Re: effective probability

From: Gilles HENRI <Gilles.Henri.domain.name.hidden>
Date: Mon, 1 Feb 1999 12:23:18 +0100

>I thought that the explanation for why the doomsday argument fails in
>the everything-exists case went like this:
>
>Either we are in a world where the human race lives for a very long
>time but we are very early in its history, or we are in a world where
>it lives for a short time and we are at a typical point in its history
>(or something in between).
>
>The first case is unlikely because we should not be so early. But the
>second case is unlikely because "we" (considered as randomly chosen
>observers from among all possible worlds) should not have ended up in a
>world with so few human observers. We would have been much more likely
>to be in the world with many humans.
>
>Either way we face an unlikely event, and from what I understand the
>detailed analyses show that the unlikelihoods exactly balance. If all
>worlds exist, we can't conclude anything about the duration of the human
>race or our likely place in it, just from knowing our birth order.
>
>Hal

I think it's true. Bayes theorem is correct but the prior probability is
very strongly in favor of worlds with many humans.
However we can do estimate something about the duration of the human race.
For most of the distributions of births (including exponential growth of
the population), the average (over all human beings) ratio of
(tf-t)/(t-ti), the time left before doomsday over the time past since the
beginning of mankind, is of the order of one. The best estimate is thus
that mankind has to live around as much time it has already lived, between
10^5 to 10^7 years.

Note that this estimate is correct for most of your own remaining time of
life (except the very few new born babies, dying old people and victims of
mortal accidents). it is correct also to guess how long the Sun will
bright, and so on...We may belong to the unfortunate part that will
disappear, but despite the growth of population, we only represent a few
percent of the 10^11 people that have probably already lived, so this
estimate would have been correct for most of them.


Gilles
Received on Mon Feb 01 1999 - 03:26:03 PST