The Drunkard's Walk

I'm rapidly becoming addicted to purchasing books in the 'Popular Science' shelves of my local bookstore. Or rather, I flick through them, make a decision, and then order online for a fraction of the price. The latest to adorn my burgeoning collection is The Drunkard's Walk by Leonard Mlodinow. Mlodinow has crafted an intriguing work on the day-to-day randomness that affects all our lives. In many respects there are similarities with the hugely popular Freakonomics, but this is a disservice to Mlodinow who's book far eclipses that of Levitt's.

All of the observations in the book have real-world implications. Mlodinow tells how he was discussing reward and punishment techniques with flight instructors when he experienced an epiphany. On of the pupils noted that when a pilot was praised for his execution of a difficult manoeuvre, he invariably performed worse next time out, whilst when he was dressed down after performing badly, the following flight saw improvements. Mlodinow has put this phenomenon down to regressing towards the mean. In essence, each pupil has an 'average' performance level, but due to the law of averages, some performances will be better than normal, and some worse. Think this through for a second – when Sir Alex Ferguson is dishing out the 'Hair Dryer' treatment after a dismal first half at Old Trafford, he is effectively wasting his time, because in the second half his team will naturally trend towards improvement without any 'interaction' from Sir Alex.

The Ask Marilyn syndicated column posed an interesting question in September 1990, later termed the Monty Hall Problem. This question regarding the correct selection of a door with a prize behind it has been much debated over the years, despite on first glance the mathematics look quite trivial. In fact, to tease out the correct result requires a combination of instinctive knowing and mathematics which is counter-intuitive. Mlodinow plots this out in such a way I experienced my own mini-epiphany and finally understood it.

The book isn't without faults – Mlodinow touches upon Benford's Law - a law that states that many real-life number sequences are distributed in non-uniform ways – this had ramifications for the Mafia in New York who unsuccessfully ran their numbers game using just such numbers! The author fails to develop this further and the reader is left dangling wondering how this law works.

But some of Mlodinow's work is staggering and absolutely jaw-dropping. In 1989 the author's doctor called him with the terrible news that there was a 999 chance out of 1000 he would be dead within a decade because he had had a blood test that returned a diagnosis of HIV+. However Mlodinow wasn't prepared to blithely accept his fate – he turned to statistics! He figured that in his demographic – white, middle class, non-drug user, faithful marriage, there would be a sample size of about 10,000 who would have had a blood test sample analysed. The false positive rate is known to be 1 in a 1000 (i.e. for every 1000 positive tests, one will not have the virus despite being notified otherwise). That means there would be 10 false positives in his sample size. So the doctor should have said, “Don't worry – there's an 11 in 10 chance your test was incorrect!”.

My old friend, the Victorian statistician Francis Galton who cropped up in my expose of Derren Brown's Lottery scam is awarded his own chapter. Galton was instrumental in the capturing of measurements such as the size of heads, noses and limbs, and even recorded the attractiveness of ladies in different cities. Much of his work has been discredited – he led the way in the field of eugenics – the selective breading of humans, later to be adopted by the Nazis. However, his measurements were useful and he proved that they fell within a normal distribution bell curve. His observations noted that abnormally tall parents do not necessarily always produce tall children, and parents of unequal heights often produce offspring tending towards the middle of the distribution curve.

The title of the book applies to the apparent random movement of particles when bombarded by molecules. The movement is caused by more molecules on one side of the particle nudging the particle forward until molecules on the other side prevail causing an oscillation effect. Remarkably, this can be applied to catastrophic accidents such as train and aircraft crashes. In such circumstances, it is rare that one dominating factor causes the wreck. Usually, it is numerous very small errors of judgement working in concert which when combined will produce the catastrophe. The issue here of course is these errors are very difficult to eliminate from life, rendering the chance of catastrophes fiendishly difficult to totally eliminate, whilst at the same time reducing the actual likelihood of it happening to practically, yet not absolutely, zero.