The pan and ace orientations are optimal in a certain mathematically rigorous sense. They factor out gender (in the definition, you don't need to know the person's gender or the person's model of gender), and they form what is called a categorical adjunction or Galois connection:

Consider the space of possible orientations. If we assume that each person has exactly one gender and that an orientation comprises a subset of attractive genders, then the space of possible orientations becomes a set \(G \times 2^G\). We can equip \(2^G\) with subset ordering; because genders aren't ordered, we'll equip *G* with the identity order (each gender is comparable only to itself). \(G\times 2^G\) has the induced product order. There is a *disorientation functor* \(\mathscr{U}:G\times 2^G\rightarrow G\) which forgets a person's orientation but not their gender. Observe that the left adjoint of \(\mathscr{U}\) assigns an ace orientation to each person: \(g\mapsto \langle g, \emptyset\rangle\). And the right adjoint of \(\mathscr{U}\) assigns the pan orientation to each person: \(g\mapsto \langle g, G\rangle\). Each one represents a certain optimally unassuming solution to recovering an unknown orientation

$$\mathbf{Ace} \vdash \mathbf{Disorient} \vdash \mathbf{Pan}$$

P.S. The evaluation map \(\epsilon\) ("apply") detects same-gender attraction: In programming, evaluation sends arguments \(\langle f, x\rangle\) to \(f(x)\). Every subset of *G* is [equivalent to] a characteristic function \(G\rightarrow \{\text{true}, \text{false}\}\). So if we apply eval to an orientation in \(G\times 2^G\), we determine whether it includes same-gender attraction.

Incidentally, the ace/pan functors have further adjunctions when, and only when, there are no genders. In this case, pan and ace become equivalent and the adjunctions form a cycle.