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 a 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, which is the smallest non-abelian simple group, and A4. 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 remained however 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 tesselation 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.