How many times will your heart beat in your life? Don’t look it up. You’ve got everything you need already.
A resting heart beats about 70 times a minute. There are 60 minutes in an hour, so that’s around 4,000 an hour. There are 24 hours in a day, so call it 100,000 beats a day. There are 365 days in a year, so roughly 36 million a year. And if you live to 75, you get about 2.8 billion heartbeats. Sit with that for a moment. You have worked out something genuinely interesting about your own body, in about thirty seconds, with no calculator, by guessing.
I want to argue that this kind of guessing, careful, structured, out-loud guessing, is one of the most useful things we could teach in school, and one of the things we teach least.
The method has a name. It’s called a Fermi estimate, after the physicist Enrico Fermi, who was famous for asking his students questions like “How many piano tuners are there in Chicago?” Nobody knows that number. But you can guess how many people live in Chicago, how many households have a piano, how often a piano needs tuning and how many pianos one tuner can manage in a year. Each of those guesses might be off. But when you multiply them together, the errors tend to partly cancel out, some too high and some too low, and you end up surprisingly close. Often within a factor of two or three of the truth, and sometimes much closer.
Fermi did this with almost anything. In 1945, watching the first atomic test from miles away, he dropped scraps of paper as the blast wave passed, watched how far they were blown, and worked out the size of the explosion in his head. He said about ten thousand tonnes of TNT. The careful measurements, which took weeks, came out at around twenty thousand. Half the true answer, from a handful of paper, in about a minute.
There are two tricks that make this work. The first is to aim for the right power of ten, not the exact number. Is the answer nearer a thousand, a million or a billion? Get that right and you know more than most people who confidently state a figure. The second trick is for when you really have no idea. Don’t pick a number. Pick a range you’re sure of, a lowest and a highest that you’d bet on, and take a value in the middle in the multiplying sense, not the adding sense. How many students are in a city’s schools? Surely more than ten thousand, surely fewer than ten million. Halfway between those, by multiplying, is about three hundred thousand. Halfway by adding would be five million, which is just your upper guess wearing a disguise.
Why does that matter? Because the world is full of numbers, and most of them are thrown at us without any way of checking. A headline says a city wastes a billion litres of water a day. A video says the average person swallows eight spiders a year in their sleep. An advert says its product will save you a lakh a year. Without the habit of estimating, you have two options: believe it, or don’t. With it, you have a third: check whether it’s even the right size. Is a billion litres a day a lot for a city of ten million? That’s a hundred litres per person, which is about what one person uses in a day anyway. Suddenly the headline needs a closer look.
Take that spider claim. Estimate it. How often would a spider choose to walk across something warm, breathing and vibrating, like a sleeping face? Biologists point out that spiders tend to avoid exactly those things. And there is no study behind the number at all; it spreads because it sounds like the kind of thing that ought to be true. Thirty seconds of estimating makes you suspicious before you’ve looked anything up.
In school, guessing is treated as what you do when you haven’t studied. I think it’s the opposite. A good guess is built from what you know, and it tells you exactly where your knowledge runs out. It turns “I don’t know” into “I know roughly, and here’s why”.
So here’s my proposal. Every week, every class, one question that can’t be looked up. How many grains of rice in a bag? How many words will you say today? How long would it take to walk to the Moon? No right answer, only better and worse reasoning. Because the people who change the world are rarely the ones who knew the answer. They’re the ones who could get close enough to know it was worth finding out.