FRACTALED FERRY TALES: I’ve read various accounts regarding the mathematical concept of “fractals”, and what a big deal it is. In a nutshell, fractals represent a mathematical situation where there exist patterns within patterns within patterns within patterns . . . . on and on. So, no matter whether you are looking at something from space or thru a microscope, the fractal pattern would be the same (give or take some random factors). A fractal surface area is kind of like a sponge, with lots of surface area in a small space. A good practical example of fractality is provided by aluminum foil. When you first cut a piece of foil from the roll, it’s nice and flat and shiny. Maybe you use it to wrap up a pound cake or something like that. After the pound cake has been eaten, many people throw the foil out. But if you’re a cheapskate like me, you save the foil and use it for something else, perhaps a muffin. After about the fourth or fifth time reusing foil, you see that it has become all scrunchy and shrunken, and isn’t much good anymore for wrapping stuff. That piece of foil was once flat, but has now become fractal, with lots of little folds and jags.

My point here is to ask what the big deal is about fractals. Mathematicians talk like they had found the holy grail. And they had some good examples, here and there. E.g., compare a shot from a space satellite of the middle of the USA, with the Mississippi River branching out into all sorts of twisty, smaller rivers, which in turn branch out into smaller rivers. on down to little creeks and brooks. Compare that with a shot of a tree. And then a close-up shot of a leaf. And then with a shot of the tiny blood vessels in your own skin. OK, so there are some recurring patterns to nature; give the math guys credit for being able to formally describe it.

But on a bigger level, the fractal idea is a big flop. I’m thinking here about the quantum world of fundamental particles, versus the bigger worlds of molecules and living beings and planets and solar systems and galaxies. There’s a huge disconnect in the way that tiny stuff acts versus bigger stuff; i.e. quantum physics versus the relativistic world of gravity. A long time ago, the atom seemed like a little solar system, with electrons revolving around the proton-neutron nucleus just as the planets revolved around the sun. (And on a higher level, billions of solar systems revolved around a black hole at the core of most galaxies). Now, if that were true, the cosmos would truly be fractal. But in fact, the atom is nothing like a mini-solar system. And the galaxy itself acts differently from a solar system because of “dark matter” (stuff we still don’t understand).

So, things do change fundamentally, depending on what level you look at them from. Aside from old aluminum foil, perhaps fractals still amount to an interesting idea that is useful in certain contexts. But sorry, mathematicians; you haven’t found the key to reality. So get back to your theorems and axioms, and call us in a few years to let us know how you’re doing.