Saturday, 3 January 2015

'Luck' is Ignorance

A new paper in 'Science' suggests that differences in stem-cell division rates strongly influence differences in cancer rates in different types of tissue. Due to some perhaps-unfortunate wording in the paper's abstract, news organisations have been reporting that two-thirds of cancer is explained by 'bad luck'. The paper almost certainly does not suggest this conclusion. But the question of whether 'luck' can be an explanation of any kind at all is an interesting one.

A naive, but pervasive, misconstrual of probabilities is that they measure some quantity in the world - as though the probability of a '6' on a six-sided die - one-in-six - is some feature of the die itself that we can measure.  This view has been largely supplanted by the Bayesian interpretation of probability - a far more powerful set of concepts - in which 'probability' is a measure of the information available to, or alternatively the ignorance of, the observer.

Dr Arbuthnot

The extraordinary John Arbuthnot, forward-thinking as ever, summed this insight as early as 1692: "It is impossible for a Die, with such determin'd force and direction, not to fall on such determin'd side, only I don't know the force and direction which makes it fall on such determin'd side, and therefore I call it Chance, which is nothing but the want of art."

In The Imaginary Invalid, Molière pokes fun at some attendant doctors who seek to explain opium's sleep-inducing properties by citing its 'vertus dormitiva'.  'Vertus dormitiva' simply means 'sleep-inducing quality', so the doctors are really saying 'opium makes you sleepy because of its sleep-inducing quality'.  It looks like an explanation, but it isn't.

It's the same with the ascription of events to 'luck' or 'chance'.  To say something happened 'by chance' is merely to say that it was caused by things of which we are ignorant, or in other words, 'because reasons'.

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