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Year 2018

Geometric theory of bio-harmony

For some years ago I developed a model of music harmony. As a surprising side product a model of genetic code predicting correctly the number of codons coding given amino-acid emerged. Since music expresses and creates emotions, one can ask whether genes could have "moods" characterized by these bio-harmonies. The fundamental realization could be in terms of dark photon triplets replacing phonon triplets for ordinary music.

  1. The model relies on the geometries of icosahedron and tetrahedron and representation of 12-note scale as so called Hamiltonian cycle at icosahedron going through all 12 vertices of icosahedron. The 20 faces correspond to allowed 3-chords for harmony defined by given Hamiltonian cycle. This brings in mind 20 amino-acids (AAs).
  2. One has three basic types of harmonies depending on whether the symmetries of icosahedron leaving the shape of the Hamiltonian cycle is Z6, Z4 or Z2. For Z2 there are two options: Z2,rot is generated by rotation of π and Z2,refl by reflection with respect to a median of equilateral triangle.
  3. Combining together one harmony from each type one obtains union of 3 harmonies and if there are no common chords between the harmonies, one has 20+20+20 3-chords and a strong resemblance with the code table. To given AA one assigns the orbit of given face under icosahedral isometries so that codons correspond to the points of the orbit and orbit to the corresponding AA. 4 chords are however missing from 64. These one obtains by adding tetrahedron. One can glue it to icosahedron along chosen face or keep is disjoint.
  4. The model in its original form predicts 256 different harmonies with 64 3-chords defining the harmony. DNA codon sequences would be analogous to sequences of chords, pieces of music. Same applies to mRNA. Music expresses and creates emotions and the natural proposal is that these bio-harmonies correlate with moods that would appear already at molecular level. They could be realized in terms of dark photon triplets realized in terms of light and perhaps even music (living matter is full of piezo-electrets). In fact, also the emotions generated by other art forms could be realized using music of dark light.
The model of music harmony is separate from the model of genetic code based on dark proton triplets and one of the challenges has been to demonstrate that they are equivalent. This inspires several questions.
  1. Could the number of harmonies be actually larger than 256 as the original model predicts? One could rotate the 3 fused Hamilton's cycles with respect to each by icosahedral rotations other leaving the face shared by icosahedron and tetrahedron invariant. There are however conditions to be satisfied.
    1. There is a purely mathematical restriction. If the fused 3 harmonies have no common 3-chords the number of coded AAs is 20. Can one give up the condition of having no common 3-chords and only require that the number of coded AAs is 20?
    2. There is also the question about the chemical realizability of the harmony. Is it possible to have DNA and RNA molecules to which the 3-chords of several harmonies couple resonantly? This could leave only very few realizable harmonies.
  2. The model predicts the representation of DNA and RNA codons as 3-chords. Melody is also an important aspect of music. Could AAs couple resonantly to the sums of the frequencies (modulo octave equivalence) of the 3-chords for codons coding for given AA? Could coding by the sum of frequencies appear in the coupling of tRNA with mRNA by codewords and coding by separate frequencies to the letterwise coupling of DNA and RNA nucleotides to DNA during replication and transcription?
  3. What about tRNA. Could tRNA correspond to pairs of harmonies with 20+20+444 codons? What about single 20+4=24 codon representation as kind of pre-tRNA?
  4. What is the origin of 12-note scale? Does genetic code force it? The affirmative answer to this question relies on the observation that 1-1 correspondence between codons and triplets of photons requires that the frequency assignable to the letter must depend on its position. This gives just 12 notes altogether. Simple symmetry arguments fix the correspondence between codons and 3-chords highly uniquely: only 4 alternatives are possible so that it would be possible to listen what DNA sequences sounds in given mood characterized by the harmony.
  5. What disharmony could mean? A possible answer comes from 6 Hamiltonian cycles having no symmetries. These disharmonies could express "negative" emotions.
See the new chapter Geometric theory of bio-harmony or the article New results in the model of bio-harmony .

Did RNA replicate in codon-wise manner during RNA era?

There was a very interesting popular article in Spacedaily with title "Scientists crack how primordial life on Earth might have replicated itself" (see this). The research paper "Ribozyme-catalysed RNA synthesis using triplet building blocks" is here.

It is possible to replicate unfolded RNA strands in Lab by using enzymes known as ribozymes, which are RNA counterparts of enzymes, which are amino-adic sequences. In the presence of folding the replication is however impossible. Since ribozymes are in general folded, they cannot catalyze their own replication in this manner. The researchers however discovered that the replication using RNA triplets - genetic codons - as basic unit can be carried out in laboratory even for the folded RNA strands and with rather low error rate. Also the ribozyme involved can thus replicate. For units longer than 3 nucleotides the replication becomes prone to errors.

These findings are highly interesting in TGD framework. In TGD chemical realization of genetic code is not fundamental. Rather, dark matter level would provide the fundamental realizations of analogs of DNA, RNA, tRNA, and amino-acids as dark proton sequences giving rise to dark nuclei at magnetic flux tubes. Also ordinary nuclei correspond in TGD Universe to sequences of protons and neutrons forming string like entities assignable to magnetic flux tubes.

The basic unit representing DNA, RNA and tRNA codon and amino-acid would consist of 3 entangled dark protons. The essential aspect is that by entanglement the dark codons do not decompose to products of letters. This is like words of some languages, which do not allow decomposition to letters. This representation is holistic. As we learn to read and write, we learn the more analytic western view about words as letter sequences. Could the same hold true in evolution so that RNA triplets would have come first as entities pairing with dark RNA codons from from dark proton triplets as a whole? Later DNA codons would have emerged and paired with dark DNA codons. Now the coupling would have have been letter by letter in DNA replication and transcription to mRNA.

It is intriguing that tRNA consists of RNA triplets combined from amino-acids and analogs of mRNA triplets! The translation of mRNA to amino-acids having no 3-letter decomposition of course forces the holistic view but one can ask whether something deeper is involved. This might be the case. I have been wondering whether during RNA era RNA replicated using a prebiotic form of translational machinery, which replicated mRNA rather than translated RNA to protein formed from amino-acids (AAs).

  1. During RNA era amino-acids associated with pre-tRNA molecules would served as catalysts for replication of RNA codons. The linguistic mode would have been "holistic" during RNA er in accordance with the findings of the above experiments. RNA codon would have been the basic unit.
  2. This would have led to a smaller number of RNAs since RNA and RNA like molecules in tRNA are not in 1-1 correspondence. A more realistic option could have been replication of subset of RNA molecules appearing in tRNA in this manner.
  3. Then a great evolutionary leap leading from RNA era to DNA era would have occurred. AA catalyzed replication of RNA would have transformed to a translation of RNA to proteins and the roles of RNA and AA in tRNA would have changed. [Perhaps the increase of heff in some relevant structure as quantum criticality was reached led to the revolution?]
  4. At this step also (subset of) DNA and its transcription to (a subset of) mRNA corresponding to tRNA had to emerge to produce mRNA in transcription. In the recent biology DNA replicates and is transcribed nucleotide by nucleotide rather than using codon as a unit so that DNA and RNA polymerases catalyzing replication and transcription should have emerged at this step. An alternative option would involve the "tDNA" as the analog of "tRNA" and the emergence of polymerases later: this does not however look attractive if one accepts the idea about the transition from holistic to analytic mood.

    The ability of DNA to unwind is essential for the emergence of the "analytic linguistic mode" as an analog of written language (DNA) decomposing codons to triplets of letters. This must have been a crucial step in evolution comparable to the emergence of written language based on letters. Also the counterpart of RNA polymerase and separate RNA nucleotides for transcription should have emerged if not already present.

    The minimal picture would be emergence of a subset of DNA codons corresponding to RNAs associated with pre-tRNA and the emergence of the analogs of DNA and RNA polymerases as the roles of amino-acid and RNA codon in tRNA were changed.

  5. How DNA could have emerged from RNA? The chemical change would have been essentially the replacement of ribose with de-oxiribose to get DNA from RNA and U→ T. Single O-H in ribose was replaced with H. O forms hydrogen bonds with water and this had to change the hydrogen bonding characteristics of RNA.

    If the change of heff =n×h0 (one has h= 6× h0 in the most plausible scenario, see this and this) was involved, could it have led to stabilization of DNA. Did cell membrane emerge and allow to achieve this? I have proposed (see this) that the emergence of cell membrane meant the emergence of new representation of dark genetic code based on dark nuclei with larger value of heff.

The communication between dark and ordinary variants of biomolecules involves resonance mechanism and would also involve genetic code represented as 3-chords, music of light, and it is interesting to see whether this model provides additional insights.
  1. The proposal is that 3-chords assignable to nucleotides as music of light with allowed 64 chords defining what I have called bio-harmony is essential for the resonance (see this, this, and this). The 3 frequencies must be identical in the resonance: this is like turning 3 knobs in radio. This 3-fold resonance would correspond to the analytic mode. The second mode could be holistic in the sense that it would involve only the sum only the sum of the 3 frequencies modulo octave equivalence assigning a melody to a sequence of 3-chords.
  2. The proposal is that amino-acids having not triplet decomposition are holistic and couple to the sum of 3 frequencies assignable to tRNA and mRNA in this manner. Also the RNAs in tRNA could couple to mRNA in this manner. One could perhaps say that tRNA, mRNA and amino-acids codons sing whereas DNA provides the accompaniment proceeding as 3-chords. The couplings of DNA nucleotides to RNA nucleotides would realy on the frequencies assignable to nucleotides.
  3. If the sum of any 3 frequencies associated with mRNA codons is not the same except when the codons code for the same amino-acids, the representation of 3-chords with the sum of the notes is faithful. The frequencies to DNA and RNA nucleotides cannot be however independent of codons since the codons differing only by a permutation of letters would correspond to the same frequency and therefore code for the same amino-acid. Hence the information about the entire codon would be needed also in transcription and translation and could be provided either by dark DNA strand associated with DNA strand or by the interactions between the nucleotides of the DNA codon.
  4. The DNA codon itself would know that if is associated with dark codon and the frequencies assignable to nucleotides are determined by the dark DNA codon. It would be enough that the frequency of the letter depends on its position in the codon so that there would be 3 frequencies for every letter: 12 frequencies altogether.

    What puts bells ringing is that this the number of notes in 12-note scale for which the model of bio-harmony (see this and this) based on the fusion of icosahedral (12 vertices and 20 triangular faces) and tetrahedral geometries by gluing icosahedron and tetrahedron along one face, provides a model as Hamiltonian cycle and produces genetic code as a by-product. Different Hamiltonian cycles define different harmonies identified as correlates for molecular moods.

    Does each DNA nucleotide respond to 3 different frequencies coding for its position in the codon and do the 4 nucleotides give rise to the 12 notes of 12-note scale? There are many choices for the triplets but a good guess is that the intervals between the notes of triplet are same and that fourth note added to the triplet would be the first one to realize octave equivalence. This gives uniquely CEG #, C#FA,DF#/B b, and DG#B as the triplets assignable to the nucleotides. The emergence of 12-note scale in this manner would be a new element in the model of bio-harmony.

    There are 4!=24 options for the correspondence between {A, T, C, G} as the first letter and {C,C#,D,D#}. One can reduce this number by a simple argument.

    1. Letters and their conjugates form pyrimidine-purine pairs T, A and C,G. The square of conjugation is identity transformation. The replacement of note with note defining at distance of half-octave satisfies this condition (half-octave - tritonus - was a cursed interval in ancient music and the sound of ambulance realizes it). Conjugation could correspond to a transformation of 3-chords defined as

      CEG# ↔ DF#Bb , C#FA↔ D#GB .

    2. One could have

      {T, C} ↔ {CEG #, C#FA} , {A,G}↔ {DF#Bb,D#GB}


      {T, C} ↔ {DF#Bb,D#GB} , {A,G}↔ {CEG#, C#FA} .

    3. One can permute T and C and A and G in these correspondences. This leaves 8 alternative options. Fixing the order of the image of (T, C) to say (C,C#) fixes the order of the image of (A, G) to (D,D#) by the half-octave conjugation. This leaves 4 choices. Given the bio-harmony and having chosen one of these 4 options one could therefore check what given DNA sequence sounds as a sequence of 3-chords (see this).

      Anyone willing to do this kind of experimentation obtains from me the program modules used the Garage band programs to produce a sequence of chords. A further interesting experiment would be check what kind of melodies come out if one assigns to a chord a note as the sum of frequencies of the chord reduced by octave equivalence to basic octave.

    That the position the frequency associated with the nucleotide depends on its position in the codon would also reflect the biochemistry of the codon and this kind of dependence would be natural. In particular, different frequencies associated with the first and third codon would reflect the parity breaking defining orientation for DNA.
See the chapter Emotions as sensory percepts about the state of magnetic body? or the article with the same title.

Dark valence electrons and color vision

By its large orbital radius dark valence electron (dark in TGD sense, heff=n× h) sees atomic nucleus and other electrons, which are ordinary, effectively as an object of charge Zeff=1. Dark valence electron has reduced mass which in excellent approximation equals to that of electron so that the spectrum of bound state energies and transition energies is scaled down by the factor (h/heff)2. This irrespective of what the atom is. The only condition is that there is single unpaired valence electron guaranteed if Z for the atom is odd. For even Z an odd number of valence electrons must be associated with valence bonds: this would be the case for OH radical for instance.

The dynamics of dark valence electrons is universal with universal transition energy spectrum. One obtains a fractal hierarchy of dynamics labelled by the value of (h/heff)2, where heff=n× h0, h0 the minimal value of Planck constant, not necessary equal to h so that one has h=n0× h0. The quantum critical dynamics characterizing living matter in TGD Universe is indeed universal.

The dark photon communications in living matter could utilize these universal energy spectra besides cyclotron energy spectrum and Larmor spectrum assignable to dark particles at flux tubes and the spectrum of generalized Josephson frequencies assignable to cell membrane. In particular, vision and even other sensory modalities could rely on the transitions induced by the absorption of dark valence electron. In TGD also other sensory percepts are communicated from sensory receptors to the sensory areas of cortex (see this) and also here same universal transition energies of dark valence electrons might be involved.

This hypothesis when combined with the earlier ideas about color qualia leads to a highly predictive and testable model for the perception of colors. In particular the condition h=n0× h0, n0>1, is necessary for the model to work. n0=4 and n0=6 look the most realistic options. For n0=4 the number of values of n=8,9,10 and correspond to the number 3 of color sensitive receptors whereas n0=6 the number of values n=12,13,14,15 suggests the existence of a fourth color receptor sensitive to red light.

The statistical aspects of color summation can be understood from TGD inspired theory of consciousness in terms of the hypothesis that self experiences the mental images of sub-self as kind of statistical averages. The identification of quark colors as fundamental color qualia, the entanglement of quarks and antiquarks to form states in one-one correspondence with charged gluons, and the twistor space of CP2 play key roles in the model of color summation.

Remark: There is experimental evidence for the notion of dark valence electron coming from the decades old anomaly related to rare Earth metals (see this). For TGD based model see this). This finding led to a proposal that valence bonds could also involve non-standard values of Planck constant (see this).

See the chapter Dark valence electrons and color vision or the article with the same title .

Does RNA code for pain?

Again an extremely interesting finding from neuroscience. The popular article "Scientists Sucked a Memory Out of a Snail and Stuck It in Another Snail" tells that the conditionings of snails produced by painful sensations can be transferred to other snails or even snail neurons in Petri dish by adding just the RNA of the conditioned snails to the dish! The article can be found at here .

Let us summarize the findings.

  1. RNA from snails is transferred to snails or to even populations of snail neurons in Petri dish!
  2. The effect involves epigenetic changes in DNA by methylation induced by RNA somehow. The reaction is to the serotonin informing for the stimulus. Avoidance behavior emerges as a response.
  3. How does RNA induce the epigenetic change? RNA should couple to a a specific part of DNA and induce the effect. A pairing of DNA with RNA in question occurring also in transcription suggests itself strongly.
  4. What in the RNA of the conditioned snail is different? RNA should somehow code for the conditioning induced by a painful sensory experience. RNA of sensory receptors should change somehow and communicate this change to DNA in brain by some mechanism. DNA-RNA pairing does not seem plausible. Could the pairing occur by some other means?
Before continuing it is good to summarize the TGD based models for music harmony providing also a model of genetic code (see this), for sensory perception (see this), for emotions (see this), and for impriting of emotions in water (see this).
  1. TGD based model for emotions and communication of emotions suggests that the communication takes place in terms of what I call music of light (also sound might be involved). Music expresses and creates emotions. Emotional state, mood, is coded by harmony or disharmony for music of light.

    12-note is fundamental for music and is represented as a closed self-non-intersecting path (Hamilton cycle) at icosahedron having 12 vertices. Icosahedron has 20 faces (triangles) and for given Hamilton cycle one can assign a 3-chord to each triangle. This gives 20-chord harmony (or disharmony). There is quite large number of 20-chord harmonies and those allowing Z6,Z4 and Z2 as symmetries is quite large. Besides this there 6 cycles with no symmetries and these could be identified as dis-harmonies.

  2. 20 is also the number of amino-acids so that it is not totally surprising that the model for bioharmony as a union of 3 different 20-chord harmonies plus 4-chord harmony assignable to tetrarhedron turns out to give a model of genetic code as 64 chord bioharmony. There are 64 basic 3-chords in one-one correspondence with DNA and RNA codons. tRNA corresponds to a union of 2 20-chord harmonies. Given amino-acid corresponds to the orbit of 3-chord under symmetries of the harmony so that number of 3-chords at the orbit is the number of DNAs coding for the amino-acid. These numbers come out correctly.
  3. There are two other representations of genetic code. The ordinary chemical representation and the representation in terms of dark proton sequences at magnetic flux tubes. The model for dark proton triplet predicts that its states divided to 64 analogs of DNA codons, 64 analogs of RNA codons, 40 analogs of tRNA codons, and 20 analogs of amino-acids. Genetic code comes out correctly also now by a natural pairing of dark proton triplets. One must couple these 3 representations of genetic code with themselves and with each other.
  4. There is indeed resonant coupling by 3-chords realized in terms of free frequencies of dark photons. The frequencies are rather low (E =heff× f, heff/h=n) but energies are same as for biophotons with energies in visible and UV range.

    Also dark variants of DNA, etc couple with each other via dark photon resonance. Dark DNA,etc couple with ordinary DNA, etc.. by energy resonance to form double strands. This means that dark photon transforms to ordinary photon in the coupling. Amino-acid couples to single frequency, which is the sum of codon frequencies coding for it.

    There is quite large number of 3-chord 3-harmonies defining DNA and RNA moods, and 3-chord 2-harmonies tRNA moods, and amino-acid 1-chord harmonies. There also 6 disharmonies with 20 chords each possible assignable to negative moods such as those generated by pain.

So: Is the communication chemical by DNA-RNA pairing or by some other means? TGD based model suggests "some other means".
  1. Pain in sensory receptor is certainly involved. In TGD based model differs from neuroscience view in that for sensory experiences sensory receptors are seats of the sensory qualia and brain only forms cognitive representations about them and also entangles with sensory receptors to share the pain. Somehow pain must affect RNA in sensory receptors? How?
  2. In this framework the stimulus in nocireceptors would induce a disharmony expressed in terms of the disharmony associated with the expression of RNA in terms of 3-chords. The dark variant of RNA in pain receptors would entangle with the dark DNA in certain neurons in brain of the snail. Nerve pulse patterns from the nociceptors would generate also magnetic flux tube connections parallel to the sensory pathway in question and make possible the communication by dark biophoton triplets to brain possible. The dark variant of DNA in brain would have resonant coupling with ordinary DNA and induce the epigenetic change by methylation as a response to the negative mood with the mediary of biophotons. After this the organism would have avoidance behaviour towards the stimulus inducing the pain.
  3. The presence of mere RNA and associated dark RNA dis-harmonious mood would do the same for any neuron by the resonance mechanism. This would allow to transfer emotions even to snail neurons in Petri dish, not only those in living snails.
The proposed mechanism provides insights to many other poorly understood problems.
  1. This mechanism also allows to understand how the transfer of emotions conditioning induces epigenetic chance also in the germ cell DNA: this is not easy to understand in the standard framework requiring chemical communication through the germ cell membrane.
  2. The models for learning (memories restricted to conditionings) based on formation of synaptic contacts on one hand and involving RNA are seen as exclusive in standard neuroscience. In TGD framework the formation of synaptic contacts might rely at the fundamental level on the same epigenetic mechanism. Neuromodulators might induce the emotional states in RNA in turn doing the epigenetic editing.

    In human brain the genomes differ in various neurons and epigenetic editing by the proposed mechanism might cause this. An interesting question is whether humans could edit their genomes intentionally. All conditionings are not useful and maybe it becomes someday possible to affect these conditionings at the level of dark DNA.

  3. Squid and octopus are known to be able to edit their mRNA (see this). Instead of DNA the mRNA produced in the transcription so that the translation produce different protein. The effect of emotional states of the dark variant of RNA associated with mRNA could be the mechanism involved.
  4. The strong emotional state of single individual induces very effectively the same emotional state in people around: consider only concert as an example. Could the "music of dark light" mediate the emotions from the dark RNA of individual - say artist - to people around. If so all art would be basically music of light!
To sum up: this finding provides rather concrete support for the vision that emotions are coded by the music of light at molecular level.

See the chapter Emotions as sensory percepts about the state of magnetic body? or the article with the same title.

The experiments of Masaru Emoto with emotional imprinting of water

Sini Kunnas sent a link to a video telling about experiments of Masaru Emoto (see this) with water, which is at criticality with respect to freezing and then frozen. Emoto reports is that words expressing emotions are transmitted to water: positive emotions tend to generate beautiful crystal structures and negative emotions ugly ones. Also music and even pictures are claimed to have similar effects. Emoto has also carried out similar experiments with rice in water. Rice subjected to words began to ferment and water subject to words expressing negative emotions began to rotten.

Remark: Fermentation is a metabolic process consuming sugar in absence of oxygen. Metabolism is a basic signature of life so that at least in this aspect the water+rice system would become alive. The words expressing positive emotions or even music would serve as a signal "waking up" the system.

One could define genuine skeptic as a person who challenges existing beliefs and pseudo-skeptic (PS in the sequel) as a person challenging - usually denying - everything challenging the mainstream beliefs. The reception of the claims of Emoto is a representative example about the extremely hostile reactions of PSs as aggressive watchdogs of materialistic science towards anything that challenges their belief system. The psychology behind this attitude is same as behind religious and political fanatism.

I must emphasize that I see myself as a thinker and regard myself as a skeptic in the old-fashioned sense of the word challenging the prevailing world view rather than phenomena challenging the prevailing world view. I do not want to be classified as believer or non-believer. The fact is that if TGD inspired theory of consciousness and quantum biology describes reality, a revolution in the world view is unavoidable. Therefore it is natural to consider the working hypothesis that the effects are real and see what the TGD based explanation for them could be.

The Wikipedia article about Masaru Emoto (see this) provides a good summary of the experiments of Emoto and provides a lot of links so that I will give here only a brief sketch. According to the article Emoto believed that water was a "blueprint for our reality" and that emotional "energies" and "vibrations" could change the physical structure of water. The water crystallization experiments of Emoto consisted of exposing water in glasses to different words, pictures or music, and then freezing and examining the aesthetic properties of the resulting crystals with microscopic photography. Emoto made the claim that water exposed to positive speech and thoughts would result in visually "pleasing" crystals being formed when that water was frozen, and that negative intention would yield "ugly" crystal formations.

In 2008, Emoto and collaborators published and article titled "Double-Blind Test of the Effects of Distant Intention on Water Crystal Formation" about his about experiments with water in the Journal of Scientific Exploration, a peer reviewed scientific journal of the Society for Scientific Explorations (see this). The work was performed by Masaru Emoto and Takashige Kizu of Emoto’s own IHM General Institute, along with Dean Radin and Nancy Lund of the Institute of Noetic Sciences, which is on Stephen Barrett's Quackwatch (see this) blacklist of questionable organizations. PSs are the modern jesuits and for jesuits the end justifies the means.

Emoto has also carried experiments with rice samples in water. There are 3 samples. First sample "hears" words with positive emotional meaning, second sample words with negative emotional meaning, and the third sample serving as a control sample. Emoto reports (see this) that the rice subjected to words with positive emotional content began to ferment whereas water subject to words expressing negative emotions began to rotten. The control sample also began to rotten but not so fast.

In the article The experiments of Masaru Emoto with emotional imprinting of water I will consider the working hypothesis that the effects are real, and develop an explanation based on TGD inspired quantum biology. The basic ingredients of the model are following: magnetic body (MB) carrying dark matter as heff/h=n phases of ordinary matter; communications between MB and biological body (BB) using dark photons able to transform to ordinary photons identifiable as bio-photons; the special properties of water explained in TGD framework by assuming dark component of water implying that criticality for freezing involves also quantum criticality, and the realization of genetic code and counterparts of the basic bio-molecules as dark proton sequences and as 3-chords consisting of light or sound providing a universal language allowing universal manner to express emotions in terms of bio-harmony realized as music of light or sound. The entanglement of water sample and the subject person (with MBs included) realized as flux tube connections would give rise to a larger conscious entity expressing emotions via language realized in terms of basic biomolecules in a universal manner by utilizing genetic code realized in terms of both dark proton sequences and music of light of light and sound.

See the chapter Emotions as sensory percepts about the state of magnetic body? or the article The experiments of Masaru Emoto with emotional imprinting of water.

How molecules in cells "find" one another and organize into structures?

The title of the popular article How molecules in cells 'find' one another and organize into structures expresses an old problem of biology. Now the group led by Amy S. Gladfelter has made experimental progress in this problem. The work has been published in Science (see this).

It is reported that RNA molecules recognize each other to condense into the same droplet due to the specific 3D shapes that the molecules assume. Molecules with complementary base pairing can find each other and only similar RNAs condense on same droplet. This brings in mind DNA replication, transcription and translation. Furthermore, the same proteins that form liquid droplets in healthy cells, solidify in diseases like neurodegenerative disorders.

Some kind of phase transition is involved with the process but what brings the molecules together remains still a mystery. The TGD based solution of this mystery is one of the first applications of the notion of many-sheeted space-time in biology, and relies on the notion of magnetic flux tubes connecting molecules to form networks.

Consider first TGD based model about condensed and living matter. As a matter fact, the core of this model applies in all scales. What is new is there are not only particles but also bonds connecting them. In TGD they are flux tubes which can carry dark particles with nonstandard value heff/h=n of Planck constant. In ER-EPR approach in fashion they would be wormholes connecting distance space-time regions. In this case the problem is instability: wormholes pinch and split. In TGD monopole magnetic flux takes care of the stability topologically. The flux tube networks occur in all scales but especially important are biological length scales.

  1. In chemistry the flux tubes are associated with valence bonds and hydrogen bonds (see this). In biology genetic code would be realized as dark nuclei formed by sequences of dark protons at magnetic flux tubes. Also RNA, amino-acids, and even tRNA could have dark counterparts of this kind (see this). Dark variants of biomolecules would serve as templates for their ordinary variants also at the level of dynamics. Biochemistry would be shadow dynamics dictated to high degree by the dark matter at flux tubes.
  2. Dark valence bonds can have quite long length and the outcome is entangled tensor net (see this). These neuronal nets serve as correlates for cognitive mental images in brain (see this) emotional mental images in body (see this). Dark photons propagating along flux tubes (more precisely topological light rays parallel to them) would be the fundamental communication mechanism (see this). Transmitters and nerve pulses would only change the connectedness properties of these nets.
The topological dynamics of flux tubes has two basic mechanisms (I have discussed this dynamics from the point of view of AI here).
  1. Reconnection of flux tubes serves is the first basic mechanism in the dynamics of flux tube networks and would give among other things rise to neural nets. The connection between neurons would correspond basically to flux tube pair which can split by reconnection. Also two flux tube pairs can reconnect forming Y shaped structures. Flux tube pairs could be quite generally associated with long dark hydrogen bonds scaled up by heff/h=n from their ordinary lengths. Flux tube pairs would carry besides dark protons also supra phases formed by the lone electron pairs associated quite generally with hydrogen bonding atoms. Also dark ions could appear at flux tubes.

    Biomolecules would have flux loops continually scanning the environment and reconnecting if they meet another flux loop. This however requires that magnetic field strengths are same at the two loops so that a resonance is achieved at level of dark photon communications. This makes possible recognition by cyclotron frequency spectrum serving as signature of the magnetic body of the molecule.

    Water memory (see this) would rely on this recognition mechanism based on cyclotron frequencies and also immune system would use it at basic level (here one cannot avoid saying something about homeopathy although I know that this spoils the day of the skeptic: the same mechanism would be involved also with it). For instance, dark DNA strand accompanying ordinary DNA and dark RNA molecules find each other by this mechanism (see this). Same applies to other reactions such as replication and translation .

  2. Shortening of the flux tubes heff/h reducing phase transition is second basic mechanism explaining how biomolecules can find each other in dense molecular soup. It is essential that the magnetic fields at flux tubes are nearly the same for the reconnection to form. A more refined model for the shortening involves two steps: reconnection of flux tubes leading to a formation of flux tube pair between molecules and shortening by heff/h reducing phase transition.
Also ordinary condensed matter phase transitions involve change of the topology of flux tube networks and the model for it allows to put the findings described in the article in TGD perspective.
  1. I just wrote an article (see this) about a solution of two old problems of hydrothermodynamics: the behavior of liquid-gas system in the critical region not consistent with the predictions of statistical mechanics (known already at times of Maxwell!) and the behavior of water above freezing point and in freezing. Dark flux tubes carrying dark protons and possibly electronic Cooper pairs made from so called lone electron pairs characterizing atoms forming hydrogen bonds.
  2. The phase transition from gas to liquid occurs when the number of flux tubes per molecule is high enough. At criticality both phases are in mechanical equilibrium - same pressure. Most interestingly, in solidification the large heff flux tubes transform to ordinary ones and liberate energy: this explains anomalously high latent heats of water and ammonia. The loss of large heff flux tubes however reduces "IQ" of the system.
The phase transitions changing the connectedness of the flux tube networks are fundamental in TGD inspired quantum biology.
  1. Sol-gel transition would correspond to this kind of biological phase transitions. Protein folding (see this) - kind of freezing of protein making it biologically inactive - and unfolding would be second basic example of this transition. The freezing would involve formation of flux tube bonds between points of linear protein and assignable to hydrogen bonds. External perturbations induce melting of the proteins and they become biologically active as the value of heff/h=n characterizing their maximal possible entanglement negentropy content (molecular IQ) increases. External perturbation feeds in energy acting as metabolic energy. I have called this period molecular summer.
  2. Solidification of proteins reducing is reported to be associated with diseases such neurodegenerative disorders. In TGD picture this would reduce the molecular IQ since the ability of system to generate negentropy would be reduced when heff for the flux tubes decreases to its ordinary value. What brings molecules together is not understood and TGD provides the explanation as heff reducing phase transition for flux tube pairs.
See the chapter Artificial Intelligence, Natural Intelligence, and TGD or the article with the same title.

Is time reversal involved with Pollack effect?

In Pollack effect negatively charges Exclusion Zeones (EZs) are formed. EZs have the very strange property that the impurities are spontaneously removed from them. This seems to be in conflict with the second law of thermodynamics according to which both temperature and concentration gradients should tend to disappear. Could one understand this as being due to a reversal of the arrow of time?

Indeed, TGD inspired theory of consciousness relying on zero energy ontology (ZEO) predicts the possibility of time reversed selves (see this). When conscious entity - self - dies, it reincarnates as a self with opposite arrow of geometric time.

  1. In ZEO zero energy states replace ordinary quantum states assigned with time=constant snapshots of time evolution in space-time. Zero energy states are pairs of ordinary quantum states at opposite light-like boundaries of causal diamond (CD) identifiable as counterparts of initial and finals states of a physical event. Conservation quantum numbers translates to a mathematical statement that the quantum numbers associated with the members of pairs are opposite. One can also say that zero energy state is analogous to a deterministic computer program or a behavioral mode. The act of free will replaces this program/behavior with a new one so that one avoids the paradox between the non-determinism of free will and determinism of physics.
  2. Causal diamond (CD) defines the imbedding space correlate of self. One can assign to the opposite light-like boundaries the attributes active and passive. During the sequence of analogs of "small" state function reductions analogous to weak quantum measurements (resembling classical measurements) the passive boundary remains unaffected as also the members of state pairs defining zero energy states associated with it. Active boundary recedes farther away from the passive boundary and the members of state pairs at it change. The size of CD thus increases and gives rise flow of geometric time as an increase of the temporal distance between the tips of CD.
  3. Eventually the first state function reduction to the opposite boundary of CD must occur, and active and passive boundary change their roles. Self dies and re-incarnates as a self with opposite arrow of geometric time: the formerly passive boundary of CD becomes now active and moves in opposite time direction reduction by reduction. In the next re-incarnation self continues almost from the moment of geometric time at which it died. It might be that we die repeatedly without noticing it at all!
  4. The many-sheeted space-time approximated with slightly curved regions of Minkowski space would certainly tend to mask the time reversals in given length scale. In elementary particle length scales the state function reductions would indeed change the arrow of time but this would occur so often that there would be no arrow of time in statistical sense: one would speak of microscopic reversibility. In time scales considerably longer than those of human consciousness the observed arrow of time would correspond to that associated with selves with very large CDs and with lifetime much longer than ours. The change of the arrow of time could be detectable in time scales relevant to living matter and human consciousness and just these scales are the scales where the anomalies occur!
Could the ghostly space-time regions - time reversed selves - have some physical signatures making possible to prove their existence empirically?
  1. Second law would still hold true but in opposite direction of geometric time for the space-time sheets with non-standard arrow of time. The effects implied by second law would be present as their reversals. The observer with standard direction of geometric time would see temperature and density gradients to develop spontaneously. Also parameters describing dissipation rates such as Ohmic resistance and viscosity could have in some situations negative values.

    This indeed seems to take place in living matter. For instance, the building bricks of molecules spontaneously arrange to molecules: DNA replication, transcription and translation of RNA to proteins are basic examples about this. The development of concentration gradients is also clear in the strange ability of EZs to get rid of impurities. Also the charge separation creating EZs could be seen as disappearence of charged separatio in reversed direction of time. Healing of living organism could be a basic example of the process in which the arrow of time changes temporarily at some level of hierarchy of space-time sheets.

  2. The generation of temperature gradients would be a clear signature for the reversal of the arrow of time. Water is the basic stuff of life, and the thermodynamics of water involves numerous anomalies summarized at Martin Chaplin's homepage "Water structure and science". TGD based explanation could be naturally in terms of dark variants of protons at magnetic flux tubes and possible change of the arrow of geometric time.
  3. There is a lot of anecdotal evidence for the effects challenging our beliefs about standard arrow of time. A spontaneous generation of temperature differences is basic example. There is a nice popular document about this boundary region of science by Phie Ambo, which even skeptic might enjoy as art experience.

    It was a great surprise for me that one of the key personalities in the document is Holger B Nielsen, one of the pioneers of string models. I have had the honor to have intense discussions with him in past: he is one of the very few colleagues who has shown keen interest on the basic ideas of TGD. The document discusses strange phenomena associated with the physics of water possibly having interpretation in terms of time reversal and formation of EZs. From the document one also learns that in Denmark physics professionals are beginning to take these anomalies seriously.

    Unfortunately, the people who claim having discovered this kind of effects - often not science professionals - are labelled as crackpots. The laws of science also tell what we are allowed to observe (and think), at least if we want to be called scientists!

  4. The ghost stories might also reflect something real - this real need of course not be ghost but something deep about consciousness. Could it be that it is sometimes possible to consciously experience the presence of a space-time region - self - with an opposite arrow of geometric time? Ghost stories typically involve a claim about the reduction of temperature of environment in presence of ghost: could this be something real and a signature for the reversal of time at some level of dark matter hierarchy affecting also dark matter? As a matter of fact, in TGD Universe our conscious experience could involve routinely sub-selves (mental images) with non-standard arrow of time (see this): motor actions could be identified as sensory mental images with opposite arrow of time.
For background see the chapter How to test TGD Based Vision about Living Matter and Remote Mental Interactions or the article Pollack's Findings about Fourth phase of Water: TGD View.

Dance of the honeybee and New Physics

For more than two decades ago mathematician Barbara Shipman made rather surprising finding while working with her thesis. The 2-D projections of certain curves in flag manifold F=SU(3)/U(1)× U(1) defined by the so called momentum map look like the waggle part of the dance of the honey bee. Shipman found that one could reproduce in this framework both waggle dance and circle dance (special case of waggle dance) and the transition between these occurring as the distance of the food source from the nest reduces below some critical distance. Shipman introduced a parameter, which she called α, and found that the variation of α allows to integrate various forms of the honeybee dance to a bigger picture. Since SU(3) is the gauge group of color interactions, this unexpected finding led Shipman to as whether there might be a profound connection between quantum physics at quark level and macroscopic physics at the level of honeybee dance.

The average colleague of course regards this kind of proposal as crackpottery: the argument is that there simply cannot be any interaction between degrees of freedom in so vastly different length scales. Personally I however found this finding fascinating and wrote about the interpretation of this finding in the framework of TGD and TGD inspired consciousness. During more than two decades a lot of progress has taken place in TGD, in particular I have learned that the flag manifold F has interpretation as twistor space of CP2 and plays a fundamental role in twistor lift of TGD. Hence it is interesting to look what this could allow to say about honeybee dance.

It turned out that one could understand the waggle parts of the honeybee dance at space-time level in terms of the intersection of the space-time surface with the image of the Cartan sub-algebra of SU(3) represented in CP2 using exponential map. This allows to code the positional data about the food source. The frequencies assignable to the wing vibrations and waggling turn could have interpretation as cyclotron frequencies as expected if the magnetic body of the bee controls the waggle dance utilizing resonance mechanism. They could also correspond to the momenta (frequencies) defining constants of motion for geodesic in U(1)× U(1) defining one particular point of flag manifold F. Also a connection with the Chladni effect emerges: the waggle motion is along time-like curve at which Kähler force vanishes. Also the transition from waggle dance do circle dance.

See the new chapter Dance of the honeybee and New Physics or the article with the same title.

How brain selectively remembers new places?

There was a very interesting link in Minding Brain related to the storage of new memories. The title of the popular article is "How brain selectively remembers new places?". The following represents TGD based view about what might happen.

  1. In TGD framework brain/body corresponds to 4-D geometric object classically - a space-time surface with complex topology (zero energy ontology, ZEO). Brain and biological body are accompanied by magnetic body (MB) defining a topological time evolution of flux tube network having neurons (and also body cells) as its nodes and it is MB, which seems to be of fundamental significance (see this and this). Memories are located in 4-D brain (body) for the first time to the time-place, where they were formed, later successful memory recalls form new copies of them.
  2. To remember is to see in time direction to geometric past. The signal sent from hippocampus backwards in geometric time scatters back in standard time direction: this is nothing but seeing in 4 dimensions. 4-D memory storage means that there is practically no limitations on memory storage since new storage capacity is created all the geometric time! Making careful distinction between experienced and geometric times allows to both avoid paradoxes and solve the paradoxes of existing theory. Remark: Also the possibility of quantum entanglement also increases exponentially the memory storage capacity (and destroys the dreams of AI afficionados about copying human consciousness as bits telling whether neuron fires or not to a computer file!).
  3. Brain is able to detect whether the sensory percept - say completely new place - is indeed new. Brain acts as novelty detector. This requires scanning of 4-D brain to see whether there are sensory percepts in geometric past, which share common features with the recent sensory percept. This requires high level conceptualization so that perceptive field is decomposed to objects with some attributes. If common objects are not found, the percept is regarded as something new. In this case a new symbolic memory representation about perceptive field is formed.
  4. This strongly suggests that the signal sent from hippocampus scatters back from brain of past and is then compared with the recent sensory percept. If they the signals are very similar - this might give rise to some kind of resonance - the experience is "I have seen this before". The information provided by the already existing memory is utilized. If not then sensory percept is regarded as new and memory representation is formed.
Where is this new memory representation constructed?
  1. The article suggests that locus coeruleus (LC) and area CA3 of hippocampus are involved. It was found that the modulation of CA3 by LC is was involved in the formation of new memory: if the modulation was prevented, no new memory was formed and the the mice behaved next day as if the place were still new.
  2. In ZEO the new memory would correspond to a collection of activated neurons in LC and CA3 accompanied by connected flux tube structure represented the new mental image as a quantum entangled structure - tensor network. This kind of mental images would have formed for some period of time in the brain of the mice and given rise to a 4-D representation of new place to be read later by sending signals backwards in geometric time.
See the chapter Emotions as sensory percepts about the state of magnetic body? or the article with the same title.

Getting memories by eating those who already have them

While writing article about emotions as sensory percepts about the state of magnetic body I learned about extremely interesting findings. I have already earlier written about some of the finding that both pieces of split planaria have the memories (identified as learned skills or conditionings) of the original planaria (see this). The news at this time was that planaria get the memories of planaria that they have eaten!

To begin with, one must carefully distinguish between genuine memories and memories as behavioral patterns) (conditionings, skills).

  1. Cognitive memories as behavioral patterns are assumed to be due to the strengthening of synaptic contacts (long term potentiation (LPT) giving rise to nerve circuits, which are active or easily activated. In TGD framework activation means formation of flux tube network giving rise to quantum entangled state with neurons at the nodes: neural activity generates transmitters serving as bridges between flux tubes associated with axons and create flux tube network carrying a conscious mental image. A quantum coherent entangled tensor network is formed and also classical communications using dark photons are possible in this state. These neurons are firing synchronously. Nerve pulses would not be signals between neurons but would induce communications to magnetic body in scales even larger than body.
  2. Genuine memories - say episodal memories - would in TGD (zero energy ontology, ZEO) correspond to neural activities in geometric past: kind of seeing in time direction. These are typically verbal memories but also sensory memories are possible and can be induced by electric stimulation of brain.
Consider now the experiments discussed in the popular article Somewhere in the brain is a storage device for memories). They all relate to the identification of memory as a behavioral pattern induced by conditioning and are therefore emotional memories.
  1. In one experiment sea slugs learned to avoid painful stimulus. This led to a generation of synaptic contacts between neutrons involving increased synaptic strength - long term potentiation (LPT). Then some drug was used to destroy the LPT. The problem was that the lost contacts were not those formed when the memory was formed!
  2. In second experiment mice were used. A conditioned fear (LPT) was induced in mice and again the generation of synaptic contacts was observed. Then the contacts - long term potentiation - was destroyed completely. Memories as conditioned fear however remained!
It was an amusing accident to learn about this just when I was building a model for emotions as sensory percepts about the state of magnetic body (MB) fundamental in TGD inspired quantum biology.
  1. MB consists of a part formed from highly dynamical flux tube tensor networks having cells and also other structures with other size scales (fractality) as nodes. MB has also a part outside body involving rather large values of heff= n× h and having to higher cognitive IQ. Corresponding emotions would be higher level emotions (like experience of beauty) whereas bodily emotions are primitive and involve positive/negative coloring inducing a desire to preserve/change the situation in turn inducing an emotional counterpart of motor activity as excretion of hormones from emotional brain with hypothalamus in the role of highest motor areas and lower glands (both in brain and in body) in the role of lower motor areas.
  2. In the recent case the memories are definitely emotional memories and in TGD framework they would be naturally at the level of body and generated as mental images associated with large numbers of ordinary cells appearing as nodes of quantum entangled flux tube networks giving rise to tensor networks (see this). Hormones would be the tool to modify and generate these networks.
  3. Emotional memories would be represented by the conditioning and analog of LPT at the level of body rather than at the level of brain! Hormones like also other information molecules would act as relays connecting existing pieces of network to larger ones! The neural activity would be involved only with the generation of memories and induce hypothalamus to generate the fear network using the hormones controlling hormonal activities of lower level glands.
  4. The model could also explain the finding that in the splitting of flatworm the both new flatworms inherit the memories and that even non-trained flatworms eating trained flatworms get their memories (defined as behavioral patterns involving emotional conditioning).
See the chapter Emotions as sensory percepts about the state of magnetic body? or the article with the same title.

Emotions as sensory percepts about the state of magnetic body?

What emotions are? How emotions are created? How are they represented: in brains, at body, or perhaps somewhere else? One can consider these questions from the point of view of neuroscience, endocrinology, and quantum physics. Emotions can be divided to lower level emotions accompanied by intention/need/desire (hunger is accompanied by the need to eat) and thus distinguishing them from sensory qualia whereas higher level emotions like catharsis and the experience of beauty not accompanied by any desire. What does does this division correspond to?

  1. TGD inspired answer to the questions is that emotions are sensory percepts about the state of magnetic body (MB). Sensory-motor loop generalizes: various glands excreting hormones to blood stream and binding to receptors give rise to the analog of motor output.
  2. Consider first neuronal level. Neural transmitters binding to receptors serve as bridges allowing to build connected networks of neurons from existing building bricks. They are accompanied by flux tube networks giving rise to tensor networks as quantum coherent entangled structures (tensor nets) serving as correlates of mental images and allowing classical signalling with light velocity using dark photons. These tensor networks represent our mental images only if they correspond to our sub-selves (see this).

    In a similar manner hormones give rise to networks of ordinary cells implying in particular that emotional memories are realized in (biological) body (BB). Nervous system gives information about the state of these networks to brain and hypothalamus serves as the analog of motor cortex sending hormones controlling the excretion of hormones at lower level glands.

  3. The hierarchy of Planck constants defines a hierarchy of dark matters and heff=n× defines a kind of IQ. The levels of MB corresponding to large/small values of n would correspond to higher/lower emotions.
MB decomposes to two basic parts: the part in the scale of BB and formed by networks having cells and larger structures as nodes (forming a fractal hierarchy) and the part in the scales larger than BB.
  1. In the scales larger than that of BB (long scales) the change the topology is not easy and the dynamics involves oscillations of MB - analogs of Alfwen waves - and analogs of ordinary motor actions changing the shape of flux tubes but leaving its topology unaffected (these actions might represent or serve as templates for ordinary motor actions in body scale (see this).
  2. In the scales larger than that of BB (long scales) the change the topology is not easy and the dynamics involves oscillations of MB - analogs of Alfwen waves - and analogs of ordinary motor actions changing the shape of flux tubes but leaving its topology unaffected (these action might represent or serve as templates for ordinary motor actions in body scale).

    Alfwen waves with cyclotron frequencies and generalized Josephson frequencies assignable to cell membrane as Josephson junction would be involved see this). The size scale of particular onion-like layer of MB corresponds to the wavelength scale for cyclotron frequencies and is proportional to heff/h=n for dark photons. For instance, alpha band in EEG corresponds to the scale of Earth but the energy scale of dark photons is that of bio-photons.

    The TGD inspired model of music harmony (see this) gives as a side product a model of genetic code predicting correctly the numbers of codons coding for aminoacids for vertebrate code. The model allows to see sensory percepts about the dynamics in large scales as analog of music experience. The notes of 3-chords of the harmony correspond to light as dark photons and frequencies defining the notes of the chord: cyclotron radiation and generalized Josephson radiation from cell membrane would represent examples of dark light. Music expresses and creates emotions and music harmonies would correspond to various emotional states/moods realized at the level of DNA and its dark counterpart (dark nuclei represented as dark proton sequences). MB would be like a music instrument with flux tubes serving as strings. It is difficult to assign any specific desire to large scale sensory percepts about MB and the interpretation as higher emotions - or rather feelings - makes sense.

See the chapter Emotions as sensory percepts about the state of magnetic body? or the article with the same title.

What could idiot savants teach to us about Natural Intelligence?

Recently a humanoid robot known as Sophia has gained a lot of attention in net (see the article by Ben Goertzel, Eddie Monroe, Julia Moss, David Hanson and Gino Yu titled with title " Loving AI: Humanoid Robots as Agents of Human Consciousness Expansion (summary of early research progress)" .

This led to ask the question about the distinctions of Natural and Artificial Intelligence and about how to model Natural Intelligence. One might think that idiot savants could help answering this kind of question but so it turned out to be!

Mathematical genii and idiot savants seem to have something in common

It is hard to understand the miraculous arithmetical abilities of both some mathematical genii and idiot savants lacking completely conceptual thinking and conscious information processing based on algorithms. I have discussed the number theoretical feats here.

Not all individual capable of memory and arithmetic feats are idiot savants. These mathematical feats are not those of idiot savant and involve high level mathematical conceptualization. How Indian self-taught number-theoretical genius Ramajunan discovered his formulas remains still a mystery suggesting totally different kind of information processing. Ramanujan himself told that he got his formulas from his personal God.

Ramajunan's feats lose some of their mystery if higher level selves are involved. I have considered a possible explanation based on ZEO, which allows to consider the possibility that quantum computation type processing could be carried out in both time directions alternately. The mental image representing the computation would experience several deaths following by re-incarnations with opposite direction of clock time (the time direction in which the size of CD increases). The process requiring very long time in the usual positive energy ontology would take only short time when measured as the total shift for the tip of either boundary of CD - the duration of computations at opposite boundary would much longer!

Sacks tells about idiot savant twins with intelligence quotient of 60 having amazing numerical abilities despite that they could not understand even the simplest mathematical concepts. For instance, twins "saw" that the number of matches scattered along floor was 111 and also "saw" the decomposition of integer to factors and primality. A mechanism explaining this based on the formation of wholes by quantum entanglement is proposed here. The model does not however involve any details.

Flux tube networks as basic structures

One can build a more detailed model for what the twins did by assuming that information processing is based on 2-dimensional discrete structures formed by neurons (one can also consider 3-D structures consisting of 2-D layers and the cortex indeed has this kind of cylindrical structures consisting of 6 layers). For simplicity one can assume large enough plane region forming a square lattice and defined by neuron layer in brain. The information processing should involve minimal amount of linguistic features.

  1. A natural geometric representation of number N is as a set of active points (neurons) of a 2-D lattice. Neuron is active it is connected by a flux tube to at least one other neuron. The connection is formed/strengthened by nerve pulse activity creating small neuro-transmitter induced bridges between neurons. Quite generally, information molecules would serve the same purpose (see this and this).

    Active neurons would form a collection of connected sets of the plane region in question. Any set of this kind with given number N of active neurons would give an equivalent representation of number N. At quantum level the N neurons could form union of K connected sub-networks consisting Nk neurons with ∑ Nk=N.

  2. There is a large number of representations distinguished by the detailed topology of the network and a particular union of sub-networks would carry much more information than the mere numbers Nk and N code. Even telling, which neurons are active (Boolean information) is only part of the story.

    The subsets of Nk points would have large number of representations since the shape of these objects could vary. A natural interpretation would be in terms of objects of a picture. This kind of representation would naturally result in terms of virtual sensory input from brain to retina and possibly also other sensory organs and lead to a decomposition of the perceptive field to objects.

    The representation would thus contain both geometric information - interpretation as image - and number theoretic information provided by the decomposition. The K subsets would correspond to one particular element of a partition algebra generalizing Boolean algebra for which one has partition to set and its complement (see this).

  3. The number N provides the minimum amount of information about the situation and can be regarded as a representation of number. One can imagine two extremes for the representations of N.
    1. The first extreme corresponds to K linear structures. This would correspond to linear linguistic representation mode characteristic for information processing used in classical computers. One could consider interpretation as K words of language providing names for say objects of an image. The extreme is just one linear structure representing single word. Cognition could use this kind of representations.
    2. Second extreme corresponds to single square lattice like structure with each neuron connected to the say 4 nearest neighbors. This lattice has one incomplete layer: string with some neurons missing. This kind of representation would be optimal for representation of images representing single object.

      For N active neurons one can consider a representation as a pile of linear strings containing pk neurons, where p is prime. If N is divisible by pk: N= Mpk one obtains a M× pk lattice. If not one can have M× pk lattice connected to a subset of neurons along string with pk neurons. One would have representation of the notion of divisibility by given power of prime as a rectangle! If N is prime this representation does not exist!

Flux tube dynamics

The classical topological dynamics for the flux tube system induced by nerve pulse activity building temporary bridges between neurons would allow phase transitions changing the number of sub-networks, the numbers of neurons in them, and the topology of individual networks. This topological dynamics would generalize Boolean dynamics of computer programs.

  1. Flux tube networks as sets of all active neurons can be also identified as elements of Boolean algebra defined by the subsets of discretize planar or even 3-D regions (layer of neurons). This would allow to project flux tube networks and their dynamics to Boolean algebra and their dynamics. In this projection the topology of the flux tube network does not matter much: it is enough that each neurons is connected to some neuron (bit 1). One might therefore think of (a highly non-unique) lifting of computer programs to nerve pulse patterns activating corresponding subsets of neurons. If the dynamics of flux tube network determined by space-time dynamics is consistent with the Boolean projection, topological flux tube dynamics induced by space-time dynamics would define computer program.
  2. At the next step one could take into account the number of connected sub-networks: this suggests a generalization of Boolean algebra to partition algebras so that one does not consider only subset and its complement but decomposition into n subsets which one can think as having different colors (see this). This leads to a generalization of Boolean (2-adic) logic to p-adic logic, and a possible generalization of computer programs as Boolean dynamical evolutions.
  3. At the third step also the detailed topology of each connected sub-network is taken into account and brings in further structure. Even higher-dimensional structures could be represented as discretized versions by allowing representation of higher-dimensional simplexes as connected sub-networks. Here many-sheeted space-time suggests a possible manner to add artificial dimensions.
This dynamics would also allow to realize basic arithmetics. In the case of summation the initial state of the network would be a collection of K disjoint networks with Nk elements and in final state single connected set with N=∑ Nk elements. The simplest representation is as a pile of K strings with Nk elements. Product M× N could be reduced to a sum of M sets with N element: this could be represented as a pile of M linear strings.

Number theoretical feats of twins and flux tube dynamics

Flux tube dynamics suggests a mechanism for how the twins managed to see the number of the matches scattered on the floor and also how they managed to see the decomposition of number into primes or prime powers. Sacks indeed tells that the eyes of the twins were rolling wildly during their feats. What is required is that the visual perception of the matches on the floor was subject to dynamics allowing to deform the topology of the associated network. Suppose that some preferred network topology or network topologies allowed to recognize the number of matches and tell it using language (therefore also linear language is involved). The natural assumption is that the favored network topology is connected.

The two extremes in which the network is connected are favored modes for this representation.

  1. Option I corresponds to any linear string giving a linguistic representation as the number neurons (which would be activated by seeing the matches scattered on the floor). A large number of equivalent representations is possible. This representation might be optimal for associating to N its name. The verbal expression of the name could be completely automatic association without any conceptual content. The different representations carry also geometric information about the shape of the string: melody in music could be this kind of curve whereas words of speech would be represented by straight lines.
  2. Option II corresponds to a maximally connected lattice like structure formed as pile of strings with pk neurons for a given prime: N= M1× pk+M2, 0≤ Mi < pk. The highest string in the pile misses some neurons. This representation would be maximally connected. It contains more information than that about the value of N.
Option II provides also number theoretical information allowing a model for the feats of the twins.
  1. As far the checking the primeness of N is considered, one can assume k=1. For the primes pi dividing N one would find a representation of N as a rectangle. If N is prime, one finds no rectangles of this kind (or finds only the degenerate 1× p rectangle). This serves a geometric signature of primeness. Twins would have tried to find all piles of strings with p neurons, p=2,3,5,... A slower procedure checkes for divisibility by n=2,3,4,....
  2. The decomposition into prime factors would proceed in the similar manner by starting from p=2 and proceeding to larger primes p=3,5,7,.... When a prime factor pi is found only single vertical string from the pile is been taken and the process is repeated for this string but considering only primes p>pi. The process would have been completely visual and would not involve any verbal thinking.
For the storage of memories the 2-D (or possibly 3-D representation) is non-economical and the use of 1-D representation replacing images with their names is much more economic. For information processing such as decomposition into primes, the 2-D or even 3-D representation are much more powerful.

See the chapter Artificial Intelligence, Natural Intelligence, and TGD or the article with the same title.

Artificial Intelligence, Natural Intelligence, and TGD

Recently a humanoid robot known as Sophia has gained a lot of attention in net (see the article by Ben Goertzel, Eddie Monroe, Julia Moss, David Hanson and Gino Yu titled with title " Loving AI: Humanoid Robots as Agents of Human Consciousness Expansion (summary of early research progress)" .

Sophia uses AI, visual data processing, and facial recognition. Sophia imitates human gestures and facial expressions and is able to answer questions and make simple conversations on predefined topics. The AI program used analyzes conversations, extracts data, and uses it to improve responses in the future. To a skeptic Sophia looks like a highly advanced version of ELIZA.

Personally I am rather skeptic view about strong AI relying on a mechanistic view about intelligence. This leads to transhumanism and notions such as mind uploading. It is however good to air out one's thinking sometimes.

Computers should have a description also in the quantal Universe of TGD and this forces to look more precisely about the idealizations of AI. This process led to a change of my attitudes. The fusion of human consciousness and presumably rather primitive computer consciousness but correlating with the program running in it might be possible in TGD Universe, and TGD inspired quantum biology and the recent ideas about prebiotic systems provide rather concrete ideas in attempts to realize this fusion.

TGD also strongly suggests that there is also what might be called Natural Intelligence relying on 2-D cognitive representations defined by networks consisting of nodes (neurons) and flux tubes (axons with nerve pulse patters) connecting them rather than linear 1-D representation used by AI. The topological dynamics of these networks has Boolean dynamics of computer programs as a projection but is much more general and could allow to represent objects of perceptive field and number theoretic cognition.

See the chapter Artificial Intelligence, Natural Intelligence, and TGD or the article with the same title.

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