Re: ascending to the concrete

Don Cunningham (cunningh who-is-at indiana.edu)
Wed, 3 Feb 1999 16:37:05 -0500

I agree with Rolfe. For example, I have often heard people
talk of the process of moving from a real problem to
a mathematical representation as mathematical abstraction.
But isn't it more a matter of transmediation, metaphor,
substitution, etc.? If you regard a real world problem as one of
that can be modeled by a mathematical representation,
aren't you focusing on particular aspects of the situation?
In one study we had students working on a problem about
irrigating a field with a moving sprinkler system -
what is the optimum spacing between sprinkler heads?
One model is to represent the problem as chord lengths
and then use the mathematical tools associated with chord lengths.
Rather than abstraction, I see that as a process of focusing
on specific elements.........djc

>It may not be what Marxians mean or meant but I've always found it
>useful, in terms of AT systems, to think of movement to the concrete not
>as a level (higher or lower) but as a Piercean developmental process: a
>progression from the less formed (but more creative perhaps) to the
>established. 'Things as they are' being the available resources
>(mediating tools) that regulate the process when it begins but which
>themselves may be transformed as the activity proceeds and new
>relationships develop.
>
>For what it's worth.
>
>Rolfe Windward
>Dept. of Education, Lindsey Wilson College
>windward who-is-at lindsey.edu
>"We know more than we can say" -M. Polanyi

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