One two three.
That was as high as we could go for a million years. It’s all you needed.
How many sheep you got?
One. Two. Three. Wait, I got many many many sheeps!
After a while we needed to count higher than three. There was four. Then five.
Making up numbers one at a time got boring. So humanity started a system involving categories of numbers. For every five numbers we created a bundle. One bundle was the same as five. We still use the bundle when we cluster our counting marks.
Not happy with even that system, some deep thinkers came up with a better system that took a number, any number, and added one to that number. Sounds easy once you get the concept, but that was a big concept.
Then those deep thinkers went crazy. What if you go on adding one to your number FOREVER?
Wow. For a while that whole idea was considered a sickness, and anyone talking about it was locked away. Then the idea sounded a bit more like only being crazy, so no one took you seriously. But then this other deep thinking dude came along and said, we can name this impossibly big thing and make it do work for us. We’ll call it, infinity.
Hello infinity. This is humanity. Humanity, this is infinity.
Many cool things started happening once we did that. For instance, it turns out that there are even different kinds of infinity. Who knew!
It gave me this crazy idea.
What if, now hang in there because this may sound crazy, maybe even sick crazy, but…
… what if …
Infinity were equal to One?
Yes, it’s crazy, but let’s play with this for only a second.
One equals Infinity.
One minus Infinity equals Zero.
Infinity minus One is still equal to Infinity.
AND, only making this even more fun,
One plus One is ALSO equal to Infinity.
One minus One would equal Zero.
One plus Infinity would still equal Infinity.
What does any of this mean, other than I may have had too much cognac?
In this system, there are no negative numbers, and there are no numbers other than these three simple concepts.
It also means that the order in which operations are performed is very important. That’s commutativity, and we take it for granted with normal math. But there are funny numbers called quaternions that don’t like being swapped around, either.
So what? I ask again.
Maybe, just maybe, this could be the math of creatures that haven’t learned to count beyond one. Maybe a bug, or a tree, or even the life form we call Gaia.
Then again, maybe it’s time to go back to counting sheep.