3 min read

#2102: Either you use math or it uses you

My wife was pregnant with our second son when she was 37. Because of her age, her doctor recommended an ultrasound to test for Down syndrome. That was 11 years ago, but the results of those tests are burned into my brain.

Before the test, the doctor told us that (based on her age and a variety of factors), my wife's "background risk" for Down syndrome was \(\frac{1}{180}\).

After the test, her "specific risk" (based on the test results) was \(\frac{1}{41}\). That was more than a four-fold increase in the chance of Down syndrome. The tech that met with my wife said we should consider an abortion.

As prospective parents we knew next-to-nothing about Down syndrome. And the risk adjustment and the tech's recommendation felt dire. The prospect triggered weeks of stress.

But as it turned out, it was just a stupid, misleading presentation from a math-ignorant institution.

Decisions to make (with math)

We spent weeks agonizing over what to do. But the more we learned about Down syndrome, the more we moved toward our conclusion: The test didn't matter. Down syndrome was not what we had planned for, but we still wanted the child.

And then by luck, our final decision became relatively easy. Sitting and thinking about the fractional results, I wondered, "What are those probabilities as percentages?"

  • My wife's background risk was \(\frac{1}{180}\). One chance in 180 is 0.6%;
  • My wife's specific risk was \(\frac{1}{41}\). One chance in 41 is 2.4%;
  • So my son's specific risk of Down syndrome had indeed quadrupled: \(\frac{2.4}{0.6} = 4\)
  • But the chance of a healthy child had fallen by only a slim margin:
    \[\frac{179}{180}\ vs\ \frac{40}{41}\equiv99.4\%\ vs\ 97.6\%\]

A 300% increase in the chance of an unplanned outcome was also less than a 2% decrease in what we hoped for.

So I asked myself, "What if this were a game in Vegas?"

Money to make (with math)

You roll into a casino, and the pit boss tells you that they only have two games available: blackjack and a new game called Getting Down. A knowledgeable player has a 49% chance of winning at blackjack. You now know that a player has a 97.6% chance of winning at Getting Down.

Which game are you going to play?

What are the effects of math, badly presented?

The prospect of abortion* entered our minds because of an accurate-but-stupid presentation of probability. Decades of joy would have been destroyed and replaced with a lifetime of nagging doubt.

How many other families have received similar information? How many times have favorable probabilities gone unknown? And what have been the consequences?

Unfortunately, the effects of Bad Math™ aren't limited to ignorant institutions. And the consequences are much less evident because the probabilities go unstated. Every time we decide, we're using some degree of math, whether we like it or not.

Myths about math

Myth #1: Disliking math matters.
"I don't like math" is not a free pass. Math is not an ice cream flavor. It's a fact of life.

I don't like paying bills, but I still pay them. The consequence of not paying them is worse.

Myth #2: You either "get it" or you don't.
"Bad at math" is a false distinction. Everyone is bad at math. Our brains much prefer uninformed intuition than they do rational thought. Feeling bad at math isn't a will/won't characteristic. It's just a question of when and at what level.

Battling with a math concept until it's understood is like lifting weights for the brain. If someone is "bad at exercise," how can they improve? By exercising.

Myth #3: Math is only equations.
"Equations don't apply here" is often correct on the surface. An exact formula for a life situation is frequently impossible. But the math-free abstractions of mathematical concepts have huge value.

Math is like gravity.

Like gravity, math has a massive impact on our lives, goes mostly unnoticed (until something painful happens), and how we feel about it is...well...irrelevant.

"The second helpful notion mimics Galileo’s conclusion that scientific reality is often revealed only by math, as if math was the language of god. Galileo’s attitude also works well in messy practical life. Without numerical fluency, in the part of life most of us inhabit, you are like a onelegged man in an ass-kicking contest."

~ Charlie Munger, "Practical Thought about Practical Thought?", 1996

* I am not advocating one way or the other on a sensitive issue like abortion. I am only describing the choice we were (seemingly) presented with and what we were thinking at that time.