Re: The Anthropic Trilemma - Less Wrong
On 14 Feb 2012, at 04:00, Stephen P. King wrote: On 2/13/2012 5:54 PM, acw wrote: On 2/12/2012 17:29, Stephen P. King wrote: Hi Folks, I would like to bring the following to your attention. I think that we do need to revisit this problem. http://lesswrong.com/lw/19d/the_anthropic_trilemma/ The Anthropic Trilemma http://lesswrong.com/lw/19d/the_anthropic_trilemma/ snip I gave a tentative (and likely wrong) possible solution to it in another thread. The trillema is much lessened if one considers a relative measure on histories (chains of OMs) and their length. That is, if a branch has more OMs, it should be more likely. The first horn doesn't apply because you'd have to keep the copies running indefinitely (merging won't work). The second horn, I'm not so sure if it's avoided: COMP-immortality implies potentially infinite histories (although mergers may make them finite), which makes formalizing my idea not trivial. The third horn only applies to ASSA, not RSSA (implicit in COMP). The fourth horn is acceptable to me, we can't really deny Boltzmann brains, but they shouldn't be that important as the experience isn't spatially located anyway(MGA). The white rabbit problem is more of a worry in COMP than this horn. The fifth horn is interesting, but also the most difficult to solve: it would require deriving local physics from COMP. My solution doesn't really solve the first horn though, it just makes it more difficult: if you do happen to make 3^^^3 copies of yourself in the future and they live very different and long lives, that might make it more likely that you end up with a continuation in such a future, however making copies and merging them shortly afterwards won't work. Hi ACW, This solution only will work for finite and very special versions of infinite sets. For the infinities like that of the Integers, it will not work because any proper subset of the infinite set is identical to the complete set as we can demonstrated with a one-to- one map between the odd integers and the integers. You should not confuse bijection (set isomorphism) and equality. Also, measure exists on infinite discrete sets, by weakening the sigma- additivity constraints. And then, finally, the measure problem bears on infinite extension of computations, and they are 2^aleph_0. Remember the one line UD program: For all i, j,k compute the kth first steps of phi_i(j). We can describe a computation a sequence phi_i(j)^0, phi_i(j)^1, , phi_i(j)^k. That set is enumerable, but the set of all sequences going through equivalent 1p-steps is not enumerable, and you can define a measure by just using the normal distribution in a manner similar to the dovetailing on the reals. This has just to be corrected to take into account the constraints of self-reference, which seems to be the origin of an arithmetical quantization, negative amplitude of probability, etc. Given that the number of computations that a universal TM can run is at least the countable infinity of the integers, we cannot use a comparison procedure to define the measure. You confuse the computations made by the UD, and observed by an outsider, and the infinite computations going through your actual 1p- state. Those includes all the dummies dovetailing on the reals, and cannot be enumerable. Think about the iterated self-duplication. It leads to the usual Gaussian. (Maybe this is one of the reasons many very smart people have tried, unsuccessfully, to ban infinite sets...) Not al all. The infinite set have been introduced to make the measure problem more easy, even for problem handling finite objects when they are very numerous. Mathematical logic explains that finite and enumerable is more complex than the continuum, which existence is basically motivated by searching to simplify the problem. For example, Fermat on the reals is trivial. Not so on non negative integers. Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: The Anthropic Trilemma - Less Wrong
On 2/12/2012 17:29, Stephen P. King wrote: Hi Folks, I would like to bring the following to your attention. I think that we do need to revisit this problem. http://lesswrong.com/lw/19d/the_anthropic_trilemma/ The Anthropic Trilemma http://lesswrong.com/lw/19d/the_anthropic_trilemma/ 21Eliezer_Yudkowsky http://lesswrong.com/user/Eliezer_Yudkowsky/27 September 2009 01:47AM Speaking of problems I don't know how to solve, here's one that's been gnawing at me for years. The operation of splitting a subjective worldline seems obvious enough - the skeptical initiate can consider the Ebborians http://lesswrong.com/lw/ps/where_physics_meets_experience/, creatures whose brains come in flat sheets and who can symmetrically divide down their thickness. The more sophisticated need merely consider a sentient computer program: stop, copy, paste, start, and what was one person has now continued on in two places. If one of your future selves will see red, and one of your future selves will see green, then (it seems) you should /anticipate/ seeing red or green when you wake up with 50% probability. That is, it's a known fact that different versions of you will see red, or alternatively green, and you should weight the two anticipated possibilities equally. (Consider what happens when you're flipping a quantum coin: half your measure will continue into either branch, and subjective probability will follow quantum measure for unknown reasons http://lesswrong.com/lw/py/the_born_probabilities/.) But if I make two copies of the same computer program, is there twice as much experience, or only the same experience? Does someone who runs redundantly on three processors, get three times as much weight as someone who runs on one processor? Let's suppose that three copies get three times as much experience. (If not, then, in a Big universe, large enough that at least one copy of anything exists /somewhere,/ you run into the Boltzmann Brain problem http://lesswrong.com/lw/17d/forcing_anthropics_boltzmann_brains/.) Just as computer programs or brains can split, they ought to be able to merge. If we imagine a version of the Ebborian species that computes digitally, so that the brains remain synchronized so long as they go on getting the same sensory inputs, then we ought to be able to put two brains back together along the thickness, after dividing them. In the case of computer programs, we should be able to perform an operation where we compare each two bits in the program, and if they are the same, copy them, and if they are different, delete the whole program. (This seems to establish an equal causal dependency of the final program on the two original programs that went into it. E.g., if you test the causal dependency via counterfactuals, then disturbing any bit of the two originals, results in the final program being completely different (namely deleted).) So here's a simple algorithm for winning the lottery: Buy a ticket. Suspend your computer program just before the lottery drawing - which should of course be a quantum lottery, so that every ticket wins somewhere. Program your computational environment to, if you win, make a trillion copies of yourself, and wake them up for ten seconds, long enough to experience winning the lottery. Then suspend the programs, merge them again, and start the result. If you don't win the lottery, then just wake up automatically. The odds of winning the lottery are ordinarily a billion to one. But now the branch in which you /win /has your measure, your amount of experience, /temporarily/ multiplied by a trillion. So with the brief expenditure of a little extra computing power, you can subjectively win the lottery - be reasonably sure that when next you open your eyes, you will see a computer screen flashing You won! As for what happens ten seconds after that, you have no way of knowing how many processors you run on, so you shouldn't feel a thing. Now you could just bite this bullet. You could say, Sounds to me like it should work fine. You could say, There's no reason why you /shouldn't /be able to exert anthropic psychic powers. You could say, I have no problem with the idea that no one else could see you exerting your anthropic psychic powers, and I have no problem with the idea that different people can send different portions of their subjective futures into different realities. I find myself somewhat reluctant to bite that bullet, personally. Nick Bostrom, when I proposed this problem to him, offered that you should anticipate winning the lottery after five seconds, but anticipate losing the lottery after fifteen seconds. To bite this bullet, you have to throw away the idea that your joint subjective probabilities are the product of your conditional subjective probabilities. If you win the lottery, the subjective probability of having still won the lottery, ten seconds later, is ~1. And if you lose the lottery, the subjective probability of having lost the lottery, ten
Re: The Anthropic Trilemma - Less Wrong
On 2/13/2012 5:54 PM, acw wrote: On 2/12/2012 17:29, Stephen P. King wrote: Hi Folks, I would like to bring the following to your attention. I think that we do need to revisit this problem. http://lesswrong.com/lw/19d/the_anthropic_trilemma/ The Anthropic Trilemma http://lesswrong.com/lw/19d/the_anthropic_trilemma/ snip I gave a tentative (and likely wrong) possible solution to it in another thread. The trillema is much lessened if one considers a relative measure on histories (chains of OMs) and their length. That is, if a branch has more OMs, it should be more likely. The first horn doesn't apply because you'd have to keep the copies running indefinitely (merging won't work). The second horn, I'm not so sure if it's avoided: COMP-immortality implies potentially infinite histories (although mergers may make them finite), which makes formalizing my idea not trivial. The third horn only applies to ASSA, not RSSA (implicit in COMP). The fourth horn is acceptable to me, we can't really deny Boltzmann brains, but they shouldn't be that important as the experience isn't spatially located anyway(MGA). The white rabbit problem is more of a worry in COMP than this horn. The fifth horn is interesting, but also the most difficult to solve: it would require deriving local physics from COMP. My solution doesn't really solve the first horn though, it just makes it more difficult: if you do happen to make 3^^^3 copies of yourself in the future and they live very different and long lives, that might make it more likely that you end up with a continuation in such a future, however making copies and merging them shortly afterwards won't work. Hi ACW, This solution only will work for finite and very special versions of infinite sets. For the infinities like that of the Integers, it will not work because any proper subset of the infinite set is identical to the complete set as we can demonstrated with a one-to-one map between the odd integers and the integers. Given that the number of computations that a universal TM can run is at least the countable infinity of the integers, we cannot use a comparison procedure to define the measure. (Maybe this is one of the reasons many very smart people have tried, unsuccessfully, to ban infinite sets...) Onward! Stephen -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: The Anthropic Trilemma - Less Wrong
On 2/14/2012 03:00, Stephen P. King wrote: On 2/13/2012 5:54 PM, acw wrote: On 2/12/2012 17:29, Stephen P. King wrote: Hi Folks, I would like to bring the following to your attention. I think that we do need to revisit this problem. http://lesswrong.com/lw/19d/the_anthropic_trilemma/ The Anthropic Trilemma http://lesswrong.com/lw/19d/the_anthropic_trilemma/ snip I gave a tentative (and likely wrong) possible solution to it in another thread. The trillema is much lessened if one considers a relative measure on histories (chains of OMs) and their length. That is, if a branch has more OMs, it should be more likely. The first horn doesn't apply because you'd have to keep the copies running indefinitely (merging won't work). The second horn, I'm not so sure if it's avoided: COMP-immortality implies potentially infinite histories (although mergers may make them finite), which makes formalizing my idea not trivial. The third horn only applies to ASSA, not RSSA (implicit in COMP). The fourth horn is acceptable to me, we can't really deny Boltzmann brains, but they shouldn't be that important as the experience isn't spatially located anyway(MGA). The white rabbit problem is more of a worry in COMP than this horn. The fifth horn is interesting, but also the most difficult to solve: it would require deriving local physics from COMP. My solution doesn't really solve the first horn though, it just makes it more difficult: if you do happen to make 3^^^3 copies of yourself in the future and they live very different and long lives, that might make it more likely that you end up with a continuation in such a future, however making copies and merging them shortly afterwards won't work. Hi ACW, This solution only will work for finite and very special versions of infinite sets. For the infinities like that of the Integers, it will not work because any proper subset of the infinite set is identical to the complete set as we can demonstrated with a one-to-one map between the odd integers and the integers. Hence why it's a measure, not a sets cardinality. Although, you're right, it's not obvious to me how this can be solved in a satisfactory manner with infinite non-merging histories. One could give up on finding a computable measure and just consider each history as it is, without trying to quantify directly over all histories. Such a measure would be most likely uncomputable, although it'd still be better than nothing. It's not obvious that some histories wouldn't be finite if one considers their mergers with other histories (consider the case of humans which have finite brains and memories, eventually a loop/merge would exist if they don't self-modify somehow, simply because of finite amount of memory, even in the case of a SIM which never dies or deteriorates due to biological issues). Given that the number of computations that a universal TM can run is at least the countable infinity of the integers, we cannot use a comparison procedure to define the measure. (Maybe this is one of the reasons many very smart people have tried, unsuccessfully, to ban infinite sets...) Unfortunately (or maybe fortunately?), one cannot avoid the countable infinity of naturals. Onward! Stephen -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
