Because I work around a bunch of living systems people, I keep bumping into fractals. I've always liked the concept of fractals. The way they were explained to me was very simple: in nature, a fractal is a pattern that you can find underlying chaos. Nature follows the simplest and most efficient path. Therefore, you have the same pattern over and over, expressed in iterations and sort of nested within one another. For example, a piece of broccoli or cauliflower is these tiny florets within florets within florets, all of which were shaped by the same material flows and thus have the same pattern. Here's a broccoli-cauliflower hybrid, which is a nice example:
So anyway, that's how I understand fractals, which is sort of a simplistic natural systems view. There is this whole fractal geometry thing that I don't get, though, because I'm bad at math. But basically, fractal geometry corresponds to actual stuff in the real world, whereas euclidian geometry is all about abstract shapes like triangles and squares. This is cool: someone was recently telling me about this law of fractal geometry which is basically when you're measuring the perimeter of something, that as your instruments become more and more calibrated your measurement will grow closer and closer to infinity. The example that was used was measuring a coastline--imagine walking along the coast with a measuring tape, which would give you one measurement. Then, imagine walking around with a string and measuring around each individual grain of sand. Your measurement would be much higher even though it was the same coastline.
So anyway, that got me thinking and googling. I was reading this thing on Mandelbrot, which was interesting, and kind of lifts up some stuff about fractal geometry vs. euclidian geometry, so I thought I'd pass it along. What frustrates me is that when they're teaching younger people math, they teach them euclidian geometry, which seems much more abstract and boring. I mean, I'm not saying you shouldn't teach euclidian geometry, because obviously it's very very difficult to get through life if you don't know how to calculate the area of an isosceles triangle. But if they were teaching kids in high school fractal geometry then I'd think that they would be much more interested, right? Because you can just run outside and find some shit to play with. Plus, it would help prepare these kids to make the most of their first acid trip. Goddammit our education system is failing us.