Take me, for example. I fancy myself smart, at least about math–I have a degree in the subject, and have written two books about it.
So here’s what happened. My wife, who works in retail, asked me the following thing. With a sales tax of eight and a quarter percent, a hundred dollar item (ticket price $100) is going to cost you $108.25 (taxed price).
But she and her colleagues had a bunch of items listed at taxed price, and they had to figure back to the ticket prices. Just subtracting eight and a quarter percent didn’t work. Why not?
Me: “Look: say the item costs $1,000 and the tax is ten percent. Taxed price is $1,100, right? But ten percent of that is $110. Subtracting $110 from $1,100 doesn’t get you back to $1,000, because you just took ten percent of something BIGGER. See?”
She was persuaded. But then: “OK, so what’s the drill? How do I get back from the taxed price to the ticket price?”
Me: “Why, just divide the taxed price by 1.0825.”
She: “Huh? What are you talking about? What happened to percents?”
Me: “Oh, you know, percent is just a way of saying numbers. A hundred percent is 1. Eight and a quarter percent is 0.0825. So your taxed price is 1.0825 your ticket price. Divide and you’ve got it, see?”
She: “No. Show me on the calculator.”
I divided by 1.0825 on the calculator.
She: “No, show me usinmg the percent key. I always use the percent key.”
Me: “I don’t know what the percent key does. Look, it’s just numbers. Percents are just numbers in thin disguise. It’s easier to work with the numbers.”
She: “I want to work with percents. I don’t really get numbers.”
That’s where we got stuck. I only do numbers, I don’t do percents. She only does percents, she doesn’t do numbers. I have never in my life used the percent key on a calculator. I don’t know what it does, and I don’t want to know. Numbers are real, all else is illusion. But not to my wife. And now she thinks I’m a fraud. All those fancy math books, and he doesn’t know how to use a percent key!
She wandered away at last muttering: “Congming fan bei congming wu“—approximately: “Smarties outsmart themselves.” Which I guess is true.