ICN5D wrote:I've heard good things about it. Sounds very interesting. I read somewhere that it's like the quantum mechanics of physics.
PatrickPowers wrote:[...]
Learning relativistic EM is a b*tch in trad notation. I can't do it. GA is SO much better. Physics is mainly for the purpose of building machines, and it's good for that. Most of them don't care that much about understanding what's going on. Even if they do care, they've given up trying to understand it. A weak understanding can be worse than nothing.
An attraction for me is that GA is a tool for extending physics to N dimensions. Clifford built it for this purpose (I think). Most physicists couldn't care less about that.
quickfur wrote: In fact, I surmise that the equations of 3D physics, cast in GA, can probably be lifted directly into 4D, as long as there are no dimension-dependent parts (or they are recast appropriately). It may turn out to be just a matter of working out the consequences of the equations in Cl4 in place of the usual Cl3.
PatrickPowers wrote:What would a second dimension of time mean? Dunno.
PatrickPowers wrote:What would a second dimension of time mean? Dunno.
gonegahgah wrote:There are also some other examples where it may be easier to use two time dimensions rather than one.
The movement of planetary moons relative to a star are easier to calculate if you have the time dimensions twice in the equations.
quickfur wrote: As for what's not to like, one thing is the geometric product itself, which, in spite of the fact that it has the most amazing algebraic properties, is a bear to actually compute. A naïve implementation of the geometric product in software is rather slow, because it requires far more operations than, say, a hard-coded cross product. So if you want any reasonable speed out of the thing, you have to check for special cases and hand-code those to be faster, which at the end of the day amounts to essentially implementing the traditional methods and dispatching to them in the special cases, only falling back to the (slow!) full geometric product when all else fails.
PatrickPowers wrote:gonegahgah wrote:There are also some other examples where it may be easier to use two time dimensions rather than one.
The movement of planetary moons relative to a star are easier to calculate if you have the time dimensions twice in the equations.
Indeed! Could you kindly indicate an example?
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