Vaclav Pinkava

The so-called Chaos Theory of mathematics has entered common parlance through James Gleick's paperback popularisation of it. We have probably all seen the Mandelbrot set posters and other beautiful graphical renditions of iterative mathematical functions like x² + c = x. Fractal screensaver shareware is there to download from many sites listed here.

Without pretending to be fully au fait with the mathematics of Chaos, I feel content that I understand the implications of Chaos Theory enough to kick off my article with it.

Unlike some mathematicians of my acquaintance, I do not consider it taboo to dabble at the edges of mathematics, and draw far-reaching, illustrative conclusion. If it is all right for M C Escher, then why not?

Chaos Theory tells us that systems behave in ways which are predictable and unpredictable at different levels of granularity, simultaneously. At one level of magnification, there is order, at another, there is chaos. You can imagine this in a 'concrete poetry' metaphor, like that illustrated in Douglas Hofstadter's book Goedel, Escher, Bach, an Eternal Golden Braid. Imagine the word CHAOS, neatly printed on a T-shirt, where every letter is made up of chaotically repeating tiny letters literally out of oRder, whilst each of these is again made up of even tinier neatly arranged CHAOS words and so ad infinitum. The magnification I'm talking about need not be spatial. The alternations in orderliness and chaos relate instead to spacetime, depending say on the frequency of oscillation, on velocities, or somesuch. Tea comes out of a teapot smoothly unless you tilt too much or too little.

One of the key notions of Chaos is expressed poetically as The Butterfly Effect: A butterfly flapping its wings on one side of the planet can effect a hurricane on the other side. Yet there is no directly trackable causal relationship between the one event and the other - at least not trackable by us.

Butterfly is a funny English word, quite likely to be a spoonerism. (My brother has convinced me of it).

Spoonerisms are named after the eccentric Oxford don William Archibald Spooner(1844-1930), who got his words mixed up in a distinctive way. Some spoonerisms are genuine, like "leave Oxford by the town drain", most are coarse inventions, like "glaze your arses to the queer old dean".

As I found out rather late in life, when reading my father's homeric greek sci-fi epic Astronautilia (fortunately shadowed by his parallel Czech translation in hexameter), the Greek word psyche means not only soul, but also butterfly. Ancient Greek is a language full of strange multiple meanings. As I mentioned in my first CER article, in the beginning was the Logo.

Going further east, Kakuzo Okakura in his 1906 Book of Tea, a book of philosophical observations about Japanese values, describes a butterfly as the only kind of flower that can escape being plucked, by being able to fly. He relates other interesting notions, from taoism, zen, shinto... The essential significance of a teapot is the space it circumscribes, its potential to be filled, not the teapot itself. Its substance is in its emptiness.

According to eastern philosophy, enlightenment comes from resolving or trying to resolve opposites and paradoxes. Like order through chaos. Meaning through absurdity. Like significance through insignificance. Perhaps through trying to grasp the differences between significant insignificance and insignificant significance. As discussed elsewhere, for me, art is the pursuit of significance but only genuine pursuit of genuine Significance is genuine Art.

Talking of riddles, there is a Czech fairytale about a clever young woman from the hills, who is challenged to come to her prince's castle to get her man, dressed yet not dressed, walking yet riding, plus a few other riddles thrown in. She arrives dressed in a fishnet, her hair half done, with only one shoe. As modified by Jan Werich in his book Fimfarum, she propels herself on a push-scooter.

Maybe a similar combination of eastern philosophy and Central European sense for the bizarre inspired the slit-eyed Vaclav Klaus (I want that bit kept in, dear Editor) to come up with the inscrutable opposition agreement between the Czech Social Democrats (CSSD) and Civic Democrats (ODS). Their friendly-enemies pact resembles a chess game on a checkerboard, interdependent and interlocking, while ostensibly two different worlds. You can argue about which colour is whose, (who makes the first moves) and which colour is the foreground and which the background. In either army some types of pieces keep to their own colour, some delight in knights' moves. But it is just a formal battlefield between playfully opposing armies, where neither king ever gets taken. Czechmate? Swap sides and play again.

There you are. Some relevance to the Central Europe of today after all. Order within Chaos.

Putting this all together, I find myself wondering whether the verbal flapping of my little soul-wings in the virtual reality of the Internet can possibly have any far-reaching consequences, especially as my psyche is so fluttery. Having read this far, what do you make of it?

Suppose I installed a hidden counter to keep a tally of your 'visits' to this article. That won't tell me how long you lingered, whether you actually read anything, and if my stuff affected your thinking. But the real point is whether your thinking is affected, not whether I get to know about it. Kakuzo Okakura has affected my thinking, and so has J S Bach. They will not know. Their butterfly effect continues, in an unpredictable non-linear chaotic cascade down history, through me to you.

Did this article strike you as chaotic and unpredictable? Where is the order in it? Guess.

To provide a bridge for the above topics of Mathematics, Metamorphosis, Oxford Reverend, Absurdity, Tea, Clever young woman, Chess and Zen-like riddles I leave you with a link or two.

Let's call it - The Caterpillar effect.

Read me?

Vaclav Pinkava, 18 October 1999