false, and their state of information leads them to assign this probability?
For example, suppose I get cloned twice, once today and once tomorrow, with no loss of memories or awareness. The only special thing about the cloning device is that it won’t copy the tattoo I have on the back of my neck. Right after I get cloned today, I will think there’s a 50⁄50 chance I have the tattoo. Then maybe I’ll go home and check in the mirror and my P(tattoo) will go close to 0 or 100%. Then tomorrow, the person with the tattoo will go get cloned again—thus learning that they have the tattoo even if they forgot to check in the mirror. Meanwhile, the person with no tattoo sits outside in the waiting room. After this second cloning, the person in the waiting room still knows they don’t have the tattoo, while the two people who just got cloned think they have a 50% chance of having the tattoo.
At no point in this story does anyone think they have either a 1⁄3 or 1⁄4 chance of having the tattoo.
“After this second cloning, the person in the waiting room still knows they don’t have the tattoo, while the two people who just got cloned think they have a 50% chance of having the tattoo”—What’s the setup? If it is known that the person with the tattoo is always the one being cloned, the first person in the waiting room can deduce that they don’t have the tattoo when the second person walks into it. So it is only the most recent clone who has a 50⁄50 chance of having the tattoo, unless I’m misunderstanding the problem?
Yes—what you’re calling “the original,” I’m calling “the person with the tattoo” (I’m choosing to use slightly different language because the notion of originalness does not quite carve reality at the joints). So, as in R Wallace’s thought experiment, the person with the tattoo is the person getting cloned over and over.
One might claim that there is a further probability in this situation—the probability you should assign before the whole process starts, that you will in some sense “end up as the person with the tattoo.” But I think this is based on a mistake. Rhetorically: If you don’t end up as the person with the tattoo, then who does? A faerie changeling? There is clearly a 100% chance that the person with the tattoo is you.
Regarding the bet with charity—the only reason the bet with charity (as I mentioned in the case where none of you have any memories that indicate which copy you might be) a 1/N result rather than a 1⁄1 result is because all copies of you have to make the bet, and therefore the copies with no tattoo pay off money. If, the day before the cloning, you bet someone that you could show up tomorrow tattoo and all—well, you could do that 100% of the time.
As I mentioned above, it’s perfectly valid to have a degree of caring about future copies, or a degree of personal identification. But the naive view that “you” are like a soul that is passed on randomly in case of cloning is mistaken, and so is the notion of “probability of being the original” that comes from it.