Published in IEEE Spectrum Magazine, July 2012

I was in a casual conversation with a friend when the subject turned to the wonders of GPS.  “How could we have ever lived without it?” he asked.

I agreed, and took the opportunity to explain briefly how GPS worked and how the critical clock correction is done.   But I was barely into this when I saw the blank expression and averting of eyes as his gaze fixed on something behind me, where, in fact, there was nothing.
“You’re an engineer, and you care about things like that,” he said dismissively.

That was obviously the end of the conversation, but it 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 was having dinner with two engineering friends and I brought up the question of whether engineers have a special curiosity.  They looked at each other with an expression of a collusion that excluded me.  “No,” said one friend while the other nodded in agreement, “we don’t have any special curiosity.”

Nonetheless, I’m still curious about curiosity.  Regardless of whether or not engineers have a special 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 does the apple always fall perpendicularly to the earth?”  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 the nested dolls that contain ever smaller ones.  Two centuries after Newton had been curious about the apple falling, Einstein asked himself why being in an accelerating elevator is similar to the effect of gravity, and that led to his theory of general relativity.   And even today physicists are curious about gravity.  How does the apple know that the earth is pulling it downwards, or perhaps I should ask how does space get warped by mass?

Recently I was reading something that mentioned the Monty Hall paradox.  I had heard of that paradox some years ago and had worked out the explanation in my mind.  But now I had forgotten that explanation, and I went to bed with curiosity echoing in my mind.  I lost sleep over it and wasn’t satisfied until the next morning I worked it out once again.

I wondered if there were a curiosity meme that I could inflict on others, so I proceeded to try the Monty Hall experiment 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 the reader.

Years ago Monty Hall was the host of a television show called “Let’s Make a Deal.”  Contestants on his show could win a new car, which was hidden behind one of three doors.  Behind the other two doors were goats.  Presumably, you preferred the car to the goats, and I’m not even sure you would have been allowed to take the goat home.

You’re given the opportunity to choose one of the three doors to be opened and to claim the prize it conceals.  Let’s say you choose door one.  Then Monty Hall, who knows where the car is hidden, opens one of the other doors, say door three, to reveal a goat.  Now you know that the car is either hidden behind door one, your choice, or door two.  So far, so good, but then Monty offers you a very puzzling alternative.  “Do you now want to switch your choice?” he asks.  If you want, you can now select door two instead of door one.

I don’t know the actual statistics, but apparently almost no one ever switched their choice.  Among the dozen friends on whom I tried the experiment, no one switched.  After all, it seems that whether or not you switch your choice, it’s still an even bet.  Moreover, the pressure is on, and if you switch and it turns out that the car was behind your original choice, you’ll look foolish.  So why switch?

However, it can be shown that switching your choice 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 win probability, they all denied that was the case, and seemed to evince no subsequent curiosity.

So I wonder.  Are you curious about this paradox?