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Which of the following phrases below are correct?

  1. The referred maps are to be thought as translations, as means of identifying the tangent spaces.

  2. The referred maps are to be thought of as translations, as means of identifying the tangent spaces.

  3. The referred maps are to be thought of as being translations, as means of identifying the tangent spaces.

  • Welcome to English Language & Usage, a question and answer site for linguists, etymologists, and serious English language enthusiasts.This site strives to provide well researched, intriguing questions. Take the site tour or have a look at the help center to find out more about good questions. Questions that do not show prior research are considered off-topic. – Helmar Sep 3 '16 at 19:25
  • @Eduardo Longa Since I'm already getting down votes on this, I might as well tell you one thing outside of the parallelism; there are compound prepositions, e.g. as of, as to, next to, along with...BUT there is NO "of as" and I challenge anyone to show, with legitimate source, fully referenced, "of as" as a compound prepositions, because the rule is you don't mix prepositions unless are recognized as being compound. So that in itself invalidates numbers 2 and 3. And just to show you, there is "as of": merriam-webster.com/dictionary/as%20of // but Webster's shows no "of as." – Arch Denton Sep 3 '16 at 21:07
  • @Helmar this question is generating quite a lot of discussion.. – Eduardo Longa Sep 3 '16 at 22:19
  • @EduardoLonga well this is not a forum, it's a Q&A site. Generating quite a lot of discussion is not the primary goal. Generating comprehensive and concise answers to intriguing questions is. Thus, a lot of discussion is no good indicator for or against a question. However most discussions stem from inaccuracies and lack of context in the original question. – Helmar Sep 3 '16 at 22:25
  • I think we aren't supposed to proofread here, but I will make an exception. Without having the whole context, I would propose: The referenced maps may be thought of as translations, which can be helpful in identifying the tangent spaces. – aparente001 Sep 4 '16 at 15:22
3

Both 2 and 3 are used in normal conversation. 1 is incorrect, although "considered translations" would be correct. However, the context appears to be mathematical and, in that case, 2 would probably more appropriate because, being mathematical, the terms "map", "translation" and "tangent space" are all precisely defined.

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Since this got all blown out of proportion, I'll just say none of your sentences are wrong, and that the first sentence is BEST in parallel form. If you had to pick, pick number 1. Parallelism is not a hard core set of rules, but it is standard practice.

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This is technical (mathematical) writing. I think what was intended is:

The set of maps referred to can be identified with the tangent space.

This is standard mathematicalese. Notice that maps referred to, although it ends with a preposition, sounds better than referred maps; the latter sounds a little off. But better would be to drop the referred, and if necessary, give the name of, or the symbol representing, the set of maps appositively, thus,

The set of maps, $symbol$, can be identified with the tangent space.

This is more natural mathematicalese.

However, because of the plural in tangent spaces, the following might have been intended:

The sets of maps referred to can be identified with tangent spaces.

or

The set of maps referred to can be identified with (the union of) tangent spaces.

The comment about dropping referred can be applied in these cases too. To be definitive, we would need more context.

Without set[s] of, the statement is sloppy, since although mathematicians will interpret it as the set of such maps, it is not the maps themselves which are identified with the tangent space (if that was intended), but merely with elements of the tangent space ...; this is a frequent source of obscurity in mathematical writing.

I don't think it is appropriate for those who are unfamiliar with mathematical writing to comment on this question.

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  • Yes, clearly this is specialist, technical language - all three second parts of the OP suggestions make no sense to me! That said, @Bold Ben makes a good point that "...thought of as (translations)..." and "...thought of as being (translations)..." are both usages found often in ordinary speech – Dan Sep 3 '16 at 22:51
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All three sentences direct the reader to "think" of the referred maps as "translations, etc." therefore:

"The referred maps are translations, used as means of identifying the tangent spaces."

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