Marvel superhero Spider-Man is better known for his wall climbing and web spurting antics than his eloquence, but he is famed for one saying: “with great power comes great responsibility”. I’d agree — but I’d say even those with limited power still have significant responsibilities. 

A scientist with 150,000 twitter followers and a well-read blog has, I believe, the responsibility not to spread scientific misinformation. One such scientist is biologist PZ Myers, who styles himself as a purveyor of science and rationality on his blog Pharyngula. It’s therefore disappointing to see him spread obvious untruths such as that biological sex is a social construct or that there are an unknown number of sexes. As I’ve written before, sex is a biological reality, not a social construct and mammals have only two sexes. As an evolutionary biologist, PZ Myers must know that sex evolved at least a billion years ago and therefore seems unlikely to be a construct of human (or even ape) society. Which makes me wonder why he would spread such obviously false information.

Recently, Myers has started breeding spiders, a project which he is documenting in great detail on twitter. What I found intriguing is that in his spider updates, any uncertainty about the reality of sex or how many sexes there are, seems to be forgotten. When he charted the growth of his arachnoid pets, he used two colours: yellow for spider-girls and blue for spider-boys with no need for intermediate hues. His blog is full of references to his female spiders producing eggs — never the males, whose function is to provide the sperm ideally without getting eaten by their mates. Quite how his spiders know about sex, given that it is (according to Myers) a social construct, is never explained. 

Sex can’t be plotted on a graph because it is a category, not a number

I noted this fascinating discrepancy on twitter and hoped he would clarify exactly what he does believe. He replied that I was wrong and that “sex is bimodal”. This is a phrase often used by Myers and others, which adds confusion rather than clarity to the issue. Many of the debates in this topic come down to disagreements over definitions. Whether sex is “binary” or “a spectrum” depends on how you define those terms — they have precise definitions in mathematics or physics but are rather less clear when applied metaphorically to biology. I therefore try to stay out of arguments about whether sex is or is not binary. However, “bimodal” has a very clear definition so that we can say with confidence that sex is not bimodal. To explain why, we need a little statistics.

In stats a “mode” is the most common value for a particular set of numbers. If you plot a graph with adult human height along the bottom axis, and how frequently that height occurs on the vertical axis, you’ll get a bell shaped hump. The top of that hump is the mode: around 168cm in the UK. Lots of people are about that tall; far fewer are 140cm or 190cm.

Some sets of data can have more than one hump. If there are two humps like a bactrian camel’s back, you have two modes and the distribution is called bimodal. For instance, the density of traffic in a city might have two peaks — one at morning rush-hour and one in the afternoon.

Finding out whether a particular variable is bimodal is easy — you just plot it on a graph. I asked Myers if he could share an example of a graph based on real data showing that sex is bimodal. His response was characteristically blunt: “You want a ‘graph of sex’? You really think it can be plotted in two dimensions? What the fuck is wrong with you?”

Therein lies the problem. Sex can’t be plotted on a graph because it is a category, not a number. I’m male, but I don’t have a maleness score. Whilst I fall well short of the platonic ideal of a stereotyped hunky six-packed alpha-male, I don’t think that makes me only 85 per cent male. For all my faults, and regardless of my gender identity, I am fully and entirely male. Since sex isn’t a value that can be quantified, the description “bimodal” is nonsense.

Nerdy side note — there is a different use of the word bimodal that does apply to categorical data, which is when two specific categories have exactly the same value. Suppose you ask your friends for their favourite drink, and eight say beer, eight say wine, and five say cider. The result is bimodal because two answers tie for the most common (beer and wine are both modes). However, even if you use this meaning of the word, sex is still not bimodal in humans. There are significantly more people who are born male (roughly 105 males to every 100 females) so sex is unimodal (the mode being male). Even if it were bimodal, that would simply be a way of saying the number of males and females is the same — which is not the contested issue.

This doesn’t stop the claim being made frequently. Indeed you’ll even see graphs purporting to show a bimodal distribution of sex. However, these graphs are never based on actual data — they’re made up cartoons drawn to make a political point. The axes are usually unlabelled or just claim to represent “sex”, never explaining how the number is arrived at.

Given that PZ Myers agrees that any kind of graph of sex is impossible, you might think he would admit that it isn’t in fact bimodal or alternatively provide evidence that it is. Sadly, no. Instead he called me a “dishonest debater” and a “lying ass” and then blocked me. Then from behind his block he called me a nitwit — which is definitely the kind of behaviour you expect from an honest debater.

He also published a blog attacking me where he lied about me and threw further insults (“dim & bigoted fanatic”). He did, however, attempt some kind of a defence for his “sex is bimodal” claim. He admits he can’t plot a single value for sex. The problem, he says, is that he can provide so many: “receptivity, courtship initiation, web twanging frequency, successful insemination frequency, dancing intensity, abdomen size, interval since last courtship, metabolism levels”.

What he has done here is change his claim entirely. He’s now saying, not that sex itself is bimodal, but that some characteristics linked to sex are bimodal. This is obviously true, and no one denies it. Some traits are indeed bimodal (for instance, testosterone levels in humans) though others are not (interestingly, height isn’t bimodal in humans despite being sex-linked, since the overlap between males and females is so great you get a single mode). Other measures may even have more than two modes. 

Are they really saying that some women are not fully female?

Sex linked characteristics can be unimodal, bimodal or multimodal. What does this mean? Statisticians will tell you that the most likely explanation for a bimodal distribution is that your sample is a mixture of two different types. Imagine you go to a popular dog walking area and weigh all the creatures you find there. You will probably get a bimodal distribution. Why? Because you’re looking at a population that includes humans (average weight around 60kg) and dogs (average weight around 10kg). The curves will merge because a large Newfoundland can weigh more than a slender adult human. What this doesn’t mean is that those large dogs are partly human or that slim people are dog-like. A bimodal distribution is not only compatible with two entirely separate types of thing — it makes the existence of two types (in this case sexes) more likely.

Sex isn’t bimodal, because it’s a category, not a value. Specific measurements can have all sorts of distributions (including bimodal) — and if those traits are bimodal, they likely have that shape precisely because we have two, and only two, sexes.

You could ask why all this matters. Partly it’s because I am, I admit, a pedant who likes to see terms used correctly — particularly by scientists. There is a much deeper reason why the “sex is bimodal” idea is so pernicious, however. Let’s put aside all of the above and imagine that the activist chart is correct — and that sex really is two-humped. Like so:

I think the suggestion that we can rank all women as more or less female (or men as more or less male) is deeply wrong, and it should have been thrown out decades ago. Yet that is a direct and unavoidable consequence of stating that sex is bimodal. I’d love to ask PZ Myers how he would measure the femaleness of a woman — but he’s still blocking me so it’ll have to be rhetorical. In the meantime I wish him well with his spiders and hope they lay lots of eggs (the female ones anyway).