# Usage of the word “orthogonal” outside of mathematics

From the roots ortho (straight) and gon (angle), its meaning in mathematics is understandable. Outside of mathematics it has various meanings depending on the context:

• Debate - orthogonal: not relevant
• Statistics - orthogonal: unrelated
• Computing - orthogonal: isolated or partitioned

There are other definitions. Most seem to imply a meaning of independence or separation. Does anyone know how it came to mean this?

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You are in good company -- even Supreme Court justices have been confused: washingtonpost.com/wp-dyn/content/article/2010/01/11/… – ash Dec 14 '15 at 4:43

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... :-)

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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.

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"linearly independent" doesn't mean "orthogonal". Orthogonality implies linear independence, but the converse is not true. – Peter Taylor Feb 11 '11 at 21:43
@Peter: Thanks; that was very stupid of me. :-) I've fixed it now. – ShreevatsaR Feb 12 '11 at 6:27

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

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".

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As Peter pointed out, orthogonal implies but is not a synonym of being independent. For instance, in the plane (two dimensions), any two vectors that are not parallel are actually independent (i.e., they are not dependent; no linear combination of them is zero; one cannot be expressed in terms of the other), but orthogonal only when they are perpendicular. – ShreevatsaR Feb 12 '11 at 6:31

In construction fields, orthogonal is used instead of perpendicular.

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