Tag Archives: education

The Drunkard’s Walk

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We’ve been discussing more and more in my office the idea that secondary education ought to require a course in probability and statistics more urgently than a course in calculus. Yes, calculus is fascinating and elegant, a true achievement of the human mind, but unless students continue pursuing science or engineering, they probably won’t use it again. I’m a big proponent of philosophia, learning for learning’s sake, but just as basic survival comes before luxuries, so too ought basic intellectual skills to come before broader learning. And what could be more basic than critical thinking to correctly interpret, analyze, and debunk the constant stream of marketing claims, political half-truths, and plain old misinformation that are presented with the veneer of scientific and mathematical certainty?

For example, say that, absent any risk factors, you take an HIV test that comes back positive. Your doctor tells you there are 999 chances out of 1000 that you will be dead within a decade, based on the 1/1000 false positive rate. What do you do? Most people might panic. If you are Leonard Mlodinow, though, you learn from the CDC that the a priori infection rate in your cohort is 1/10000, and correctly recalculate the odds that you really are infected after the test to be 1/11. (Do you see how?) Big difference!

These are the types of anecdotes that abound in Mlodinow’s acclaimed book The Drunkard’s Walk: How Randomness Rules Our Lives. The book’s approach is narrative, focusing on the various historical figures and events that led to advances in probability and statistics, and explaining some interesting probabilistic brain teasers, such as the Monty Hall problem. The final chapter touches on the role of chance and perseverance in personal success (à la Outliers).

Mlodinow explains a few concepts, such as sample spaces and Pascal’s triangle, and talks about (but does not explain in any technical depth) others, such as combinatorics and Bayesian statistics. In this regard, I found the book a bit lacking, but I am probably not the target demographic, being mathematically savvy, having studied some of these concepts before, and going through a wannabe-amateur-statistician phase.

Where the book excels is in illustrating why an understanding of probability and statistics is so important. If it leads to more students choosing or being required to learn about these fields, it will have done its job.

Raising success

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Part of the American narrative is the story of the self-made person. Work hard, we believe, and success will follow. Some chosen few are natural geniuses and they will rise to the top effortlessly in our level, meritocratic playing field.

We know the truth is not that simple. Accidents of birth and circumstance play a large role in how a life unfolds. It is these accidental circumstances that Malcom Gladwell explores in his book Outliers: The Story of Success. His thesis is that our family, cultural, and social environments provide ever-shifting opportunities for success in a given field. These, of course, are post hoc patterns that he discerns, but his case is compelling:

  • most of the best Canadian hockey players are born in early months of the year, because they are the oldest children in the yearly selection class with a Jan. 1 cutoff;

  • many Silicon Valley titans were born in the mid-1950s, young enough to be part of the computer revolution but not old enough to miss it;

  • the perfect birth date for becoming a successful New York Jewish lawyer is 1930, because one would have belonged to a demographic trough that meant smaller class sizes, one would have had enough time excluded from the prestigious law firms to hone legal skills and grow a professional reputation in a sub-field that would become important in the 1970s, and one would have been able to observe, growing up, one’s immigrant family do meaningful work where assertiveness and extra effort were rewarded

…and so on. Natural talent and hard work matter, of course, but what is also needed are the right sets of opportunities to appear and the initiative or luck to be able to seize them.

The book would make an interesting a child-rearing manual of sorts. Not that it is particularly prescriptive, but Gladwell does identify some common traits of success: putting in enough time to become an expert in something (10,000 hours seems to be the pattern across various fields); cultivating social as well as analytic intelligence; exemplifying for one’s children meaningful work, where the reward increases in relation to the effort put forth; noting how much of the education discrepancy among social classes is due to the availability of learning opportunities in the vacation months.

I recommend this easy but thought-provoking read.