It’s a turn-off, I know, but I need to write something about maths. Wrestle with it. I can’t do maths but I have a probably unjustified feeling I dimly understand its broader contours. Whatever, I am drawn to it unlike other seemingly impenetrable subjects like voodoo, haute cuisine and chess.Fearful of bidding my readership goodbye let me invoke a 1960 article by the physicist Wigner called "The unreasonable effectiveness of mathematics in the natural sciences". It starts with a truism – that physics has a mathematical structure. But then comes the rather more startling point: equations decribing relationships in physics often contain pointers about the way physics may develop in the future. I find this fascinating.
Lazy people like me have often referred to maths as a language, a way of saying something precisely and rigorously. It is of course but it’s much more. There is a case for saying that the maths of physics is physics. For Wigner adds that in some cases these so-called pointers to the future are far from airy-fairy; they may be regarded as empirical (ie, susceptible to development by observation, experience and experiment).
There are many examples but the classic one is the work done by Maxwell on elementary electrical and magnetic phenomena in the mid-19th century. His equations also describe radio waves which were discovered by Hertz in 1887 a few years after Maxwell’s death. And radio waves are at the heart of the later physics we all love and are totally baffled by. Hey, doesn’t this sort of stuff leave astrology bobbling about in its wake?
Sorry about that. Regard it as an aberration.
