[HN Gopher] All Hail Geometric Algebra ___________________________________________________________________ All Hail Geometric Algebra Author : agarttha Score : 58 points Date : 2020-11-18 21:15 UTC (1 hours ago) (HTM) web link (crypto.stanford.edu) (TXT) w3m dump (crypto.stanford.edu) | centimeter wrote: | This is wild. Very glad I saw this. | hardwaregeek wrote: | Well, it's certainly easier than Algebraic Geometry. | howling wrote: | relevant xkcd: https://xkcd.com/2028/ | thechao wrote: | I cannot recommend Alan MacDonald's two books enough (Linear and | Algebra; and, Vector and Geometric Calculus). They literally | replace _reams_ of texts on complex numbers, quaternions, | octonions, spinors, etc. under a single unifying concept. (They | don 't _replace_ those concepts; and, for sure, if you want to | learn quantum you 're going to need them; but they make getting | your head around them so much easier.) | | One issue is that most of the "online" references are _crap_. | MacDonald 's presentation is a wonderful slow ramp: it starts | with really basic linear algebra and then just slowly segue's | into geometric algebra. | | I firmly believe that in 100 years we just won't be teaching | 'bare' linear algebra, complex, quaternions, ... we'll just teach | GA and then introduce the physical concepts separately. | yiyus wrote: | Those books are great. They are my favorite GA books (together | with Hestenes' papers). I just wanted to add that he also has | wonderful youtube videos. | | And I also agree with that 100 years prediction. I'm even | trying to do my part so that we do not have to wait so much! | topspin wrote: | To save others the effort the two books are: | | Linear and Geometric Algebra (October 2020 printing) | 978-1453854938 $30 new @Amazon | | Vector and Geometric Calculus (also Oct. 2020 prining) | 978-1480132450 $35 new @Amazon | topspin wrote: | To save others the effort the two books are: Linear and Geometric | Algebra (October 2020 printing) 978-1453854938 $30 new @Amazon | Vector and Geometric Calculus (also Oct. 2020 prining) | 978-1480132450 $35 new @Amazon | chairmanwow1 wrote: | I did a deep dive on this topic a few months ago to try and see | if I could write cleaner graphics code and it was an absolute | treat. | | Really interesting way to think about complex objects and | geometric primitives. | creata wrote: | Do you have some before-and-after code that you can share? | | I've seen two other completely unrelated efforts in that very | general direction: | | * "Let's Remove Quaternions from Every 3D Engine"[0], which was | underwhelming: let's ask other people to rename existing code | for no practical benefit? | | * "Klein"[1], a projective geometric algebra library that is | _amazingly_ nice to use, and is apparently very fast, too. | | [0]: https://marctenbosch.com/quaternions/ | | [1]: https://www.jeremyong.com/klein/ | agarttha wrote: | This is the paper that hooked me: | | "Imaginary numbers are not real--The geometric algebra of | spacetime" | | https://link.springer.com/article/10.1007/BF01883676 | | (http://geometry.mrao.cam.ac.uk/wp-content/uploads/2015/02/Im...) ___________________________________________________________________ (page generated 2020-11-18 23:00 UTC)