RE: Shooting room paradox

Hal Finney (
Fri, 6 Dec 1996 09:40:32 -0800

From: Richard Brodie <>
> Wonderful! Do you see the error in your reasoning? Half the people who
> ever lived are still alive. What are the chances that George Washington
> is still alive? And how infinitesimal the probability that, out of all
> the eons of the existence of the universe, you and I lived now! But it's
> not unlikely, don't you see? The probability of anything having happened
> after it has already happened is 100%. There are an infinity of equally
> likely scenarios that didn't happen.

I don't think you can usefully take the view that everything which has
happened has simply happened, and we can draw no useful probability
conclusions from the evidence we see.

If I flip a coin 100 times and it comes up heads every time, I can't
just say, oh, well, that's what happened and so the probability of that
having happened is 100%. Instead, I must entertain the possibility that
I am dealing with a two headed coin.

I say, if I had had a normal coin the chances of that series of coin
flips would have been infinitesimal. If I had had a two headed coin
the chances would have been certain. Now I factor in my a priori belief
that I had a two headed coin (probably they are outnumbered by regular
coins by a factor of a billion or so) and I conclude that there is a
pretty good chance that I do in fact have a two headed coin.

Similarly, if I see myself in circumstances which are highly improbable
given that humanity will expand to engulf the galaxy, while they would
be relatively probable if the human race is about to die out, then I
must raise my estimate of the probability of the latter possibility.
Saying that the probability of my existence is 100% because I exist does
not provide any useful information, any more than doing that in the coin
flipping example would have.


P.S. Please let me know in private mail if you think I am posting too
much on this topic.