{"id":166,"date":"2009-08-16T20:03:00","date_gmt":"2009-08-16T20:03:00","guid":{"rendered":"http:\/\/jimgworld.com\/blog1\/2009\/08\/16\/166\/"},"modified":"2010-05-09T19:41:08","modified_gmt":"2010-05-10T00:41:08","slug":"166","status":"publish","type":"post","link":"https:\/\/jimgworld.com\/blog1\/?p=166","title":{"rendered":"Chaos and Relationships"},"content":{"rendered":"

Over the past few months I’ve been trying to learn about chaos theory<\/span> using a method that almost no one else uses. The people who are interested in chaos theory are generally mathematicians, scientists, information\/ciber-theorists, and philosophers. The math and science people take graduate courses that use highly abstract paradigms involving matrix math and complex multi-dimensional geometries. This stuff takes many years to learn, even if one has the time, interest, and the right kind of brain. Being young helps; old people have a harder time climbing the mountains of abstraction involved, and usually have day jobs and intricate family issues to compete for their attention. <\/p>\n

The philosophers have their own forms of abstraction, based around words. They would grasp chaos theory in terms of layers and layers of speculative ontological and epistemological concepts, around philosophies of science and the nature of knowledge. Then there are the “new age” people who have heard a bit here and there about chaos theory and think that it represents a triumph of nature and “the feminine” over the logical, paternalistic structures of science. They see it as a growing wisdom affirming reality as “a dance” on the stage of mystery, a mystery that can only be plumbed through contemplation and intuition on the part of a few wise “mystagogues”. <\/p>\n

I’m trying to get a feel for chaos theory the way that a child tries to get a feel for riding a bike. And that is by getting my hands on it and manipulating it, watching what happens when you try this move or turn that lever up or down. I’m using a plain old Excel spreadsheet in my explorations, and I’m having some luck. I’ve been able to recreate and plot out some of the wacky effects that result from seemingly simple math equations, equations that involve time lags (inputting the last output value as one of the inputs to calculate the new value) and cross-dependencies (the output from one equation goes into the other, and vice versa, in calculating the next values in time). Last week I was finally able to recreate and plot out the classic Lorenz “strange attractor”<\/a>, which almost looks like a butterfly (much to the delight, no doubt, of the new agers!). <\/p>\n

This trial-and-error approach will not teach me any deep mathematical truths regarding what equation formats, parameters and starting points will result in a “strange attractor”. That would take an understanding of vector math, which I might have had for a few months when I was in college (35 years ago), but have long since lost the ability to grasp, along with “state space” topologies (such as Hilbert or Riemann manifolds). And throw in some fractal dimensionality. But my own purposes are somewhere between the philosophic and new age approaches. I want to respect the “hard math” that is going on in my computer when I cook up new graphs and plots of chaotic systems, and yet I want to draw some conclusions that help me reflect on “the way things are”, in an existential and human-focused sense. <\/p>\n

Back in May, I wrote a comment<\/a> in my blog about an article by chaos mathematician Steven Strogatz with some semi-serious thoughts on applying chaos theory concepts to one’s personal and emotional life. I’m not sure if Strogatz wanted to be taken seriously about that, but I decided to do so anyway. So I’m going to make some observations here about what chaos theory, in its search for patterns and “attractors” amid zig-zagging, nonsensical conditions (think of a pot of boiling water), might tell us about our lives on the social level; i.e., about our all-important relationships with others. <\/p>\n

My theory is this: In our relationships with other people, and perhaps with the world in general, we are trying to find “chaotic attractors”, a.k.a. “strange attractors”. Let’s think about the various kinds of attractors. There are point attractors; the equation outputs settle down over time to a single fixed point, with no movement away from it. There is a perfect equilibrium. Psychologically, we don’t like this kind of situation. It’s boring; actually, it’s like death. Nothing ever changes. NOTHING. That’s not<\/span> what we’re looking for in our lives.<\/p>\n

Then there are the “limit cycles” or cycle attractors. When you plot these out, they look like circles (could also be ovals). There is continuous movement, but it stays on a fixed track. It’s better than death, but you eventually become frustrated with it. We complain about “going around in circles”. We have a movie about just how bad it would be if every day repeated itself precisely (Groundhog Day). So, we don’t want to get into a limit-cycle either.<\/p>\n

Then there is the situation where there isn’t any attractor. Or even worse, there is an attractor for a while, but at some point in time it stops working and the system goes nuts. The output values skyrocket out of control, sometimes swinging back and forth between ever widening extremes. We can’t live our lives when emotions reach that state. Relationships blow up under those circumstances. I’ve learned that with just a small tweek of an input variable or an equation parameter, a system that was showing a stable attractor pattern can go bonkers. That’s not where we want to be; we need some limits, some form of predictability, some sense of reliance on something.<\/p>\n

Thus the beauty of the “strange attractor”. With just three simple Lorenz equations”<\/a>, plus the right equation coefficients and the right form of time iteration, my Excel spreadsheet comes up with a plot that weaves and wanders back and forth. It goes a few loops in one circle, then switches over to another loop for a while, then back to the original area. The path never seems to exactly repeat itself. There’s always a bit of “dancing”, of novelty. And yet, no matter how far in time you take the Lorenz system, it stays within a general neighborhood. It doesn’t reach a point in time when the values start going out of control. It’s actually pretty amazing that some fairly simple mathematics can yield something like this. It looks a lot like what we want life to be like. A nice mix of change and predictability, movement and familiarity, novelty and dependability. Basically what marriage should be like, or any other good relationship between two or more human beings.<\/p>\n

What made me sad came after I noticed that the Lorenz equations seemed sort of “special”. I decided to come up with a more generic math system having more parameters. By setting the parameters one way, you would come up with the Lorenz “strange attractor” butterfly plot. But what happens when you change some of the variable parameters? Or change the basic Lorenz format, what happens when you mess with the variable parameters? I came up with a scheme to try combinations of randomly selected numbers for these parameters, to see how the results plot out. With a push of the F9 button, I would change the set up.<\/p>\n

Unfortunately, what I found was that you lose the “strange attractor” zone quite quickly. Mostly what happens is that the output numbers go out of bounds, i.e. no attractor at all results. Sometimes you get a point attractor (i.e., the dead-zone). Occasionally you get a circular, repeating attractor. But the on-going chaotic attractors that the Lorenz system gives are quite rare. <\/p>\n

What’s worse, over many pushes of that F9 button, I saw some interesting-looking plots that seemed much like a strange attractor; i.e., the plot repeated a general pattern but never in the exact same way. But when you extended these plots further and further in time, they often reached an unexpected blow-up point. Kin
\nd of like a marriage or friendship that was doing just fine for years and years, then ironically seemed to go out of control. Even more ironic, I saw one or two plots where a fuzzy circle or figure-8 resulted for a time, but eventually the values went out of bounds and seemed ready to skyrocket out of control. But then they settled down into a new, larger fuzzy orbit. Happy ending? No, after a time of strange attractor-like bliss, this situation then lost all control and fell apart. <\/p>\n

Gee, seems like real life. <\/p>\n

There was still another kind of attractor that I saw which seems to reflect a form of dysfunctional relationship. That is when the plot spirals inward toward a point attractor, but never precisely makes it to the fixed “death point”. In this case, the plot values get closer and closer to some fixed end point, they spiral around what appears to be an end point, they get smaller and smaller, incredibly tiny. And yet they never stop, the swirling pattern just gets more and more tiny, on and on into infinity. This is actually an example of a “fractal”<\/a>, whereby a pattern repeats itself whether the scale of the plot is 1 foot, 1 inch, 1 micron, down to the level of molecules then atoms and then quarks. (Thank goodness quantum theory would finally put this eternal diminishment to a merciful end). If you look hard enough, you can people who have lived lives swirling around some “fixed point” of power or glory or some other neurotic attraction, and continually diminish their own souls as they swirl around and around seeking to land on this “attractor”.<\/p>\n

Well, this is all terribly unscientific and off-the-wall. But when you see just how rare the true (Lorenz-like) “strange attractors” are amidst the oceans of “state space” that determine complex equation parameters, it makes you ponder the frailty of complex phenomenon like human relationships. Psychology will never bring our lives and our relationships down to a set of math equations with fixed parameters and starting points. Shrinks cannot apply manifold theory and vector analysis to tell us what circumstances will lead to happiness. But it’s still amazing how a set of math equations with certain parameters and starting points CAN put on a show that reminds one of real life. <\/p>\n

A good psychologist might tell me that I’m just “projecting” my own experiences onto an artifact (i.e., my Excel spreadsheet) that has some accidental similarities; and thus there are NOT any deep insights to be had through this. And that’s probably true. But that also might describe the entire field of psychology. It’s all just a way to think about our lives and our place with other people.<\/p>\n

So for now, I’ll think about life in terms of continuing to push the “F9” button, looking for circumstances where stable and yet interesting and novel human interactions will result. Once you find one, take care to appreciate it; you may not run across another anytime soon.<\/p>\n

P.S.: some further searching turned up a recently published book by Molly Ludlam and Viveka Nyberg, called Couple Attachments Theoretical and Clinical Studies<\/a>. In this book is an article entitled “Marriage is a Strange Attractor: Chaos Theory, a Paradigm Shift for Couple Therapy” by David E. Scharff and Jill Savege Scharff. How ’bout that? Also, I came across the web site of another guy who had my thought<\/a>. He posts diagrams of a wide variety of different strange attractor patterns, and explains how each one relates to a different human interaction. Nothing new under the sun, I guess!<\/p>\n","protected":false},"excerpt":{"rendered":"

Over the past few months I’ve been trying to learn about chaos theory using a method that almost no one else uses. The people who are interested in chaos theory are generally mathematicians, scientists, information\/ciber-theorists, and philosophers. The math and science people take graduate courses that use highly abstract paradigms involving matrix math and complex […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22,9],"tags":[],"_links":{"self":[{"href":"https:\/\/jimgworld.com\/blog1\/index.php?rest_route=\/wp\/v2\/posts\/166"}],"collection":[{"href":"https:\/\/jimgworld.com\/blog1\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/jimgworld.com\/blog1\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/jimgworld.com\/blog1\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/jimgworld.com\/blog1\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=166"}],"version-history":[{"count":3,"href":"https:\/\/jimgworld.com\/blog1\/index.php?rest_route=\/wp\/v2\/posts\/166\/revisions"}],"predecessor-version":[{"id":1504,"href":"https:\/\/jimgworld.com\/blog1\/index.php?rest_route=\/wp\/v2\/posts\/166\/revisions\/1504"}],"wp:attachment":[{"href":"https:\/\/jimgworld.com\/blog1\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=166"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/jimgworld.com\/blog1\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=166"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/jimgworld.com\/blog1\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=166"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}