[stuartcr]

Still means perpendicular to me, can't see the compatibility. I must be spacially challenged, because it seems to me that you could consider anything compatible, if you apply the right variables. I guess it's in the interpretation.

[donh]

because it seems to me that you could consider anything compatible

Well, it's a bit of a fuzzy concept in ordinary use, but in math, it refers to the indepedence of parameters of an equation.

Let's make up a chesslike game with a more indicative example. Suppose the rook can only move a number of squares related to, say, how many squares he last moved a bishop.

In the original chess rules, the number of squares the rook can move is orthogonal to the behavior of the bishop, in our new game, it is not. The idea of the word extends beyond merely physically perpindicular, and is, by my lights, a pretty useful and compact word.

[tortoise]

What he is saying is that the axis for each of those is orthogonal to each other in a multi-dimensional space. For any such space, all orthogonal axes are going to be compatible in the sense that all points in that space contain components of each (including zero, along the axis origins). I thought it was pretty clear what they meant; it doesn't take a rocket scientist. It makes perfect sense, even if you don't get it.