Believe – Part 2, The Necessity of Chaos

In the past several decades, we’ve come to realize that there is a sort of rhythm to various systems. It took a while to recognize much of this because all too often this rhythm seems to be random…chaotic. And it is chaotic. At any point in time, a specific measurement could seemingly be anything, and yet, once you examine them, you find that they are bound to rather well-defined constraints. These “strange attractors”, such as the Lorenz Attractor (or Lorenz Butterfly [source of the term “the butterfly effect”]) describes for us a necessary ingredient to any AAI system. We have to design it to conform to some strange attractor so that chaos can work its magic.

The key, it would seem, would be to find the mathematical fomula(e) that would describe our strange attractor. So far, biology has offered up few clues. Many maps look like wadded up balls of fishing line. Some, especially rats having epileptic-type symptoms, can resemble a 2-torus (basically think of a spindly Lorenz Attractor stuck on top of that wad of fishing line. I have, however, seen some crude scans of humans that look promising.

In what I describe as a Crown of Celtic Knots or as a Crown of Thorns, it comes off as more of a multi-level, intertwined Möbius loop. Think of it sort of like several turk’s head knots, all connected, each with a different frequency, and all fit one inside the other.

That’s really the best visual I can give, but I think the description that really comes closest isn’t visual at all. It’s actually a very famous jazz tune known as “Rondo in Blue by Turk”. (This one of those synaesthesia things some people, like me, experience sometimes.) While the music itself doesn’t really describe the math of the attractor, the global attractor itself is strongly hinted at.

Even on a basic level, the elements of the performance also hint at how to make the disparate pieces interact. The drums, especially the high-hat, give us the background chaotic noise that all neural tissue seems to require to prevent a seizure. The piano and sax are the actual process going on in active and resting states. The bass is the moderator, the central force binding all of it together.

Obviously it’s much more involved, but I hope you get the sense of how this necessary strange attractor would work in any AAI system. The regulator, controller, and active processes have to meld into a harmony that resists finding a steady state that might cause a fatal seizure.

I realize that some are wondering if I’m off my nut… using a jazz number to describe how an AAI might work. To answer that, I’ll leave you with some words from Richard Feynman:

I was in the cafeteria and some guy, fooling around, throws a plate in the air. As the plate went up in the air I saw it wobble, and I noticed the red medallion of Cornell on the plate going around. It was pretty obvious to me that the medallion went around faster then the wobbling.

I had nothing to do, so I start to figure out the motion fo the rotating plate…It came out of a complicated equation!

…

[Hans Bethe] says, “Feynman, that’s pretty interesting, but what’s the important of it? Why are you doing it?”

“Hah!” I say. “There’s no importance whatsoever. I’m just doing it for the fun of it.”

…

There was no importance to what I was doing, but ultimately there was. The diagrams and the whole business that I got the Nobel Prize for came from that piddling around with the wobbling plate.

— Richard Feynman, “Surely You’re Joking, Mr. Feynman!” 1985

I’m in no way implying that my little supposition is anywhere that class, but merely point out that if you’ve been working on a problem long enough, sometimes it’s the most innocuous thing that will spark an important connection.