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Tetration and selfroot as a topological transformation of CP1 into itself
And this twisting in and out of (spinor=null) space into Euclidean and back.. is spin. Twisting accross geometries is spin.

If we want to measure it in Euclidean space, observe, we BRING it to Euclidean space, so it is always aligned.

So the numerical value of h is hidden neither projective space, nor Euclidean, but in space of all geometries, and how this space represents numbers.

This twisting between geometries is also responsible for QUANTIZATION as such ( see also Regge Calculus with its strange fit to gravity).

Conformal geometry seems to be the geometry as if the twists are observed from outside. In Conformal geometry, 4 dimensions must play than a fundamental role (and they do, see tetracyclical and pentaspherical coordinates) , as twisting happens in 4 cycle between other geometries.
Null -Projective- Euclidean (affine)- Projective(?) - Null -etc...

So in Conformal geometrical space, tetration would be continuous. Perhaps.

So the generalization of logarithm I mentioned elsewhere should work as the correspondending values will be found in different geometries.
Perhaps ( I am not sure) generalized logarithm can be found as a continuous function in Conformal 5D (projective) space.

Also... Non-integer and imaginary, negative operations [x] would be linked to position in a twist between certain geometries. This operation count must have 4 cycle, as I indicated somewhere else in this forum, and may have link to alpha constant ( also I calculated it from Andrews pentation asymptotics) .

Non- integer values has to mean that operation happens BETWEEN geometries.


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RE: Tetration and selfroot as a topological transformation of CP1 into itself - by Ivars - 12/18/2008, 01:58 PM

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