Mike
Here is a sort of expansion (and I am by no means sure about the
authoring business, but the process sounded somehow similar) and
perhaps the best place to begin is with a story. A number of year ago
I was teach a graduate course in mathematics and had, for most of the
period, been working on one or two proofs. At the end of class, a
young woman approached me (she was, my impression, one of the more
knowledgeable students) and said something like "I understood
everything you did, but I didn't understand why you did it. I don't
think I'll ever be able to do proofs." I said the usual dumb thing
something like "It is just a matter of writing down what you were
doing and you'll catch on after doing it for awhile and I've just
been doing it for awhile" and left it at that.
Latter that day and yet still I've been thinking about this. I
tend, I suspect like a lot of others who teach some content, to have
an idea of the direction and a 'feel' for the terrain and then,
depending on where people are at, tend to somewhat improvise. What
makes it difficult is that the young woman was asking me for a
'formula' for proof and there, in a sense, isn't one. One's beginning
constrains one somewhat, one pulls out of experience some likely
scenarios which have their own affordances and limitations, and one
sort of keeps one's end in sight (sort of what Dewey talks about in
the Theory of Inquiry).
Perhaps another way to say it is that in a moderately complex
proof there seems to before the 'novice' a huge amount of leeway as
almost every time you write a line you come to a bifurcation point.
However, that is misleading as what has gone before both supports and
simultaneously constrains where you can 'reasonably' go next (holding
that end in sight).
Let me be more specific and give a very simple example (there is a
lot missing form this so this isn't exactly what I had in mind, but
it perhaps illustrates). Okay, I want to prove there are an infinite
number of prime numbers. The wrong way to do this is write some
formula which gives you an infinite number of primes. There isn't
one. [bifurcation] So a scenario would be to assume the converse -
i.e. there are only a finite number of primes and show this leads to
a contradiction (hence, showing 'logically' that there is indeed an
infinite number of primes). [bifurcation] Now you have an finite
number of something so you write them down (skipping 1 just in case
you want that to be a prime) p1, p2, p3, out to pN and, of course as
you are working with primes (and they are mucked up with
multiplication and division), you write the product p1*p2* out to pN
and set that equal to K. [bifurcation] Then you look at K+1.
[bifurcation] Well, K+1 certainly isn't divisible by p1 or p2 out to
pN so either K+1 is a prime or there is a prime pm less than K+1 that
was not in the original list. Hence a contradiction as was hoped for.
Okay, I've used some basic knowledge about primes to begin and
that with some arithmetic has both constrained and enabled the proof
at each step. However, there is a sense in which I know that the
appropriate thing to do is multiply the primes and then, of course,
adding 1 is the elegant thing to do (smile).
Does this help?
Ed
>Ed--
>Never mind off topic. We are always shifting topics. And I would be happy to
>respond usefully to your query if I knew how!! The problem is that I do not
>understand
>what you wrote! I am GUESSING that what you are talking about has to do with
>origins and
>change. ("the mathematics one does is both circumscribed and supported by
>the math one is
>doing" coupled with expertise-- which I think of as a developmental
>process). But I cannot get
>from that to authoring a novel. And I am not even sure what the math example
>is about. Can you
>expand?
>
>I am not sure, either, what David is after. My suggestions were intended to
>focus on the origins
>or graphic representations of ....... things.... ideas...... language (all
>big issues in the history of writing).I picked my
>suggestions for David thinking that what he was interested in the origins of
>scripts of various kinds. Others have gone
>to goody and watt on the consequences of writing, ong, etc. Havelock is an
>interesting "half way" point because he makes
>a big deal of the special properties of the alphabet and hits on Chinese
>ideographic writing.
>
>Perhaps you can expand? (And be ready for someone to comment on the article
>of the month-for-discussion, although who knows!!)
>
>mike
>On 1/2/07, Ed Wall <ewall@umich.edu> wrote:
>>
>>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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