About the origin of multicellularity in the TGD Universe

A living organism consists of cells that are almost identical and contain DNA that is the same for all of them but expresses itself in different ways. This genetic holography is a fundamental property of living organisms. Where does it originate?

Dark DNA associated with magnetic flux tubes is one or the basic predictions of the TGD inspired biology. One can say that the magnetic body controls the ordinary biomatter and dictates its development. Could one have a structure that would consist of a huge number of almost identical copies of dark DNA forming a quantum coherent unit inducing the coherence of ordinary biomatter? Could this structure induce the self-organization of the ordinary DNA and the cell containing it.

Could one understand this by using the TGD based spacetime concept. There are two cases to be considered. The general option is that f_i are analytic functions of 3 complex coordinates and 1 hypercomplex (light-like) coordinate of H and (f₁,f₂)=(0,0) defines the space-time surface.

A simpler option is that f_i are polynomials P_i with rational or even algebraic coefficients. Evolution as an increase of number theoretic complexity (see this) suggest that polynomials with rational coefficients emerged first in the evolution.

1. For the general option (f₁,f₂), the extension of rationals could emerge as follows. Assume 2-D singularity X²_i at a particular light-like partonic orbit (m_i such orbits for f_i) defining a X²_i as a root of f_i. If f₂ (f₁ ) is restricted to X²₁ resp. X²₂ is a polynomial P²_i with algebraic coefficients, it has m₂ resp. m₁ discrete roots, which are in an algebraic extension of rationals with dimension m₂ resp. m₁. Note that m₂ can depend on X²_i. Only a single extension appears for a given root and can depend on it. The identification of h_eff=n_ih₀ looks natural and would mean that h_eff is a local property characterizing a particular interaction vertex. Note that it is possible that the coefficients of the resulting polynomial are algebraic numbers.

   For the polynomial option (f₁,f₂)=(P₁,P₂), the argument is essentially the same except that now the number of roots of P₁ resp. P₂ does not depend on X²₂ resp. X²₁. The dimension n₁ resp. n₂ of the extension however depends on X²₂ resp. X²₁ since the coefficients of P₁ resp. P₂ depend on it.

2. The proposal of the number theoretic vision of TGD is that the effective Planck constant is given by h_eff=nh₀, h₀<h is the minimal value of h_eff and n corresponds to the dimension of the algebraic extension of rationals. As noticed, n would depend on the roots considered and in principle m=m₁m₂ values are possible. This identification looks natural since the field of rationals is replaced with its extension and n defines an algebraic dimension of the extension. n=m₁m₂ can be also considered. For the general option, the degree of the polynomial P₁ can depend on a particular root X²₂ of f₂ .
3. The dimension n_E of the extension depends on the polynomial and typically seems to increase with an exponential rate with the degree of the polynomials. If the Galois group is the permutation group S_m it has m! elements. If it is a cyclic group Z_m, it has m elements.

For the original view of M⁸-H duality, single polynomial P of complex variable with rational coefficients determined the boundary data of associative holography (see this, (see this, and this). The iteration of P was proposed as an evolutionary process leading to chaos (see this) and led to an exponential increase of the degree of the iterated polynomial as powers m^k of the degree m of P and to a similar increases of the dimension of its algebraic extension.

This might generalize to the recent situation (see this) if the iteration of polynomials P₁ resp. P₂ at the partonic 2-surface X²₂ resp. X²₁ defining holographic data makes sense and therefore induces a similar evolutionary process by holography. This could give rise to a transition to chaos at X²_i making itself manifest as the exponential increase in the number of roots and degree of extension of rationals and h_eff. One can consider the situation also from a more restricted point of view provided by the structure of H.

1. The space-time surface in H=M⁴× CP₂ can be many-sheeted in the sense that CP₂ coordinates are m₁-valued functions of M⁴ coordinates. Already this means deviation from the standard quantum field theories. This generates a m₁-sheeted quantum coherent structure not encountered in QFTs. Anyons could be the basic example in condensed matter physics (see this). m₁ is not very large in this case since CP₂ has extremely small size (about 10⁴ Planck lengths) and one would expect that the number of sheets cannot be too large.
2. M⁴ and CP₂ can change the roles: M⁴ coordinates define the fields and CP₂ takes the role of the space-time. M⁴ coordinates could be m₂ valued functions of CP₂ coordinates: this would give a quantum coherent system acting as a unit consisting of a very large number m₂ of almost identical copies at different positions in M⁴. The reason is that there is a lot of room in M⁴. These regions could correspond to monopole flux tubes forming a bundle and also to almost identical basic units.

   If m_i corresponds to the degree of a polynomial, quite high degrees are required. The iteration of polynomials would mean an exponential increase in powers d^k of the degree d of the iterated polynomial P and a transition to chaos. For a polynomial of degree d=2 one would obtain a hierarchy m=2^k.

3. Lattice like systems would be a basic candidate for this kind of system with repeating units. The lattice could be also realized at the level of the field body (magnetic body) as a hyperbolic tessellation. The fundamental realization of the genetic code would rely on a completely unique hyperbolic tessellation known as icosa tetrahedral tessellation involving tetrahedron, octahedron and icosahedron as the basic units (see this and this). This tessellation could define a universal genetic code extending far beyond the chemical life and having several realizations also in ordinary biology.
4. The number of neurons in the brain is estimated to be about 86 billions: 10¹²≈ 2⁴⁰. If cell replications correspond to an iteration of a polynomial of degree 2, morphogenesis involves 40 replications. Human fetal cells replicate 50-70 times. Could the m almost copies of the basic system define a region of M⁴ corresponding to genes and cells? Could our body and brain be this kind of quantum coherent system with a very large number of almost copies of the same basic system. The basic units would be analogs of monads of Leibniz and form a polymonad. They could quantum entangle and interact.
5. If n=h_eff/h₀ corresponds to the dimension n_E of the extension, it could be of the order 10¹⁴ or even larger for the gravitational magnetic body (MB). The MB could be associated with the Earth or even of the Sun: the characteristic Compton length would be about .5 cm for the Earth and half of the Earth radius for the Sun).

Could this give a recipe for building geometric and topological models for living organisms? Take sufficiently high degree polynomials f₁ and f₂ and find the corresponding 4-surface from the condition that they vanish. Holography=holomorphy vision would also give a model for the classical time evolution of this system as classical, and not completely deterministic realization of behaviors and functions. Also a quantum variant of computationalistic view emerges.

See the article TGD view about water memory and the notion of morphogenetic field or the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

See the article TGD view about water memory and the notion of morphogenetic field or the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.