The Drunkard's Walk is a fascinating book, but it is so maddening at times that I wished I had the author, Leonard Mlodinow, on the phone to elaborate on his conclusions and convince me that what he says is logically sound. As it is, I was on my own, which is unfortunate considering the great number of insightful ideas explored in the book.
The ultimate objective of The Drunkard's Walk is to bring to light the great effect that random chance (or luck) has on our everyday lives. We so often ignore or misunderstand this effect that Mlodinow's effort is vital. The issue of randomness isn't the sole domain of statisticians, physicists, and gamblers; we all have to make decisions based on our understanding of randomness and probability, and these decisions could come in life-or-death situations. Mlodinow asks us not to panic and points out that recognizing our prejudices or erroneous thinking is the first step in correcting it.
The Drunkard's Walk goes to great lengths to define these mistakes and to explain them. The biggest mistake we make comes from our overdeveloped sense of pattern recognition. Obviously, a strong sense of pattern recognition serves a strong evolutionary purpose; by learning which actions do or do not achieve a desired result, we succeed – or at least we should.
The Drunkard's Walk describes an experiment in which subjects were shown two sets of cards: red and green. Red cards show up roughly twice as often as green. The observer is then asked to predict, based on the previous sequence, what color will come up next. Most humans will try to figure out the pattern, even if there isn't one evident. Some will try to guess which is next based on the last few cards: if four reds show up in a row, then a green must be "due." Other people will act according to their understanding of probability: they'll guess red two-thirds of the time since it occurs two-thirds of the time.
The most successful strategy is to keep guessing red because regardless of the previous sequence, red will always be the most likely card to appear next. Rats, when confronted with a similar experiment, get it right more often than we do. Humans, with our amazing brainpower, are thus thwarted by an elementary tenet of probability.
There are numerous examples of this sort in the book. Humans look for patterns when there are none; we think we've cracked the system. This mistake could be made by a dedicated gambler who's convinced he's found a "loose" slot machine. It could be your Uncle Joe who swears he has a "knack" for picking hot stocks. The error could even come from a baseball fan who thinks a player with a 20-game (or 30-game) hitting streak is "hot." The fact that mere luck is an explanation — in fact the most likely explanation — for these events rarely occurs to us. We humans will stubbornly resist admitting that randomness plays any part in our successes, although we'll easily attribute a series of terrible misjudgments to "bad luck."
The chapters spent addressing these questions almost make the book worthwhile, but there are still issues. One drawback is that Mlodinow addresses not only the theories underlying probability, but the people who developed them, their lives, and the relative importance of their discoveries within their discipline. That's not necessarily a bad thing, but unless you're already fascinated by the history of scientific or mathematical theory, a short biography of the life and works of Blaise Pascal or Jakob Bernoulli isn't likely to capture your interest.
Mlodinow does a brave job of bringing these half-familiar names out of the textbooks with a lively description, but one simply cannot get past the fact that as we focus on the struggles and paradoxes faced by these famous figures, any reader without an advanced degree in the subject will be either frustrated and befuddled or utterly lost. It's not Mlodinow's fault that the work of Alan Bayes is so counterintuitive as to make one's head spin, but the author simply cannot convey in one book what would take most of us a full semester (at least) to fully comprehend.
It's frustrating enough for a layman to wrap his mind around the practical applications of Pascal's triangle. Even more vexing is being forced to accept some of the proofs presented by Mlodinow. At one point, Mlodinow brings up the following problem: a pregnant woman is giving birth to fraternal twins and she wants to know the sex of her children. "What is the probability," he asks, "given that one of the children is a girl, that both children will be girls?" In my head, I answered 50%. All things being equal, there are two possible outcomes — male or female — and barring the birth of a transgender child, it will be one or the other. Right?
Wrong. I structured the problem incorrectly, it seems. The probabilities of the sexes of the two babies are, according to Mlodinow: boy/boy, boy/girl, girl/boy and girl/girl. Given that one of the children is a girl, we can eliminate the first outcome. Therefore, the odds of the second child being a girl are 1/3, or 33%.
Has Mlodinow added an outcome? Or (more likely) am I working with an incomplete understanding of probability? I don't doubt that Mlodinow is right and I am wrong. He does have Stephen Hawking on his side. The problem is that he makes only a passing attempt to persuade me over to his point of view, and thus he utterly fails to correct my (apparent) misunderstanding.
I don't mean to harp on one facet of the book, but there were other problems presented in the book in which the "right" answer was confusing and the given explanation was insufficient. I am admittedly a layman when it comes to advanced probability, but if I cannot understand Mlodinow's reasoning, how can I recommend the book? Surely you shouldn't have to have a bachelor's degree to access The Drunkard's Walk. It's meant to be accessible, or at least "a readable crash course in randomness," according to The New York Times Book Review. That it is not is a great shame, because what the book has to say is so very relevant to all of us, especially at a time when we are met with a deluge of data in our everyday lives.
If the problems I've discussed don't bother you at all, if you completely understand the 33% answer, or if you just think I'm an isolated case (an "outlier," in stat-speak), then by all means pick up the book. Otherwise, I feel compelled to warn you that, after reading the book, it will take a few days for your brain to return to its original, upright position.