Fermi questions

Nobel laureate in physics and father of the "atomic age," Enrico Fermi was also a gifted guesser. Rather than tackle complex problems head-on, Fermi would break them apart into tiny, simpler chunks, then compose these chunks to get back at the whole. It's a strategy we have much to learn from.

This process is perhaps best reflected in the paradox that bears Fermi's name. At a lunch in 1950, he raised the following question to his audience: where is everybody? (The extraterrestrials, that is.) Fermi followed with a characteristic calculation that anticipated the Drake equation:

\times &\text{Prob}\,(\text{a star bearing planets}) \\ \times &\text{Prob}\,(\text{a planet bearing life}) \\ \times &\text{Prob}\,(\text{evolving intelligence}) \\ \times &\text{Prob}\,(\text{developing radios}) \\ \times &\text{Duration}\,(\text{existence}). \end{align}

Even with moderate guesses for the later parameters, the sheer number of stars led Fermi to conclude that "we ought to have been visited long ago and many times over" (Jones 1985). Hence the paradox.

Fermi understood that the more guesses he fit into his break-down, the more reliable his final answer would be. That's because as long as your errors are unbiased, they will tend to balance each other out. Guess a little too much over here, a little too much over there, and your answer will come out in the reasonable middle.1 ^dc6a5a

Thus Fermi was able to estimate the energy of a nuclear blast from the movement of a floating piece of paper and the number of piano tuners in Chicago without turning to yellow pages. He wouldn't get the exact figure, but he could expect a reasonable order-of-magnitude (power of ten) estimate.

Like the paradox, these kinds of back-of-the-envelope questions are now known as Fermi questions. It's worth learning how to solve Fermi questions. First, because you'll hone your bullshit detector for the statistics garbage floating around cyberspace and dinner tables. Next, because practice with Fermi questions weaponizes your internal store of facts (see Memorizing numbers and Memorizing units). You'll be able to construct quantitative arguments on the fly that grant your reasoning a significant credibility boost.

Now I hate to give a cop-out answer, but the best way to learn how to solve Fermi questions is to solve Fermi questions. Keep an eye out and a notepad handy. If you're desperate for more structured practice, you can check out the book, Guesstimation, by Lawrence Weinstein and John A. Adam, which has dozens of excellent examples. But, really, everyday debates should present enough opportunities for practice.

That said, one thing you can do which really will help is to memorize reference figures and statistics. So that you can collapse a few of your guesses onto certainties to make your conclusions all the more likely. Check out the Anki deck I made for learning units for a previous article.



  1. For this to work, your guesses should have similar, not-too-large error margins. This is why we can't really judge Fermi's claim of omnipresent aliens. Who knows what the chance is of a planet bearing life? Or of a species developing intelligence? Escaping the dark ages? Circumventing anti-vax-climate-change-denying-nuclear-war-hawks?