[taoistextremist]

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

[vishnugupta]

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.

[Maybestring]

>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.

[romwell]

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

[Maybestring]

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.

[romwell]

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

[Maybestring]

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.

[Maybestring]

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.