Monday, June 1, 2009

Becoming One with Chaos Theory

by Elaine Walker, June 11, 2009

Chaos theory is like a mathematical mirror of the natural world. Once I realized this I began seeing the same universal patterns of chaos theory and fractals in everything I observed - galaxy formation, the stock market, weather, plant growth, celestial orbits, dripping faucets and even morality. Some of these things leave a kind of freeze frame image that clearly shows residual fractal patterns, such as galaxies, clouds and plants. Some, like morality, the economy, or faucet-dripping, are more elusive, where the patterns are not only hard to see but get lost in time. These patterns don't happily stick around in the same ultra-slow-motion-3D-picture like the previously mentioned items do. 

It's easy, however, to record and graph a faucet dripping and observe fractal patterns emerging, much the same way we see patterns in the stock market through our recordings of it, which give us a glimpse into economic trends. In the natural evolution of morality, the chaotic/fractal patterns are much more hidden and arbitrarily hard to record. Yet I think they are there. I think they are everywhere.

A question that I constantly battle with is how much we should meddle in any of these processes. We are human, so is meddling with human morality really meddling, or is that part of the natural process? Is meddling with our own economy really meddling? Or is it part of the process? Liberals and Conservatives would say yes to one and no to the other, and vice versa. There is something wrong with that picture. Libertarians say no to both, which is, at least, more consistent. But as I said, it is a constant battle for me.

If there is a correct answer at all, it's probably something like, "Yes, we may want to meddle a bit now, while we are still so primitive that we must think in abstract geometric patterns, as we are not yet fully able to grasp chaotic processes in our daily lives. But once we evolve beyond this stage, we would do better to not impose our abstract linear geometry on top of nature." That said, we can argue endlessly to what degree we should meddle at this stage in our evolution.

Most animals don't exhibit abstract thought to a degree anywhere near humans abstract thought. They certainly don't picture a tree like a child does, with a long rectangle for a trunk, and a circle for the leaves. They mark their territory more with smell and other complex natural cues, rather than thinking of a rectangle or oval area.

Obviously, developing self awareness and the ability of abstract thought was an important and necessary step in the evolution of our intelligence. Our self awareness evolved gradually. Our cameras that once only acted as a window to the world, gradually turned to point directly at ourselves (see I am a Strange Loop by Douglass Hofstadter). Once this happened, an amazing feedback loop started and we became able to fully ponder ourselves. We could even ponder ourselves pondering ourselves. Abstract thought was born, along with our creativity, and the intense advantage we have over all other lifeforms on Earth.

I offer the camera feedback visualization because it is the best analogy I've heard so far to get this point across. If you have never played with camera feedback, do it now. Plug a camera into your computer and open a video program. Point your camera in record mode to your computer screen. Aim to the center of the screen until you see the familiar endless tunnel, as if two mirrors are in parallel. When you get the angle just right, the feedback image will "lock in". You will know what this means when you see it. 

It will initially look like a series of windows, smaller and smaller, tilting successively into an endless hallway. If the hallway curves off to the side, point the camera straight at the screen until it is endless, then tilt the camera and move closer and farther until it "locks in". The image will almost suddenly look more like a galaxy or sphere of light, or perhaps something else, rather than a series of tilted windows. It becomes something new. It would be hard to reverse engineer the locked in image if we hadn't just gone through the process of creating it ourselves.

At this point we naturally start to describe this new image in abstract terms like "galaxy" or "glowing sphere" other than using more complex and detailed language to describe each separate recursive window, each separate degree of tilt and size difference. Our ability as humans to see a "galaxy" or "sphere" and feel comfortable with such macro descriptions - knowing full well it is really a result of a recursive chaotic process (video feedback) and not really a solid object at all - could be seen as a virtue, but in some cases, our downfall.

Surely, when we first became fully self-aware, able to ponder our own pondering, abstract thought was necessary in order to become who we are today; to ponder things like celestial orbits that we saw in the sky, to develop mathematics as a new language, to build structures beyond cave dwellings, to mark our territory, and so on. And now we have shown the beginnings of an ability to reconnect with nature's roots by thinking about dynamical systems and fractals - in essence, chaotic processes. 

But still, it is too easy to forget the dynamical and all-too-delicate chaotic processes that go into things like "morality" and "economy" and "weather". We tend to cram them in to abstract categories or mere snapshots in time, to describe them purely subjectively, as if to multiply and divide them linearly, ignorant of the actual mathematical descriptions that would be much more true to the nature of these processes. We may even forget that they are dynamical and evolving processes to begin with. The way we treat these things like flattened abstracted constructs will be our potential downfall. 

We have built the eiffel tower and many bridges based on fractal structures rather than linear shapes. We study fluid dynamics and even understand now that heart beats exhibit fractal patterns through time. Some of us (certainly not all) can grasp the fact that these processes self-organize and exhibit extreme complexity and robustness and evolve in a bumpy but steady, strangely robust balance, like a tree that can go without water and sun, then come bouncing back when the circumstances improve.

I am willing to bet that in our future, more and more, we will develop chaotic techniques, perhaps even "growing" our homes as more stable structures that are in tune with the surroundings and able to repair themselves. We may use more fuel efficient chaotic orbits for spacecraft, which is already happening to a small degree, and any other number of unpredictable inventions. What I am worried about is that we may not see past our rigid abstract thinking - our arbitrary categorizing, simplistic hierarchal organizing, and harmful once-size-fits all "solutions" - soon enough to let our societies stir and bloom along with the rest of nature.

We really must begin teaching chaos theory in grade school classrooms, which only need involve simple recursive algebra, the concept of recursive feedback loops, and images of natural process and fractals, allowing kids to develop a sense of what nature is - simple seeds with simple processes embedded, all feeding back into themselves and nearby systems, resulting in complex and beautiful patterns that occur in everything we know. And we should compare and contrast to everything human-made, which is better described with Euclidean geometry than chaos theory.


Copyright © 2009 by Elaine Walker. Permission to reprint in whole or in part is gladly granted, provided full credit is given and author notified.