Unfortunately, physical self-sampling without self-indication has odd consequences of its own. Consider the following thought experiment:
Physicists have conclusively figured out what the theory of everything is. We know roughly how the cosmos will behave until a trillion years into the future. However, it’s still unclear what will happen at this point: either (T1) the universe will end, or (T2) the universe will continue for another trillion trillion years, but be unable to support intelligent life. A hard mathematical calculation can show which of these is true, but before doing the calculation, each theory has a 1⁄2 prior probability (in the same sense that before doing the calculation, you have a 1⁄10 subjective probability that the trillionth decimal digit of pi is a seven).
Physicists want to schedule supercomputer time to determine the answer. Enter Presumptuous: “By physical self-sampling, the probability of T2 given our observations is only about one in a trillion. This calculation is a waste of money!”
She calculates as follows. P0(T1) = P0(T2) = 1⁄2. According to T2, the universe contains a trillion more space-time locations than according to T1. But according to both theories, the universe contains only one location consistent with our evidence. According to the definition given in the previous comment, this makes T2 much less likely that T1.
Intuitively, the argument is, “According to T2, there are a trillion more places we could have found ourselves at (at most of which we would not have been conscious observers, but taking that into account would be supernatural wonder tissue). So having found ourselves at this particular place is much more surprising according to T2.”
But this argument doesn’t sound very convincing to me. From where do we get this supposed lottery over space-time locations? At least, the argument sounds much less intuitively convincing than the following: “Our uncertainty is mathematical, and our observations would be exactly the same according to each theory—we can’t conclude anything about the mathematical result from the fact that one would destroy the universe, while the other would only leave it barren.”
In the next comment, I’ll develop that intuition into a more formal argument supporting self-indication.
Unfortunately, physical self-sampling without self-indication has odd consequences of its own. Consider the following thought experiment:
She calculates as follows. P0(T1) = P0(T2) = 1⁄2. According to T2, the universe contains a trillion more space-time locations than according to T1. But according to both theories, the universe contains only one location consistent with our evidence. According to the definition given in the previous comment, this makes T2 much less likely that T1.
Intuitively, the argument is, “According to T2, there are a trillion more places we could have found ourselves at (at most of which we would not have been conscious observers, but taking that into account would be supernatural wonder tissue). So having found ourselves at this particular place is much more surprising according to T2.”
But this argument doesn’t sound very convincing to me. From where do we get this supposed lottery over space-time locations? At least, the argument sounds much less intuitively convincing than the following: “Our uncertainty is mathematical, and our observations would be exactly the same according to each theory—we can’t conclude anything about the mathematical result from the fact that one would destroy the universe, while the other would only leave it barren.”
In the next comment, I’ll develop that intuition into a more formal argument supporting self-indication.