virus: Hyperbolic Growth

David Leeper (
Wed, 08 Nov 95 18:18:00 PST

Reply To Damien R. Sullivan:

>I haven't even seen "hyperbolic growth" in my math classes. Could
>someone define it?

Linear Growth: Growth rate is independent of quantity. Example: 2, 4, 6, 8,
10, 12, ...

Exponential Growth: Growth rate increases linearly with quantity. Example:
2, 4, 8, 16, 32, 64, 128, 256, ...

Hyperbolic Growth Rate: Growth Rate increases in proportion to the square of
the quantity. Example: 2, 6, 42, 1806, 3353442, ...

Hyperbolic Growth is the only type of growth (of the three presented here)
which can become infinite in a finite period.

I've done even more checking on growth rate since I posted the message
you're replying to. The book which I quoted the hyperbolic growth rate from
was referencing a source from 1974. After surfing the World Health
Orginization's web pages, I've found that population predictions have
changed drastically since then. According to the WHO, we are currently
experiencing exponential growth in world population (so I was wrong, or at
least out-dated) and even this is expected to stop a few decades in the
future. At that time, population growth will be between linear and
exponential. The causes for this strange shift were not explained.

Was humanity _ever_ experiencing hyperbolic growth? Yes. It took all of
mankind's history up to 1800 to reach 1 billion people. The next billion
took 125 years, the next billion took 25 years, the next billion took 20
years, the next billion took 10 years. The WHO is simply saying that
hyperbolic growth has recently (somewhere between 1974 and now) become
exponential, and that in the future even this will change. If anyone has
information about what data the WHO used to make its predictions, I'd love
to read it.

Of course, Game Theory has an answer to the sudden change in population
growth. Available resource can no longer support such incredable growth
rates. If this is the case, I really wasn't wrong, since I (easily)
predicted that this would be the result of our population explosion.

Well.. what do you think folks? Is starvation and destruction of resources
starting to effect man's ability to reproduce or even stay alive in some
areas? Are we seeing the beginnings of Ragnarok (or at least massive human
suffering)? If so, what can our memes do to help prevent such massive


Dave Leeper
"Ragnarok 'n' Roll!" - David Leeper
/growing exponentially, the other said it was growing linearly. So from
/three books, we have three different answers.

Thing is, population usually grows exponentially if it can. The number
of children is propotional to the current population, then the next
number of children is proportional to the new population, and so on.
A1=k*A0. A2=k*A1. A3=k*A2=k*k*A1=k^3*A0. An=k^n*A0. Not quite the
usual derivation, which involves some calculus I can't remember how to
set up off hand, but that should give the idea. 2 rabbits, 4 rabbits, 8
rabbits, 16 rabbits, etc. Again, that's given ideal situations, like
cooperative bacteria in a petrie dish. But when Africa's population is
said to be growing at 3% a year, that's exponential.

I haven't even seen "hyperbolic growth" in my math classes. Could
someone define it?

-xx- Damien R. Sullivan X-) <*>