posted on Aug, 17 2017 @ 08:00 AM
originally posted by: SevenThunders
a reply to: delbertlarson
I find a lot of the multi-dimensional math is greatly simplified by the use of quaternions/Clifford Algebras and the use of differential forms. There
is no universally agreed best embedding but Hestenes's Geometric Algebra has got some traction among physicists.
You can for example render Maxwells equations as a single differential equation in Geometric Algebra.
www2.montgomerycollege.edu...
Thank you. That looks to be an extremely interesting book, and I have saved a copy of the PDF to my desktop. I then went straight to page 173 to see
the manipulation of Maxwell's equations into a single simple equation. It does appear to be some powerful math.
However I believe that approach takes us further from what I consider to be the physics. To me, physics should start with the modeling of nature in
terms of tangible things that we can describe in words that people can readily understand. Then we should apply the most straight-forward math
possible to describe those tangible things. Then we should use that math to make predictions for tests to see if our modeling represents nature. If it
passes the test, then our physics is good; if not, we should adjust our models. My work uses precisely this approach to arrive at Maxwell's
Equations.
By rolling all of Maxwell's equations into the single equation del F = J (or nabla F = J), what has been done is to take the four equations and roll
their contents into notations (F and J) that are themselves internally complicated. This takes us further from our underlying understanding of our
models, since the internal complexity is now merely hidden within simple notation. Hence, I believe the old school ways of straight vector calculus
are superior for revealing the thought process involving tangible things, at least in this instance.
However, I do readily admit to the power of the approach you bring to my attention, since once one knows the rules for manipulation of the new simple
notation one can arrive at further results more simply and be less prone to error. So there is certainly good in both approaches, and I again thank
you for the link to what looks to be a very valuable resource for my future study!