From: Wei Dai (weidai@eskimo.com)
Date: Sat Mar 27 1999 - 17:36:59 MST
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
own number.
My questions are (1) is this correct 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.
This archive was generated by hypermail 2.1.5 : Fri Nov 01 2002 - 15:03:24 MST