Tue Jan 5 16:51:04 CET 2016

Projective geometry

Is there a point in looking at circuits through the lens of projective
geometry, to avoid infinities that would otherwise appear?
E.g. infinite conductivity (short), infinite resistance (open)?

The affine view (one inverse of the other):
   - G V = I
   - R I = V

Trouble is that some of these might be singular, caused by shorts or
open.  In the standard approach, those shorts and opens are
structurally removed.

Does it actually make sense to have infinite current and voltage
(compare to point at infinity in computer graphics, projective
geometry)?  No, but it does make sense to have infinite derivatives.

Is there a way to represent this while the coefficients are elements
of a projective space?  E.g. the derivative (actuall, first order
approximation) is a projective space.

Actually, this problem goes away when looking at the manifold in an
abstract way.  It only appears in representation.  Is that right?  The
tangent space of a manifold is a vector space, but is there a
"condition" problem there?  Is it possible that the actual space is

It seems that the problem is present at the abstract manifold level.

Is this in any way related to sympectic manifolds?  E.g. do current
and voltage (or some kind of composite object) need to appear both as

What is the integral of a projective space?