Watching a great Numberphile video about how the number –1/12 keeps showing up in calculations that involve infinite series. To recap, a modern mathematician (Terrance Tao) figured out that this number shows up because it’s buried within the very fabric of how math deals with simplifying infinities.
I’m a lover of numbers, and of math in general. Triangles are a turn on. Despite the sharp points.
However, I’ve dedicated my life to understanding behavior. Not just about people. Animals. Bugs. Trees. Bacteria. Even Gaia – the whole Earth.
And looking at math from the perspective of a bacterium has opened my eyes.
Strangely enough. It wasn’t my idea to look at math from a bugs eye point of view. A guy named John Conway gave me the idea. And another guy named Knuth wrote about it in a way that I could *almost* understand.
Here’s one of my older posts about Conway and how his new numbers may in fact be old numbers.
Anyway, the discussion about infinity was something I didn’t think about, until now.
Infinity really isn’t real. It can’t be.
We know the universe is finite. We know that the resolution of the universe is finite. We know that light only travels a certain speed. We know that the universe can be only so many years old. And that time, and energy, can only be so small before they simply don’t exist anymore.
Each of those things is a limit. Can’t be too big. Can’t be too small. Can’t live too long.
So where’s infinity?
In our minds. It’s a make believe concept that has proven valuable for figuring out problems. But it’s not real. And that’s why math runs into problems. And physics, too.
Does the number pi go on forever? Absolutely. The ratio is something that we looked for, and we define it in terms of our made-up numbers.
Can we prove it goes on forever?
Absolutely NOT. We can’t because there isn’t enough time, enough space, enough energy.
So it’s not infinite.
Same for every other “irrational” number that exists. We made it up. And we have to live with the consequences.
What does this mean for those of us forced to live in “reality?”
Until a math genius comes along and turns the math world inside out, we have to wrestle with these imaginary problems.
Until we think of “surreal” numbers and “irrational” numbers as real as “natural” numbers, we’re going to have problems.
And this is where behavior comes in.
Because the problems aren’t math. The problems are us. In our minds.
Think about it. But not for long! We don’t have infinite time. LOL
Behavior, study of... 