In *Cyberia: Life in the Trenches of Hyperspace* (chap II) Douglas Rushkoff says about this post

Operating from Total Oblivion

The fractal is the emblem of Cyberia. Based on the principles of chaos math, it's an icon, a metaphor, a fashion statement, and a working tool all at the same time. It's at once a highly technical computer-mathematics achievement and a psychedelic vision, so even as an image it bridges the gap between these two seemingly distant, or rather "discontinuous,'' corners of Cyberia. Once these two camps are connected, the real space defined by "Cyberia'' emerges.

Fractals were discovered in the 1960s by Benoit Mandelbrot, who was searching for ways to help us cope, mathematically, with a reality that is not as smooth and predictable as our textbooks describe it. Conventional math, Mandelbrot complained, treats mountains like cones and clouds like spheres. Reality is much "rougher'' than these ideal forms. No real-world surface can accurately be described as a "plane,'' because no surface is absolutely two- dimensional. Everything has nooks and crannies; nothing is completely smooth and continuous.

Mandelbrot's fractals--equations which grant objects a fractional dimensionality--are revolutionary in that they accept the fact that reality is not a neat, ordered place. Now, inconsistencies ranging from random interference on phone lines to computer research departments filled with Grateful Deadheads all begin to make perfect sense. Mandelbrot's main insight was to recognize that chaos has an order to it. If you look at a natural coastline from an airplane, you will notice certain kinds of mile-long nooks and crannies. If you land on the beach, you will see these same shapes reflected in the rock formations, on the surface of the rocks themselves, and even in the particles making up the rocks. This self- similarity is what brings a sense of order into an otherwise randomly rough and strange terrain. Fractals are equations that model the irregular but stunningly self-similar world in which we have found ourselves. But these iscontinuous equations work differently from traditional math equations, and challenge many of our assumptions about the way our reality works. Fractals are circular equations: After you get an answer, you plug it back into the original equation again and again, countless times. This is why computers have been so helpful in working with these equations. The properties of these circular equations are stunningly different from those of traditional linear equations. The tiniest error made early on can amplify into a tremendous mistake once the equation has been "iterated'' thousands of times. Think of a wristwatch that loses one second per hour. After a few days, the watch is only a minute or so off. But after weeks or months of iterating that error, the watch will be completely incorrect. A tiny change anywhere in a fractal will lead to tremendous changes in the overall system.

The force causing the change need not be very powerful. Tremendous effects can be wrought by the gentlest of "feedbacks.''

Feedback makes that loud screeching sound whenever a microphone is brought close to its own speaker. Tiny noises are fed back and iterated through the amplification system thousands of times, amplified again and again until they are huge, annoying blasts of sound. Feedback and iteration are the principles behind the now-famous saying, "When a butterfly flaps its wings in China, it can cause a thunderstorm in New York.'' A tiny action feeds back into a giant system. When it has iterated fully, the feedback causes noticeable changes. The idea has even reached the stock market, where savvy investors look to unlikely remote feedbacks for indications of which way the entire market might move once those tiny influences are fully iterated. Without the computer, though, and its ability to iterate equations, and then to draw them as pictures on a screen, the discovery of fractals would never have been possible.

Mandelbrot was at IBM, trying to find a pattern underlying the random, intermittent noise on their telephone lines, which had been causing problems for their computer modems. The fact that the transmission glitches didn't seem to follow many real pattern would have rendered a classical mathematician defenseless. But Mandelbrot, looking at the chaotic distribution of random signals, decided to search for signs of self-similarity-- that is, like the coastline of beach, would the tiny bursts between bursts of interference look anything like the large ones? Of course they did. Inside each burst of interference were moments of clear reception. Inside each of those moments of clear reception were other bursts of interference and so on. Even more importantly, the pattern of their intermittency was similar on each level.

This same phenomenon—self -similarity--can be observed in many systems that were previously believed to be totally irregular and unexplainable, ranging from the weather and the economy to the course of human history. For example, each tiny daily fluctuation in the weather mirrors the climatic record of the history of the planet. Each major renaissance in history is itself made up of smaller renaissance events, whose locations in time mirror the overall pattern of renaissances throughout history. Every chaotic system appears to be adhering to an underlying order of self-similarity. This means that our world is entirely or interdependent than we have previously understood. What goes on inside any one person's head is reflected, in some manner, on every other level of reality. So any individual being, through feedback and iteration, has the ability to redesign reality at large. Mandelbrot had begun to map the landscape of Cyberia.

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