Knotty inflation and dimensionality of space-time

I had a strange dejavu experience while reading popular article "Scientists Propose a Radical Theory About Why the World Has Three Dimensions" inspired by the article Knotty inflation and dimensionality of spacetime" by Berera et al.

I had the experience of reading TGD vision about early phase of Universe! The strong feeling was that the scientists had forgotten to mention that the idea came from my homepage and perhaps from the articles published in Prespacetime Journal edited by Huping Hu. This has happened so many times during years.

Of course, I might be oversensitivized by this kind of sad experiences during years. So many key ideas of TGD have been "independently discovered" in watered down and hopelessly poorly understood form during years. It is very difficult to move a plant from TGD Universe to say string model Universe without killing it. I of course hope that I am wrong. Perhaps the authors indeed invented it themselves. But it is so difficult to believe that professional scientists could be blind enough to avoid learning about the existence of TGD during IT era. If so, they do not deserve to be called scientists.

What is the message of the authors.

1. The authors do not talk about flux tubes in TGD sense (as 3-D surfaces, here string theorist could talk about 3-D branes) but in the sense of gauge theories in D-dimensional space-time. The proposal is that the network of tightly knotted linked flux tubes is topologically stable only in space-time dimension D=4.
   
   
2. Dimension d=3 is indeed unique as space dimension and D=4 as space-time dimension. The point is that n-dimensional objects are knotted in dimension n+2 and linked in dimension 2n+1. d= 3 = 1+2=2×1+1 allows both knotting and linking of 1-D objects simultaneously, and is therefore a unique dimension of space. Even more, in space-time dimension D=4 the 2-D orbits of knots form 2-knots which add still more topological complexity to D=4 and makes it unique.
   
   

In TGD framework gas of flux tubes carrying monopole fluxes is identified as the primordial stage of Universe: I have called them cosmic strings. They are definitely not flux tubes of gauge theories except in some aspects. Neither are they cosmic strings in the usual sense of the word that is defects of GUTs).

1. These flux tubes - cosmic strings - are 3-D surfaces in M⁴×CP₂ with 2-D minimal surface (string world sheet) as M⁴ projection and 2-D complex surface of CP₂ as CP₂ projection. During the primordial period one had gas or plasma of cosmic strings.
   
   
2. After the primordial period the 4-D space-time in the sense of GRT began to emerge as space-time regions with 4-D M⁴ projection. The M⁴ projection of flux tubes became 4-D instead of 2-D and began to thicken in spatial directions. Flux tubes topologically condensed at thicker flux tubes (glued by tiny wormhole contacts to larger 3-surfaces). As approximately 1-D objects they could form knots and get linked. Their approximately 2-D orbits could also get knotted and these 2-knots are something completely new. This transition is the TGD analog of inflationary period and solves its grave problems.
   
   
3. Knotting and linking are not actually approximation notions. Fermionic strings parallel to cosmic strings were present and served as topological representatives for the flux tubes. They knotted and linked in 3-D sense and 2-knotted in 4-D sense.
   
   
4. Cosmic strings as flux tubes carrying magnetic monopole flux are fundamental for the entire TGD Universe and appear in all length scales. Flux tubes are also fundamental in TGD variant of hadronic physics, nuclear physics, molecular physics, quantum biology, etc...
   

   For their cosmological role see this. For the solution of galactic dark matter problem in terms of cosmic strings see this.
   
   

D=4 as a unique space-time dimensions emerges in several manners in TGD framework.

1. Generalization of conformal invariance is possible for 3-D light-like surfaces since their metric dimension is D=2. Boundary of light-cone in 4-D Minkowski space has this generalized conformal invariance. Also the 3-D light-like surfaces between Euclidian and Minkowskian regions have this symmetry. This gives rise to the huge conformal symmetries extending stringy conformal symmetries implying among other things strong form of holography in which locally 2-D data determined 4-D space-time surfaces and quantum states.
   

   A kind of record in professional arrogance is that I have been preaching about this simple but overall important observation for almost three decades and in vain! Colleagues simply refuse to listen! They read only prestigious journals as one my finnish colleagues formulated it! Collective stupidity is one of the most irritating and fascinating sociological phenomena.
   
   

2. In number theoretical vision about TGD associativity condition of space-time as surfaces in 8-D space with octonionic structure forces D=4. Associativity holds for space-time surfaces assignable to external particles. Not for interaction regions and this leads to a beautiful interpretation of dynamics (see this).
   
   
3. The twistor lift of TGD by generalizing twistor structure to its 8-D variant and inducing 4-D twistpr structure is possible only for this space-time dimension. Induced twistors are essentially 4-D notion. Also this makes sense only 4-D space-time surfaces in 8-D imbedding space M⁴×CP₂ (see this and this).
   
   

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

Articles and other material related to TGD.

How the ionization is possible in living matter?

The appearance of ions in living matter looks mysterious. Same is true concerning ions in electrolytes. It is easy to talk about cold plasma but much more difficult to answer the question how this cold plasma can be created. Usually the formation of plasma involves ionization, which requires high temperature of order of the atomic binding energy for the valence electrons of the atom. For hydrogen atom the binding energy is around 13 eV, which corresponds to a temperature of roughly 130,000 Kelvin! This is three orders of magnitude higher than room temperature! In electrolyte the presence of rather weak electric fields cannot explain why the ionization takes place.

For some reason chemists and biologists do not spend much time in pondering fundamentals and theoreticians enjoying monthly salary have a highly irreverent attitude to these disciplines as an intellectual entertainment of lower life-forms. Therefore also this question has been guided under the rug and stayed there.

TGD based explanation for the paradox is simple. If the value of h_eff/h=n for valence electrons is high enough, the binding energy, which is proportional to 1/n², becomes so high that a photon with rather low energy, say infrared (IR) photon, can be ionize the dark atom. One can say that the atoms in this state are quantum critical, a small perturbation can ionize them.

1. In the TGD based model of cold fusion as dark nucleosynthesis the atoms would have n=2¹²= 2056 and the ionization would create dark nuclei as sequences of dark protons at magnetic flux tubes (see this).
   
   
2. In the TGD based model for the analogs of DNA/RNA/amino-acid sequences/tRNA as dark proton sequences the value of n would be of the order of 10⁶ higher so that the distance between dark protons, would be a same as between DNA letters, about 3 Angstroms. For these values of n dark atoms are unstable at room temperatures.
   
   
3. In Pollack effect (see this) the irradiation by IR light or visible light or by pumping energy to the system by some other means produces negatively charged exclusion zones (EZs) in which water molecules form hexagonal layers and obey the effective stoichiometry H_3/2 O. Part of protons (every fourth) goes to magnetic flux tubes as dark protons. How it is possible to create this state by IR radiation?
   
   
   1. The original assumption was that in second OH bond of water molecule is excited to a high energy state near to ionization energy so that IR photon can split the bond. The question is: why and how? Do the UV photons from solar radiation cause the excitation?
      
      
   2. A more elegant option is that the value of n for the second O-H bond is so large that the bond binding energy is so small that IR photon can split the bond. Solar UV photons could induce the dark excitation. Taking 5 eV as rough estimate for the bond binding energy in the normal state water, this requires the reduction of energy by a factor of order 10³ to give IR energy .05 eV (energy scale assignable to the membrane potential eV). n would increase by factor of order 2⁵=32 from its value for O-H bond according to standard chemistry. A small push by absorption of IR photon can split the O-H bond and create dark proton at flux tube. Any perturbation feeding to the system this energy can induce the kicking of dark proton to flux tube. The generalization of this mechanism to various atoms could be one of the basic mechanisms of quantum criticality in living matter.
      
      

See the article Does valence bond theory relate to the hierarchy of Planck constants? or the chapter Quantum criticality and dark matter.

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

Articles and other material related to TGD.

Have galactic cosmic strings been observed?

I have been talking for a couple of decades or so about cosmic strings in TGD sense as explanation for the galactic dark matter. Long cosmic strings would have galaxies as knots in the simplest model of galaxies as pearls in necklace. The model explains the old observation that galaxies indeed form linear structures. Constant velocity spectrum for distant stars is predicted as being due to the gravitational field of cosmic string: string tension is the only parameter of the model. No dark matter halo, which is recently in deeper difficultiest than ever, is needed.

In pearls-in-necklace model (see this) galaxies are knots in long cosmic string. These knots in turn can decompose to further knots connected by more or less straight portions and one can image fractal structure continuing down to the level of stars. The straight portions would give rise to filament like structures connecting regions of sub-knots, which should correspond to regions. where star formation is taking place. Even the beams of particles from neutron stars could be associated with cosmic strings. Note that the string tension of cosmic string decreases as it thickens.

Quite recently I learned that there exists evidence for this kind of filaments (see this). The first filaments found were roughly orthogonal to the galactic plane but later filaments with random directions were found. This conforms with the knots along knots along... model.

Quite recently came a report by Morris, Zhao and Goss about a new filament found in Milky Way. As the title "A Nonthermal Radio Filament Connected to the Galactic Black Hole? " of the article tells that the filament visible at radio frequencies might emerge from galactic blackhole. There is also a popular article about the finding with title "A Mysterious Filament Is Stretching Towards Our Galaxy's Supermassive Black Hole".

The filament - known as Sgr A West Filament (SgrAW) - was actually discovered back in 2012. What is new that the new image suggests that the 2.3 light-year long filament is associated with the galactic blackhole Sagittarius A*. This suggests that galactic blackhole like object could be associated with a tight knot or self-intersection of cosmic string. Article consider the possibility that a low mass density cosmic string has been anchored to Sgr A*. Sgr A* would be a source of relativistic particles constrained to diffuse along ordered local field lines. Simplest model (vanishing of total momentum for particles coming out) suggests that the particle beam along filament is bi-directional. Filament is however seen only on one side of Sgr A*.

In TGD framework filament could be ordinary matter gravitationally bound with cosmic string and moving along it in essentially free motion. The beam could be due to ithe transformation of dark matter and/or energy of cosmic string to ordinary matter.

1. The transformation of Kähler magnetic energy to particles would be TGD analog for the decay of the vacuum energy of inflaton field to particles. If Kähler magnetic energy dominates over volume term as it should, the thickening of cosmic string would weaken Kähler magnetic field and energy density and therefore string tension. The magnetic energy would be transformed to ordinary particles.
   
   
2. A possible explanation for why the filament is seen only on one side of Sgr A* is that the decay of magnetic energy generates beams moving to opposite directions so that total momentum vanishes. The first beam remains inside cosmic string as dark particles and second beam leaks out as ordinary particles. Second possibility is that magnetic flux tube contains a beam of dark particles, which partially leaks out as ordinary particles.
   
   

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

Articles and other material related to TGD.

About the biological role of low valence ions

A comment about the role of biologically important ions is in order. As a rule they tend to have low valence, especially those whose cyclotron frequencies for B_end=.2 Gauss seem to be important biologically. The possibly existing valence bonds between atoms towards the left end of the rows of the periodic table (Li,Na,K,Ca, Mg,..) - if they even exist at all - have low valence and low value n satisfying n≥ 6 (note that the valence of the bond is the valence of the atom with higher valence).

1. The potential negentropy content of low valence bonds is low and also metabolic energy content defined as difference of energy from the situation in which one has n=6 derived from the experiments of Randell Mills (see this). Thus low valence bonds are not important for metabolism.
   
   
2. Low valence ions have however different role: they appear as biologically important positive ions important for the communications to and control by MB. For instance, dark photons with cyclotron frequencies in magnetic fields of flux tubes would be involved with control by dark photons. These dark photons could also transfer energy to MB. The values of n for dark photons can be as high as n ∼ 10¹² or even higher from the condition that the energies of dark photons with frequencies in EEG range are above thermal energy or even in visible and UV range for bio-photons.
   

   Values of n for dark ions could be thus much higher than for electrons at valence bonds if their cyclotron energies correspond to dark photon energies. Dark photons and dark cyclotron condensates would represent a higher level of evolutionary hierarchy and control and coordination in quite long length scales responsible for the quantum coherence of living matter.
   

   Remark: Recall that the assumption hbar_eff=hbar_gr= GMm/v₀, where v₀>c has dimensions of velocity, m mass of the charged particle, and M some large mass, guarantees universality of cyclotron energy spectrum (spectrum of bio-photons in visible and UV range). This gives n∼ 10¹³ for 10 Hz cyclotron frequency photon energy about 1 eV. Fe⁺⁺ has f_c=10 Hz in B_end=.2 Gauss.
   
   

One can consider some examples about biologically important ions.

1. In TGD protons H⁺ appear as dark protons. The small value of the atomic binding energy would explain why hydrogen appears as ion: dark atoms with this value of n would have extremely large size. Dark protons need not of course have the value of n characterizing dark EEG photons. Rather, entire hierarchy of frequency scales is expected ranging down to the energies of IR photons still above the thermal energy.
   
   
2. Hydrogen bond carrying de-localized proton would serve as the simplest example and be associated with magnetic flux tube. Hydrogen bonded water molecule clusters are crucial for life. Hydrogen bonds are also formed between OH groups of say water and some other high valence atoms.
   

   Dark DNA/RNA/amino-acid/tRNA realized as dark proton sequences at magnetic flux tubes and realizing vertebrate genetic code (prediction) would be second realization giving rise to dark nuclei (see this). Cell membrane as generalized Josephson junction would involve electronic Cooper pairs and dark protons or even their Cooper pairs (see this). At microscopic level membrane proteins defining various ion channels and pumps would act as generalized Josephson junctions.
   
   

3. What about heavier ions? Their dark variants appear at MB and play a key role in TGD based model for quantum biology and neuroscience. They appear at flux tubes assignable to generalized Josephson junctions and at layers of MB in much longer scales (note that hydrogen bond is analogous to Josephson junction). Dark ions carrying much more information in BE condensates than dark valence electrons would serve control purposes whereas dark electrons at valence bonds would carry metabolic energy.
   
   
4. What about noble gases? Can one say that they have maximal valence or do they have vanishing valence and therefore n=6 as the findings of Mills suggest? If they had maximal valence they should be biologically important but they are not: thus n=6 identification is feasible. Ions at the right end of the rows of periodic table, say Cl^- ion, are like noble gas atoms as far as valence is considered. The electronic negentropy of H-Cl understood as H⁺ bonded with Cl^- (ionic bond rather than valence bond) and metabolic energy content would be minimal. Cl^- could however form cyclotron condensates with a large value of n, which would explain its biological importance.
   

   Amusingly, plastic balls in plasma of Ar⁺ ions appear in the experiment demonstrating life like properties of this system ("breathing") (see this). Ar⁺ would have maximal possible valence and thus maximal value of n and would appear at flux tubes.
   
   

See the article Does valence bond theory relate to the hierarchy of Planck constants? or the chapter Quantum criticality and dark matter.

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

Articles and other material related to TGD.

Why Alzheimer does not destroy some aspects of consciousness?

Some aspects of consciousness seem to survive Alzheimer. Alzheimer patient can understand singing and also express himself by singing (see this). Why?

1. Singing is conventionally associated with holistic aspects of consciousness whereas language corresponds to reductionistic, local, and linear representation of conscious experience. Holistic-reductionistic dichotomy is often associated with right-left dichotomy. One should be of course cautious with this identification and be happy with holistic-reductionistic dichotomy.
   
   
2. In any case, we know that left brain talks and right brain sings. Singing is a representation in terms of frequencies. It is 2-dimensional because also the pitch matters unlike in the case of speech. Everyone familiar with Fourier transform knows that frequency representation is holistic: Fourier amplitude carries information about the function in the entire domain of definition but not about details for low enough frequencies such as occur in singing (maybe the duration of duration of nerve pulse of order millisecond could serve as standard, could notes with pitch below kHz frequency be low frequencies?).
   
   
3. Why cognition does not survive in Alzheimer is easy to understand. Cognition is by definition about details: left brain is responsible for language and language indeed local , linear(!), and reductionistic. Maybe 1-D neural strings and loops assignable to magnetic loops provide a realization of spoken and written language? Alzheimer would destroy synaptic connections and would split these strings. The disappearence of even single bridge in the loop/string splits the loop/string (into two): this is just 1-D topology. Communication line would be broken. Cognitive skills and language would be lost.
   
   
4. Why would the holistic aspects of consciousness survive in Alzheimer? Suppose that right brain involves 2-D net-work like structures instead of 1-D neural strings having much more connections and giving rise to quantum tensor network (see this) as it would be fashionable to say. Quantum entanglement is very probably involved and would be actually responsible for the holistic and hologram-like aspects of neural activities known for a long time. It would not be surprising if brain waves with frequency spectrum below kHz would be important for this representation. EEG waves are almost by definition in the range 1-100 Hz.
   

   What happens to 2-D networks in the destruction of synapes. Practically nothing! Quite a number of synaptic connections can disappear but this does not split the 2-D network into pieces as it splits 1-D string: 2-D topology! Communications take place and the structure can take care of itself. Holograms are not affected by the local splitting of the synaptic connections. The right brain would happily continue its singing!
   

   Note that 2-D networks are also natural for the representation of sensory data as images and the language of images is different from the language of words: I have discussed the differences between these two different languages here).
   

   The natural question is whether could one approach to Alzheimer rely on activation of right brain: could art therapies such as music and visual arts help in Alzheimer? Could guided transition to holistic, artistic mood of conscious existence help to overcome the negative effects of Alzheimer?
   
   

See the article Is it possible to reverse Alzheimer's disease? or the chapter Quantum Mind and Neuro Science of "TGD based view about consciousness, living matter, and remote mental interactions".

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

Articles and other material related to TGD.

Could Alzheimer's disease be cured?

I am reading a marvellous book of Dale Bredesen titled The End of Alzheimer's - thanks for my friend Pertti for an excellent Christmas gift.

Alzheimer's disease (just AD in the sequel) has been regarded as a disease without any effective treatment. A lot of progress has however occurred during last years in the understanding of AD and related diseases causing neuro-degeneration. Bredesen's group has developed a programme to stop and even reverse the development of cognitive decline and dementia.

Programme for reversing AD

The first chapter of the book contains a long list about the symptoms of AD. One must be cautious while reading this list. A strongly introvert and unpractical person like me having suffered from strong social fears during childhood, youth and mid age might conclude having been AD patient for all his life. Our personality however means that we have our strengths and weaknesses. Only if we begin to lose our strengths, there is a good reason to get worried.

AD involves brain inflammation causing a generation of amyloid, a plaque that destroys synaptic connections crucial for various learned skills. This leads to the symptoms of AD. Amyloids were for long time thought to be the cause of AD but it turned out to be only a manner how brain defends itself: in AD this defence has only developed to over reaction: somewhat like too strong immune response causing allergy.

In an attempt to to cure AD one can do three things (in collaboration with a professional since AD has strongly patient dependent profile).

1. Get rid of the brain inflammation.
   
   
2. Eliminate the sources of inflammation: both infection by microbes and sugar containing proteins.
   
   
3. Provide brain with the needed nutrients including metabolic energy, hormones, and trophic factors helping the regeneration of synapses.
   
   

This program requires nothing less than changing of the life style.

AD as suicidal behavior at neuronal level

The motivation for this post emerged as I started to read a chapter about how the new view about AD developed through the study of AD in Petri dishes, a completely new lab level approach initiated by Bredesen's group. Two big surprises were in store.

1. It was found that in AD the neurons perform a suicide instead of fighting against the disease! They just give up! This was something totally unexpected.
   
   
2. The researchers had an idea that there are receptors in brain stem, which could relate to neuro-degeneration. The idea was that when the receptors bind to corresponding ligands, the neuron dies. It would be kind of organized suicide. But this did not occur! Neurons die if the ligand is not present! A healthy neuron must have both the ligands and receptors. These ligands can be christened as neurotrophins since they support the growth of cell.
   
   

Some basic notions of TGD inspired biology

While reading, I realized that this fits nicely with the TGD based vision that magnetic body (MB) of the organism (biological body (BB)) or part of it takes care of BB, such as brain by receiving information as signals from brain and sending back control commands. Before continuing it is good to briefly summarize some key aspects of TGD view about biology and brain. There are several new notions.

1. The notion of MB distinguishes between TGD and Maxwellian (gauge theory) view about fields. In many-sheeted space-time one can say that physical object has field identity, field body. Given for instance a magnetic flux tube realized as topological field quantum -tubular 3-surface - one can tell, which physical system it emanates from. The double formed by organism and its environment is replaced with a triple formed by MB , BB , and environment, and this changes profoundly the view about possible disorders of organism.
   
   
2. Hierarchy of Planck constants h_eff/h=n making possible macroscopic quantum coherence in various scales is a key element of TGD inspired quantum biology. This hierarchy emerges as a prediction of adelic physics suggested to provide a unification of ordinary physics and of physics of cognition by introducing besides real number based physics also various p-adic physics serving as a correlate of cognition. h_eff/h=n hierarchy and p-adic length scale hypothesis define fractal hierarchies of length and time scales: this fractality means that the standard length scale reductionism breaks down and that interesting new effects emerge in all scales. I have been identifying these effects for more than two decades now: the information flux from web has been indispensable in this task. Living matter would be one of the most striking deviations from the naive reductionism. Even molecular physics and chemistry fail to reduce to atomic physics as the reductionistic dogma dictates.
   

   MB carries dark cyclotron condensates and dark photons with with non-standard value of h_eff/h=n. Cyclotron condensates and cyclotron radiation are crucial for the control of organism by its MB. The feed of metabolic energy generates cyclotron condensates.
   
   

3. The view about sensory perception and function of nerve pulse transmission differs from the standard view. Nerve pulse transition would not be communication between parts of CNS but building of communication line for dark photons making possible communications with maximal signal velocity.
   
   
   1. This would allow generation of sensory mental images at sensory organs by an iteration involving virtual sensory input from brain to sensory organs. Pattern recognition would be realized as a build-up of an artwork representing standardized mental image as near as possible to the original sensory input.
      
      
   2. Neurotransmitters and all information molecules would be bridges needed to construct connected communication lines. Learning as formation of permanent synaptic connections would be generation of permanent bridges of this kind.
      
      
4. Cell membrane and perhaps also other structures serve as generalized Josephson junctions. The (generalized) Josephson radiation generated by nerve pulses would give rise to EEG (and perhaps also to its fractal counterparts) as communication of neural information from brain to MB via Josephson frequency modulation. The size scale of the layer of MB wold be rather large, of the order 1/f_c, of the order Earth size in alpha band (f_c≈ 10 Hz).
   
   

Disorders as problems in the communications between BB and MB and as problems at BB and MB

Both the failure of the communication and control links between magnetic body and problems at BB or MB can give rise to disorders/diseases. Many things can go wrong.

1. Magnetic flux tubes serve as kind of wave guides carrying signals consisting of dark photons. Telephone network gives an idea about the situation. The flux tube network would consists of permanently existing pieces, which can be connected to single connected communication line by attaching small bridges (relays) between disjoint flux tubes. This process is nothing attachment of information molecule (say neurotrophin ligand) to the receptor and thus serving as a bridge.
   

   If the connecting ligands are absent, the communication line does not exist and MB does not receive information from brain: MB cannot see its protege. Also the control of MB can fail if it involves this kind of bridges: MB becomes lame unable to help its protege.
   

   This is of course not the only mechanism. There might be ligands, which are competing for binding but not serving as relays so that the connection would not be built. This turns out to be the case in AP. The dynamical equilibrium between genuine bridges (trophins) and fake bridges (antitrophins) determines how much communication between MB and brain takes place. When fake bridges dominate, one has fully developed AP. This picture seems to be very general and apply also to a wide variety of other diseases, in particular Mad Cow disease.
   

   Could the blindness of MB with respect BB be the cause of A?! Could AD -and presumably many other diseases - be disorders in communications between BB and MB due to the broken communication lines? Does MB of brain as God of neurons purposefully reject some neurons? Sounds cruel but the limited metabolic resources could force to select between organism and individual neurons.
   
   

2. If MB is dynamical, some layers in its onion-like structure could even disappear. At the level of brain the structures of MB are indeed dynamical. The formation of mental image would involve the generation of connected quantum coherent flux tube network by the formation of bridges.
   

   Nerve pulse patterns would give rise to this kind of structure with neurotransmitters giving rise to small bridges between pre- and post-synaptic neurons. The formation of amyloid plaques would destroy the synaptic connections and destroy the MBs is the scale of brain.
   

   Remark: Watch-up network would serve as an analogy here.
   
   

3. The dark photons mediating the signal might fail to be generated at brain or at MB. Also depression involves brain inflammation. Depressive mood rather literally is characterized by a feeling of being rejected by God. MB has indeed forced to reject the patient if the signals from brain or to brain cannot propagate for some reason.
   

   Cyclotron radiation by biologically important ions would be needed to generate the dark photons needed in communications to and control from MB. EEG would be basic example of this kind of communications, which are however expected to be present in several frequency scales. Control commands could come via genome along flux sheets traversing DNA strand.
   

   Generalized Josephson radiation from neuronal membranes could mediate "sensory" information from brain to MB. The frequencies of generalized Josephson radiation are sums of differences of cyclotron frequencies at the two sides of the neuronal membrane and genuine Josephson contribution ZeV/h_eff coding for the nerve pulse patterns representing information as frequency modulation.
   

   At least the lack of Li and Mg are known to induce depression and suicide rates correlate with Li depletion.
   

4. Also control can fail. It is also possible that cyclotron condensates at MB are not generated so that MB cannot generate the dark cyclotron radiation driving the oscillators at biological body representing the control commands. This could be due to the lack of metabolic energy feed from BB to MB.
   
   

What AD actually is?

A further reading of the book taught more about what AD actually is.

1. It was found that peptide amyloid-beta (Aβ) is toxic to neurons acting as anti-trophin competing with trophin making possible the well-fare of neuron. The interpretation is in terms of competition between real and fake bridges. Since metabolic resources are finite, antitrophin can have healthy effect in many situations.
   
   
2. Amyloids was originally seen as the cause of AD. There exists dependence receptor known as amyloid precursor protein (APP): one might say that it monitors the state of neuron. There exists molecular scissors (proteases), which can split APP to either 2 peptides or 4 peptides.
   

   The members of peptide pair are inside and outside the cell membrane. They maintain the wellfare of the neuron. The 4 peptides divide two groups of 2 peptides inside outside of the membrane and include Aβ. Too high concentration of amyloid beta destroys synapses and leads to neuron death.
   

   Dynamical equilibrium between these two kinds of peptides determines the fate of the neuron. If the equilibrium shifts to the side of 4 bad peptides increasing their concentration, there is a risk that AD develops.
   
   

3. What determines the equilibrium between these two kinds of peptides? APP is a receptor than can bind to kinds of ligands, let us call them good and bad. The good ligand is known as netrin-1. In this case APP splits into to peptides supporting neuronal well-fare. Netrin-1 is trophin.
   

   Remark: Netrin comes from word "netr", which is sanskrit and means "one who guides". Netrin would indeed serve as a link to MB, which indeed guides!
   

   The bad ligand is Aβ! This leads to positive feedback. The higher the concentration of Aβ produced in splittings to 4 peptides is the faster the rate for the new similar splittings. This causes a catastrophe: an uncontrolled exponential growth of Aβ concentration analogous to cancer. Similar mechanisms appear also in cancer and Mad Cow disease. Peptides able to amplify their own concentration are known as prionic.
   
   

4. There are many causes of AP explaining why the usual single cause - single medication approaches to AD have failed. Bredesen's group as identified 36 independent causes of AD! One of these causes is APOE4. It was originally thought to reduce the clearance of amyloid from brain. This is true but it was also found to have much deeper role. It can affect gene expressing by binding to the promoter regions of DNA and preventing the transcription of genes coding for proteins promoting the well-fare of neuron. APOE4 is thus an active tool for inducing death of neuron.
   
   
5. Bredesen takes business organization in market economy as a metaphor. Brain must monitor whether the neurons are useful and whether metabolic and other resources are enough for survival. At older age these resources deplete. Brain must destroy the neutrons when there is shortage about nutrients, vitamins, hormones. Also neurons, which are inactive or somehow damage, must go.
   
   

TGD view about AD

The interpretation of this picture in TGD framework should be now rather obvious.

1. The simplest view is that netrin serves as a genuine bridge to MB and Aβ as the fake bridge. The dominance of fake bridges means that connection to MB is lost.
   
   
2. Brain must survive and decides to kill the neurons or force them to perform suicide, and uses APOE4 as one particular tool to realize this. MB would be innocent, so to say.
   
   
3. Or could MB serve as Stalin actively promoting neuronal death by activating mechanisms leading to neuronal death? Could the connections via the flux sheets of MB of DNA making possible control of BB allow this: is the activation of APOE4 preventing transcription of important genes related to this. One could argue that MB affects only DNA via promoter regions and APOE4 generated by brain itself prevents this. MB would not be Stalin after all.
   
   
4. Irrespective of who did it, in TGD Universe there is a hierarchy of selves and layers of MB serving as "Gods" and it includes also us. We can change our life style and prevent Alzheimer and many other diseases if we act early enough. We can do good deeds - also to our our biological bodies! Perhaps this is easier!
   

   Remark: This inspires the question whether same applies in capitalism/market economy, which is a fractal copy of biology at cell level in TGD Universe. We can transform biology to culture by bringing in ethics, values and moral.
   
   

Questions about memory

Alzheimer's disease also inspires questions about memory. Neuroscientists often identify memories as skills. There are however memories such as sensory memories, which can be induced in any-one by electrical stimulation of temporal lobes. Also dreams involve these memories. One can have spontaneous memory of some smell or suffer pain in non-existing leg. Some people often regarded as cognitively impaired might have sensory memories regularly: this could explain their amazing memory feats. Some people hear music all the time in their head: Tchaikovsky is one example of this.

I find it difficult to believe that sensory memories would reduce to strengthening of synaptic connections in the brain now: they are not learned skills. In TGD picture the new view about time leads forced by zero energy ontology (ZEO) leads to the idea that the perceptive field is 4-D causal diamond (CD, 2-D visualization helps to understand) and that sensory memories are mental images (sub-CDs) located near either boundary of CD. The remaining mental images inside CD would be represented symbolically so that it would make sense to speak about "sensory now" in 3-D sense. Cognitive impairment would mean a loss of the symbolic representations and sensory representations might replace it and make memory feats possible.

Remark: In ZEO one can even make the scifi sounding question whether the brains of geometric past still in good shape could be used? There are people who have lost most of their brains but still can cope with challenges of everyday life.

Could this view be tested? Could Alzheimer patients have long term memories about time when brain was still healthy? Could they have sensory memories about that time? This might be the case: my grandmother lost her cognitive skills during her last years but re-lived her youth very intensely: she had even strong intention of going to dance!

See the article Is it possible to reverse Alzheimer's disease? or the chapter Quantum Mind and Neuro Science of "TGD based view about consciousness, living matter, and remote mental interactions".

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

Articles and other material related to TGD.

DMT, pineal gland, and the new view about sensory perception,dreams/hallucinations, and imagination

The recent discussions with artist Sini Kunnas (see this) about perception as creation of an artwork inspired additional insights about how sensory perception, imagination as almost sensory perception, dreams and hallucinations as virtual percepts, and their motor analogs relate to each other.

What distinguishes TGD from neuroscience is that sensory receptors are assumed to serve as carriers of sensory percepts. Zero energy ontology (ZEO) providing new view about time and memory allows to solve the basic objections related to phantom limb phenomenon: pain in phantom limb would be sensory memory.

The assumption that sensory percepts are artworks rather than passive records of sensory input requires virtual sensory input from brain to sensory organs and build-up of the final percept by pattern recognition - an iterative procedure involving very many forth-and back signals. Nerve pulse transmission is quite too slow process to allow this and signals propagating with maximal signal velocity are suggestive.

Nerve pulses and neurotransmitters would not represent real communication but give rise to temporary intra-brain communication lines along which communications as dark photon signals would take place with maximal signal velocity using dark photons (characterized by h_eff/h=n) transforming to biophotons in an energy conserving manner (see this and this). Neurotransmitters and also other information molecules (hormones, messengers) attached to receptors would serve as bridges fusing permanent but disjoint communication lines along axons to a connected temporary communication line for dark photons to propagate. Nerve pulses would also generate generalized Josephson radiation allowing communications between biological body (BB) and magnetic body (MB) using EEG. Meridian system would be permanently connected system of communication lines.

This picture leads to a concrete proposal about the roles of DMT and pineal gland concerning imagination and dreams and hallucinations.

A new view about the role of nerve pulses in sensory perception

Sensory perception would in TGD generate sensory mental images at sensory organs: this would solve a basic problem of neuroscience due to the similarity of neural tissue in various sensory areas. The new view about time and memory implied by ZEO solves the problem cause by the phantom limb. The pain in phantom limb is sensory memory of pain. The stimulation of temporal lobes indeed generates sensory memories, and people with cognitive inpairment are known for memory feats such as being able to draw some building seen in past with every detail or to learn music pieces with single listening. These feats can be understood if memories correspond to "seeing" in time direction with beam of dark photons travelling to past reflected back. ZEO allows this.

Also Libet's findings about active aspects of consciousness involving subject person deciding to raise his index finger and reporting it to experimetner can be understood in ZEO without giving up the notion of free will. In the quantum jump also the geometric past would be affected and this would explain why neural activity begins fraction of second before the conscious decision the subject person decides to raise his index finger.

Since perception involves a lot of processing this would require forth-and back signaling between brain and sensory organs. There would be virtual sensory input from brain or via brain. Sensory percept would be an artwork, standardized mental image, resulting as pattern recognition assigning to sensory input standardized mental image nearest to the input.

1. Nerve pulses would not mediate information inside brain (for TGD view about nerve pulse see this). They would only build short connections between existing flux tube connections parallel to axons. Same happens in old fashioned telephone network by relays: it would be energy consuming to keep the connections on all the time.
   

   The velocity of nerve pulse conduction is quite too slow to realize the iteration leading to a standardized sensory mental image. If the signal velocity is light velocity, duration of order 1 ms for nervepulse also for 10 cm neural pathway about 10⁶ forback travels between sensory cortex and retina.
   

   Communications would occur by dark photons signals with h_eff/h=n and with maximal signal velocity allowing for an iteration leading to standardized percepts as near as possible to the sensory input and representing only the essential features. Dark photons could transform in energy conserving manner to biophotons with energies in visible and UV range (at least) and thus above thermal energy and therefore having effects not masked by thermal radiation. Brain is known to emit biophotons and they are also associated with axons (see this and this)
   
   

2. All information molecules (neural transmitters, hormones, messengers) would be connection builders so that the view of neuroscience would be badly wrong here. I have discussed this idea earlier but in slightly different form: the proposal was that information molecules are attached to the end of a flux tube getting longer as the molecule travels to its target. This is possible but un-necessary since it is enough to build just the bridge between existing connections.
   

   Remark: The view of neuroscience might be very different if information technologies would have been known century ago. Same applies to homeopathy and water memory (see this and this), which still remains curse words in mainstream science, although a lot about the mechanisms involved is known.
   

   The standard view about learning as strengthening of synaptic connections would translate to a gradual build-up of permanent flux tube connections so that communications with dark photon signals would be possible all the time.
   This would lead to fusion of sender and receiver to single quantum entangled system.
   

   If the meridians of acupuncture network correspond to this kind of permanent network, they would not require nerve pulses, transmitters, nor information molecules.
   
   

3. Nerve pulse patterns would however generate Josephson radiation at EEG frequencies propagating from brain to its MB from axonal membranes serving as Josephson junctions. EEG would code the nerve pulse patterns as frequency modulated Josephson radiation (see this).
   
   

The role of DMT and pineal gland

Concerning sensory perception, dreams, hallucinations (psychedelic experiences), and imagination the roles of DMT and pineal gland are extremely interesting and suggests a unified view about these aspects of consciousness.

1. Pineal gland is third eye in quite concrete sense for some amphibians and reptiles. This suggest that it still has some function: biology does not invest metabolic energy without return. Could pineal gland serve as the eye of imagination?
   

   Dark photons would arrive from brain or via brain to pineal gland and give rise to imagined sensory experiences (almost seeing, almost hearing, ... thoughts as internal speech, etc...). All these signals would be realized in terms of dark photons in different wave length ranges for various sensory qualia and the entire energy range of biophotons could be involved: visible light involves one octave in good approximation. At this level perception would be basically "seeing".
   
   

2. DMT (N-N dimethyltryptamine) is the only psychedelic manufactured by brain itself: in pineal gland in the case of rodents and therefore also in the case of higher mammals.
   

   Remark: In "DMT "N-N" refers to two nitrogen atoms; "Dimethyl" refers to two CH₃ groups replacing H; ttryptamine is the only amino-acid having two aromatic rings.
   

   Endogenous DMT could have same role as psychedelics and could induce dreams. The state between wake-up and sleep is somewhat analogous to REM sleep and characterized by hallucination like sensory percepts. This cold be due to DMT. During wake-up state dreams would be intefere with genuine sensory percepts and would be replaced by imaginations. It would seem that the virtual sensory percepts associated with the build-up of sensory percept and
   via pineal gland must be independent.
   
   

3. The binding of DMT to receptors in pineal gland would give rise to small bridges connecting disjoint dark photon carrying flux tubes to connected flux tubes going down to sensory organs, where the dark photon signals would give rise to dreams and hallucinations. What would be needed is that dark photons induce sensory stimulus at sensory organ.
   

   Remark: Interestingly, the inverted structure of the lense in eye is optimal for receiving virtual visual input.
   
   
   

4. Also motor actions would be prepared by iterative process analogous to the build-up of sensory percept but in reverse direction of time as Libet's findings about active aspects of consciousness (volition) suggest. Motor action would be sensory perception in opposite direction of time: this makes sense in ZEO one makes distinction between experienced and geometric time. Imagined motor actions would be mediated by similar mechanism involving DMT and pineal gland.
   
   

A further fascinating possibility is that the flux tube connections extend even to outer space, to the brains of members of advanced civilization in distant galaxies. Could the experiences about encounters with ETs or god-like creatures reported by the uses of psychdeles could be real?

1. This is in principle possible since in TGD Maxwellian fields are topologically quantized. Magnetic field decomposes into flux tubes represented as flux sheets in many-sheeted space-time. One can say that any system has field identity, field body.
   
   
2. Dark photons can travel along the flux tubes of MB to arbitrary distances without weakening of the signal as in Maxwellian world.
   
   
3. ZEO allows also signals in non-standard time direction so that it is possible to send signal which is time-reflected back as signal in opposite time direction: this can happen almost instantaneusly so that finite light-velocity ceases to be a restriction to communications.
   
   

See the article DMT, pineal gland, and the new view about sensory perceptionor the chapter Quantum model for nerve pulse of "TGD and EEG".

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

Articles and other material related to TGD.

Valence bond theory from the hierarchy of Planck constants

The idea that valence bonds, or at least some of them, correspond to non-standard value of h_eff/h=n (see this) is very attractive. It could allow to understand what chemical bonds really are and allow a detailed view about how reductionism fails in the sequence of transitions from atomic physics to molecular physics to chemistry to biochemistry.

1. The standard value of n, call it n_min need not correspond to n_min=1 and the findings of Randell Mills (see this) suggesting that hydrogen atom and possibly also other atoms can have binding energies coming as k² multiples of ordinary ones with k=2,3,6, suggests that n_min=6 could correspond to the standard value of h_eff for atoms. n>n_min would mean reduced binding energy and this would mean the possibility of high energy valence bonds.
   
   
2. The binding energy of atom would scale as 1/n² so that for non-standard values of n>n_min would correspond to smaller binding energy scale. The finding that heating of rare-earth atoms leads to a disappearance of some valence electrons (see this) suggests that the value of n for some valence electrons increases from n_min in these situation. The same effect might be achieved by irradiation at suitable photon energies corresponding to energy difference between ordinary state and dark state of electrons. An entire spectroscopy of atoms with dark valence electrons would be waiting to be discovered.
   
   
3. n>n_min would explain why valence bonds are carriers of metabolic energy liberated in catabolic part of metabolism. The temporary of energy involving temporary reduction of n would in turn make possible bio-catalysis by kicking the reactants over the potential wall making the reaction slow. The shortening of long flux tube bonds between reacts as the value of n is reduced could explain why bio-molecules are able to find each other in the molecular crowd.
   
   
4. The Bohr radii of valence electrons of atoms scale as a_B∝ m²/Z_eff², where m (usually denoted by n) is the principal quantum number determining the value of energy in the model based on Schrödinger equation. Z_eff is in good approximation equal to the unscreened nuclear charge Z_eff=n_V equal to the number of valence electrons. If the superposition of atomic orbitals restricted to valence bonds is the essence in the formation of molecules, one an argue that the lengths of bonds and radii of molecules should decrease rapidly with Z_eff. However, the empirical fact is that the bond lengths vary in a rather narrow range, roughly by factor 2!
   
   

The solution of the problem looks rather unique.

1. The value of n assignable to the valence bond is scaled so that nm/Z_eff is near to unity so that the Bohr radius is near to that for hydrogen atom. Z_eff is naturally the charge unscreened by the closed electron shells and equal to the number Z_eff=n_V of valence electrons. This conforms with the periodicity of the periodic table. Since the value of n is same for both bonded atoms, the value of Bohr radii differ which implies that electronic charge is shifted towards the atom with larger n_V and electro-negativities of atoms parameterizing this behavior are different for the atoms of the bond. This conforms qualitatively with the valence bond theory.
   

   For n>n_min one would have a_B∝ (n²/n_min)²m²/Z_eff², and if nm/(n_minZ_eff) is constant in reasonable approximation, the estimate for bond length does not depend much on Z. Could the weak variation of bond lengths be a direct indication that the reduction of molecular physics to atomic physics fails? Also the size of atoms in lattice about 2a_B(H) (one Angström) depends only weakly on Z_eff: could the constancy of nm/(n_minZ_eff) be true in reasonable approximation also for lattice bonds?
   
   

2. The predicted lengths of valence bonds should be realistic: this forces n>n_H and n∝ Z_eff is a rough guess. One should also understand the values of electro-negativities χ(X) allowing quantitative understanding about the distribution of charge along the bond. The bond lengths assignable to the bonded atoms are in general different and the one one with shorter bond length for electrons is expected to be more electronegative since the electrons for it are less de-localized.
   
   

See the article Mysteriously disappearing valence electrons of rare Earth metals and hierarchy of Planck constants or the chapter Quantum criticality and dark matter of "Hyper-finite factors, p-adic length scale hypothesis, and dark matter hierarchy".

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

Articles and other material related to TGD.

Does instability of Einstein's equations explain accelerated expansion?

The article Doing without dark energy: Mathematicians propose alternative explanation for cosmic acceleration (thanks for link to Steven Crowley) makes a very interesting claim. The instability of Einstein's equations requires accelerated expansion usually assumed to be due to a small value of cosmological constant. I understood that the instability of Einstein' cosmological solutions around cosmological solutions is however not proven.

What is remarkable that the exact analog of this instability occurs in TGD.

1. I believed for a long time that Kähler action alone determines the dynamics. The special feature of Kähler action was its huge vacuum degeneracy, which I interpreted in terms of 4-D spin glass nature of theory and did not regard it as a problem. This instability however destroyed all hopes about path integral approach to the quantum TGD and led to the notion of "world of classical worlds". It became soon clear that it really works and leads to a beautiful physical interpretation. Mistakes sometimes force to see a really big problem and even solve it!
   

   In particular, for the canonically imbedded empty Minkowski space, which should give rise to an analog of massless field theory, the field equations give 0=0! The propagator defined by the kinetic term vanishes identically. The situation if of course mathematically very singular and the interpretation is as instability since the infinite-D matrix defined by the second order functional derivatives has not only some vanishing eigenvalues but vanishes identically. One expects a hierarchy of singularities with increasing number of non-vanishing eigenvalues.
   
   

2. Few years ago my views changed as I started to think about twistorialization of TGD at the level of space-time dynamics. The basic idea is simple: in TGD framework particles are massless in 8-D sense but can be massive in 4-D sense. 8-D twistorialization could solve the basic problem of ordinary twistorialization due to massive particles.
   

   Twistor lift of space-time surfaces is needed. This requires the introduction of 6-D twistor space of space-time surface as a dynamical entity: a sphere bundle of space-time surface receiving twistor structure by induction from the product of twistor spaces for M⁴ and CP₂.
   

   What puts bells ringing is that M⁴ and CP₂ are the unique 4-D manifolds with twistor space possessing Kähler structure. This makes possible the generalization of Kähler action to its 6-D variant in the 12-D twistor space of M⁴×CP₂. The existence of twistor lift of TGD would lead to standard model symmetries and fix TGD completely!
   

   The allowed solutions of field equations/preferred externals should be twistor spaces of spacetime surfaces. The natural guess is that they are also extremals of 6-D Kähler action, which is a generalization of Maxwell action. Dimensional reduction for 6-D Kähler action to sum of Kähler action and volume term serving as analog of cosmological term is proposed to determine the 6-D preferred extremals, which should correspond to 6-D twistor spaces of 4-D space-time surfaces (sphere bundles with space-time surface as base space). It however seems that cosmological term at GRT limit of TGD corresponds to the sum of Kähler action and volume term rather than only volume term: here I must be however cautious.
   

   Twistor space property for 6-surface should determine the dynamics completely. This generalizes Penrose's approach reducing Maxwell's equations to holomorphy. A generalization of the approach of Penrose from gauge fields to induced gauge fields would be in question.
   
   

Preferred extremals for Kähler action plus volume term come in two classes.

1. Minimal surface solutions for which field equations reduce to holomorphy conditions. One has minimal surfaces and the equations for Kähler action and volume term are separately satisfied and reduce to holomorphy conditions. These solutions are analogs of light-like geodesic lines: massless particles but in 8-D sense allowing massive particles in 4-D sense so that the basic problem of ordinary twistor approach is solved.
   
   
2. Second type of solution corresponds to an analog for the motion of massless particle in Abelian gauge field, which is however internally determined and vanishes in equiibrium situations: that is for external particles entering causal diamond. Physically these solutions describe interaction regions and minimal surfaces to external particles with interactions coupled off.
   
   

The addition of volume term solves the instability/degeneracy problem and the analog of volume term is indeed cosmological constant term in GRT! The spin glass degeneracy could quite well remain as approximate property since the cosmological constant in recent cosmology is extremely small and just takes care that the degeneracy disappears. At the limit of infinitely long p-adic length scale cosmological constant vanishes and one has vacuum degeneracy. The reason is that cosmological constant depends on p-adic length scale going like 1/p-adic length scale squared propto 1/p. This predicts that cosmological constant evolves and approaches its maximal and very large value in the early Universe. Its value is not "un-natural" anymore. One should however be critical and check for whether two strong assumptions are made. Everything is guesswork after all.

1. The preferred extremals in the interaction regions correspond at the level of M⁸ (recall M⁸-H duality) to space-time surfaces, which are not associative/quantum critical (having quaternionic (associative) tangent or normal space) so that they cannot be mapped to surfaces in M⁴ ×CP₂ (requires quaternionicity of tangent space). It is however enough to do this only for external particles which are associative surfaces and correspond to quantum criticality. Kähler action +volume term take care of the time evolution inside CDs once 3-surfaces at boundaries of CD are known.
   
   
2. For minimal surfaces defining external particles dynamics is determined by holomorphy and holomorphy is the key feature of twistorialization. Could it be that twistor bundle property for the 6-D sphere bundle is true only for external particles? This would correspond to associativity of external particles at the level of M⁸. Could it be that twistor space property (characterizing also for standard twistors free gauge fields) fails in interaction regions - CDs - and is true only for external particles? Just asking;-).
   
   

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

Articles and other material related to TGD.

DMT: connector to God or bio-chemical waste?

In FB I got a link to a very interesting article about DMT. DMT is psychedelic or hallucinogen - depending on one's attitudes. DMT is used for spiritual and healing purposes in many cultures. The effect is short-lasting: from 5 to 15 minutes. DMT induces mystical experiences, euphoria, dynamical geometric hallucinations of geometric forms, experiences about meeting of higher intelligences, extraterrestrials, elves, and even God.

First some facts about DMT.

1. DMT is found in both plants and animals and is the only naturally occurring psychedelic. Its occurrence in the pineal gland of rodents and therefore also of mammals has been reported.
   
   
2. Chemically DMT is a structural analog of serotonin and melatonin and involves aromatic 6-cycle and 5-cycle with common edge appearing in amino-acid tryptophan. Also DNA nucleotides A and G have this double cycle structure but have however more than one nitrogen atom.
   
   
3. The biosynthesis of DMT from amino-acid L-tryptophan (occurring endogenously in plants but not in animals) has been detected in rabbit's lungs. Whether DMT is produced by brain is still an unsettled question. It has been even argued that DMT is mere waste.
   

   In TGD framework aromatic cycles serve as indication that molecule contains paired valence electrons with the value of h_eff/h=n higher than its standard value: this explains the delocalization of electrons to longer than atomic length scale. n would serve as a kind of intelligence quotient: the larger the value of n is, the larger the maximal value of entanglement negentropy of the system is (understanding of this statement requires going outside the framework of the mathematical framework of standard physics: I call this framework adelic physics).
   

   In this picture the interpretation as a waste does not look sensible and the proposal that DMT is produced by brain or some other parts of body looks more reasonable. Biology does not usually manufacture anything without purpose. Especially so, if the manufacturing process requires metabolic energy. The biosynthesis of DMT from tryptophan does not occur spontaneously and requires N-methyltransferase enzyme as a catalyst. Also the highly non-trivial positive effects of DMT on consciousness suggests that it cannot be waste.
   
   

To understand what the purpose of DMT could be, one must have some idea about sensory perception in TGD Universe (I have already earlier written about DMT and psychedelics, see this).

1. TGD view about sensory perception relies on the idea that sensory qualia are at the level of sensory organs: this view makes sense if one accepts macroscopic quantum coherence (see this). TGD based view about time (zero energy ontology (ZEO)) allow to circumvent basic objections such as phantom leg: pain in phantom leg would be sensory memory of pain and in geometric past when the leg still existed. These sensory memories can be produced by stimulating parietal lobes in any subject person. One also avoids the challenge of explaining why structures consisting of essentially identical neutrons can produce so different sensory qualia.
   
   
2. This model however requires virtual visual feedback from brain realized as dark photons, which leak to ordinary photons identifiable as biophotons with energied in visible and UV range. The presence of virtual visual input could explain why the retina has inverted structure not expected in engineerish thinking.
   

   Sensory percept would be an artwork created by the perceiver. This conforms with the fact that when congenitally blind people receive their vision, they report only seeing of diffuse light. The percept would be a standardized sensory mental images emerging as an outcome of iteration in which dark photons signals travel forth and back and give rise to a pattern recognition by transforming sensory input to standardized input nearest to it.
   
   

3. Dark photon signals would travel along magnetic flux tubes between brain to sensory organs and even between brain and magnetic body (MB) in much longer scales. Flux tubes would gives rise to a connection network analogous to a telephone network. This network would have permanent part and dynamical part consisting of switches allowing to connect two flux tubes to single flux tube by a short bridge. Information molecules such as neurotransmitters, hormones, and messengers could act as switches/bridges: as the information molecule attaches to a receptor, the bridge is formed and signals can propagate.
   

   Also nerve pulses could induce flux tube bridges between neurons of the neuronal pathway by using neurotransmitters and learning as amplification of synaptic connections would be essentially the gradual stabilization of these flux tube bridges. Nerve pulse patterns need not serve as communications inside brain but could only make possible communications in much shorter time scales using dark photons. For 1 meter long axons about million forth and back signals are possible during millisecond.
   

   Nerve pulses would however frequency modulate Josephson radiation from the generalized Josephson junctions defined by membrane proteins serving as ion channels. This modulation would code nerve pulse patterns to signals to MB mediated by EEG: EEG could also have fractally scaled variants corresponding to various layers of MB. This would explain the function of EEG.
   
   

4. Virtual sensory input need not always end up down to the sensory organs: there would be some kind of blocking stopping the virtual sensory input to higher level so that one would have only almost sensory percept: an imagined sensory experience. The virtual sensory input associated with imagination could proceed along different route than that associated with the buildup of percept. Also imagined motor actions would be halted motor actions. During REM sleep the blocking would not be present and the virtual sensory input would enter to sensory organs, in particular retina.
   
   
5. Pineal gland represents a kind of photoreceptor, "third eye", which still serves as eye in some animals. Could the dark photons involved with imagination be received in pineal gland. Could they continue to travel to sensory organs during dreams and hallucinations? Pineal gland would be an organ of imagination besides serving as seat of soul! What is nice from the point of view of biological economy is that pineal gland would not be useless evolutionary remnant but would have found a new function.
   
   

Accepting this schematic view one can ask about the possible function of DMT.

1. DMT molecules could make possible REM dreams by providing the bridges making possible the propagation of dark photons to the retina. Pineal gland would be the natural relay station. Same mechanism could work for other sensory modalities if dark photons mediate the virtual sensory input transformed to ordinary percept at sensory organs. Also hallucinations would rely on this mechanism.
   
   
2. MB has very large layers, there is even evidence that galactic magnetic field is in contact with personal MB (personal MB could have flux tubes inside flux tubes of galactic magnetic field). Since magnetic field in Maxwellian world extends to infinity and since in TGD systems have field identity (field body/MB), one can even image that there are connections to distant civilizations with very weak magnetic field strengths at corresponding flux tubes carrying dark matter.
   

   These connections could make possible a genuine sharing of sensory experiences and the encounters with ETs and alike could be genuine remote meetings! We might have these encounters during sleep quite routinely but would not remember anything since the sensory information would stop at the third eye! Only during dreams situation might change but also now sensory input would be virtual and represent imaginations.
   
   

Remark: I have told many times that I am working intensely and close my eyes lightly, I see a dim flow consisting of points and resembling an incompressible hydrodynamic flow. There are vortices and the flow goes back and forth. The flow lines are mathematically equivalent with field lines of a magnetic field in Maxwell's theory and in TGD with flux tubes of MB in 1-1 correspondence with the points of the flow. Could this be seeing MB with the "third eye"?

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

Articles and other material related to TGD.

LIGO: no gravitational radiation from cosmic strings

LIGO has reported that there is no evidence for so called cosmic strings, which are a basic prediction of GUTs. It is becoming painfully clear that GUTs have led the entire theoretical physics to a wrong track. Regrettably, we have spent for more than four decades at this wrong track now. Also superstring models and M-theory assume GUT as their limit at long length scales so that this finding should finally wake up even the most sleepy colleagues.

As Peter W*it tells in N*t Even Wr*ng (for some reason Lubos wants to write "o":s as "*":s in this context), cosmic strings has been one of so called qualitative predictions of many variants of superstring theory. This is true but since Lubos is one of the few remaining superstring fans, Woit's blog post made him very irritated.

What about TGD? Do I have reasons to get irrirated? Cosmic strings appear also in TGD but are very different objects than those of GUTs. They differ also from those of superstrings theories, where they can appear at the GUT limit or as very long fundamental strings.

Cosmic strings in GUTs and superstring theories

What mainstream cosmic strings are?

1. In GUTs cosmic strings are 1-D defects associated with singular gauge field configurations. There is a phase, which grows by a multiple of 2π as one goes around the defect line. One has essentially vortex line locally. At the singularity the modulus of field variable associated with the phase must vanish.
   

   Here comes in the fundamental difference between gauge fields in GUTs and in TGD where they are induced and QFT limit of TGD does not allow either GUT cosmic strings, GUT monopoles, nor instantons implying strong CP breaking plaguing QCD.
   
   

2. In superstring theories one also has these defects almost unavoidably if one believes that some kind of GUT defines the long length scale limit of superstring theories. Superstring theories also suggests that fundamental strings somehow give rise to very long fundamental cosmic strings: I cannot say anything about the details of the proposed mechanism.
   

The dynamics of string like objects is almost universal.

1. The first parameter is string tension μ predicted by GUTs. There are strong bounds on μ in terms of 1/G. The upper bound μG ≈10^-7 emerges from the fact that cosmic strings have not been found yet. The string tension of TGD cosmic strings satisfies this condition.
   
   
2. Second parameter characterizes the dynamics of string networks and is reconnection probability p for strings. It would be p≈ 10^-1 for strings with topological origin (GUT strings) and p≈ 10^-3 for possibly existing long superstrings. Using these parameters one can build dynamical models and perform numerical simulations. In LIGO article several models are discussed together with their predictions.
   
   

Reconnections lead to a generation of oscillating string loops and these would generate gravitational radiation at harmonics of the frequency, which is essential the inverse of the length of the string. In particular, the kinks and cusps (string moves with light-velocity locally) propagating along these strings would generate gravitational radiation.

1. One expects that kinks and cusps correspond to delta function singularities in energy momentum tensor serving as sources of gravitational radiation. In cusps the determinant of 2-D induced metric vanishes and the energy momentum tensor proportional to 2-D contravariant metric diverges like 1/det(g). This seems to produce a singularity.
   
   
2. Energy momentum tensor serving as the source of gravitational radiation seems to be however only discontinuous at kinks. Naively one might think that the ordinary divergence of energy momentum tensor having delta function singularity tells how much energy momentum goes out from string as gravitational radiation. My guess is that one must add to the action an additional term corresponding to the discontinuity and depending on Christoffel symbols at the discontinuity to describe curvature singularity. This term would serve as a source of gravitational radiation.
   

   This term is essentially the second fundamental form for the imbedding of the singularithy as a 3-surfaces and its trace would define the interaction term just as the naive picture would lead to expect. The interpretation of this term is essentially as the analog of acceleration and accelerating particle indeed creates radiation, in particular gravitational radiation. As a matter fact, this kind of term must be also added in 2-D case to the curvature scalar to get correctly Gauss-Bonnet law for polygons having corners.
   
   

There are two kinds of space-time surfaces in TGD Universe

To discuss the question whether cosmic strings radiate in TGD one must say something general about the dynamics of space-time surfaces in TGD.

There are two kinds of space-time surfaces in TGD Universe. These two kinds fo space-time surfaces appear at the boths sides of M⁸-H duality: here one has H=M⁴× CP₂. In the following I stay at the H-side of the duality.

There is a rather precise analogy with the vision about what happens in particle reactions. External particles decouple from interactions and interactions take place in interaction regions, where interactions are in some sense coupled on. This is realized for the preferred extremals of the action determining space-time surfaces in rather precise sense. The twistor lift of TGD predicts that the action is sum of Kähler action and volume term analogous to cosmological term.

1. The preferred exremals can be minimal surfaces in which case field equations are satisfied separately for Kähler action and volume term: the two interactions effectively decouple. The dynamics reduces to holomorphy conditions and coupling constants disappear completely from it. This corresponds to the universal dynamics of quantum criticality.
   

   The minimal 4-surfaces are direct 4-D analogs of geodesic lines, free particles. Also cosmic strings are surfaces or this kind and presumably also the magneti flux tubes. In Zero Energy Ontology (ZEO) these surfaces represent external particles entering or leaving causal diamond (CD). Free particles do not emit any kind of radiation and this would be indeed realized now.
   
   

2. Inside CDs Kähler action and volume term do not decouple and there is genuine interaction between them. One does not have minimal surfaces anymore and coupling constants appear in the dynamics. In this region the emission of radiation and also of gravitational radiation is possible.
   
   

Cosmic strings in TGD sense

Also TGD predicts what I call cosmic strings.

1. Ideal cosmic strings a la TGD string like objects, space-time surfaces. They are not singular densities of matter in 4-D space-time which would be small deformation of Minkowski metric. Rather, they are 4-D surfaces havng 2-D string world sheets as M⁴ projection. String world sheet and string like object are minimal surfaces and should emit no radiation.
   

   Remark: Since M⁴ projection is not 4-D GRT limit does not make sense for cosmic strings and the GRT based calculation for gravitational radiation does not apply in TGD framework.
   
   

2. Cosmic strings dominate the dynamics in very early universe. In reasonable approximation one could speak about gas of cosmic strings in M⁴- or strictly speaking in M⁴× CP₂. The transition to radiation dominated era is the TGD counterpart for inflationary period: the space-time in GRT sense emerges as space-time sheets having 4-D M⁴ projection. Stringlike objects topologically condense at 4-D space-time sheets. Also their M⁴ projection becomes 4-D and begins to thicken during cosmic evolution so that magnetic field strength starts to weaken.
   

   Cosmic strings can carry Kähler magnetic monopole flux explaining the mysterious long ranged magnetic fields in cosmological scales. Reconnection and formation of closed loops is possible. Many-sheetedness is an important aspect: there are flux tubes within flux tubes.
   

   Cosmic strings/magnetic flux tubes play a key role in the formation of galaxies and larger (and even smaller) structures. Galaxies are along cosmic strings like pearls along necklace: the simplest model assumes that pearls are knots along cosmic strings (note the amusing analogy with DNA having coding regions as nucleosomes along it). Flux tubes and their reconnections play also key role in TGD inspired quantum biology.
   
   

Does TGD survive the findings of LIGO?

The question of the title reduces to the question whether the cosmic strings in TGD sense emit gravitational radiation.

1. If cosmic strings are idealizable as minimal surfaces and therefore as stationary states outside CDs they do not produce any kind of radiation. Radiation and gravitational radiation can emerge only in space-time regions, where there is a coupling between Kähler action and volume term. In particular, the purely internal dynamics of ideal cosmic strings cannot produce gravitational radiation.
   
   
2. One can of course argue that topologically condensed thickened cosmic strings actually interact and ought to be described as something inside CD. In any case, there is a coupling between Kähler degrees of freedom and geometry of string and this means that GRT based model cannot apply. This is of course clear already from the fact that string like objects in TGD sense are hardly describable as a singular mass distribution in slightly curved piece of M⁴.
   

   One can of course ask whether GRT based calculation for the emission of gravitational radiation makes sense for thickened cosmic strings having 4-D M⁴ projection. This requires going to the GRT-QFT limit involving the approximation of the many-sheeted space-time with GRT space-time: this means replacing sheets with single sheet and identifying deviation of the metric from M⁴ metric and gauge potentials with sums of the corresponding induced quantities.
   

   There would be however no emission in the approximation with genuinely 2-D objects and the calculation must involve also other than purely geometric degrees of freedom. There is also the question about whether kinks and cusps are possible for preferred extremals satisfying extremely tight symmetry conditions realizing strong form of holography. If not, they are not expected at QFT limit either.
   
   

See the article Three findings by LIGO or the chapter Quantum Astrophysics of "Physics in Many-Sheeted Space-time".

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

Articles and other material related to TGD.

Model for RNA life

Ulla gave a link to a very interesting paper about the possible mechanism giving life-like properties to RNA system during the conjectured RNA era. The title of the article is "The life story of hydrogen peroxide II: a periodic pH and thermochemical drive for the RNA world. "Life-like" would mean "breathing" realized as these oscillations and would require a metabolic energy source.

I try to interpret the proposal on basis of my own model bringing in the control of chemistry by magnetic body (MB). The idea is that MB adapts to the chemical dynamics and gets a control over it by driving forces realized in terms of dark cyclotron radiation form MB resonating with the chemical oscillations. "Breathing" would basically correspond to the periodic formation of flux tube network with high connectivity giving rise to crystal-like or gel-like state and subsequent decay to plasma-like state with low connectivity and would require metabolic energy feed.

1. The periodic drive is central in TGD based model and gives rise to "breathing". Metabolic energy feed must be involved. In the model for life-like properties of plastic ball system it would be dark nucleosynthesis. In another experimental system acoustic wave feeds energy to the magnetic body (MB). The peroxide (H-O-O-H) bond between oxygens would be the source of the metabolic energy. Peroxide - usually regarded as a mere nuisance (highly Reactive Oxygen Species causing biological damage) - would serve as the "food" of the system. This is the new and radical idea. According to the article the primary energy source would be solar or geothermal. In TGD one can consider dark nucleosynthesis preceding ordinary nucleosynthesis as the source (it might have even given rise to Fe in the core of Earth!).
   
   
2. Figure 1 in the article illustrates that peroxide H₂O₂ would produce in presence of S₂O₃^-2 or S₂O₃^-1 thermal and pH oscillations: "breathing". Peroxide is also told to produce oxidized sulfur species and oxidixe RNA nucleotides: this could also liberate metabolic energy stored in RNA. The outcome would be the replication of RNA. Oxidation of thiosulfate ion by H₂O₂ mentioned in the abstract would naively mean that S₂O₃^-n, n=-1 or -2, gives 1 or 2 electrons to H₂O₂. Table 1 listing various reactions involved in oxidation is however rather complex. It begin to accept that I will never really understand what chemists mean with oxidation! In any case, also the oxidation reaction for S₂O₃^-1 can happen in several steps.
   
   

Consider next the situation from quantum TGD point of view.

1. Periodic oxidation would correspond to breathing generating repeatedly connected magnetic body with quantum coherence and larger h_eff - following the model for breathing plastic ball system as a periodic formation of crystal-like and plasma-like states.
   
   
2. Cyclotron radiation from cyclotron condensates of some important ions would serve as clocks - breathing in several time scales. What are these ions? In plastic ball system protons and Argon ions. 300 Hz is the frequency for B=B_end=.2 Gauss and also the rate of ATP:s produced by ATPase: of course, it was not present at that time. Thiosulfate cyclotron frequency would be 5.4 Hz in B_end for charge of -2 units.
   

   The chemical oscillation periods emerging in the model of authors are measured in fraction of hour whereas the cyclotron periods for ions are fractions of second for ions for B=B_end. Therefore the strength of the magnetic field is much lower than that of Earth. Intergalactic magnetic fields are of order nanoTesla and this would bring scale factor of about 10⁴ to cyclotron periods and they would be of same order of magnitude as the time scales coming from chemical kinetics. For proton the cyclotron period would be 33 seconds. For S₂O₃^-2 cyclotron time scale would be scaled up by the atomic weight 112 giving roughly 40 minutes. This suggests that RNA era occurred in intergalactic space if it occurred at all. If it continues in recent biology, the dark matter must reside at the flux tubes of intergalactic magnetic field. This does not make sense in Maxwell's theory but makes sense in the many-sheeted space-time of TGD Universe.
   
   

3. pH oscillation means that at least dark protons would be involved. pH could be quite generally a direct measure for the density of dark protons. The density of dark protons oscillating periodically meaning formation of cyclotron condensate and its decay could correspond to oscillating pH.
   
   

See the articles Life-like properties observed in a very simple system and About a model for the control of biological body by magnetic body.

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

Articles and other material related to TGD.

Questions inspired by quantum associations

Associations have (or seem to have) different meaning depending on whether one is talking about cognition or mathematics. In mathematics the associations correspond to different bracketings of mathematical expressions involving symbols denoting mathematical objects and operations between them. The meaning of the expression - in the case that it has meaning - depends on the bracketing of the expression. For instance, one has a(b+c)≠ (ab)+c , that is ab+ac≠ ab+c). Note that one can change the order of bracket and operation but not that of bracket and object.

For ordinary product and sum of real numbers one has associativity: a(bc)=(ab)c and a+(b+c) = (a+b)+c. Most algebraic operations such as group product are associative. Associativity of product holds true for reals, complex numbers, and quaternions but not for octonions and this would be fundamental in both classical and quantum TGD.

The building of different associations means different groupings of n objects. This can be done recursively. Divide first the objects to two groups, divide these tow groups to to two groups each, and continue until you jave division of 3 objects to two groups - that is abc divided into (ab)c or a(bc). Numbers 3 and 2 are clearly the magic numbers.

This inspires several speculative questions related to the twistorial construction of scattering amplitudes as associative singlets, the general structure of quantum entanglement, quantum measurement cascade as formation of association, the associative structure of many-sheeted space-time as a kind of linguistic structure, spin glass as a strongly associative system, and even the tendency of social structures to form associations leading from a fully democratic paradise to cliques of cliques of ... .

1. In standard twistor approach 3-gluon amplitude is the fundamental building brick of twistor amplitudes constructed from on-shell-amplitudes with complex momenta recursively. Also in TGD proposal this holds true. This would naturally follow from the fact that associations can be reduced recursively to those of 3 objects. 2- and 3-vertex would correspond to a fundamental associations. The association defined 2-particle pairing (both associated particles having either positive or negative helicities for twistor amplitudes) and 3-vertex would have universal structure although the states would be in general decompose to associations.
   
   
2. Consider first the space-time picture about scattering (see this). CD defines interaction region for scattering amplitudes. External particles entering or leaving CD correspond to associative space-time surfaces in the sense that the tangent space or normal space for these space-time surfaces is associative. This gives rise to M⁸-H correspondence.
   

   These surfaces correspond to zero loci for the imaginary parts (in quaternionic sense) for octonionic polynomial with coefficients, which are real in octonionic sense. The product of ∏_iP_i) of polynomials with same octonion structure satisfying IM(P_i)=0 has also vanishing imaginary part and space-time surface corresponds to a disjoint union of surfaces associated with factors so that these states can be said to be non-interacting.
   

   Neither the choice of quaternion structure nor the choice of the direction of time axis assignable to the octonionic real unit need be same for external particles: if it is the particles correspond to same external particle. This requires that one treats the space of external particles (4-surfaces) as a Cartesian product of of single particle 4-surfaces as in ordinary scattering theory.
   

   Space-time surfaces inside CD are non-associative in the sense that the neither normal nor tangent space is associative: M⁸-M⁴× CP₂ correspondence fails and space-time surfaces inside CD must be constructed by applying boundary conditions defining preferred extremals. Now the real part of RE(∏_iP_i) in quaternionic sense vanishes: there is genuine interaction even when the incoming particles correspond to the same octonion structure since one does not have union of surfaces with vanishing RE(P_i). This follows from s rather trivial observation holding true already for complex numbers: imaginary part of zw vanishes if it vanishes for z and w but this does not hold true for the real part. If octonionic structures are different, the interaction is present irrespective of whether one assumes RE(∏_iP_i)=0 or IM(∏_iP_i)=0. RE(∏_iP_i)=0 is favoured since for IM(∏_iP_i)=0 one would obtain solutions for which IM(P_i)=0 would vanish for the i:th particle: the scattering dynamics would select i:th particle as non-interacting one.
   
   

3. The proposal is that the entire scattering amplitude defined by the zero energy state - is associative, perhaps in the projective sense meaning that the amplitudes related to different associations relate by a phase factor (recall that complexified octonions are considered), which could be even octonionic. This would be achieved by summing over all possible associations.
   
   
4. Quantum classical correspondence (QCC) suggests that in ZEO the zero energy states - that is scattering amplitudes determined by the classically non-associative dynamics inside CD - form a representation for the non-associative product of space-time surfaces defined by the condition RE(∏_iP_i)=0. Could the scattering amplitude be constructed from products of octonion valued single particle amplitudes. This kind of condition would pose strong constraints on the theory. Could the scattering amplitudes associated with different associations be octonionic - may be differing by octonion-valued phase factors - and could only their sum be real in octonionic sense (recall that complexified octonions involving imaginary unit i commuting with the octonionic imaginary units are considered)?
   
   

One can look the situation also from the point of view of positive and negative energy states defining zero energy states as they pairs.

1. The formation of association as subset is like formation of bound state of bound states of ... . Could each external line of zero energy state have the structure of association? Could also the internal entanglement associated with a given external line be characterized in terms of association.
   

   Could the so called monogamy theorem stating that only two-particle entanglement can be maximal correspond to the decomposing of n=3 association to one- and two-particle associations? If quantum entanglement is behind associations in cognitive sense, the cognitive meaning of association could reduce to its mathematical meaning.
   

   An interesting question relates to the notion of identical particle: are the many-particle states of identical particles invariant under associations or do they transform by phase factor under association. Does a generalization of braid statistics make sense?
   
   

2. In ZEO based quantum measurement theory the cascade of quantum measurements proceeds from long to short scales and at each step decomposes a given system to two subsystems. The cascade stops when the reduction of entanglement is impossible: this is the case if the entanglement probabilities belong to an extension of extension of rationals characterizing the extension in question. This cascade is nothing but a formation of an association! Since only the state at the second boundary of CD changes, the natural interpretation is that state function reduction mean a selection of association in 3-D sense.
   
   
3. The division of n objects to groups has also social meaning: all social groups tend to divide into cliques spoiling the dream about full democracy. Only a group with 2 members - Romeo and Julia or Adam and Eve - can be a full democracy in practice. Already in a group of 3 members 2 members tend to form a clique leaving the third member outside. Jules and Catherine, Jim and Catherine, or maybe Jules and Jim! Only a paradise allows a full democracy in which non-associativity holds true. In ZEO it would be realized only at the quantum critical external lines of scattering diagram and quantum criticality means instability. Quantum superposition of all associations could realize this democracy in 4-D sense.
   
   
   

A further perspective is provided by many-sheeted space-time providing classical correlate for quantum dynamics.

1. Many-sheeted space-time means that physical states have a hierarchical structure - just like associations do. Could the formation of association (AB) correspond basically to a formation of flux tube bond between A and B to give AB and serve as space-time correlate for (negentropic) entanglement. Could ((AB)C) would correspond to (AB) and (C) "topologically condensed" to a larger surface. If so, the hierarchical structure of many-sheeted space-time would represent associations and also the basic structures of language.
   
   
2. Spin glass is a system characterized by so called frustrations. Spin glass as a thermodynamical system has a very large number of minima of free energy and one has fractal energy landscape with valleys inside valleys. Typically there is a competition between different pairings (associations) of the basic building bricks of the system.
   

   Could spin glass be describable in terms of associations? The modelling of spin glass leads to the introduction of ultrametric topology characterizing the natural distance function for the free energy landscape. Interestingly, p-adic topologies are ultrametric. In TGD framework I have considered the possibility that space-time is like 4-D spin glass: this idea was originally inspired by the huge vacuum degeneracy of Kähler action. The twistor lift of TGD breaks this degeneracy but 4-D spin glass idea could still be relevant.
   
   

See the article From amplituhedron to associahedron or the chapter Does M⁸-H duality reduce classical TGD to octonionic algebraic geometry? of "Physics as generalized number theory".

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

Articles and other material related to TGD.