Posts tagged with gender

Railing against “grey areas” has become a favourite rant topic. People think that they’ve covered their bases and are being really open-minded when they switch from {0,1} to [0,1]—but no false dichotomies are avoided in this transition from discrete to continuous.

Let’s take the example of sex & gender. Most of the tick-boxes and bathrooms we face in life are labelled “M” or “F”, which covers most of us but not all.

(And I want to apply a kernel weighted to extra-count the forgotten individuals, since as minorities they’re more vulnerable. This can be seen in data such as e.g. higher suicide rates and higher murder rates.) The University of Hawai’i’s guidelines for dealing with individuals possessing ambiguous genitalia (Archives of Pediatrics and Adolescent Medicine) use words like

  • chromosomes—XX, XY, or other
  • micropenis, labia-scrotum fusion, gonadal dysgenesis
  • androgen insensitivity syndrome, hypospadias, kiinefelter syndrome, congenital adrenal hyperplasia, Turner’s syndrome
  • true hermaphroditia

which raises the question of where the “grey area” between [M,F] ~= [0,1] could come from. Chromosomes either come in whole units — for example people with Klinefelter’s syndrome have 47 chromosomes “XXY” — or have a much more complicated structure if you want to dig into the DNA string. Other aneuploidies include XYY, monosomy or partial monosomy, trisomy 21 (which I don’t think affects genitals or sex assignment), distal 18q−, mosaicism, the list goes on. How are we going to assign a total order there in order to define a continuous variable? I don’t see any way to—just more possibilities to add to the domain of a categorical variable (and making it much more confusing than the usual gender dummy!).

The paper above, to give another example of non-orderability, notes that various chemicals usually squirt at you in fœtal development but they vary in their squirtular timing. So androgen, progesterone, and so on aren’t mutually fungible (as the different “coloured edges” in Ramsey theory), and además we’re dealing with time series like Ed Küpfer’s pictures of sports scores:



Those kinds of pitures, but with different coloured spiketrains representing the incommensurability of androgen vs testosterone and so on.

So how do you get total orderability (necessary for a “grey area”) from a time series of incommensurable chemtrains? I don’t see it. The geometry is more interesting than just a line segment.

Further reading: transgender mathematician (Leigh Noble), transgender computer programmer (Tim Chevalier @eassumption), transgender economist (Deirdre McCloskey @deirdremcclosk), transgender electrical engineer (Lynn Conway). Jeff Eugenides’ Middlesex.


  • chimp and neandertal musculature versus modern human musculature
  • and the Wadabi tribesmen dress up in women’s garb and makeup, and starve themselves, before performing beauty dances to please the women. They expend enormous efforts (time and calories) obtaining cosmetics; favourite gift is a mirror.
  • Akaa pygmies reproducing with everyone and the typical evo psych concept of sexual jealousy seems to not apply.
  • Akaa fathers do more of the parenting than the mums.
  • 1:07 — Bedouin Wa-alla sons speak to their fathers ~3 times up to age 18, and transgressions punished by stabbing with a sabre.

My friend and I were talking about hard bodies, which are normative in US culture.

Hardbodies Poster
Do you think it's feminine when a guy works out a lot to get a hot body?

She told me her theory that they are normative because US culture is pro-masculine in such a way that everyone has to perform masculinity in some way.

A feminine man, I was looking for a photo of a wimpy vegetarian in Birkenstocks shopping at an organic grocery store and being otherwise overly sensitive. But I was basically picturing Todd Louiso's character from High Fidelity. In this shot it looks like he's trying to appear more maculine. // The original conversation that led to this train-of-thought was about the Whitney Houston movie The Bodyguard, which I haven't seen but it came to mind as an example of perhaps a beautiful man being chased by a successful woman. But, still not having seen it, I speculate that there will be some point in the story where the man takes charge of the romantic pursuit, in order to maintain his attractiveness by recovering his masculinity.

I don’t know if I agree with that thesis or not, but it got me thinking about how a pro-masculine culture might be reflected in the economy, in the utility functions, and what an alternative on that dimension might look like.


So obviously, Estadounidenses work out; "Fitness is a $19 billion industry"; those who don’t are shamed.


But hard-ness might be reflected in utility functions in other ways as well.

  • preference of work (“I worked my #rse off to get where I am today”), busy-ness, regimens, organised workspaces, getting things done, goal-setting, achievement
    Larry Wall is disarrayed, chaotic, relaxed, embraces stillness, but I think he comes off as perhaps a bit of a feminine hippie.
  • a preference for doing over not-doing (or maybe doing over being-done-to)
  • a preference for hard-force over soft-relaxedness soft causing
  • shaming of laziness, softness, sloth, people who are too relaxed or don’t work enough, people who aren’t busy, have no career, have no ambition
  • a preference for my-own-space over shared-space
  • a preference for working hard, even if it’s to the point of overworking (overworking is actually kind of a compliment)
    "Work, work, and more work, and I expect it shall continue to be so." OK, obviously it's not _only_ US culture that preferes busy-ness to not-busy-ness.
  • a preference for individualism over communalism
  • a greater need for personal space (people stand relatively far apart from each other)
  • "I wish I could spend more time with my spouse and kids, but I’m too busy running this business empire!”
  • "I wish I could take a real vacation, or for longer”
  • Confidence, competence, winners, power over gentleness, flabbiness, passiveness, meekness, passivity, sensitivity.
  • creative destruction, building things, knocking them down, refurbishing, rebranding, striving for better, striving for more.

What about the alternative—what would a “soft” economy look like? Well, besides performing services and producing goods for each other, people can give utils to each other directly with

  • sex —the most obvious example of pure hedonic pleasure, uncounted in GDP, and “being good at it” (for men) may have less to do with a Big Man with a Big Dick, and more to do with openness, acceptance, creativity, curiosity, playfulness, sensitivity—characteristics which can be somewhat opposite to the Hard Body No Sleep Driven Successful macho man model
  • hugs
  • touching
  • softness toward each other
  • compliments
  • massages
  • Tumblr Likes
  • conversation
  • listening to each other
  • playing games together (think “childrens’ games” — why are they for children?)
  • sitting next to each other
  • holding hands
  • communicating that “I accept you as you are” or “I care what you think” or “I think you’re awesome”

(and equally they can harm each other with innuendo, bickering, hurrying or harrying each other, glares, invocation of rank/status, backhanded compliments, body language, and other perhaps “feminine” moves).

Somehow I got to think about Odo from Star Trek.
In at least one episode, the others of his shape-shifting race want him to return to live with them so they can all shape-shift into a goo and flow around in each other’s beings and experience each other. Which is one idea of Heaven. But Odo (a hero on a US TV show) wants to keep exploring, penetrating the cosmos to greater lengths. Maybe a “more feminine” economy, though, would look more like that. People touching each other, lazily hanging out,

I think there’s a reason that “California Buddhism”
looks like finding peace on a marathon instead of this:

Look at that fat guy! He’s just sitting there! So, but what do you do? I mean, what do you do, do?

Amazing New Easy Way Puts on Pounds and Inches
Firm, Solid Flesh without overeating

Life Magazine Ad. 1964


Amazing New Easy Way Puts on Pounds and Inches

Firm, Solid Flesh without overeating

Life Magazine Ad. 1964

(Source: httpcolonslashslash)


I’m totally convinced that ∃ more connections between mathematics and the humanities than the university culture I once stewed in would suggest.

Probably due to personality differences, but also lack of familiarity with each other’s subject matter, I never saw inter-departmental collaborations and—as I’ll discuss in another post—even the idea of data is seen as a four-letter word in the gender studies department. (Likewise, ethnography and anecdote are four-letter words within the economics field, and statisticians also concern themselves only with structured data.)

Nevertheless I see mathematical shapes all over cultural analysis, and I mean to record them. (However typing up a coherent few paragraphs, let alone adding drawings, takes several orders of magnitude more time than simply thinking a thought.)


After reading her essay crowing that millennials do not see themselves as special, I went on to read more of Phoenix and the Olive Branch, which talks about rehabilitation from “Quiverfull” fundamentalist upbringing—particularly gender issues that arose as a Quiverfull young woman.

(Relevant to the “value of liberal arts" question, Sierra writes that "College literally saved my life"—without the critical thinking skills—not science or programming skills—that she learned at college, her mind and heart and … uterus would have remained ensnared in the “Quiverfull” fundamentalist mindset she grew up in. Just an interesting sidelight.)


Sierra has a very logical way of describing a flaw with sexist views:

Check out this gem from “Reclaiming the Mind”:

You see, when people are truly committed and consistent egalitarians, they have to defend their denial of essential differences. In doing so, they will advocate a education system in the home, church, and society which neutralizes any assumption of differences between the sexes. In doing so, men will not be trained to be “men” since there is really no such thing. Women will not be encouraged to be “women” since there is no such thing. The assumption of differences becomes a way to oppress society and marginalize, in their estimation, one sex for the benefit of the other. Once we neutralize these differences, we will have neutered society and the family due to a denial of God’s design in favor of some misguided attempt to promote a form of equality that is neither possible nor beneficial to either sex.

As a truly committed and consistent egalitarian, yes, yes I do deny “essential” differences. You know why? My essential nature is not “woman.” My essential nature is me. Sierra. It’s who I am. …[M]y best friend[’s] essential nature [is] not identical to mine. It might have similar colors and shapes, but so would mine and my fiance’s. Because people are different. “Men” are not more different from women than they are from other men.

In statistical or mathematical language, I would interpret this as saying "The fact that gender==Woman is not entirely determinate of everything about me.”

If I were writing a computer program to mimic the kind of sexism Sierra is talking about, it would take one input for gender and, if the answer is male, then prompt for further details on the personality, achievements, background, interests, thoughts. Elsif gender == female, then the only questions worth asking are “Fat? Hot?" Otherwise, break; because there is no else.

Not that the "Being a minority is determinate of everything and only males can show variation” is limited to gender. On Reddit we find:

"I can’t imagine a black guy saying ‘anywho’"

as if blackness is somehow so determinate of behaviour. Charmed, I’m sure.


In statistics the paradigm is that data go into a model and a couple numbers come out. Some of the numbers parameterise the model. But other numbers tell us how good the explanation is. There are numbers to tell us how well individual parts fit, how well the overall whole fits, and several numbers that are warning indicators for various types of traps that can make the other numbers mess up.

Thinking that everything about a minority is determined by their minority status is a bit like ignoring all the model-fit numbers.

If we explored some data with a large number of linear models, progressing from coarse (few terms) to fine (many terms), we would probably see gender differences as a significant term among coarse models. But those models would also have a low specificity and explanatory power. Then as we added more explanatory terms (finer models), those other explanators—correlates of gender/race, but not gender/race itself—would start to steal explanatory power away from the gender  dummy variable.

To give a physical example, 100m sprint times show differences across male/female, but training is more determinate of the sprint time. If we could measure personality and thoughts and the kinds of traits that Sierra might say define her as a person, we would probably be left with very little t-value on the gender dummy.


One more mathematical parallel. The idea that “minorities show no variation; only the privileged group can be variable” is isomorphic to Jim Townsend’s mathematical-psychology model of racism. Substitute “minority” with “other group” and “privileged group” with “self" or "my group" and you have the same model of a negatively curved metric space:

negatively curved metric space for self versus other (privileged group versus minority group)

So you thought postmodernism was opposite to science? Here is Derrida’s “privileged hierarchy” where “one term dominates the other” — at least one mathematical interpretation of those words.

"There is more difference within the sexes than between them."
‒Ivy Compton-Bennett, Mother and Son

"In all of human biology, there is no greater difference than of that between men and women."
—Some biology notes I found online

These two statements sound like rhetorical opposites, but in fact both are true.

(Says me. I can’t prove this, but I bet that taking everything into consideration, divisions between men & women are greater than those between liberals & conservatives, blacks & non-blacks, tall & short, sick & well, D&D players and people who get laid, etc.)

Let me show how both statements can logically live together harmoniously.

Just like how most men are slower than female Olympians, but at the same time the average man is faster than the average woman.

NB: Not real data.


Even when differences are statistically significant enough to draw conclusions (such as: “boys sprint faster than girls”), the magnitude may be really small so that the difference, while indisputable, is also unimportant. (“Statistical significance” is a confusing term in this respect.)

Consider that there are many ways you could measure differences among people. Here are some that come up frequently in the gender wars, grouped suggestively:

  • height, weight, curvature
  •   IQ, SAT scores, reading tests
  • speed, throwing distance, fine motor skills
  • communication skills, emotional intelligence
  • went to college, profession is engineer
  • finding things in the refrigerator, ability to focus, ability to multitask

There are many ways to measure each of these “dimensions”. For example, does "speed" mean in the 100m dash, 200m dash, marathon, trail running, bike race, or triathlon? While the answers wouldn’t be independent, they wouldn’t be one-to-one either.

A billion points in a million-dimensional space

Now you are faced with 6.7 billion points in an N-dimensional space, where N is the number of things you could measure. Let’s say like a billion points in a million-dimensional space. (Some dimensions may be collinear.)

On the one hand, there are always lots of pink and blue dots mixing in with each other (e.g. men who sew better than most women)‒and directly from Ivy’s point, the distance among pinks (variation among men) is greater than the distance from the pink centroid to the blue centroid (variation between men and women).

At the same time, though, if you had to choose just one factor by which to color these dots and get maximal classification power, it would have to be gender.

In other words, gender differences may generate a maximally separating hyperplane, but Euclidean distances between differently-gendered points are often small, and Euclidean distances between same-gendered points are often large.

"They don’t have money for a gym membership. They don’t have money for a 24-hour gym pass. This is a ghetto pass. They work out in the ‘hood. A lot of these guys are creative, because they’ve been incarcerated. They know how to work out with [whatever’s around]. And you know, these guys are just as toned, just as ripped. They look better than some of the cats at any fitness club around the world.”

Two women dressed up in men’s suits, c. 1920 (Marie al-Khazen)
via tarrifiq

Two women dressed up in men’s suits, c. 1920 (Marie al-Khazen)

via tarrifiq

Earlier I wrote that gender is like a maximally separating hyperplane, including vast within-gender differences? I was trying to use maths to end the war of the sexes.

Some who read it didn’t know what a support vector machine was. You can find out by playing around with this SVM tool. Sprinkle around some pink, blue, and gold dots like I had.

  • There should be lots of distance among blues and lots of distance among pinks.
  • There should be some clustering of pinks and some clustering of blues.
  • I don’t have any data or presuppositions about the golds [trans, queer, hermaphrodite, etc] so I just put them wherever.

Set the kernel to linear (-t 0) or radial (-t 2), hit Run and you’ll see the maximally separating hyperplane — just a line in 2-D.

Thanks to James Grahn for sharing the link to the SVM tool.

Playing around with this, you’ll realise that my earlier claims were less than precise (as some readers pointed out at the time). That’s OK. The point of bringing up gender differences was to suggest a different way of thinking, not to claim I have all the answers.

Just like it’s good to think of men’s and women’s 100m dash times as distributions, the SVM-in-a-high-dimensional-space metaphor is better for thinking about Gender Differences than the most obvious ways we conceive of them (“boys scored 3 points lower than girls on their verbal SAT? Oh no! Our boys can’t communicate!”).

To restate what I said before: In real life, the blue & pink dots are distributed in high dimensional space with vast within-gender differences and lots of overlap among the genders. Too, there are meaningful differences between men and women and an SVM is one way of showing that those exist. In fact, considering the totality of human differences, the SVM should classify better for male-vs-female than dividing along racial lines, economic lines, etc.

That’s my quantitative interpretation of the statement “There is a great difference between the sexes.”

Is God a man or a woman?

Definitive answer: God is sexless.

The differentiation of organisms into sexes evolved because it increases fitness. Specifically, sex allows species to spread useful mutations throughout the population quickly, thereby avoiding extinction. It’s not useful enough in every species to justify the cost; species with large populations benefit more from sex.

Sex ratios vary. One boy can inseminate lots of girls so 1:1 only happens under special circumstances. Some organisms have more than two sexes. Or just one.


What we call "females" are organisms that make regular-sized gametes (eggs)—OK, maybe they got a little bigger in response to the development of "males"—those who evolved to make lots of small gametes (e.g. human sperm).  In species with many sexes, each “mating type” cannot reproduce like with like.

Reproduction v Recombination v Sex

Reproduction (birth) and recombination (meiosis) do both occur in isogamous species, like paramecium. Some isogamous species produce gametes and some do not. Think bacteria v trees v mites v fungi v disgusting parasites. All part of creation.


I assume God is not acted on by natural selection—that is, that God does not reproduce, mutate, and have selective mutant offspring killed off.

The usual concept is that God is immortal and unchanging. God doesn’t produce gametes (right, Leda?)—just telekinetically impregnates virgins, whose offspring usually lecture about enlightenment and goodness before passing away childless (right, Linda Fiorentino?).


Sex is generally much more complicated in nature than it is in humans. Sex evolves because of selective pressures. God does not experience selective pressure or bear new godlings that experience selective pressure. So there would be no reason for God to evolve a sex. So God is sexless.