Yesterday morning, I had the pleasure of talking to Kalid, founder of betterexplained.com, writer of ebooks explaining math, and a generally all around awesome guy. He happens to live in my neighborhood.
I think about math a lot, but there’s always more, and he gave me ideas on how to think about the chain rule, e, and the Pythagorean Theorem that were new to me. It was great.
I’d like to take a moment to officially recommend his website for anyone interested in great explanations of math ideas, concepts, and problems. Here’s a fun post of his, explaining the Monty Hall problem. This problem is incredibly counterintuitive. Marilyn Vos Savant famously wrote about in her column, in 1990:
Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, “Do you want to pick door #2?” Is it to your advantage to switch your choice of doors?
What do you think?
When I first heard the answer, I was in college, and I actually thought people were playing a kind of prank on me. Mathematicians responded to Vos Savant’s column with angry remonstrations, only to have her respond in her next column that, no, she had indeed present the correct answer.
So the answer is a bit counterintuitive.
Kalid presents an explanation that not only is correct, but gives his way of thinking about it, and turns the disbelief into, for me, a sense of aha! I think that’s what we all want from an explanation.