The ramblings of an Eternal Student of Life
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Wednesday, January 4, 2012
Music ... Science ...

Just a quick thought tonight on chaos theory and fractals . . . and music. Chaos theory, in the strict mathematical sense, is based on the notion that many natural processes and social networks operate in a fashion in which their future state, e.g. how things will be tomorrow or next year, is largely determined by their present state.

However, this does not mean that things stay the same. Systems such as the weather or the stock market become chaotic because the relationship between present and future states is “non-linear”, i.e. based on mathematical functions that in-and-of themselves twist around. There is no straight-line proportionality. Things jump around a lot; but in the long run, there are patterns that can be found within that jumping around. That’s the crux of chaos theory. Chaos theory does not deny that future states are also heavily influenced by “exogenous shocks”, i.e. “black swans”, things that aren’t part of the pattern nor within the “state space” region where the system usually noodles around.

Fractals are in some ways much like chaos and in other ways different. Fractals focus on repeating patterns that may not be obvious at first when beholding the spatial design of something; e.g. a tree leaf has a network of branching veins, but the tree itself is also a network of branching branches. And that tree may grow in a forest that surrounds a river system, which itself is composed of spreading branches as you travel up towards its source; think about the Mississippi River and the huge network that it makes up with its many tributaries, including the Ohio River, Missouri River, Red River, Tennessee River, etc. So nature sometimes present repeating spatial patterns that can be seen at many different levels of magnification, permeating the big system and its components.

In fact, a popular way of visualizing and charting chaos, the “orbit diagram”, itself shows fractal patterns; you see a branching pattern, then pick a smaller segment of it and zoom in and see the same pattern; then pick out a small segment of that segment and zoom in and . . . etc. So, chaos is concerned with patterns underlying events in time, and fractals reflect repeating patterns in space. And events in time can be depicted in space, through the good old chart. Which is what an orbit diagram is, i.e. a chart showing pathways evolving along a time axis (typically the horizontal axis of the orbit diagram). So, patterns in time can be expressed as patterns in space, and then their fractal properties can be seen.

I wondered to myself, what about the opposite? Can patterns in space somehow be transmuted and expressed as patterns in time? It took some pondering, but I think that I finally came up with something that arguably reflects the fractal patterns of the 3-dimensional real world, in a time context. And that is . . . MUSIC. Music is the way by which we directly experience time, especially patterns in time. Of course, the best music is not just a boring repeating pattern, e.g. a metronome. We like interesting music, complicated music, music with a bit of chaos. But not a total random fray of differing notes and unrelated beats (well, some modern music fans do seem to enjoy such noise). We like to challenge our minds with musical ups and downs and jinks that still fall around some grand theme, some repeating underlying pattern. Often the music we like has two or more interacting patterns that weave together over time, with little eruptions of other short-term patterns and breaks, etc.

Well, if music (and maybe also poetry; many song lyrics qualify as poetry) is a way of “charting” something about the real world of length, height and breadth, just what is it that is being charted? Obviously, most of our music is about something much more complex than the Mandelbrot set (the most popular representation of fractalism), the coastline of Norway (which is very fractal with all its jagged inlets and sub-inlets and sub-sub-inlets), or how day-to-day patterns in stock prices aren’t much different from year-to-year patterns. Our music is usually about relationships and feelings. So, is music a way for our mind to sub-consciously examine what is “fractal” amidst the complexity of our social and emotional interactions? Can music express things that our “left brains” cannot grasp, things that are hard to express with words and concepts but are very relevant to our lives?

That’s something to think about – or better, something to hum along with, the next time a favorite tune of yours is played. Music is my biggest distraction in meditation; when I sit quietly, sometimes my mind can become a little juke box or mp3 player. But maybe that’s not a bad thing; perhaps music in the mind can be the lead-in to the “ultimate fractal sense” that deep meditation can lead to . . . on a good day, anyway!

◊   posted by Jim G @ 9:42 pm      

  1. Jim, I like this blog very much; something of the artistic, “musical” (obviously), even somehwat mystical about it. And little of the logical in this one–I mean that as a compliment. Not that the “logical” is not good, but as a steady diet it becomes (what’s the word?) stale, old hat, needs some “perking up”? A little of the artistic, intuitive, etc., is a wonderful thing.

    As to your questions: I say *Yes* music is a way for our mind to subconsciously examine the fractal in our social and emotional interactions. And *yes* it definitely does express what our left brains cannot.

    I would tend to say that music is *not* a distraction to your meditation; perhaps it’s leading you, somewhat like following the path of a labyrinth. (I deliberately contrasted the “leading” with “following” here.)

    As to any music that might be “fractal”, I’d say the jazz called “fusion” is just that–fractal. Each person plays his/her own “song” (musical composition). Sometimes they seem to clash; yet more often, amidst the “chaos”, there is a new blending that leads to a new composition.

    I think you’ve hit the nail on the head with these tho’ts in this blog. If I didn’t think that “love” is an inappropriate word here, I’d say I “loved” this blog; instead I’ll say I truly like it–very much. MCS

    Comment by Mary S. — January 5, 2012 @ 3:13 pm

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