Undergrad Is Geometric Algebra inconsistent/circular?

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The discussion centers on the challenges of understanding Geometric Algebra as presented in the textbook by Doran and Lasenby. The geometric product of two vectors is defined using axioms, but the computation of this product raises concerns about circularity, especially regarding the definitions of the inner and outer products. Participants highlight that the geometric product results in a scalar and a bivector, complicating the associative property when starting from the inner and outer products. Suggestions for alternative resources, such as works by Dorst and papers on rigorous definitions, are shared to aid in understanding. The conversation also touches on the broader educational implications of teaching Geometric Algebra in schools.
  • #31
micromass said:
I'm actually planning to do an insight series about it too!

Wonderful idea! I am really looking forward to see it published soon.
 
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  • #32
Although I've postponed learning geometric algebra (GA) [putting my efforts into differential forms instead],
I have found myself having to learn to it in order to understand/decode some calculations.

In writing an Insight,
it might be useful to include translations between statements and calculations in GA
and statements and calculations in (say) more-standard tensor-calculus and/or vector-calculus,
accompanied by some diagrams.
To me, the notation found in various sources in quite dense, rather abstract for a beginner, and not quite standardized,
forcing the reader to juggle the various objects and operations.

My $0.03.
 
  • #33
I guess the original idea for the insight was not to focus only on the details of GA, but more generally on "Non-mainstream but useful math to know". As micromass said:
micromass said:
There are many other things in mathematics that I feel should be basic knowledge for undergrads, but that is somehow something that is only known to a select few.
 

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