Clifford Algebra Discussion includes discussion points which have been made in the past.
Why not RefactorExtractBaseClass?
on Complex and Point? This is one way of looking at CliffordAlgebra
, an attempt to unify numeric and spatial computation. It results in many laws of Physics taking on very simple mathematical forms, which in certain circles is widely regarded as a Good Thing.
One very important fact about CliffordAlgebra
is that several of the Physics faculty at Cambridge University are mad keen on it, but it's not on the Physics syllabus. This means that there's invariably at least one question on the first year Physics exam which is a bit of a slog using the methods taught in lectures, but can be solved in a moment using CliffordAlgebra
. -- PeterHartley
A friend pointed out to me quite recently that the semi-new Algebraic Geometry foundation espoused in Hestenes's 2002 Oersted Medal Lecture was in fact the same thing, modulo ...something, as CliffordAlgebra
s, which I had missed before, since I haven't digested the new foundational approach being championed. Incidentally I got side tracked and hadn't reached page 36 yet, which is why I was surprised when, upon describing the paper to a friend, he said "CliffordAlgebra
". I hadn't spotted nor read about an equivalence. They cannot be identical topics, as opposed to equivalent, though, as I think JohnFletcher
would agree considering his comment on CliffordAlgebra
, since the latter is mostly approached purely algebraically, whereas the new foundations suggested by Hestenes inherently is about the geometric
application. -- Doug
Some people prefer to say GeometricAlgebra instead of CliffordAlgebra. See page 36 in Hestenes paper (below). JohnFletcher
Reference:Hestenes's 2002 Oersted Medal Lecture, "Reforming the Mathematical Language of Physics" (http://modelingnts.la.asu.edu/pdf/OerstedMedalLecture.pdf
). (see HestenesOerstedMedalLecture
) It is much quoted from in these CliffordAlgebra
[edit notes] Old discussion moved from CliffordAlgebraDetails
- Geometric or Clifford Algebra has IMO a lot to offer in many fields of science and engineering. In particular, some problems which are nonlinear in the usual formulation, are linear if reformulated in terms of the appropriate geometric algebra.
- Geometric Algebra can be shown to be consistent and inclusive of other formulations, including vectors in three dimensions, complex numbers and quaternions.
See also CliffordAlgebra GeometricAlgebra