Fermi questions, answers, and landmarks

A Fermi question is something like, How many rolls of toilet paper do the residents of Columbus Ohio use in a week? Fermi questions are silly but embody some serious thought. Namely, how do we think about the world?

There’s some fun little math behind a Fermi question but the hardest part is often the start. For instance, how many people live in Columbus Ohio? Tim Harford knows. Rather, Tim Harford has a suggestion.

“Andrew Elliott—an entrepreneur who likes the question so much he published a book with the title Is That a Big Number?—suggests that we should all carry a few ‘landmark numbers’.”

Landmark numbers are figures we can use to guide our thoughts about the world. For instance, there are about four million Americans at any age under sixty. New York City has a population of about nine million. Columbus Ohio has a population of about one million. This is actually quite helpful just for a start.

Using a Zeckhauser maxim, “when you are having trouble getting your thinking straight, go to a simple case.” If every resident of Columbus Ohio used half a roll a week, how many rolls of toilet paper would they use? That’s easy! We have a million people, each uses half a roll, and that’s 500,000 rolls per week. No wonder we had a shortage.

Tsk tsk, Enrico Fermi would scold us. You can do better. And indeed we can. That is the point of thinking about Fermi questions. We can do better and even if we make a mistake, even if we make a few mistakes, we can still very likely be right. The reason is because of the random walk nature of our guesses. Some of our guesses will be too high (Columbus actually has 898,000 residents) and some will be too low, but overall these kinda-sorta balance out and that puts us in the right ballpark. Not only that, but making additional steps doesn’t necessarily mean additional steps in error. That, and more examples are here.

Good decision making takes nouns and verbs. We’ve got good verbs like inversion, mean reversion, extreme examples, and such. Landmark numbers give us a few nouns to work with too.

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The very good Fermi book inspired this post: Fermi Knowledge.