RE: [xmca] Math Question

From: Ed Wall (ewall@umich.edu)
Date: Wed Jan 03 2007 - 09:27:42 PST


Intriguingly Dewey uses such words as valuation, discrimination, etc.
arguing that number is a rational processes, not a sense (or
non-sense) fact.

Ed Wall

>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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