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The concept of the opposite of a word is well known, for example black/white, on/off.

In mathematics, there is the concept of 'orthogonal', meaning geometrically perpendicular.

Is there a metaphorically related concept to 'opposite', but means something like 'not opposite, not the same, not on the same axis even, but on the same plane'

For example, could 'orthogonal' be used to describe the following pairs red/green, left/forward, wrong/left?

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    Why should dog/lion or dog/gerbil not be "opposite", in that case? What is the actual problem that you face?
    – Andrew Leach
    Feb 13, 2015 at 11:15
  • the idea comes from some code I wrote years ago. it dawned on me that each checkbox is orthogonal to the next (and to each other):demonstrations.wolfram.com/1125899906842624Pictures
    – JMP
    Feb 13, 2015 at 11:49
  • @Jon, when you say "each checkbox is orthogonal to the next", are you implying, for example, that "two dots" is orthogonal to "molecule"? If so, how?
    – Dan Bron
    Feb 13, 2015 at 11:56
  • the confusion is whether we're talking positional relativity (go ask UX.SE) or some form of metaphysical relativity (go ask linguistics). that the checkboxes are stacked in a vertical column suggests they are above one another, does not suggest they are perpendicular to the labels for said checkboxes.
    – Erich
    Feb 13, 2015 at 12:05
  • the closest example to what i think he's getting at is the left/straight/right concept. or perhaps yes/maybe/no. some form of quantum english.
    – Erich
    Feb 13, 2015 at 12:10

2 Answers 2

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The current dictionary entries for 'orthogonal' all have mathematica senses (geometrically perpendicular, linearly independent).

Though not an official semantic entry, the word is used metaphorically to mean independent in the non-mathematical sense of not-related or not dependent. This is often to distinguish from situations where X depends on Y. If X and Y are related, but X doesn't depend on Y and Y doesn't depend on X, then they might said to be orthogonal.

You ask with respect to word pairs. In lexical semantics, there are a number of terms to describe relations between two words. 'Synonym' is for words which have a lot of semantic overlap and might replace one for the other. 'Antonym' is for two words which are on the same scale or dimension but at opposite ends. 'Hyponym' is for a word which describes a subset of concepts described by another word. And there are others.

Back to 'orthogonal'. let's take the positional words left, right, in front, behind. Left and right are opposites, and front/behind are also. You're asking about, say, what the relation is between left and behind. "Is 'left is orthogonal to behind' correct usage?".

Maybe that's a straw man, but the more appropriate usage would be to compare the dimensions, not the words themselves. This example is a little too literal (because they are really directions which are what the linear algebra use of orthogonal is trying to compare).

'Orthogonal' could be used coherently for comparing say gender vs ancestry. 'brother' and 'sister' are both gendered versions of 'sibling' (and so hyponyms of sibling). 'mother' and 'grandmother' are gendered versions of 'parent' and 'grandparent'. So I would say it is poor usage of the word 'orthogonal' to say 'sister is orthogonal to parent' but better usage to say that ancestry is orthogonal to gender.

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You are correctly describing the mathematical sense of orthogonality. The y dimension on a graph is orthogonal (at right angles) to the x dimension. The z dimension on a 3-D graph is orthogonal to both the x and the y dimensions.

I would suggest that very term, dimension, to describe an aspect of the orthogonality. Dimension could describe points that are not on the same axis, yet in the same plane (or 3-space or n-space).

One can think of colors for an additive system (used for computer screens) as being described through the points or vectors of the dimensions red, blue, and green. Or if you are using a subtractive system (in printing, for example) you would use the dimensions, cyan, yellow, magenta, and black.

You could describe red, blue, and green as orthogonal choices in the color dimension. (To select from only red and blue would not adequately describe the color.)

You might describe left/right in a turning dimension. For left/forward, you might explicitly describe the two dimensions as a turning dimension (left/right) and a progress dimension (forward/back).

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