That second one really seemed to miss the point of non-binary and thought they could get around it by just using the gender binary multiple time.

I think the proper solution is to create an abstract gender class and leave it to the user to implement their specific gender.

This is very clever if nothing else.

If you want to actually mathematize this for some reason, let me offer a better approach.

Take everything you want to mathematize about people and define the elements as sets of dimensions in an N-dimensional metric space. We choose N dimensions because we don’t know how many we’re going to ultimately need, but we can intuit the number will be proportional to the complexity of what we are trying to characterize. So let’s start by just dealing with the dimensions we need to characterize “gender,” even if we acknowledge that it’s vastly incomplete.

So let’s start with the proposed dimensional representation of a binary dimension - a single line with two points, male and female. Aside from it not being very interesting, it’s not a great representation of the phenomenon. Are all males equally masculine? Do we have societies that have such a binary conceptualization? Is a fireman or a US Marine more masculine than a pastry chef or ballet dancer? Some occupations are seen by society as being more masculine than others, and statistically have a greater number of men than women in them. Some incorporate physiological demands more likely to be met by men (without trying to dig too deeply into that term yet).

So we can instead try a single dimensional metric with a point of origin and two directions - masculine and feminine. We can draw this orthogonal to our binary dimension. Now we can plot an individual in this 2d space as male or female and as masculine or feminine to an arbitrary degree. But now we have to ask if masculine and feminine are really opposites. If a cultural definition of femininity includes getting married and raising children, how to we position a celibate Catholic nun? We might say she’s less feminine (although some would argue against that, we’re talking about a particular cultural definition), but would it be entirely correct to take the differentiating characteristics and say they make her more masculine? Celibacy, poverty, service to others, non-violence, contemplation… these aren’t generally things we’d associate with increasing masculinity.

So we can split that out into two dimensions, one for femininity and one for masculinity. That gives us a 3d space. Someone might be a 1 (male) on the male-female dimension (values assigned via deliberate Freudian motivation), 4.25 in the masculine, and -1.75 on the feminine dimension. That means they have a male gender, are relatively masculine, and relatively anti-feminine. These are arbitrary and illustrative assignments for now.

But two dimensions might not be enough either. People are complex, and have aspects of their personalities that are contextually determined, and even more importantly have aspects of themselves that may differ in their degrees of masculinity and femininity. So to keep this short(er), let’s just say that there’s M dimensions (M < N) around gender-concepts which maybe we can map using pairs of masculine-feminine dimensions. If we really want to, we can take a point in this M-dimensional space and map it into a lower d space, gaining compression but losing possibly important detail.

Let’s go back to that binary dimension, though. Male-ness and female-ness are complex physiological characteristics that are themselves determined and influenced by complex physiochemical processes. As a simple example, individuals vary quite a bit in terms of their production and employment of sex hormones. Developmental biology only adds to the complexity by determining many aspects of fetal development with factors that vary widely across individuals and which themselves are determined by any number of sociological and physio-biological factors such as nutrition and stress levels.

As a result, the physical aspects we associate with maleness (like secondary sex characteristics) vary widely between individuals, and even between societies and cultures. If we’re considering the influence of genetics, hormones, bodily characteristics and the like and mapping them onto a concept of “male” (as we do when we say “a male is a person with a penis”), then we can also ask whether the 6’4” 265 lb professional quarterback is more male than the 5’2” 95 lb asthmatic chess player. The former has more aspects we traditionally associate with being male, and they’re indeed largely controlled or influenced by sex hormones. It’s probably better to use a continuous space for this as well. We can toss in other dimensions too - aggressiveness for example is not 100% determined by maleness but can exhibit a correlation that has physiological and cultural influences. Again, we can project the higher dimensional space into a lower dimensional one, but always with a loss of accuracy.

We’ve also been using the word “cultural” a lot. Some aspects might be pan-cultural, others might be multi-cultural, and others might be unique to a culture. In any case, we might need additional dimensions or at least some concept of frames to make sure we’re taking those data into account.

A final point is that, even when we do manage to map a person into our N-space, we have to acknowledge that there’s a time dimension that will cause them to move through the other dimensions. We can change our hormone balances through things like diet, exercise, and medicine. We may change in our metrics of masculinity/femininity when we’re considering how those terms are derived from behavioral tendencies (eg, getting in touch with our feminine side). These changes themselves may be discontinuous (eg, an experience might cause a single large and dramatic shift without hitting any in-between points), so we can still take advantage of the metric space but have to acknowledge that a person can move along a discontinuous trajectory.

So you can then transform all of this into a binary representation if you want to by simply representing the N-space with positions represented by floating point numbers and the dynamic part represented by continuous time. You can map in as many people as you want, and calculate distances between them using any subset of dimensions you feel are relevant to the question. You can build models of correlations between position in N-space and social behaviors.

In short (no c language data type pun intended), a simple one bit representation is so ludicrously oversimplified that we’d expect it to be rejected by the intuition of a reasonably intelligent five year old. We can compress this massive amount of data down by projecting it into lower order dimensions, with a loss of information proportional to the delta in number of dimensions. You can even project it into what we started with - a 1d binary space, but the only way to lose more information would be to project it into a 0d space where we just end up with “person” that has no characteristics. However, when we do so, we have to remember that we’re dumbing down the data and making it less reflective of reality, not more.

In even shorter, life is more complex than can be captured by a form that forces you to fill in one of two bubbles.