A Multi-Dimensional Gender Spectrum
Lies, Damned Lies, and Statistics
“Therefore shoddy and inept application of words lays siege to the intellect in wondrous ways.” Francis Bacon
Truer words were never spoken. But they are of particular relevance to the whole transgender clusterfuck which is characterized by pretty much everyone engaging in those “shoddy and inept” uses of words. And particularly so in the rather unedifying and quite enervating squabbles over how to define “sex” and “gender”. Misuses there which are almost criminally negligent and ideologically incoherent, particularly when peddled by various so-called biologists and philosophers — like
, , , , and Alex Byrne — who should know better. Motivated or sloppy “reasoning” as far as the eye can see, the upshot of which is a pervasively toxic “battle royale” of truly epic proportions. No wonder then that there’s some reason to argue — as did and Helen Joyce — that transgenderism is something of a “civilization-threatening” if not “civilization-ending movement”.So this post is, once again, an attempt to separate wheat and chaff, notably in trying, gamely, to “steelman” the concept of “gender” by developing and illustrating the idea of a multi-dimensional gender spectrum. And the “texts” for that “lesson” will largely consist of a couple of quite illuminating articles (here, & here) by one Janet Shibley Hyde — professor, emeritus, of psychology at the University of Wisconsin — or by her and a merry band of (other) feminist ideologues. Although there are still a great many useful insights and perspectives therein.
But, as a start to unraveling that Gordian Knot, the proximate cause for that quote of old Sir Francis was a recent post at Reality’s Last Stand by
and Lisa Littman which described their objections to a challenge to their ROGD thesis by Jack Turban. Bit of a dog’s breakfast all around, but Sapir and Littman quote some useful bits & pieces from the “US Transgender Survey [2015]”, published under the rather tarnished auspices of Harvard University, which highlight some profoundly inconsistent, incoherent, and quite unscientific definitions for both sex and gender. To wit:3.1 At about what age did you begin to feel that your gender was “different” from your assigned birth sex? [pg. 259]
Of course they’re “different” since, by the more scientifically credible perspectives and definitions from the late great US Justice Anton Scalia [note, pg. 157], from
of Genspect fame [see their Glossary], and even from Wikipedia’s article on Gender, they’re entirely different kettles of fish. In their lexicons, “gender” generally refers to sexually dimorphic — i.e., feminine and masculine — behaviours, personalities, and stereotypes typical of, but not unique to, human males and females, whereas “sex” generally refers only to a very limited subset of reproductive abilities or aspects thereof.But it seems that Harvard and the authors of that Survey — the “National Center for Transgender Equality” which might reasonably be thought to have some “biases” — don’t know whether they’re on foot or horseback since they frequently use “sex” and “gender” as synonyms:
This included, for example, respondents who indicated in Q. 2.1 that the gender on their original birth certificate was female ... [pg. 60]
Respondents were required to select one response to the question about the sex listed on their original birth certificate in Q. 2.1 — either “female” or “male” — in order to proceed ... [pg. 60]
Though even Turban apparently gives some indication of recognizing a fundamental dichotomy there:
Participants were asked the age at which they first realized their gender identity was different than societal expectations based on their sex assigned at birth …
Seems rather clear that he and his co-authors at least differentiate between sex — even if they’re apparently clueless or pigheadedly ignorant about standard biological definitions (lot of that goin’ round these days) — and the “social expectations” of behaviour — AKA, gender — that “normally” attend membership in the biological categories of “male” and “female”. For instance, Turban, writing in the sadly misnamed Scientific American some three years earlier about how “Trans Girls Belong on Girls’ Sports Teams”, argued that:
It turns out that when transgender girls play on girls’ sports teams, cisgender girls can win. In fact, the vast majority of female athletes are cisgender, as are the vast majority of winners. There is no epidemic of transgender girls dominating female sports.
Though it kind of raises a question as to which sex category he “thinks” those “transgender girls” are members of. And whether he “thinks” sports should be segregated by sex — nominal or actual — or by “social expectations” or by the cuts of our jibs ... 🤔🙄
Categories, imperatives, and all that:
However, pretty much all of that is due to a general carelessness — to some “shoddy & inept” language, if not cluelessness on virtually all sides of the fence — about the profound differences between the traits that must be present to qualify individuals as members of particular categories, and those that are merely typical of, but not unique to, members of different categories.
For example, most people don’t seem to have much of a problem in recognizing that, regardless of how we define “man” and “woman” — regardless of what is “essential” to qualify as members of those categories — their heights are irrelevant to that question. While men are, on average, some 4” [10 cm.] taller that women, that does not change the fact that some women are still taller than some men — about 40% in each case in fact. Nor do most people seem to have any problem in recognizing that it is essential to be 13 to 19 to qualify as a teenager, and that “race, creed, and colour” is totally irrelevant to any determination of “teenagerness”. As I’ve argued elsewhere — reprising a useful conversation I’ve had with
, the mother of a dysphoric teenage daughter — height is an “accidental” property of the categories “man” and “woman”, and “race, creed, and colour” are likewise accidental properties of the category “teenager”.However, that understanding seems to get lost when we consider all of the personalities, personality types, behaviours, expressions, and social roles that, as indicated above, generally fall into the categories of masculine and feminine genders — the infamous “gender binary”. And particularly when given traits or properties are not at all unique, not “essential” to a given category. For an example illustrated in the following table, if it were the case that 60% of women could be described as “agreeable” (green) and the balance of 40% as “disagreeable” (light red) and only 40% and 60% of the men could be described likewise then it would still follow that some 40% of the men are more agreeable than 40% of the women:
In which case we can, and then do say that “agreeableness” is a more “feminine” trait than a “masculine” one. From which it necessarily follows that some “man” exhibiting untoward levels of agreeableness is clearly “gender non-conforming” if not shading off into the outer darkness — clearly beyond the pale — of being “transgender” …
But that is more or less exactly what the following more scientifically justified population distribution of agreeableness versus sex is saying: women are, on average, more agreeable than men. If we say that the cross-over point (at about 3.8) on the two plots for each sex of prevalence — “Density” on the vertical axis — versus degree — “Agreeableness” on the horizontal axis — is the dividing line between “agreeable” and “disagreeable” then it should be manifestly obvious that there are many more agreeable women than there are agreeable men. Although it should be equally clear that there are still a bunch of “disagreeable” women (surprise, surprise), i.e., those on the left-hand side of the dividing line:
But problems arise — growing like dragon’s teeth — because many people — like Matt Walsh, and other scientifically illiterate grifters, charlatans, & political opportunists — seem to think that that particular stereotypical behaviour, and many other similar ones, are essential and defining traits of the categories “man” and “woman”. They seem to “think” that if some man isn’t out raping and pillaging — sadly, a rather stereotypical male behaviour — then he too is beyond the pale, and doesn’t qualify as a “real man (tm)”. But all of that really isn’t very helpful at all, particularly for adjudicating claims for access to facilities and opportunities like toilets, change rooms, and sports leagues: will we have one set of toilets for the “agreeables”, and another set for the “disagreeables”?
Which is why there are a great many scientifically, logically, philosophically, and biologically justified reasons for boiling the definitions for the sexes down into the bare minimum and most essential set of traits that cover the largest number of species. The question, a rather “pregnant” one in fact, is, which traits are common to ALL females, and to ALL males of ALL anisogamous species? For examples, see Paul Griffiths’ “What are biological sexes?”, and a Wiley Online Library article which emphasizes the “problematic” conclusions which follow from those definitions. As Griffiths cogently puts it in a quote of evolutionary biologist, and transwoman, Joan Roughgarden:
But no general definition of sexes can rely on these features [chromosomes, hormones, & sex organs] because, as Roughgarden puts it, “the criteria for classifying an organism as male or female have to work with worms to whales, with red seaweed to redwood trees.”
But once we have a solid definition — and sets of defining or “essential” criteria — for the “male” and “female” sex categories we are then in a position of being able to ask which other traits are more or less typical of, though not necessarily unique to, each of those sexes. “Sexual dimorphism” writ large, a topic and idea which has far reaching consequences of rather profound social and psychological import. As biologists Parker [with an FRS to his name] and Lehtonen put it in the Abstract of their “Gamete competition, gamete limitation, and the evolution of the two sexes”:
Biologically, males are defined as the sex that produces the smaller gametes (e.g. sperm) [females similarly defined as the sex that produces the larger gametes; see their Glossary] …. The ancestral divergence and maintenance of gamete sizes subsequently led to many other differences we now observe between the two sexes, sowing the seeds for what we have become.
Sexual Dimorphism:
However, while the ramifications of those biological definitions seem to be stickier wickets for some [
, , , & “biologist” PZ. Myers] than for others — and which I or others have discussed in some detail elsewhere [here, here, here, & here] — the issue of sexual dimorphism is substantially more relevant to the topic at hand, i.e., how it justifies viewing gender as something of a multi-dimensional spectrum. Although, somewhat en passant, the stumbling block for those particular “usual suspects” is their rather desperate, and quite unscientific, insistence on turning the sexes into identities rather than labels for particular reproductive abilities — past, present, or future depending on whether one favours folk-biology, or the more durable and useful scientific definitions.But while there is actually a great deal of merit in that idea of a gender spectrum, the way it has been presented or (mis)interpreted has tended to preclude or vitiate its benefits. For instance, Substackers
& have exercised great wroth — with some justification — over Mermaids’ “Gender Identity Spectrum”:
Though their “confusion”, and that of too many others, seems to be due to pervasively contradictory definitions for “man” and “woman” — either as subcategories of sexes (“adult human males and females”) or as genders (“anyone with any passing resemblance to typical adult human males and females”). Not for nothing is there the principle — of venerable provenance — that says, “from contradiction, anything follows” [ex falso sequitur quodlibet].
But while a “gender identity spectrum” is somewhat “problematically” untenable — largely because it’s based on unobservable subjectivities and (mis)perceptions — a “gender spectrum” is rather more credible since there are literally dozens, if not hundreds, of sexually dimorphic traits — even in the realm of personalities, behaviours, social roles, and modes of expression which are objectively quantifiable, more or less, and are commonly seen to come in under the rubric of masculine and feminine “genders”. For example, see this 4thWaveNow article — for people “who question the medicalization of gender-atypical youth” (indeed) — and quite illuminating population distribution — similar to the “agreeableness” one above — even if many people [for example,
and] don’t quite understand, or are “obstinately” unwilling to consider the ramifications of it:
Which is more or less exactly what Mermaids was getting at, or at least trying to get at, by using “Barbie” and “GI Joe” as bookends to that spectrum — using them, using “man” and “woman” as genders (more or less endorsed by Merriam-Webster), and as extreme stereotypes somewhat typical or characteristic of some subsets of “adult human males and females”. Even if they were unable or unwilling to grapple with the devils in the details, even if they weren’t able to provide much in the way of traits that would “flesh out” the intervening spectrum. Which is maybe understandable, given all of the many traits in which there are noticeable — stereotypical — differences in the sexes, particularly apart from the strictly biological ones.
However, as indicated above, a generally useful and quite illuminating article on “Gender Similarities and Differences” by Janet Hyde herself may provide a way off the horns of that dilemma, a way forward out of some rather mephitic and quite toxic swamps. It also provides a useful framework and way of illustrating the profound differences between sex and gender, between essential properties and accidental ones — which far too many want to try sweeping under the carpet. But there are still a great many flaws, oversights, misperceptions and unexamined assumptions in her oeuvre — particularly notable in a second article by her and a couple of other feminist gender ideologues and scientific illiterates, Daphna Joel in particular — although the most salient and relevant one in both articles is in not clearly defining exactly what she and/or they mean by “sex” and “gender”.
However, with a bit of judicious reading between the lines, it seems manifestly obvious that what they mean by “gender” is a range, a spectrum of psychological and behavioural traits, typically described as “masculine” or “feminine”, that are “sexually dimorphic” — their words — and that show some differences in prevalence between the male and female sexes. Even if she seems somewhat “biased”, being charitable, on several important points. But as some notable points of reference in developing that framework, here are several quotes and a Figure from the second article with Joel & her merry band of gender ideologues, scientism-ists, and a transwoman thrown in for good measure. Of note is that I’ve capitalized Hyde’s “d” to suggest similarity with 4thWaveNow’s “D”, although she has something of a point with her own assertion that “D is the multivariate generalization of the d statistic”:
sexual dimorphism of the human brain; … the notion of genetically fixed, nonoverlapping, sexually dimorphic hormonal systems;
Two fundamental assumptions underlie current thinking about sex as a biological system and about its relations with other systems: (a) that sex is a dimorphic system (i.e., a system that can take one of only two forms), and (b) that the effects of sex on other systems (e.g., the brain, gender identity) are characterized by a dimorphic outcome (e.g., male vs. female brain, male vs. female gender identity). …. As noted earlier, for more than a century, psychologists have devoted themselves to research on psychological gender/sex differences. That research rests on an assumption that there are just two categories of people: females and males.
Figure 1 shows four possible alternatives for the distribution of males’ and females’ scores on a trait, which could be anything from hippocampus size to mathematics performance. Panel A shows a very large gender/sex difference (D = 5.0)—a dimorphism, in the language of biology, because this difference is so large that there is virtually no overlap between the two distributions. Panels B, C, and D show the overlap of male and female distributions when D = 0.20, 0.50, and 0.80, respectively. Even for D = 0.80, there is still substantial overlap in distributions, that is, the trait is not dimorphic.
In contrast, most humans possess both feminine (i.e., more common in women than men) and masculine (i.e., more common in men than women) psychological characteristics, …. Even for these highly gendered behaviors, which showed very large gender differences (1.0 < D < 2.03), less than 1% of the students exhibited only feminine or only masculine behaviors, whereas over 55% showed some combination of both feminine and masculine behaviors (feminine and masculine were defined here as the scores characteristic of the most extreme 33% of women and men, respectively). Thus, although stereotypes of women and men clearly exist, individuals who consistently match these stereotypes are rare.
However, an article in the Encyclopedia of Evolutionary Biology, by one Daphne Fairbairn, kind of knocks those claims of Hyde and Company into a cocked hat:
The term dimorphism denotes a trait that occurs in two distinct forms or morphs within a given species and traits that differ consistently between males and females are sexual dimorphisms. Sexually dimorphic traits may differ so radically between sexes that they can be reliably used to differentiate males from females. …. However, many sexual dimorphisms are not as extreme as this. Any trait that differs on average between sexes is considered sexually dimorphic, even if the trait distributions overlap considerably between sexes. Height in humans provides a familiar example of this type of sexual dimorphism.
But there are a couple of points in those quotes of Hyde and Company that bear emphasizing, and which may illustrate exactly where and how they — and too many others — are going off the rails and into the weeds. First off is Hyde’s “assumption” that “sex is a dimorphic system (i.e., a system that can take one of only two forms)”, and that everyone has to be either male or female. While she is quite correct that there are only two sexes — by definition — that most certainly does NOT mean that every member of every anisogamous species — including the human one — is either male or female: many members of such species — including the human one — are, in fact, neither. For some corroboration or justification of that argument, see the Glossary in the aforementioned Parker & Lehtonen article, one by Paul Griffiths [“What are biological sexes?”] in the PhilPapers Archive, and the Wiley Online article that underlines Griffiths’ salient point:
Wiley: “Another reason for the wide-spread misconception about the biological sex is the notion that it is a condition, while in reality it may be a life-history stage. For instance, a mammalian embryo with heterozygous sex chromosomes (XY-setup) is not reproductively competent, as it does not produce gametes of any size. Thus, strictly speaking it does not have any biological sex, YET.” [my emphasis]
From zygote, to embryo, to fetus, to the onset of puberty, none of us are or were "reproductively competent" — we are not or were not yet male or female; we are or were sexless. If that's the case then it's simply incoherent, and quite unscientific, to insist that we are all either male or female right from conception to death. Which may then make it somewhat moot as to how sexless individuals can be said to have a gender … non-binary, perhaps? 🤔🙄
However, somewhat more important in emphasizing Hyde’s rather egregious and quite unscientific biases is her “special pleading” with regard to their Panels A and D (above). Clearly the traits in question in both cases are entirely separate “dimensions” — “anything from hippocampus size to mathematics performance” — each of which encompasses a different range, a spectrum of values from -3 to +8 in one case, and -3 to +3.5 in the other case. Equally clear is that in none of their four cases can they say that there are “only two forms”, there being many “forms”, a continuous range of them from one extreme to the other. All they can reasonably say is that, in all four of their examples, one particular “form” — the male average — is more prevalent in males, and another particular “form” — the female average — is more prevalent in females. As they say themselves, “more common”, regardless of how much separation there is between the averages. But that is more or less exactly what people talk about with the “infamous” bimodal distribution which even many so-called biologists clearly haven’t much of a clue about. Wikipedia:
Though it should be emphasized, as does that Wikipedia article, that those bimodal distributions are, in effect, the sums of the distributions for each sex — again as suggested by Hyde’s Figure 1. However, the depth of the trough between the two “humps” is a consequence of how much separation there is between the two averages, and of the standard deviations for each sample. For example, it generally takes a separation of more than twice the standard deviations of the samples — as with the 4thWaveNow graphs above, with their “D=2.06” which is typically seen as extreme and uncommon — to get anything like a noticeable bimodal distribution. The following graph illustrates two separate cases — nominally the heights, in centimeters, of men and women in which the averages are 175 and 165 cm, respectively — where the standard deviations are either 4 or 5 cm. In which cases, the fixed separation (10 cm.) is then two and a half times or two times the deviations which yield values of 2.5 and 2.0 for D/d. But notice — in the green-shaded graph — the effect that adding the two different distributions has on the degree of “bimodality”:
And, of some relevance to later elaborations, that is generally why it is more useful to plot the individual graphs for men and women to see clearly how much, if any separation there is between the averages — the distinctiveness gets lost in adding the two individual graphs. But, in passing, it might be emphasized that since the average values tend to be the most common ones they tend to become the stereotypes for those traits, even though they may apply only to a small fraction of the whole population. As Hyde and Company put it, “Thus, although stereotypes of women and men clearly exist, individuals who consistently match these stereotypes are rare.”
So, with all of that under our belts we’re now in a position, finally, to consider and utilize some useful insights and perspectives from Hyde’s own first paper:
What does it mean to say that there are large differences in personality, lumping together distinct aspects such as emotional stability, dominance, and vigilance? Certainly contemporary personality theorists do not argue that there is a single dimension to personality. Overall, then, this application of Mahalanobis D produces results that are biased toward finding a large difference because of taking a linear combination that maximizes group differences, and it appears to yield results that are uninterpretable.
While she may have a point in her criticisms there of the basis for the 4thWaveNow article — and which are generally outside my salary range — I’m still not entirely sure that she’s justified in her charge of “uninterpretable”. More particularly, it seems that every last “aspect of personality” that shows any significant differences in trait values, on average, between males and females is therefore “sexually dimorphic” and can therefore be included in a single dimension of “gender”. And that each one of those aspects has a range of values — as emphasized by Hyde’s Figure 1 — which then constitutes a second dimension — orthogonal (as they say) or perpendicular to the first one. Which then provides us with our two-dimensional spectrum of individual genders — some more common than others — and which emphasizes the range of traits or “aspects”, as well as individual aspect values or “trait scores” for each aspect. For example:
In the example above, I’ve chosen three of the “Big Five Personality Traits” which, Wikipedia informs us, “suggest five broad dimensions used in common language to describe the human personality, temperament, and psyche”. And the three specific traits I’ve chosen are — for each sex and from foreground to the left background on the left horizontal axis — Conscientiousness (Con-M, & Con-F), Agreeableness (Agr-M, & Agr-F), and Neuroticism (Neu-M, & Neu-F). Although that group of three could probably be enlarged to include dozens if not hundreds of other “sexually dimorphic” traits — that leftward axis could be extended indefinitely off into and over the horizon into never-never-land.
And on the other horizontal axis from the foreground to the right background are the percentage values corresponding to all of the “Scores on [a] Trait” as per Hyde’s Figure 1. Although I’ve exaggerated the disparities in the averages for each sex for the sake of illustration and clarity. However, they generally reflect the fact that women, on average, score higher on both neuroticism and agreeableness, and that men, on average, score higher on conscientiousness. And, finally, the vertical axis gives a measure of what percentage of the population is in each one percent of a given “trait score”.
But for emphasis, consider an example or two. Most of us are likely to reside somewhere between the two peaks or “modes” of the bimodal distributions for each and every one of those traits in the spectrum of genders. But consider a couple of “atypical” cases for both men and women where they score, say, 80% on conscientious, 70% on agreeableness, and 30% on neuroticism. Then we might say that those individuals have a hyper-masculine conscientiousness gender, a hyper-feminine agreeableness gender, and a hyper-masculine neuroticism gender — regardless of which sex, or neither, that they might admit to.
Bit of a risible formulation and some cumbersome terminology. And rather moot whether it has much more than an academic utility and value beyond providing some entertainment for the boffins in their ivory towers. Hardly much better than another personality model, the Myers-Briggs Type Indicator system [MBTI] which some have quite reasonably called “pseudoscience”, and “no better than a Chinese fortune cookie”.
No doubt that there are some other variations on that theme that might be a bit more useful. For instance, Hyde suggests that the 4thWaveNow article has used some “linear combinations” of each of those individual genders to yield some composite value, even if that may over-emphasize some disparities between averages between each of the many “genders” on tap. Similarly, a post by another Substacker,
, writing on that age-old question, “What is a Woman?”, suggests a more or less simple weighted average of scores on a range of traits that might be said to comprise her own “gender spectrum”. Although it too apparently suffers from masking or distorting a “true” picture — mashing everything together is, at least in effect, just ignoring the devils in the details, or trying to sweep them under the carpet.However, it seems that that model of a “multi-dimensional gender spectrum” — actually, a two-dimensional spectrum — serves to emphasize the rather profound differences between essential and accidental properties, between those that are definitive of and unique to particular categories, and those that are merely typical of, but not unique to members of them. It may also serve to emphasize the “unwisdom” of arguing — venality writ large — that individuals who are “gender atypical or non-conforming” should mangle their genitalia to more closely resemble those of the other sex to hide, mask, or diminish the degree of that “atypicality”. Talk about “conversion therapy” — a crime of the century, a medical scandal to top the Tuskegee Syphilis Study and “Doctor” Mengele combined and compounded.
“Philosopher” Alex Byrne — in an old Medium article on “What is Gender Identity? The elusive true gender self” which is likely to figure centrally in his forthcoming book on the “Trouble With Gender: Sex Facts, Gender Fictions” (indeed) — still manages to draw some welcome attention to the misperceptions that may help to differentiate between various “gender identities” — rather subjective at best — and the more scientifically tenable and objectively sound concept of gender itself [my emphasis & qualifications below]:
Perhaps Hines’s “combination” of “being male, female” was a misleading way of saying something straightforward, like [gender being]: a combination of masculine and feminine personality traits and interests? Although a later page in her book suggests as much, it is unlikely that this is the correct interpretation. No one thinks that a very feminine [gendered] man is prevented from having a male gender identity, or that a very masculine [gendered] woman is prevented from having a female gender identity. What’s more, practically everyone has some traits more prevalent in the other sex, but “male” and “female” gender identities are supposed to be the norm, not rare exceptions.
Philosopher Will Durant had an elaboration on a quote by Voltaire which I think gets to the heart of the matter that Byrne is alluding to, and of the problematic conflation of sex and gender which Stella O’Malley has usefully underlined in an earlier comment of hers. But Durant’s insightful observations:
If you wish to converse with me,' said Voltaire, 'define your terms.' How many a debate would have been deflated into a paragraph if the disputants had dared to define their terms! This is the alpha and omega of logic, the heart and soul of it, that every important term in serious discourse shall be subjected to strictest scrutiny and definition. It is difficult, and ruthlessly tests the mind; but once done it is half of any task.
If we can't agree on what words mean — and on which properties it takes to qualify as members of various categories and on which properties are irrelevant to that question — then we haven't a hope in hell of dealing with any problems that turn on them.
Skimmed the article and look forward to digging into it further later on. But wanted to respond to this point on collapsing many gender-related dimensions into one:
"mashing everything together is, at least in effect, just ignoring the devils in the details, or trying to sweep them under the carpet."
I disagree. I think it's valuable to highlight the different dimensions that inform our read of someone's gender, but at the end of the day we do collapse those dimensions into one when we decide to refer to someone as "he" or "she" (or "they"). Gender categories are determined by the presence of some "critical mass" of related traits unlike sex categories which are determined by the presence of particular essential traits of that category.
Happy New Year, Steersman!
I see you took on the Big 5/trans angle: nailed it. Well researched, and a great read!