After Reading "The Drunkard's Walk"

I probably came across The Drunkard's Walk - How Randomness Rules Our Lives by Leonard Mlodinow in a library book-sale. I have seen some reviews of this book in various blogs although I do not remember the reviews in detail. From taking a course on the Monte Carlo method, I had some idea on the drunkard\'s walk method of solving partial differential equations. So, the title kind of attracted me. I think it also helped that the book was placed in either a 50 cents pile or 1 dollar pile in the book sale.

When I started the book, I had a very high expectation. The first two chapters were not that exciting as they talked about basic randomness in nature and conditional probability and how these things are of mistaken by humans. I wanted to say general population but it appears that even esteemed mathematicians also feel prey to them. One interesting thing was how Greeks struggled with probability as their pure geometrical world had no place for it. Also, the very practical nature of Roman mathematics drew the Romans to understand the games of chance and probability. Also the first chapter talks about the concept of regression to the mean. This clearly explains why as a sports fan, I have a miserable time after my teams win a few games in a row.

The third chapter is where things start to get interesting. The author talks about the famous three door game show problem. Until this point, I have never really understood the problem. I have seen a movie, where the main character explains it to his math professor, but I could not make any sense out of that explanation. But, I think now I have a better idea of why you should always switch given the opportunity.

The fourth and fifth chapter deals with how various concepts around probability were being developed during european renaissance. There were some interesting factoids around probability and counting. For example, the frequency how numbers appear in consecutive sums can be utilized to detect financial frauds. Also, the author nicely pointed out that when we are talking about probability, we are actually using two quantities, one is the probability of some event to happen and also, the error margin of our prediction. Often times, the latter is left out and people can be manipulated by just looking at the first number.

The sixth chapter is where I learnt something very useful. There is a metaphor that Bayes used to explain how statistics and probability are linked. Or in other words, how to use statistics (experimental knowledge) to deduce probability of something (with in a certain error tolerance). This is very helpful, as I start learning about sampling and various statistical analysis. Chapter seven again comes back to the point that what happens if we only use probability without pointing out the tolerance in our calculation of that probability.

Chapter eight and nine are complementary. One talks about how patterns emerge from seemingly random behavior of events. The other talks about how we get fooled by patterns we assume out of a complete random event. The main takeaway is that even if the product of a random process seems predictable, the process is random and we should be careful about making any prediction.

The final chapter stresses on the idea of inherent randomness of the universe and why humans feel the desire to find patterns out of that randomness. Overall it was a good read. I had a high expectation at the beginning that dipped as I was moving through the first few chapters and then it got interesting around chapter 5. There are some nice takeaways which will be useful for my attempts at learning statistics.