How to Solve Any Problem Using Only Common Sense


Growing up, whenever I did my math homework, I would go look for my mom. I would often find him on the living room sofa, unwinding after work, catching the news with both the local Cantonese news station ringing on the TV and The Economist open on his lap.

“I don’t know how to do this,” I would complain, as I settled down by the feet of the rug.

“Read me the question.”

I would read: “Sarah takes six hours to paint a fence and John takes 12 hours to paint the same fence. If they work together, how long will it take to paint a fence twice as long?”

Didn’t even look at the page.

“How many hours do you think it will take?”

“I don’t know, or I wouldn’t have asked you!”

“One digit? Tens of hours? Hundreds of hours?”


My mother was finishing her doctorate. Studied physics, he was unexpectedly driven to run his family’s business, but he never lost his love for scientific methods. one of her favorite books “Power of Ten” A flipbook blanket 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 to the blue marble of our Earth, until you arrive at a couple lying on a picnic. The book dives into the ants on the grass, then into the invisible world of shrinking atoms and subatomic particles. My mom’s brain worked like that book, moving up and down the ten floors ladder, always looking for a big-picture point of view. He nudged me to do the same, sniffing the formula I copied from my textbook and assessing it from afar: “Does that make sense, Caroline? Look at your answer. How can painters spend more hours painting the fence together than they do alone?”

If we put all the pasta we eat in a year end to end, what percent of the Earth’s circumference does this occupy?

The estimation problems my mother liked to pose have a name: Fermi Problems, named after the Italian physicist Enrico Fermi, who had an uncanny knack for making point predictions with very little real data. One of the most famous examples is this: How many piano tuners are in Chicago?

Without looking, I can estimate that Chicago’s population is somewhere between one and five million. Using 2.5 million for a start and assuming there are four people in an average household, we have 625,000 households. Let’s say there is a piano in one out of every five houses; which brings us to about 125,000 pianos. Let’s say they are all adjusted once a year. The question now is how many pianos a tuner can service per year. My guess is that three pianos can be tuned a day. Multiply that by five days a week for 50 weeks a year, and that’s about 750 pianos per tuner per year. If we divide the number of pianos (125,000) by 750, we get about 170 tuners across Chicago. The goal here is not to know the exact number, but to be able to guess the correct order of magnitude using nothing but common sense.

When I was younger, I was overwhelmed by my mother’s questioning, I was more concerned with doing my homework so I could play. But now that I don’t have any real problem sets, I find myself going back to these problems as a way to amuse myself, the more ridiculous the better.

At dinner with my husband, I asked: If we put aside all the pasta we’ve eaten for a year, what percent of the Earth’s circumference does this occupy? Lying side by side in bed: How many penguins do you think would fit in our bedroom? As our cat jumps on my breastbone and wakes me up before my alarm: What do you think the volume of the Polo is in cubic inches?

But after we’ve made our best guesses, we turn to our phones for the internet’s answer. In fact, Google usually isn’t that helpful. “How many square feet does a penguin take up?” does not give satisfactory answers. Reddit suggests that typically, the best way to calculate a cat’s volume is to stun the poor animal and throw it into a tub of water, then measure the amount of water displaced. Still, we always learn fun things in between giggles. Now I know that the smallest penguin in the world is called the fairy penguin. Spaghetti was traditionally 20 inches long before it was cut in half to accommodate modern packaging.

I could argue about the practical benefits of the Fermi mindset, but that’s not why I like these questions. Thinking about Fermi problems makes me wonder about the world and how things relate to each other. The pasta question intrigued me, how big the Earth is. (We thought even eating the hottest pasta would only save us 0.01 percent around the Equator.) If you’re interested in trying one, consider this: What would you like to know if you didn’t limit yourself to questions you know Google has a ready-made answer? It’s about imagining the infinite cosmos, not organizing, labeling or conquering it.

One evening in the early days of the epidemic, while I was out for a walk with my husband, I got bored of the empty streets and stopped to look at the night sky.

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

And so, we wandered around discussing light-years and spools of waxed string, just wondering, not worrying about answers.

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


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