[FOM] Nonstandard Methods

[Todd Wilson]

On Wed, 30 Jul 2003, Harvey Friedman wrote:
> On 7/30/03 1:33 AM, "Alexander M Lemberg" <sandylemberg at juno.com> wrote:
> > More significantly, does it reflect the original heuristic motivations
> > for infinitesimals and origins of calculus? I believe that  the theory of
> > "smooth analysis" does so to a far greater extent.
> 
> I would like to see you say something for the FOM about what the theory of
> smooth analysis is. E.g., I am not sure if you just mean Bishop style
> constructive analysis, or something else.

Concerning smooth infinitesimal analysis, I have pointed FOM readers
before to the book on the subject by JL Bell:

    John L. Bell, A Primer of Infinitesimal Analysis, Cambridge
    University Press, 1998.

There is perhaps no better place to go than the Introduction of this
book for a non-technical summary of the theory.  More immediately to
hand (or to mouse) are two preprints that Bell has written:

    An Invitation to Smooth Infinitesimal Analysis.
    http://publish.uwo.ca/~jbell/invitation%20to%20SIA.pdf

    Infinitesimals and the Continuum.
    http://publish.uwo.ca/~jbell/New%20lecture%20on%20infinitesimals.pdf

More can be found on his homepage:

    http://publish.uwo.ca/~jbell/

-- 
Todd Wilson                               A smile is not an individual
Computer Science Department               product; it is a co-product.
California State University, Fresno                 -- Thich Nhat Hanh