I believe in the, quite common, context just used it's meant as non-parallel. Or the two ideas don't track at all.

Yeah, but they were saying in math related contexts, in which orthogonal is almost equivalent to perpendicular.

I believe even in the context of mathematics orthogonal means independence. I.e., one can move along x and y axis without having y or x value being changed. However if you move along any line that's not parallel to x or y axis then both x and y value change simultaneously. That's how I interpret orthogonality in the context of math anyway.

>However if you move along any line that's not parallel to x or y axis then both x and y value change simultaneously.

A third orthogonal axis is neither parallel to x and y, nor do x and y vary as you move along it.

Replace parallel with linearly indepent, and you are spot on.

No need to replace anything; the implicit assumption is a 2D space.

Then you can only talk about two concepts. I would like to be able to say, intelligence, morality, and obesity are mutually orthogonal.

If your model is 2D, then you are requiring a relationship between at least two of them.

The example was in 2D. The reader is able to generalize from there, we hope, no? :)

As long as you don't rely on concepts that don't generalize to higher dimensions. To the extent that you use concepts that don't generalize in your example, you are using a poor example.

That's the idea, and these ideas do intersect. Rate your belief in them on a scale of 0..1. if your rating was (0,0) you are at the intersection.

Yes, the poster above has assumed the meaning of 'orthogonal' from its etymology, but the use he criticises comes from statistics (https://stats.stackexchange.com/questions/12128/what-does-or...)