Artificial Intelligence

Not Fractals but Maples: the New Math

Mathematics is great. I love it. But I think it has too much power. For instance, the maple below is not solely a function of mathematics. To say it was would be to say that this is a fractal, a repetitive form that holds its shape no matter how large or small, one that maples exploit. But the thing is, maples were there before fractals. We should say “This is maple”, instead of “This is a fractal,” but of course mathematics needs to generalize, to find universal principles. That is its value, but also its limitation, because at the end of the day this is a maple. If it is a fractal at the same time, then that is a function of the universe. Mathematicians would agree, but perhaps without saying “The Universe is a maple.”

This is not a trivial distinction, because if we are to contemplate healing the Earth, we will have to step off from mathematics at some point and speak the Earth’s life, the way it fits into fractals. And that is to speak maple. How are we going to do that, if we don’t practice? Well, simply, we won’t. Of course, it’s not just maple. There’s bunchgrass, for instance.

Look at that beautiful stuff. That’s not a fractal. It’s bunchgrass. It’s only a fractal if you look at your response to it, rather than look into the variability of the grass itself. A different kind of math, perhaps? Of course, it’s bunchgrass. I wonder, though, what the mathematicians might make of this:

Geese, eh. Don’t look at the lines or the near-fractal pattern. Don’t look at the chaos mathematics here, or the statistics. Just look at the clumping into hollow circles.  That’s not the geese. That’s us. In fact, everything in that image is us, and that’s the secret of mathematics: it can only guess at the world. It’s powerful and beautiful, but it can only look at it through numbers and pattern, inferring the existence of a real world from that. We know there is a real world. We are designed to manipulate it.

It would be best to say that this is not an image of a sumach but a self-portrait. Sure, as humans we are able to look at faces, but we are able to do more than that.

2 replies »

  1. Such a thoughtful perspective. If only the heliocentrists had been so open as to say that the make-up of the universe should take precedence over their conceptualization of an infinitely stable two body system. They were trapped by the math of the two-body problem, which was really no problem at all, since it didn’t intersect with chaos. Now we’ve stretched out our computational wingspan to welcome in the three-body problem and the more complex subtleties of our chaotic existence that extend our awareness of the universe out to the mathematical boundaries of fractals. Now for us to stop there would place us square upon the next fractal iteration of the plateau in scientific advancement, where the heliocentrists last left off. Tracking that sine wave of temporal progress (or increasing resolution in fractal terms), we notice that we’ve arrived at a node on the bifurcation diagram, choosing between advancement beyond fractal awareness or decline into chaos.

    Interesting to note that we as inhabitants of Earth are currently experiencing a traceable decline from order to chaos. It just might be that we’re at such a critical turning point, where a next advancement of mathematical perception of the universe incorporating, and building upon fractals would lead us back on track toward sustainable progress toward higher order singularity. (By singularity, I mean the pathway of choices through a chaotic period, which lead toward a coalescing of all humans on the planet toward an aligned purpose.)

    So anyway, great stuff!

    Like

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