Writing grants and teaching, not to mention trying to get some actual research done, has taken up a considerable amount of my time this quarter. I mean, sheesh, I’ve barely had any time to read! This has, of course, made me grumpy. So when the publisher of The Drunkard’s Walk: How Randomness Rules Our Lives by Leonard Mlodinow offered me a review copy of the book, I was very happy. I mean, I love probability and I love, um, well….you know ?
First of all, let me say that Mlodinow’s book is preaching to the converted! A large portion of his book is devoted to showing how randomness is ubiquitous yet unrecognized and how we totally flub up understanding the role of randomness which surrounds us. Ah, these are good friends of mine! I believe both that randomness plays a greatly under appreciated role in our lives and that we humans are absolutely horrible at understanding the basics of probability (okay I’ll admit, having taught probability, that even I have to scratch my head more thinking about probability, than say, doing a classical mechanics problem. Our brain is probably wired to incorrectly deal with probabilities due to some predator chasing us up a tree. Why mine seems to be better at classical mechanics is surely, then, a mystery.) Mlodinow’s book is very well written, and passed the “didn’t irritate me” hurdle I commonly encounter when reading popular science. Its full of lots of good stories about probabilities and even made me dream about probability while I was falling asleep reading the book. The Uncertain Chad expresses similar sentiments.
Now back to that first effect, that randomness is under appreciated. This is one of the reasons I have a hard time reading the type of blog article that says “how to succeed at problem X!” where X can be “getting into grad school,” “landing a job in academia,” “getting tenure,” or any of the other many minutia that seem to waste large chunks of the academy’s collective neuron trust. Sure such advice is usually good advice, but it amazes me how little those who have succeeding in, say, landing a faculty position fail to realize that it might be possible that they got there by some amount of chance. And these said offending blog articles are full of the type of recipedic (ooh, new word!) advice which completely and totally ignores the possibility that chance might be involved.
Okay, so I know: that’s blasphemy! Of course all faculty members (they of the ivory cars and ivory teeth and ivory thoughts) got their jobs because of all their hard work and dedication and sheer brilliance. And even if there was some randomness involved, those other factors surely overwhelm chance, right? Well its exactly that last statement which I find so fascinating: actually what is occurring, I think, is much like what happens in the game of tennis.
Which brings me to one of the topics about probability, not discussed by Mlodinow in his book, but which struck me at an early age through reading Game, Set and Math: Enigmas and Conundrums by Ian Stewart. Suppose there are two tennis players who each have a fixed probability of winning a rally when they serve. For instance, suppose that player one, call him Dr. Bacon, wins on serve fourty percent of the time. Suppose that the second player, call him Dr. Stuffyfacultymember, wins on serve fifty percent of the time. What do you think the probability is that Dr. Bacon wins a match of three out of five sets? The answer, it turns out is about 4.9 percent. With such close probabilities of each player winning on their serve, the game of Tennis is structured in such a way that this translates into a lopsided probability of one player winning because repeated successes are necessary to win games, repeated games are needed to win sets, and repeated sets are needed to win a match. Ever since I saw this result growing up I remember being wary of those who’ve succeeded in games that aren’t one-up events. While they may think that they are vastly superior to their competitive peers, in reality they need only be slightly better to show vastly different amounts of success.
Of course this doesn’t invalidate the advice that is given: if small differences in upping your probability of succeeding at repeated trialled events can lead to long term wins, then you should definitely follow the advice. But, just remember, the advice givers are drunken tennis players whose delusions of prowess may just be an illusion of some basic probability.