How To Solve Any Problem Using Just Common Sense

Whenever I got stuck on math homework growing up, I would go get my mom. Often times I would find her on the living room couch relaxing...


Whenever I got stuck on math homework growing up, I would go get my mom. Often times I would find her on the living room couch relaxing after work, catching up with the news with both the local Cantonese news station screaming on TV and The Economist open in her lap.

“I don’t know how to do that,” I complained, settling on the carpet at his 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 will take them?” “

“I don’t know, otherwise I wouldn’t ask you!” “

“One digit? Dozens of hours? Hundreds of hours?

“Mom…”

My mother was finishing her doctorate. studying physics when she was unexpectedly diverted into running her family’s affairs, but she never lost her love for scientific methods. One of his 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, on our solar system, then the blue marble of our Earth, until arriving at a couple lying on a picnic blanket. The book dives right down to the ants on the grass, then smaller and smaller into the invisible world of atoms and subatomic particles. My mother’s brain functioned like this book, moving up and down the scale of powers of ten, always seeking a holistic perspective. She urged me to do the same, to pull my nose out of the formula I was copying from my textbook and to assess from a distance: “Does that make sense, Caroline?” Look at your response. How could painters spend more hours painting the fence together than if they were doing it alone? “

If we put in all the pasta we eat throughout a year, what percentage of the earth’s circumference would it take?

There is a name for the estimation problems my mother liked to ask: Fermi Problems, named after the Italian physicist Enrico Fermi, who had a strange knack for making precise approximations with little real data in hand. One of the best-known examples is: How many piano tuners are there in Chicago?

Without looking, I could guess that Chicago’s population is between one and five million people. Using 2.5 million initially, and assuming an average household has four people, we would have 625,000 households. Suppose that one in five households owns a piano; that brings us to about 125,000 pianos. Let’s say they are all settled once a year. Now the question is how many pianos a tuner can maintain each year. I guess you can tune three pianos a day. Multiply by five days a week, for 50 weeks a year, and that’s about 750 pianos per tuner per year. Divide the number of pianos (125,000) by 750, and we have about 170 tuners across Chicago. The goal here is not to know the exact number but rather to be able to estimate the correct order of magnitude using only common sense.

When I was young, I was irritated by my mother’s questions, more concerned with doing my homework so that I could play. But now that I don’t have any issues to deal with, I’ve found myself revisiting these issues as a way to entertain myself, the more absurd the better.

During a dinner with my husband, I asked: if we put all the pasta we eat throughout a year, what percentage of the circumference of the earth would it take? Lying together in bed: how many penguins do you think there would be in our room? As our cat jumps on my breastbone, waking me up before I wake up: what do you think is Polo’s volume in cubic inches?

It is only after making our best estimates that we turn to our phones for the internet answer. In fact, Google is generally not very helpful. “How many square feet does a penguin occupy?” »Gives no satisfactory answer. Reddit, typically ironically, suggests that the best way to calculate a cat’s volume is to stun the poor animal and throw it in a tub of water, then measure the amount of water displaced. In the midst of a lot of laughter, however, we still learn some funny things. Now I know the smallest penguin in the world is called the fairy penguin. Spaghetti traditionally measured up to 20 inches, before shrinking in half to accommodate modern packaging.

I could argue for the practical benefits of a Fermi mindset, but that’s not why I like these questions. Contemplating Fermi’s problems keeps me curious about the world and how things relate to each other. The pasta issue impressed me how big the Earth was. (We figured even our hottest pasta consumption would only get us 0.01% around the equator.) What would you like to know? It is about imagining the infinite cosmos, not about organizing it, labeling it or conquering it.

One evening at the start of the pandemic, as I was walking with my husband, I grew tired of the empty streets and stopped to look at the night sky.

“Hey, how many boxes of dental floss do you think it would take to get to Alpha Centauri?” “

And so we meandered around, discussing light years and coils of waxy string, careless of answers, content to wonder.


Caroline Chen is an investigative health and science reporter for ProPublica.

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