finite models of gender identity
Neutrali am interested in the discussion of the functioning of gender identity as a serious subject of study.
my interest in this comes from the superimposing of the following observations:
consider that for a biological organism to continue its existence (if it wishes to), it has available to it four or five principle mechanisms:
what i propose then is that any model of a finite number of gender identities is to be derivative from this model, therefore, must apply one or more functions that input a set of previously-constructed gender identities.this is the first meta-model, but does not account for gender-related preferences not accounted for here, which leads to the interesting question of what is missing from this first meta-model.
for example: an easy function to use is simply "juxtaposition", leading to 2^4 - 1 = 15 or less genders depending on if we have well-motivated reason to omit any of the combinations. however, this wouldn't account for asymmetric mixes, so we could recurse once to get something complex but with an extremely symmetrical and easy-to-understand mathematical structure.
i will also note that: importantly, for the purposes of discussion, we will do the rather crude thing of associating the four trivially-obvious pronouns to these four archetypes (1 = it, 2 = she, 3 = he, 4 = they). then we can refer to a gender like [he] (male) or [he+they] (midpoint) or [it/they] ([it] primarily, [they] secondarily), which could be seen as a notation to use for unweighted (midpoint) and weighted (mainly this, less that, less this third thing, ...) combinations.
there is many possible finite sets, all with their own advantages and flaws, that i find interesting, so the purpose of the discussion is instead to focus on what general flaws to disqualify systems by, as well as important the focus on what is missing from the basic premise.
my interest in this comes from the superimposing of the following observations:
- everyone progressive agrees that there is at least 3 genders: male, female and other, with the last either being a placeholder or actually being interpreted as a kind of rhizomatic grouping gender depending on the perspective of the person you're talking to
- many ppl sense something must be wrong with there being an unbound number of gender identities, which itself is evidence of the first point as a common model to use.
- yet almost all progressive ppl agree there is more than 3 valid gender identities, but they can't seem to agree on what that implies necessarily.
- gender identity must be distinct from identity, and that this is the problem leading to (2.).
- we assume a reasonable definition of gender identity as being that which is the preimage of the ideal form of gendered expression. note that this definition has the advantage that if someone is comfortable not gender-expressing themselves in accordance with their gender-identity, it doesn't impact the definition's correctness, and instead refers to a different preference or circumstance. however, it immediately raises the question as to how to measure genderedness as distinct from other measures of identity, to which i propose…
- a pseudo-naturalist explanation based on the following idea: as gender is ultimately the indirect construct of the machinations of biological beings, it should follow that the archetypes are motivated by what those machinations might imply across many possible contexts. fittingly, this is not something that is consistently implied, but rather allows an objective lens through which to analyse what is and isn't gendered. this last point is more controversial likely, so here's where my basic model comes into play.
consider that for a biological organism to continue its existence (if it wishes to), it has available to it four or five principle mechanisms:
- self-replication, or more rarely, immortality, which we will categorise as being of the same essence for simplicity and due to the likely rareness of the latter among biological lifeforms
- female (being able to produce a lifeform from a code, but requiring another code to produce)
- male (being able to give codes without being able to produce a lifeform)
- hermaphrodite (having the capacities of both male and female). in this category we will also count hermaphrodites capable of self-replication, due to the likely rareness of this among biological lifeforms
what i propose then is that any model of a finite number of gender identities is to be derivative from this model, therefore, must apply one or more functions that input a set of previously-constructed gender identities.this is the first meta-model, but does not account for gender-related preferences not accounted for here, which leads to the interesting question of what is missing from this first meta-model.
for example: an easy function to use is simply "juxtaposition", leading to 2^4 - 1 = 15 or less genders depending on if we have well-motivated reason to omit any of the combinations. however, this wouldn't account for asymmetric mixes, so we could recurse once to get something complex but with an extremely symmetrical and easy-to-understand mathematical structure.
i will also note that: importantly, for the purposes of discussion, we will do the rather crude thing of associating the four trivially-obvious pronouns to these four archetypes (1 = it, 2 = she, 3 = he, 4 = they). then we can refer to a gender like [he] (male) or [he+they] (midpoint) or [it/they] ([it] primarily, [they] secondarily), which could be seen as a notation to use for unweighted (midpoint) and weighted (mainly this, less that, less this third thing, ...) combinations.
there is many possible finite sets, all with their own advantages and flaws, that i find interesting, so the purpose of the discussion is instead to focus on what general flaws to disqualify systems by, as well as important the focus on what is missing from the basic premise.
Just Monika
> gender identity must be distinct from identity
Why?
Also? I find it pretty easy to imagine sexless ponies whom still are divided into 'mares' and 'stallions' nonetheless, not even embodying the archetypal image of 'strong, domineering male' by default or whatever. Honestly could think about it for a while and maybe gather something interesting.
Me, personally, I would be fine being a stallion for Twilight. That is all to be said.
I also don't entirely see how 1. connects to the rest of the model properly. Have you seen stuff like the... Genderbread Person? I guess the two-dimensional nature of it might annoy you.
I hate talking about gender because it is stupid. Not in an 'abolish gender' way. I just think it's stupid.
Why?
Also? I find it pretty easy to imagine sexless ponies whom still are divided into 'mares' and 'stallions' nonetheless, not even embodying the archetypal image of 'strong, domineering male' by default or whatever. Honestly could think about it for a while and maybe gather something interesting.
Me, personally, I would be fine being a stallion for Twilight. That is all to be said.
I also don't entirely see how 1. connects to the rest of the model properly. Have you seen stuff like the... Genderbread Person? I guess the two-dimensional nature of it might annoy you.
I hate talking about gender because it is stupid. Not in an 'abolish gender' way. I just think it's stupid.
The artists gave me form, the writers added intelligence, and the fans bestowed purpose. But, above all...
here are some primitive models:
midpoint minimal
[he] [he+they] [they]
[it+he] [it+they]/[she+he] [she+they]
[it] [it+she] [she]
as well as [it+he+they+she] as the midpoint-midpoint.
midpoint maximal adds the following: [it+he+they], [it+she+they], [he+it+she], [he+they+she]
the midpoint maximal model has the advantage that alignments against one or more of the archetypes can be modeled because of the mathematical symmetry of the system; that is, we can simply define ¬gender as the midpoint of all genders not present in the "sum" notation, EG ¬[it+he] = [she+they], then ¬[it+she+they+he] is its own negation both by necessary structure and because if that negation was truly intended, one of [it] (or [it+other] more generally) or [they] (or [they+other] more generally) should (by symmetry) be an admissable alternative, as alternate answers to what exactly is trying to be negated. that is, if the problem is genderedness, [it], while if the problem is ungenderedness, [they].
another model to discuss which is more speculative (due to potentially undermining the point of the exercise) is the preference-ordered system, wherein we have one to four of four primitive categories, hence 4 + 4*3 + 4*3*2 + 4*3*2*1 = 64 categories*. the 4 categories would be [it], [he], [they], [she]. the 4*3 = 12 categories formed from 2 archetypes would thus be visualisable as a 4x4 graph with the 4 primary archetypes in the corners:
he he/they they/he they
he/it he/she they/it they/she
it/he it/they she/he she/they
it it/she she/it she
continued thoughts towards the shape of that which is the target of finitisation by all theories derivative of the aforeproposed basic model
this leads to the interesting question of the dimensionality of the space of the full 64 categories, but *64 might be judged as too many due to being dominated by (what one might call) "preference distributions" [A/B/C/D] that can be simplified by omitting the last entry (=> [A/B/C]), therefore, in practice one would consider 4 + 4*3 + 4*3*2= 40 categories at most, s.t every non-corner category derives two "flavour-variants", which though elaborate, is at least an interesting model.
the synthesis of these two models could be attempted by defining [A+B] as having 1 > A = B > 0 and [A/B] as having 1 > A > B > 0, so any reasonable choice satisfying this should work.
what we want to consider is a normalisation constraint. that is, [A+B] expressed as [A]/2 + /2 should be considered equal to [A] + by principle of normalisation. that is, if we consider the space as 4-dimensional (with axes amount of [it], amount of [he], amount of [they], amount of [she]), we're asserting that any given ratio is to be considered independently. this has the convenient property of allowing counter-ratios to exist. for example, for an [A]::[C]:[D] system, the counter-ratio of 2[A] + is the counter-ratio of 2:1:0:0 which is hence 0:1:2:2, as we maximally-invert the dominant gender identity [A] while maximally-inverting the absent ones to be evenly sharing the space of dominant, therefore the secondary gender identity, , becomes the only thing that persists. that is, the normalisation makes this equal to 1:1/2:0:0 and thereby the inversion is simply 1 minus [value] leading to 0:1/2:1:1. therefore, a trivial way to normalise the system is by constraining the values in the 0 to 1 range s.t the inversion is by definition always trivially available by any complete enumeration (finite categorisation) of the 4D space. then, as discussed, 1:1:1:1 becomes its own inversion, implying the second algebraic constraint. that is, in order for 1:1:1:1 = 0:0:0:0 to be true, we need them to be invalid values somehow, instead preferring some x:x:x:x, which is most obviously either x=1/2 or x=1/4. interestingly the former, which appears intuitive as a symmetry, is actually consistent with a 4D sphere (confusingly called a 3-sphere in literature) as (1/2)^2 * 4 = 1/4 * 4 = 1.
a sixteenth of a 3-sphere (= 4D sphere's surface)
the 4 archetypes thus become the corners of the structure. midpoint minimal adds axis-pairs that are at positions that are a permutation of (1/sqrt(2), 1/sqrt(2), 0, 0), because they lie at a 45-degree angle on a quarter of a circle between those axes. midpoint maximal adds axis-trios that are at positions that are a permutation of (1/sqrt(3), 1/sqrt(3), 1/sqrt(3), 0). therefore we might conveniently consider [A/B] as at (1/2, 1/sqrt(2), 0, 0) by taking advantage of the special angles that are multiples of 30 degrees, but ofc that's just one possible solution, corresponding to a 2:1:0:0 weighting. by contrast, [A/[B+C]] would be at (1/sqrt(2), 1/2, 1/2, 0). if we include all such things, we get 4 possible choices of primary gender identity and 3 possible choices of "shadow" gender (gender that one really does not want to be), leading to 12 choices as expanding the 4 archetypes and the 4*3 = 12 midpoints for those archetypes.
this seems like an interesting model because things that intuitively are most obviously recognisable correspond to obviously interesting coordinates, as we've seen.
midpoint minimal
[he] [he+they] [they]
[it+he] [it+they]/[she+he] [she+they]
[it] [it+she] [she]
as well as [it+he+they+she] as the midpoint-midpoint.
midpoint maximal adds the following: [it+he+they], [it+she+they], [he+it+she], [he+they+she]
the midpoint maximal model has the advantage that alignments against one or more of the archetypes can be modeled because of the mathematical symmetry of the system; that is, we can simply define ¬gender as the midpoint of all genders not present in the "sum" notation, EG ¬[it+he] = [she+they], then ¬[it+she+they+he] is its own negation both by necessary structure and because if that negation was truly intended, one of [it] (or [it+other] more generally) or [they] (or [they+other] more generally) should (by symmetry) be an admissable alternative, as alternate answers to what exactly is trying to be negated. that is, if the problem is genderedness, [it], while if the problem is ungenderedness, [they].
another model to discuss which is more speculative (due to potentially undermining the point of the exercise) is the preference-ordered system, wherein we have one to four of four primitive categories, hence 4 + 4*3 + 4*3*2 + 4*3*2*1 = 64 categories*. the 4 categories would be [it], [he], [they], [she]. the 4*3 = 12 categories formed from 2 archetypes would thus be visualisable as a 4x4 graph with the 4 primary archetypes in the corners:
he he/they they/he they
he/it he/she they/it they/she
it/he it/they she/he she/they
it it/she she/it she
continued thoughts towards the shape of that which is the target of finitisation by all theories derivative of the aforeproposed basic model
this leads to the interesting question of the dimensionality of the space of the full 64 categories, but *64 might be judged as too many due to being dominated by (what one might call) "preference distributions" [A/B/C/D] that can be simplified by omitting the last entry (=> [A/B/C]), therefore, in practice one would consider 4 + 4*3 + 4*3*2= 40 categories at most, s.t every non-corner category derives two "flavour-variants", which though elaborate, is at least an interesting model.
the synthesis of these two models could be attempted by defining [A+B] as having 1 > A = B > 0 and [A/B] as having 1 > A > B > 0, so any reasonable choice satisfying this should work.
what we want to consider is a normalisation constraint. that is, [A+B] expressed as [A]/2 + /2 should be considered equal to [A] + by principle of normalisation. that is, if we consider the space as 4-dimensional (with axes amount of [it], amount of [he], amount of [they], amount of [she]), we're asserting that any given ratio is to be considered independently. this has the convenient property of allowing counter-ratios to exist. for example, for an [A]::[C]:[D] system, the counter-ratio of 2[A] + is the counter-ratio of 2:1:0:0 which is hence 0:1:2:2, as we maximally-invert the dominant gender identity [A] while maximally-inverting the absent ones to be evenly sharing the space of dominant, therefore the secondary gender identity, , becomes the only thing that persists. that is, the normalisation makes this equal to 1:1/2:0:0 and thereby the inversion is simply 1 minus [value] leading to 0:1/2:1:1. therefore, a trivial way to normalise the system is by constraining the values in the 0 to 1 range s.t the inversion is by definition always trivially available by any complete enumeration (finite categorisation) of the 4D space. then, as discussed, 1:1:1:1 becomes its own inversion, implying the second algebraic constraint. that is, in order for 1:1:1:1 = 0:0:0:0 to be true, we need them to be invalid values somehow, instead preferring some x:x:x:x, which is most obviously either x=1/2 or x=1/4. interestingly the former, which appears intuitive as a symmetry, is actually consistent with a 4D sphere (confusingly called a 3-sphere in literature) as (1/2)^2 * 4 = 1/4 * 4 = 1.
a sixteenth of a 3-sphere (= 4D sphere's surface)
the 4 archetypes thus become the corners of the structure. midpoint minimal adds axis-pairs that are at positions that are a permutation of (1/sqrt(2), 1/sqrt(2), 0, 0), because they lie at a 45-degree angle on a quarter of a circle between those axes. midpoint maximal adds axis-trios that are at positions that are a permutation of (1/sqrt(3), 1/sqrt(3), 1/sqrt(3), 0). therefore we might conveniently consider [A/B] as at (1/2, 1/sqrt(2), 0, 0) by taking advantage of the special angles that are multiples of 30 degrees, but ofc that's just one possible solution, corresponding to a 2:1:0:0 weighting. by contrast, [A/[B+C]] would be at (1/sqrt(2), 1/2, 1/2, 0). if we include all such things, we get 4 possible choices of primary gender identity and 3 possible choices of "shadow" gender (gender that one really does not want to be), leading to 12 choices as expanding the 4 archetypes and the 4*3 = 12 midpoints for those archetypes.
this seems like an interesting model because things that intuitively are most obviously recognisable correspond to obviously interesting coordinates, as we've seen.
Just Monika
expanding on that the preference distribution create too many categories, one can simplify further, using the observation that [A/[B+C]] has convenient coordinates (1/sqrt(2), 1/2, 1/2, 0) s.t it can represent the "weighted sum-average" of the following niche gender identities: [A/B/C], [A/C/B], [A/[B+C]], [A+¬D]. it should be noted that the last choice is significant theoretically as corresponding to choosing a gender identity to be and a gender identity to not be. therefore, it expands the midpoint systems in a logical and significant way, while creating grounding for the divide between "strongly felt binary gender identities" and "less strongly felt binary gender identities". for example, my subjective sense of gender identity is something like [he + it + ¬her] or [he + ¬her], so likely [he/it + ¬her].
in regards to the genderbread person model, i'd like to offer that i am specifically modelling gender identity under the guidance of the following ideas:
in regards to the genderbread person model, my concern is im not quite sure i understand what the motivation of a distinction between gender identity and "sex gender" is, which is also explainable from the perspective of the assumptions of my model, so it'd be a good point to address to try to assess potential blindspots.
in regards to the genderbread person model, i'd like to offer that i am specifically modelling gender identity under the guidance of the following ideas:
- the deliberate omission of the complex landscape of forces of sexual and romantic attraction generally. i deliberately posit that any such model should be an abstraction over a more fundamental model of gender identity, as that would be its logical relation insofar as it concerns gender at all, as the gendered component of the attraction would be attraction to some combination of the gender identity and the various possible gendered expressions, which themselves are by construction to be derivative of the gender identity. (but also, my personal interpretation and observation is that attraction is basically a complete mess in humans.)
- the deliberate omission of the complex landscape of expressions of gender identity, which by definition, is (up to whether, how and why one cares about expression conformant to one's gender identity) equal to the full measure of expression categorisable as gendered (strictly gender-related). (one could also observe that this landscape is similarly very messy, but has some common cross-cultural themes to do with humanity's history as a species, which helps with potential concretisation of what im modelling.)
- in following with the themes of the last two points of clarification, the deliberate abstraction of sexual characteristics into archetypes.
in regards to the genderbread person model, my concern is im not quite sure i understand what the motivation of a distinction between gender identity and "sex gender" is, which is also explainable from the perspective of the assumptions of my model, so it'd be a good point to address to try to assess potential blindspots.
Just Monika
enumeration of algebraically-convenient coordinates (as arbitrary representatives of broader ambiguous ranges up to symmetries) and speculative notations for corresponding gender identities.
firstly, the obviously-easy-to-define are the archetypes and the midpoint maximal system, as this system contains its own inversions. let (A, B, C, D) be any arbitrary permutation of ([it], [she], [he], [they]). then we have...
[it] = (1, 0, 0, 0), [she] = (0, 1, 0, 0), [he] = (0, 0, 1, 0), [they] = (0, 0, 0, 1).
...as the unabstracted expression of [A] = (1, 0, 0, 0). to see what i mean by this, let's look at the abstracted and unabstracted expressions of the midpoint minimal model:
[A+B] = (1/sqrt(2), 1/sqrt(2), 0, 0) yields:
[it+she] = (1/sqrt(2), 1/sqrt(2), 0, 0), [it+he] = (1/sqrt(2), 0, 1/sqrt(2), 0), [it+they] = (1/sqrt(2), 0, 0, 1/sqrt(2)),
[she+he] = (0, 1/sqrt(2), 1/sqrt(2), 0), [she+they] = (0, 1/sqrt(2), 0, 1/sqrt(2)), [he+they] = (0, 0, 1/sqrt(2), 1/sqrt(2))
so here we see that we can derive how many categories a general form takes from observing the basic combinatorics of counting the number of permutations of its coordinates.
thus, trivially, we have 4 more coordinates from the 4 positions that 0 could be in in [A+B+C] = (1/sqrt(3), 1/sqrt(3), 1/sqrt(3), 0), and 1 coordinate from [A+B+C+D] = (1/2, 1/2, 1/2, 1/2).
in order to expand this set, one would need to consider what is most obviously missing. not wanting to be certain gender identities is one such example. the problem is answering the question of where it's missing, as by symmetry we have [¬A] = [B+C+D] and [¬A+¬B] = [C+D]. therefore, what's missing might instead be distillations of preference-strength. observe that what we're modelling here is a kind of symmetry existing on the sixteenth of a 3-sphere, that of the symmetries of its coordinates, so technically this might be related indirectly to group theory, a discipline i've always wanted to study, given the themes of permutations and defining new systems by invariants on systems with higher dimension.
in other words, what we did earlier is reject the group of symmetries [A/B/C/D] = (x, y, z, w) with x > y > z > w and x^2 + y^2 + z^2 + w^2 = 1 as being an "overnuanced" alternative [A/B/C] (the solution where w=0) or [A/[B+C]] (the solution where additionally we have y=z).
but as an exercise, we would have 4! = 4*3*2*1 = 24 gender identities in the unabstracted expression generated by the abstracted expression [A/B/C/D], and for the same reason (symmetry), we have 24 gender identities generated by [A/B/C], so as this is quite a lot, we should consider whether we can find symmetries somewhere else in the system, though as a mathematical exercise of completeness, i do also want to enumereate all the possible symmetries, to see how much fat we have to trim in the first place, as well as out of interest for the structure of the mathematical object.
the mathematical object
essentially, we are to consider 1 > x > y > z > w > 0 under the constraint that x^2 + y^2 + z^2 + w^2 = 1. at each step, we can either choose = or >. we can therefore enumerate all subfamilies of symmetries systematically:
1=x yields 4 symmetries (archetypes), forcing 1=x > y=z=w=0. therefore all other alternatives are 1 > x, so we can consider 1 = x > y > z > w > 0 as being a special case of the more general structure 1 > x > y > z > w > 0. that gives 2^4 = 16 possibilities, but as we have w = 0 at the end as potentially introducing pathology, we must observe where that pathology eliminates options, and the only such cases are 1 > x > y = z = w = 0 (as that's a degenerate version of 1 = x case) and 1 > x = y = z = w = 0 (as that's a degenerate version of the 1 > x = y = z = w > 0 case), implying 14 possibilities. we can enumerate these via binary counting using = as 0 and > as 1:
A=B=C=D= (omitted)
A=B=C=D> (omnigender [A+B+C+D]; part of maximal midpoint system)
A=B=C>D= (not [gender] AKA [A+B+C]=[¬D]; part of maximal midpoint system)
A=B=C>D> (not [gender] (specifically [¬D]) with a nonstrong preference: [[A+B+C]/D])
A=B>C=D= (midpoint [A+B]; part of maximal midpoint system)
A=B>C=D> ([[A+B]/[C+D]] AKA [A+B] with nonstrong preference)
A=B>C>D= ([[A+B]/C])
A=B>C>D> ([[A+B]/C/D] which i wonder if should be equated with [[A+B]/C])
A>B=C=D= (the 4 archetypes [A]!)
A>B=C=D> ([A/[B+C+D]] AKA [A] with a nonstrong preference; part of an "other"-based extension of the minimal preference-ordered system)
A>B=C>D= ([A/[B+C]] AKA [A+¬D])
A>B=C>D> ([A/[B+C]/D] AKA [A+¬D] with a nonstrong preference)
A>B>C=D= ([A/B]; part of the minimal preference-ordered system)
A>B>C=D> ([A/B/[C+D]] AKA [A/B] with a nonstrong preference)
A>B>C>D= ([A/B/C]; part of the minimal preference-ordered system)
A>B>C>D> ([A/B/C/D] AKA [A/B/C] with a nonstrong preference; part of the minimal preference-ordered system)
firstly, the obviously-easy-to-define are the archetypes and the midpoint maximal system, as this system contains its own inversions. let (A, B, C, D) be any arbitrary permutation of ([it], [she], [he], [they]). then we have...
[it] = (1, 0, 0, 0), [she] = (0, 1, 0, 0), [he] = (0, 0, 1, 0), [they] = (0, 0, 0, 1).
...as the unabstracted expression of [A] = (1, 0, 0, 0). to see what i mean by this, let's look at the abstracted and unabstracted expressions of the midpoint minimal model:
[A+B] = (1/sqrt(2), 1/sqrt(2), 0, 0) yields:
[it+she] = (1/sqrt(2), 1/sqrt(2), 0, 0), [it+he] = (1/sqrt(2), 0, 1/sqrt(2), 0), [it+they] = (1/sqrt(2), 0, 0, 1/sqrt(2)),
[she+he] = (0, 1/sqrt(2), 1/sqrt(2), 0), [she+they] = (0, 1/sqrt(2), 0, 1/sqrt(2)), [he+they] = (0, 0, 1/sqrt(2), 1/sqrt(2))
so here we see that we can derive how many categories a general form takes from observing the basic combinatorics of counting the number of permutations of its coordinates.
thus, trivially, we have 4 more coordinates from the 4 positions that 0 could be in in [A+B+C] = (1/sqrt(3), 1/sqrt(3), 1/sqrt(3), 0), and 1 coordinate from [A+B+C+D] = (1/2, 1/2, 1/2, 1/2).
in order to expand this set, one would need to consider what is most obviously missing. not wanting to be certain gender identities is one such example. the problem is answering the question of where it's missing, as by symmetry we have [¬A] = [B+C+D] and [¬A+¬B] = [C+D]. therefore, what's missing might instead be distillations of preference-strength. observe that what we're modelling here is a kind of symmetry existing on the sixteenth of a 3-sphere, that of the symmetries of its coordinates, so technically this might be related indirectly to group theory, a discipline i've always wanted to study, given the themes of permutations and defining new systems by invariants on systems with higher dimension.
in other words, what we did earlier is reject the group of symmetries [A/B/C/D] = (x, y, z, w) with x > y > z > w and x^2 + y^2 + z^2 + w^2 = 1 as being an "overnuanced" alternative [A/B/C] (the solution where w=0) or [A/[B+C]] (the solution where additionally we have y=z).
but as an exercise, we would have 4! = 4*3*2*1 = 24 gender identities in the unabstracted expression generated by the abstracted expression [A/B/C/D], and for the same reason (symmetry), we have 24 gender identities generated by [A/B/C], so as this is quite a lot, we should consider whether we can find symmetries somewhere else in the system, though as a mathematical exercise of completeness, i do also want to enumereate all the possible symmetries, to see how much fat we have to trim in the first place, as well as out of interest for the structure of the mathematical object.
the mathematical object
essentially, we are to consider 1 > x > y > z > w > 0 under the constraint that x^2 + y^2 + z^2 + w^2 = 1. at each step, we can either choose = or >. we can therefore enumerate all subfamilies of symmetries systematically:
1=x yields 4 symmetries (archetypes), forcing 1=x > y=z=w=0. therefore all other alternatives are 1 > x, so we can consider 1 = x > y > z > w > 0 as being a special case of the more general structure 1 > x > y > z > w > 0. that gives 2^4 = 16 possibilities, but as we have w = 0 at the end as potentially introducing pathology, we must observe where that pathology eliminates options, and the only such cases are 1 > x > y = z = w = 0 (as that's a degenerate version of 1 = x case) and 1 > x = y = z = w = 0 (as that's a degenerate version of the 1 > x = y = z = w > 0 case), implying 14 possibilities. we can enumerate these via binary counting using = as 0 and > as 1:
A=B=C=D= (omitted)
A=B=C=D> (omnigender [A+B+C+D]; part of maximal midpoint system)
A=B=C>D= (not [gender] AKA [A+B+C]=[¬D]; part of maximal midpoint system)
A=B=C>D> (not [gender] (specifically [¬D]) with a nonstrong preference: [[A+B+C]/D])
A=B>C=D= (midpoint [A+B]; part of maximal midpoint system)
A=B>C=D> ([[A+B]/[C+D]] AKA [A+B] with nonstrong preference)
A=B>C>D= ([[A+B]/C])
A=B>C>D> ([[A+B]/C/D] which i wonder if should be equated with [[A+B]/C])
A>B=C=D= (the 4 archetypes [A]!)
A>B=C=D> ([A/[B+C+D]] AKA [A] with a nonstrong preference; part of an "other"-based extension of the minimal preference-ordered system)
A>B=C>D= ([A/[B+C]] AKA [A+¬D])
A>B=C>D> ([A/[B+C]/D] AKA [A+¬D] with a nonstrong preference)
A>B>C=D= ([A/B]; part of the minimal preference-ordered system)
A>B>C=D> ([A/B/[C+D]] AKA [A/B] with a nonstrong preference)
A>B>C>D= ([A/B/C]; part of the minimal preference-ordered system)
A>B>C>D> ([A/B/C/D] AKA [A/B/C] with a nonstrong preference; part of the minimal preference-ordered system)
Just Monika
concretisation of theory into a justification for MMS
so, i'd like to observe a fairly natural progression of increasingly high-resolution sets of N categories (crude general-purpose rhizomatic gender identities) that doesn't seem to originate from anywhere in particular that i considered in the past, where in case it was glossed over we use the notation [expression] to denote a gender identity in such a way that its relation to the 4 archetypes is described using the 4 archetypes' standard pronouns:
3: female = [she], male = [he], both/neither/ambiguous/other = [they];
4: almost same as 3 but plus an identity absent of genderedness & fine with (or self-conceptualising in tandem with) absence of sexuality in mind and body ([it]), AKA the 4 archetype system [it], [she], [he], [they];
6 (v1): same as 4 but plus two imbetween genders: [she+they] (crudely*, masculine girl) and [they+he] (crudely*, feminine boy); (*where we note that these descriptions are ofc misleading as being misinterpretable by english language convention as descriptions of [she] and [he], which they would have to be simplified to in the case of 3 and 4 (or else be simplified to [they]).)
5: though this isn't intended as a serious model, being the same as 6 (v1) but removing the [it] category artificially, it's theoretically notable as being a discretisation of a "male-to-female" spectrum to 5 points, which therefore (like the 3 gender identity system) can be conceptualised as either occurring in one dimension (crudely) or two dimensions (accounting for they being separate to [he+she]);
it is at this stage that i want to observe that in terms of archetypes, [they] is materialistically definitionally equivalent to [he+she] s.t it is expected to inherit attributes of both archetypes while developing its own characteristics due to unique material implications of its construction. therefore, it is a common theme in all systems i propose for there to be ambiguity as to whether [it], [she], [they], [he] are corners of a square or whether [it], [she], [he] are corners of a triangle and [they] is the midpoint of [she] and [he], because remember importantly that midpoint genders of the Maximal Midpoint System are not merely "averages" of the genders they are midpoints of, because it is expected that there is both a component of the identity that does work like a superset or blend of the components and that there is a component that arises from the unique social, sexual, cultural, etc. conditions of the uniqueness of its identity as contrasted to these components. with this in mind, and with the observation of this ambiguity, there is an alternative 6-category system:
6 (v2): {[it], [it+she], [she], [they], [he], [he+it]}; (where we can notice that [they] is structured as though it's derived purely as [she+he], though ofc notwithstanding the considerations about the dynamics of midpoint definitions aforedescribed. a related system is to include an [all] "superfluid"-esque "omni" gender, leading to...)
7 (v2): the same as 6 (v2) but adding [it+she+he] = [all];
7 (v1): the same as 6 (v1) but adding [it+she+they+he] = [all].
at this point the systems get a little more complex, because we start having to think more carefully and explicitly about the kinds of dimensions implicit in the set of gender identities being proposed. what i observe is that up to gendered expression not conformant with one's gender identity (whether by preference or misfortune), we essentially have a three-dimensional space, which is consistent with the 3-sphere, but it's not immediately clear what the dimensions are. it is clear that two of those dimensions concern the square (or triangle) made by {[it], [she], ([they],) [he]}, so we clearly have a masculine-to-feminine dimension (which we will observe henceforth as taking 5 values s.t the 5 category system describes a higher-accuracy phenomena) and what we might crudely describe as an ungendered-to-gendered dimension ([it] to [they]). in other words, all the systems henceforths will explicitly be extensions of 6 (v1) = 5 + [it]. the first observation we can make is that it is common and practical to distinguish between gender identity [they] and the [all] gender identity, but that the definitions vary between the two 7 category systems, due to the ambiguous relation of [they] to [she] and [he] caused by analysing closely the axioms of the basic model introduced in the first post. therefore, one might deliberately omit the definition of [all], leaving it ambiguous as an omni/maximally fluid gender. the second observation, going back to the beginning of this paragraph, is that there is a dimension of fluidity of gender, in the sense of the capacity for comfortable gender-conformant expression to vary, and the ways in which it varies, and between what archetypes (because remember we are deliberately abstracting as many details out of finite models of gender identity as possible, to allow those details to naturally inform the usage and understanding of those categories), wherein we can see something like a tiered progression [it], [he]/[she], [he+they]/[they]/[they+she], [all]. therefore the third dimension is what i call fluidity.
with all of this in mind... an obvious system to consider is a merge of all the most elaborate systems discussed so far, which is really only 2 systems:
7 (v1) = 6 (v1) + [all] = { [it], [she], [she+they], [they], [they+he], [he] } + { [all] }
7 (v2) = 6 (v2) + [all] = { [it], [it+she], [she], [they], [he], [he+it] } + { [all] }
between these systems we have { [it], [she], [they], [he], [all] } in common, for a total of 7 + 7 - 5 = 9 categories, which can be organised like so:
[he] [he+they] [they]
[it+he] [all] [she+they]
[it] [it+she] [she]
note that this system has the convenient property of having a 2D diagram where the "fluidity" is the distance from the centre category. especially note that this is also true if we skew the diagram into the shape of a triangle with corners { [it], [she], [he] }. this is a very elegant system that is surprisingly minimal, though it doesnt make a distinction between [it+they] and [all], though im also not sure whether such a distinction is warranted. it should be noted that iirc i came across this system before but it seemed "too trivial to be true" due to its extreme elegance of structure (for example notice it has the symmetries of 8 equidistant points on a circle plus a central point that is its own point of symmetry).
(tangentially, in regards to symmetry, it makes me wonder about other studies of symmetry adjacent to group theory; for example, what operations does a circle with 2n equidistant points plus a central point have? everything has an inverse but there is no "operation" to speak of, but rather something like a graphlike relation or adjacency function.)
so, i'd like to observe a fairly natural progression of increasingly high-resolution sets of N categories (crude general-purpose rhizomatic gender identities) that doesn't seem to originate from anywhere in particular that i considered in the past, where in case it was glossed over we use the notation [expression] to denote a gender identity in such a way that its relation to the 4 archetypes is described using the 4 archetypes' standard pronouns:
3: female = [she], male = [he], both/neither/ambiguous/other = [they];
4: almost same as 3 but plus an identity absent of genderedness & fine with (or self-conceptualising in tandem with) absence of sexuality in mind and body ([it]), AKA the 4 archetype system [it], [she], [he], [they];
6 (v1): same as 4 but plus two imbetween genders: [she+they] (crudely*, masculine girl) and [they+he] (crudely*, feminine boy); (*where we note that these descriptions are ofc misleading as being misinterpretable by english language convention as descriptions of [she] and [he], which they would have to be simplified to in the case of 3 and 4 (or else be simplified to [they]).)
5: though this isn't intended as a serious model, being the same as 6 (v1) but removing the [it] category artificially, it's theoretically notable as being a discretisation of a "male-to-female" spectrum to 5 points, which therefore (like the 3 gender identity system) can be conceptualised as either occurring in one dimension (crudely) or two dimensions (accounting for they being separate to [he+she]);
it is at this stage that i want to observe that in terms of archetypes, [they] is materialistically definitionally equivalent to [he+she] s.t it is expected to inherit attributes of both archetypes while developing its own characteristics due to unique material implications of its construction. therefore, it is a common theme in all systems i propose for there to be ambiguity as to whether [it], [she], [they], [he] are corners of a square or whether [it], [she], [he] are corners of a triangle and [they] is the midpoint of [she] and [he], because remember importantly that midpoint genders of the Maximal Midpoint System are not merely "averages" of the genders they are midpoints of, because it is expected that there is both a component of the identity that does work like a superset or blend of the components and that there is a component that arises from the unique social, sexual, cultural, etc. conditions of the uniqueness of its identity as contrasted to these components. with this in mind, and with the observation of this ambiguity, there is an alternative 6-category system:
6 (v2): {[it], [it+she], [she], [they], [he], [he+it]}; (where we can notice that [they] is structured as though it's derived purely as [she+he], though ofc notwithstanding the considerations about the dynamics of midpoint definitions aforedescribed. a related system is to include an [all] "superfluid"-esque "omni" gender, leading to...)
7 (v2): the same as 6 (v2) but adding [it+she+he] = [all];
7 (v1): the same as 6 (v1) but adding [it+she+they+he] = [all].
at this point the systems get a little more complex, because we start having to think more carefully and explicitly about the kinds of dimensions implicit in the set of gender identities being proposed. what i observe is that up to gendered expression not conformant with one's gender identity (whether by preference or misfortune), we essentially have a three-dimensional space, which is consistent with the 3-sphere, but it's not immediately clear what the dimensions are. it is clear that two of those dimensions concern the square (or triangle) made by {[it], [she], ([they],) [he]}, so we clearly have a masculine-to-feminine dimension (which we will observe henceforth as taking 5 values s.t the 5 category system describes a higher-accuracy phenomena) and what we might crudely describe as an ungendered-to-gendered dimension ([it] to [they]). in other words, all the systems henceforths will explicitly be extensions of 6 (v1) = 5 + [it]. the first observation we can make is that it is common and practical to distinguish between gender identity [they] and the [all] gender identity, but that the definitions vary between the two 7 category systems, due to the ambiguous relation of [they] to [she] and [he] caused by analysing closely the axioms of the basic model introduced in the first post. therefore, one might deliberately omit the definition of [all], leaving it ambiguous as an omni/maximally fluid gender. the second observation, going back to the beginning of this paragraph, is that there is a dimension of fluidity of gender, in the sense of the capacity for comfortable gender-conformant expression to vary, and the ways in which it varies, and between what archetypes (because remember we are deliberately abstracting as many details out of finite models of gender identity as possible, to allow those details to naturally inform the usage and understanding of those categories), wherein we can see something like a tiered progression [it], [he]/[she], [he+they]/[they]/[they+she], [all]. therefore the third dimension is what i call fluidity.
with all of this in mind... an obvious system to consider is a merge of all the most elaborate systems discussed so far, which is really only 2 systems:
7 (v1) = 6 (v1) + [all] = { [it], [she], [she+they], [they], [they+he], [he] } + { [all] }
7 (v2) = 6 (v2) + [all] = { [it], [it+she], [she], [they], [he], [he+it] } + { [all] }
between these systems we have { [it], [she], [they], [he], [all] } in common, for a total of 7 + 7 - 5 = 9 categories, which can be organised like so:
[he] [he+they] [they]
[it+he] [all] [she+they]
[it] [it+she] [she]
note that this system has the convenient property of having a 2D diagram where the "fluidity" is the distance from the centre category. especially note that this is also true if we skew the diagram into the shape of a triangle with corners { [it], [she], [he] }. this is a very elegant system that is surprisingly minimal, though it doesnt make a distinction between [it+they] and [all], though im also not sure whether such a distinction is warranted. it should be noted that iirc i came across this system before but it seemed "too trivial to be true" due to its extreme elegance of structure (for example notice it has the symmetries of 8 equidistant points on a circle plus a central point that is its own point of symmetry).
(tangentially, in regards to symmetry, it makes me wonder about other studies of symmetry adjacent to group theory; for example, what operations does a circle with 2n equidistant points plus a central point have? everything has an inverse but there is no "operation" to speak of, but rather something like a graphlike relation or adjacency function.)
Just Monika
so under the enlightening observation that in theory someone might wanna kill me if i proposed this 9 category seriously, it seems that at least [she+he] and [it+they] are missing (when we compare to the arcane 2^4 - 1 = 15-category system), with the former being androgyne and the latter being (when expressed) complete gendered departure from gendered expression inherited from sexual dimorphism in general due to a felt category error, with the latter admittedly being a slight misnotation/category error as it's the closest to being an [other] category, so should be considered in terms of the (relative to binary gender) alienness of [they] (which might in practice be felt more as a sociocultural-aesthetical queer phenomenon when expressed) and [it] (which i feel doesnt need explanation due to archetypal self-evidentness, as explanation would itself imply a kind of imposed gendered expression unbefitting of its archetype, s.t it's defined by contrast). this is interesting because this is almost identical to the aforeproposed midpoint minimal system except we manually add a a special distinguished gender identity/category [all] (superfluidity) as distinct from [it+they] (xeno-/apora-), [she+he] (androgyne) and [they] (hermaphrodite, queer-leaning) simultaneously, so could be considered midpoint minimal+ due to the implied (and by symmetry arguably potentially necessary) midpoint of everything that is the negation of [it].
Just Monika