A recent conversation with a friend turned to the wonders of GPS. “How could we have ever lived without it?” he asked.
I agreed, and began to explain how GPS worked and how the critical clock correction was done. But I quickly saw a blank expression on my friend’s face, and an averting of eyes.
“You’re an engineer, and you care about things like that,” he said dismissively.
The conversation left a strange aftertaste. Do you have to be an engineer to care about how things work? Do engineers have an innate sense of curiosity that is largely absent elsewhere?
Shortly thereafter, I brought up the question with two engineering friends. They looked at each other with an expression of collusion that excluded me. “No,” said one, while the other nodded and said in agreement, “We don’t have any special curiosity.”
Nonetheless, I’m still curious about curiosity. This sense has always been a powerful stimulant for creativity and innovation. I have a mental image of Isaac Newton watching the apple fall. According to a contemporary biographer, Newton asked himself, “Why should that apple always descend perpendicularly to the ground?” Had no one ever been curious about this before? After all, apples had been falling since Eve.
Newton’s curiosity led to his law of gravitation. But asking “Why?” is often a recursive exercise, like opening nested dolls. Two centuries later, Einstein asked himself why being in an accelerating elevator is similar to the effect of gravity. His curiosity led to the theory of general relativity. And even today physicists are curious about gravity. How does the apple know that Earth is pulling it downward—or perhaps I should ask, how does space get warped by mass?
Recently I read something that mentioned the Monty Hall paradox. Some years ago I had worked out an explanation in my mind, but now I had forgotten it. I lost sleep over it—I went to bed with my curiosity reverberating and wasn’t satisfied until I worked it out again the next morning.
Still wondering if there was a curiosity meme that I could inflict on others, I tried the paradox on a dozen friends. The result of my small experiment was that no one else had any curiosity about it. However, I’m not giving up yet, and I’m about to try it on you, dear reader.
Years ago Monty Hall was the host of the TV game show “Let’s Make a Deal.” Contestants on his show could win a new car if they guessed which of three doors it was hidden behind. Behind the other two doors were goats. Presumably, they preferred the car to a goat—even if the show and their local ordinances allowed them to take a goat home.
Let’s say you chose door No. 1. Instead of directly revealing whether you were right, Monty, who knew where the car was hidden, would open one of the other doors, say door No. 3, to reveal a goat. Thus the car was either hidden behind door No. 1 or door No. 2. So far, so good, but then Monty would offer you a puzzling alternative: “Do you now want to switch your choice?” he would ask.
Apparently, almost no one ever switched from the door they chose to the other remaining one. Among the dozen friends on whom I tried the experiment, no one switched. After all, it still appears an even bet, whether or not you switch. Moreover, the pressure is on, and if you switch and it turns out that the car was behind your original choice, you’ll feel like a goat yourself.
However, it can be shown that switching doubles your probability of winning. This seems completely counterintuitive. Surely the probability of winning for either of the two remaining doors is the same. But it isn’t. When I told my friends that they had missed the chance of doubling their chances of winning, they all denied that was the case and evinced no subsequent curiosity.
So I wonder. Are you curious about this paradox?