My twin 10^29^29 ly away… if he picks up an astronomy atlas, will he find the exact same objects listed with the exact same coordinates digit for digit?
Probably not. Copies of bokov are pretty rare in the universe (one every 10^(10^29) meters), but copies of bokov together with a correct copy of the whole observable universe have got to be vastly rarer. Only one out of every (insanely huge number) would see the same night sky you do.
In general, you’re not guaranteed to see any particular pattern more than once, or for the pattern of repetition to be particularly neat. The pigeonhole principle says that with an infinite number of pigeons placed into a finite number of slots, at least one of the slots needs to contain more than one pigeon (in fact, one or more of them needs to contain an infinite number of pigeons). But it doesn’t say that all of the slots need to be filled more than once.
Is cyclicity a necessary consequence of filling an infinite space with things that can only have a finite number of configurations?
Eventually you have to return to a point you have been before, but the cycle need not encompass all the possibilities. For example an infinite string of the numbers 0-5 could go as follows 1, 2, 3, 4, 5, 0, 5, 0, 5, 0, …
If so, does that mean if I zoom in on a Mandelbrot set far enough I will see an exact replica of the image I started with
Not necessarily, because the number of “possible” images (a continuous infinity, equivalent to R^R) is not smaller than the number of possible “zoom” positions (a smaller continuous infinity equivalent to R).
if I run a cellular automaton long enough I will get a regular pattern?
You’re not guaranteed to see any particular pattern, as I said, and in fact conway’s game of life has “garden of eden” configurations, which can’t be obtained by running the cellular automaton from any possible starting position. So you don’t even go through all the “theoretically possible” states before cycling.
But, in the case Eliezer mentioned, I think it’s fairly reasonable to assume that there is in fact a copy of you somewhere out there, assuming the world is infinite, because of things like quantum “randomness” and thermal noise that give each section of space an independent chance of spontaneously manifesting pretty much any configuration of matter, and those chances add up to “certainty” after an infinite number of chances.
Hope I am not spamming you, but noticed something else.
Not necessarily, because the number of “possible” images (a continuous infinity, equivalent to R^R) is not smaller than the number of possible “zoom” positions (a smaller continuous infinity equivalent to R).
Isn’t the space of spatial coordinates in the same sense a smaller infinity than the number of quantum configurations possible at any given set of spatial coordinates? So that would refute the assertion that twins of us must exist. At least in the sense of inhabiting our Everett branch somewhere far beyond our Hubble volume.
But, in the case Eliezer mentioned, I think it’s fairly reasonable to assume that there is in fact a copy of you somewhere out there, assuming the world is infinite, because of things like quantum “randomness” and thermal noise that give each section of space an independent chance of spontaneously manifesting pretty much any configuration of matter, and those chances add up to “certainty” after an infinite number of chances.
I.e. Boltzmann brains? That makes me realize another thing. If all of them have an identical configuration, why should some of them dissolve back into the thermal noise whence they came while others do not?
In general, you’re not guaranteed to see any particular pattern more than once, or for the pattern of repetition to be particularly neat. The pigeonhole principle says that with an infinite number of pigeons placed into a finite number of slots, at least one of the slots needs to contain more than one pigeon (in fact, one or more of them needs to contain an infinite number of pigeons). But it doesn’t say that all of the slots need to be filled more than once.
What if slots are not discrete and the contents of each location are a function of previous contents of all locations within its light-cone?
I must say, this twin thing sounds cool and all but I’m starting to think maybe it’s too strongly stated.
Probably not. Copies of bokov are pretty rare in the universe (one every 10^(10^29) meters), but copies of bokov together with a correct copy of the whole observable universe have got to be vastly rarer. Only one out of every (insanely huge number) would see the same night sky you do.
Since someone who has read that Tau Ceti is in a different location than I read it is will no longer be identical to me, can I make myself unique by learning a lot of astronomy?
Or are most bokovs merely similar and only occupy identical configurations by mistake, e.g. by misreading information in the same way? But wouldn’t we each still be entangled with enormous numbers of objects that are entangled with the true locations of our respective stars called Tau Ceti?
If we restrict our attention to identical bokovs living on relatively earth-like, or at least life supporting worlds, what generally happens is that on some planet an atom-by-atom identical copy of you suddenly spontaneously materializes (due to quantum/thermal noise). The first thing this copy will notice is that it seems to be somewhere other than it was before, since it has your memories: the last thing it remembers is sitting down reading this site. Then, if it’s night time, it will notice that the stars are in completely wrong places and eventually become very different to the bokov here as it gets used to living on the alien world.
ETA: Yeah, as with boltzmann brains, actually the majority of patterns identifiable as bokov will be manifested in very bad places to live, like in space, in stars or oceans. And they will immediately die, or be reduced to random particles again in the case of a bokov formed inside a star.
And if we don’t restrict our attention in this manner, this number is dwarfed by the number of bokovs being spawned inside gas giants and stars. Which are in turn dwarfed by random blobs of particles containing random bokov body parts spawning.
So your answer to the question of subjective expectation is “never mind red room or green room, you should expect to wake up boiling alive and/or freezing while gasping for air and clutching at the spot you legs used to be”.
But by that logic, given that so far I have not been, I should assign this explanation a very low posterior probability.
So your answer to the question of subjective expectation is “never mind red room or green room, you should expect to wake up boiling alive and/or freezing while gasping for air and clutching at the spot you legs used to be”.
Well, no, while the existence of the boltzmann bokovs is intuitively obvious to me, I currently prefer to keep an open mind regarding if and how that matters for subjective expectation.
Probably not. Copies of bokov are pretty rare in the universe (one every 10^(10^29) meters), but copies of bokov together with a correct copy of the whole observable universe have got to be vastly rarer. Only one out of every
(insanely huge number)would see the same night sky you do.In general, you’re not guaranteed to see any particular pattern more than once, or for the pattern of repetition to be particularly neat. The pigeonhole principle says that with an infinite number of pigeons placed into a finite number of slots, at least one of the slots needs to contain more than one pigeon (in fact, one or more of them needs to contain an infinite number of pigeons). But it doesn’t say that all of the slots need to be filled more than once.
Eventually you have to return to a point you have been before, but the cycle need not encompass all the possibilities. For example an infinite string of the numbers 0-5 could go as follows 1, 2, 3, 4, 5, 0, 5, 0, 5, 0, …
Not necessarily, because the number of “possible” images (a continuous infinity, equivalent to R^R) is not smaller than the number of possible “zoom” positions (a smaller continuous infinity equivalent to R).
You’re not guaranteed to see any particular pattern, as I said, and in fact conway’s game of life has “garden of eden” configurations, which can’t be obtained by running the cellular automaton from any possible starting position. So you don’t even go through all the “theoretically possible” states before cycling.
But, in the case Eliezer mentioned, I think it’s fairly reasonable to assume that there is in fact a copy of you somewhere out there, assuming the world is infinite, because of things like quantum “randomness” and thermal noise that give each section of space an independent chance of spontaneously manifesting pretty much any configuration of matter, and those chances add up to “certainty” after an infinite number of chances.
Hope I am not spamming you, but noticed something else.
Isn’t the space of spatial coordinates in the same sense a smaller infinity than the number of quantum configurations possible at any given set of spatial coordinates? So that would refute the assertion that twins of us must exist. At least in the sense of inhabiting our Everett branch somewhere far beyond our Hubble volume.
I.e. Boltzmann brains? That makes me realize another thing. If all of them have an identical configuration, why should some of them dissolve back into the thermal noise whence they came while others do not?
What if slots are not discrete and the contents of each location are a function of previous contents of all locations within its light-cone?
I must say, this twin thing sounds cool and all but I’m starting to think maybe it’s too strongly stated.
Since someone who has read that Tau Ceti is in a different location than I read it is will no longer be identical to me, can I make myself unique by learning a lot of astronomy?
Or are most bokovs merely similar and only occupy identical configurations by mistake, e.g. by misreading information in the same way? But wouldn’t we each still be entangled with enormous numbers of objects that are entangled with the true locations of our respective stars called Tau Ceti?
If we restrict our attention to identical bokovs living on relatively earth-like, or at least life supporting worlds, what generally happens is that on some planet an atom-by-atom identical copy of you suddenly spontaneously materializes (due to quantum/thermal noise). The first thing this copy will notice is that it seems to be somewhere other than it was before, since it has your memories: the last thing it remembers is sitting down reading this site. Then, if it’s night time, it will notice that the stars are in completely wrong places and eventually become very different to the bokov here as it gets used to living on the alien world.
ETA: Yeah, as with boltzmann brains, actually the majority of patterns identifiable as bokov will be manifested in very bad places to live, like in space, in stars or oceans. And they will immediately die, or be reduced to random particles again in the case of a bokov formed inside a star.
And if we don’t restrict our attention in this manner, this number is dwarfed by the number of bokovs being spawned inside gas giants and stars. Which are in turn dwarfed by random blobs of particles containing random bokov body parts spawning.
So your answer to the question of subjective expectation is “never mind red room or green room, you should expect to wake up boiling alive and/or freezing while gasping for air and clutching at the spot you legs used to be”.
But by that logic, given that so far I have not been, I should assign this explanation a very low posterior probability.
Well, no, while the existence of the boltzmann bokovs is intuitively obvious to me, I currently prefer to keep an open mind regarding if and how that matters for subjective expectation.