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?
>>
>>
>>
>>
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>
>
>
>
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Charles Bloom email "cb" http://www.cbloom.com
