What use is mental math in 2022?
Now that most people are carrying around a powerful computer in their pocket, what use is it to be able to do math in your head?
Here's something I've noticed lately: being able to do quick approximations in mid-conversation is a superpower.
When I'm on Zoom with a client, I can't say Excuse me a second. Something you said gave me an idea, and I'd like to pull out my calculator app." Instead, I can say things like That would require collecting four times as much data. Are you OK with that?"
There's no advantage to being able to do calculations to six decimal places on the spot like Mr. Spock, and I can't do that anyway. But being able to come up with one significant figure or even an order-of-magnitude approximation quickly keeps the conversation flowing.
I have never had a client say something like Could you be more precise? You said between 10 and 15, and our project is only worth doing if the answer is more than 13.2." If they did say something like that, I'd say I will look at this more carefully offline and get back to you with a more precise answer."
I'm combining two closely-related but separate skills here. One is the ability to simple calculations. The other is the ability to know what to calculate, how to do so-called Fermi problems. These problems are named after Enrico Fermi, someone who was known for being able to make rough estimates with little or no data.
A famous example of a Fermi problem is How many piano tuners are there in New York?" I don't know whether this goes back to Fermi himself, but it's the kind of question he would ask. Of course nobody knows exactly how many piano tuners there are in New York, but you could guess about how many piano owners there are, how often a piano needs to be tuned, and how many tuners it would take to service this demand.
The piano tuner example is more complicated than the kinds of calculations I have to do on Zoom calls, but it may be the most well-known Fermi problem.
In my work with data privacy, for example, I often have to estimate how common some combination of personal characteristics is. Of course nobody should bet their company on guesses I pull out of the air, but it does help keep a conversation going if I can say on the spot whether something sounds like a privacy risk or not. If a project sounds feasible, then I go back and make things more precise.
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