Put your floaties on, because this part of The Pool is deep.
Geometry must be cool because smart people do it, right? We can all draw straight lines, circles, and recognize triangles (maybe not the hypotenuse part), got a Spirograph for Christmas, and have heard of tangents, whatever they are. Yeah, that.
Geometry must be DECIDEDLY cool.
Here’s the rub. Are you sitting down? It’s all self-deluded balderdash.
There was a Greek guy named Euclid that hung out at the forum about 300 years before Jesus showed up.
Euclid was really organized, and unfortunately, a good writer. He created a bunch of “axioms” and “proofs” that swept everybody off their logical feet for a couple thousand years.
Euclid’s Geometry axioms were about lines and triangles and planes and stuff that we all learned about in junior high school. They sounded logical, and looked air tight.
Uh, well, check your floaties. Houston, we have a problem.
There are no straight lines, or perfect circles. There is nothing, at all, that is straight, or round, as we know it. We think perfect lines or circles into being, because that’s how our brains do business. But, sorry, no lines, or circles or triangles or hypotenii, or anything else that goes by the name Geometry exist in the real world.
Here’s why. The fundamental structure of everything, isn’t straight. It is the shape of how we think of a black hole, like a whirlpool no matter what angle you view it from. The closest thing to geometry that fits what the Universe really looks like would be a sphere, sort of, because that is the closest thing that our brain can think of. It’s not really spherical at all, but hey, our pea brains have to start somewhere.
The underlying shape of everything is fractal, and there is zero overlap between fractal structures and what we learned as geometry. Can we draw really pretty pictures of fractals made of straight pieces? Jeaaahhh, but they are not found in the fabric of the universe, anywhere.
There is, technically, room for a discussion about fractal geometry, but it has not been invented yet, at least not in terms other than straight lines and other stuff that doesn’t really exist, so the current body of fractal geometry is balderdash too.
In a Universe made of scaled fractals, straight lines are crutches we use to build buildings and bridges and stuff. If you are a mechanical design engineer, you know that NOTHING wants to be in a straight line, so you have to build fudge factors to make stuff look straight, or round, for a short while anyway.
Geometry = fail, sorry. If you are a Geometry teacher, your secret is safe, FOR NOW, but don’t hold your breath, because Binary Dimension Theory is coming to a school near you soon, and Geometry is the first thing out the window.
Are your floaties still working? Remember to paddle.