MathematicsMathematics is a strange area of human thought. As I child, I was crap at it. In maths class I really didn't know what on earth it was I was studying - I simply didn't know what it was. Looking back, I think that is because it is taught in an utterly bizzare way - it is taught totally as an abstraction, as if it was completely disconnected from the world - calculus, geometry, trigonometry etc are taught more or less without any context whatsoever: the working out of a piece of maths seemed to start from nowhere and end up nowhere. Even now, looking back at maths books, I haven't got a clue as to what the purpose was of much of the mathematics I learned - I now want to grab hold of a maths teacher and say, right you, I'm not a child, you explain to me what the point of that is.I am going to say something utterly subversive - mathematics is part of a way of looking at the world, but it involves assumptions that we had all better be aware of, so as to understand that it is not the only way of looking at the world - there are others. I dare say that at a higher level of mathematics there is a case for exploring maths as pure abstraction - but only if one is already aware of what the relationship between maths and the world actually is and that the point of exploration is clarification leading to a clarified understanding of the world. That's OK for people who can see the point, but the only point for school and most college student is to solve particular kinds of real problems. So any maths teacher should start off with a problem typical of the kind of problem that area of mathematics is dealing with. It took me a long time thinking about it to come up with a very simple definition of mathematics: "mathematics is a way of modelling and analysing relationships between quantities". I know that this is technically incorrect - I have been told that there are areas of mathematics which are non quantitiative - but the definition of mathematics I have just given is one which worked as a sort of seed crystal to help me understand things. The definition of maths I have just given rests on an idea of something called quantity, and this is where things get interesting. A quantity is a repeat of a quality, but a quality is a completely arbitary abstraction from the world. This goes back to the wonderful Indian story of The Blind Men and the Elephant - what you are doing when you measure a quantity is to isolate a few properties from the world - and then to create a model based on the data which correspond to those qualities. What you have found is certainly empirically true, and you can certainly make it sit up and do tricks for you - our entire industrial civilisation is based on it - but useful and fascinating as these models may be, they are only abstractions from the world - and which abstractions are found to be useful depends on social and political factors. Back to review of "The Web of Life" |
