Usage of the word "orthogonal" outside of mathematics

because in mathematics orthogonal is synonym of being independent or absolute lack of dependence.There are intermediate states from no dependence to complete dependence (aka parallel) which is given by vector product

http://en.wikipedia.org/wiki/Covariance

Update: I did not want to implicate but without it my answer is not answering direct question.

In Russian primary school the vectors are studied in the 4-7th form and after that children tell in conversations "parallel" instead of "dependent and "orthogonal" (or "perpendicular") instead of "independent".

If you think about (simplified for convenience) mathematical usage of "orthogonal", it is referring to vectors at right angles to each other, so motion in the direction of the first vector produces no corresponding motion in the direction of the second vector. This independence is what motivates the other meanings; an orthogonal line of argument in debate might be interesting in itself, but doesn't advance the main thrust of the debate, for instance.

It's just as well that the mathematical use of "normal" doesn't bleed across like this, because "normal people" would then be at right-angles to reality. Then again... :-)

As Wikipedia says about the derived meanings of orthogonal, they all "evolved from its earlier use in mathematics".

• In statistics, the meaning of orthogonal as unrelated (or more precisely uncorrelated) is very directly related to the mathematical definition. [Two vectors x and y are called orthogonal if the projection of x in the direction of y (or vice-versa) is zero; this is geometrically the same as being at right angles.]
  The statistical meaning comes exactly from this: one can think of random variables as living in a vector space, and correlation between two random variables is zero precisely when the two vectors are orthogonal/"perpendicular". See this post for details.

• In debate(?), "orthogonal" to mean "not relevant" or "unrelated" also comes from the above meaning. If issues X and Y are "orthogonal", then X has no bearing on Y. If you think of X and Y as vectors, then X has no component in the direction of Y: in other words, it is orthogonal in the mathematical sense.

• In computing, the use of orthogonal for isolated or partitioned (which I don't actually recall encountering) would come from the same meaning: the behaviour of one component has no bearing on (is isolated from) other components; so they are orthogonal.

In construction fields, orthogonal is used instead of perpendicular.

There seems to be another sense of orthogonal as "orthogonal categories" eg suppose we have two sets of categories I {A, B,..} and II {C, D,...} then to claim " I and II are orthogonal" seems to require the existence of: A-C, A-D,... and B-C , B-D ...; this interests me because I have a problem , where I am uncertain whether I and II are "orthogonal" or "non-orthogonal". Non-orthogonal would seem to imply A==C and B==D etc but is this unique or would non-orthogonal also include the possibilities A==D , B==D etc