**Authors:** Matti Pitkänen

A brief summary of various competing visions about the basic principles of quantum Topological Geometrodynamics (TGD) and about tensions between them is given with emphasis on the recent developments. These visions are following. Quantum physics as as classical spinor field geometry of the "world of classical worlds" consisting or light-like 3-surfaces of the 8-D imbedding space H = M4xCP2; zero energy ontology in which physical states correspond to physical events; TGD as almost topological quantum field theory for light-like 3-surfaces; physics as a generalized number theory with associativity defining the fundamental dynamical principle and involving a generalization of the number concept based on the fusion of real and p-adic number fields to a larger book like structure, the identification of real and various p-adic physics as algebraic completions of rational physics, and the notion of infinite prime; the identification of configuration space Clifford algebra elements as hyper-octonionic conformal fields with associativity condition implying what might be called number theoretic compacticitation; a generalization of quantum theory based on the introduction of hierarchy of Planck constants realized geometrically via a generalization of the notion of imbedding space H to a book like structure with pages which are coverings and orbifolds of H; the notion of finite measurement resolution realized in terms of inclusions of hyperfinite factors as the fundamental dynamical principle implying a generalization of S-matrix to M-matrix identified as Connes tensor product for positive and negative energy parts of zero energy states; two different kinds of extended super-conformal symmetries assignable to the light-cone of H and to the light-like 3-surfaces leading to a concrete construction recipe of M-matrix in terms of generalized Feynman diagrams having light-like 3-surfaces as lines and allowing to formulate generalized Einstein's equations in terms of coset construction.

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[v1] 26 Oct 2008

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