Re: effective probability

From: Gilles HENRI <Gilles.Henri.domain.name.hidden>
Date: Tue, 2 Feb 1999 13:47:51 +0100

>Gilles HENRI wrote:
>>[hal wrote:]
>> >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).
>
>> >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.
>
>It is not correct to apply time as a measure for the human race, because
>you and I are members thereof, and because the number of people per unit
>of
>time has not been uniform. John Leslie is correct in using the birth
>order
>of people as a measure of time passage. You and I are indeed not in
>peculiar positions by this measure, while we are by direct time measure.

but if you take the average value for all people, you don't give you a
peculiar position. You are just looking for a value that mimimizes the
number of people who are wrong in choosing it.


>
>It is interesting to note that the "Copernican" estimate that you give
>originally, to my knowledge from Gott, does seem to give plausible time
>estimates, but has the following property that makes me very suspicious
>of Copernican estimates. (First, the Copernican estimates as a whole
>do not have a finite expectation, but the median estimate is for future
>interval = observed past interval). Then for Copernican estimates on
>humans (as if they were made by an alien). The time, as you indicate
>is 10^5 to 10^7. The number of people is about 60 10^9. The pair of
>forecasts can both be met if the total forecast is for a rapid decline
>of current population, then a long period of very few members. This
>is oddly reminiscent of a reversal of past history.

It's true, I saw this estimate somewhere and I lost the references.
Isn't the absence of expectation value due to unphysical distribution of
births? (function extending down to -infinity). I checked rapidly (I may be
wrong) that for a function starting at a finite time -T with f(-T) = 0 ( a
convenient approximation if one assumes a "first Eve", with 46 chromosoms
for example), there is indeed a finite expectation value.
The symmetry of population seems to arise from the fact that you want both
a median in birth rank and in time. So indeed it is more correct to choose
the forecast on the number of people still to be born. Of course the
remaining time depends on the actual population growth rate. I made a
mistake in my first calculation, but I agree that if the growth is
exponential, the expectation value of (tf-t)/(t-ti) can be much smaller
than 1 if the total life time is much larger than the typical growth time.
Both methods are not contradictory.


>
>I rather suspect that there could be a lot of empirical cases in which
>the Copernican forecasts would be right, but it is hard to reconcile
>that with the apparent basis in a time reversal.
>


Thinking further of it, maybe the problem comes from the fact that you put
another piece of information : the past curve of growth of the mankind. It
may well be that the overall population curve is nearly symetrical, for
example if the mankind reaches a quasi-steady state around 20 billions
people during some millions of years, before genetic mutation or the impact
of an asteroid (for example) makes it disappear. But it means that we are
*not* in a typical rank. Considering the very recent explosion due to the
large progress of medicine in this century, we could be at a rather
particular stage, just as if you try to predict the life time of a baby by
this way. Morality: to make predictions, it's better to try a realistic
model including the maximal information about all physical processes than
relying on pure mathematics...

Gilles
Received on Tue Feb 02 1999 - 04:52:03 PST