It’s about 5:30 am. A man stands facing a hastily built wooden tower many miles away, grasping a handful of torn paper. As a mechanical sounding voice counts down to zero, the man begins to dribble the handmade confetti into the air. For a moment, all is deadly quiet. Then, a light many times brighter that the sun illuminates the nearby mountain ranges. The blinding white gradually transitions to deep purples and blues. The tranquility and beauty of this moment persist undisturbed for a few moments, and then a tremendous roar overtakes the man, and a wave of pure force pushes at him, dragging his clothes backward, away from the wooden tower that no longer exists. The confetti moves too, wavering from its initial descent trajectory. The man thinks for a moment. Then, satisfied, returns to the base.
That man was Enrico Fermi, preeminent atomic scientist. The event was the Trinity test, the first major test of a nuclear weapon. The strips of paper were the only measuring apparatus that Fermi wanted to use to calculate the force of the explosion. The most fascinating part of the story is that his calculation was close to accurate. Using no more sophisticated a gauge than some crudely ripped paper, Enrico Fermi figured out, within one order of magnitude, the approximate kiloton yield of an event never before seen by mankind.
So what does this mean in practical terms? Two things. One, a creative use of simple metrics can often give you insight that is less than obvious at first glance. Two, we know more than we think we know.
Fermi’s ability to gain valuable insights into events by making educated assumptions has given way to an intriguing way of thinking about things, namely, that by clearly identifying and making educated guesses about relevant variables, we can make fairly accurate observations. In the business world, that means that as long as we have a good idea about how things have behaved in the past, how much things cost, or how much time was spent on something, we can make good guesses about future behavior. That is why it is so important to build a backlog of important business data, and keep it up to date and accessible, so that these types of estimates can come naturally.
Theoretical physicists often use “Fermi Problems” to train themselves to think in this way. The classic problem asks, “How many piano tuners are there in Chicago?” Of course, it is possible to look up this data, but that’s not the point of the exercise. Rather, one approach might look like this:
1. There are approximately 5,000,000 people living in Chicago.
2. On average, there are two persons in each household in Chicago.
3. Roughly one household in twenty has a piano that is tuned regularly.
4. Pianos that are tuned regularly are tuned on average about once per year.
5. It takes a piano tuner about two hours to tune a piano, including travel time.
6. Each piano tuner works eight hours in a day, five days in a week, and 50 weeks in a year.
Therefore, by calculating:
(5,000,000 persons in Chicago) / (2 persons/household) × (1 piano/20 households) × (1 piano tuning per piano per year) = 125,000 piano tunings per year in Chicago.
(50 weeks/year)×(5 days/week)×(8 hours/day)/(2 hours to tune a piano) = 1000 piano tunings per year per piano tuner.
We can easily divide to find:
(125,000 piano tunings per year in Chicago) / (1000 piano tunings per year per piano tuner) = 125 piano tuners in Chicago, an estimate that, if the assumptions are good, will be relatively accurate.
Here are some more problems of this type:
How many dog groomers are there in New York?
How many hairs do you have on the top of your head?
How many competitors does a tech company have?
How many baths does the population of the United States collectively take in a month?
How many successful projects does it take to become a billion-dollar company?
Remember, these questions are intentionally vague and there is no one “right” answer. Rather, there are many reasonable answers based on the assumptions you make going into the question. Give one a try and share how you reached your answer in the comments below. And remember, no cheating!