Thursday, November 20, 2014

The Drunkard’s Walk

Book Review : The Drunkard’s Walk
Author : Leonard Mlodinow
My Rating : 5 out of 5 stars

The complete title of the book is “The Drunkard's Walk: How Randomness Rules Our Lives”.

It’s almost a cliche to say that, we as a society are not quite good at math. But what parts of math? How does it matter if on an average we don’t really understand calculus? I say, it doesn’t matter much. I think what does matter is, we are particularly inept at handling probability, or evaluating uncertainty. The success of many lottery systems worldwide is a good indication of that. I would even argue that the entire city of Las Vegas is built upon our inability to handle probabilities correctly.

The need to handle uncertainty goes beyond gambling and betting. Author Leonard Mlodinow shows how it’s part of our everyday life. Probability assessments happen in legal arguments, medical evaluation, large scale data analysis and so on.

He gives numerous examples of how we get it wrong. Ask yourself. What is more probable? A person being vegetarian, or a person being vegetarian for ethical reasons? This example is innocuous. Other examples, alas, are not so. What is more likely? A defendant fleeing the scene of crime, or a defendant fleeing the scene of crime because of fear of being accused? Most people say second is more probable, not realizing that it is a subset of first.

He uses such examples, to explain the subtleties involved, and also to build the story of how the study of Probability became a formal branch of mathematics. As you can expect, the initial reasons were indeed related to winning at gambling. Probability is closely related to Combinatorics. Instead of using mathematical terms like factorials, he tells us the story of Pascal who came with the ‘Pascal’s Triangle’ to help with calculations.

Interesting - as in simple but subtle - examples are numerous and present throughout the book. Consider my favorite. In a family of 2 children, what is the probability that both children are girls? Yes, it’s 1 out of 4. Let’s change the question slightly. In a family of 2 children, what is the probability that both children are girls, if one of them is known to be a girl? Or this. In a family of 2 children, what is the probability that both children are girls, if one of them is known to be a girl with name Florida. Read the book to understand how such conditional probabilities are calculated.

It’s not just for solving puzzles. The author mentions a terrifying personal experience, when his blood test gave a false positive for HIV. The doctor incorrectly concluded that his chance of dying soon is 999 out of 1000. Author mentions that similar erroneous conclusions happen in many forms of testing, including doping tests for athletes. Even more seriously, such wrong logic was used to convict a British woman of murdering her own children, in 1999. Astonishingly a similar mistake had also happened in the all American trial of OJ Simpson. Mishandling probabilities can have serious consequences.

Probability is also closely related to Statistics, and Statistics is closely related to Economics and Finance. This is about large scale data analysis. How do we determine how closely the data reflects the actual probability? How do we infer probability from a series of measurements? Topics such as the Gaussian curve and standard deviation, are wonderfully explained without getting overly mathematical.

In later chapters, there is some philosophical discussion on the role of chance in our life. Similar to luck versus abilities debate. I didn’t think the author handled these intractable problems well. These discussion are way too big and subjective for a book like this. That’s not a major complaint though.

I absolutely recommend this book. The real life examples, as well as topical puzzles are interesting. The writing is smooth and funny. This is the second book by the same author that I have reviewed, the first one being Euclid’s Window. The real strength of both the books, is how lucidly Leonard Mlodinow explains the complex mathematical concepts. It’s a real feat. This book, just like the previous, is immensely accessible, and will leave you educated and entertained.
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