RE: [xmca] Math Question and Words/Language

From: Leroy Clarke (lcclarke@rogers.com)
Date: Wed Jan 03 2007 - 04:42:52 PST


Michael G. and All Xmcaers,
  Happy New Year to all! I am a red dot in Ontario, Canada and am always inspired and enriched by the lively discourse taking place on this listserv. I am not a mathematician by training but I could add 2+2 and come up with what is conventionally accepted.
   
  Michael your comment about "great writers are past the use of words as symbols, what they are writing is what is happening at the moment for them - the characters* takes on lives of their own." is truly profound and I consider it rather apt as I currently pore over some qualitative interview data. I would certainly want to quote you if it is your original statement (in any case, thanks for bringing it to our attention.) It adds some balance to Denzin's statement about language as a "window" to a research informant/respondent: "There is no absolutely clear window into the inner life of an informant/respondent, for any window is always filtered through the glaze of language, signs and the process of signification. And language, in both its written and spoken forms is always inherently unstable, in flux, and made up of the traces of other signs and and symbolic statements. (N. K. Denzin, 1989) p. 14.
   
  What do you mean by characters? (are they symbols e.g. alpanumeric and others or are they persons such as research informants or can they be both sympols and persons.)
   
  Isn't a great leap when we add some much confidence to data that is only a "window" that is so tentative, fluid and ambigous?
   
  Denzin, N.K. (1989). Interpretive biography. Newbury Park, CA: Sage
   
  Michael Glassman <MGlassman@ehe.ohio-state.edu> wrote:
  Are we talking about two different mathematics. I have been told that mathematics doesn't start getting really creative until you stop using numbers. Not being a mathemetician I can't grasp this at all - but I have gotten this from two sides - the successful mathematician who said to really work on math you have to move beyond the use of numbers, and to a fellow who flunked out of the Courant Institute (sp?) because he could not get past the use of numbers. I think this is true of writing - that really great writers are past the use of words as symbols, what they are writing is what is happening at the moment for them - the characters takes on lives of their own. I think in reading you can always tell who has gotten past this point and who hasn't. Some people simply write words down on a piece of paper, and for some writers the words are only residue - what is left over from the experience. So perhaps mathematics and writing are in many ways the same process along
 different trajectories.

Michael

________________________________

From: xmca-bounces@weber.ucsd.edu on behalf of Cathrene Connery
Sent: Tue 1/2/2007 9:54 PM
To: ewall@umich.edu; xmca@weber.ucsd.edu
Subject: [xmca] Math Question

Hi Ed and everyone,
What an interesting question. It is true that so many writers and artists as well have stated that they felt the ideas they mediate cross a line in the creative process where mind and activity and object seems to blurr and the work seems to create itself so to speak. Michelangelo wrote that his sculptures spoke to him as he carved the marble. Sometimes when I am painting, the same phenomenon occurs. From a Vygotskian perspective, this experience has interesting appeal when considering the inner voice. Vera John-Steiner's Notebooks of the Mind and Creative Collaborations document this psychological activity.

To apply it to mathematics is a fascinating question. Being someone who can barely balance a checkbook, I am not sure how it would apply.......however, I suspect different domains in mathematics would reflect variations of this experience as they each depend or are derived from various forms of cognitive pluralism. have you looked at Reuben Hersh's work?
Best,
Cathrene

M. Cathrene Connery, Ph.D.
Assistant Professor of Bilingual & TESL Education
Central Washington University
>>> Ed Wall 01/02/07 5:06 PM >>>
Mike and all

This is not quite on the topic (and, thus, I have held back a
bit), but given the amount of expertise that people are bringin I ask
a question I have asked elsewhere (I apologize for how it is phrased,
but something like this was appropriate in that particular community):

> I had a question and wonder if you might point me in a useful
>direction(s). The situation is such: It has been argued of late that
>the work mathematicians do - proof and the such - proceeds within the
>mathematics being created. That is, without going into a lot of
>detail, the mathematics one does is both circumscribed and supported
>by the mathematics one is doing. This is not exactly a matter of
>prior knowledge or the hermeneutic circle per se although it might
>have something to do with being an 'expert.'
> The reason why I am asking is that, the other day in a somewhat
>philosophic discussion around a novel, a participant noted that some
>authors describe the authoring process as open-ended in the sense
>that what finally takes place may differ from what was originally
>intended. That is, in a certain sense, the writing writes itself. As
>this sounded somewhat parallel to the phenomenon I mentioned in
>mathematics, I was wondering if you knew of someone(s) who makes
>remarks about a similar phenomenon re writing.

Ed Wall

>Hi David--
>
>There is a LOT of material on the topic of writing systems.
>Two interesting places to start are:
>
>D. Schmandt-Besserat, Before Writing:. U of Texas Press. 1992 (two volumes)
>
>R. Harris. The origin of writing. Open Court. 1986.
>
>David Olson has written extensively on this topic, primarily from secondary
>sources.
>
>I am unsure of best sources that delve into origins of writing in China
>which were more or less co-incident with
>events in Euphrates area.
>mike
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