Abstract in the sense that one is doing something complex which has little or nothing to do with human affairs, although I suppose a cognoscenti might talk about a fold being aggressive or sentimental.
On the other hand, the sort of foldings you get when you casually drape a piece of soft cloth over, for example, a part of a body or a piece of furnture, are a strange mixture of the random and the organised.
At first glance, it is all very random. The cloth just seems to have been chucked down. Then, looking more carefully, you start to see how the geometry of the support has influenced that of the cloth. But still with a large random component.
And this morning I started to think how the detailed folding of cloth was not random at all. A cloth can be thought of as a two dimensional sheet, a sheet which can bend but not stretch. And I dare say bending which is parallel to one of the two axes of the weave - we assume a woven cloth - is easier than other sorts of bend. I dare say also that a bend likes to be one dimensional, one usually bends something around a straight edge. Some materials will not bend around anything else. All this can, I imagine, be turned into a set of equations which can be solved.
Chuck the cloth over the chair and there will be one or more solutions to the equations. There may be lots of solutions, perhaps obtained by permuting the set of local solutions. It may be that the solution at the right big toe is largely independent of that at the left knee. But not completely; the flapping of the butterfly's wings at the big toe might propagate through to a tornado at the left knee. That said, my belief is that, for practical purposes, there is some randomness going on here. There is room for the axiom of choice.
So perhaps what the artist is doing when he paints the result, is expressing one solution to those equations, bringing them closer to the surface. And it may be that his choice of solution does have some connection with his personality, history or state of mind on the day. This being the expressionism part of the phrase of the title of this post. In a successful painting of cloth, we will, at some level, understand how those equations have been solved. The painter might, in order to achieve this, simplify things a bit, not attempt to express all the detail, to keep the result within the bounds of what the viewed can comfortably take in at one sitting.
I wonder if there is anyone out there who is seriously into the computer modelling of all this?
With thanks to Cortana and Bing (see reference 1), whom I now use from time to time to see how Microsoft compares with Google, for the image included above. They offered a similar, but slightly better choice than Google on this occasion, including this rather fuzzy reproduction of a drawing by Leonardo da Vinci. There was a better one, but it was rather small for present purposes.
PS 1: I leave translating these musings to the Goldberg Variations as an exercise for the reader.
PS 2: with thanks to Aldous Huxley for prompting my interest in all this in his book 'The Doors of Perception'.
PS 3: Bing failed to come up with the goods, with the computer models. There were programs which worry about how to cut clothes out of sheets of material with the minimum of waste, programs to help robots to fold things, programs which knew about the folding of complex chemicals and programs which knew about how sheets of cells grow in growing animals. Or how the cerebral cortex folds as it grows. But nothing which quite hit the required spot.
Reference 1: http://www.psmv2.blogspot.co.uk/2015/09/more-windows-10.html.
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