Jacques, I agree with what you are basically saying below.
Thanks,
Fred
Jacques M. Mallah wrote:
> On Sat, 8 Jan 2000, Fred Chen wrote:
> > Jacques Mallah wrote:
> > > That's not true. The population size distribution is determined
> > > by the effective probability distribution for the various histories that
> > > could happen. We don't know what that distribution is.
> >
> > I may have been unclear here. Rather than population size at a given
> > moment, the population size should be taken to be the number of people
> > since the dawn of time.
>
> And until the end. It was understood.
>
> > True, we don't really know what the distribution is, but the natural
> > expectation is that since events that can wipe out mankind at any given
> > instant are still considered rather unlikely, the probability
> > distribution, whatever it is, is expected to favor longer-lasting
> > populations.
>
> Here you are invoking additional information, so you are really
> _not_ addressing the 'doomsday argument' which explicitly says, in the
> absence of additional information, ...
> Besides, it is not so clear that such events are so
> unlikely. Disease, nuclear war, asteroids, etc. could all do the
> trick. But I do agree that with the information we have it is reasonable
> to modify the prior distribution so as to expect larger populations than
> one would predict just from birth order.
>
> > > You are not likely to be the
> > > last person ever born! You are probably around the middle of the pack,
> > > which is the point.
> >
> > Okay, this depends on the population growth pattern, and for some reason I was
> > envisioning a population that grows linearly or faster up to a certain point
> > (N=10^14, or 10^11, or whatever), and terminates. Then the
> > instantaneous probability of finding yourself in a particular order
> > becomes more likely the later you appear.
>
> Actually it doesn't matter. The point of maximum probability
> density is of no significance, what matters is that the region of birth
> order between, say, 10% < you < 90% is quite likely.
>
> > But this is indeed very artificial and in fact does not reflect the real world's
> > behavior either, as I'll mention below.
> >
> > > > (Now, the current world population growth rate is ~5 people every 2 seconds.
> > > > So each moment we find ourselves in a less and less likely position in the
> > > > history of the human race.)
> > >
> > > Again, the above make no sense.
> > > In general, in a period of exponential growth, would would expect
> > > that growth to reverse within a time constant or so. Of course, we do
> > > have some additional information that modifies that in this case.
> > >
> >
> > Well, the population is indeed still growing, but the rate may not be increasing as
> > much as it used to (which is probably very good for the planet). It's 6 billion now.
> > In 1960, the population was 3 billion. In 1800, it was 1 billion, most of whom died
> > before the 1960 count. So there were at least ~4 billion to account for between 1800
> > and 1960. If the world ended in 2000, we will find ourselves 'exceptionally' late
> > (past the median) in the group between 1800 and 2000. And if you include those before
> > 1800, that only makes us appear even later. (Source:
> > http://ssl.zpg.org/popframe.htm). For us to be in the middle, the world has to keep
> > on going for maybe at least another century. But then what will our children
> > conclude?
>
> Of course our children *should* predict a later "doomsday",
> because the information they would have on birth order is, by definition,
> different from the information we have.
> For example, suppose population was constant for 10^6 years. We
> would then expect it to remain so for about another 10^6, betting that
> sometime around then doomsday would occur. But if we were born around
> 2*10^6 years, our expected timescale would double. It would keep
> increasing until, one day, some of our ancestors would be proved
> right. This end would come as a surprise to those alive at the end, but
> this betting proceedure would maximize the fraction of people whose bets
> were in the right ballpark over all time.
>
> - - - - - - -
> Jacques Mallah (jqm1584.domain.name.hidden)
> Physicist / Many Worlder / Devil's Advocate
> "I know what no one else knows" - 'Runaway Train', Soul Asylum
> My URL: http://pages.nyu.edu/~jqm1584/
Received on Thu Jan 27 2000 - 00:02:18 PST