Bingo! :-)
Ana
(PS: could not resist it)
Michael Glassman wrote:
> So Ed, would you say that number is a process that gets us to an end in
> view and that it has not symbolic meaning outside of the equation that
> you are working on at the moment? And if the numbers to not get us to a
> rational end in view that we are looking for, then we have to develop
> new numbers as processes?
>
> Michael
>
> -----Original Message-----
> From: xmca-bounces@weber.ucsd.edu [mailto:xmca-bounces@weber.ucsd.edu]
> On Behalf Of Ed Wall
> Sent: Wednesday, January 03, 2007 12:28 PM
> To: eXtended Mind, Culture, Activity
> Subject: RE: [xmca] Math Question
>
> 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
>>>>> _______________________________________________
>>>>> xmca mailing list
>>>>> xmca@weber.ucsd.edu
>>>>> http://dss.ucsd.edu/mailman/listinfo/xmca
>>>>>
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>> Andy Blunden : http://home.mira.net/~andy/ tel (H) +61 3 9380 9435,
>> AIM identity: AndyMarxists mobile 0409 358 651
>>
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