Quantity (as opposed to Quality). Number is a *much* narrower concept.
a
At 04:50 AM 3/01/2007 -0800, you wrote:
>Ed,
>
> I think that focusing on proofs misses the point about mathematics
> since proofs are common to both logic and mathematics but math has an
> object about which proofs are developed. That object is transcendent and
> can't be reduced to logic (Godel, no?) And that object is, in all its
> manifold complexity, Number.
>
> A more fruitful direction for looking at what's going on with
> mathematics should relate it back to activity as in Gary Urton's "The
> Social Ontology of Numbers".
>
> Paul Dillon
>
>Ed Wall <ewall@umich.edu> wrote:
> Michael
>
>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.
> >
> >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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> >
> >
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