Tuesday, July 21, 2015

Review of the Drunkard's walk by Mlodinow: To increase your number of successes you must simply increase your number of failures

This was a great book. It had just the right balance of anecdotes, mathematics, scientific studies and history to offer the reader a comprehensive and informative, yet thoroughly enjoyable introduction to the field of randomness. As the author rightly points out, again and again, people are blind when it comes to the role that chance or randomness plays in their lives, which is in fact very big. We tend construct our life narrative around situations where we made a decision that seemed to be crucial, which makes it seem as if we have been in the driving seat for much of our life. Still, most people can come up with seemingly random events that shaped the rest of their life. For example, I would never have met my wife had I not turned down a job one summer 10 years ago and I would not have ended up as a scientist had my grades been good enough to become a psychologist. If you would change just a few minor details in my history, and I might have lived a completely different life today. 

Mlodinow begins the book by discussing some real life examples where people often fail to see the underlying mathematical truths. When a company does well, a CEO is rewarded with sometimes ridiculous bonuses, only to be fired the next year because the company suddenly did fare so well. This is the case despite the fact that fluctuations in the market are inescapable. The same is true in the world of sports where managers are frequently fired following dips in form which necessarily occurs if luck is a factor which it always is in sports.

After this introduction Mlodinow goes through the history of probability theory. I was surprised to learn that the Greek really didn’t get probability. They were excellent when it came to mathematical axioms and deducting knowledge, however, they apparently thought uncertainty had no place in maths and therefore ignored the field entirely. More than a thousand years passed before a man began to investigate the rules of probability in the mid 16th century. His name was Cardano and he was, of course, a gambler. With some very elementary knowledge regarding uncertainty, Cardano won lots of money which he used to finance his studies in Medicine.

Mlodinow continuous to move through history, while also making sure that the reader understands the theories that are being developed. Among others one encounters Galileo, Pascal, Bernoulli and Laplace who all worked on probability in different ways. One learns about the normal curve, chaos theory and bayesian statistics. Again, everything is written in an engaging yet simple fashion and I personally felt I learnt a lot even though I have studied statistics at University.

This book also deserves credit for being the first to explain the Monty Hall problem in a way that made me feel I really get it. Imagine you are a contestant on TV show, there are three doors and behind one of them is a car, while the other two doors have goats behind them. You pick one door (that you don’t open), then the TV host open one of the other two doors behind which there is a goat. At this point you have to choose to open the door you picked initially, or switch to the other door. What do you do? Even though more than 90% in polls, as well as thousands of mathematicians, passionately believed that it did not matter whether or not you switched, the correct answer is in fact that you will double your chance of winning if you switch to the other door. As Mlodinow explains you really have to guess which of the following two scenarios you are in:

1. The door you initially picked was the correct one (chance one third). If you switch you will find a goat.

2. You initially picked the wrong door (chance two thirds). Since the host will always open a door with a goat the correct one is the one the host did not open and which you did not pick. If you switch you will win.

In other words, if you picked the wrong door initially you will win if you switch and since it is more likely to pick the wrong door than the right door your chances are better if you switch.

In the last part of the book, Mlodinow return to the role that randomness plays in our life. After he has convincingly demonstrated how great this role is he arrives to the question of how one should act in the face of such uncertainty. Given that our successes or failures to a large extent are a result of random events, should we just stop trying? No! Mlodinow eventually arrives at the quote that is the title of my review. If you want to increase your success rate, you should increase your failure rate. Those who succeed in the end tend to be those who try again and again and again i.e. those who throw the dice over and over again will, eventually, end up with a six. Having read this book, I am determined to go out in the world and start failing. Thank you Mlodinow for the inspiration and for this excellent book!

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