GAME23 Martin Roelfs - Hidden in the Fold

[@timothyhavel2703]

I found this lecture quite elegant and insightful, but would point out that the basic ideas behind PGA were developed by Friedrich Bachmann in his 1973 work "Aufbau der Geometrie aus dem Spiegelungsbegriff", albeit without the advantages provided by geometric algebra. Some of it is also implicit in earlier work on screw theory and rigid body statics, see e.g. Sir Robert Stawell Ball "A Treatise on the Theory of Screws" (1886).

[@rotgertesla]

1:06:00 You should specify that those are the dual space R*

[@AMADEOSAM]

Excellent work! Using the invariants of 2k reflections for k invariant irreducible rotors …

[@rotgertesla]

41:52 For R[X]R[X^-1] = gamma^2XX^-1, How do we know that both gamma are supposed to be 1? What ifR[X] = +X and R[X^-1] = -X ? That would mean R[X]R[X^-1] could also equals -gamma^2XX^-1

[@AMADEOSAM]

Where can I find the work of David on spinors?

[@bivector]

It will be released 1 august, stay tuned! And moreover, a new video will be released every Wednesday afternoon LA timezone from now on!

[@AMADEOSAM]

@@bivectorGreat!

[@mervynlarrier9424]

Why would we hide the GA and convert back to linear algebra?

[@Kruglord]

Because many people already know how to do certain complicated geometric transformations using the Linear Algebra framework, so he was demonstrating that the geometric algebra approach is actually isomorphic to the linear algebra approach. But his point was actually that once you know the geometric algebra approach, you'd never actually want to use the linear algebra approach, hence the joke about "making a million dollars for Big Linear Algebra."

[@wraithlordkoto]

Oh STAP you

[@BlueGiant69202]

This lecture makes me grind my teeth in annoyance. I've been following developments in GA since stumbling upon "Clifford Algebra to Geometric Calculus" by David Hestenes in the mid 1980's. Dr. Hestenes wrote several papers and gave speeches in which he made it clear that he was intent on developing a unified mathematical language for math and physics and wanted to appropriate the name "Geometric Algebra" for this to differentiate it from the existing "Clifford Algebra" notations already being used in physics beside vectors, matrices, tensors, spinors, differential forms etc. For Dr. Hestenes and for myself, Geometric Algebra is not just another name for Clifford Algebra. However, in the last decade many people getting on the GA band wagon have been equating GA with CA like it was still 1958 and missing the whole point of the Oersted Medal lecture Dr. Hestenes gave about reducing the redundancy and overlap in the notation systems of mathematical physics. This lecture makes me feel that Dr. Hestenes was talking to an empty room like Newton because it seems to ignore numerous papers written by Dr. Hestenes in the 1990's as well as his book "New Foundations for Classical Mechanics", all of which contained material on much of the content of this old-school lecture but in the language of Geometric Algebra and Geometric Calculus.

[@hamish_todd]

It is surprising to me that you say this; from my point of view, what Martin is presenting here is a huge step along the path you are describing, because Geometric algebra in Martin's conception is much bigger than Clifford algebra as you say (algebraists would not think of the "Clifford" product as being reflection composition, or think of the Clifford-Lipschitz group as being a reflection group). Is there some specific notation or rule from the Oersted lecture that you think Martin went against?

[@BenHutchison]

🙄

[@Pluralist]