How Not to Be Wrong: The Power of Mathematical Thinking

I recently read this book by Jordan Ellenberg, and I wanted to briefly discuss it. My first impressions:

  • Is that really where “not” belongs in the title? (Answer: yes.)
  • This is nothing like The Grasshopper King.
  • The footnotes are fun.

Jordan introduces the book with a college student asking why math is so important. This book is an answer of sorts: It provides a bunch of simple, yet profound morsels of mathematical thinking. Actually, most of Jordan’s examples reveal how to properly think about the sort of math you might encounter in a newspaper (e.g., statistical significance that balding signifies future prostate cancer). I wonder if this book could form the basis of a “Math for the Humanities” type of class. Such a class might have more to offer the non-technical college student than calculus would. Overall, I highly recommend this book to everyone (including my mathematically disoriented wife).

I had a few thoughts while reading the book. I’m posting them here to highlight what interested me, but also to provide some book club–type comments:

I feel like the Abraham Wald story should have been posed as a riddle, e.g., “Given the data, where should the armor go?” I read the answer too quickly to figure it out on my own.

The main graph in “Less like Sweden” has the look and feel of an xkcd-esque editorial cartoon. I would love to see more of these on Jordan’s blog.

For some reason, I was expecting Jordan to illustrate how linear regression does a good job of approximating the Pythagorean theorem.

“More pie than plate” blew my mind. The main idea can be captured in a riddle: In March 2012, there were 740,000 more unemployed Americans (and 683,000 more unemployed American women) than there were in January 2009. During his campaign in April 2012, Mitt Romney stated that women account for 92.3% of all jobs lost under Obama. But is that good math?

I’m pretty sure the wrong letters are bolded in “DON YOUR BRACES ASKEW” — perhaps this is one of the errors Jordan referred to on his blog.

I really like the identification between rejecting the null hypothesis and proving by contradiction. I remember both of these concepts were difficult for some of my classmates to come to terms with (evidence of their similarity).

I had no idea about p-hacking. I also never thought about the file drawer problem. Both are negative consequences of a standardized notion of statistical significance (which I now understand to be a misnomer).

What did Albert Einstein actually think about telepathy?

How do you put numbers to a prior? I was expecting Jordan to mention Intrade.

Buffon’s needle is perhaps the most beautiful application of linearity of expectation. Jordan has good taste in proofs.

I’m impressed by how naturally Jordan introduces the projective plane, finite geometry, and error-correcting codes.

Interesting to read that a slime mold makes decisions which violate independence of irrelevant alternatives. How many experiments would it take to determine the voting scheme it uses? Reminds me of a RadioLab episode about how we make decisions.

One thought on “How Not to Be Wrong: The Power of Mathematical Thinking

  1. The misbolding in “DON YOUR BRACES ASKEW” was fixed for the second printing and should now be correct on Kindle — along with all the other typos I alluded to on the blog…

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