In order to fully understand ourselves, we have to open our minds to the fact that everything we do that is “unnatural” is an aspect of our behavior.
If I let my computer fall into the tub, I have witnessed a natural event; gravity working its magic on my computer, on the moon, planets and stars.
However, what could I have been thinking in order to drop my computation box into the tub? That question is “unnatural” and in the realm of behavior.
Math is the same thing. Much of what mathematicians do is solidly in the realm of the unnatural, saying more about our behavior than Nature herself. Many times the very things mathematicians learn can be applied to our lives in very helpful ways. Counting sheep comes to mind. So does complex prime numbers for encryption.
There are many instances where mathematicians discover something that doesn’t seem to have any relationship to Nature. Then after a century or two some genius comes along and figures out what that discovery can be used for in our daily lives.
John Horton Conway is such a brilliant mathematician of the first kind. Among his many discoveries is something called the Monster Group. It’s a place where objects exist within higher dimensions. He was born in 1937, and he’s afraid that he won’t live long enough to learn what that Monster can be applied to in our reality.
As one who solidly believes that the study of higher math is also the study of an aspect of behavior, I would like to humbly submit this to Professor Conway.
The “Monster” is among us.
The key is to understand (which I don’t, by the way) that the monster lives within a dimensional space that is the product of 47 times 59 times 71. That’s a lot of dimensions. But the fact that this dimensional number is the product of three primes might be revealing in itself. Here’s why.
In the simplest behavioral theory, we still have to accommodate Nature as a component. The easiest way to do that is to collapse everything we understand in the natural sciences into their most basic “atoms.” Like the Ancient Greeks, our atoms of behavior can be Energy, Space, Matter, and Time. Collectively we can call these Resources, but there are no more than these four atoms in any behavioral question. Time only goes one way at the macroscopic level, so let’s ignore it.
The other three behavioral atoms are more than complex enough such that they may be represented by 47, 59, and 71 different states. The possible interplay between each of their “dimensions” with all of the others could give rise to your Monster.
I propose your Monster Group as a better representation of real atoms, from Hydrogen to Plutonium. Every atom in the universe becomes one of your Monsters.
There you have it. Crazy idea, no doubt. But wasn’t it Hilbert who described one of his former students as not having enough imagination to be a mathematician?
Thank you for everything you have given humanity.