Book review: The Drunkard's Walk by Leonard Mlodinow

I was first introduced to the writing of Leonard Mlodinow when I read Euclid’s Window as an undergraduate in mathematics. It was (and still is) one of the most delightful books on maths I have ever read. So it was with great anticipation that I looked forward to the Drunkard’s Walk.

The subtitle, How Randomness Rules Our Lives, is probably a more apt description for the book, as the question of the Drunkard's Walk is not really discussed. If you are unaware of it, it relates to the probability that a drunk person, staggering around randomly will eventually return to where they started from. Given enough time, this probability tends towards 100% if they travel in two dimensions, but not if they travel in three dimensions. So if you're looking for an explanation of why, this is not the book for you.

Rather, this is about probability and statistics. The mathematics in it is not particularly technical, although there are some concepts in it that seem to go against common sense. In fact, common sense is a running theme throughout the book; but only insofar as how unreliable common sense can be (here I am distinguishing between “common” sense and “good” sense). The book takes us on a wide and varied journey through history, sports, finance, gambling and medicine, amongst other things, looking at the way in which chance events are commonly understood, how they should be understood and getting to grips with the consequences of what happens when there is a gap between the two.

It is written in a highly engaging way, with enough humanity in it to keep the lay reader interested and just enough technical detail for the more mathematically minded to stay the course. There are, however, a few small points to pick up on. Mlodinow himself is a physicist, not a statistician . This results in a couple of explanations appearing a little muddled. For example, his explanation of why the probability of two independent events both occurring should be multiplied together may not be clear to someone without any maths knowledge beyond GCSE level.

The slightly bigger issue is in his philosophical interpretation of randomness. There is very little discussion over different interpretations of randomness and of what probabilistic measures mean. The conclusion that Mlodinow seems to reach is that it applies to unpredictability. However, in various places throughout the book, he seems to get this confused with purposelessness, which leads to a few unjustified conclusions on specific matters.

That said, this is a minor distraction in an otherwise excellent book.