A Brief Reply
Medium is not particularly friendly towards attaching images in comment replies, so I figured it would be easier to reply in a post since we are talking about “graphing” political orientation. In this case, images can explain my thinking much more succinctly than words could:
You suggest we think of Capitalism and Socialism as “orthogonal dimensions.” This is an interesting perspective, but I’m not sure the analogy holds.
If we think of people charting themselves with Cartesian Coordinates of Capitalism vs. Socialism, it implies everyone believes some degree of both ideologies. If a person’s political orientation is defined as a point (x1, y1), and the x & y axes are Capitalism & Socialism, then every person has a value in both dimensions. We are all some degree Capitalist and Socialist, or (c1, s1):
This perspective could help us add some texture to the way we discuss our political orientations. But you seem to suggest that Capitalism and Socialism are “orthogonal dimensions” in that they must exist in opposition to each other; a believer of one must inherently reject the other. Indeed, I would agree that people who self-identify as either “Capitalist” or “Socialist” often do outright reject the opposing side without consideration for their ideas. The words are poisoned wells, and everyone has their own preconception about what they mean.
If this is our basic assumption, then every person would simply have their one-dimensional value and nothing in the other dimension [eg., (c1, 0) or (0, s1)]. In this case, the “two-dimensional” graph becomes no more helpful than a linear dipole, as I suggested.
Orthogonal axes in two dimensions are these Cartesian coordinates so I’m focusing on this part of the analogy. I’m not sure if you meant to highlight the polar coordinate metaphor, because this makes the matter even more ambiguous:
You’re correct that a polar coordinate system requires a magnitude and direction (r, θ). But the analogy falls short of connecting the math back to reality: is someone 100 units in the direction of capitalism? Is someone 50 units political, at 60 degrees socialist?