It’s hard to bring sex and mathematics together, but I like a challenge, and so I direct your attention to this story in the * UK Telegraph * about the changing sexual habits of the French.

Yes, I know, other than for the math, who cares?—but stick with me for a moment. The story describes a recent study that reaches the following conclusion: “A woman’s average number of [sexual] partners has risen from under two in 1970 to over five today, while a man’s has remained the same for four decades, almost 13.”

What’s interesting about this claim is that it’s mathematically impossible. That is, if we leave aside cases of homosexuality and assume that the number of men is equal to the number of women, then the average number of sexual partners for men must exactly equal that for women. It’s mathematically impossible that the men have on average more partners than the women.

This isn’t hard to see. Define a * coupling * as an ordered pair— * x,y * —where * x * is a woman, * y * is a man, and * x * has had sexual intercourse with * y * . Then the average number of sexual partners for women is the total number of couplings divided by the number of women, and the average number of sexual partners for men is the total number of couplings divided by the number of men. Since the numerators here are the same—the total number of couplings—and since the denominators are the same too (we assumed there are as many men as women), it follows that the quotients are the same as well. The average number of sexual partners for men and for women are therefore the same.

To illustrate, imagine that there are 100 men and 100 women, and 90 of the women are celibate, but the other 10 each copulate with all 100 of the men. If you think this means that the men have on average more sexual partners than the women, you haven’t been paying attention. Among the men, since each man has 10 partners, the men average 10 partners. Among the women, since 90 women each have zero partners and 10 women each have 100, the average is the sum of zero plus 1,000, all divided by 100, which is again an average of 10 partners. Or, to use the terminology from above, we have 1,000 couplings, and whether we divide that 1,000 by 100 men or by 100 women, we get an average of 10 sexual partners. (For those really interested in mathematics, the * modes * for the men and women do differ here: 10 for men, but zero for women.)

So what follows from this? Well, the authors of the study seem to think that it’s a great thing for sexual equality if French women are becoming as promiscuous as French men, so perhaps they’ll be happy to learn that, assuming promiscuity is properly measured by the average number of sexual partners, it’s bang-on certain that the women of France are as promiscuous as the men.

Of course, this has also been true in every other society that has ever existed, and a failure to excel at sexual promiscuity might be hard on the French ego. Not only do the Americans keep winning the Tour de France, but now it turns out that the French are no better sexually than, say, the Irish. Even worse, with French women reporting many fewer sexual partners than French men, it seems clear that the women are putting up a pretense of chastity while the men are bragging about non-existent sexual conquests.

The study thus seems to show that the French still harbor what may be thought traditional—even chauvinistic—attitudes about sexual promiscuity, i.e., that it’s good for him but not for her. That would be a bad job indeed and a grievous blow to France’s profound national commitment to * libertÃ© et Ã©galitÃ© de sexualitÃ© * , but, then again, if French women want to tell one set of lies about sex while French men want to tell another, perhaps the French would put the best face on it and say, * vive la diffÃ©rence! *