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Year 2014



Harmony, music, and religious myths

I have talked about the notion of harmony based on icosahedral representation of 12-note scale and its connection with biology and consciousness coming from the observation that the number of faces of icosahedron is 20 - the number of amino-acids. The link connecting music with biology would be via the geometry of Platonic solids: icosahedron and also tetrahedron.

The 12 vertices of icosahedron correspond to the notes of the 12-note scale and to some Hamilton's cycle defining a closed curved connecting nearest neighbour vertices: it is closed by octave equivalence and does not intersect itself. Quint cycle assigns to each vertex a note of the scale and thus also to every face (triangle) of the icosahedron a chord. These chords define the harmony and there are 11 cycles/harmonies allowing symmetries (6 cycles without symmetries). They fall in three types corresponding to symmetry group Z6= Z3rot× Z2refl, Z4=Z2rot× Z2refl , and Z2= Z2rot or Z2=Z2refl, which is subgroup of icosahedral isometries A5× Z2refl having 2× 60 elements. Just these groups appeared in the model of genetic code inspired by observations about the structure of the code table telling the numbers N(d) of amino-acids coded by d codons.

These symmetries define a hierarchy of symmetry breakings. This hierarchy has amazing connections with the myths, which I believe to reflect deep facts about consciousness and biology at fundamental level. The story of genesis is a good representative in this respect.

  1. The hierarchy of symmetry breakings proceeding from Z6 down to Z2refl brings strongly in mind evolution as loss of innocence. For Z6 one as 4 orbits. One orbit contains 2 triangles (chords, DNA codons assignable to ile). The other orbits correspond to six codons assignable to amino-acids ser, arg, and leu. The chords at the orbits are major chords and 7-chords, and minor chords and 6-chords for the inverse of the harmony.

    There are no dissonant chords in 0-quint sector: dissonances appear only for the remaining groups as 0-quint chords. This is musical representation of paradize. This harmony is based on 6-note scale for the basic notes of the chords and used by impressionistic composers. Amino-acids correspond to selections of preferred chord from each orbit and there are only four different chords: this sub-harmony is very simple. Life in paradize is simple!

  2. Next comes an intriguing observation. The number of amino-acids obtained as projections of the icosahedral DNA orbits is 19, not 20! One chord does not correspond to amino-acid: it is non-playable chord! Could it be impossible to have 20 amino-acids as projections of the orbits and that 19 is the maximum number? The reason for 19 is that the number of amino-acid of type Z6 is 3+1=4 rather than 5. Therefore there is one "non-playable" chord - located at the "paradize orbit" -, which does not correspond to any amino-acid. The natural identification of the non-playable chord is as one of the aug type chords (say CEG#, which is the last breath in many finnish tangos telling about unhappy love end - something between happy CM and sad Am, "raueta" is finnish word for this manner to come to an end: "expire" might be the nearest english counterpart). This chord is located at the 2-chord orbit related to the other chord of the orbit by half-octave shift (chords could be CEG# and F#BbD), the tritonus denied by church.

    One cannot avoid the associations between non-playable chord and the denied fruit hanging in the tree of good and bad knowledge in the story of Adam and Eve, and its analog in many fairy tales. The non-playable chord also brings in mind the hilarious story of Gödel-Escher-Bach about non-playable record (a truth unprovable in given axiom system).

  3. The hierarchy of symmetry breakings leading from Z6 to Z2refl encourages one to continue with the biblical analogies. Z6, Z4 and Z2rot cycles have half-octave shift as a symmetry: good and evil do not exist in paradise, but dissonances are already there for Z4 and Z2 harmonies - the evil snake! These states correspond to the consciousness of animals, children, and saints. Note that bio-harmony corresponds to the presence of one sub-harmony of type Zn, n=6,4,2.
  4. The banishing from the paradize takes place as Z2refl symmetric harmony replaces Z2rot harmony: half-octave shift is not a symmetry anymore, and one can tell between good and evil, and eventually church decides to deny tritonus as a symbol of evil! Paradise is left as icosahedral and tetrahedral code are fused to form the tetra-icosahedral code - the ordinary genetic code leading to the breaking of Z2refl symmetry.
  5. In banishment punct ("empty" amino-acid) as a counterpart of chord shared by tetrahedron and icosahedron emerges and means stopping of the music piece altogether. Death of the sinner! For unfused codes this chord is playable as Sec/Pyl and the music piece is never-ending: life is eternal in paradise! No notion of time, no sin, no death! Amusingly, impressionist music with 6-note scale is music of "now", attempt to catch this moment.

For details see the chapter Quantum model for hearing or the article Geometric theory of harmony.



Updated version of geometric theory of harmony

For some time ago I introduced the notion of Hamiltonian cycle as a mathematical model for musical harmony and also proposed connection with biology: motivations came from two observations. The number of icosahedral vertices is 12 and corresponds to the number of notes in 12-note system and the number of triangular faces of icosahedron is 20, the number of amino-acids and the number of basic chords for the proposed notion of harmony. This led to a group theoretical model of genetic code and replacement of icosahedron with tetra-icosahedron to explain also the 21st and 22nd amino-acid and solve the problem of simplest model due to the fact that the required Hamilton's cycle does not exist.

This article was meant to be a continuation to the eralier article providing a proposal for a theory of harmony and detailed calculations. It however turned out that the proposed notion of bio-harmony was too restricted: all isosahedral Hamilton cycles with symmetries turned out to be possible rather than only the 3 cycles forced by the assumption that the polarity characteristics of the amino-acids correlate with the properties of the Hamiltonian cycle. This working hypothesis had to be given up. The fuel of the minirevolution was the observation the symmetries of the Hamiltonian cycles (Z6, Z4, Z2) are nothing but the icosahedral symmetries needed to predict the basic numbers of the genetic code and its extension to include also 12st and 22nd amino-acids! Thus icosahedral Hamiltonian cycles predict genetic code without further assumptions. Mathematician cannot simply neglect this kind of connection!

One also ends up with a proposal for what harmony is leading to non-trivial predictions both at DNA and amino-acid level.

  1. 3-adicity and also 2-adicity are essential concepts allowing to understand the basic facts about harmony. The notion of harmony at the level of chords is suggested to reduce to the notion of closeness in the 3-adic metric using as distance the distance between notes measures as the minimal number of quints allowing to connect them along the Hamilton's cycle. In ideal case, harmonic progressions correspond to paths connecting vertex or edge neighbors of the triangular faces of icosahedron.
  2. An extension of icosahedral harmony to tetra-icosahedral harmony was proposed as an extension of harmony allowing to solve some issues of icosahedral harmony relying on quint identified as rational frequency scaling by factor 3/2.

    This extension is kept also now. One must however give up the idea about correlation between polarity characteristics of proteins and properties of Hamilton cycles. One must allow all 11 icosahedral harmonies with symmetries as bio-harmonies: their symmetry groups Z6, Z4, Z2 can be identified as the symmetry groups defined the decomposition of 60 DNA codons to 20+20+20 codons in the model of the genetic code. The 4 remaining DNAs and amino-acids can be assigned to both tetra-icosahedron and tetrahedron and icosahedron regarded as defining separate genetic codes. This explains why stopping codons can code for the 21st and 22nd amino-acid under some circumstances.

    Tetrahedral code is second member in the hierarchy of genetic codes inspired by the notion of Combinatorial Hierarchy M(n+1)= MM(n)= 2M(n)-1 giving the numbers 2, 4,7, 64, 2126,... as numbers of DNA codons. The fourth member would correspond to what I called "memetic code" allowing representation of codons as sequences of 21 DNAs. It is not known whether the Combinatorial Hierarchy of Mersenne primes continues as Hilbert conjectured.

  3. The notion of bio-harmony is partially characterized by the triplet n= (n0,n1, n2), characterizing the numbers of 0-, 1-, and 2-quint chords which in turn correspond to DNA codons in consistency with the observation that codons indeed correspond to triplets of nucleotides. n-quint chord corresponds to a triangle (face of icosahedron) containing n edges of the Hamiltonian. Particular bio-harmony requires a selection of a specific Hamiltonian cycle from each class of cycles (1 Z6 symmetric cycle having n= (2,12,6), 2 Z4 symmetric cycles n ∈{(0,16,4), (4,8,8)}, 3 Z2=Z2rot with n∈{(0,16,4),(2,12,6),(4,8,8)} and 5 Z2=Z2refl symmetric cycles with (n∈ {(2,12,6), (4,8,8)}. Note that the are only three different triplets n.
  4. The model gives for the fusion of icosahedral and tetrahedral cycles just the ordinary genetic code so that it is consistent with the proposal that genetic code is realized also by dark proton sequences. For de-fused icosahedral and tetrahedral codes the common face would code for Pyl and Sec, the well-known 21st and 22nd amino-acid. An amusing "co-incidence" is that met to which genes realized as mRNA code is the first codon of gene. At the level of music met would correspond to the basic chord, "home" from which the simple music pieces often begin!
  5. The original idea was that the rules of bio-harmony could be applied to amino-acid sequences interpreted as sequences of basic 3-chords. DNA would have represented the notes of the music. For given choice of harmony as Hamiltonian cycle meaning selection of of 4, 5 or 10 amino-acids coded by the 20 DNAs in question, the hypothesis had to be modified by replacing amino-acid sequences with DNA sequences.

    These DNA sequences however define also amino-acid sequences identifiable as specific triangle at the orbit of Zn defining the DNA codons assigned to that amino-acid (there is a singular fiber space structure). Together the three 20-plets of DNAs define an amino-acid harmony with (4+5+10 =19 chords with tetrahedral extension defining a harmony with 22 chords/amino-acids). Hence both DNA sequences and amino-acid sequences define "bio-music".

  6. The assumption that harmonic transitions between chords (DNA codons) minimize the distance between chords defined by quint-metric leads to highly non-trivial and testable predictions about both DNA sequences and amino-acid sequences. Negentropy Maximization Principle (NMP) suggests that evolution favors the generation of harmony which should thus increase in the proposed sense for DNA sequences defining particular genes or other functional units of DNA during evolution. Large quint-distances between subsequent codons/chords would tend to polished out under evolutionary pressures.
  7. Could icosahedron, tetrahedron, and tetra-icosahedron have direct physical counterparts in living matter? For instance, water molecules form icosahedral clusters and the chlathrates associated with synaptic contacts have icosahedral symmetries. Tetra-icosahedron has 13 vertices with the added vertex representing one note- say E- in C-key as note with slightly different frequency to resolve the basic problem of rational number based 12-note scale (12 quints give slightly more that 7 octaves). Intriguingly, microtubules consist of basic structures consisting of 13 tubulins with 2 states defining bit: could these bit sequences define representation for the 3-chords and thus representation of sequence of DNA codons and realization of genetic code.
  8. Music is language of emotions and peptides are molecules of emotion as Candace Pert expressed it. Could bio-harmonies serve as direct correlates for emotions? What is bio-music? A natural TGD inspired guess is that sounds can be replaced with heff=n× h dark photons with low frequencies and having energies in the range of bio-photons (visible and UV range maximally effective biologically) as proposed on basis of some physical facts and theoretical ideas kenociteallb/hearing. The frequency spectrum of dark cyclotron photons along magnetic flux tubes would define bio-music as "music of dark light" and bio-harmonies would correlate with emotions and moods.
If one can find various icosahedral Hamilton's cycles one can immediately deduce corresponding harmonies. This would require computer program and a considerable amount of analysis. My luck was that the all this has been done. One can find material about icosahedral Hamilton's cycles in web, in particular the list of all 1024 Hamilton's cycles with one edge fixed (this has no relevance since only shape matters). If one identifies cycles with opposite internal orientations, there are only 512 cycles. If the cycle is identified as a representation of quint cycle giving representation of 12 note scale, one cannot make this identification since quint is mapped to fourth when orientation is reversed. The earlier article about icosahedral Hamiltonian cycles as representations of different notions of harmony is helpful.

The tables listing the 20 3-chords of associated with a given Hamilton's cycle make it possible for anyone with needed computer facilities and music generator to test whether the proposed rules produce aesthetically appealing harmonies for the icosahedral Hamiltonian cycles. Biologist with access to DNA sequences could experiment with DNA codons to see whether their are harmonious in the sense that the distance between subsequent chords assignable to DNA codons tend to be small in quint metric. Note that DNA decomposes to pieces corresponding to different Hamiltonian cycles (harmonies) so that the comparison is not quite straightforward.

For details see the chapter Quantum model for hearing or the article Geometric theory of harmony.



Geometric theory of harmony

For some time ago I introduced the notion of Hamiltonian cycle as a mathematical model for musical harmony and also proposed a connection with biology: motivations came from two observations (see this). The number of icosahedral vertices is 12 and corresponds to the number of notes in 12-note system and the number of triangular faces of icosahedron is 20, the number of aminoacids and the number of basic chords for the proposed notion of harmony. This led to a group theoretical model of genetic code and replacement of icosahedron with tetraicosahedron to explain also the 21st and 22nd amino-acid and solve the problem of simplest model due to the fact that the required Hamilton's cycle does not exist.

This led also to the notion of bioharmony. This article is a continuation to the mentioned article providing a proposal for a theory of harmony and detailed calculations.

  1. 3-adicity and also 2-adicity are essential concepts allowing to understand the basic facts about harmony. The notion of harmony at the level of chords is suggested to reduce to the notion of closeness in the 3-adic metric using as distance the distance between notes measures as the minimal number of quints allowing to connect them along the Hamilton's cycle. In ideal case, harmonic progressions correspond to paths connecting vertex or edge neighbors of the triangular faces of icosahedron.
  2. An extension of icosahedral harmony to tetraicosahedral harmony was proposed as an extension of harmony allowing to solve some issues of icosahedral harmony relying on quint identified as rational frequency scaling by factor 3/2.
  3. The idea that the rules of bioharmony realized on amino-acid sequences interpreted as sequences of basic 3-chords leads to highly non-trivial and testable predictions about amino-acid sequences.
If one can find various icosahedral Hamilton's cycles one can immediately deduce corresponding harmonies. This would require computer program and a considerable amount of anlysis. My luck was that the all this has been done. One can find material about icosahedral Hamilton's cycles in web, in particular the list of all 1024 Hamilton's cycles with one edge fixed (see ) (this has no relevance since only shape matters). If one identifies cycles with opposite internal orientations, there are only 512 cycles. If the cycle is identified as a representation of quint cycle giving representation of 12 note scale, one cannot make this identication since quint is mapped to fourth when orientation is reversed. The earlier article about icosahedral Hamiltonian cycles as representations of different notions of harmony is helpful.

The tables listing the 20 3-chords of associated with a given Hamilton's cycle make it possible for anyone with needed computer facilities and music generator to test whether the proposed rules produce aesthetically appealing harmonies for the icosahedral Hamiltonian cycles.

For details see the chapter Quantum model for hearing or the article Geometric theory of harmony.



Does DNA understand speech or should you sing to it?

There is an interesting popular web article about the work of Peter Gariaev with whom I have written a couple of articles. One of the findings of Gariaev's group is that the intronic portion of the DNA has a statistical resemblance to the structure of language (words of language correspond to DNA codons and Zipf's law appears to be obeyed). The question whether introns could code language at molecular level comes to mind.

It is also reported that the connection with language is much more concrete. The words of spoken language generate response at the level of DNA: DNA "hears" and maybe understands language (or is it us who understand the language in this manner?). If one accepts that even water has memory and reacts to signals inducing emotions in living organisms, this would not be so surprising. In fact, in TGD framework water would be primitive life form with dark DNA consisting of protonic strings such that proton states would be in 1-1 correspondence with DNAs, RNAs, amino-acids and perhaps even tRNAs (see this). Vertebrate genetic code follows from natural assumptions between dark counterparts of DNAs and amino-acids.

So the claim is that spoken language modulating em radiation has effect on DNA. In standard physics context it is difficult to see how this could make sense. The energies of phonons at audible frequencies are simply so low that understanding the effect in terms of phonons does not seem to be possible. Could it make sense in TGD inspired quantum biology? One can at least try and this is what is done in the sequel. The explanation relies on the basic assumptions of TGD inspired quantum biology distilled during last 10 years.

  1. Dark matter corresponds to a hierarchy of phases labelled by the values of effective Planck constant given by heff= n×h (see this). This hypothesis can be reduced to the failure of strict determinism for the basic variational principle of TGD and is consistent with the the notion of gravitational Planck constant defined as hgr= GMm/v0, where v0 is characteristic velocity assignable to the two particle system consisting of masses m and M (see this). This formula holds true at flux tubes mediating gravitational interaction in terms of gravitonic "massless extremals" (MEs) topologically condensed at them.

    For elementary particles,ions, atoms, even biomolecules this formula is consistent with heff=hgr. Equivalence Principle implies that the formula for hgr must be assumed only for them to explain approximate Bohr orbitology for planetary orbits. For Earth-charged particle system the formula predicts Planck constant for which dark cyclotron photon energies in endogenous magnetic fields are in visible and UV range at which also biophoton energies are. Gravitational Compton length does not depend on the mass of particle - essential for macroscopic quantum coherence and consistent with Equivalence Principle. For Earth-Sun system the gravitational Compton lengths is of the order Earth radius, which suggests that at dark matter level Earth is macroscopic quantum system.

  2. This picture conforms with the hypothesis that biophotons are ordinary photons resulting in heff changing phase transition (see this). Since the energy levels of biomolecules belong to visible and UV range, dark photons could control biochemistry by dark-to-bio-photon transitions. This would give the missing interaction link between biochemistry and magnetic body. The standard hypothesis is that biophotons are side products of biochemistry: in TGD Universe biophotons would become active controllers of biochemistry and would be used by magnetic body.
  3. Living matter as a random soup of biomolecules is replaced with a highly organized structure. Dark matter can be seen as a library of Akashic records realized in terms of negentropic entanglement (see this). Each dark particle, atom, molecule, etc is at its own magnetic flux tube characterized by heff=hgr. One can say that each book in the Akashic library resides neatly at its own book shelf labelled by the value of magnetic field strength and heff. The communication between levels of dark matter hierarchy (book shelves) would take place by using heff changing transition of dark photons having a universal energy spectrum independent of the particle mass and depending on the strength of magnetic field at the flux tube. Visible photons correspond to single energy octave which suggests connection with music discussed in the earlier posting (see this).
In this framework it is not too difficult to understand how DNA could "hear" and maybe even "understand".
  1. DNA codons carry -2 units of em charge per single nucleotide due to the presence of one diphosphate in the sugar backbone. The ratio Qtot/Mtot= 2N(tot)e/Mtot=2e/M(ave) to which cyclotron frequency is proportional, is inversely proportional to the average mass M(ave) of the unit of DNA sequence. Hence DNA sequences are coded by cyclotron frequencies and to "wake up" given unit of DNA it is enough to irradiate it with dark photons at this cyclotron frequency. For long sequences of DNA cyclotron frequency becomes essentially constant if DNAs obey statistical a distribution with single Gaussian peak. One can consider the possibility that the distribution is many-peaked and fractal.

    This is not the only one possible option that one can imagine. Cyclotron frequencies could be also assignable - not to DNA itself but - to charged particles at the flux tubes associated with the basic units of DNA.

  2. There are two ways to "wake up" DNA: frequency resonance at the level of dark matter and energy resonance at the level of visible matter. The first manner to wake up DNA is by a transformation of acoustic signal to dark photons at cyclotron frequencies which are also cyclotron frequencies of DNA molecules. DNA units would be analogous to the frequency specific hair cells in cochlea. The TGD inspired model of hearing indeed assumes that the hair cells carry out this transformation. Second manner to wake up DNA is to transform the dark photons first to biophotons with a transition energy of DNA molecule and thus inducing the chemical transition. These dark photons could then excite the DNAs resonantly at cyclotron frequencies or a chemical transition energies after transition to bio-photon. This mechanism breaks quantum coherence.

    If the excited DNAs correspond genes or to a portion of DNA inducing gene expression, acoustic signal (say speech) would be transformed to genetic expression and thus generate a physiological response. Introns could also generate em signals transformed to acoustic signals giving eventually rise to internal speech. Here the cyclotron resonance mechanism could be at work. This mechanism respects quantum coherence.

  3. Right brain sings - left brain talks metaphor suggests an interpretation for these two mechanisms. For the singing right brain the cyclotron resonance for dark photons could dominate. For the talking left brain the chemical excitation using biophotons could dominate.
Gariaev's experiments suggest that amplitude modulation of light signal by acoustic signal, say speech, is enough.
  1. The carrier wave with single frequency modulated by single frequency would consist of a superposition of signals with frequencies which correspond to sum and difference for the frequencies involved. They could naturally correspond to parallel space-time sheets (MEs) (but this is not necessary): the test particle touching both sheets indeed experiences the sum of the effects caused by the two signals. The naive expectation would be that these signals are detected as such. This would not however allow the proposed mechanism.

    Another possibility is that the resulting photons at either or both space-time sheets having frequency and energy of (say) visible photons are transformed to dark photons with the frequency of phonon in the frequency range involved with the speech. This condition fixes the value of heff to be essentially the ratio of visible and audible carrier frequencies and fixes also the value of the endogenous magnetic field strength from the condition that cyclotron energy scale is same as the energy of visible photon. The MEs in question should be topologically condensed at the magnetic flux tubes.

  2. These dark photons transform to biophotons inducing a response both at the level of biochemistry and at the level of DNA sub-units (talking and singing) : heff in question is correct, the DNA sub-unit corresponding to flux tubes with the value of heff associated with dark photons is excited and can induce protein translation or some other form of gene expression so that the incoming signal finds expression.
  3. One can consider also acoustic signals transformed directly to dark photon electromagnetic signals propagating along flux tube-massless extremal pairs to DNA since living matter consists of piezo-electrets performing these transformations. These would correspond to communication by "singing": singing could correspond basically frequency modulation induced by the modulation of magnetic field strength ("whale's song"). The variation of membrane voltage by waves and by nerve pulses induce similar frequency modulation.

For details see the chapter Quantum model for hearing or the article Pythagoras, music, sacred geometry, and genetic code.



Pythagoras, music, sacred geometry, and genetic code

The idea that the 12-note scale could allow mapping to a closed path covering all vertices of icosahedron having 12 vertices and not intersecting itself is attractive. Also the idea that the triangles defining the faces of the icosahedron could have interpretation as 3-chords defining the notion of harmony for a given chord deserves study. The paths in question are known as Hamiltonian cycles and there are 1024 of them. There paths can be classified topologically by the numbers of triangles containing 0, 1, or 2 edges belonging to the cycle representing the scale. Each topology corresponds to a particular notion of harmony and there are several topological equivalence classes.

The vision about DNA and amino-acids as analogs of notes and music piece produced by the translation machinery from mRNA is also attractive and induce the idea that the 20 amino-acids could somehow correspond to the 20 triangles of icosahedron. The combination of this idea with the idea of mapping 12-tone scale to a Hamiltonian cycle at icosahedron leads to the question whether amino-acids could be assigned with a topological equivalence class of Hamiltonian cycle and whether topological characteristics could correspond to physical properties of amino-acids. It turns out that the identification of 3 basic polar amino-acids with triangles containing no edges of the scale path, 7 polar and acidic polar amino-acids with those containing 2 edges of the scale path, and 10 non-polar amino-acids with triangles containing 1 edge on the scale path would be consistent with the constraints on the Hamiltonian cycles. One could of course criticize the lumping of acidic polar and polar aminoacids to same group.

The number of DNAs coding for a given amino-acid could be also seen as such a physical property. The model for dark nucleons leads to the vertebrate genetic code with correct numbers of DNAs coding for amino-acids. It is however far from clear how to interpreted DNAs geometrically and the problem whether one cold understand genetic code geometrically remains open.

For details see the chapter Quantum model for hearing or the article Pythagoras, music, sacred geometry, and genetic code.



Gravitational Mother Gaia and life

In an earlier summary I have told about considerable progress in understanding TGD inspired quantum biology. The basic result is that the gravitatational Planck constant hgr inspired by Nottale's observations and heff inspired by the effects of ELF radiation on vertebrate brain can be one and same thing at least in elementary particle scales where hgr is defined for a pair formed by elementary particle (say) and Earth, or Sun or some massive body. It is of course possible that heavier objects than elementary particle can appear as second member in the pair. The objects are connected by gravitational flux tubes mediating gravitational interaction.

The big surprise was that hgr is indeed of same order of magnitude as needed for the energies of EEG photons to be in visible-UV range so that their decay products can be interpreted as biophotons. Dark cyclotron photons with universal energy spectrum in this range would control bio-chemical reactions by resonance mechanism in living matter.

This picture generalizes to other interaction and the notion of hem= Z1Z2e2/v0. Now the surprising numerical accident is that for ATP synthase which is motor with rotating shaft rotating with velocity v0 and generating three ATPs from ADP during single turn hem seems is same order of magnitude as hgr(particle,Earth) for elementary particles.

These findings lead to fascinating speculations about the role of quantum gravitation in living systems.

Negentropic entanglement (NE) is one of the key notions of TGD inspired quantum biology. For instance, it would seem that NE would look more natural metabolic resource than energy. Nutrients should carry it. NE is however not single particle property but between nutrient and some other system in the recent case. What can one say about this system? Can it be part of nutrient? Could it correspond to oxygen molecules? Or could it be gravittional Mother Gaia identified in some sensible manner?

If one believes on the presence of gravimagnetic flux tubes and their role as generator of macroscopic quantum coherence in biology then one is forced to consider seriously also NE between its ends. If this is the case then the view of religions about life might be nearer to truth than that of hard-born materialists.

To make this more concrete, let us first look what the transfer of NE could mean.

  1. Suppose that nutrient N has NE with unknown system A which a priori could be part of nutrient. Assume that the transfer of NE of nutrient with A is formed by reconnection of U-shaped flux tubes associated with N (or glucose G produced from it) and A so that two parallel flux tubes connecting N and A are formed.
  2. The basic operation allowing transformation of N-A NE to P-A NE is following. The two flux tube portions of U-shaped flux associated with the receiver R are reconnected with the two parallel flux tubes connecting N and A so that two flux tubes connecting R to A are formed. NMP strongly suggests that the entanglement remains negentropic in the process.
  3. NE is first transferred to P using this process so that P and A are now NE-connected. After this P attaches to ADP to yield ATP and ATP attaches to B and the transfer process leads to NE between B and A.

    For ATP synthase the hem consisting two elementary charges is of the same order as hgr. This is probably not an accident. Could this mean that this kind of flux tube can reconnect with gravitational flux tube? Could this make possible a reconnection transforming N-Earth NE to P-Earth NE? This looks plausible.

Consider now the identification of A.
  1. If one assumes that the negentropic entanglement corresponds to gravitational flux tubes for N-Earth system then A should be gravitational Mother Gaia, whatever its precise definition might be. N (and glucose) molecules would be alive in the sense that they have NE with Mother Gaia.
  2. Could oxygen have some deeper role? For instance, could O2 molecules serve as analogs of cell membrane receptors for Mother Gaia meaning that gravitational flux tubes go through O2 molecules? This does not look plausible since metabolism is possible also as fermentation involving no oxygen.
  3. In this picture the role of breathing and fermentation would be to make possible the transfer of NE from nutrients to the living system.
This picture allows to imagine about what might happen in biological death. Biological death takes first place only at the highest level of self hierarchy assignable to the our biological body. Cells continue for some time their life even after the last breath. The notion of hgr together with Equivalence Principle suggests that the living biological body has negentropic flux tube connections to both electromagnetic magnetic body (personal magnetic body) and to gravitational Mother Gaia (MG) (especially during sleep) representing collective consciousness in the scale of Earth. Also connections to higher levels are possible. Also personal magnetic body and MG have connections. At the moment of biological death the negentropic flux tube pairs connecting the personal magnetic body to biological body are split and only those with MG remain or are generated in this process. This would happen later at lower levels of biological self hierarchy such as organ and organelles and eventually for cells and biopolymers. The magnetic bodies of the resulting decay products have negentropic entanglement with MG and and can be used as nutrients to transfer this entanglement to bio-molecules.

The quantum model for metabolism allows to understand life as a process in which negentropic entanglement of gravitational Mother Gaia with nutrients is transformed to that of molecules of biological body with personal magnetic body and further processed and enriched. At the moment of biological death this information returns to the personal magnetic body which now connects only gravitational Mother Gaia or higher levels in the hierarchy. By NMP information is not lost but increases steadily giving rise to "Akashic records". This view conforms with the core ideas of spiritual and religious teachings.

For details see the chapter Quantum model for bio-superconductivity: II or the article Implications of strong gravimagnetism for TGD inspired quantum biology.



Implications of strong gravimagnetism for TGD inspired quantum biology

Physicists M. Tajmar and C. J. Matos and their collaborators working in ESA (European Satellite Agency) have made an amazing claim of having detected strong gravimagnetism with gravimagnetic field having a magnitude which is about 20 orders of magnitude higher than predicted by General Relativity.

Tajmar et al have proposed the gravimagnetic effect as an explanation of an anomaly related to the superconductors. The measured value of the mass of the Cooper pair is slightly larger than the sum of masses whereas theory predicts that it should be smaller. The explanation would be that actual Thomson field is larger than it should be because of gravimagnetic contribution to quantization rule used to deduce the value of Thomson field. The required value of gravimagnetic Thomson field is however 28 orders of magnitude larger than General Relativity suggests. TGD inspired proposal is based on the notion of gravitational Planck constant assignable to the flux tubes connecting to massive objects. It turns out that the TGD estimate for the Thomson field has correct order of magnitude. The identification heff=hgr at particle physics and atomic length scales emerges naturally.

A vision about the fundamental role of quantum gravitation in living matter emerges. The earlier hypothesis that dark EEG photons decay to biophotons with energies in visible and ultraviolet range receives strong quantitative support. Also a mechanism for how magnetic bodies couple bio-chemistry emerges. The vision conforms with Penrose's intuitions about the role of quantum gravity in biology.

For details see the chapter Quantum model for bio-superconductivity: II or the article Implications of strong gravimagnetism for TGD inspired quantum biology.



Possible implications of Pollack's findings for pre-biotic life in TGD Universe

I discussed in previous posting the fourth phase of water whose existence is convincingly demonstrated by Gerald Pollack and known with many other names: one of them is Brown's gas known for a long time - standard scientists have refused to admit its existence. In TGD framework the fourth phase of water has nice interpretation in terms of magnetic body and dark proton strings at its flux tubes giving rise to a realization of genetic code. If the fourth phase of water defines pre-biotic life form then the phase transition generating fourth phase of water and its reversal are expected to be fundamental elements of the ordinary metabolism, which would have developed from the pre-biotic metabolism. The following argument demonstrates that the findings of Pollack interpreted in this manner allow to understand what happens in photosynthesis and metabolism at deeper level and also shed light to the newest dramatic discovery related to metabolic pathways.

  1. Cell interiors, in particular the interior of the inner mitochondrial membrane are negatively charged as the regions formed in Pollack's experiments. Furthermore, the citric acid cycle, which forms the basic element of both photosynthesis and cellular respiration, involves electron transport chain in which electron loses gradually its energy via production of NADP and proton at given step. Protons are pumped to the other side of the membrane and generates proton gradient serving as metabolic energy storage just like battery. The interpretation for the electron transport chain in terms of Pollack's experiment would be in terms of generation of dark protons at the other side of the membrane.
  2. When ATP is generated from ADP three protons per ATP flow back along the channel formed by the ATP synthase molecule (perhaps Josephson junction) and rotate the shaft of a "motor" acting as a catalyst generating three ATP molecules per turn by phosphorylating ADP. The TGD based interpretation is that dark protons are transformed back to ordinary ones and possible negentropic entanglement is lost.
  3. ATP is generated also in glycolysis, which is ten-step process occurring in cytosol so that membrane like structure need not be involved. Glycolysis involves also generation of two NADH molecules and protons. An open question (to me) is whether the protons are transferred through an endoplasmic reticulum or from a region of ordered water (fourth phase of water) to its exterior so that it would contribute to potential gradient and could go to magnetic flux tubes as dark proton. This would be natural since glycolysis is realized for nearly all organisms and electron transport chain is preceded by glycolysis and uses as input the output of glycolysis (two pyruvate molecules).
  4. Biopolymers - including DNA and ATP - are typically negatively charged. They could thus be surrounded by fourth phase of water and neutralizing protons would reside at the magnetic bodies. This kind of picture would conform with the idea that the fourth phase (as also magnetic body) is fractal like. In phosphorylation the metabolic energy stored to a potential difference is transferred to shorter length scales (from cell membrane scale to molecular scale).
One of the basic questions of biology is whether metabolism preceded basic biopolymers or vice versa. RNA world scenario assumes that RNA and perhaps also genetic code was first.
  1. The above view suggests that both approaches are correct to some degree in TGD Universe. Both metabolism and genetic code realized in terms of dark proton sequences would have emerged simultaneously and bio-chemistry self-organized around them. Dark proton sequences defining analogs of amino-acid sequences could have defined analogs of protein catalysts and played a key role in the evolution of the metabolic pathways from the primitive pathways involving only the phase transition between ordinary water and fourth phase of water.
  2. There is very interesting article telling that complex metabolic pathways are generated spontaneously in laboratory environments mimicking hot thermal vents. Glycolysis and pentose phosphate pathway were detected. The proposal is that these pathways are catalyzed by metals rather than protein catalysts.
  3. In standard biology these findings would mean that these metabolic pathways emerged before basic biopolymers and that genetic code is not needed to code for the metabolic pathways during this period. In TGD framework dark genetic code would be there, and could code for the dark pathways. Dark proton strings in one-one correspondence with the amino-acid sequences could be responsible for catalysts appearing in the pathways. Only later these catalysts would have transformed to their chemical counterparts and might be accompanied by their dark templates. One cannot even exclude the possiblity that the chemical realization of the DNA-aminoacid correspondence involves its dark analog in an essential manner.

For details see the chapter Dark matter hierarchy and hierarchy of EEGs or the article What is EEG made of?.





What is EEG made of?

The usual classification of EEG frequencies by EEG bands is more or less a convention and the definitions of various bands vary in frustratingly wide ranges. In a more ambitious approach bands should be replaced with some substructures identified on basis of their physical origin and function. In the proposed framework this is possible. This identification of substructures of course applies only to that part of EEG from which evoked potentials, noise, and possible other contributions are subtracted.

The recent developments in TGD inspired quantum biology lead to a more detailed form of TGD inspired model for EEG as a communication and control tool of magnetic body.

  1. Sensory data are communicated from cell membrane to magnetic body as Josephson radiation and induced transitions at harmonics of cyclotron frequencies determined by the mass number A and charge Z of ion in question (also electron and proton are included) plus the local strength of the magnetic field Bend having nominal value Bend=.2 Gauss in the simplest situation.

    Communications take place at resonance so that one has fJ= ZeV/heff=fc= ZeBend/2πAmp, heff=2k× A× h, where A is the atomic weight of the ion for the fundamental frequencies a more general resonance condition for harmonics reads as mfJ=nfc. This condition is a new ingredient to the earlier model and is extremely restrictive - especially so if one assumes only bosonic ions forming Bose-Einstein condensates. Also electron and proton are needed to represent frequencies which are of order kHz or higher: this is true for hearing for which frequency range to be represented varies up 20 kHz.

  2. Information is coded in frequency modulations of Josephson frequency induced by neural activity and feedback from the magnetic body coming via DNA at harmonics of cyclotron frequencies. Frequency modulations have emotional content in music, which suggests that the "sensory experiences" of magnetic body defined by the Josephson radiation have emotional content dictated by the frequency modulation.

    Also the variations of resting potential induces frequency modulations and the quantum model for hearing suggests that the variations of the voltage could define analog of music scale consisting of discrete spectrum of resting potentials corresponding to cyclotron frequencies of ions belonging to the octave 10-20 Hz and having frequencies fc∼ 10 Hz in alpha band as basic frequency.

  3. Basic facts about EEG at various stages of sleep and the fact that octaves of 10 Hz frequency appear as resonance frequencies together with music metaphor suggests that EEG can be regarded as superposition of frequencies spectra very much analogous to frequency spectra associated with music scale. In particular, octaves of heff=2km and Bend suggested also by p-adic length scale hypothesis appear. In the simplest situation the EEGs associated with various ions would be time scaled versions of each other making possible "stories" as representations of same events in various time scales: this is believed to be a basic ingredient of intelligence.
  4. The model leads to a detailed identification of sub-bands of EEG in terms of cyclotron frequencies assignable to bosonic ions. One can understand the basic features of various EEG bands, why conscious experiences possible occurring during sleep are not remembered and the four stages of sleep, why beta amplitudes are low and tend to be chaotic, the origin of resonance frequencies of EEG. Also a model for how Schumann resonances could affect consciousness emerges.

    Music metaphor allows to develop in more detail the earlier proposal that nerve pulse patterns defined a languages with "phonemes" having duration of .1 seconds and obeying genetic code with 6 bits. Also the right brain signs metaphor can be given a detailed quantitative content in terms of the analog of music scale associated with the resting potential.

To sum up, the model gives very strong quantitative support for the notion of magnetic body and makes several testable predictions.

For background and details see the chapter Quantum model for EEG or the article What is EEG made of?.



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