Abstracts of two articles involving tesselations in hyperbolic 3-space

Abstracts of two articles involving hyperbolic tesselations. I have written two articles involving the tessellation of hyperbolic 3-space. I attach the abstracts of the articles below.

About tessellations in hyperbolic 3-space and their relation to the genetic code

M⁸-H duality and the realization of holography in M^8 strongly suggests the importance of tessellations of H³ (analogous to lattices of E³) in the TGD based physics. These tessellations form a scale hierarchy and can thus appear in all scales. The hierarchy of effective Planck constants labelling dark matter as phases of ordinary matter indeed predicts quantum coherence in arbitrarily long scales and gravitational quantum coherence corresponds to the largest scales of quantum coherence among basic interactions.

There are 5 Platonic tessellations known as honeycombs: the 4 regular honeycombs correspond to cubic, icosahedral, and 2 dodecahedral honeycombs and a quasiregular icosa-tetrahedral honeycomb having tetrahedra, octahedra and icosahedra as cells. The icosa-tetrahedral honeycomb might define a universal realization of the genetic code as an induced structure so that the genetic code would be much more than a biochemical accident. These 5 Platonic honeycombs could occur also in astrophysical scales as gravitational tessellations. The recent discovery of gravitational hum might have an explanation as gravitational diffraction in this kind of a honeycomb.

In this article the properties of hyperbolic honeycombs are considered in detail and also a detailed view about the realization of DNA double strand in terms of the icosa-tetrahedral honeycomb is considered. The emerging model is surprisingly quantitative. Also a connection with the notion of memetic code and the realization of memetic codons in terms of 21 DNA codons are suggested by the model.

See the article About tessellations in hyperbolic 3-space and their relation to the genetic code or the chapter with the same title.

The TGD view of the recently discovered gravitational hum as gravitational diffraction

The strength of gravitational hum is unexpectedly large. The basic insight of the TGD view is that diffraction produces very high intensities but only in preferred directions and that in diffraction the amplitude of the scattered field is proportional to the square N² of the number N of scatterers rather than N. The identification of dark matter as phases of the ordinary matter with an arbitrarily large value of Planck constant suggests the existence of tessellations of the hyperbolic 3-space identifiable as light-cone proper time hyperboloid of Minkowski space. Gravitational diffraction could occur in astrophysical scales at these tessellations.

See the article The TGD view of the recently discovered gravitational hum as gravitational diffraction or the chapter Quantum Astrophysics .