If I’m understanding what they’re putting out, it’s not… much. Cute, but there’s no hidden mysteries here.

Think of the vectors proposed here to be an arrow pointing from some imagined origin point in any of three orthogonal dimensions. Let’s say Masc is to the right, Fem is up, and “non-binary / I don’t know what their plan was for n but I’m going to consider NB” is forwards, away from you.

Now the idea is that everyone has a unit vector, that is a stick with an arrow on the end and all the same length we’ll call 1, that points in a direction to indicate their gender expression. Someone who is full Masc is an arrow fully to the right, a pure Fem would be fully up and down, and if someone is “Masc leaning but not full Masc” they can’t just have a shorter stick, all sticks are the same length, so they either need to be half way between Fem and Masc (the 1:30 position on a clock in front of you), or if that doesn’t feel right, you can use the 3rd non-binary dimension and it can be flat (no Fem) but angled 45 degrees away from you. At the 1:30 position when viewed from above where 3:00 would be full Masc again, and noon would be fully NB (no Masc no Fem, right in the center from our earlier upright perspective)

Okay, so that’s our setup. Now for the math, which is pretty “simple”. The dot product basically just measures how big the angle is between two different vectors. So the gist here is that if you are pretty Masc and your partner is pretty Masc, your two arrows have a large degree of overlap and so it’s “pretty gay”. On the other hand, a full Fem and a full Masc have zero overlap, they’re pointing in completely opposite directions, so it’s “not that gay”. A Masc and a Fem can both be with an NB without it being that gay, but two NBs together is pretty gay, by these standards.

So again, cute, but it’s really just a mathy way of codifying “its gay to be with someone with gender similar to your own, and less gay the more different they are”

The cross product finds a line that is orthogonal (goes in a separate direction) to the other two. So in a sense it finds the person most different from the two of you. A Masc and a Fem crossed would result in a pure NB. If a Masc and an NB crossed it would output a Fem. But if you had a person that was fully Fem crossed with a person that’s half-Fem half-Masc, what you’d get is a person that’s half-NB and nothing else. This doesn’t fit our original rule about everyone having the same sized-pointing stick, but we don’t care about that for now, because what they’re actually doing with this operation is just taking the absolute value, which in this case means measuring the length of the stick.

So a Fem and a Masc producing a full NB means the length is 1, and our half couple before only spit out a half-NB, so that’s 0.5 with the idea being that there’s some straightness between the Fem and the Masc parts of the two people, but it’s not fully straight because there’s also overlap between the Fem and Fem parts. Remember when I said this outcome wasn’t a stick the same size as everyone else’s? In a sense that’s what this is measuring. How close to a real person is this hypothetical “most different person”. In the case of full NB and full Masc the answer is easy, it’s a full Fem person. So that’s a pretty straight relationship because the person who is least like you two is themselves a full person. Or in another sense you could “complete the triangle” with three unique full people. But our more nuanced couple from before already has some ambiguity and overlap, even if it’s not in the NB direction, and so you really only need a little bit of NB to cover the difference, so it’s not that straight. Some, but not fully. I don’t know that this one has that clear of an intuition, honestly, I think they just liked the math properties. Or maybe there’s a better intuition about the cross product than mine!

It’s been too long since I took this kind of math myself to know where “A cross B” is different than just “1 - (A dot B)”, as in, where is Gayness not just the opposite of Straightness. Which couple is either both Gay and Straight or neither Gay nor Straight. I could look it up… but I won’t because that would deprive someone of the joy of telling me!