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In British English and in the context of mathematics, is it more correct to say one parameterises a curve, or one parametrises a curve?

In other words, which spelling should be used to align with the intended meaning?

Glen Wheeler
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5 Answers5

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This depends a bit on how one defines "correct". Various dictionaries might accept either or both uses. If you go by the scientific literature, both seem to be widely used.

On the other hand, if you are looking for a spelling that is suggestive of the correct meaning, then you should go with "parametrize" (or "parametrise").

You are not transforming the curve into a parameter, nor are you making it like a parameter. You are making the curve into a parametric curve (not a "parameteric" curve).

Similarly, one does not "meterize" a topological space to make it into a metric space, and likewise, Thurston didn't pose a "geometerization" conjecture that one can turn certain topological 3-manifolds into living, breathing geometers.

Also, for what little it's worth, as far as mathscinet is concerned, "parametriz*" is almost twice as frequent as "parameteriz*" (13961 hits vs 7720). Not to mention that the earliest use of "parametriz*" in that database is from 1933:

McShane, E. J. Parametrizations of saddle surfaces, with application to the problem of plateau. Trans. Amer. Math. Soc. 35 (1933), no. 3, 716–733. 53A10 (49Q05)

predating the first recorded use of "parameteriz*" by 3 years:

Morse, Marston; A special parameterization of curves. Bull. Amer. Math. Soc. 42 (1936), no. 12, 915–922.

M W
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    A difference of three years is not really significant. It's possible both where in common usage in non-published text concurrently and one just happened to get published a few years earlier. If it were a much longer duration that might be a better indicator of what was common at the time. – Huckle Mar 07 '16 at 01:38
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    "a spelling that is suggestive of the correct meaning" It seems this is the crux. Apparently parametri[s/z]e comes from math circles re parametric curves; parameteri[s/z]e seems borrowed to talk about applying parameters to something in general to modify the outcome. Programmers as a matter of course apply parameters to a display to show/hide/add/subtract or otherwise alter what a user sees depending on applicable parameters, so it seems both are valid based on context? – gordon Jul 15 '16 at 15:36
  • I'm not sure I buy this argument. We metrise a metric space by giving it a metric (not a meter); Thurston's conjecture talks of geometrising spaces by giving them a geometry (not a geometer, as indeed you note!) - but we paramet(e)rise a model by giving it parameters (not parametrics, or similar). – psmears Feb 14 '22 at 14:02
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Both parameterize and parametrize are acceptable according to the ODO.

Both parameterise and parametrise are acceptable in BE as per Collins.

coleopterist
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    True that. I'd go with parameterize, ordinarily, because parameter is the root word, making it more clear. If I were feeling lazy, I'd go with parametrize. – Wolfpack'08 Sep 02 '12 at 08:14
  • Good to know both are OK, though I suppose it would look stupid to choose randomly at each use within a single work. That is what I'm fixing in my math paper this evening... – DarenW Aug 08 '17 at 02:12
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For what it's worth, parameterize has 1,100,000 search results on Google, while parametrize has 500,000. I would take that as evidence that both are acceptable and in widespread usage.

qdread
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  • Given the various complex strategies for query expansion used by Google Search, I wouldn't assume it's worth very much to count hits for variants like this. – Will May 05 '16 at 13:14
  • I would expect the words "parametrization" and "parameterization" to be just as commonly used as their verb counterparts. – user3932000 May 13 '16 at 05:46
  • Perhaps huge demand for coders tilts the ratio of them vs mathematicians so no surprise the Google hits are favoring parameteri[s/z]e over time? (see my comment above re difference of usage/context) – gordon Jul 15 '16 at 15:42
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For consistency, I agree with MW above. Although one cannot necessarily argue on the basis of consistency in English, it is nice to try to keep things consistent. Thus, metrizable -> parametrizable -> parametrize, etc.

It depends on what you think "correct" means. If the majority of people on Google prefer parameterize, to me, that simply means that the majority of people do not think about it. The English language is too precious and wonderful an invention to be left for majority vote.

The same holds for the -ize vs -ise spelling. Although I am not American, I write -ize because it is more etymologically correct (Greek). Even Groves says so. The =ise spelling comes via French, and so has little to do with what one should write in English.

user237533
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    Except that a lot of English came from French via the Norman invasion. What is "more correct" is often merely a matter of opinion, as your second paragraph demonstrates. – Andrew Leach May 24 '17 at 10:03
  • "ize" is coming from Greek "ίζω" (https://en.wiktionary.org/wiki/-ίζω) It is used to turn nouns into verbs. – Gouz May 22 '22 at 16:36
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Not being a linguist, I would use parameterise in British English. Reasons

  1. metre is a length measure, while meter is an instrument for measurement.
  2. Whatever the origin, BE is characterised by ise and not ize, typical of North-American English, which by definition is a derived language.
Alessandro
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    Your answer could be improved with additional supporting information. Please [edit] to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers in the help center. – Community Feb 14 '22 at 13:19
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    If you look at Google 1-grams for parameterise, parametrise, parameterize and parametrize, you'll not find supporting evidence for the preference of 'parameterise' in 'BrE'. The -ise / -ize debate has been covered pretty fully on ELU, and it has been claimed that 'BrE', 'AmE' are fanciful, broad-brush classifications. I think the ise/ize divide in the UK was last estimated at 3:2, hardly a mandate to prescribe. – Edwin Ashworth Feb 14 '22 at 14:53