For me, life is just a series of Fermi questions.
“How big is the book publishing market in the U.S.?” my friend John asked me as we strolled through the Harvard Coop.
I remembered reading somewhere that the average American buys 5 books per year. Or maybe I made it up; either way, seems about right. Call that $100 per capita. With 300 million of us, that’s a $30 billion market.
(Actual number: $26 billion.)
“Guess how much blood a 16-week-old fetus pumps per day?” my wife quizzed me.
Well, I know an adult has 8 liters of blood. Say that it circulates once per minute. That’s 1500ish times per day. Hence, 12,000 liters per day. But a fetus is perhaps 1/10th the height, so its blood volume is 1/1000, giving us 12 liters per day. Then again, their heart-rate is twice as fast, so let’s double that to 24 liters per day.
(Actual number: 25 quarts. Basically identical.)
You might know them as “Google interview questions”; those funky estimation problems that you’d never know off the top of your head, but to which you can reason your way.
Whatever you call these exercises, I find them inordinately fun.
Since Fermi questions are so fun and useful, why aren’t they more widely taught? Why isn’t every middle school student doing one of these per week all year long?
I suspect a prosaic reason: they’re hard to grade fairly. Math education is accustomed to cut-and-dry answers. Fermi work is more like an essay, where there are many plausible answers, and reasoning trumps conclusions.
All the more reason to embrace them, I say!