Something that's always bothered me is that the word "transversal" is very commonly used as an adjective, but my understanding is that "transverse" is the correct adjective, and that "transversal" is a noun which means "an object which is transverse [to a given object]." So for example you would say "transverse intersection" and "pick a transversal for the line."

However, I could be wrong. I'd like people to answer with their opinion on which is the correct word for the adjective. I'm making this a community wiki since it's too soft to gain reputation over.

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    $\begingroup$ I've been reading some physics recently, and it puts me in mind of my favorite Grand Unified Theory: at high energy scales, my theory predicts, nouns and verbs and adjectives all become the same thing. :) $\endgroup$ – Theo Johnson-Freyd Jul 13 '11 at 17:32
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    $\begingroup$ Theo, I see that you enjoy the quarks of language as much as I do. $\endgroup$ – Tom Goodwillie Jul 13 '11 at 17:41
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    $\begingroup$ @Theo: Any noun can be verbed. $\endgroup$ – Andreas Blass Jul 13 '11 at 18:28
  • $\begingroup$ FWIW: I just checked in the Oxford American Dictionary and it lists transversal both as an adjective and as a noun with derivatives transervality and transversally. $\endgroup$ – Theo Buehler Jul 14 '11 at 2:26
  • $\begingroup$ A verb is just a noun smeared through time. $\endgroup$ – Spice the Bird Jul 14 '11 at 4:21

"Transversal" is a good old geometry word, a noun, as you say. It goes way back to long before anybody was thinking of transversality in the modern sense.

It grates on me to hear it used as an adjective, and this owes something to the fact that in my impressionable youth I saw one of the chapter-heading quotations in Hirsch's graduate text on differential topology: From Whitehead, "'Transversal' is a noun. The adjective is 'transverse'". No doubt this also had an impact on others who (like me) tend to be fussy about language.

On the other hand, language does drift along, and there's no stopping it, and generally no harm is done. By the time you perceive a serious need to tell the world that some usage is wrong, a case can always be made that it is no longer wrong.

In the case at hand it's understandable that "transversal" has come to be used an adjective; after all, "-al" looks like an adjective ending. (But there are words in English where people have been fooled by that, changing the language. "Bridal" is an example.)

By the way, if we were going to be sticklers on this point, mightn't we want to go back and change "transversality" to "transversity"?

  • $\begingroup$ "Reversal" is another noun with an "al" ending. $\endgroup$ – Jim Conant Jul 13 '11 at 17:18
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    $\begingroup$ How about "commutative" versus "commuting" diagram? $\endgroup$ – John Klein Jul 13 '11 at 17:52
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    $\begingroup$ How about "homotopic" versus "homotopy equivalent" (or "homotopy-equivalent") for a relation between two spaces? $\endgroup$ – Tom Goodwillie Jul 13 '11 at 18:21
  • $\begingroup$ That one also annoys me. $\endgroup$ – Jim Conant Jul 13 '11 at 18:48
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    $\begingroup$ I suppose the correct use is that homotopical::homotopic = historical::historic. Historic things live inside history, historical things live outside history and deal with it. Homotopic things (like pairs of maps) are related by homotopy, homotopical things (like topologists, conferences, and certain areas of mathematics) deal with it. $\endgroup$ – James Cranch Jul 14 '11 at 7:59

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