How to Solve Any Problem Using Just Common Sense

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 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?”

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?

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