I've recently read the book How Not to Be Wrong by Jordan Ellenberg. As the author states in the introduction, it is an exposition of simple yet profound ideas in mathematics, meant for laypeople. Topics include nonlinear phenomena (in opposition to naïve linear extrapolation), probability, Bayesian reasoning, and statistical testing of hypotheses. All chapters refer to many examples in politics, economics, and everyday life to make the concepts easier for laypeople to digest.
I found the book to be fairly easy to follow. I can't say that I learned much in terms of concepts, as these are all concepts that I've come across one way or another in school, college, graduate school, or my work now, though I did appreciate the discussion of how conspiracy theorists like to add hypotheses after the fact to make a conspiracy theory harder to fully disprove, how the fact that random fluctuations in many phenomena observed over time are time-reversal invariant implies that the phenomenon of regression toward the mean is also time-reversal invariant in a probabilistic sense, and the intuitive explanations of common causes & common effects in leading to correlations between random variables that are otherwise not causally connected. Additionally, I felt like this book did a better job than the book Algorithms to Live By by Brian Christian & Tom Griffiths (which I have reviewed on this blog before [LINK]) in having some structure in the progression from one chapter to the next and in using topics from earlier chapters in later chapters even though this book, unlike that book, didn't pretend to have a unified message. My only quibbles are the claim that the impossibility of accurately running the fundamental equations describing atmospheric & oceanic dynamics for more than 2 weeks implies impossibility in forecasting through other methods (like machine learning models looking for patterns in weather effects & progression) and the fact that the chapter connecting ideas from probability, geometry, and signal processing (particularly around error correction) took me a fair bit of effort to follow (unlike the other chapters, which tells me that laypeople will likely struggle with that chapter much more). Additionally, I think readers should be aware that the author often makes reference to sports that are mostly popular in the US and to US politics and that the author at a few points espouses more liberal or progressive political views (though I think such espousal is not gratuitous but is done in a way that fits well with broader discussions of assumptions underlying mathematical, political, and legal judgments). Overall, I think the author has done a good job of fulfilling the goal of communicating these ideas to a lay audience, so I recommend this book to anyone who might be interested in these ideas.
