How Not To Be Wrong

How Not To Be Wrong shows you that math is really just the science of common sense and that studying a few key mathematical ideas can help you assess risks better, make the right decisions, navigate the world effortlessly and be wrong a lot less.

The most beautiful thing about math is that it allows you to determine with 100% certainty whether something is true or not. Of course, the occasions where you apply Pythagoras’s Theorem in daily life are few, but that doesn’t mean you don’t use the underlying principles of math.

Jordan thinks of math as “the science of not being wrong.” This makes solving even common problems by intuitively using logic and reason “math” problems, though you’d never call them that.

For example, in WWII, military advisors looked at all the American planes that returned from Europe, covered in bullet holes. Because the fuselage often had a lot more holes in it than the engine, they suggested better protecting that part of the plane.

However, one mathematician pointed out that those planes were only the ones that survived and returned home, suggesting that the ones who did take lots of shots to the engines were probably those that never made it back.

This is called survivorship bias, which is the mistake of focusing on only the positive results or data points, when analyzing things. It’s the same force at play when you hear about another huge startup exit, because the media always neglect the thousands of companies that fail.

Note: I recently found a great video that explains survivorship bias in even more detail, which you can watch here.

Here’s another mistake we often make: Confusing probability and risk. Because we use probability to assess how risky a bet, an investment, or an action we want to take is, we think that’s all there is to it – but it’s not. For example, if you went to play roulette at a casino, you could simply calculate the probability of winning vs. losing money in the long run by computing what’s called your expected value. On a French roulette wheel, there are 37 numbers, ranging from 0 to 36. Half are red, half are black, with the 0 being green, a neutral color, which you can’t bet on. If you bet $1 on red, you have an 18/37 chance of doubling your money (because 18 of the 37 numbers are red) and an 18/37 chance of losing that dollar. However, because there’s an extra 1/37 chance of losing your dollar (because you’ll also lose if the wheel lands on 0), your expected value becomes: 18/37 * 1 (you win) – 19/37 * 1 (you lose) = -$0.027 Knowing…