I first learned of the explosion on Twitter when my timeline filled up with authoritative descriptions alleging various explosive materials and photographs with red circles around some dot in the sky that the Twitter user claimed was a missile or fighter plane. Last week, I saw an important example of Fermi estimation in the wake of the horrendous explosion in Beirut. In chapter two of Range, I talk a bit about Fermi estimation, and mention that it’s one of the topics in the University of Washington course INFO 198/BIOL 106B, or, by its more popular name: “Calling Bullshit.” The instructors use a news case study to demonstrate “how Fermi estimation can cut through bullshit like a hot knife through butter.” I use Fermi estimation constantly to consider whether news articles and academic papers even make sense on their face before I bother to dive deeper some of my articles and parts of my books were born when Fermi estimation helped me realize that certain scientific papers or popular news articles made no sense and couldn’t possibly be accurate. More importantly, understanding and practicing Fermi estimation ultimately became one of the most useful tools in my cognitive garage. I don’t know anything about piano tuning, but using the Fermi strategy I could easily have realized that my 10,000 answer was nonsensical. (Future Range Report topic: confirmation bias!) I prefer to stick with 83, because New York City has about three times the population of Chicago, and 83 x 3 is 249, so that’s more favorable to my estimate. WIRED reported that the Yellow Pages lists 83 tuners in Chicago, with a few duplicates, so WIRED thinks about 60. According to WIRED, Google has used “How many piano tuners are there in Chicago?” as a question in job interviews.
Now what’s the actual answer? I don’t know exactly-I just redid that in real time with a series of guesses, as I should have the first time around-but I’m pretty sure I got the right order of magnitude. So 300,000 pianos divided by 1,200 pianos-per-tuner-per-year means we need 250 piano tuners to keep NYC in tune. How many days does a piano tuner work? There are about 260 weekdays in a year, minus a few weeks of holidays, so say 240 workdays, which would mean that one piano tuner can tune about 1,200 pianos a year.
How many pianos can one tuner service in a day? Hmmm…let’s say an hour per piano, plus transit and breaks and all that, so let’s say five per day. How often is a piano tuned? I certainly don’t know, but sounds like an annual thing, or at least in that ballpark. What portion of households do I think have a piano? Not really sure…some Upper East Siders probably have two, but let’s say one in ten overall. How many people are in the average household? Let’s say three.
How many people do I think live in New York City? About 9 million. Here’s how I should have addressed the piano tuners: The strategy entails breaking the problem down into many pieces and making estimates for each one none of the estimates has to be particularly accurate for the end result to be sensible. Part of his lesson was that a certain mental strategy is often more important for attacking a problem than is detailed prior knowledge.
The questions were examples of so-called “Fermi problems.” Enrico Fermi-who created the first nuclear reactor beneath the University of Chicago football field-often made (and asked others to make) back-of-the-envelope estimates to help approach problems. Far from ridiculous, that question and others like it led to one of the most useful lessons I have ever learned in a classroom. In retrospect, I was very wrong about the question, too. My thought process went approximately like this: No fair! WTF is this? I have no idea… 10,000? “How many piano tuners are there in New York City?” That’s the one I remember most vividly. They came completely out of nowhere, like a piano falling from the sky. At the time, I thought the questions were just ridiculous.Įvery exam contained one problem that had nothing at all to do with first-year college chemistry.