Re: reasoning under computational limitations

Nick Bostrom (
Sat, 3 Apr 1999 12:10:03 +0000

Wei Dai wrote:

> 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.

Whatever turns you on. Doesn't do the trick for me, unfortunately.

> 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 fact that I am an observer gives me some reason to believe that the
> total measure of observer-instants is large.
> 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.

We don't get an exact cancellation of the DA unless the SIA has the property that, other things equal, if there are ten times more people on hypothesis A than on hypothesis B, then A is ten times more probable than B after conditionalizing on your own existence. And this does of course mean that your existence should make it a priori certain (probability one) that there are infinitely many people, provided that had a non-zero probability to start with. And that seems wrong.

Nick Bostrom Department of Philosophy, Logic and Scientific Method London School of Economics