Railing against “grey areas” has become a favourite rant topic. People think that they’ve covered their bases and are being really open-minded when they switch from {0,1} to [0,1]—but no false dichotomies are avoided in this transition from discrete to continuous.

Let’s take the example of sex & gender. Most of the tick-boxes and bathrooms we face in life are labelled “M” or “F”, which covers most of us but not all.




(And I want to apply a kernel weighted to extra-count the forgotten individuals, since as minorities they’re more vulnerable. This can be seen in data such as e.g. higher suicide rates and higher murder rates.) The University of Hawai’i’s guidelines for dealing with individuals possessing ambiguous genitalia (Archives of Pediatrics and Adolescent Medicine) use words like

  • chromosomes—XX, XY, or other
  • micropenis, labia-scrotum fusion, gonadal dysgenesis
  • androgen insensitivity syndrome, hypospadias, kiinefelter syndrome, congenital adrenal hyperplasia, Turner’s syndrome
  • true hermaphroditia

which raises the question of where the “grey area” between [M,F] ~= [0,1] could come from. Chromosomes either come in whole units — for example people with Klinefelter’s syndrome have 47 chromosomes “XXY” — or have a much more complicated structure if you want to dig into the DNA string. Other aneuploidies include XYY, monosomy or partial monosomy, trisomy 21 (which I don’t think affects genitals or sex assignment), distal 18q−, mosaicism, the list goes on. How are we going to assign a total order there in order to define a continuous variable? I don’t see any way to—just more possibilities to add to the domain of a categorical variable (and making it much more confusing than the usual gender dummy!).

The paper above, to give another example of non-orderability, notes that various chemicals usually squirt at you in fœtal development but they vary in their squirtular timing. So androgen, progesterone, and so on aren’t mutually fungible (as the different “coloured edges” in Ramsey theory), and además we’re dealing with time series like Ed Küpfer’s pictures of sports scores:



Those kinds of pitures, but with different coloured spiketrains representing the incommensurability of androgen vs testosterone and so on.

So how do you get total orderability (necessary for a “grey area”) from a time series of incommensurable chemtrains? I don’t see it. The geometry is more interesting than just a line segment.

Further reading: transgender mathematician (Leigh Noble), transgender computer programmer (Tim Chevalier @eassumption), transgender economist (Deirdre McCloskey @deirdremcclosk), transgender electrical engineer (Lynn Conway). Jeff Eugenides’ Middlesex.


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