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>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.

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