Jordan Ellenberg’s book How Not to Be Wrong: The Power of Mathematical Thinking was a pleasant part of my winter break. I don’t really care for the title, and it’s somewhat difficult for me to articulate what the book was about. Broadly, it intertwined anecdotes about mathematicians with mathematical concepts and illustrated these concepts in action with pithy vignettes about selection bias among surviving war planes, the expected value of a prior iteration of the Massachusetts lottery, and regression to the mean among the sons of tall fathers. Somehow, it was a page turner.
Non-linearity was a concept described brilliantly early in the book: “Nonlinear thinking means which way you should go depends on where you already are.” Ellenburg applies this concept to the Laffer Curve (and provides a humorous counterexample of a writer with a sharply discontinuous utility function with respect to wages who is incentivized to work more hours if tax rates go up) and a conservative polemic that America should not try to become more like Sweden (tax and redistribute more) if Sweden is trying to become more like America (tax and redistribute less) (Ellenburg implies in rebuttal that there may be an optimal amount of government intervention in the economy straddling these two points).
Shortly after finishing this book, I encountered a clear example of nonlinearity in my own life. I was buying light bulbs for my standing lamp, which is my primary light source for my apartment when the sun is down. I had the bright idea to purchase slightly less luminous bulbs than I was using previously — more environmentally efficient, I thought, and maybe better at night as I’m winding down. As it turns out, this was not correct. It’s now not quite bright enough for me to read, so I also turn on a small table lamp. The net effect: because I decreased the amount of light emitted by my standing lamp, I now use two lights; reducing the electricity consumed by one light increased my total electricity consumption. Brilliant and definitely non-linear.