How to Make a Math of Art


Is math relevant?

As far as the laws of mathematics refer to reality, they are uncertain, and as far as they are certain, they do not refer to reality.

-- Albert Einstein

Stand firm in your refusal to remain conscious during algebra. In real life, I assure you, there is no such thing as algebra.

-- Fran Leibowitz

Galileo said that mathematics is the language of nature "and its characters are triangles, circles, and other geometrical figures"

Mathematics ... would certainly not have come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude.

-- Friedrich Nietzsche

clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line

-- B. B. Mandelbrot

(and fractals, representative of "other geometrical figures", can describe these phenomena.)

Is art relevant?

Nature is inside art as its content, not outside as its model.

-- Northrop Frye

Art is the imposing of a pattern on experience, and our aesthetic enjoyment is the recognition of that pattern.

-- Alfred North Whitehead

Art does not reproduce the visible; rather, it makes visible.

-- Paul Klee

Art is science made clear.

-- Jean Cocteau

Can math and art combine?

Pythagoreans believed that all things have form, all things are form; and all forms can be defined by numbers.

In the final analysis, every force finds expression in number; this is called numerical expression. In art at present, this remains a rather theoretic contention, but, nevertheless, it must not be left out of consideration. We today lack the possibilities of measurement which some day, sooner or later, will be found beyond the Utopian. From this moment on, it will be possible to give every composition its numerical expression, even though this may at first hold true only of its "basic plan" and its larger complexes. The balance is chiefly a matter of patience which will accomplish the breaking down of the larger complexes into ever smaller, more subordinate groups. Only after the conquest of numerical expression will an exact theory of composition be fully realized.

-- V. Kadinsky

A new form of art redefines the boundary between 'invention' and 'discovery', as understood in the sciences and 'creativity' in the plastic arts. Can pure geometry be perceived by the 'man in the street' as beautiful? To be more specific, can a shape that is defined by a simple equation or a simple rule of construction be perceived by people other than geometers as having aesthetic value -- namely, as being at least surprisingly decorative -- or perhaps even being a work of art? When the geometric shape is a fractal, the answer is yes.... Therefore we shall argue that fractal geometry appears to have created a new category of art, next to art for art's sake and art for the sake of commerce: art for the sake of science (and of mathematics).

-- B. B. Mandelbrot

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