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Topic: How do we Evaluate This Form on S^1?
Replies: 11   Last Post: Jan 22, 2013 4:17 PM

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Bacle H

Posts: 283
Registered: 4/8/12
Re: How do we Evaluate This Form on S^1?
Posted: Jan 22, 2013 4:17 PM
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On Tuesday, January 22, 2013 6:51:49 AM UTC-8, bacle...@gmail.com wrote:
> On Tuesday, January 22, 2013 6:07:41 AM UTC-8, Seymour J. Shmuel Metz wrote:
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> > 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.
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> Well, you seem to be criticizing a lot but you're not offering anything better;
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> you're not being very constructive/helpful yourself.



Just to add that W.Dale Hall has been inmensly helpful in responses to
previous posts (thanks again, Dale Hall).If you believe there is something wrong with what he says,explain and let us know how to improve; we may learn something. Otherwise,you're coming off a bit aggressive, criticizing without offering better alternatives.
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> > --
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> > Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>
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> > Unsolicited bulk E-mail subject to legal action. I reserve the
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> > right to publicly post or ridicule any abusive E-mail. Reply to
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> > domain Patriot dot net user shmuel+news to contact me. Do not
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> > reply to spamtrap@library.lspace.org





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