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"Spectra are isomorphic to any other continuous Euclidean space!" I scream as I'm dragged off stage. "A gender line with 'male' and 'female' at the endpoints contains the same descriptive power as a square or a cube or a boundless void!"

I am hurled into the back of a truck. There are chalkboards and chalk there to distract me. I stop screaming and am never heard from again.

It's up to you whether this is an indictment of spectra or a vindication of the "gender line".

@kelbesque hmm. noobish talk, & I'm already on record that "more numeric variables won't do for the same reason" (i.e., agreeing w/u), but ig I'd ask if total ordering is a meaningful trait that distinguishes 'the gender spectrum'/a 1D real segment from higher-order real spaces? like, say, a cube has an arbitrary ordering, in that you Can pigeonhole it with the real line but there are many possible ways to choose to do that, where arithmetic/comparison gives strict ordering to the 1D reals

@byttyrs well, ordering on a line is still arbitrary--there are infinitely many total orderings on [0,1], we just have a default, intuitive one.

@kelbesque hmm... something something, metric spaces... in 1D, the equivalence class "points whose Euclidian distance from point A = x" is no greater than 2, whereas in 2+D that equivalence class has the cardinality of the reals... but the "total number of points" describable is still the same (cardinality of the reals), there's just a more complex logic possible about that concept of distance

sorry Eve, Idk why I'm defending "just put another axis on it!," an approach to modeling I hate

@kelbesque oh big same, whew, I thought I was being the dick for following the math train of thought

@byttyrs nope! I'm just being Dr. Eve: I Studied Geometry For Way Too Long And Sometimes I Have To Let It Out

@kelbesque thank you, as a person who is roughly That Way despite not actually Knowing Her Shit, I appreciate you for being this way and Knowing Your Shit

@byttyrs from there, you start to worry about what those orderings do and don't preserve. Do you care about the triangle inequality? That is, is relative distance an important measure?

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