Galois Groups and Genetic Code

Abstract

This article was inspired by the inverse problem of Galois theory. Galois groups are realized as number theoretic symmetry groups realized physically in TGD as symmetries of space-time surfaces. Galois confinement as an analog of color confinement is proposed in TGD inspired quantum biology. Galois groups, in particular simple Galois groups, play a fundamental role in the TGD view of cognition. The TGD based model of the genetic code involves in an essential manner the groups A5 (icosahedron), which is the smallest non-abelian simple group, and A4 (tetrahedron). The identification of these groups as Galois groups leads to a more precise view about genetic code. The question why the genetic code is a fusion of 3 icosahedral codes and of only a single tetrahedral code however remained poorly understood. The identification of the symmetry groups of the I, O, and T as Galois groups makes it possible to answer this question. Icosa-tetrahedral tessellation of 3-D hyperbolic space H3, playing central role in TGD, can be replaced with its 3-fold covering replacing I/O/T with the corresponding symmetry group acting as a Galois group. T has only a single Hamiltonian cycle and its 3-fold covering behaves effectively as a single cycle. Octahedral codons can be regarded as icosahedral and tetrahedral codons so they do not contribute to the code.