How Not to Be Wrong: The Power of Mathematical Thinking – Jordan Ellenberg

Thoughts: It’s been a while since I read this, but I remember enjoying it while I was reading it. At the end of the entry on it in the notebook where I used to keep my book notes, I wrote, “In general: to do: learn more statistics, learn more math, do more math problems.” Evidently, I found it inspiring.

(The notes below are not a summary of the book, but rather raw notes - whatever I thought, at the time, might be worth remembering.)

Ellenberg, Jordan. 2014. How Not to Be Wrong: The Power of Mathematical Thinking. Penguin.

• 46: to read: “Winning Ways” by Berlecamp, John Conway and Guy
• 78: “The slogan to live by… is: don’t talk about percentages of numbers when the numbers might be negative.”
• 116: Darwin using faulty logic to argue, “‘It can hardly be supposed that a faulty theory would explain, and so satisfactory a manner as does the theory of natural selection, several large classes of facts above specified.’” “In other words: if natural selection were false, think how unlikely it would be to encounter a biological world so thoroughly consistent with its predictions!” - present Jacob: why exactly is it faulty? because he’s using the evidence that led him to propose the theory as a test/verification of the theory, à la Feynman’s anecdote about license plates?
• 170: difficulty in working with p-values: sometimes it gives us one conditional probability, Y given X, when we’re really interested in X given Y.
• 247: utils of money (or anything) - possible curves as they increase: linear (probably not)? Logarithmic? Plateaued? More complicated?
• 255: “The richer you are, the more risks you can afford to take.”
• 279: Lojban’s roots are designed to be phonetically distant from each other. ~Hamming distance; cf. Ro
• 281: possible book to read: “Symmetry and the Monster”, Mark Ronan
• 290: “see Gary Becker and Kevin Murphy’s theory of rational addiction” (!)
• 302: “That’s what causes regression to the mean: … the simple workings of heredity intermingled with chance.”
• 317: Types of isopleths: isotherms, isobars, isonephs (cloud cover), isohypses (contour lines)
• 343: “Correlation isn’t transitive.” e.g. niacin <-> HDL; HDL <-> heart attacks; but niacin <-x-> heart attacks
• 414: Poincaré’s essay, “Mathematical Creation”, re: creativity, mathematical creativity
• 419: Approval voting: each voter votes for as many candidates as they’d like.
• 429: “As the philosopher W. O. V. Quine put it, ‘To believe something is to believe that it is true; therefore the reasonable person believes each of his beliefs to be true; yet experience has taught him to expect that some of his beliefs, he knows not which, will turn out to be false. A reasonable person believes, in short, that each of his beliefs is true and that some of them are false.’”
• 431: to read?: Charles Seife, “Proofiness”
• “As F Scott Fitzgerald said, ‘The test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function.’”
• 433: “When you’re working hard on a theorem, you should try to prove it by day and disprove it by night.”
  • 434: apply this to all your beliefs – social, political, scientific, philosophical