Subject: Re: [HM] Barrow
From: Alejandro Rivero (arivero@free4all.co.uk)
Date: Sun Jan 02 2000 - 11:53:10 EST
I have read the article from Mahoney in the book that Julio suggested.
It says that the relation between the Geometrical Lectures and the
invention of calculus is mostly "read into" by contemporary authors.
But on other hand, I am afraid that the article has the same problem;
it seems to assume that differential calculus is about infinitesimals,
ie limits when things go to zero. In that sense not a lot can be
extracted from this work.
On the contrary side, I have read that Bourbaki ascribes to Barrow not
the calculus, but the duality between differentiation and integration.
And Majid ascribes to Barrow a sort of deformed q-calculus. Such
attributions do not require a mastery of infinitesimal limits, but on
the other hand they seem to require some intuition of duality, very
much in the context of Alain Connes' theory, which is too modern.
I would be glad of hearing some opinions about this in the list. What
is exactly the small triangle of Barrow?
On a related theme, I find amusing to refer to infinitesimals as "atoms",
Latin "individua"... Anyone know the origin of this?
Alejandro
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