Sunday, March 16, 2008

Math and art

Anselmo-b raised all kinds of interesting issues in his comments in response to my "Aesthetic Realism" post (March 11). Since we can't see the threads well in this blog, I'll make a new post. He said that with math, the proof might be analogous to a work of art, but the theorem itself is truly impersonal -- not in the way that I was talking about with other works of art, which way amounts, I think to the work being a perfect version of itself, as my friend Howard would say, but instead literally: the theorem, he says, would be exactly the same no matter who thought of it, or how they went about showing that it has to be so.

I don't know enough about math to be able to comment, but it's interesting and I wish I did. A question that it raises for me is: are we sure that theorem and proof are as separable in practice as they are analytically? I mean, how would we want to characterize the activity of working on a problem? Is it like doing aesthetic work in some other medium? It seems to me that it might be. But I don't know.

Anselmo, can you say more about the evil art question? I spent some time recently wondering about art that is ugly (viz., wondering if there is such a thing, and if so what makes it be art still), a question that I'd got to by wondering why raunchy writing about sex is so often bad writing, and if it's in the nature of the case that it would have to be. I decided no, that you could have ugly art, be it writing or visual. But are you asking something different? Say more. Others too.


Anonymous said...

The following theorem was once presented to me as a riddle. I was not able to solve it, I was too impatient to hear the answer and too lazy to try really hard. The theorem says:
A chessboard, from which two corners, lying on opposite sides of one of the diagonals, are missing, cannot be tiled with dominoes in such a way that each domino lies completely on the board and each square of the board is covered.
An acquaintance did look for and actually wrote a six page proof involving group theory and what not. The more dismayed he was when he was presented with the following proof which is simple, elegant and beautiful.
because all horizontally or vertically adjacent squares on a chessboard are of different colour, a domino must always cover one white and one black square. Therefore a tiling in which every domino lies completely on the board must cover an equal amount of black and white squares.
Chessboard corners lying on opposite sides of one of the diagonals are of the same colour. Therefore, a board missing a pair of such corners has two squares less of one colour. That is, such a board has an unequal amount of black and white squares. Therefore a tiling as required cannot be found.
That is nine lines against six pages, a beautiful proof understandable to the layman and requiring only reasoning immediate to the problem, against six pages of higher mathematics. The theorem is valid as soon as one valid proof is provided and it remains unchanged regardless of how many other valid proofs are added. Just for the fun of it and in order to strengthen the point I went and wrote the proof in form of a sonnet. Math is not a science, it does not deal with physical reality. It is also not an art but I just took a good step towards understanding why it is not an art, thanks to the line of thoughts your postings got me to follow.
Now, regarding the matter of evil I must admit that I am threading on thin ice, I hope others come to assist or to refute me; Maybe the jcs with their vast erudition? What I was talking about was evil artists, not really evil art. With that I mean artists whose relationship with the Good is in the best of cases dubious but who undoubtedly have created true art. Let’s say, someone like Leni Riefenstahl. What occurred to me is that maybe such artists are in the category that the last question of your post of the eleventh referred to. But as I said in my original comment, I was just throwing in ideas, hoping to learn something out of the conversation.

t-ruth said...

It's interesting. I mean, I was heading towards thinking that art just isn't a voluntaristic assertion of self, can't be -- regardless of whether or not someone experiences it as that. That if what they'd made was art, then if they experienced it as being constituted entirely by the impulses of their own subjectivity, then they would just be mistaken in their self-understanding. On that kind of ultra-realist account, art made by evil people would, qua art, be just as "objectively" structured in some sense as art made by nice people. (Though maybe the evil ones would be more likely to not realize this.) But the question that is raised, even assuming such a certainly-questionable realism, is whether or not the existence of evil artists suggests that the aesthetic and the moral don't, in fact, coincide. If you wanted to say that they do coincide, evil artists notwithstanding, you'd have to say that the site of the convergence is the work itself - and maybe the process as well - and that it is possible to pursue the Good incidentally, via the pursuit of the Beautiful (to use the Platonic language), without pursuing it in other contexts. I think that that might be what I think is so. Not sure.

I can't believe that you wrote a sonnet, just like that.

Anonymous said...

As I said initially, I have no clearly formed opinion on this and I look forward to see these thoughts of yours developing here. Right now I tend towards the view, as I think you do, that it is closer to the mark to say “0 muse, sing to me of the man” than to say “Arms, and the man I sing”, because I think there must be absolutes. But my explanation is too simple and leaves a lot of questions unanswered. How did you arrive at your opinion?
Regarding the matter of the evil artists, your last paragraph reminds me of that line of Mephistopheles’ in Goethe’s Faust “(Ich bin) Ein Teil von jener Kraft die stets das Böse will und stets das Gute schafft”/ (I am) Part of that Power which eternally wills evil and eternally works good.
I think we carry in us an expectation that Art be a part of what is Good and above human shortcomings. Why should it otherwise be, that we tend to be so distrustful of critique and secondary literature in our youths (I mean apart from the fact that it puts a finger into the wound of our vast ignorance), or that we are so disappointed to learn that the author of a work we admire does not conform to the idealized image we have formed of him or her?
And yet we sometimes are awed by the works of people we’d rather not ever meet.

I did not write a sonnet just like that, it took me hours! But I was itching to write one again and that was a fun topic to write about…

JC said...

I had a dream the other night that a sort of orthodox Jewish cult was established onthe land contiguous to mine. The members were out burning brush. I had brush to burn too, and would have liked to add my brush to theirs, though I'm not Jewish. I brought it over, but the young men themselves weren't sure. We discussed whether a non-conscious being (zombie or robot) could commit unKosher or forbidden acts.

Sort of the reverse of a theorem that anyone can think, but no one must.

In the old 1939 Encyclopedia Brittanica I have, under Art, there are two small text illustrations. One is a sort of curving penstroke; the other is a tangled squiggle. One is labeled "An Essentially Beautiful Line" and the other "An Essentially Unbeautiful Line."