Coin

Yesterday I posted about the sex binary once again, this time giving a letter I wrote to the San Francisco Chronicle explaining the male/female binary in humans (and all other animal species, as well as most plants). My letter is archived here.

In it, I said this about the standard biological definition of biological sex, which is based on gamete size and the apparatus used to produce gametes:

This standard definition applies not just to animals but also to nearly all plants, and is indeed binary: only about 1 human in 5,500 is an exception.

Well, that statement brought out the Pecksniffs: those gender activists who are determined to claim that sex is a spectrum. To them, if exceptions are only 0.018%, as they are, well, that means that sex isn't really a binary trait. (That figure comes from this paper on the proportion of intersex people born; but even those intersex individuals aren't regarded as members of a "third sex"!) Only if there were NO sex-indeterminate humans would these people accept sex as a binary trait. (Again, even if intersex people were more common, they still wouldn't be members of a third biological sex.) 0.018% exceptions is about as close as you can get to a binary.

I read somewhere else that the chances of a tossed coin landing on its edge—something I’ve never seen happen—is about 1 in 6,000, very close to the proportion of intersex individuals born. I checked out that coin-tossing figure, and it turns out to be true, at least if you’re tossing an American nickel. Click on the screenshot below to go to the Physical Review E paper that comes up with that figure:

They did a complicated calculation and came up with an equation for coins of various weights and sizes landing on their edge when tossed. Then they actually did an experiment using hexagonal brass nuts of various sizes that were tossed in the air. After that, they extrapolated to an American 5¢ piece, and got this:

Since the agreement between the model and experiment shows no systematic deviation as p gets smaller, it is tempting to extrapolate the curve to thicknesses of familiar coins. One example will be considered here, which is the American nickel (five American cents, 5p). The diameter of this coin is 21.25 mm and the thickness is 1.96 mm at the rim. This gives an aspect angle of 0.092 rad. However when tip-over angles are measured, the results are 0.037 rad for tipping over with the President's head up and 0.051 rad for tipping over with the President's head down. In other words, a slight disturbance of a nickel which is set up on edge on a level table is more likely to result in the coin falling over "heads. " The experiment to verify this is entertaining and easy to perform. The difference between tip-over angles between heads and tails is reproducible among several coins of this denomination. If p=0. 04 is selected as a representative tip-over angle, the extrapolation of the model leads to a probability of landing on edge of 1 in 6000 tosses. This has not been tested experimentally.

Note that they didn't have the moxie to toss a nickel thousands of times, but I’m betting that at least one reader of this site has seen a tossed coin land on its edge. And if that happens only once, the "heads/tails" binary is violated. I was amused at this, for when we toss coins, people call either "heads" or "tails"; they never call "edge"! Yet the chance of it landing on its edge appears to be about the same as the chance of an intersex individual being born. For all practical purposes, then, just as the heads/tails dichotomy is an effective binary, so is biological sex, which becomes indeterminate at about the frequency that a coin lands on edge.

Thus, the calculated chance of a tossed nickel landing on its side is almost the same as the chance of a human being born as an "intersex", supposedly violating the sex binary by being neither male nor female. Yet we don't, when tossing coins, say, "Call it: heads, tails, or edge." If you’re going to insist that there be NO production of humans that are neither male nor female—even in a trillion individuals—before you accept a binary, you are being obtuse—and denying the reality of how nature really works.

And again, I emphasize that intersex individuals, or those of indeterminate sex, are not considered members of another sex, and so don't violate the binary nature of biological sex. Further, I’ll note again that our concern and respect for individuals that become trans men or trans women has absolutely nothing with the frequency of intersex individuals in nature. Our treatment of gender-changing people is a question of civility and morality that should not be justified by referring to what we see in nature.

Finally, and I should have guessed this, there is indeed a video of two people tossing a nickel that lands on its edge. YouTube has it all! They don't give the number of tries before the successes, though. And I think they’re tossing it in a way that maximizes the chance of the coin landing on its edge.