The power of mathematical thinking

Today is a fresh day, a clean slate on which to create our life. Will we take the opportunity? 

I’m currently reading “How not to be wrong: The power of mathematical thinking” by University of Wisconsin-Madison mathematics professor Jordan Ellenberg.  This after reading "Being Wrong: Adventures in the Margin of Error” by journalist Kathryn Schulz which she argues that we should embrace our errors both large and small. Seemingly a posing views. Ellenberg shows that using a mathematical model of thinking sure can help counterbalance our biases, but Schulz is right, I think, in that when we are in error it is healthy to understand that this normal and in some ways heathy. We are in error about so many things both with a huge social impact and things in our everyday lives and knowing a little math can help.

Anyways, back to the power of mathematical thinking. What impacted me most in the early chapters was the notion that we are often confused by lines and curves. Things like comparing “Swedishness” with prosperity with a graph X being "Swedishness" and Y being prosperity. Should it be a line or a curve? Famously, the Cato Institute posted a blog titled “Why is Obama Trying to Make America More Like Sweden when Swedes Are Trying to Be Less Like Sweden?” This introduces the Laffer curve, an interesting curve where a value first rises in comparison with a second, then falls. Unless you know where you are on the curve you don’t know whether or not increasing or decreasing the second value will rise or lower the first. Ellenberg uses the Laffer curve to talk about our confusion around economics, taxes especially and social policy. 

The content of the middle parts of the book I didn’t find so interesting. The writing kept me engaged. The part where the student from MIT gamed the Massachusetts State lottery using math skills was either above my intellect or my complete disinterest in gambling swage me. Lots of math and I get it, they figured out that the value of a ticket was greater then the cost by enough that by buying hundreds of thousand of tickets you could win tens of thousands of dollars.

Now the book in getting real interesting. Mediocrity and regression are the topics. A lot is made of Francis Galton, scientist and first cousin to Charles Darwin and his book “Hereditary Genius” and his study of the heights of fathers and sons. Here we get introduced to scattergraphs and isopleths.

Overall a great read. Ellenberg is engaging as a writer and the ideas he presents are unique, eye opening and mind bending. Math is cool and is everywhere. This book would be a great companion to "Love and Math: The Heart of Hidden Reality" by Edward Frenkel, compelling somewhat autobiographical romance with math. One of his thesis is that if we were taught to draw like we are taught math in grade school, we’d never graduate beyond stick figures and later in life we’d hate art.