RE: [xmca] Math Question

From: Ed Wall (
Date: Tue Jan 02 2007 - 21:32:55 PST


     I have perhaps slanted this with my talk of proof since this is a
Western notion although I could spoken of the Indian notion of
upapatti instead. I do see very strong indications of this in quite
young children where, in a sense (and this is the best way I have in
speaking about it), they get inside of a piece of mathematics and it
somehow becomes a way of doing/thinking - the tool and the user sort
of blend. The notion of logogenesis re Mattheissen and Halliday seems
to have some bearing here as, I have thought for some time,
Vygotsky's discussion of everyday and scientific concepts in
Development of Scientific Concepts.

    The business about creativity may be in the eye of the beholder. I
used to think that some of the drawings of my daughter on the
refrigerator were pretty creative. She, now, being quite a bit older
might disagree.

Ed Wall

>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.
>From: on behalf of Cathrene Connery
>Sent: Tue 1/2/2007 9:54 PM
>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?
>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
>>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.
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