Excerpt from: Molnar, François. "The Unit and The Whole: Fundamental Problem of the Plastic Arts. In Module, Proportion, Symmetry, Rhythm. Vision and Value series. Gyorgy Kepes, ed. New York: George Braziller, 1966.
The Golden Number is a geometrical progression whose formula is: a+b/a = a/b and after a slight mathematical manipulation, we get the formula: À = 1 +/-æÌ5/2. [NOTE: View source for the transcription of the formula] [p. 206] This mathematical formula has a number of remarkable aspects. But it is far from being the only interesting formula: mathematics is very rich in curious formulas that play an important role in science.
From our point of view, however, it is immaterial whether the basis of the composition of a work of art is the Golden Number or some other numerical relationship, some other "harmonic series." The mathematical beauty of a work of art is not perceptible immediately but only after long reflection, and furthermore, without mathematical knowledge it is not perceptible at all. Not even a mathematician's head contains any built-in ruler or scale or calculating machine to perform the requisite operations fast enough. One's aesthetic pleasure fades during that brief lapse of time the psychologists call "the density of the present." What goes on in our head in that fraction of a second, we scarcely know. It is hard enough to imagine that we can manage a not very complicated calculation, when we know that the time needed for simple operation is more than the density of the present, and this even for a man highly trained in mental calculations.
No matter how many rational or irrational properties there are in a pentagon, it is not beautiful because of that. If it is beautiful, the reason for its beauty must be sought elsewhere. Of course, mathematics too has its beauty but we have to traverse a long road of reflection before we perceive it. We have to "understand" mathematics, in the strictest sense of the word. At the end of the road that we travel to understand it, we can find true joy, true feelings, that belong in aesthetic categories such as "superb," "monumental," "marvelous," etc. On the other hand, the beauty of a work of art must reveal itself, it ought immediately to impart itself, as we have said above. This, of course, does not mean that the beauty of a work of art cannot remain hidden as long as desired under certain conditions--longer, perhaps, than the sense of mathematics to a mathematician. Indeed, mathematics explains itself, conveys itself. The work of art, on the other hand, cannot be explained. Its beauty may or may not reveal itself, but it does not explain itself. It is possible to help someone become permeable to this beauty, but we certainly cannot explain it to him, for there is nothing to explain. [p. 207]
[Merriam-Webster's Collegiate Dictionary, 10th Edition. Springfield, MA, USA: Merriam-Webster, Inc. 1995.]
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