Monday, March 21, 2011

Make maths useful: response to Baez blog post

For a decade and more my wife complained about word processing people, and I kept telling her: you'll never get documents created as you want in a timely fashion unless you do it yourself. Programming is a bit like that too: and spreadsheet programming shows that people want to program if the environment is accessible enough. It is nice when sophisticated mathematics makes a difference. It is nice when real mathematicians can cooperate with people in other fields and use semi-sophisticated mathematics to help them. Yet I feel that the real need is for everybody to understand unsophisticated mathematics enough so that when they have a problem amenable to mathematical treatment they at least recognise that and look for help. The Internet seems a wonderful tool for educating people about mathematics, but I feel there won't be much progress until the educational authorities stop regarding mathematics as an optional skill. At any rate one of the issues seems to be that mathematicians love to generalize, but the implications of the general theorems don't percolate down. I remember an memoir by a famous mathematician (perhaps Arnold) complaining about papers published on how to solve particular types of PDE, when they were just special cases of a "well known" general theorem. Unless mathematicians are also involved in the real world, or at least the less unreal world, then they won't know how their understanding can make the difference it should.
If plants keep their leaf pores smaller, that means that particular plant types can grow in drier conditions. At the edge (if rainfall stays the same) that means more tree covered areas which is a negative feedback on CO2. In other places I presume it means that you eventually get different trees (basically because trees which are adapted to relatively dry conditions lose out to trees that don't have those adaptations where those adaptations aren't necessary). So its tricky. And isn't this typical of so much relevant stuff. You see a summary of a result and you wonder: "did they allow for this or that?". It would be interesting to develop an oracle (like Watson?) which could absorb a lot of information and answer questions like that.