### Finished "The Drunkard's Walk", 3/5

Jan. 18th, 2010 03:28 pm*The Drunkard's Walk: How Randomness Rules Our Lives*by Leonard Mlodinow. I'm giving this one a 3/5. Short summary: a must read if you are not familiar with the basic ideas of probability and statistics, and still a good read if you are familiar with the math but enjoy "history of mathematics" books (and I do!).

If I had to summarize this book in one sentence, I would quote page 11, "We habitually underestimate the effects of randomness." We assume, for example, that the hugely successful must have some secret or superior knowledge or talent. However, Mlodinow shows how, for example, given two people with the same skill, one may have a string of successes that makes them look like a superstar while another just does okay. This is most clearly demonstrated in sports where it is easier to assess someone's skill level (e.g., batting average), but the concept generalizes.

Each chapter focuses on a differen mathematical concept. We get some history of the concept, amusing stories about the people involved, a high level explanation, and examples. The concepts the book introduces are

- "A and B" is always less likely than "A" or "B" alone.
- Sample spaces. If all outcomes are equally likely, you can figure out the probability of "winning" by comparing the number of outcomes considered wins with the total number of outcomes.
- If the outcomes are not all equally likely, you can still apply the idea of a sample space, but you have to weight the different outcomes.
- A large number of samples is required before what you observe can be expected to match the predicted probability.
- What you know changes what you know about the probability of an event (the gist of Bayesian reasoning without the math).
- Measurements have errors. Difference within the bounds of these errors are meaningless.
- Random variations over large populations tends to have discernible patterns (e.g., life expectancy), and there will always be some members at the extremes.
- People are really bad at telling whether or not data is random. They will perceive random data as non-random and non-random data as random.

The level of mathematical detail decreases as the book progresses, but the chapters build upon each other. Although explained in the least mathematical detail, the last two concepts are the most important. I think that understanding these concepts is required for a basic level of mathematical literacy. I think pseudoscience would do less well if we made sure that our education system achieved this level of mathematical literacy.

Actually, on that note, I think that given the importance of probabilistic and statistical literacy, we should be teaching that in high school, maybe instead of calculus. (And, of course, I am influenced by Prof Benjamin from Mudd. (Watch the talk. It's only 3 minutes!))