Tuesday, June 04, 2024

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 fi 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 fi are polynomials Pi 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 X2i at a particular light-like partonic orbit (mi such orbits for fi) defining a X2i as a root of fi. If f2 (f1 ) is restricted to X21 resp. X22 is a polynomial P2i 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 X2i. Only a single extension appears for a given root and can depend on it. The identification of heff=nih0 looks natural and would mean that heff 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 heff=nh0, h0<h is the minimal value of heff 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 nE 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 Sm it has m! elements. If it is a cyclic group Zm, 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 mk 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 X2i making itself manifest as the exponential increase in the number of roots and degree of extension of rationals and heff. 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 mi corresponds to the degree of a polynomial, quite high degrees are required. The iteration of polynomials would mean an exponential increase in powers dk 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=2k.

  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=heff/h0 corresponds to the dimension nE 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.

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