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There is an ambiguity in the relation between science and the arts. They have, in one obvious sense, an intimate connection. Both are fields dedicated to an incisive pursuit of truth, fields of deep inquiry to which traditionally genius flocks, to which the most high-temperature intellects over the centuries devote their energies. But even so, they are also disposed in diametric opposition. The truths they tell are not merely different—their truths have proved to be essentially incompatible. Increasingly, art and science are tending to negate each other.Mathematics stands at the intersection of the two fields. It bears its own intimate relationship to each. The pertinence of math to art is long standing and well understood. Math is the foundation of harmonics in music, it regulates compositional strategies in visual art, most evidently in perspective rendering, it is the measure of meter in poetry. By the same token, mathematics is the heart of the scientific enterprise. Hard science is not just expressed but conceived in the formulations of mathematics, to such an extent that when science is at its most ambitious, when it is at its purest, math is the only form of conception and expression available to it—verbal phrasing becomes unavailing.And that speaks to the core of the opposition between their aspirations for truth telling. Art is dedicated to human experience. The intimate details of human experience, and the precise qualities of sensory and subjective experience, are its raw materials. Art is about the human condition—the examination of the qualities of being human is very nearly its defining characteristic. However, increasingly, over the last several centuries science has departed from the intimacies of how human beings directly experience the world. After a series of what Freud called "Copernican Revolutions", not only has the status of the human species been reduced from the assumption that we are the crown of creation to the recognition that we are an inconceivably minor event occurring on an unremarkable planet in a merely typical galaxy, but—far more significant—the truth of the physical universe has proved to be something unavailable to the human senses and incomprehensible to human thought in any manner other than through mathematical formalisms. We are capable of experiencing through our senses at best 4% of what exists, leaving aside the equally evident fact that over the course of the history of our species, we will directly encounter nearly none of even that small portion. Science has shown that the truth of things is unvisualizable and conceivable only in equations. It cannot be seen, not even by the mind's eye. And so the intimate specifics of direct personal experience, the very material of art, is, to the search for the truth of things, irrelevant.Early in the twentieth century, the artists of Modernism, and most particularly the visual artists, confronted the problem by adopting geometric composition in place of observations from nature—in place of the direct personal, sensory experience. But the challenge they began to face remains: if art has no choice but to reflect the truth as science is discovering it, in what sense is art still needed, what can it contribute, and in what sense is it still, recognizably, art? How can art wrestle with our new knowledge of a world that is fundamentally unlike what we understand ourselves to be, and do so in a form that remains legitimately artistic, that reflects the art of our heritage and relates it to the demands of our time?

DOI: 10.1007/978-3-319-57259-8_2

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