FOM: FOM : Jurassic pebbles on the beaches of infinity

[Lincoln Wallen]

I'm afraid I missed this reply from Olivier Souan

   Date: Wed, 18 Mar 1998 22:43:55 +0100
   From: Olivier Souan <zalmoxis at club-internet.fr>

   Kanovei wrote :
   >The Largange theorem is a product of social activity,
   >and as such it most likely did not exist before L
   >proved it.

   Lincoln Wallen wrote :
   >if a
   >Jurassic beach were *to all relevant intents and purposes* the same as
   >a beach I can take you to now, the same things would hold.  Of course.
   >That is the point of stating explicitly, or implictly "all relevant
   >intents and purposes".

   Let me develop your viewpoint, to which I do not subscribe.
   The Lagrange theorem has not sprung from nothing. The reason of its
   existence is the social context in which he had taken place, and more
   peculiarly the "intents and purpose" of a social community. I have a
   goal
   (counting pebbles), so I use the Lagrange's theorem for that (tell me if
   I
   do distort your thoughts). Mathematics' reason of being is thus social
   activity.
   1) Let us say that social purposes are necessary reason of existence 
   (one
   should add as an example, the "production" of geometry from land
   surveying
   in Egypt in order to avoid the Nile floods, etc.). But are they
   sufficient?
   I do not think so. You have to reach sufficient levels of abstraction in
   order to contemplate the situation and formulate a solution. You have to
   make a model of reality (model not used in the technical sense), to find
   a
   scheme which works in all cases and in all situations. Those levels of
   abstraction are not at all included as such in practical activities,
   even if
   those benefits from them. They are used by accident, not for their very
   sake, not for themselves, but for their applications.

   [...]

Olivier Souan wrote more, but I just wanted to give enough context to
point out I had not been sufficiently clear in my use of words.  By
"practical" I don't mean "physical" or "applied".  I used it as a turn
of phrase to suggest "ordinary" pragmatic activities recognisably
constitutive of "doing mathematics".  So, writing, discussing,
proving, calculating, drawing, revising etc.  The ambiguity arises
because the thought experiment involved arranging pebbles on a beach.

I don't think Kanovei's position and mine are the same.  I see it as a
matter of mathematical practice to develop ideas about objects which
are, in Kanovei's sense, not feasible.  But I haven't compared his
position with mine in detail so I don't want to say more at this point.

Lincoln Wallen