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    • CommentAuthorskullpatrol
    • CommentTimeDec 19th 2010 edited
     
    Dear Professors,

    I am looking for any articles on the uses of the preposition "of" in mathematics. I once read in a teacher's edition of a pre-algebra textbook that suggested students should be taught, as early as possible, the many uses of the preposition "of" in mathematics, but I have been unable to find anything on this particular question/topic. Could anyone please try to help me find something? Or better still could anyone give me an outline of these uses?

    Yours respectfully, Rob
    • CommentAuthortheojf
    • CommentTimeDec 19th 2010
     

    Hi Skullpatrol,

    Your question (closed at http://mathoverflow.net/questions/49905/mathematical-uses-of-the-preposition-of) is an interesting one for pedagogy or linguistics forums. But I don't think it is a good one for MathOverflow: it doesn't have a single answer, and is very dependent on the individual voice of the speaker/answerer. I don't know the linguistics literature, but I suspect this question has not been taken up --- that said, you might write to Language Log with the question.

    The question is even more inappropriate for meta.mathoverflow, which is mostly about issues of running MO (not a back door for questions that have been closed).

    -Theo

    P.S. I do like the idea of starting "linguistics.mathoverflow.net", seeing as we do have a lot of questions about voice and style in mathematical (and, more broadly, academic) writing.

    • CommentAuthorYemon Choi
    • CommentTimeDec 19th 2010
     
    Thinking of uses of "of" in the writings
    Of mathematicians just seems a strange use
    Of one's time; but of course there are plenty of sightings
    Of "of" every day. The question seems loose.
    • CommentAuthorHarry Gindi
    • CommentTimeDec 19th 2010 edited
     

    Dear Skullpatrol,
    Understand, please that this is a website designed exclusively for mathematical questions, not just
    mathematics-related questions. Perhaps if you looked in that pre-algebra book again, got a citation, and ran it
    by the people over at math.SE, you might be able to get some sort of answer.

    Just because your question is math-related, doesn't mean that you should post it there, however.
    Every question on that site should be sure to have actual mathematical content.
    Remember that!
    Kudos
    !

    • CommentAuthortheojf
    • CommentTimeDec 20th 2010
     

    +1 Yemon

    • CommentAuthorskullpatrol
    • CommentTimeDec 20th 2010 edited
     
    Does anybody want to try and answer the question?

    I am looking for any articles on the uses of the preposition "of" in mathematics. I once read in a teacher's edition of a pre-algebra textbook that suggested students should be taught, as early as possible, the many uses of the preposition "of" in mathematics, but I have been unable to find anything on this particular question/topic. Could anyone please try to help me find something? Or better still could anyone give me an outline of these uses?
  1.  
    No, nobody (at this site) wants to try to answer the question. Please go away.
  2.  
    I have tried every possible site from linguistics to the physics forum and including alot of math teachers forums. Nobody has an answer.
    • CommentAuthorWillieWong
    • CommentTimeDec 20th 2010
     

    (1) See Gerry's comment above.

    (2) If you did ask everyone, have you entertained the notion that nobody has an answer because, well, nobody knows the answer?

    (2a) Does the question really make sense as you asked it? (2b) If so, have you considered doing your own primary research in the area? (2b') Those linguistic sites may give you some pointers on where to find databases of linguistic bibliographic data.

    (3) Do mathematicians really use "of" differently than laypeople? Is there a usage not covered in the Oxford English Dictionary?

  3.  
    Dear Sir,

    Please look at the 63 definitions in the OED before you make such a statement.

    Yours respectfully
    • CommentAuthorEmerton
    • CommentTimeDec 20th 2010
     

    Dear Skullpatrol,

    Presumably you have looked at the 63 definitions in the OED, which means that you are in a position to answer Willie Wong's question (3). I don't see why you expect him to look in the OED when you are the one asking people here to help you with your research, and he has aksed you an entirely reasonable question about whether mathematicians' usage of the word "of" differs from standard English usage. (Incidentally, in my experience, there is no difference, at least that I've noticed.)

    Yours sincerely,

    Matthew Emerton

  4.  
    Dear Mr. Emerton,

    This reference-request is not about the OED it is about:

    ... looking for any articles on the uses of the preposition "of" in mathematics. I once read in the teacher's edition of Pre-algebra: An Accelerated Course by Dolciani that students should be taught, as early as possible, the many uses of the preposition "of" in mathematics, but I have been unable to find anything on this particular question/topic. Could you please help me find something?...

    Yours respectfully.
    • CommentAuthorCSiegel
    • CommentTimeDec 21st 2010
     
    skullpatrol,

    Have you considered the possibility that the book that you're using as a reference for this is not very good, and has some words placed in an order that creates a syntactic sentence but not a semantically meaningful one? The consensus seems to be that mathematicians don't use the word "of" differently from how it is used in normal English, with the sole dissenter being some pre-algebra book's teacher's edition, and other than this, you've provided no evidence that mathematicians use the word "of" in a unique way.
  5.  

    A preposition that mathematicians tend to use in a very strange way is "to"! Of course, we may "assign something to something else", we may "attach something to something else", and we may even "associate something with something else", but dear sirs, we may not associate an object to another object!

  6.  

    @Skullpatrol: We professional mathematicians really do not know the answer to your question.

    Moreover, your question is very "localized" in the sense that the only person who seems guaranteed qualified to answer it is whoever wrote that part of the teacher's manual. It stands to reason that if you really want to know the answer, your best bet is to contact the author of the textbook, the author of the teacher's manual and/or the publishing company in question.

    But I can't help but wonder: why is this passing remark written in some teacher's manual so important to you if you can't find anyone else to corroborate it? In general "teacher's manuals" are not a genre of literature renowned for their careful writing. (Note that they are often not written by the author(s) of the text, but who the actual author is may not be so clear either. It may have been written by a consortium of educators, publishers and students / assistants of the actual author of the text. This is not a recipe conducive to deep contemplation of the significance of individual sentences.) I promise you that in the few circumstances where I have consulted the "teacher's solution manual" for a text, I found so many mistakes so as to become suspicious whether some of them were inserted intentionally to see whether I was awake and paying attention.

  7.  
    Dear Professors,

    Thank you for your constructive comments
  8.  
    I am not trying to say that mathematicians use the word "of" any differently than most people; what I am looking for are any articles on the uses of the preposition "of" in mathematics.

    I once read in the teacher's edition of Pre-algebra: An Accelerated Course by Dolciani that students should be taught, as early as possible, the many uses of the preposition "of" in mathematics.

    Should it not be the mathematians, that preserve the language of mathematics, who provide such a guide to this most grammaticalised of all prepositions? But, alas I have been unable to find anything on this particular question/topic. Could you please help me find something?...

    Yours respectfully
    • CommentAuthorEmerton
    • CommentTimeDec 21st 2010
     

    Dear skullpatrol,

    I think it is clear that no-one here knows any such articles of the kind your are looking for. Also, no-one here particularly seems to agree with the sentiment of the book that you are quoting from. Thus, I respectfully suggest that you pursue your literature search elsewhere.

    Your sincerely,

    Matthew Emerton

  9.  

    "Could you please help me find something?... "

    For the last time, no. Nobody here accepts the premise that mathematicians use the word differently from anyone else, and nobody here knows of any articles which discuss the usage of this word in mathematics.

    (Mathematicians also use the word "no" in the same way everyone else does. Please stop asking.)

    • CommentAuthorWillieWong
    • CommentTimeDec 21st 2010
     

    @skullpatrol: one last comment.

    Should it not be the mathematians, that preserve the language of mathematics, who provide such a guide to this most grammaticalised of all prepositions?

    If you look at a typical mathematics paper, you will see equations, symbols, and diagrams galore. That is partly because Mathematicians have long since learned of the inherent ambiguity of natural language. So while we may "describe" proofs and ideas in natural language, strictly speaking you cannot dissect the "language of mathematics" grammatically as you would English, and in particular you cannot pick-out what is the preposition "of". To put it another way: what English we do use in "mathematical writing" we use it like anyone will use English, except for a smattering of nouns and adjectives that form the jargon of mathematics. The rest, the symbolic and diagrammatic language of mathematics does not admit the word "of".

    As an aside: it is a sad state of affairs that the teaching of mathematics have been reduced to the teaching of a supposed language of mathematics, which no practicing mathematician ever speaks. See Lockhart's Lament for a pungent description of why I consider comments about "many uses of the proposition 'of'" actually detrimental to mathematics education.

  10.  
    Dear Professors,

    "Well, I think I have an idea about a pyramid inside a cubeā€¦"
    is a suitable conclusion for this question/topic
    since none of the nine contributors to this thread
    have been able to provide me with any sort of outline to my question
    as I originally requested in my post:
    "Or better still could anyone give me an outline of these uses?"

    I would like to thank you again for your constuctive comments
    and if you are at all interested in what I have found so far try the google book preview of
    Martin, Richard Milton's chapter X OF 'OF' in Pragmatics, truth and language

    Yours respectfully.
    • CommentAuthorYemon Choi
    • CommentTimeDec 21st 2010
     

    Dear SP: you have failed to give any evidence of why there should be "mathematical" uses of the word "of" in mathematical discourse, as distinct from its uses in "ordinary" English. As such, coming to a site such as MO or meta.MO and passively-aggressively repeating your question, noting that apparently "people cannot answer my question", seems misguided if not downright uncivil. It may be that we cannot answer your question because it rests on a premise we don't accept.

    The uses of "of" in mathematics are precisely the uses of "of" in everyday English, as far as I know, and if you are aware of a counterexample then you should have stated it at the beginning. On the other hand, if you want examples of uses of the word "of", then I suggest reading the collected works of Charles Dickens and Henry James, which should probably give you a more than ample supply of data. Then go and search on Language Log.

    My apologies if this seems brusque, but I am one of those old-fashioned types who can't bring himself to agree with the maxim that "there is no such thing as a stupid question". Consequently, this will be my last comment on this thread.

  11.  
    Dear Sir,

    As I have already mentioned I once read in a pre-algebra textbook that students should be taught early, the many uses of the word 'of' in mathematics, but to my disappointment, I found after desperately searching for any study of the logic of this mighty little word that "this seems to have never been studied, and there is precious little in traditional grammar concerning it."I have only found Martin, Richard Milton's chapter X OF 'OF' in Pragmatics, truth and language which I have quoted.


    Without a proper authoritative analysis available concerning the logic of this mighty little word, anyone with little or no experience in mathematics who tries honestly to study the subject is left at the mercy of the author of the work and left guessing which of the 63 definitions classified under 17 senses is being used or abused whichever maybe the case. I have tried to clarify this "intrinsic" difficulty with the subject by using the O.E.D. and sense XIV as it applies to definition 50 because this is where I found the most mathematical examples.


    My point is that this "intrinsic" difficulty need not exist in the subject if the proper authoritative analysis could be found. But since "this seems to have never been studied, and there is precious little in traditional grammar concerning it" the mathematician must therefore be part logician when expressing his ideas; and the student must also have experience with the the many uses of this mighty little word.


    This "intrinsic" difficulty has, in my opinion, been carried on in the subject by tradition since "there is precious little in traditional grammar concerning it" the grammarians leave the interpretation of 'of' to the logicians who have ignored it and left it to the experience of the mathematicians to use it in whatever application they are working on. But the above leaves the inexperienced student rightfully confused! and I have tried to clarify this confusion with sense XIV as it applies to definition 50 of the O.E.D. as my authoritative source of analysis.


    Yours respectfully.
  12.  
    This is getting absurd. I request that the moderators close this thread.
  13.  
    Yemon, you call that "brusque"? "skullpatrol: GO AWAY!" Now, that's brusque. But not, I think, entirely uncalled-for.
  14.  

    This is getting absurd. I request that the moderators close this thread.

    Yes!