Categorisation of gender: Gordon’s art exhibition, part 2

By Gordon Rugg

I have an art exhibition at Keele University until October 25th. The exhibition consists of twelve canvases.

The first six examine depictions of women in epic texts, described in my previous article.

Canvases seven to twelve examine ways of categorising gender, which will be the topic of this article. image8

The first canvas of this second set shows a way of categorising gender that is widely used across cultures.

image1 Canvas 7: Binary crisp sets. Image copyleft Hyde & Rugg.

It’s an either/or division into two genders, sharply divided, with no other options available.

It’s often subsumed in a broader system, which bundles together biology, societal gender roles and sexual orientation, into a “male package” and a “female package”.


This method of categorisation occurs across many times and cultures. It’s often combined with a three-level model of the universe that includes the divine, the human, and the animal, like this.


Dividing the universe by gender and divinity. Image copyleft Hyde & Rugg.

That’s neat and tidy, but it doesn’t correspond with reality. There are a lot of borderline cases that don’t fit neatly into any of the categories above.

Texts such as the biblical book of Leviticus go into great detail about how to categorise borderline cases, not just in relation to gender, but in relation to the world generally. There’s a strong case for arguing that the stance of Leviticus on homosexuality is more to do with category separation than with gender or sex

A recurrent major theme in Leviticus is keeping categories and category packages clearly separate from each other. This occurs in numerous forms, such as a prohibition on mixing different fabrics within one cloth, and a prohibition on sowing different crops in the same field. The prohibitions about clean and unclean foods are an interesting example of this, where the two elements of the package are explicitly stated. One element is about chewing the cud; the other is about being cloven hoofed. We can represent the possible permutations as a table, like this.

leviticus cleanv7

Category permutations in Leviticus. Image copyleft Hyde & Rugg.

If an animal chews the cud and is cloven hoofed, then it’s clean; if it neither chews the cud nor is cloven hoofed, then it’s also clean. Animals that don’t fall into either of those packages are unclean. Pigs are unclean because they’re cloven hoofed but don’t chew the cud. Camels and rabbits are unclean because they chew the cud but aren’t cloven hoofed.

The phrasing of Leviticus on homosexuality in this context is interesting; it’s phrased in terms of a man lying with another man as with womankind (King James Version) – i.e. it’s being phrased in terms of mixing of categories, rather than as about sexuality in itself.

We’ll return to the issue of “package” categories later. First, we’ll look more closely at reasons for particular cases not fitting neatly into an either/or categorisation.

Some cases don’t fit because of a clearly-defined issue. For instance, most people are chromosomally either XY male or XX female. However, some people are chromosomally XYY or XXY. Both XYY and XXY are clearly defined, but neither of them fits into either the XY or the XX category. We can represent such cases like this.


Canvas 8: Three crisp sets. Image copyleft Hyde & Rugg.

In reality, the other category tends to be treated as a “dustbin” category, both in terms of using it to hold anything that doesn’t fit in the two “proper” categories, and in terms of how cultures usually stigmatise people in the “other” category.

Another problem for the two-box model involves cases that don’t fit into two crisply-separated categories because they fall on a greyscale, without any clear dividing points along the scale.


Canvas 9: Greyscale. Image copyleft Hyde & Rugg.

Greyscales may look innocuous, but they’ve produced some acrimonious controversies over the years. One pivotal case was the work of the American researcher Kinsey, when he studied human sexual behaviour in the 1940s. When he asked respondents to describe their sexual orientation, he used a greyscale, rather than a crisp divide into heterosexual or homosexual. This was at a time when homosexuality was illegal in the USA, and viewed as a mental illness by many psychiatrists, so the greyscale’s implicit assumption that there wasn’t a clear-cut distinction between “normal” and “pathological” sexuality sparked widespread outrage among traditional moralists.

Even within mathematics and logic, the concept of fuzzy logic, which is closely linked to greyscales, provoked heated debate when invented by Zadeh in the 1960s.

Greyscales can be used to represent “other” gender categories, as in the example below, where a greyscale occurs between traditional male and female crisp sets.


Canvas 10: Binary crisp sets plus greyscale. Image copyleft Hyde & Rugg.

One particularly interesting extension of greyscales to gender research is Bem’s work on androgyny theory. Previous approaches viewed “masculinity” and “femininity” as opposite poles of a single spectrum. (There’s a whole other debate about what, if anything, is meant by “masculinity” and “femininity” but I’m leaving that to one side for the moment, so as to focus on the representational issues of gender.)

Bem’s approach instead treats “masculinity” and “femininity” as two separate scales, so that an individual can be described both in terms of how “masculine” they are and how “feminine” they are. This can be shown diagramatically, as in the next image.


A two-axis representation of gender roles. Image copyleft Hyde & Rugg.

Within this representation of gender roles, Maeve of Connaught would probably score highly both in traditional masculinity (the “warrior” part of “warrior queen”) and in traditional femininity (she had numerous male lovers, had several children, and was married more than once). Helen of Troy would score high on traditional femininity and low on traditional masculinity. Helen’s husband Menelaus would score high on traditional masculinity and low on traditional femininity.

The same type of two-scale plot can also be used for sexual orientation, with the strength of sexual orientation towards men on one axis, and towards women on the other.

This is a powerful and flexible approach, but it doesn’t include a space for the types of crisp set issues described above, such as people who are genetically XXY. One way of handling the range of issues involved is to use a multiple representation such as the one below. For simplicity, it only shows one “other” crisp set and one fuzzy set, but in practice it would be easy to include more.


Canvas 11: Three crisp sets plus greyscale. Image copyleft Hyde & Rugg.

This representation handles a wide range of cases, but it still contains an implicit assumption that male and female are the two “real” anchoring values, with the others as in-between cases that don’t fit into the two main “proper” boxes.

The representation below is one way of avoiding this problem, by using a two-dimensional mosaic-style representation, with no obvious scalar values on either axis, and including a mixture of crisp sets and greyscales. This could be extended indefinitely to accommodate a wide range of gender categories.


Canvas 12: Multiple types of categorisation. Image copyleft Hyde & Rugg.

In principle, this approach could be used to map all the logically possible combinations of biological gender, social gender and sexual orientation recognised within a given culture. From a legal perspective, this would make it much easier to check whether any gender-related legislation included provision for all of the categories that the legislation would need to cover, or whether any categories had been omitted. We’ll be blogging about this, and related, applications for formal category visualisations in a later article. For now, though, we’ll conclude with some thoughts about wider issues involving gender.


Gender is clearly a more complex issue than a simple male/female dichotomy, as has long been realised by many communities. The mosaic model above, though fairly complex, is still a simplified version of reality.

Representations offer insights into the nature of gender as it is construed in different cultures. However, there is an underlying question that isn’t addressed by the representations above, namely: Why bother? Why do societies treat gender as such a big issue, rather than a private matter like musical preferences? Why do most cultures exhibit widespread prejudice and social marginalisation on the basis of gender?

It’s a good question. Much of the prejudice and marginalisation is couched in terms of values (traditional, or religious, or political) rather than practical factors. Whether this is more than just a rationalisation for some deeper issue is an open question.

The most commonly cited practical factors affecting gender involve providing privacy and safe spaces for women and girls, such as toilets, and changing rooms at swimming pools. Safety with regard to sexual violence is a very real issue, but there are simpler ways of improving the situation than by imposing normative gender roles on the entire community; for instance, by having attendants in public toilets, which is a well-established tradition in many countries, and by having individual rather than communal showers and changing cubicles at swimming pools.

There’s still a lot to be discovered about how cultures treat categorisations of gender. I hope that the approaches described above will help researchers to untangle what’s really going on, and will help us move towards a more tolerant world.


The Bem approach to modelling androgyny can also be used for other, very different topics. In my book Blind Spot, for instance, I used the same two-dimension approach to show how handedness can be modelled more realistically this way than by using the traditional one-dimensional scale from left-handed to right-handed.

This article has been about categorisations of gender, but, interestingly, almost exactly the same points could be made about how cultures categorise mental health, from a binary crisp set model of “sane” and “insane” to something more complex and more closely corresponding to reality. These similarities are probably no accident. More likely, they’re the result of people using the same underlying approach to categorisation across different issues, whether as part of a general strategy of minimising mental load, or as part of an ideological position, or a mixture of both.

With regard to visualisations, I’ll be blogging in a later article about how systematically structured visualisations can be used to map out all the logically possible combinations for a given case, with a view to ensuring that any regulations, legislation etc in that field will include provision for all the possibilities. Historically, this approach has been viewed with suspicion in some fields, such as mathematics and the law, but viewed in other fields such as computer science as the most rigorous and systematic way of handling complex problems. There’s probably a moral in that somewhere…

We’ve blogged previously about categorisation here:

We’ve blogged about gendered language in Shakespeare here:

Blind Spot is available on Amazon:

The canvases in the exhibition have a vellum patterned background. I’ve used a light granite pattern in the images for this article since that worked better visually on the smaller scale of a computer screen. I’ve also made some changes to the colours in the final mosaic image, to fit better with the content of this article; the original canvas had to be simpler, since it was accompanied only by a short explanatory text.

As usual, the images in this article are copyleft Hyde & Rugg; you’re welcome to use them for any non-commercial purpose, including lectures, provided that you state that they’re copyleft Hyde & Rugg.


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