> Dear Colleagues,
>
> Sam's latest posting encouraged me to submit to our forum the following
> presentation by Reviel Netz about his book,
>
> "The Shaping of Deduction in Greek Mathematics"
>
> given at Harvard, April 1999. I must thank Reviel for his kindness in
> sending me the paper appended below.
>
> Warm regards from freezing Montevideo, Julio.
>
> ==========
>
> I have to apologise, this is not a *paper*. What I want to do now is
> really to introduce the book, to lead to a discussion. I shall describe,
> very quickly, what happens in the book, especially following the
> selection I have prepared.
>
<snip>
> There are two main components to the Greek mathematical practice, the
> visual and the linguistic. ...
> I have chosen to concentrate, in your sample, on one central feature of
> the practice: how diagrams and text are integrated. The intuition behind
> the question is very simple. A text is accompanied by a diagram - this
> is the universal rule in Greek mathematics - and in some way the two must
> be correlated, so that they can belong together. How is that done? What
> is the practice underlying that? There are all sorts of forms such an
> integration of diagram and text can take in principle. Which depends on
> which? What is involved in reading a text with a diagram, in seeing a
> diagram with a text? ...
<snip>
> This then was the starting point for what I had to say on the practice
> of diagrams. I went on to show how arguments actually rely on diagrams,
> how diagrams are perceived as the metonym for mathematics and for a
> mathematical proposition - so that when a Greek thought of a mathematical
> proposition, he could probably think of it as a diagram introduced by a
> text, rather than a text accompanied by a diagram, etc. ...
> Generally speaking, I have tried to show not just that diagrams are more
> important than usually thought, but something slightly more complicated
> - that instead of thinking of diagrams alone, or of texts alone, and then
> of a relation between the two, we should think of a single vehicle of
> information, the diagrammatic text or the textualised diagram, which is
> the vehicle of information used in Greek mathematics. This was their way
> of doing things, of conveying information - not through text alone or
> through diagram alone, but through a composite unit. I shall return to
> say more about this notion of ways of doing things, of practice.
It is illuminating to think about how Reviel Netz's analysis of Greek
mathematical practice, regarding the integration of visual and the linguistic
representations, diagrams and texts, might serve to ground and inform the
future development of pedagogical practice in mathematics. I am especially
interested in what he describes as "their way of doing things, of conveying
information - not through text alone or through diagram alone, but through a
composite unit." But now suppose we permit the composite unit to change, this
is what I call a 'kinetigram'. In the following article, I try to make a modest
beginning by discussing kinetigram definitions:
Intuiting Mathematical Objects Using Diagrams and Kinetigrams
http://www.bham.ac.uk/ctimath/talum/newsletter/talum10.htm
As a continuation I am working on kinetigram conjectures and proofs, and I look
forward to reading Reviel Netz's book which should be quite helpful here.
(Julio & Reviel --Thanks for posting this introduction.) Any other suggestions
would be much appreciated.
Best wishes from humid-wet-sunny St. Louis,
John Pais