Tue, 24 Aug 1999 01:35:15 EDT
In a message dated 8/23/99 6:35:22 AM Eastern Daylight Time,
> > Or as you would say it: a 1-dimensional surface in
> > a 2-dimensional space in a 4-dimensional space in
> > an 8-dimensional space in a 16-dimensional space, etc.
> One might think hierarchy of this kind.
> The construction of configuration space geometry however
> relies crucially on 4-dimensionality of basic dynamical
> objects (4-surfaces) and on the fact that the geometry
> of imbedding space is *non-dynamical* and possesses the high
> symmetries it does. The generalization you propose would
> require totally new approach to the quantization of the
> theory. It is difficult to say whether this kind of
> theory exists without spending 20 years or so trying to
> construct it!(;-)
1) Volume is explained as a 1-D function of the cube of R.
2) Elliptical orbits are explained as 2-D functions of R and theta.
3) Positions in space are 3-D functions of R, theta, phi.
4) You say, that standard cosmology and spinor structure are
explained as being revealed in a 4-D surface
What I see is a 3-D world possessing 1-D, 2-D, and 4-D
And you say that the 4-D structures that we see are in an
8-D space; that this is your objective or real object. My
speculation is that your object is really a subjective or
incomplete object since it is in part based on properties
that are subjective in themselves. That 8-Ds is sufficient
to be your objective object, I have no doubt, but I feel that
additional concepts are involved that we may never detect.
But these concepts still form a part of the whole and must
be accounted for by some infinite form in order to be
entirely objective. Your prediction of 20 years to generalize
TGD in this manner might be true, but I may possess today
the coordinate transformation factors of this still unrealized
geometry. My belief is that your already having described
a portion of the object makes you the only person in this
world who would even have a shot at it (within my lifetime).
The concept of the "Problem of Induction" leaves a bad
taste in many mouths, and is in part probably a reason
not to attempt such an obviously inductive solution. :-)
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