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As the title says, I'm wondering if "non-linear" is an acceptable spelling of the word "nonlinear."

A bit of research on this site turns up Is the use of a hyphen between "non" and an adjective strictly necessary?, in which Monica Cellio commented that some of these "non"-prefixed words have entered the language in unhyphenated form. This is the way I'm used to seeing "nonlinear." But other people I work with spell it with the hyphen, "non-linear." Is that valid, or should I point it out as a correction? (This is in a scientific paper going to publication; I wouldn't care in a less formal context)

More generally, what reference(s) would I look at to answer questions like this in the future, about whether a particular compound can/should be spelled with or without a hyphen?

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    While it's strictly correct to omit the hyphen, and technically it's either incorrect or out of favor to use the hyphen, in my experience only the tiniest percentage of people know this, even very formal writers, especially if they are not English geeks like us. ;) I'll bet you find non-linear in plenty of reputable publications. (Note: By all means, I strongly recommend omission of the hyphen!)
    – John Y
    Commented Jul 1, 2011 at 19:33
  • @JohnY: Just a few months ago, I had that moment of enlightenment, where I became conscious about the fact that in my country (Germany), there is no law about one, correct grammar. Surely, I've known it before; but never thought about it. And the more I thought about it, the stranger it seemed to me to test pupils' grammar performance in school. That's just as brainf***ing (pardon) as thinking about "guilt" in law systems ... Whoa. Personally, I've always taken an intuitive approach to writing correctly. Seems I have some builtin-talent for it (in German at least), but I hardly can dissect ...
    – phresnel
    Commented Nov 26, 2017 at 11:34
  • ... the grammatical anatomy of what I write (Plusquamperfekt? Uh). This heureka, that there is no law for correct German, made me more relaxed regarding writing style. What counts is that the message, the "information" as it's called in Computer Sciences, is transferred correctly. And if I can ensure that by adding a grammatically incorrect (by whichever grammar in use at the time of writing) hyphen, paragraph or whichever anarchist device, I go for it. Also, running monetized blogs, I learned to pervert style sometimes anyways; copywriting is a huge and often ugly topic.
    – phresnel
    Commented Nov 26, 2017 at 11:39

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According to Hyphenated Words: A Guide

You would not use a hyphen with the prefix non unless it is before a proper noun.

Do not hyphenate words prefixed by non, un, in, dis, co, anti, hyper, pre, re, post, out, bi, counter, de, semi, mis, mega, micro, inter, over, and under (among others).

Examples: nonaffiliated, nonemergency, uninfected, inpatient, disorder, disbar, coworker, copayment, antismoking, antimanagement, hyperactive, hyperrealism, preoperative, prejudge, reoccur, readjust, resubmit, postoperative, posttraumatic, outpatient, outmoded, bimonthly, biannual, counterrevolutionary, counterculture, decompress, semifinal, semiannual, misinformed, misprint, megabyte, microcircuit, interconnected, interoffice, overempha­size, override, underrepresent, underestimated.

EXCEPTIONS: When the second element is capitalized, as in Un-American and non-English, a hyphen is used. Also, occasional exceptions exist where the prefix and the second element have not (yet) "grown together," such as de-emphasize, pre-owned, co-op (to distinguish from coop) and anti-inflammatory (and all words with anti- prefix and second element beginning with i)

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    I think that, on top of the one exception for capitalized proper nouns, if the use of "non-" preceding a term is previously unseen then the hyphenated spelling may be acceptable. However, this doesn't excuse "non-linear" as the term is common in mathematics (which I hope we all took to a point where this term is known); the spelling is "nonlinear" and the hyphen should not be used here.
    – KeithS
    Commented Jul 1, 2011 at 20:07
  • That guide's proposed rule looks suspicious to me. Particularly, "nonemergency", "antismoking", "antimanagement", and "interoffice" look strange without a hyphen. Also, "posttraumatic" (though the DSM spells it without a hyphen)
    – Mechanical snail
    Commented Oct 11, 2011 at 1:56
  • Some people use the diaeresis, such as "coöp", and "reëvaluate", but I've never seen "antïinflamatory".
    – Oskar Limka
    Commented May 7, 2021 at 19:19
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The first three dictionaries I looked in all give nonlinear as the entry with no alternate non-linear. Here's NOAD:

nonlinear |nänˈlinēər| adjective
1 not denoting, involving, or arranged in a straight line.
• Mathematics designating or involving an equation whose terms are not of the first degree.
• Physics involving a lack of linearity between two related qualities such as input and output.
• Mathematics involving measurement in more than one dimension.
• not linear, sequential, or straightforward; random : Joyce's stream-of-consciousness, nonlinear narrative.
2 of or denoting digital editing whereby a sequence of edits is stored on computer as opposed to videotape, thus facilitating further editing.

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  • +1; in addition to nonlinear, searching the dictionary reveals plenty of words that start with non but do not include a hyphen. Examples: nonblack, nonbiological, noncombatant.
    – MrHen
    Commented Jul 1, 2011 at 19:08
  • Most mathematicians consider nonlinear to be a superclass of (including, and not disjoint from) linear.
    – Oskar Limka
    Commented Dec 4 at 13:20
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The Oxford Dictionary (which I personally consider the reference for the English language) lists "non-linear" as the correct British spelling and no alternative is given. But if you switch to the US English dictionary, the only entry is "nonlinear".

Source: http://www.oxforddictionaries.com/

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  • Correct, @Sentry, but in the OED entry examples use "nonlinear", should one assume that the hyphen is discretionary? I looked up "unhyphenated", out of curiosity, and the only entry is "un'hyphenated" (yes, with the apostrophe).
    – Oskar Limka
    Commented Jan 11, 2019 at 13:46

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