Poor Foundations in Geometric Algebra
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Poor Foundations in Geometric Algebra
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Re: Poor Foundations in Geometric Algebra
#2Oh man, I didn't know there was going to be a special episode of Friday Night Smackdown!
Re: Poor Foundations in Geometric Algebra
#3Note don't to be confused with Algebraic Geometry they are different;
When I first came across this topic it was eye opening, especially the fact that you could squeeze Maxwell's equations into one and the fact that pseudovector create by cross product from physics is just a bivector which in 3d could be represented like a vector orthogonal to the plane created by the two vectors in the product
Primer on the topic https://www.youtube.com/watch?v=60z_hpEAtD8 (And other videos on his channel) Another greate playlist is https://www.youtube.com/watch?v=0VGMxSUDBH8&list=PLLvlxwbzkr...
BTW the author has the following page https://projectivegeometricalgebra.org/ with great infographics and references
Re: Poor Foundations in Geometric Algebra
#4This explains very nicely why despite working through lots of GA resources, I never quite grasped it. It’s logically incoherent!
Re: Poor Foundations in Geometric Algebra
#5> very real toxicity within the geometric algebra community. I can’t do much about
I was hoping the article would be about this instead. OP wondering if you have any elaborations for us to hear.
Re: Poor Foundations in Geometric Algebra
#6This explains very nicely why despite working through lots of GA resources, I never quite grasped it. It’s logically incoherent!
This is not a critic of all geometric algebra and especially not of its more basic parts. Therefore it is not an excuse for not grasping e.g. what Hestenes has written about GA, or what Eric Lengyel himself has written, e.g. in his new book that is advertised in this article.
It is a critic of many books about geometric algebra, which have made attempts to expand and further develop some parts of its theory, but those attempts have not been thought carefully and they have produced various inconsistent or useless definitions.
It is also a critic of attempts of presenting geometric algebra as preferable for applications where in fact it is not optimal, by showing misleading "benchmarks". Unfortunately this tactic is not at all specific to geometric algebra, but it is frequently encountered for almost any kind of algorithm known to mankind when it accumulates for one reason or another some kind of fan base.
Re: Poor Foundations in Geometric Algebra
#7Ouch.
I love it when people say what they mean and don't beat around the bush.
Re: Poor Foundations in Geometric Algebra
#8This explains very nicely why despite working through lots of GA resources, I never quite grasped it. It’s logically incoherent!
The author has books on Geometric Algebra so it makes no sense to assume that he is going against GA as a whole.
Re: Poor Foundations in Geometric Algebra
#9So much education content is so very poor. And even the best of it... A first-tier physics professor at a munch was delighted - he regaled believing he had found an error in a highly-regarded introductory textbook! But, upon many day's of thought, and several close reads of the text, he had realized it had been very carefully worded so as to be not incorrect. And so he was so delighted - yay! He thought of this as a good state of affairs, reflecting well on the text, and associated instruction. I... afterwards wished I'd pointed out that the target audience for an intro textbook, was perhaps not well modeled as first-tier experts with a week to wrestle with and closely ponder a paragraph in order to avoid being misled.
I'm unclear on how we get better at this. I've seen OER texts with open errata databases still struggle. Perhaps a github-like fine-grain (Xanadu-like transclusion) wikipedia? Or "nLab all the fields"? Or... ??
Re: Poor Foundations in Geometric Algebra
#10[flagged]