Numbers

WHEN does informed guesswork on the stock exchange turn into insider dealing? When does rubbing a cricket ball with dirty hands become cheating? Eubulides of Miletus, 4th-century philosopher, knew little of takeovers or reverse swing, but his thoughts on baldness and piles of stones may be relevant.

If you remove one hair from the head of a man who is obviously not bald, Eubulides argued, he will still be obviously not bald. So you may remove another hair. It follows, by the principle of mathematical induction, that you may remove any number of hairs without making him bald. If you have a number of stones too small to make a pile, adding one single stone cannot be sufficient to cross the boundary into pileness. The inductive arguments seem to show that no man can go bald and no amount of stones can be a pile.

The paradox of Eubulides is known as sorites, or the slippery slope fallacy, and is caused by misapplying the logic of mathematical induction to a continuum which has no identifiable demarcation point between opposite poles, such as bald and non-bald, cheat and non-cheat. Similar illogic bedevils the debate on abortion concerning the turning point between life and non-life.

Supporters of Michael Atherton may slide easily from sweaty fingers to dirty pockets while his detractors glide just as convincingly from gouging balls with bottle tops to rubbing them with earth- soiled fingers. In either case, their logic is fundamentally flawed: there can be no mathematical exactitude.