There has been much written about Schwitters and his relationship with the modernist/ formalist tradition and the formal qualities of the Merzbau as seen in existing photographs and the reconstruction of it in Hannover, compared to his other work with found items, his ability to use material to hand, his habit of taking an empty suitcase on his travels to fill with material for his art.
In this context, for a few days, I’ve been mulling over formal considerations of simplicity and complexity, organic compared to the rigidly geometric, minimalist tendencies opposed to expressionism and so on. Following are a few related notes on geometry:
The groundwork for Einstein’s General Theory of Relativity was done in the middle of the 19th century by Riemann with his work on non-Euclidean geometries and higher dimensions. The simplest and most directly visual representation of this was one he borrowed from his teacher Gauss. He asked us to imagine a bookworm on a crumpled piece of paper. The bookworm experiences only 2 dimensions but is prevented from moving in a straight line by the force (i.e. gravity) caused by unseen warping in the 3rd dimension. By analogy, forces in our world might be explained by warping of space in higher dimensions.
Riemann said that 6 numbers are required to describe each point in 3 dimensional space whereas 20 are required for points in 4 dimensions. In describing space numerically like this, we have to go elsewhere for qualitative differences between simple and complex surfaces.
In nature, the combination of relatively simple molecules produces a world of wonderful complexity. The geometry of the large organic molecules (i.e. those having a long hydrocarbon chain) making up this complexity is the same as that of simpler molecules: linear, trigonal planar, tetrahedral, and trigonal pyramid. When a molecule consists of many atoms, each carbon, oxygen and nitrogen atom may be the centre of one of these geometries. The molecule as a whole will be the sum of all the individual geometries to give an overall shape to the molecule.
Following the recent blog post by Duncan McAfee referring to the viral nature of infection by The Thing in John Carpenter’s 1982 film, the essential geometry of infection has 2 stages – the lock and key fit of attachment proteins when the virus attaches to the host cell, and ultimately the copying of the host cell’s DNA to make new proteins for the virus.
Crazily, it’s snowing outside, but I shall resist the temptation to mention crystalline geometry and sign off.
Shapes by David Degreef-Mounier and Phil Dobson