Jacques M. Mallah wrote:
> Happy New Year to all.
>
Happy New Year to you too, Jacques. I am glad everyone has survived or is dealing
well with Y2K.
> On Mon, 13 Dec 1999, Fred Chen wrote:
> > Jacques M. Mallah wrote:
> > > The Doomsday argument still works. The uncertainty is not which
> > > "universe" you're in; as you say, if both universes exist and you know
> > > that, there's no Doomsday argument. But the thing is, you don't know
> > > that. Suppose there are N "universes" that all exist. Some X of them
> > > have 10^11 people, (N-X) have 10^14, but you don't know what fraction X/N
> > > is.
> >
> > Generally, and conservatively, this is true. For AUH, however, N>>1
> > and population size is allowed to vary freely among the universes, so we
> > would expect many, many more universes with populations maximally
> > exceeding the current population, i.e., as large as possible within constraints
> > of cosmic evolution.
>
> 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.
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.
>
>
> > > If your number is 5*10^10, this suggests X/N is large: Doomsday.
> >
> > X/N is not known, as you said. What I understand you to mean is that
> > for N=1, 10^11seems far more likely than 10^14, according to the
> > Doomsday argument. But the most likely number of people should be 5*10^10,
> > in this case.
>
> Your last line doesn't make sense. 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.
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?
> - - - - - - -
> 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 Sat Jan 08 2000 - 21:42:04 PST