Geometry, what is it good for?


I ended my last post with the following questions:

“So what’s the point of all this fiddling about with geometry and structure? And if I’m so into that, what’s with the parts of the painting that don’t conform to any ratio, and why do some of the lines kind of follow the structure and kind of not? Why don’t I just paint the diagram, like any sensible reductionist would do?”

I have two major reasons for using geometry to structure to my compositions. The first is the simplest. As I noted before, many of the painters I consider to be my major influences were also keen on the whole geometry thing. Part of my goal as a painter is to establish continuities between my painting and the work of those who came before me, and my use of geometry is one of the ways I do that.

To expand on that a bit, I question the conventional wisdom that says painting, and more generally contemporary art, has to be, always and all the time, about disrupting continuities and repudiating the work of those who have gone before. Given that we live in a time of perpetual, ever-accelerating discontinuities, it is at least possible to argue that establishing continuities is more important than creating additional sites of rupture. There’s probably a whole other post here, but before leaving this topic I will also note that my particular current of modernism has always had both forward-looking and retrospective aspects to it. The canonical quote about Cezanne wanting to redo Poussin by way of Impressionism points in both directions, one might notice.

The other reason has to do with what I think composition is for. Why do we compose at all, rather than just painting an unstructured mess? My belief is that one of the pleasures of painting, for the viewer, is that it provides an opportunity to intuit or discover hidden orders. Note that here I am not saying that order is interesting. Too much order is generally boring, just like too much chaos is boring in a different way. What I am speculating is that humans probably have an innate fascination with the discovery of order, some more than others presumably, and that painting can provide a kind of canned experience of something that occurs naturally in other circumstances. I don’t think there’s anything particularly mystical about this myself, although the concept of “hidden orders” has often been linked to the mystical, and symbolically at least we have to take that into account. I think the ability to sense underlying order in apparent disorder is something that probably confers an evolutionary benefit and relates both to language acquisition (the discovery of order in patterns of sound) and the pleasure we get from music.

So if the pleasure of painting is the experience of intuiting order, rather than simply the presence of order, that would explain why I don’t simply paint the underlying compositional geometry, and why not all of the composition conforms rigorously to it. Composition is a dialogue between order and disorder, not the rigid imposition of order.

Finally, one other thought about why the Golden Section is so useful. As I mentioned last time, equal divisions of the surface of the canvas are considered bad form. I can think of at least two reasons: 1. because equivalent areas are obvious, and hence boring (too easy to intuit), and 2. because in representational painting you’re supposed to emphasize what your painting is about, and equivalent areas (of say, land and sky) work against that. The Golden Section works to divide the surface area of the canvas into unequal yet related areas, establishing an armature of related shapes while at the same time avoiding the pitfall of equal divisions of the canvas.


The illustrations this time are from A Manual of Decorative Composition by Henri Mayeux (1889), and show how the rule about equal divisions was applied to decorative objects.

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