**“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.

Thanks to Stats in the Wild, here’s some real data on the ages of Olympians that makes the point:

### Measurement

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:

- height, weight, curvature, angle of femur
- 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. 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.

Tags: 4-D, binary, data, data mining, gender, gender binary, gender wars, geometry, high dimensional spaces, hyperplane, LGBTQ, math, mathematics, maths, maximally separating hyperplanes, n-dimensional, queer, statistics, support vector machines

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