Don’t short-circuit the queen20 August 2001
Do you share my incredulity at reports of lowered esteem in some academic circles for the rôle of the queen of sciences, mathematics, in education? Can anyone in this science-dependent age thus controvert a wisdom dating back almost to the dawn of civilisation? It was a wisdom expressed in classical Greece by, among others, the philosopher Plato. He held that ‘calculation’ should be studied by statesmen as well as traders, and that leading lights should not be ‘amateurish’ in their exercise of ‘pure thought’ for their understanding of number.
Readers who are well-versed in electric circuit theory will, during their education, have been introduced to the concept of the Riemann plane. It is said that Bernhard Riemann, the man who discovered the properties of this abstraction, exulted after he had done so. He rejoiced because he believed he had, at last, done some mathematics that was absolutely ‘pure’ and above any practical use. The story is that he was infuriated when, later, his ‘pure’ mathematical thought was proved applicable to electric circuits.
Quite another sort of character was Oliver Heaviside, famously a pioneer of circuit theory, who had an entirely different attitude to mathematics. If a method gave him demonstrably correct results, that suited him down to the ground. He did not care if the origin of the method was obscure, and he declared that it would be absurd for him to restrict himself solely to techniques that he could understand.
The purported frontier between pure and applied mathematics has been pushed about by computers but mathematics as a whole has been much affected by them. The consequent teaching problem was well put, I thought, by a UK academic in the following words.
‘Mathematics is above all things an exact subject, a discipline. It would be a complete mistake if, with a view to introducing a wider range of mathematical ideas, we reduced the extent to which the student had to carry through a precise argument, without mistakes, without uncertainties, without any but explicit assumptions. The computer, unfortunately, has not made mathematics easier; on the contrary, by doing the easy parts itself, it has made our part of the job more difficult.’ Some of my friends seem to believe that computerdom arrived not so long ago, with the American software tycoon, Bill Gates. They might be surprised to learn that the above words were spoken by the Vice-Chancellor of the UK’s Durham University, one Dr D G Christopherson, in 1962.
I’m saving some less respectful remarks about the queen for next month.
Nuclear watchdog rescues public
Once upon a time, last century, children had their feet measured radiographically in some of the world’s shoe shops. The marketing ploy was that better fittings and better health resulted. In those times, too, scrap metal used to include radioactively over-egged luminous clocks, surplus military instruments and other such discards, so that the recycled metal came out with qualities stimulating to Geiger counters.
Societies concerned for the health and safety of their members no longer allow that kind of thing. In fact they forbid it. The French authorities, for example, outlaw any presence of artificial radioactive elements in ordinary consumer goods. So when, last winter, some Hong-Kong-assembled watches were sold in France by Europe’s largest retailer, Carrefour, and found to be radioactive, official action instantly followed. All further sales were suspended, and persons who had bought the offensive goods were ‘invited’ to return them to Carrefour. The company was asked to report how many of the watches had been sold and how many had been returned, so that further invitations might be issued if necessary.
The contamination was first discovered by Electricité de France when an employee at the Tricastin nuclear plant was being checked in the customary way. EdF’s investigation traced the activity to some Co-60 in the watch-bracelet’s steel adjusting links, not the timepiece itself. The French ionising radiation regulator, OPRI, duly alerted, measured wrist dose rates of thirty to forty microsieverts an hour. Not immediately dangerous to wearers, the authority granted, but it nevertheless decreed the watches’ withdrawal.
The nuclear plant was declared entirely innocent. EdF’s employee had been contaminated entirely by the watchborne Co-60 from Hong Kong. Can you doubt that the function of detecting radiologically hazardous consumer goods will henceforward be recognised by a grateful public as just one more benefit of nuclear plants?