One of the consequences of having a great deal of math and physics education, is that whenever I learn about something, I internally encode it as math, even if nobody else is thinking of it that way. Today I’m going to share one of the more ridiculous examples, the analogy between identity labels and topology.
I’m mainly thinking about sexual identity labels, and especially arguments over boundaries of those labels. I’m thinking of how people claim “everyone is a little bisexual”; or they argue about the validity of bisexual lesbians; or they ask “isn’t demisexuality just normal?”; or they draw sharp distinctions between asexual, gray-asexual, and allosexual.
In all these arguments, there is the essentialist viewpoint, which says that everyone has an underlying sexuality, and each word covers (or should cover) a specific space of sexualities. If your underlying sexuality falls within the domain of the identity label you use, then your label is “correct”, and if it doesn’t, then your label is “incorrect”.
I disagree with the essentialist viewpoint, and I frequently point to prototype theory, family resemblance theory, and Wittgenstein as alternatives. But I also feel that if you’re going to take the essentialist viewpoint, obviously you should take it all the way, and learn about the math that you’re implicitly using. I am not going to “prove” that essentialism is wrong, and if you summarize my essay as “Mathematics disproves essentialism” then so help me, you did not read the fourth paragraph. The goal is to explore the implicit mathematical framework of essentialism, and point out its unaesthetic aspects.
Of course, I don’t recommend actually using this in an argument, since it relies on teaching people math.