Thu Jul 7 23:28:09 CEST 2011

A Primer of Infinitesimal Analysis

A nice one to stack next to dual numbers[3] and automatic
differentiation.  Link from [2], which is quite an interesting post in
itself.  ``Smooth space-time, say `R^4`, allows only smooth motion and
smooth distribution of mass. If we place non-smooth mass in it, the
space will change to a _subset_ of `R^4` which carries additional
information about the anomalies contained in it.''

I started reading [1][5] and I must say it's quite interesting to reason
with non-non-existing entities ;)  In the book they are likened to
virtual particles: something that's not really present in end results,
but useful as a tool in calculations.

[1] isbn://0521624010
[2] http://math.andrej.com/2008/08/13/intuitionistic-mathematics-for-physics/
[3] http://en.wikipedia.org/wiki/Dual_numbers
[4] http://en.wikipedia.org/wiki/Smooth_infinitesimal_analysis
[5] md5://3f3da3bbc8da4d430677acc78cb9c7c3