Suppose you wake up in a universe which contains a total of 20 people. Ten
of them have been assigned numbers 0 to 9, and the other ten have been
assigned the number equal to the 100!-th digit in the decimal expansion of
PI. You are told your number but not anyone else's, and you are
asked to guess the 100!-th digit of PI. Assuming that you can't actually
compute that digit, it seems intuitive that your best guess would be your
My questions are (1) is this
My questions are (1) is thiscorrect and (2) are there principles of reasoning under computational limitations (perhaps extensions of probability theory?) that can be used to derive or justify this and similar conclusions? Any relevant references would be appreciated.