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Wednesday, November 2, 2016 3:48

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Morphogenesis represents one of the basic unsolved problems of biology. Molecular biology and gene hypothesis have not allowed to understand what is involved. The probable reason is that biochemistry is local approach whereas morphogenesis is a non-local phenomenon. There have been attempts to understand morphogenesis using the catastrophe theory of Thom . Sheldrake has done highly interesting work with morphogenesis too. Robert Merrick's article harmonic theory of evolution (see this) suggests a connection between the notion of harmony as expressed by 12-note scale and morphogenesis.

The basic building bricks of TGD vision about morphogenesis would be following.

- Macroscopic quantum coherence is to my view a necessary ingredient of morphogenesis and hierarchy of Planck constants allows to realize it. The notion of magnetic body (MB) is also necessary. MB would guide the morphogenesis. For instance, the replication of living system would be induced by that for MB. The fundamental dynamics takes place at the level of MB and biochemical level is only a shadow of this dynamics. “Topological light rays” (“massless extremals”, MEs) is second key element. MB would use MEs to control visible living matter, in particular to guide morphogenesis. The challenge is to understand how MB achieves this.
- The notion of harmony assignable to various musical scales realized as Hamiltonian cycles at Platonic solids is central. The TGD based model for harmony was actually inspired by the book of Merrick's theory of music. The model for harmonies assignable to 12-note scale led to a model for genetic code in terms of so called Hamiltonian cycles on icosahedron and tetra-hedron predicting correctly the numbers of DNA codons coding for given amino-acid and also predicted two additional amino-acids Pyl and Sec appearing in Nature.
- The fusion of real physics for sensory experience and various p-adic physics for cognition gives rise to adelic physics. In particular, one can speak about adelic variants of space-time surfaces and he notion of monadic geometry emerges. Geometric objects have discrete “spine” for which points have coordinate values in an algebraic extension of rationals for some preferred coordinate system dictated by the symmetries of the imbedding space M
^{4}× CP_{2}. Space-time surfaces are also locally continuous and smooth so that classical partial differential equations defining space-time surfaces as preferred extremals of Kähler action or its twistor lift make sense.

Platonic solids represents unique monadic geometries since they correspond to finite discrete subgroups of the 3-D rotation group giving rise to 3-dimensional structures as their geometric representations. Also planar polygons represent this kind of realizations and can be assigned to the inclusion hierarchy of von Neuman algebras knowns hyper-finite factors of type II_{1} and very probably also to the analogous fractal hierarchy of sub-algebras of super-symplectic algebra isomorphic to the full algebra.

12-note scale could be by its special mathematical features and by preferred extremal condition fundamental from the point of view of morphogenesis. The lengths of flux tubes are quantized. One can imagine two options. The effective length of given flux tube can be varied as done in guitar or the tensor network would be like piano or harp: the lengths of flux tubes assignable to the tensor network would have quantized lengths coming as rational multiples of fundamental length in such a manner that a representation of the 12-note system would be obtained.

The model of music harmony and 12-note scale would be assignable to icosahedron which would aslo define a very natural monadic geometry. This harmony would also related to genetic done. Monadic geometry could in turn emerge naturally in morphogenesis so that genetic code could after all lurk behind morphogonesis but being realized in terms of 3-chords rather than triplets of DNA nucleotides. Morphogenesis could be a realization of genetic code in terms of interfering fields.

How morphogenesis could then be realized in this picture?

- Chladni mechanism is a clever trick to make the nodal curves associated with standing waves visible. This mechanism could transcend to a basic mechanism of morphogenesis. The idea is very simple. Biomolecules could end up to the nodal surfaces for a standing waves of say electric field since the force on them would vanish at the nodal surfaces. This would give stationary structures. MB could control morphogenesis by using this kind of standing waves forcing the formation of various structures at their nodal surfaces.
- The objection is that TGD does not allow single-sheeted realizations of standing waves. This objection is not lethal. In many-sheeted space-time one can realize effective sinusoidal standing waves as 2-sheeted structures from two MEs propagating to opposite spatial directions and carrying plane waves with a fixed frequency. These two-sheeted structures would serve as basic building bricks. The test particle having necessarily wormhole contacts to both MEs would experience the force caused by the sum of the induced gauge fields assigned to the two MEs. The force would be same as that caused by a standing wave with separable temporal and spatial dependence not realizable as preferred extremal: that is a product of trigometric functions – say sin(ω t) sin(k x). The force would vanish at nodal surfaces, which would thus define naturally the shape of a stationary structure defined by molecules.

One can take several primitive MEs and allow them to have different directions but common frequency. One would obtain effective standing wave with common factorized time dependence and spatial dependence given by the sum of spatial parts of the sinusoidal waves. The nodal surface for this wave would correspond to the nodal surface for the sum of the spatial waves and one would obtain arbitrarily complex nodal surfaces.

The nodal surfaces for these waves would naturally associated with the nodes of the tensor network, where the flux tubes of MB indeed meet. Fractal structure with tensor networks with nodes of tensor networks can be assumed in TGD framework.

For background the chapter Quantum model for hearing. See also the article What could be the physical origin of Pythagorean scale?.

For a summary of earlier postings see Latest progress in TGD.