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I Found One Statement Very Interesting

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Posted by Richard Ruquist on March 28, 2002 18:42:31 UTC

I believe this came from Dr. Stafford:

**No, what I notice is that it is impossible to set up a self consistent closed system of concepts which do not obey those particular laws. A rather surprising result.**

By these particular laws, I assume Dr. Stafford means his final equations. I would hope that Dr. Stafford will comfirm this assumption.

If so, then I feel challenged to come up with a closed, self-consistent system of mathematical concepts that do not use all of his axioms, or use differenr ones.

This goes back to my long held view that the final equations depend on the axioms, and in particular on the symmetries used in the analysis, as Harvey points out in the above post.

My counter example comes from plane geometry. The usual Euclid form of plane geometry contains the shift symmetry. However, the same theorems of plane geometry can be derived from a space that is not continuous, but rather is a set of three dimensional arrays of points. The shift symetry fails for such a space. Yet a closed, self-consistent theory of plane geometry can be derived for such a space.

However, it just turns out to be Euclids geometry, except in the limit that the spacing of the points is quite large. Perhaps the shift symmetry was not needed to get Stafford's final equations and the tautological nature of nature is even more profound than previously thought.

Regards,

Richard

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