[HN Gopher] All Hail Geometric Algebra
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       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...)
        
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       (page generated 2020-11-18 23:00 UTC)