The proposal modifying the earlier proposal is G= R2/ngrℏ0, where ngr is the order of Galois group Ggr "at the bottom" of the hierarchy of extensions, and one has ℏ=6h0. One would have n=n1n2...ngr. Ggr "at the bottom" is proposed to represented number theoretically geometric information about the imbedding space by providing a discretization for the product of maximal finite discrete sub-group of isometries and tangent space rotations of imbedding space. By M8-H duality these sub-groups should be identical for H and M8. The prediction is that maximal Ggr is product of icosahedral group I with 3 copies of coverings of I.
Rather remarkably, the prediction for G is correct if one assumes that the value of R is what p-adic mass calculation for electron mass gives.
Since the hierarchy of Planck constants relates to number theoretical physics proposed to describe the correlates of cognition, the connection with cognition strongly suggests itself. Icosahedral and tetrahedral geometries occur also in the TGD based model of genetic code in terms of bio-harmony, which suggests that genetic code represents geometric information about imbedding space symmetries. These connections are discussed in detail.
See the article Can TGD predict the value of Newton's constant? or the chapter About the Nottale's formula for hgr and the possibility that Planck length lP and CP2
length R are related.
For a summary of earlier postings see Latest progress in TGD.
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