I note that it isn’t particularly difficult to construct scenarios in which a given party would have a nonzero probability of never being returned to their own time. I shudder to think what might happen to them in that case.
Even if the party is completely incompetent it still seems there must be at least some chance that by a series of extraordinary coincidences they will win. Regardless of how low your chance of victory is if you have enough tries you will win eventually with probability 1.
No. Not if the infinite collection of universes is arranged in such a way such that you go up against successively more and more skilled competitors. If so, the probability of success on a given iteration could go down each time. If it goes down fast enough, the probability of success in the limit can be less than 1.
I don’t think it can go down forever. There’s some nonzero probability of quantum tunneling directly to the treasure before anyone else has a chance to do anything.
Also, I’m not sure what Kin is trying to say. Either there’s a finite number of universes, and you’d just finish last, or she doesn’t know what “infinity” means.
That assumes that the Goblins universe operates on some form of QM laws. Considering that this is a universe where beings have hit points and gain levels (and are explicitly aware of this) it seems that assuming that its physical laws have a quantum mechanical substrate would be unjustified without some direct evidence for it. (Something like “And in the next installment Big Ears will attempt to do the double slit experiment and see it if applies to photons produced by magical auras” seems unlikely to me. )
Also, I’m not sure what Kin is trying to say. Either there’s a finite number of universes, and you’d just finish last, or she doesn’t know what “infinity” means.
Or she just hasn’t thought much about infinities before. Sure, examples are easy, but if you’ve haven’t thought about it, and have never heard of set theory, it need not be obvious that an infinite sequence of distinct elements of an infinite set doesn’t need to cover the whole thing.
The process repeats until infinity is satisfied and every alternate reality in which we’ve entered the Maze of Many has ended with our success.
Infinity is never satisfied. If there really are an infinite number, the process would repeat forever. There would always be universes in which the Maze of Many hasn’t yet ended in success.
I don’t think it can go down forever. There’s some nonzero probability of quantum tunneling directly to the treasure before anyone else has a chance to do anything.
Man, I don’t even want to begin to imagine the implications that many-worlds quantum mechanics would have for this game.
I note that it isn’t particularly difficult to construct scenarios in which a given party would have a nonzero probability of never being returned to their own time. I shudder to think what might happen to them in that case.
Really?
Even if the party is completely incompetent it still seems there must be at least some chance that by a series of extraordinary coincidences they will win. Regardless of how low your chance of victory is if you have enough tries you will win eventually with probability 1.
No. Not if the infinite collection of universes is arranged in such a way such that you go up against successively more and more skilled competitors. If so, the probability of success on a given iteration could go down each time. If it goes down fast enough, the probability of success in the limit can be less than 1.
I don’t think it can go down forever. There’s some nonzero probability of quantum tunneling directly to the treasure before anyone else has a chance to do anything.
Also, I’m not sure what Kin is trying to say. Either there’s a finite number of universes, and you’d just finish last, or she doesn’t know what “infinity” means.
That assumes that the Goblins universe operates on some form of QM laws. Considering that this is a universe where beings have hit points and gain levels (and are explicitly aware of this) it seems that assuming that its physical laws have a quantum mechanical substrate would be unjustified without some direct evidence for it. (Something like “And in the next installment Big Ears will attempt to do the double slit experiment and see it if applies to photons produced by magical auras” seems unlikely to me. )
I think that every time one group wins there is a possibility that one or more new groups will join in the next game.
Or she just hasn’t thought much about infinities before. Sure, examples are easy, but if you’ve haven’t thought about it, and have never heard of set theory, it need not be obvious that an infinite sequence of distinct elements of an infinite set doesn’t need to cover the whole thing.
Infinity is never satisfied. If there really are an infinite number, the process would repeat forever. There would always be universes in which the Maze of Many hasn’t yet ended in success.
Man, I don’t even want to begin to imagine the implications that many-worlds quantum mechanics would have for this game.
I follow that comic and yea it’s cool, but could you elaborate more on how it’s relevant to LW?
Decision theory in many worlds, I presumed. I thought it set out the concept amusingly and clearly.