I was recently watching some kids play in the airport. They had a toy airplane that they would wave around through the air and pretend it would fly. I was thinking about what makes play so much fun, and then realized that whenever I learn something new, I also enjoy flinging it around and seeing what its really made of. For adults, it may be things like calculus, bayes theorem. I remember when I first learned about limits in calculus, it really changed how I thought about things like, say, physical movement and speed and acceleration. I thought about it all the time, past the time I felt like I really got it simply because it was fun to do so. Graduate school has involved a lot of playing with Bayes theorem and information theory and related ideas. Every time I learn a new one (say, explaining away, graphical models, rational analysis, etc) I find myself playing with it in a way that I think is a lot like children’s play. Think of some examples, some neat cases, look for it in new places. See what happens when you throw it at the wall. Of course, for kids the amazing new concepts are simpler things–like elephants, flight, gender, chivalry, and revenge. I wonder if I was just learning these things, if I’d be enthusiastic about thinking about them as a kid is. Maybe we just all like to take our shiny new concepts out for a drive.
But there’s something beside the shoreline, moving across the beachhead
A funny thing came up in conversation a few days ago. Do you think the following is true:
Men on average have more relationships than women.
Sounds plausible enough, right? The funny thing is that (assuming for simplicity that every man is in a relationship with a woman and vice versa and there are equal numbers of men and women) this can’t possibly be true! Because if exactly one man and one woman is in each relationship, then the sum of all men in relationships and the sum of all women in relationships must be equal. But if there are equal numbers of men and women, the averages must be the same.
Is the first sentence as tempting as,
On average, men are in longer relationships than women.
Or
There are more men in relationships than women.
It just seems very compelling to me that yes, it’s true men have more relationships than women. And it takes a little reasoning to see why this can’t be true. But these two other sentences seem progressively less compelling. I wonder why. Celeste suggested it might be that men talk (or lie!) about more relationships than women do.
I think the mistake is maybe on par with things like the conjunction fallacy. So does “average” really mean arithmetic mean, as opposed to, say, mode, or median? Or when we answer the first question, are we answering a question about typicality or representativeness (as with Linda)? Is it more typical–whatever that means–for a man to have more relationships than a woman?