The primary objective of early undergraduate math courses is not the
ostensible content but to inculcate the student with the ethos of 'rigor.'
Prior to the middle of the 19th century' mathematics was informal. Proofs
were sketches that were accepted by consensus. This system broke down in the
19th century because the informality could not cope with mathematical
investigations that went beyond normal human experience. As an example, the
concepts of infinities and infinitesimal were critical in calculus and more
advanced analysis. Careless use of these concepts lead to apparent
paradoxes that inhibited mathematical progress.
The great 19th century project in mathematics was to eliminate the
uncertainties in the foundations of mathematics. Mathematics developed the
concept of rigor in which strict definitions and valid reasoning eliminated
the uncertainties that prevented progress.
Mathematicians as a community created an ethos that allowed progress. The
object of beginning mathematics courses is to allow the student to
understand this ethos and by doing so understand how mathematics works.
Using the example above, mathematicians eliminated the problems created by
infinitesimals by eliminating them from their reasoning. They eliminated the
fuzzy concept of a number smaller than any other number and replaced it with
the concept of 'limit' which could be formally and unambiguously (i.e.
I do not see why this cannot be true of undergraduate English course as
well. Much effort has gone into the development of techniques by means of
which literature can be appreciated. The student wants not to be left to
his/her own devices but to be taught the techniques that have proven to be
useful. In mathematics, one technique that has proven useful at all level of
study from undergraduate to the most advanced student, is to set a series of
problems whereby the student can be guided in developing the theory on
his/her own. In doing so, the student sees the difficulties that were faced
by the developers and learns to appreciate the beauty of the final theory.
Unfortunately this is not the most common way that early undergraduates are
taught. Most commonly the student hears lectures on the necessity of rigor
and valid proof and then is required to memorize and reproduce standard
proofs. The student obtains a superficial understanding but has no
appreciation of the true and exceeding beauty of mathematics.
So, if mathematics and the sciences can be a guide, not all techniques,
interpretations . are equal. The community through much effort has created
the techniques by which the beauty of the subject can be created and
understood. It is the responsibility of the teacher to bring the student
into the understanding of the techniques that will allow him/her to perceive
this beauty. Without the knowledge generated by the community the student
will not be able to do this.
Thus the teacher's responsibility is to make the student understand the
common meanings that have been created. The teacher may best do this by
guiding the student in his/her own recreation of these meanings. Never the
less the student is being formed (in the sense of the French word for
education, 'formation') and is being introduced into the meaning-generating
----- Original Message -----
From: "Vishvesh Obla" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Saturday, July 16, 2005 8:55 PM
Subject: Re: Meaning, shoes, ships and sealing wax. was: Re: TWL query on
the king my brother
> 'The fact that they tend not to be stood up to and
> by their colleagues causes me to have very serious
> scepticism about
> academia in general. Its value deserves serious
> questioning by society.'
> I second you. It is an infection, as it seems to me,
> causing a serious damage in the intellectual
> conditions supposed to be generated by the academia.
> --- Peter Montgomery <[log in to unmask]> wrote:
>> Every idea is a red herring.
>> If a student came to me with an apparently absurdly
>> rather than generating a negative learning response,
>> I would investigate
>> occasioned that response by the student, and do my
>> best to turn it into
>> a positive learning occcasion, or adjust my own view
>> if the student's
>> response turned
>> out to have justification. In effect NO response to
>> a poem is wrong.
>> Who was it who said something like
>> A poem must not mean but BE.
>> I agree that it is absurd to make students agree
>> with one's own opinion,
>> but in fact that absurdity is perpetrated ALL the
>> time by many in power
>> in academia. The fact that they tend not to be
>> stood up to and challenged
>> by their colleagues causes me to have very serious
>> scepticism about
>> academia in general. Its value deserves serious
>> questioning by society.
>> Nancy Gish wrote:
>> >This is an absurd red herring. The issue is not a
>> simple dichotomy of
>> >all or nothing. The fact that a poem may mean many
>> things and diverse
>> >things does not mean that it can mean anything.
>> Otherwise there is no
>> >reason for it at all.
>> >In any reading there are several elements (I am
>> drawing on other
>> >scholars; this is not my formulation): the text,
>> the reader, the
>> >"author" (whoever made the marks on the page or the
>> notes or the paint
>> >or whatever), and whatever the "author" meant to
>> refer it to. To
>> >eliminate any of these is to distort reading. If a
>> poem has nothing
>> >whatever to do with the words that comprise it,
>> there is no reason to
>> >make those black marks on white pages.
>> >It is nothing so silly or naive as requiring
>> students to agree with
>> >whatever the professor thinks: saying that is just
>> a way of shifting
>> >the discussion away from any serious idea. It is
>> about the nature of
>> >texts at all.
>> >>>>[log in to unmask] 07/15/05 4:52 AM >>>
>> >Nancy Gish wrote:
>> >>I don't know where it comes from, but my students
>> seem to start out
>> >with this idea, that a poem (unlike anything else,
>> apparently), is
>> >"about" whatever one thinks it is. I point out
>> that if you think TWL is
>> >about the joys of rural life in a pastoral
>> landscape with cows and shows
>> >that nature will teach you about god, you are, in
>> fact, just wrong.
>> >>The words on the page are also involved in what a
>> poem is about; they
>> >are not just a point of departure for anything on
>> one's mind
>> >Why not (except in an advanced English lit class,
>> of course,
>> >where one is in a state of potential existential
>> crisis if one
>> >disagrees with the "teacher" and expresses it)?
>> >Eliot, T.S. "The Music of Poetry." ON POETRY AND
>> POETS. NY:Noonday,1961.
>> > (originally Faber, 1947).
>> >... when I learn that a difficult sonnet was
>> inspired by seeing a
>> >painting on the ceiling reflected on the
>> polished top of a table, or
>> >by seeing the light reflected from the foam on a
>> glass of beer, I can
>> >only say that this may be a correct embryology,
>> but it is not the
>> >meaning. If we are moved by a poem, it has meant
>> something, perhaps
>> >something important, to us; if we are not moved,
>> then it is, as poetry,
>> >meaningless. We can be deeply stirred by hearing
>> the recitation of a
>> >poem in a language of which we understand no word;
>> but if we are then
>> >told that the poem is gibberish and has no meaning,
>> we shall consider
>> >that we have been deluded -- this was no poem, it
>> was merely an
>> >imitation of instrumental music. If, as we are
>> aware, only a part of
>> >meaning can be conveyed by paraphrase, that is
>> because the poet is
>> >occupied with frontiers of consciousness
>> beyond which words fail,
>> >though meanings still exist. A poem may
>> appear to mean very
>> >different things to different readers, and all of
>> these meanings may be
>> >different from what the author thought he meant.
>> For instance, the
>> >author may have been writing some peculiar personal
>> experience, which
>> >he saw quite unrelated to anything outside; yet
>> for the reader the
>> >poem may become the expression of a general
>> situation, as well as
>> >of some private experience of his own. The reader's
>> interpretation may
>> >differ from the author's and be equally valid -- it
>> may even be better.
>> >There may be much more in a poem than the author
>> was aware of. The
>> >different interpretations may all be partial
>> formulations of one thing;
>> >the ambiguities may be due to the fact that the
>> poem means more, not
>> >less, than ordinary speech can communicate.
>> So, while poetry
>> >attempts to convey something beyond what can be
>> conveyed in prose
>> >rhythms, it remains, all the same, one person
>> talking to another; and
>> >this is just as true if you sing it, for singing
>> is another way of
>> >talking. The immediacy of poetry to conversation
>> is not a matter on
>> >which we can lay down exact laws. Every revolution
>> in poetry is apt to
>> >be, and sometimes to announce itself to be, a
>> return to common speech.
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