Beauty cannot be defined by abscissas and ordinates; neither are circles and ellipses created by their geometrical formulas.
Carl von Clausewitz
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And we must invent dynamic designs to go with them and express them in equally dynamic shapes: triangles, cones, spirals, ellipses, circles, etc.
Giacomo Balla
We can... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics.
Hans Reichenbach
To appreciate the nature of fractals, recall Galileo's splendid manifesto that "Philosophy is written in the language of mathematics and its characters are triangles, circles and other geometric figures, without which one wanders about in a dark labyrinth." Observe that circles, ellipses, and parabolas are very smooth shapes and that a triangle has a small number of points of irregularity. Galileo was absolutely right to assert that in science those shapes are necessary. But they have turned out not to be sufficient, "merely" because most of the world is of infinitely great roughness and complexity. However, the infinite sea of complexity includes two islands: one of Euclidean simplicity, and also a second of relative simplicity in which roughness is present, but is the same at all scales.
Benoit Mandelbrot
The creative faculty, the god-power, is not used here with anything less than literalness. When beauty was created by a godly mind, beauty existed, as surely as the paintings of Botticelli or the concerti of Vivaldi exist. When mercy was created, mercy existed. When guilt was created, guilt existed. Out of a meaningless and pointless existence, we have made meaning and purpose; but since this creative act happens only when we relax after great strain, we feel it as 'pouring into us' from elsewhere. Thus, we do not know our own godhood and we are perpetually swindled by those who assure us that it is indeed elsewhere, but they can give us access to it, for a reasonable fee. And when we as a species were ignorant enough to be duped in that way, the swindlers went one step further, invented original sin and other horrors of that sort, and made us even more 'dependent' upon them.
Robert Anton Wilson
Man believes that the world itself is filled with beauty — he forgets that it is he who has created it. He alone has bestowed beauty upon the world — alas! only a very human, an all too human, beauty.
Friedrich Nietzsche
Clausewitz, Carl von
Clavell, James
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