pAdicizable discrete variants of classical Lie groups and coset spaces in TGD frameworkpAdization of quantum TGD is one of the long term projects of TGD. In the sequel the recent view about the situation is discussed. The notion of finite measurement resolution reducing to number theoretic existence in padic sense is the fundamental notion. pAdic geometries replace discrete points of discretization with padic analogs of monads of Leibniz making possible to construct differential calculus and formulate padic variants of field equations allowing to construct padic cognitive representations for real spacetime surfaces. This leads to a beautiful construction for the hierarchy of padic variants of imbedding space inducing in turn the construction of padic variants of spacetime surfaces. Number theoretical existence reduces to conditions demanding that all ordinary (hyperbolic) phases assignable to (hyperbolic) angles are expressible in terms of roots of unity (roots of e). For SU(2) one obtains as a special case Platonic solids and regular polygons as preferred padic geometries assignable also to the inclusions of hyperfinite factors. Platonic solids represent idealized geometric objects ofthe padic world serving as a correlate for cognition as contrast to the geometric objects of the sensory world relying on real continuum. In the case of causal diamonds (CDs)  the construction leads to the discrete variants of Lorentz group SO(1,3) and hyperbolic spaces SO(1,3)/SO(3). The construction gives not only the padicizable discrete subgroups of SU(2) and SU(3) but applies iteratively for all classical Lie groups meaning that the counterparts of Platonic solids are countered also for their padic coset spaces. Even the padic variants of WCW might be constructed if the general recipe for the construction of finitedimensional symplectic groups applies also to the symplectic group assignable to Δ CD× CP_{2}. The emergence of Platonic solids is very remarkable also from the point of view of TGD inspired theory of consciousness and quantum biology. For a couple of years ago I developed a model of music harmony relying on the geometries of icosahedron and tetrahedron. The basic observation is that 12note scale can be represented as a closed curve connecting nearest number points (Hamiltonian cycle) at icosahedron going through all 12 vertices without self intersections. Icosahedron has also 20 triangles as faces. The idea is that the faces represent 3chords for a given harmony characterized by Hamiltonian cycle. Also the interpretation terms of 20 aminoacids identifiable and genetic code with 3chords identifiable as DNA codons consisting of three letters is highly suggestive. One ends up with a model of music harmony predicting correctly the numbers of DNA codons coding for a given aminoacid. This however requires the inclusion of also tetrahedron. Why icosahedron should relate to music experience and genetic code? Icosahedral geometry and its dodecahedral dual as well as tetrahedral geometry appear frequently in molecular biology but its appearance as a preferred padic geometry is what provides an intuitive justification for the model of genetic code. Music experience involves both emotion and cognition. Musical notes could code for the points of padic geometries of the cognitive world. The model of harmony in fact generalizes. One can assign Hamiltonian cycles to any graph in any dimension and assign chords and harmonies with them. Hence one can ask whether music experience could be a form of padic geometric cognition in much more general sense. The geometries of biomolecules brings strongly in mind the geometry padic spacetime sheets. pAdic spacetime sheets can be regarded as collections of padic monad like objects at algebraic spacetime points common to real and padic spacetime sheets. Monad corresponds to padic units with norm smaller than unit. The collections of algebraic points defining the positions of monads and also intersections with real spacetime sheets are highly symmetric and determined by the discrete padicizable subgroups of Lorentz group and color group. When the subgroup of the rotation group is finite one obtains polygons and Platonic solids. Biomolecules typically consists of this kind of structures  such as regular hexagons and pentagons  and could be seen as cognitive representations of these geometries often called sacred! I have proposed this idea long time ago and the discovery of the recipe for the construction of padic geometries gave a justification for this idea. See the chapter Number Theoretical Vision or the article pAdicizable discrete variants of classical Lie groups and coset spaces in TGD framework..
