Differentiating the Sexes

My higher level maths class for Leaving Certificate (the state exam at the end of secondary school in Ireland) was entirely populated with boys. I think there were one or two girls in the class at the beginning of the year, but they found the subject too time-consuming relative to the six or seven others that students study at that age; they dropped maths to ordinary level pretty early in the year.

My Leaving Cert. physics class was similarly populated.

In my first year of theoretical physics in university, one of my thirteen peers was a lady. In second year, she was no longer around. I studied almost entirely under male lecturers, and I graduated surrounded by male classmates.

My life is one big anecdote in support of the proposition that men are better at maths and hard sciences than women are. It’s particularly important, then, for me to always be aware of that wonderful assertion that “the plural of anecdote is not data”.

In that light, putting away my anecdote and replacing it with real data, we can find out the truth about gender and maths: that poor female performance in maths is strongly correlated with societal gender disparity; that stronger male performance in maths is accompanied by a corresponding weaker male performance in maths (i.e., that us guys push out both ends of the bell curve—for every genius there’s, well, someone less successful); and that young girls are more likely than young boys to inherit the maths anxieties of their teachers, setting them off on a course towards poor maths performance in later life. In short: women underperform in maths when they spend their lives being told that they will.

I’m delighted to see real results based on real data about maths performance. We will desperately short-change ourselves if we continue to discourage half of our potential mathematicians and scientists with baseless stereotypes. Not only that, but we’ll condemn more young men to an academic life devoid of the fairer sex. I moved out of physics into computer science for the girls, which gives you some indication of the sorry state of the physical sciences.

Maybe computer engineer Barbie will help.

Lose the 10¢ — it’s worthless

Inspired by this analysis of coin efficiency at the Freakonomics blog, I’ve written a short Python script to calculate the efficiency of the Euro coin set. Like in the blog post, efficiency here means the lowest average number of coins needed to sum to any sub-Euro total (where all totals are assumed to occur equally frequently). For example it requires five coins to sum to 48¢: two 20¢, a 5¢, a 2¢, and a 1¢.

It turns out the average number of coins you’ll need is about 3.43, given the current set of six coins (I exclude the Euro and two Euro coins, since they’re no help in reaching sub-Euro totals). The maximum number of coins you ever need to reach any total is six. Note that we get this efficiency, much higher than the US’s 4.70, by cheating. We have six coins to play with, where they have only four.

The interesting part is in figuring out which coin would have the least negative impact on efficiency if it were removed. You might like to take a moment to ponder which is your least favourite coin before I reveal the answer. If you’re anything like me you probably hate the one cent coin, but sadly that’s the only one this analysis won’t let us remove: it’s required to form the total of 1¢, obviously. Every other coin is expendable, but with differing effects on the efficiency of the coin set.

Or so you might think. In fact, the coins barely differ at all in their effect. The 2¢, 5¢, 20¢, and 50¢ coins would each reduce the efficiency of our coinage by 0.81 if they were to disappear overnight. Only 10¢ differs, having a smaller effect of reducing efficiency by only 0.40.

So if we wanted to reduce the number of different coins all of us have to deal with (the principals are the same for me in the UK with Sterling, having 1p, 2p, 5p, etc.) with the minimum impact on efficiency, we should get rid of the 10¢ and 10p coins.