Why is gender a Hilbert Space?

In mathematics, the concept of a Hilbert Space is fairly simple. It takes the notion of 2D and 3D Euclidean spaces, and generalizes them to any n dimensional Euclidean space, often referring to an infinitely dimensional Euclidean space.

Gender is often seen as a binary structure; forget two dimensional. Uneducated individuals are often misinformed in thinking there are only two genders, "male" and "female." Oddly enough, the traits and personalities associated with the concept of "male" and "female" are incredibly arbitrary, yet they're the ones touted to be the only valid genders. They're so uninformed that they reject the medical reality of intersex individuals and their experiences. Some, slightly more woke psychologists suggest that gender is a 2-dimensional spectrum, with one axis being masculinity and the other being femininity. The origin would be seen as one form of androgynous expression (what one would more sensibly call agender) and the further end of y = x is seen as more of a bigender androgynous expression.

The problem with seeing gender as merely a 2D spectrum is that it fails to account for individuals who fall entirely out of the binary, or have an expression that only partially lies within the binary. At the same time, we can't merely make a third dimension that's simply labeled "nonbinary" as there isn't one way to identify as non-binary, just as there isn't just one way to be feminine or masculine. In fact, there's an arbitrarily large, effectively infinite ways to identify, each with a spectrum being from a-(gender) to demi-(gender) to the full gender. The simple masculine/feminine graph also fails to account for the fact that there are masculine females and feminine males, without them being androgynous or bigender, as there's a difference between gender identity and gender expression.

This is why gender is a Hilbert Space. Furthermore, gender isn't a coordinate point, or even a vector within the Hilbert Space. Gender is a tensor. Gender is a parametric equation. Gender is fluid, and not a static feature.

The important thing to recognize is that there isn't a single imaginary portion to the gender; however, despite that, gender is still complex.