Tuesday, 4 December 2018

Seeing systems whole (and topology in Bataille's "Eroticism")

I've been giving a few seminars on the work of Stafford Beer recently. I've tended to concentrate on the work from Platform for Change, working backwards to the viable system model, and forwards to syntegration. One of the things which has really struck me is the topological coherence of Beer's thinking. If I can sum it up in a nutshell, it is simply that every whole system has "undecidables" which require a metasystem whose job it is to maintain the whole. This means that we make a mistake if we conceive of any "whole" as simply a boundary around a system (i.e. a circle). The undecidables are the hole within the whole. To put it most simply, "Every whole has a hole" (this is probably another way of expressing the Conant-Ashby theorem)

Another way of thinking about it is to see a whole as a Möbius strip. One side of the strip is the system and the other is the metasystem. The hole is (obviously) in the middle. If you flatten a Möbius strip, you get a trihexaflexagon which is also a trefoil knot. That's three arms which constrain each other: system, metasystem, environment. But maybe that's stretching things a bit.

A three-dimensional Möbius strip produces a Möbius snail. What a fascinating thing that is!

There are similar objects like "klein bottles", but in each case there is a hole in the whole.

I was looking up a book cover for Bataille's "eroticism" the other day and came across this erotic image which is used as a cover for one of his other books:

There's a strong similarity in these images, isn't there? And in fact there are holes in wholes everywhere we look... Here's one I've spent a lot of time looking at over the last year...

Is the optic nerve a hole within the whole? It certainly connects to the metasystem (the brain)...

Returning to Bataille for a second, he says something in the introduction to Eroticism which is very similar to Beer:

By seeking to present a coherent whole, I am working in contradiction to scientific method. Science studies one question by itself. It accumulates the results of specialised research. Eroticism cannot be discussed unless man too is discussed in the process. 
Bataille is in the hole in more ways than one!

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