Home: Scrying: Grasping complexity

Grasping complexity

April 10, 2006

I’ve written about both complexity and time lately (with more to come!) and I figure it’s time to explain my personal obsession with these subjects, and chaos too. Why not? The “what is a chaotic utopia” link describes my theories, but doesn’t explain how I worked them out. Since the subjects have been coming up lately, and life seems to be getting a bit more complex and chaotic (did someone say the president has gone insane and will soon invade another country?) I figure it might be a good time. Besides, then if there are any mysterious delays here over the next few weeks (read: term papers and final exams) you can figure I’m thinking about complexity and chaos. So here goes:

I used to stare at one of the Escher drawings in my mother’s books. (She’s always been a fan; we used to have his waterfall image hanging over the fireplace. Is the water going up? “It just looks that way; it’s an optical illusion.”) Belvedere by MC Escher, 1958My favorites, like my mother’s, were always the strange buildings with columns that never lined up quite right. In one lithograph, a ladder rests on the floor inside a structure, and ends leaning against the same structure. (Click here to open the full-size image in a new window.) Odd, true, but it wasn’t what always caught my eye. On a bench, under the structure, sat this little guy with a box. The box isn’t any ordinary box. He seems to have assembled it wrong—the wrong corners connect—what’s up with that? What seem to be the instructions lie on the ground nearby, showing nothing more than a rough cube with a few circles where lines intersect. Such a simple image, yet so ambiguous. Is it in, or is it out? The instructions confuse the little guy, and the little guy and his box confused me.

Finally, a friend who was a mathematician brought up the little guy with his box. I’d asked him his opinion of the fourth dimension—what would it be? (That was another fascination of mine, fueled by reading the book “Flatland”.) “Stephen Hawking thinks that the fourth dimension is time. On the other hand, that might be what the guy in Escher’s drawing is looking at—a shape that is both in and out at the same time. I think the truth is probably somewhere in between.” With that, I was on my own. It took me a few years, and reading some of Hawking’s work before I understood the time angle. When I did, it was no surprise that my mind returned to the cube by Escher’s ladder.

While thinking of that cube, I’d often wondered about dimensions… if, geometrically, something one-dimensional would be points stretching in one direction to make a line, something two-dimensional would be lines arranged on a plane, something three-dimensional would be planes arranged together to make a whole, like a ball or a cube. But then what would the fourth dimension be? Wholes arranged together to make a what? Trying to visualize it hurt my head. But I had to know. I eventually realized, with a small grasp of physics, that time fit the pattern.

You have a series of moments, or wholes, arranged together to make..well.. a history. This left me wanting, still, as there seemed to be something missing. Living in a fourth dimensional world made some sense. Every thing had a solid form, repeated throughout time. But this was all too solid..nothing to explain why things seemed inside-out—why life was so repetitively weird. If it was so solid, even if not enduring, then why was everything so different? How could the same forms be repeated in so many different and distinct ways? Maybe four dimensions wasn’t sufficient enough to explain it.

Hawking’s books suggested the string theorists were up to eleven or so… but they were working on a different problem, weren’t they? Physics vs. aesthetic patterns and shape. Not even close, I figured. There was no way I was going to run off and get a degree in physics. I’d been out of school for nearly 10 years, had a baby, and was never good at even algebra. Still, string theorists seemed to be the only ones trying to explain those dimensions. All higher dimensions, five and up, according to string theory, are so curled up on themselves that they make no difference to you and I. I would have no hope of picturing a fifth dimension.

But it still bugged me. Maybe there was a connection.  So I asked what a fifth dimension would look like. Around this time, I wasComplex patterns found in nature: (from center, clockwise) Tibetan River Braid, Lichen in sandstone, the palm of my hand, branches of a crabapple tree, and a computer directory tree. seeing fractals all over the place… they’d been popping up in science magazines for a few years, and eventually it hit me—they exhibited that same strange repetition of patterns. Fractals involved dimensions, true. But they were drawn in partial dimensions—between two and three. The patterns in life, like the growing branches of a tree or meandering arms of a river, always involved at least the four dimensions, like depth and time, right?

I was ready to ditch fractals and go back to the physics view. The “curled up” view seemed intriguing… I began to picture the fifth dimension as a twist of time. Not time, itself, twisting, but the object existing with five dimensions has a twist. Not only does it occupy certain coordinates in physical space and time, but it also exists in such a way that it changes, rearranging slightly with the passages of time. You could say each changing aspect is timeless, but “timefull” might be more accurate: the product of past, future, and present. So… reality, with a twist? Now we’re talking about things as obscure as evolving ecosystems and inside-out boxes.

So… I had an idea of what it looked like… but what was it? I’d never have asked if I’d pictured the fourth dimension without naming it “time.” Fascinated still by fractals, I started picking up books on chaos theory. There was a strong resonance between the systems chaos theory was describing and my idea of the fifth dimension. I kept expecting to turn the page and see it printed: Chaos is a dimension, like time or space. Or: chaos is the fifth dimension. I realized quickly why I hadn’t. First, it sounded vaguely like cheesy old-school sci-fi. Second, no one had yet seen it the way I had.

I felt rather uneasy about the whole issue—maybe I had something important… or maybe I was just nuts. Since I’d been gathering all of my answers from borrowed or bought books, my credentials were a bit rusty, ok, non-existent—folks were probably going to choose the “nuts” view. So I went for the major-life-change option.

Picture this: I’d spent 10 years out of school, not really knowing what I should study if I went. Everything fascinated me, but the only thing I excelled at was writing, followed closely by research. I loathed the idea of an English degree… I knew how to write with proper grammar, when I chose to, or needed to. I didn’t want to spend another 10 years being shown how. I couldn’t pick a single science either. I thought of going into the culinary arts, or interior design—my relatives constantly wanted my help in menu planning, or organizing china cabinets. Unfortunately, the challenge there was staying competitive—and I’m more the type to work with others in my field, not against them. So, avoiding school, I went for the other option: I got married and had a kid. When I realized, a decade after giving up, that I needed my college degrees. I had plenty of gaps in my knowledge, waiting to be filled… but also a family to manage.

That’s about where I am now… it gets overwhelming at times, and I get behind. (If you ever wonder about a delay in my blogging, that’s probably why.) I still read as much material on chaos and complexity as I can (as you’ll see on my reading list.) So far, it fascinates me, and seems to coincide perfectly with my ideas, without ever stating the same thing. Sometimes, I’m tempted to write the Santa Fe Institute, where they deal with this stuff, but I still hesitate for lack of credentials. I’ve kept a 4.0 so far… but I’ve been hiding at Front Range Community College. I’ve shared my ideas with some professors in subjects like biology and philosophy who were able to understand, and offer ideas and encouragement. But I hesitate to leave. I’ve hesitated so much, in fact, that I missed the priority deadline for transfer students at CU Boulder. I’m hitting one of those overwhelmed times. I’ll be trying to help my son learn the difference between the little letter “b” and the letters “d”, “p”, and “q” when I start seeing those patterns again. Isn’t it weird that the shape would repeat throughout our alphabet, like that, and create such a diverse potential of words and convey such a diversity of ideas?

In about one month, I’m done with school for the summer, and the pressure will lighten somewhat. My son will be off to kindergarten next fall… and I’ll figure out where I’m going.

Maybe Boulder. Maybe Santa Fe. Maybe insane. Oh…wait… did that already. Well, then, back to homework…. and riding the waves.


Image credits: “Belvedere” by MC Escher, 1958, via McEscher.com. Tibetan River Braid via NASA’s Visible Earth  Other images in the complexity picture were taken by me.