The problem is, I just can’t accept the idea that anthropic/ethical problems are “indeterminate” and that we should rely on our “intuitions”.
I’m not saying that we should rely on our intuitions in this matter (which we can’t anyway since they are contradictory, or at least mine are, as I pointed out in the above linked post), but they do perhaps offer some starting points for thinking about the problem.
It seems that some anthropic problems must have well-defined solutions.
Well, that’s your intuition. :)
I’m not sure what you mean by “limiting frequencies” here, but here’s a thought experiment attempting to show that they may not be very relevant.
Suppose we take a subject and label him A0. In each round, we take the copy that was previously labeled A0, make two more copies of him, which we’ll label B0 and C0, then ask the three of them to guess A or Not-A (without letting them observe their labels). After that, we tell them their labels, and make one more copy of each of the three, to be labeled A1, B1, C1. If A0 guessed correctly, we give A1 a nice experience, for example eating a cake. Do the same for B1 if B0 guessed correctly, and similarly for C1/C0. (The reason for making extra copies after the guess is so A0 doesn’t get sick of eating cakes.) At the end of the round, delete B0, C0, A1, B1, C1.
Again, I’m not sure how you define “observed limiting frequency”, but it seems that F(A)=1. However you’re better off always betting on Not-A, since that results in twice as many of your copies eating cake.
Killing observers to change the limiting frequency is cheating :-)
Consider a simpler example: I flip a coin and show you the result. Then if it came up heads, I kill you, otherwise I repeat the experiment. I think you’d be correct (in some yet-undiscovered sense) to have a “subjective anticipation” of 50% heads and 50% tails before the throw, but counting the surviving branches after many trials gives a “limiting frequency” of mostly tails. This doesn’t look to me like a fair interpretation of “limiting frequency”, because it arbitrarily throws away all observations made by those of you who ended up dying. If I could resurrect them and include them in the poll, I’d get a different result.
If you resurrect them and include them in the poll, and assuming you average their observed frequencies, don’t you still get F(A)=1? As I said, I’m not sure what you mean by “limiting frequency”, but I don’t see how you can get something other than F(A)=1 in my example.
If I count all observer-moments that get told their labels, the fraction of observer-moments that get told A is 1⁄3. If each observer has a fixed amount of “reality fluid” that gets split in equal parts when copies are made and disappears when copies die, the total fraction of “reality fluid” in observer-moments that get told A is also 1⁄3, but by a different calculation. Maybe both these methods of counting are wrong, but the answer 1 is still far from certain.
I’m not saying that we should rely on our intuitions in this matter (which we can’t anyway since they are contradictory, or at least mine are, as I pointed out in the above linked post), but they do perhaps offer some starting points for thinking about the problem.
Well, that’s your intuition. :)
I’m not sure what you mean by “limiting frequencies” here, but here’s a thought experiment attempting to show that they may not be very relevant.
Suppose we take a subject and label him A0. In each round, we take the copy that was previously labeled A0, make two more copies of him, which we’ll label B0 and C0, then ask the three of them to guess A or Not-A (without letting them observe their labels). After that, we tell them their labels, and make one more copy of each of the three, to be labeled A1, B1, C1. If A0 guessed correctly, we give A1 a nice experience, for example eating a cake. Do the same for B1 if B0 guessed correctly, and similarly for C1/C0. (The reason for making extra copies after the guess is so A0 doesn’t get sick of eating cakes.) At the end of the round, delete B0, C0, A1, B1, C1.
Again, I’m not sure how you define “observed limiting frequency”, but it seems that F(A)=1. However you’re better off always betting on Not-A, since that results in twice as many of your copies eating cake.
Killing observers to change the limiting frequency is cheating :-)
Consider a simpler example: I flip a coin and show you the result. Then if it came up heads, I kill you, otherwise I repeat the experiment. I think you’d be correct (in some yet-undiscovered sense) to have a “subjective anticipation” of 50% heads and 50% tails before the throw, but counting the surviving branches after many trials gives a “limiting frequency” of mostly tails. This doesn’t look to me like a fair interpretation of “limiting frequency”, because it arbitrarily throws away all observations made by those of you who ended up dying. If I could resurrect them and include them in the poll, I’d get a different result.
If you resurrect them and include them in the poll, and assuming you average their observed frequencies, don’t you still get F(A)=1? As I said, I’m not sure what you mean by “limiting frequency”, but I don’t see how you can get something other than F(A)=1 in my example.
Averaging observed frequencies sounds weird...
If I count all observer-moments that get told their labels, the fraction of observer-moments that get told A is 1⁄3. If each observer has a fixed amount of “reality fluid” that gets split in equal parts when copies are made and disappears when copies die, the total fraction of “reality fluid” in observer-moments that get told A is also 1⁄3, but by a different calculation. Maybe both these methods of counting are wrong, but the answer 1 is still far from certain.