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Today I was trying to figure out an orthogonal word for "aesthetics", and was having a bit of trouble searching for it as "aesthetics orthogonal" and "aesthetics antonym" gave nothing useful—the latter just yielded synonyms to "ugly". (Didactic was the word I eventually settled on after coming up with it and double-checking the definition, but that's another issue)

"Orthogonal" would seem to be what I want, and as a scientist makes sense to me, but another question makes me think twice about using it in a broader context.

In short, what is the term for a word that would run along a different continuum that is perhaps related but distinct, for example:

  • beauty vs. intelligence
  • agility vs. power
  • height vs. width
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    I'm not sure you are using orthogonal correctly. Things are orthogonal when a movement along the axis of one things is completely independent of a movement along the other- in a graph the X and Y axes are orthogonal. I might say that utility might be orthogonal to aesthetics in that how useful something is has nothing to do with whether it looks good or not. – Jim Aug 19 '13 at 23:30
  • A "branch concept"? – Mussri Aug 19 '13 at 23:33
  • @Jim just like in mathematics, there can be many orthogonal vectors, utility seems orthogonal (to varying degrees...language is not math) to both aesthetics as well as the informational value (didacticisim). – Nick T Aug 19 '13 at 23:36
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    @Jim the OP is using 'orthogonal' correctly. It is a dead metaphor of mathematical concept. – Mitch Aug 19 '13 at 23:48
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    Words may or may not have antonyms; quite often they are multi-dimensional, so that "opposite" is meaningless in general. Here's a sample ontology of verbs of cutting, for instance; most of them don't admit any "opposites". – John Lawler Aug 19 '13 at 23:57
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Orthogonal indeed seems suitable, particularly when taken in its sense “Of two or more problems or subjects, independent of or irrelevant to each other” or perhaps in its sense “Statistically independent, with reference to variates”. The zero-inner-product sense also will seem appropriate to people familiar with mathematics.

However, the term complementary might be more useful, due to its common sense of “Acting as a complement”, that is, acting to complete something else. Also consider tangential.

Regarding something orthogonal or complementary to aesthetics (“The study or philosophy of beauty”), consider pragmatism (“The pursuit of practicality over aesthetic qualities; a concentration on facts rather than emotions or ideals”), or the aforementioned utility or its philosophical form utilitarianism (“A system of ethics based on the premise that something's value may be measured by its usefulness”).

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Might dichotomy be the word you're looking for?

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The early 20th century German Dada movement was a rejection of aesthetics. Dadaism, would be, perhaps, on point. The adjective form is dadaistic.

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Measure.

The effectiveness of a football player depends on both agility and power. Those who measure high in effectiveness will typically have some balance of these two attributes.

Sexual attractiveness is hard to measure precisely, yet most people feel that beauty without intelligence is no more appealing than intelligence without beauty. A measure of sexual attractiveness is inevitably personal and subjective.

We define the "squareness" of the river barges as a measure of their length relative to their width.

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The word you are looking for maybe "intermittence" (or "interruption").

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