... I m still thinking this over. I m inclined to think that the the curvature isn t going to cause the linear independence. I think that s practically the
Message 1 of 5
, Apr 8, 2011
On Apr 5, 2011, at 11:55 PM, Richard Briet wrote:
I just commented on your other email. I think we do not have to go to higher dimensional spaces as you suggested. Curved space, like for example on the surface of a sphere, will do the trick.
If I may quote you:
If we could find a case wherethreedifferent forces cancelled out without being in the same plane or on the same line through the origin, we'd have proof that we had a four-dimensional space at that point.
Therefore, instead of saying "we'd have proof that we had a four-dimensional space at that point." I would have said "we'd have proof that space is curved at that point." Do you agree?
I'm still thinking this over. I'm inclined to think that the the curvature isn't going to cause the linear independence. I think that's practically the definition of "dimension": How many independent vectors can we have? So, if we had four uniform fields that we couldn't cancel out, we'd have proof that we were in "four dimensional space" when it came to those forces. (I got it wrong above.)
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