# Who Knew That Math Could Give Me Nightmares

Today in my math class, we were learning about a type of population growth model known as the Doomsday Model.

The Doomsday Model refers to a situation where there is a population explosion, one in which the population becomes unbounded (infinite) in a finite period of time.

Here’s the example he used in class:

The time rate of change of an alligator population P in a swamp is proportional to the square of P. The swamp contained a dozen alligators in 1988, and two dozen in 1998. When will there be four dozen alligators in the swamp? What happens thereafter?

I’ve written before about my unhealthy phobia about alligators, so I didn’t really want to imagine a situation where alligators were growing at an alarming rate.

Anyway, for those of you who may be interested, here is an image of the solution:

(DE stands for differential equation, which is the course I am taking.)

Written in plain English, here’s how one can interpret the results. It took 10 years for the alligator population to go from 12 to 24. It then just took 5 more years to go from 24 to 48. And then, just 5 years later again, the population of alligators has reached infinity.

Let me say that again, the population of alligators has reached infinity.

If that isn’t enough to keep you awake at night, and if and when you do fall asleep, to have the worst nightmares imaginable, I don’t know what would.

I’ve actually incorporated the possibility of seeing an alligator into my retirement planning. I’ve always thought one of the worst things that could happen to me is to be out for a walk somewhere and come within 20 yards of an alligator. If there are cities where there is a good likelihood of that happening, it’s not going to be high on my list as a retirement choice.

But now that I’ve just learned about a scenario where the alligator population can reach infinity, then no place on Earth would be safe. Hopefully they will have colonized by Mars before such a scenario plays out.

I should point out that there is one potential bright spot.

At the end of class, the teacher mentioned something about an Extinction Model being covered in the next class.

Maybe if he uses an alligator example for that one, the nightmares will end…

P.S. If you’d like to know more about the Doomsday Model, here’s a brief excerpt from Wikipedia:

The Doomsday Model came out of a 1960 article in Science magazine written by Heinz von Foerster and his colleagues P. M. Mora and L. W. Amiot. The article looked at the growth of the human population, and predicted that population growth would become infinite by Friday, November 13, 2026 – which just so happened to be von Foerster’s 115th birthday anniversary. Many viewed the predication as being made tongue-in-cheek.

And while an infinite population of humans would certainly not be an ideal situation, I wouldn’t consider it in the same league as the Doomsday associated with an infinite population of alligators…