ART MATRIX PO 880 Ithaca, NY 14851-0880 USA (607) 277-0959, Fax (607) 277-8913 'The Paths of Lovers Cross in the Line of Duty.' THE BEAUTY PRINCIPLE Copyright (C) 1990 by Homer Wilson Smith All rights reserved. 'This love affair with fractals is disturbing to mathematicians like myself who see too many people believing that this stuff is serious mathematics. Fractal geometry has not solved any problems. It is not even clear that it has created any new ones.' Steven Krantz, Research News, 27 July 1990. The Beauty Principle states that if a theory or idea is beautiful chances are it is useful. It also says in reverse that if something is useful, chances are beauty will be found in it. Beauty is surely in the eye of the beholder, and as such, beauty is surely connected to the fundamental nature of that beholder. Life consists basically of survival, of winning, of besting the elements, even of dying in such a way as to live better as a species. Thus the deer is beautiful because it can run, and the tiger is beautiful because it can chase. Those that could not run and those that could not chase long ago passed away, and what is left are those that won the game of survival. As for dying, grass is edible because manure helps it grow. Being eaten (dying) helps grass grow better. Thus the deliciousness of grass is not an evolutionary failure of grass to out survive its enemies. If grass had wanted to be poisonous it could have done so, easily. The tasty stuff survived better BECAUSE it was tasty. Get it? Everything in nature, with few exceptions, whose form has been molded by success in its own element, has beauty in it for the eye of the human beholder. From the wing of the bird hovering in the halcyon winds of summer, to the flight of the Challenger as it lands on the run way, there is beauty in the form BECAUSE THE FORM WORKS, form that has been developed over millions of years of evolution when all the non working ones were left behind as rubble and dust in the wind. That the form of a bird's wing could be turned into the wing of an aeroplane, does not diminish the wisdom contained therein, and the beauty that results either in the wing or the plane, is directly proportional to its rightness in the game of survival in a given environment. The human body itself (although maybe not the conscious unit within) is also built on the same principles, and its internal structure, from its bones to its brain, it based on the simple mathematics of survival that everything in this physical universe is. It is not unreasonable to assume that when the body is placed near or in communication with another entity built on similar principles also having withstood the tests of time, that a certain resonance would take place resulting in an awareness of the beauty, functionality and inherent rightness in the design of the other thing. It is also reasonable to assume that such a human body, put into direct communication with the basic mathematics of its own internal structure, would elicit a similar reaction of aesthetic appreciation. Being able to appreciate the wing of a bird, or your own body is no different, each is the workmanship of ages of survival, and one would assume that, given enough intelligence, each would be able to appreciate the ideas and mathematics and design principles that went into each other and their present state of success with existence. In other words for those to whom survival is beautiful, one would expect them to find their own design principles beautiful too. Thus one imagines a direct harmonic resonance between the human central nervous system and fractal images. The communication line between the two could not get more direct, as the optic nerve and the brain are MADE of the very mathematics that are displayed in the fractal image. If you like fractals, it is because you are made of them. If you can't stand fractals, its because you can't stand yourself. It happens. This is not a matter of some artistic, philosophical or religious mumbo jumbo. We are talking physics at the level of tuning forks on a sounding board. Absolutely ground level. Such a statement will surely be held against me all the rest of my days, but it will be well worth it as our future history books will record who was the fool and who wasn't. If it IS true that fractal mathematics has produced no new problems or solutions it is only because the people who work with fractals are as yet too dense to figure them out, which is very too bad, because much of world is still out of control and there is a crying need for increased understanding, especially in the field of how things do and do not survive in their environments. It is unlikely that the underlying mathematics of this universe is utterly complex in nature. In fact one finds the simplest non linear equations abounding in everything you study in classical physics, such as planetary motion. Fractals are not something special, anymore than the parabola is something special. The parabola is a visual representation of the EVALUATION of the simplest non linear equation Y = X*X + C, and the Mandelbrot Set is a visual representation of the ITERATION (repeated evaluation) of the SAME SIMPLEST POSSIBLE non linear equation. It is also unlikely that iteration is any less important than simple evaluation, especially for systems that are a function of themselves a moment before plus their environment, and so it is unlikely that the Mandelbrot Set is any less important than the parabola. And to claim that the parabola is unimportant would be unwise at this time. Homer