© Copyright 1996 Mario Hilgemeier

Today the ellipse is the tool of the engineer and scientist, and fractal mathematics are becoming more widely used, for example in solid state physics (quasicrystals, spin glasses) and in control theory (chaotic). French researchers have produced aerogels, which they claim the first totally fractal material of the world (down to the molecular level). Aerogels are known for their diverse fields of application from detectors to solar architecture [6]. Let me speculate about developments in the next century. The fractal metaphor has now grown into a mental tool like the ellipse but is still in its youth (or infancy). This mental tool is already used not only by engineers [5] but by artists as well [8, 9]. Consumer products with more "artificial intelligence" than exist today will surely exhibit fractals in a variety of ways in their programs and designs. Maybe there will not even be such a thing as a consumer product, as people order directly from a factory which can produce millions of variations. If we look forward to the zeitgeist of the next century, it might be strongly influenced by the fractal metaphor that is already so applicable and useful. Many natural-scientific and artistic disciplines will re-discover what they have in common. One may be tempted to believe that a unifying theory, based on IS, will re-unite different sciences. Science will not only mean natural science, but also the science of art, social science, mental science and others. Science may even mean something like religion in the end, with some caveats described below. As the classical architecture of the Romans and Greeks liked circles and golden rectangles, as the baroque liked the ellipse, so the present likes the fractal metaphor. What will be the next metaphor? Nonlinear dynamical systems were the "blind spot" (or taboo theme) that was touched on only slightly by the grand mathematicians of previous centuries. The metaphor "chaos and fractals" also has a blind spot. I have a vague feeling that fractals are already very good, but something is missing; I'll try to speculate wildly what this may be: It may be an object of mathematical theory that has more complexity (or complexity of another kind) than fractals which is applicable to wider fields of knowledge. Maybe another measure of complexity will be found. This object once found, it may lead to a paradigm not as mechanistic as deterministic chaos, arriving at new "natural laws" (maybe a superset of quantum theory?) possibly undermining the law of cause and effect. Then predictability of another kind might become applicable (perhaps coupled to a "many worlds" theory, or predicting specific events in the far future, or backwards in time, or in light-year distance). One might call this a "new paradigm" in physics or "new metaphor" in mathematics. The art objects generated with this "new metaphor" could look or sound even nearer to life than those works of art based on fractals. The new mathematical art possibly appears more "real" and with an even better "ring of truth" than fractals already have. The new metaphor may be accessible (or constructable) without computers as we understand them today, enabling people to solve problems that are (mechanically) incomputable today. A type of computer beyond massive parallelism might evolve. The usefulness of the new metaphor is demonstrable but not (or seldom) provable by traditional mathematical tools. the above paragraph before editing Remember, we're past the event horizon - a place in spacetime about which nothing can be known now; this is just my hunch. Maybe we will see the end of that kind of natural science which is looking for natural laws and the finite "model of the world." Fractals promise that such a model may exist, if we lower our expectations for predictability. But the metaphor could carry us beyond itself to the realization that "one metaphor fits all" is just a metaphor for the human quest for understanding, trying to fit infinity into a nutshell. The voyage does not really end here. Rather, it has just begun. To see a World in a Grain of Sand, And a Heaven in a Wild Flower, Hold Infinity in the palm of your hand, And Eternity in an hour. (William Blake 1757-1827) [1]next page content page

* © Copyright 1993, Mario Hilgemeier, email:
contact
homepage
*