Bob Cavezza's Blog

How Not To Be Wrong

Lessons in mathematical thinking

I recently started reading How Not To Be Wrong by Jordan Ellenberg. It was recommended by Bill Gates in 2016.

The book starts out by talking about mathematical thinking. They explain an example of a math problem in war. How do you most efficiently armor an airplane? Too much armor slows it down. Too little armor makes bullet holes more likely to crash the plane.

If you were presented with the following data about planes that made it home on missions during WW2, what would be your conclusion?

Section of Plane                            Bullet holes per square foot

Enginer                                        1.11

Fuselage                                        1.73

Fuel System                                 1.55

Rest of the plane                         1.8

What would your assessment of the situation be? Where do you think more armor should go?

“The armor … doesn’t go where the bullet holes are. It goes where the bullet holes aren’t: on the engines”

The reason planes were coming back with fewer hits to the engine is that planes that got hit in the engine weren’t coming back.

An analogy is “[i]f you go to the recoery room at the hospital, you’ll see a lot more people with bullet holes in their legs than people with bullet holes in their chests. But thta’s not gecause people don’t get shot on tine chest; it’s because people who get shot in the chest don’t recover” 6

This was the insight of Abraham Wald, a member of the Statistical Research Gropu (SRG) during World War II.

“Why did Wald see what the officers, who had vastly more knowledge and understanding of aerial combat, couldn’t? It comes back to his math-trained habits of thought. A mathematician is always asking, “What assumptions are you making? And are they justified? This can be annoying. But it can also be very productive.”


We started to cook a lot a few months ago. It was with the help of a BlueApron competitor called MarleySpoon. It’s awesome! We get around 5 meals every week with directions on how to make them.

The food is fantastic.

Some people think it’s expensive, but for us, the typical alternative is going out to eat – and MarleySpoon is much cheaper than that.

Music in my life

Recently, I’ve been listening to a lot of classical music. I like to listen to classical music when I drew. I drew more in the last 2 weeks than I have in my entire life. I typically listen to this 3 hour classical music youtube video.

I have a lot of music in Amazon that I’ve downloaded over the last few years. When I listen to something on Amazon and try to work, it’s usually Welcome Reality by Nero. I can listen to this album over and over and not lose concentration.

I’ve also become a huge fan of Chance the Rapper in the last year. These two songs are my favorite: Angel and No Problems.


“Whatever excites you, go do it. Whatever drains you, stop doing it” –Derek Sivers

§837 · January 23, 2017 · Daily Digest · · [Print]

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