


Volume 9 No 4 (2011)
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Surmounting the Cartesian Cut: Klein Bottle Logophysics, the Dirac Algebra and the Genetic Code
Diego Lucio Rapoport
Abstract
We reintroduce the Klein Bottle (KB) logophysics at the foundations of the
unification of quantum geometry, cell biology, embryology and evolution, to extend
it to the genetic code and allosteric recognition. We find that the genetic code has
three possible fractal topologies: two different families of KBs embedded in
HyperKBs, or still a 2-torus, depending which pair of three subalphabets for the
genetic “letters” is chosen; this does not require the double helix. We complete the
genetic codification of embryological differentiation introduced in an accompanying
article. We discuss the Hadamard-KB representation of this codification and discuss
its robustness and that of embryological development with respect to environmental
noise. We discuss this KB codification of the 64 codons with its isomorphic
representation in terms of the Dirac Algebra (DA) of Quantum Mechanics, in the
Nilpotent Universal Computational Rewrite System (NUCRS), a self-referential syntax
that generates much of mathematics and the fundamental symmetries of physics.
We show that the double helix can be obtained from the duplication of the KB
associated with the bistable perception of the tetrahedron representation of the
four genetic letters. The DA and its double tetrahedron codification in NUCRS is
found to be associated with a pair of superposed KBs, yielding the double 3D (space
and momentum) space of physics, and the double helix of DNA, which thus appears
related to a pair of KBs, being the case that only one is necessary to construct the
genome. We show that the depth-time variable of visual perception materializes as
space Thus, the DA is derivable from two KBs, and the purported dualism of physics
as presented in NUCRS, is rendered to be based in the non-dualistic KBL. We discuss
the relations with a theory of evolutions, and between biological periodicities and
the KB of the Mendeleev table (Boeyens). We present relations between
metacognition and the HyperKlein Bottle, and evolution in terms of time waves
defining in toto the different structures. We present rudiments of the
ontoepistemology of the Hyper KB Logic, its relations with the anthropic principles
and the universal physical constants, which are found to be contextual
Keywords
klein bottle logic, time waves, genetic code, allosterics, logophysics
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