Here is an excerpt from an article written by Caroline Chen for Harvard Business Review and the HBR Blog Network. To read the complete article, check out the wealth of free resources, obtain subscription information, and receive HBR email alerts, please click here.
Credit: Photo illustration by Tamara Shopsin
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Whenever I got stuck on math homework while growing up, I would go looking for my mother. Often I would find her on the living-room couch unwinding after work, catching up on the news with both the local Cantonese news station blaring on the TV and The Economist open in her lap.
“I don’t know how to do this,” I would complain, settling on the carpet by her feet.
“Read me the question.”
I would recite: “Sarah takes six hours to paint a fence, and John takes 12 hours to paint the same fence. How long will it take to paint a fence twice as long if they work together?”
She wouldn’t even look at the page.
“How many hours do you think it’ll take them?”
“I don’t know, or I wouldn’t be asking you!”
“Single digit? Tens of hours? Hundreds of hours?”
My mother was finishing her Ph.D. studies in physics when she was unexpectedly diverted into managing her family’s business, but she never lost her love for scientific methods. One of her favorite books is “Powers of Ten,” a flip book that opens with an image of the universe with speckled galaxies, then zooms in, one order of magnitude at a time, to our solar system, then the blue marble of our Earth, until we arrive at a couple lying on a picnic blanket. The book plunges on, to the ants on the grass, then smaller and smaller into the invisible world of atoms and subatomic particles. My mother’s brain worked like that book, moving up and down the ladder of powers of 10, always seeking a big-picture vantage point. She nudged me to do the same, to pull my nose out of the formula that I was copying from my textbook and assess from a distance: “Does that make sense, Caroline? Look at your answer. How could the painters spend more hours painting the fence together than if they were doing it alone?”
There’s a name for the estimation problems my mother liked to pose: “Fermi Problems,” named after the Italian physicist Enrico Fermi, who had an uncanny knack for making spot-on approximations with little actual data on hand. One of the most famous examples is: How many piano tuners are there in Chicago?
Without looking, I could guess that Chicago’s population is somewhere between one and five million people. Using 2.5 million to start, and assuming an average household has four people, we would have 625,000 households. Say one out of five households has a piano; that gets us to about 125,000 pianos. Let’s say they all get tuned once a year. Now the question is how many pianos a tuner can service annually. I’ll guess that one can tune three pianos a day. Multiply by five days a week, for 50 weeks a year, and that comes out to about 750 pianos per tuner per year. Divide the number of pianos (125,000) by 750, and we get roughly 170 tuners across Chicago. The goal here isn’t knowing the exact number but rather being able to estimate the right order of magnitude using nothing but common sense.
Here is a direct link to the complete article.
Caroline Chen is an investigative reporter covering health and science for ProPublica.