I spend a good bit of time at the weekend drawing geometrical surfaces trying to better understand political opinions.
The Political Compass Test has added another axis, authoritarianism, and while it gives a better picture it still seems myopic.
SFO presented a triangle, the corners of which represent Freedom, Equality and Tradition. People who's highest ideal is freedom are in the Freedom corner. People who value equality above all else (whether it's sexual equality, financial equality, racial equality, ...) are in the Equality corner. People who prize some traditional view of governance (Traditional Britishness, Christian Morals, White Ethnostate, One nation under an ayatollah, ...) are in the Tradition corner.
This triangle seems useful because it does help us to understand some of the division and confusion that we see. The people in the freedom corner can barely differentiate between the Communists and the Nazis because they're both anti-freedom, authoritarian, and happy to silence political dissent. The equality advocates see the Freedom corner and the Tradition corner as the same because they both stand in the way of the radical new structure that they wish to introduce. Both the classical liberals and the traditionalists rail against the overthrow of whatever structure the equality brigade are trying to tear down (patriarchy, capitalism, western democracy, meritocracy). From the Traditionalist corner, the freedom people and the equality people look indistinguishable.
This is all well and good, and I think it's a useful lense through which to examine one's own prejudices and the opinions of others. However, it upsets my sense of dimensional analysis. You can't represent three axes on a flat triangle.
My first assumption was that the three axes are orthogonal to each other. That gives us a three dimensional space in which you can plot political opinions. That doesn't help, there's a point where you care about nothing, and a point where you care about all three things to the fullest extent. Neither really makes sense.
My second assumption is that you have to care "so much" and all you can do is point the direction in which you care. In other words there is an arrow, starting at the origin, which is 1 unit long (I give exactly 1 shit) and a description of your political ideology is the direction of that arrow.
The rest of my weekend was spent worrying about what that surface looked like, and where the graduations fall on it. (The lines of iso-sentiment if you will.)
Here's a rough sketch of the surface that piqued my interest.
This is a moderately accurate projection of it, to show how the lines and regions intersect.
When my father described the Mercator projection to me, I was told to imagine that we covered the globe with pasty, slit it down the Pacific, and then rolled it out.
This is the best I can do as a flat projection of the surface. It is symmetrical and the areas aren't molested too badly, but the angles are all shot.
Richard "projection" B