On Thu, Apr 01, 1999 at 10:08:57PM +0000, Nick Bostrom wrote:
> Yes you can do this, but I don't see how it helps decide whether the
> SIA is true. (For other people following this thread: The
> Self-Indication Axiom states roughly that upon finding that you
> exist, you should increase your probability for hypotheses according
> to which many people exist. (There would be "more slots for you to be
> born into" if there were more persons.) It can be shown that
> adopting the SIA leads to the exact cancellation of the probability
> shift required by the DA. This would seem the main reason to adopt
> the SIA. However, there are big problems with the SIA which seem to
> make it ultimately unacceptable.)
Using the 100!-th digit of PI in the thought experiment instead of the coin flip makes it more obvious, at least to my intuition, that SIA is true. I do think SIA should be modified to avoid the problem of infinity (where one concludes that with probability one the universe contains an infinite number of observers), as follows:
The "total measure of observer-instants" can be thought of as the fraction of the universe (the entire history of the universe, not just its current state) that consist of observers.