From: Charles Bloom <cb2@cb...>  20040830 19:31:25

The advantages of GA are also its disadvantages. GA is=20 dimensionindependent and coordinate frame free, but in practical problems= =20 there are a lot of advantages to knowing what dimension you're in and=20 specialcasing to coordinate axes. GA is generally a very nice way to=20 write the laws of the universe in a vacuum, but not very convenient for=20 solving 2d and 3d geometry problems. 0d through 3d are very weird special= =20 dimensions that we live in. Everything 4d and up is sort of "normal" in=20 the sense of not having all the strange properties of the lower dimensions;= =20 the rotation groups of 3d and lower are very unusual, as is the topology of= =20 the space itself and the symmetry groups. At 01:38 PM 8/30/2004 0500, Jonathan Blow wrote: >Also there's a big difference between solving a problem on paper using GA,= =20 >and writing code that manipulates GA entities. > >I find that GA is the natural way that I approach a lot of problems when I= =20 >am thinking about them in my notebook. (Though, uhh, I don't do the 5D=20 >conformal stuff). But usually I use it to figure out the answer, then see= =20 >what equations the answer turns into. Invariably it's something that=20 >doesn't require generic multivector manipulation. > >Though for bigger problems as we go into the future, that may no longer be= =20 >a practical approach. Hard to say. > >Anyway, I like GA, but I don't write GA code, even for 3D... > > J. > > >robin_green@... wrote: > >> >>If I may veer OT for a second, yes, you are right. 5D conformal GA is=20 >>inefficient on current machine architectures. But if you analyse the=20 >>algorithms used in terms of the parallelism of individual operations=20 >>you'll find that most operations inside, say, a JOIN or a MEET operation= =20 >>are independent of each other. If we were to create a machine that=20 >>executes 32way MIMD, you would end up with fewer cycles to generate a=20 >>more accurate result, and without exceptions in the algorithm (e.g. no=20 >>need for tests for coplanar elements, it just works). >> >>GA is faster, but not on current hardware and there's basically a free=20 >>PhD and a guaranteed career in there for the first person to do the=20 >>analysis and propose the machine architecture. At the moment it seems to= =20 >>me that the Mathematicians are off admiring GA's elegance and trying to=20 >>prove basic assertions (e.g. multivectors never occur in typical usage),= =20 >>the Physicists are off recoding old proofs in the new form to get better= =20 >>insights and the CompSci people are... well... sitting on their thumbs as= =20 >>far as I can tell. >> >>I mean, you know, I *would* work on it, but I'm just a little busy with=20 >>this thing right now. >> >> Robin Green. >> >> >>Christian Sch=FCler wrote: >> >>> >>>Besides, who will ever be going to implement this conformal 5Dzeugs in= =20 >>>an actual >> >> > application, I mean, 32x32 matrix products anyone? >> >> >> >> >>This SF.Net email is sponsored by BEA Weblogic Workshop >>FREE Java Enterprise J2EE developer tools! >>Get your free copy of BEA WebLogic Workshop 8.1 today. >>_______________________________________________ >>GDAlgorithmslist mailing list >>GDAlgorithmslist@... >>https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist >>Archives: >>http://sourceforge.net/mailarchive/forum.php?forum_ida88 > > > > >This SF.Net email is sponsored by BEA Weblogic Workshop >FREE Java Enterprise J2EE developer tools! >Get your free copy of BEA WebLogic Workshop 8.1 today. >_______________________________________________ >GDAlgorithmslist mailing list >GDAlgorithmslist@... >https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist >Archives: >http://sourceforge.net/mailarchive/forum.php?forum_ida88  Charles Bloom email "cb" http://www.cbloom.com 