Bacle H
Posts:
197
Registered:
4/8/12
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Re: How do we Evaluate This Form on S^1?
Posted:
Jan 22, 2013 9:51 AM
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On Tuesday, January 22, 2013 6:07:41 AM UTC-8, Seymour J. Shmuel Metz wrote:
> In <lbGdnZWOCuemA2DNnZ2dnUVZ5rmdnZ2d@giganews.com>, on 01/21/2013
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> at 11:59 AM, "W. Dale Hall" <wdhall@alum.mit.edu> said:
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> >Which statement is the "in fact, false" non-sequitur?
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> "tangent vectors to different points on S^1 aren't quite identifiable
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> with one another"
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> >I maintain that my first statement is perfectly correct.
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> You can maintain it all you want, but it remains false.
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> >Otherwise, why would one ever worry about the whole machinery of vector bundles?
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> Because in the general case you're not dealing with a flat affine
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> connection.
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> >A beginner needs to learn that the tangent bundle is something
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> >other than a vector space;
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> For which purpose S^2 is mopre suitable than S^1.
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> >I suspect that the OP knows little to nothing about parallel transport.
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> It might have been useful to mention it, stressing that what is true
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> of S^1 is not true in general, even for S^2.
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> >Again, I regard it as a pedagogical error to use machinery without
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> >adequate justification
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> I regard it as a pedagogical error to oversimplify.
Well, you seem to be criticizing a lot but you're not offering anything better;
you're not being very constructive/helpful yourself.
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> --
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> Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>
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