Re: poly: population singularities

From: Hal Finney <>
Date: Mon Apr 13 1998 - 11:12:52 PDT

Robin Hanson writes:

> >> by Kapitza S.P.
> >> linked from:

> He says it is clear that we now see deviations from hyperbolic, but when
> I plotted the data out on a spreadsheet, it's not so clear. And when I
> did a quick plot of total world product, it's much less clear we've seen
> deviations yet.

An approximation he gives for population in the hyperbolic portion is
200 billion divided by (2025 - YEAR). This of course goes infinite in
the year 2025.

One interesting characteristic of hyperbolic growth is that the rate of
growth is proportional to the population squared. This is unlike ordinary
biological growth rates which tend to be proportional to the population,
absent constraints.

How could you have growth be proportional to population squared? With n
people there are n squared pairs. It would seem to be necessary that
somehow how readily I can reproduce receives an influence proportional
to the number of other people in the world.

If I were able to interact individually with every other person in the
world and gain some benefit from that, then population could grow at an
n squared rate. Obviously this is not possible. However an efficient
global economy could bring me some benefits from each individual so
perhaps it could work in that case.

You can also get the same effect if there is some property which only a
tiny fraction of people possess, and if I am able to benefit from each
of those individual's efforts. This could correspond to those rare
individuals who are able to make significant advancements in technology.
They are few enough that it is more likely that I am able to receive
a full measure of benefit from each one's efforts, without diminishing

Some people have predicted that technology might hit a singularity and
reach an infinite level in a finite time (e.g. Vernor Vinge's novel,
Marooned in Real Time). It would be necessary for the rate of growth of
technology to be proportional to (at least) the square of the technology
level for this to be true. It seems that growth rates are presently
receiving a benefit proportional to the population. If we identify this
"benefit" with technology level, this suggests that technology level is
proportional to population size during this hyperbolic regime, and is
also on a hyperbolic curve.

If population levels off and does not go to infinity by 2025, technology
levels will probably also depart from their hyperbolic trend. However
even if population becomes stable, technology will still advance, so
the simple proportionality between the two will no longer apply.

Received on Mon Apr 13 18:21:33 1998

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