# Book Review: “How Not To Be Wrong: The Power of Mathematical Thinking” by Jordan Ellenberg

This is another book that a mathematician attempt to make some sense of the real world problems using mathematics. It’s supposed to answer people’s or his students’ question: when we’ll ever use this stuff? As an engineer, I have benefited a great deal with mathematics. Otherwise, my life could be very miserable and the world would be in a very different shape than it’s now. But this book is not for the light-hearted – unless you’re curious about some of the topics, this book could be overwhelming and hard to digest.

My takeaways from this book:

The missing bullet holes. The focus of the book is on the profound/simple quadrant.

I. Linearity:
when things are not linear, there’s a min/max – like the Laffer curve on a napkin.
a. Linear regression – each extra SAT point could cost you \$28 in tuition.
b. Don’t always extrapolate linearly – obesity apocalypse (100% obese).
c. Law of large number: converges to 50% for coin toss when the number of tries go up. NBA best free shot throwers play least games – small number.
d. Large number of tries dilutes the previous results – not change of probability. Very important lesson.
e. Don’t talk about % of numbers when numbers can be negative.

II. Inference:
a. The Baltimore broker: They send you the correct stock prediction by process of elimination. By keep trimming off the mailing list of their incorrect prediction, they ensure all the remaining ones get the correct prediction. From them, they’ll have the confidence of the people and send them their money.
b. Reductio Ad Unlikely: Suppose null H is true, it follows from H that certain outcome O is very improbable (< 5%), but O is actually observed. Therefore, H is very improbable. Bible coders. III. Expectation a. Massachusetts State lottery: expected value should be average value. Playing the WinFall. b. Utility: maximize the utility vs. missing the plane. Stigler's argument: “If you never miss the plane, you're spending too much time in airports.” c. Tying geometry to picking the “random” lottery number, and hamming code. IV. Regression a. Triumph of mediocrity. Scatter plot of father-son height (oval shape), b. Correlation is not transitive (e.g. blood relation). c. Berkson's fallacy: Mean-nice vs. ugly handsome curve. V. Existence a. Public opinion doesn't exist b. Bush/Gore/Nadar election: how best to elect public officials when there are more than 3 candidates. c. Condorcet Paradoxes d. How to be right. General Comments: 1. eBook or hardcopy book is probably better than the audiobook. Easier to visualize on a physical book. 2. Good history of mathematicians and some of how the theorems came about. 3. Not for the faint of heart. Some mathematics are required of interest in it.