This image from xkcd is entitled 'Purity or Reductionism'. Reductionism is a problem in my area of biology. It takes different forms but as a general rule it is an approach which seeks explanations for higher level phenomena at ever lower levels of organisation. What must not be forgotten, however, is that at each level there are phenomena that are unique to that level. For example, the position of the hands on a clock tells the time. Even though these hands may be connected to cogs inside the clock and cannot move without them, the position of those cogs does not tell the time as such. That only appears are the clock face.
Something I must say that I dislike very much is the way in which mathematicians are claiming that it is mathematics that lies behind everything and that it is something of a driving force of Nature. There have been a number of programmes on British television this summer advocating this view. I think that this is entirely misguided. Mathematics may provide excellent ways of depicting patterns in the natural world using equations etc. It may even, at times, be a very good predictor of what may follow from a certain set of conditions. However, mathematics describes. It is a tool. It has no independent existence outside the human mind (although I know there is some debate about this). We may live in a patterned and connected universe but that does not mean that the methods used to describe that universe also drive it or underpin it in some metaphysical way.
