Art as discovery and mathematics as art

There is a very large but probably finite number of possible images that the human eye can distinguish. Among these possible images, it seems that a relatively small subset is very beautiful (or has some other aesthetic quality to a high degree—I'll just stick to beauty for now). One way to see that visual artist is as a discoverer and communicator of beautiful images: in that very large finite space of possible images, she discovers a beautiful one, and then realizes it. The realization makes it possible for her to communicate her discovery to others. (Of course, the tools of discovery will often not be entirely mental—paintbrushes, texture of canvas, and the like all are tools of discovery, like a scientist's instruments or a mathematician's calculator or scrap paper.) Likewise, the musician searches the very large but probably finite number of possible sequences of sounds that the human ear can distinguish for that small minority that are very beautiful, and realizing the possible sequence communicates her discovery to others.

This model of the artist as discoverer and communicator makes the artist not that different from the pure mathematician, who also searches a large space of abstracta—say, the space of proofs or the space of theorems—for the few that exhibit some property, often an aesthetic one such as beauty (mathematicians also talk of "interest", but when the mathematics is pure, that "interest" is a kind of aesthetic quality, and for simplicity I'll stick to beauty) and then communicates these to others.

How exactly the analogy between the artist and the mathematician works out depends on whether Platonism about propositions (and similar objects) is true. The musician and painter in producing sounds and paintings do not merely represent the beauty of the possible sound or image: they make the possible sound or image actual. If such Platonism is true, then the mathematician does not realize possibilia in presenting a proof or a theorem, but only represents them. In this way, the mathematician is more like a composer or a novelist whose product is also a representation of a thing of beauty, rather than the thing of beauty itself. (Of course, the inscription of a theorem or a musical composition can be beautiful—the the quality of the calligraphy, say, but this is not mathematical or musical artistry per se.) On the other hand, if Platonism is false, then we might think of the very token inscriptions of a theorem or a proof as realizations of the possibilia that the mathematician has discovered: the mathematician searches the space of possible theorem inscriptions and finds beautiful ones.

Of course the discovery model of the artist's work isn't the only model of the artist's work. I think a creation model is more common. This model lays an emphasis on producing a thing of beauty (or other aesthetic qualities, of course). But I think that the discovery model works particularly well for a composer, who can be a great composer upon composing a beautiful work even if no one performs it.

The creation model makes the artist more like God. Is that a merit or demerit of the model?

But remember I am no philosopher of art.