“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”—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.