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Jul
23
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Jul
19
comment Looking for a clear definition of the geometric product
@rschwieb (cont'd) ...aren't at all easy. But at least in these cases it is possible to give a non-rigorous description of what a differential, or a delta-function, is... For the geometric product I don't have even an informal, hand-waving definition!
Jul
19
comment Looking for a clear definition of the geometric product
@rschwieb (cont'd) ...be natural and thus useful it would have to start from some pretty easy-to-grasp definitions and rules. Consider the opposite: "The axioms underlying this approach are so complex that I can't write them down simply, but the approach is really natural and useful." I realize that this is a bit of a caricature, but I'm just trying to convey where I'm coming from. For example, I'm aware of the fact that thinking in terms of differentials in calculus, or of Dirac deltas in linear systems theory, can be very useful, even though the corresponding rigorous formalisms...
Jul
19
comment Looking for a clear definition of the geometric product
@rschwieb: I remind open-minded (and in fact hopeful) that GA will live up to its advocates' claims, but I admit that I have a hard time wrapping my head around the conjunction of (a) the claims for the naturalness and utility of GA formalism; (b) (according John Macdonald, in p. 82 of L&GA) "[t]he geometric product is the key innovation of geometric algebra"; (c) (again, according to Macdonald; see his answer below) "I do not think it possible to give a quick definition of the general geometric product." IOW, my (admittedly, very naive) expectation is that for a formalism to ...
Jul
19
revised Looking for a clear definition of the geometric product
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Jul
19
comment Looking for a clear definition of the geometric product
And thank you also for your critique of the other answers.
Jul
19
comment Looking for a clear definition of the geometric product
"I do not think it possible to give a quick definition of the general geometric product." I take your word for it, but I never asked for a "quick" definition. That said, this would be the only instance (in my admittedly narrow experience) in which such foundational specifications are not amenable to a succinct statement. (This is just to say that your statement is somewhat rattling to my provincial expectations...) Thank you for correcting my statement regarding the book's intended audience. I have reworded my post accordingly. I apologize for the error.
Jul
19
revised Looking for a clear definition of the geometric product
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Jul
19
revised Looking for a clear definition of the geometric product
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Jul
18
awarded  Good Question
Jul
16
comment Looking for a clear definition of the geometric product
As an aside, let me add that in my (admittedly very brief) acquaintance with "geometric algebra" I have gotten the impression not only that it's a field is plagued with an excess of unclear wording (as described in my post), but also that it is relegated to some sort of "alternative math" ghetto. I.e. the field is kept alive by a small but feisty fringe of diehards. I wonder if these two "first impressions", to the extent that they are correct, are related somehow. Does the sheer complexity of the geometric algebra formalism necessarily keep it outside of the "mainstream" of math education?
Jul
16
revised Looking for a clear definition of the geometric product
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Jul
16
asked Looking for a clear definition of the geometric product
Jul
9
accepted Example of a module for non-mathematicians
Jul
8
revised Is the identiy function continous on equivalent metric spaces
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Jul
8
revised Is the identiy function continous on equivalent metric spaces
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Jul
7
answered A Young Math Enthusiast's Fear
Jul
6
revised Is the identiy function continous on equivalent metric spaces
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Jul
6
revised Is the identiy function continous on equivalent metric spaces
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Jul
6
revised Is the identiy function continous on equivalent metric spaces
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