On maps and fractals
Anyone looking at the writernet home page for the last couple of years will have noticed a map of the UK
Geometry and play are woven together in Benoit Mandelbrot’s Fractal Geometry of Nature, now just over 25 years old.
Benoit Mandelbrot compares the length of the border between Spain and Portugal. The Portuguese atlas shows the border 20% longer than the Spanish atlas. Should Spain break off diplomatic relations with Portugal? No, The Spanish surveyors based their instruments on a larger unit of distance than the Portuguese, and therefore measured fewer squiggles on the line defining the border….
Something very interesting and wonderful happened when Mandelbrot was measuring the coastline of Britain. He was not observing nature but devising ways to use mathematics to generate things “like” nature.
To analyse the coastline of Britain (or the border between Spain and Portugal) mathematically, Mandelbrot creates a fractal line that behaves like a coastline. In other words he makes a mathematical model.
The word fractal is derived from the Latin frangere to break, to create irregular fragments…
The writernet map of the UK correlates to the division into regions and nations promulgated by the Arts Council, but it comes with a caveat drawn from analysis of the opening image of the movie Casablanca.
....A Hollywood mogul famously decreed that a movie should always open with a map.
In the map at the beginning of the film Casablanca, the map shows what is supposedly Casablanca. However, Casablanca is not that far north. The city actually shown is more like Tangier, as Casablanca, while a coastal city, is actually farther south.
Nature , as far as Mandelbrot can represent it, is radically elusive and probably monstrous and without doubt terrifying to any right-minded disciple of Euclid….
Much has been made over the past 12 months in McMaster’s Review, and James Purnell’s pronouncement during the 5 minutes he was Culture Minister, of the need to replace a culture of measurement with one of excellence.
Instead of pitting measurement against excellence I want to turn to Edward Bond’s key note speech which he gave a few years back at a symposium on Young People’s Theatre
On instrumental knowledge and imagination
Edward Bond says
“Drama tends to be put aside as entertainment or something extra and it’s never regarded as a fundamental. Up until a few hundred years ago, drama was the foundation of all education, and indeed of all culture, either in the form of stories, plays or religion, which is a form of drama. It’s only quite recently, since really the 18th century perhaps, that other forms of knowledge have become predominant. We live in two great spheres of knowledge: one is instrumental knowledge, and the other is creativity…..But it’s a very different form of knowledge, and a society, which is mainly based on instrumental knowledge, finds it difficult to cope with this other form of knowledge.
The image I want to give you is a bit more practical. It goes absolutely to the root of theatre, because the human mind is a theatrical structure and if it were not, we could not be human. A child is sitting in its high chair, and it has this little table in front of it, and there is on the edge of its table an object, and the child reaches for the object. Now we know that animals can do that. Primates, for instance, can put sticks together in order to reach bananas and all this sort of thing. The reason I use this image is because I want to argue against reduction, because drama is drama. It cannot be reduced to its biological antecedents in any way, and that’s very important. We are dealing with a specific subject. The child reaches for the object. Is it doing what an animal would do when it reaches for the object? No, it is not doing that, because the child will get the object, as an animal will, but also it will create a concept. It will create the concept of the gap between it and the object. That is unique. No animal has a concept of nothingness, of the gap. Once that concept is there, you are into the whole of human history. You’re into something entirely different. You’re into something which must be dramatised. You’re into imagination.
Imagination is a dangerous word, and we ought to try and define it. If we don’t define it and if we don’t understand how it works, then it becomes a trap for us, or it becomes a word too easy to use. Children are told ‘you’ve got too much imagination’ and the next day the child will be told ‘you have no imagination’. It’s a word we just use without really bothering to define it. If we could define it, it would become of great practical use to us.
So what is imagination? Well, imagination has been evolved, and evolution doesn’t involve anything if it doesn’t have a need for it. It appears to be exactly the opposite of reason, because reason tells me I’m in this world. Imagination seems to be able to create something called fantasy. That seems odd. It’s as if, you know, one foot pointed one way, the other foot pointed the other, and evolution doesn’t make mistakes. What is that about? Or if it does make mistakes, it wipes the mistake out very quickly. One has to say it is because of imagination that we enter history. We move from evolution to history. Imagination is absolutely necessary to anything that is self-conscious. You cannot have self-consciousness without imagination. The idea is ungraspable. This says something important, because if we are the self-conscious species, the species capable of making concepts and interrogating concepts, then imagination is vital to us. We are human not because we reason but because we have imagination, and because of that we become self-conscious….
…..But the huge problem you face is that if we live in an unjust society, cannot deal with the pathology of imagination which is the source of our humanness, then you start inventing instrumental solutions. That is precisely what Himmler meant when he said ‘I gassed the Jews out of love’. He had an instrumental solution to a problem of imagination….
…. There is no ethical text that has not been corrupted by its strongest adherents, no vestment of virtue that has not been soiled by its wearer with blood or mud – nor could there be. Drama wants to give you the question ‘why?’ and make you responsible for answering it. Oedipus is wise and the Sphinx says to Oedipus – you know the riddle: what goes on four legs in the morning, two legs at noon and three legs at dusk? – and Oedipus says ‘the human being’. And then there is a play, and the play is very strange because it produces that being which goes on five legs. Oedipus, when he finally knows who he is, goes on five legs – his own, Antigone’s and his stick. The wise sphinx gets it wrong, and only drama can create the truth….”
Thank you, have a fabulous day.