Is there an agreed-upon way to say "complexes" in the sense of "the set of complex numbers" (as in "solve over the complexes")? Do we keep the stress on the first syllable (as in "complexes of buildings") or do we shift it to the second one (as in "complexity" or "non-complex")?
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In maths don't you always say the full term?– mmmmmmCommented Sep 19, 2021 at 17:16
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1@mmmmmm You can occasionally come across the plural form in print or on the web but rarely in speech (and that was the main reason for the question). Also the term is quite popular among the users of Wolfram Mathematica – you indicate the set of complex numbers with Complexes (but again, normally you can only see it printed not pronounced).– BuckminsterCommented Sep 19, 2021 at 17:27
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2Although I've never come across the usage (and I taught maths beyond A-Level) there are over 3 000 000 hits for "over the complexes" over the Googles. It seems to be gaining in respectability. I'd advise you to ask this one over on Mathematics.SE.– Edwin AshworthCommented Sep 19, 2021 at 18:04
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1@Edwin Thank you for the response, Edwin. I've already followed your advise and here's the answer I received: "You may get a better explanation at english.stackexchange.com of how the lexical stress shifts based on the part of speech".– BuckminsterCommented Sep 19, 2021 at 18:09
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1(1) Maths specialists are far better placed to comment on the idiomaticity of suggested terminology so obviously confined to their field. // (2) As for pronunciation, this also is a function of domain of use as well as general patterning in the language. Take 'integral', for instance. There are two main valid pronunciations for the adjective, but only one for the noun, which as far as I know isn't used in a non-technical register. And even pattern-predicting is a minefield: Lexico offers 3 distinct pronunciations for the adjective 'complex'.– Edwin AshworthCommented Sep 19, 2021 at 18:25
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2 Answers
As a math major as an undergraduate who studied complex analysis, among other subjects (i.e. the calculus of complex numbers), the pronunciation we used (in an Ohio liberal arts college and an Ohio public university in the late 1980s amd 1990s) was to keep the stress on the first syllable (as in "complexes of buildings") and was not to shift it to the second one (as in "complexity" or "non-complex").
Given the diverse educational and regional backgrounds of my professors and the unanimity of the pronunciation, I believe that this is a fairly reliable indicator of the American English norm.
The term when referring to the set of all complex numbers should be plural (i.e. complexes, not complex) because the concept is inherently plural (akin to the reals, the rationals, the irrationals, etc.) and is generally given a plural character grammatically. (For what it is worth, mathematicians are, in my experience, also more likely to treat the word "data" as a plural rather than singular word, than non-mathematicians.)
This said, lots of people who would talk in public about the complexes are introverts who grew up mispronouncing many words that they learned through book reading, and are not infrequently non-native English speakers, so there would be tolerance of alternative pronunciations in most cases.
If you don't want to rely merely on the SE, I would recommend watching educational YouTube videos where this topic would come up, or online video of mathematics and theoretical physics conferences where the term would be used (e.g. twistor theory in physics), which is vastly more widely available than it was even pre-pandemic, since almost all major academic conferences in the past two years have been held in an online format.
answered Sep 19, 2021 at 21:05
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To be nonambiguous I would just add a syllable or two: "over the complex numbers" or "over all complex", or perhaps "in the Complex domain". Whereas "reals", "rationals", et similar are more immediately clear, "complexes" sounds unusual and like it could refer to something else (akin to "simplexes", which is not a number object). Within context or in text it is not an issue, but when spoken I would opt for non-shortcut in this case.
If I were to shorten it, I would also drop the "s" and stress the second syllable (disambiguating from the 'building structure' sense): "over the comPlex". If you feel compelled to follow the identical pattern as with other plural-groups of numbers, then "over the compLexes" sounds sort of natural to me.
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1Google reveals over 3 million cases of "over the complexes" (though probably not all of them are unique or belong to mathematics), so the form is used but can rarely be heard. What would it sound if you were to say it? Commented Sep 19, 2021 at 18:03
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1Personally, if I were to speak about "the complexes" meaning "the domain of complex numbers", I would opt for what you suggested in the question (stressing the second syllable). If the conversation is regarding math and the context is about domains, then the syllable-stress isn't a huge issue. Were not it for the other non-math and math- meanings of word, I would just say it by default in the same manner as I do other collectives, stressing it the exact same as in "the complex numbers" but with 'numbers' ellipted. A math- motivation for stressing the second syllable is to distinguish it from– 11qq00Commented Sep 19, 2021 at 18:10
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..from implying that the term means an opposite of "simplexes" which I think is stressed on the first syllable.– 11qq00Commented Sep 19, 2021 at 18:12
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Thank you for the numerous examples and clarification – now I feel reassured, since stress on the second syllable seems more natural and unambiguous to me as well. Commented Sep 19, 2021 at 19:15
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"I would also drop the "s" and stress the second syllable (disambiguating from the 'building structure' sense): "over the comPlex"." This would not be standard usage in the sense of referring to the set of all complex numbers, which is plural in both concept and in grammar. Commented Sep 19, 2021 at 21:07