I think that the problem here is that you still need info to distinguish yourself from shot-you. Consider a universe that contains one copy of every possible thing. In this universe, the information to locate you is identical to the information to describe you. In this case, describing you includes describing every memory you have. But if you have memories of reading a physics textbook and then doing some experiments, then the shortest description of your memories is going to include a description of the laws of physics. One copy of everything theory is a bad theory compared to physics.
If you have a simple physical law that predicts 1 human surrounded by 3^^^3 paperclips, then locating yourself is easy. Many simple algorithms, like looking for places where hydrogen is more abundant than iron, will locate you. In this universe, if Omega duplicates you, its twice as hard to point to each copy. And if he shoots one copy, it’s still twice as hard to point to the other copy. (the search for things that aren’t paperclips comes up with 2 items) In this universe, you would reject the third part of the deal.
Suppose that the universe was filled with interesting stuff in the sense that the shortest way to point to you was coordinates. Being duplicated gives 2 places to point to, so you expect that you were duplicated with probability 2⁄3. Once one copy is shot, you expect that your prob of being the other copy is 1⁄2. In this universe you would reject the first part of the deal.
In both cases you perform a Bayesian update based on the fact that you are still alive.
Yeah, this implicitly depends on how you’re being pointed to. I’m assuming that you’re being pointed to as “person who has had history [my history]”. In which case you don’t need to worry about doing extra work to distinguish yourself from shot-you once your histories (ballistically) diverge. (EDIT: I think. This is weird.)
If you’re pointed to with coordinates, it’s more likely that copies are treated as not adding any complexity. But this is disanalogous to the Presumptuous Philosopher problem, so I’m avoiding that case.
In which case you don’t need to worry about doing extra work to distinguish yourself from shot-you once your histories (ballistically) diverge. (EDIT: I think. This is weird.)
You do need to distinguish, it’s part of your history. If you are including your entire history as uncompressed sensory data, that will contain massive redundancy. The universe does not contain all possible beings in equal proportions. Imagine being the only person in an otherwise empty universe, very easy to point to. Now imagine that Omega makes 10100 copies, and tells each copy their own 100 digit id number. It takes 100 digits more complexity to point to any one person. The process of making the copies makes each copy harder to point to. The process of telling them id numbers doesn’t change the complexity. You only have 2 copies with id’s of “shot” and “not shot”.
Right, but suppose that everybody knows beforehand that Omega is going to preserve copy number 0 only (or that it’s otherwise a consequence of things you already know).
This “pays in advance” for the complexity of the number of the survivor. After t_1, it’s not like they’ve been exposed to anything they would be surprised about if they were never copied.
Ah, wait, is that the resolution? If there’s a known designated survivor, are they required to be simple to specify even before t_1, when they’re “mixed in” with the rest?
I think that the problem here is that you still need info to distinguish yourself from shot-you. Consider a universe that contains one copy of every possible thing. In this universe, the information to locate you is identical to the information to describe you. In this case, describing you includes describing every memory you have. But if you have memories of reading a physics textbook and then doing some experiments, then the shortest description of your memories is going to include a description of the laws of physics. One copy of everything theory is a bad theory compared to physics.
If you have a simple physical law that predicts 1 human surrounded by 3^^^3 paperclips, then locating yourself is easy. Many simple algorithms, like looking for places where hydrogen is more abundant than iron, will locate you. In this universe, if Omega duplicates you, its twice as hard to point to each copy. And if he shoots one copy, it’s still twice as hard to point to the other copy. (the search for things that aren’t paperclips comes up with 2 items) In this universe, you would reject the third part of the deal.
Suppose that the universe was filled with interesting stuff in the sense that the shortest way to point to you was coordinates. Being duplicated gives 2 places to point to, so you expect that you were duplicated with probability 2⁄3. Once one copy is shot, you expect that your prob of being the other copy is 1⁄2. In this universe you would reject the first part of the deal.
In both cases you perform a Bayesian update based on the fact that you are still alive.
Yeah, this implicitly depends on how you’re being pointed to. I’m assuming that you’re being pointed to as “person who has had history [my history]”. In which case you don’t need to worry about doing extra work to distinguish yourself from shot-you once your histories (ballistically) diverge. (EDIT: I think. This is weird.)
If you’re pointed to with coordinates, it’s more likely that copies are treated as not adding any complexity. But this is disanalogous to the Presumptuous Philosopher problem, so I’m avoiding that case.
You do need to distinguish, it’s part of your history. If you are including your entire history as uncompressed sensory data, that will contain massive redundancy. The universe does not contain all possible beings in equal proportions. Imagine being the only person in an otherwise empty universe, very easy to point to. Now imagine that Omega makes 10100 copies, and tells each copy their own 100 digit id number. It takes 100 digits more complexity to point to any one person. The process of making the copies makes each copy harder to point to. The process of telling them id numbers doesn’t change the complexity. You only have 2 copies with id’s of “shot” and “not shot”.
Right, but suppose that everybody knows beforehand that Omega is going to preserve copy number 0 only (or that it’s otherwise a consequence of things you already know).
This “pays in advance” for the complexity of the number of the survivor. After t_1, it’s not like they’ve been exposed to anything they would be surprised about if they were never copied.
Ah, wait, is that the resolution? If there’s a known designated survivor, are they required to be simple to specify even before t_1, when they’re “mixed in” with the rest?
The centermost person and the person numbered 0 are simple to specify beforehand.
Given that you know what’s going on in the rest of the universe, the one that doesn’t get shot is also simple to specify.