Comparing the Berry phase model of super-conductivity with the TGD based model

Hiroyasu Koizumi (see this) has proposed a new theory of superconductivity (SC) based on the notion of Berry phase related with an effective magnetic field assignable to adiabatically evolving systems. The model shares similarities with the TGD inspired view about SC. The article also mentioned anomalies that were new to me. This motivated a fresh look in the TGD inspired model. The outcome was an integration of two separate ideas about supraphases.

1. Space-time surfaces as preferred extremals with CP₂ projection of dimension D=2 or D=3 would naturally correspond to 4-D generalizations of so called Beltrami flows, which are integrable flows defined by the flow lines of the induced K\"ahler field. The existence of a global coordinate z varying along flow lines requires the integrability of the flow. Classical dissipation is absent so that these surfaces are excellent candidates for the space-time correlates of supra flows. The exponential of z gives a phase factor associated with the complex order parameter of a coherent state of Cooper pairs as a counterpart of the Berry phase. K\"ahler magnetic monopole flux defines the TGD counterpart of "novel" magnetic field.
2. The identification of supra phases as dark matter as h_eff>h phases at magnetic flux quanta (tubes and sheets) implies that Cooper pairs correspond to dark fermions associated with the members of flux tube pair, which actually combine to form a closed flux tube. Also single electrons can define supraflow.
3. The Cooper pairs must be created by bosonic oscillator operators constructed from fermionic oscillator operators by bosonization. This is possible only in 1+1-dimensional situations. Thanks to the Beltrami flow the situation is effectively 1+1-dimensional. Bosonization makes it possible to identify SU(2) Kac-Moody algebra, which has an interpretation in the TGD framework.

The assumption that Cooper pairs reside at the magnetic flux quanta solves the 4 problems of standard framework mentioned by Koizumi: high-Tc SCs have two transition temperatures; electron mass m_e instead of its effective mass m_e^* appears in Thomson moment; the reversible phase transition in an external magnetic field inducing a splitting of Cooper pairs does not involve dissipation; why the erratic calculation of the Josephson frequencies in standard model neglecting the chemical potentials gives a correct result?.

The formation of the Cooper pairs appears as a condition stabilizing the space-time sheets carrying dark matter and all preferred extremals could satisfy the conditions guaranteeing integrable flow and existence of a phase factor varying along flow lines. Could supra phases exist in all scales? Could the breaking of supra phases be only due to the finite size of the space-time sheets? Could even hydrodynamic flow involve super-fluidity of some kind - perhaps based on neutrino Cooper pairs as speculated earlier?

See the article Comparing the Berry phase model of super-conductivity with the TGD based model or the chapter with the same title.

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

Articles and other material related to TGD. 


Galois groups and genetic code

Galois groups are realized as number theoretic symmetry groups realized physically in TGD a symmetries of space-time surfaces. Galois confinement as an analog of color confinement is proposed in TGD inspired quantum biology .

Galois groups, in particular simple Galois groups, play a fundamental role in the TGD view of cognition. The TGD based model of the genetic code involves in an essential manner the groups A₅ (icosahedron), which is the smallest non-abelian simple group, and A₄ (tetrahedron). The identification of these groups as Galois groups leads to a more precise view about genetic code. The question  why the genetic code is a fusion of 3 icosahedral codes and of only a  single tetrahedral code  remained however poorly understood. 

  The identification of the symmetry groups  of  the I, O, and T  as Galois groups  makes it possible  to  answer this question. Icosa-tetrahedral tesselation of 3-D hyperbolic space H³, playing centrl role in TGD, can be replaced with its 3-fold covering replacing  I/O/T with the corresponding symmetry group acting as a Galois group.  T has only  only a single Hamiltonian cycle and  its 3-fold covering  behaves effectively as a  single cycle. Octahedral codons can be regarded as icosahedral and tetrahedral codons so they do not contribute to the code.

See the article Galois groups and genetic code.

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

Articles and other material related to TGD.

About the role of Galois groups in TGD framework

The inverse problem of Galois theory is highly interesting from TGD viewpoint. Galois groups are realized as number theoretic symmetry groups realized physically in TGD a symmetries of space-time surfaces. Galois confinement is as analog of color confinement is proposed in TGD inspired quantum biology .

Two instances of the inverse Galois problem, which are especially interesting in TGD, are following:

Q1: Can a given finite group appear as Galois group over Q? The answer is not known.

Q2: Can a given finite group G appear as a Galois group over some EQ? Answer to Q2 is positive as will be found and the extensions for a given G can be explicitly constructed.

The TGD based formulation based on M⁸-H duality in which space-time surface in complexified M⁸ are coded by polynomials with rational coefficients involves the following open question.

Q: Can one allow only polynomials with coefficients in Q or should one allow also coefficients in EQs?

The idea allowing to answer this question is the requirement that TGD adelic physics is able to represent all finite groups as Galois groups of Q or some EQ acting physical symmetry group.

If the answer to Q1 is positive, it is enough to have polynomials with coefficients in Q. It not, then also EQs are needed as coefficient fields for polynomials to get all Galois groups. The first option would be the more elegant one.

The inverse problem is highly interesting from the perspective of TGD. Galois groups, in particular simple Galois groups, play a fundamental role in the TGD view of cognition. The TGD based model of the genetic code involves in an essential manner the groups A₅ (icosahedron), which is the smallest simple and non-commutative group, and A₄ (tetrahedron). The identification of these groups as Galois groups leads to a more precise view about genetic code and answers to a key open question of the model in its recent form.

About the role of Galois groups in TGD framework or the chapter with the same title.

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

Articles and other material related to TGD.

What could 2-D minimal surfaces teach about TGD?

In the TGD Universe space-time surfaces within causal diamonds (CDs) are fundamental objects.

1. M⁸-H duality means that one can interpret the space-time surfaces in two manners: either as an algebraic surface in complexified M⁸ or as minimal surfaces in H=M⁴× CP₂. M⁸-H duality maps these surfaces to each other.
2. Minimal surface property holds true outside the frame spanning minimal surface as 4-D soap film and since also extremal of Kähler action is in question, the surface is analog of complex surface. The frame is fixed at the boundaries of the CD and dynamically generated in its interior. At frame the isometry currents of volume term and Kähler action have infinite divergences which however cancel so that conservation laws coded by field equations are true. The frames serve as seats of non-determinism.
3. At the level of M⁸ the frames correspond to singularities of the space-time surface. The quaternionic normal space is not unique at the points of a d-dimensional singularity and their union defines a surface of CP₂ of dimension d_c=4-D<d defining in H a blow up of dimension d_c.

In this article, the inspiration provided by 2-D minimal surfaces is used to deepen the TGD view about space-time as a minimal surface and also about M⁸-H duality and TGD itself.

1. The properties of 2-D minimal surfaces encourage the inclusion of the phase with a vanishing cosmological constant Λ phase. This forces the extension of the category of real polynomials determining the space-time surface at the level of M⁸ to that of real analytic functions. The interpretation in the framework of consciousness theory would be as a kind of mathematical enlightenment, transcendence also in the mathematical sense.
2. Λ>0 phases associated with real polynomials as approximations of real analytic functions would correspond to a hierarchy of inclusions of hyperfinite-factors of type II₁ realized as physical systems and giving rise to finite cognition based on finite-D extensions of rationals and corresponding extensions of p-adic number fields.
3. The construction of 2-D periodic minimal surfaces inspires a construction of minimal surfaces with a temporal periodicity. For Λ>0 this happens by gluing copies of minimal surface and its mirror image together and for Λ=0 by using a periodic frame.

   A more general engineering construction using different basic pieces fitting together like legos gives rise to a model of logical thinking with thoughts as legos. This also allows an improved understanding of how M⁸-H duality manages to be consistent with the Uncertainty Principle.

4. At the physical level, one gains a deeper understanding of the space-time correlates of particle massivation and of the TGD counterparts of twistor diagrams. Twistor lift predicts M⁴ Kähler action and its Chern-Simons implying CP breaking. This part is necessary in order to have particles with non-vanishing momentum in the Λ=0 phase.

See the article What could 2-D minimal surfaces teach about TGD?.

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

Articles and other material related to TGD. 


Cosmic spinning filaments that are too long

The inspiration for writing this posting came from a highly interesting popular article (see this) providing new information about the cosmic filaments (thanks to Jebin Larosh for the link). The popular article tells about the article published in Nature (see this) and telling about the work of a team led by Noam Libeskind.

1. Findings

What has been studied is a long filament with length of order 10⁸ ly characterizing the sizes of large cosmic voids. The filament consists of galaxies and the surprising finding is that besides moving along the filament, the galaxies associated with the filaments spin around the filament axis.

This finding suggests a network of filaments of length of order 10⁸ ly and thickness of order 10⁶ ly intersecting at nodes formed by large galaxy clusters. The larger the masses at the ends of the filament are, the larger the spin is.

How angular momentum is generated is the problem. The problem is quite general and is shared by both Newtonian and General Relativistic Universes. The natural assumption is that angular momentum vanishes in the original situation. Angular momentum conservation requires a generation of compensating angular momentum. This should happen in the case of all rotating structures. Already the case of galaxies is problematic but if the length scale of the structure is 10⁸ ly, the situation becomes really difficult.

Gravitationally bound states have as a rule angular momentum preventing gravitational collapse but how the angular momentum is generated in a process believed to be a concentration of a homogeneous matter density to astrophysical objects? The basic problem is that the Newtonian description relies on scalar potential so that the field lines of the Newtonian gravitational field are never closed. It is difficult to imagine mechanisms for the generation of angular momentum by rotation. In the GRT based description gravi-magnetic fields, which are rotational, emerge but they are extremely weak. The proposal is that tidal forces could generate angular momentum but the generation of angular momentum remains poorly understood.

2. TGD view about the angular momentum generation

Could one understand the recent finding, and more generally, the generation of angular momentum, in the TGD framework? What raises hope is that in the TGD framework K\"ahler magnetic fields, whose flux tubes can be regarded as space-time quanta, are key players of dynamics in all scales besides gravitation.

2.1 Cosmic strings as carriers of dark matter and energy

The basic difference between GRT and TGD are cosmic strings and flux tubes resulting from their thickening. Cosmic strings are preferred extremals which are space-time surfaces with 2-D string world sheet as M⁴ projection and complex surface of CP₂ as CP₂ projection.

1. The presence of the long filaments is one of the many pieces of support for the fractal web of cosmic strings thickened to flux tubes predicted by TGD. The scale is the scale of large voids 10⁸ ly forming a kind of honeycomb like structure. The density of matter would be fractal in the TGD Universe (see this and this).
2. Long cosmic string has a gravitational potential proportional to 1/\rho, \rho the transverse distance. This predicts a flat velocity spectrum for the stars rotating around the galaxy. No dark matter halo is needed. The model contains only a single parameter, string tension, and also this can be understood in terms of the energy density of the cosmic string. The motion along the string is essentially free motion which allows to distinguish the model from the halo model. In fact, the article reports linear motion along the filament.

   Amusingly, the same day that I learned about the spinning filaments, I learned about a new evidence for the absence of the galactic halo from a popular article (see this) telling about the article by Shen et al (see this).

2.2 Compensating angular moment as angular momentum of dark matter at cosmic string

Consider now the problem of how the compensating angular momentum is generated as visible matter starts to rotate.

In the TGD framework the picture is just the opposite.

1. The basic assumption of the Newtonian and GRT based models for the generation of angular momentum is that all astrophysical objects are formed by a condensation of matter along perturbations of the mass density. The flow of mass occurs from long scales to short scales.
2. Cosmic strings are the basic objects present already in primordial cosmology. Long cosmic strings form tangles along them in a local thickening, which gives rise to flux tubes. This involves the decay of dark energy and matter at cosmic string to ordinary matter around them as the string tension is reduced in a phase transition decreasing the coefficient of the volume term present in the action besides K\"ahler action as predicted by twistor lift of TGD. This parameter corresponds to length scale dependent cosmological constant Λ.

   Λ depends on p-adic length scale L_p∝ p^1/2, p≈eq 2^k and satisfies Λ(k)∝ 1/L²(k)². Λ(k) approaches zero in long p-adic length scales characterizing the transversal size of flux tubes. This solves the cosmological constant problem. The thickness d≈ L(k) of the flux tube, which is rather small, determines the string tension. To L(k) there is associated a long p-adic length scale which is of order size of observed cosmology if d≈ L(k) is of order of 10^-4 meters, which happens to be the size of a large neuron.

3. The phase transitions reducing Λ reduce string tension are analogous to the decay of the inflaton field vacuum energy to ordinary matter. Now inflaton field vacuum energy is replaced with the dark energy and matter associated with the thickening cosmic string. Each phase transition is accompanied by an accelerated expansion. The period known as inflation in stanaard cosmology is the first phase transition of this kind. The recent accelerated expansion would correspond to a particular period of this kind and will eventually slow down.

What could happen in the decay of the energy of a flux tube tangle of a cosmic string to visible matter?

1. The visible matter resulting in the decay of the cosmic string must start to rotate around the cosmic string since otherwise it would fall back to the cosmic string like matter into a blackhole. The cosmic string must somehow generate a spin compensating the angular momentum of the visible matter.
2. One should understand angular momentum conservation. Generation of visible matter with angular momentum is possible only if the dark cosmic string is helical or becomes (increasingly) helical in the phase transitions. The angular momentum would be accompanied by the longitudinal motion along the string: this motion has been observed for the filaments.

   The helical structure could be present from the beginning or be generated during the decay of energy of the cosmic string leading to the local thickenings to flux tube giving rise to galaxies as tangles along a long cosmic string. Also the dark matter and energy at the cosmic string already have angular momentum so that the dark matter that transforms to visible matter would inherit this angular momentum.

   The reported correlation between the masses at the ends of the filament and the spin of the filament could be understood if the masses at the ends are formed from the dark energy and mass of the filament having angular momentum. The amount of spin and mass at the ends would be the larger, the longer the decay process has lasted.

3. The identification of the galaxies as tangles along long cosmic strings explains the flatness of the galactic velocity spectrum. Galaxy rotates and also now the angular momentum conservation is the problem. The simplest solution is that the cosmic string portions between the tangles generate the angular momentum opposite to that of the visible matter.

   This would happen not only for the portions of cosmic string between galaxies but also those between stars in the galactic tangle. Stars would be flux tube spaghettis and the angular momentum of the star would be compensated by the angular momentum associated with the helical cosmic string continuing outside the star and connecting it to other stars.

The illustration of the popular article brings in mind a DNA double strand and inspires a consideration of an alternative, perhaps unnecessarily complex, model.

1. Suppose one has a double helix of cosmic strings, call them Alice and Bob. Two stellar objects can form a gravitationally stable state only if relative rotation is present. This would be true also for a cosmic double strand to prevent gravitational collapse in 2-D sense.
2. Alice could remain a cosmic string and thus dark so that we would not see it. Bob would thicken to a flux tube and produce ordinary matter as galaxies as ordinary matter realized tangles along it. The matter would inherit the angular momentum the dark matter and energy producing it already has. The string tension of Bob would be reduced in this process. Of course, both Alice and Bob could have tangles along them. The experiments however support the view that spin direction is the same along the filament.
3. If the helical pair of cosmic strings is actually a closed loop in which the second strand is a piece of the same string, the motion of matter along strands is automatically in opposite directions and spins are opposite. The rotational motion as a stabilizer of a gravitationally bound state is transformed to a helical motion. The problem is however why only the other strand decays to ordinary matter (in the case of ordinary DNA there is an analogous problem due to the passivity of the second strand).

2.3 Is quantum gravitation in cosmic scales involved?

There is an interesting connection to atomic physics suggesting that quantum effects are associated with gravitationally bound dark matter even in astrophysical scales.

1. The basic problem was that the electron should radiate its energy and fall into the atomic nucleus. The Bohr model of the atom solved the problem and non-radiating stationary states prevented the infrared catastrophe. Also in the gravitational case something similar is expected to happen for gravitational interaction.
2. The Bohr model of solar system, originally introduced by Nottale, relies on the notion of gravitational Planck constant ℏ_gr= GMm/β₀ predicts angular momentum quantization.
3. Angular momentum quantization as multiples of ℏ_gr could occur also for the matter rotating around the cosmic string. In the case of the filament, the mass M could be replaced with the mass of the cosmic string (or possibly several of parallel cosmic strings) and m could correspond to the mass of a galaxy rotating around it. The velocity parameter β₀=v₀/c has a spectrum of values proposed to come as inverse integers.

See the article Cosmic spinning filaments that are too long or the chapter Cosmic string model for the formation of galaxies and stars.

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

Articles and other material related to TGD.

Questions related to coupling constant evolution

There are several open questions related to the hierarchy of Planck constants and p-adic coupling constant evolution in the TGD framework.

1. p-Adic length scale (PLS) hypothesis states L_p =p^1/2R(CP₂), Is this hypothesis correct in this recent form and can one deduce this hypothesis or its generalization from the basic physics of TGD defined by Kähler function of the "world of classical worlds" (WCW)? The fact, that the scaling of the roots of polynomial does not affect the algebraic properties of the extension forcesn to conlude that p-adic prime does not depend on purely algebraic properties of EQ. In particular, the proposed identification of p as a ramified prime of EQ must be given up.

   Number theoretical universality suggests the formula exp(Δ K)= pⁿ, where Δ K is the contribution to Kähler function of WCW for a given space-time surface inside causal diamond (CD).

2. The understanding of p-adic length scale evolution is also a problem. The "dark" coupling constant evolution would be α_K = g_K²/2h_eff = g_K²/2nh₀, and the PLS evolution g_K²(k)=g_K²(max)/k should define independent evolutions since scalings commute with number theory. The total evolution α_K= α_K(max)/nk would induce also the evolution of other coupling strengths if the coupling strenghts are related to α_K by Möbius transformation as suggested.
3. The formula h_eff=nh₀ involves the minimal value h₀. How could one determine it? p-Adic mass calculations for h_eff=h lead to the conclusion that the CP₂ scale R is roughly 10^7.5 times longer than Planck length l_P. Classical argument however suggests R\simeq l_P. If one assumes h_eff=h₀ in the p-adic mass calculations, this is indeed the case for h/h₀=(R/l_P)². This ratio follows from number theoretic arguments as h/h₀= n₀= (7!)². This gives \alpha_K=n₀/kn, and perturbation theory can converge even for n=1 for sufficiently long p-adic length scales. Gauge coupling strengths are predicted to be practically zero at gravitational flux tubes so that only gravitational interaction is effectively present. This conforms with the view about dark matter.
4. Nottale hypothesis predicts gravitational Planck constant ℏ_gr= GMm/β₀ (β₀=v₀/c is velocity parameter), which has gigantic values. Gravitational fine structure constant is given by α_gr= β₀/4π. Kepler's law β²=GM/r=r_S/2r suggests length scale evolution β²=xr_S/2L_N = β²_0,max/N², where x is proportionality constant, which can be fixed.

   Phase transitions changing β₀ are possible at L_N/a_gr=N² and these scales correspond to radii for the gravitational analogs of the Bohr orbits of hydrogen. p-Adic length scale hierarchy is replaced by that for the radii of Bohr orbits. The simplest option is that β₀ obeys a coupling constant evolution induced by α_K.

   This picture conforms with the existing applications and makes it possible to understand the value of β₀ for the solar system, and is consistent with the application to the superfluid fountain effect.

See the article Questions about coupling constant evolution or the chapter with the same title.

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

Articles and other material related to TGD.

Sensory hubs in the brain are shifting although they should not

Sensory hubs (see this ) of sensory cortex responsible for integrated brain function are found to behave in an unexpected manner (see this. According to the textbook wisdom, sensory hubs responsible for sensory percepts should be static structures. Sensory hubers are however drifting in time scale of months. The phenomenon is called representational drift.

Sensory hubs are groups of highly connected neurons believed to be responsible for the integration of sensory experiences. They are present already from childhood and shift during childhood from the primary sensory areas receiving the sensory input from thalamus to the association areas. The connectivity strengthens, especially at frontal areas, from birth to adulthood. Note that also this shifting can be interpreted as a representational drift but in longer scale. Could this kind of evolution of sensory hubs be present also in time scale of months and make the drift necessary?

The findings

The popular article describes some examples of representational drift. The odor specific sensory hubs found by Carl Schoonover and Andrew Fink to drift around the piriform cortex is the first example.

1. It is odor specificity that drifts. Sensory hub is clearly like a moving vortex in a flow - moving self-organization pattern of water flow rather than moving water. The connection structure between neurons essential for the formation of associations as learning is drifting. The drift seems to involve learning, which cannot be induced by the ordinary sensory input. Could there be a "teacher" that provides virtual sensory input? Learning analogous to that encountered in AI comes first in mind.
2. In the case of odor perception studied for mice, daily sniffing slows down the drift. Why would the sensory input slow down or even prevent the virtual learning that seems to be present? Could the real sensory input interfere with the virtual sensory input?
3. Experiments using weak electric shocks to induce conditioning of neurons of the hub, show that the conditioning is preserved in the drift. Is it really neurons that are conditioned at the fundamental level? Could the conditioning takes place at some other, in some sense higher level? Emotions are involved with conditioning. Who is the experiencer of these emotions? Does this higher level entity, kind of Mr. X, teach also the conditioning to the recruited neurons of the drifted sensory hub.

   Interestingly, the analogy with dark matter is noticed by Schoonover and Fink. Maybe they suggestt that something analogous to dark matter might be involved with living matter.

Also other examples are discussed.

1. Hippocampal place cells are mentioned as a second example. Motion of an organism from position A to B is represented by certain place cells of the hippocampus, which are firing during the movement. The locus of firing place cells drifts slowly. Standard neuroscience interpretation would be as an overwriting of memories. Mice moving in a T-shaped maze are mentioned as an example. The neuronal groups in the posterior parietal cortex involved with spatial reasoning are drifting.
2. Representational drift in the visual cortex is slower or not present. Could the slowness and possible absence be due to the more complex and precise organization? Or could it be due to the presence of a continual visual input interfering with the virtual sensory input needed for the drift? However, for the mouse that watched the same movies over many days, the drift took place. Pan-psychist might imagine that the neurons or something else related to the sensory hub got tired or bored while seeing the same movie from day to day and became a poor perceiver so that fresh neurons had to be recruited?

Questions

These findings just describe raise the following questions:

1. How the representational drift is possible? The new neurons must learn associations and become conditioned. Ordinary sensory input cannot take care of this. Is there some kind of virtual sensory input from mysterious Mr. X present, which teaches the conditionings giving rise to specific sensory perceptions?

   How can the conditionings be preserved in the drift? Does this Mr. X also teach the conditionings to the recruited neurons by using virtual sensory input inducing them.

2. Why does the drift occur and what would cause it? Could the neurons of the sensory hub get "bored" and become non-alert perceivers so that new neurons must be recruited? Or could one think that serving as a hub neuron or its MB is hard work and also neurons or their MBs must have "vacation" and rest.
3. Why sensory input slows down the drift? Does it interfere with or prevent the learning process of the recruited neurons?
4. Could the analogy of drifting sensory hub with a moving vortex, self-organization pattern of flow, serve as a guideline? Note that incompressible hydrodynamical flow is mathematically highly analogous to a magnetic field. Could one see neurons as particles of an analog of hydrodynamic flow or perhaps its counterpart at the level of magnetic field?

These purposefully leading questions should make it easy for any-one familiar with the TGD based view about neuroscience to guess the TGD inspired model for the representational drift. Before introducing the model, some basic ideas about the brain in the TGD Universe are discussed.

TGD view about sensory perception and emotions

The representational drift provides a new challenge for the standard dogma that sensory qualia are somehow constructed at neuronal level in the brain. There is also the problem that the neuronal stuff looks the same in all sensory areas: how could this give rise to so different sensory qualia.

Magnetic body (MB) defines the basic notion.

1. Magnetic body (MB) carrying h_eff=g×h₀ behaving like dark matter has IQ characterized by n, which is identifiable as a measure of complexity of an n-D extension of rationals associated with the polynomial defining a region of space-time surface assignable to MB. n characterizes also the scale of quantum coherence at MB and this quantum coherence induces the ordinary (non-quantal)vcoherence of biomatter. By its higher IQ MB serves as a boss for layers of MB with smaller IQ and at the bottom of hierarchy is the ordinary matter with h_eff=h.

   MB has both "small" parts with size scale of brain structure and "large" parts having size scale even larger than scale of Earth which corresponds to EEG frequencies around alpha band. Also highly neuron groups have both small MB and larger part of MB. Small MB would have flux tubes parallel to axons and these flux tubes could induce the self-organization leading to the formation of axons and synaptic contacts.

2. The primary sensory qualia are at the level of sensory organs and the brain builds only cognitive representations (also secondary sensory representations not directly conscious to us are possible) and pattern recognition by receiving the input from the sensory organs and providing feedback as a virtual sensory input to sensory organs (see this). REM dreams and hallucinations are a good example of an sensory experience due to mere virtual sensory input. Also imagination can be understood. The picture generalizes to the level of motor actions.

   Phantom limb serves as an obvious objection: if the sensation is sensory memory this objection can be circumvented. Sensory memories can be produced by electrical stimulation of temporal lobes artificially.

3. In the TGD framework the sensory data are communicated to MB by EEG and its fractally scaled variants, where the fundamental representations reside. Neurons are analogous to RAM memory which is organized at the MB. The selection of neurons responsible for the construction of the sensory perceptions as kinds of artworks and for the communication of data to MB can be dynamical.

   There is indeed evidence that neurons in the brain obey an effective hyperbolic geometric determined statistically (see this). Neurons functionally close to each other are near to each other in this geometry. Their images at MB would indeed be near to each other and this geometry would be hyperbolic as a geometry of hyperboloid of Minkowski space. One weird finding conforming with this picture is that salamander survives in a process reshuffling of its neurons.

4. Sensory perceptions correspond to standardized mental images created bu a combination of a real sensory input communicated to MB and inducing as a response virtual sensory input from MB via brain to sensory organs as dark photons signals.

The TGD inspired model model for representational drift

1. Sensory hub is a higher level structure having MB controlling it. It is MB that experiences emotions as higher level sensory experiences by entangling with sensory organs and receiving sensory input also as dark photon signals. The highly connected flux tube structure of MB induces the neuronal connections of the sensory hub. Structural hubs are present from birth.
2. Either the small MB or its big brother would control the sensory hub by sending control signals and virtual sensory input. MB could even teach neuronal groups various associations and conditionings. This would be somewhat like teaching of a neural network in AI.
3. Emotions are associated with conditionings and they would represent higher level sensory perceptions of MB and be essential for the conditioning. The "big" part of MB would be responsible for higher level emotions and "small" part for more primitive emotions like hunger and first essential for conditioning of neurons.
4. The fact that sensory hubs are present already in childhood suggests that standardized sensory mental images could be genetically determined and therefore inherited. One can wonder whether this could relate to the inheritance of long term moods. Could also moods and emotional patterns be genetically coded and also inherited to some degree?

   The TGD based model for the genetic code indeed leads to this picture. The key element of ZEO is that not only structures but also temporal patterns (functions, behaviors) are inherited.

5. Representational drift requires that the connection structure for the neurons of a new hub is recreated by learning. Ordinary sensory input cannot generate the hubs with standardized sensory mental images at neuronal level.

   Does MB as a boss teach standardized mental to neurons by using virtual sensory input just at it would do to induce standardized mental images? This would be analogous to teaching in associative learning and in AI.

6. Why does the drift occur? Why would MB recruit new neurons and teach them to produce standardized mental images?

   Does something happen to the neurons of the hub. Do they get bored or tired and lose their alertness after experiencing the same mental images again and again? The notion of aging is a universal phenomenon in TGD view about life and consciousness (see this): could the the neurons of the sensory hub begin to suffer from problems caused by aging?

   The sensory hubs shift from primary areas to the associative cortex during childhood and their connectivity increases. Could this mean some kind of personal evolution at the level of the sensory hub, analogous to professional at the level of human society.

To sum up, MB might be doing for the brain the same as we are now doing for robots, that is teaching them. Could our AI technology be an externalization of what MB is doing for the biological body?

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

Articles and other material related to TGD.

Some questions concerning zero energy ontology

The article Some comments related to Zero Energy Ontology (ZEO) written for few years ago challenged the basic assumptions of ZEO. One tends to forget the unpleasant questions but now it was clear that it is better to face the fear that there might be something badly wrong. ZEO however survived and several ad hoc assumptions were eliminated.

Progress at the level of basic TGD

The basic goal is to improve the understanding about quantum-classical correspondence. The dynamics of soap films serves as an intuitive starting point.

1. In TGD frame 3-surfaces at the boundaries of CD define the analog of frame for a 4-D soap film as a minimal surface outside frame. This minimal surface would be an analog of a holomorphic minimal surface and simultaneous exremal of Kähler action except at the frame where one would have delta function singularities analogous to sources for massless d'Alembert equation.
2. There is also a dynamically generated part of the frame since the action contains also Kähler action. The dynamically generated parts of the frame would mean a failure of mimimal surface property at frame and also the failure of complete determinism localized at these frames.
3. At frame only the equations for the entire action containing both volume term and Kähler term would be satisfied. This guarantees conservation laws and gives very strong constraints to what can happen at frames.

   The frame portions with various dimensions are analogous to the singularities of analytic functions at which the analyticity fails: cuts and poles are replaced with 3-, 2-, and 1-D singularities acting effectively as sources for volume term or equvavelently Kähler term. The sum of volume and Kähler singularities vanish by field equations. This gives rise to the interaction between volume and Kähler term at the loci of non-determinism.

4. H-picture suggests that the frames as singularities correspond to 1-D core for the deformations of CP₂ type extremals with light-like geodesic as M⁴ projection, at partonic 2-surfaces and string world sheets, and at 3-D t=t_n balls of CD as "very special moments in the life of self" which integrate to an analog of catastrophe.

   Deformations of Euclidian CP₂ type extremals, the light-like 3-surfaces as partonic orbits at which the signature of the induced metric changes, string world sheets, and partonic 2-surfaces at r=t_n balls taking the role of vertices give rise to an analog of Feynman (or twistor -) diagram. The external particles arriving the vertex correspond to different roots of the polynomial in M⁸ picture co-inciding at the vertex.

The proposed picture at the level of H=M⁴ × CP₂ has dual at the level of (complexified) M⁸ identifiable as complexified octonions. The parts of frame correspond to loci at which the space-time as a covering space with sheet defined by the roots of a polynomial becomes degenerate, i.e. touch each other.

There is a nice analogy with the catastrophe theory of Thom. The catastrophe graph for cusp catastrophe serves as an intuitive guide line. Imbedding space coordinates serve as behaviour variables and space-time coordinates as control variables. One obtains a decomposition of space-time surface to regions of various dimension characterized by the degeneracy of the root.

Progress in the understanding of TGD inspired theory of consciousness

The improved view about ZEO makes it possible to define the basic notions like self, sub-self, BSFR and SSFR at the level of WCW. Also the WCW correlates for various aspects of consciousness like attention, volition, memory, memory recall, anticipation are proposed. Attention is the basic process: attention creates sub-CD and subself by a localization in WCW and projects WCW spinor field to a subset of WCW. This process is completely analogous to position measurement at the level of H. At the level of M⁸ it is analogous to momentum measurement.

One can distinguish between the Boolean aspects of cognition assignable to WCW spinors as fermionic Fock states (WCW spinor field restricted to given 3-surface). Fermionic consciousness is present even in absence of non-determinism. The non-determinism makes possible sensory perceptions and spatial consciousness.

A precise definition of sub-CD as a correlate of perceptive field at WCW level implies that the space-time surfaces associated with sub-CDs continue outside it. This gives powerful boundary conditions on the dynamics. For the largest CD in the hierarchy of CDs of a given self, this constraint is absent, and it is a God-like entity in ZEO. This leads to a connection between the western and eastern views about consciousness.

A connection with the minimal surface dynamics emerges. The sub-CDs to which mental image as subselves are assigned would be naturally associated with portions of dynamically generated frames as loci of non-determinism. If one identifies partonic 2-surfaces as vertices, one can interpret the collection of possible space-time surfaces for a fixed 3-surface at PB as a tree. All paths along the tree are possible time-evolutions of subself. The dynamics of consciousness for fixed 3-surface at PB becomes discrete and provides discrete correlate for a volitional action as selection of a path or a subset of paths in the tree. The reduction of dynamics of mental imagines to discrete dynamics would mean a huge simplification and conforms with the discreteness of cognitive representations.

Challenges

There are many challenges to be faced. The discreteness dynamics of sub-self consciousness certainly correlates with the notion of cognitive representation based on adelic physics and implying a discretization at both space-time level and WCW level. The Galois group for the extension of rationals acting on the roots of the polynomial plays a key role in this dynamics.

One teaser question remains. Localization requires energy quite generally and this conforms with the fact that mental images demand metabolic energy feed. It is possible to redirect attention and remain unclear whether the mental image disappears totally or suffers BSFR.

See the article Some questions concerning zero energy ontology.

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

Articles and other material related to TGD.

Water oxidation and photosynthesis in TGD framework

Water oxidation in which water splits into 4 electrons, 4 protons and oxygen molecule O₂ is the first step of photosynthesis.  The catalytic mechanism behind water oxidation remains rather  poorly understood. The total binding energy of H₂O is about 75 eV and the catalyst should  provide this energy to temporarily overcome this barrier. Zero energy ontology (ZEO), which is behind the TGD based quantum measurement theory,   predicts that "big" (ordinary) state function reductions (BSFRs) involve time reversal. The time reversal of water oxidation occurs spontaneously in a  reversed time direction and second BSFR establishing the original arrow of time  makes it possible  to achieve water oxidation.  This mechanism involving two BSFRs applies quite generally to  catalysis.

 The  function of the  catalyst is to make possible the BSFR and the natural expectation is that the description of catalysis as a process with apparently standard arrow of time is possible.  The reduction of the value of $h_{eff}$ for cyclotron states of dark  particles at magnetic flux tube liberates energy assignable to cyclotron states of dark particles and could kick the reactants over the potential wall making the reaction extremely slow otherwise.

See the article Water oxidation and photosynthesis in TGD framework or the chapter Quantum criticality in TGD Universe: part III

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

Articles and other material related to TGD.

Chemistry revolution

Thanks for Moore Thaung for a very interesting article of new chemistry. Unfortunately, a subscription to New Scientist is required. One can however find in the web several popular articles telling about the changing views of chemical bonds.

This weird chemical bond acts like a mash-up of hydrogen and covalent bonds tells about hybrids of hydrogen and and covalent bonds. For short bond lengths these bonds become strong valence bonds and for long bond lengths weak hydrogen bonds which can even have length of 3 Angstrom.

Strange bonds entirely new to chemists predicted in ammonia hydrides tells that ammonium NH₃ can form in the presence of hydrogen in very high pressure an exotic compound NH₇, which can decay to NH₄⁺ + H₂+ H. NH₄⁺ is also exotic.

Sticking together: Another look at chemical bonds and bonding discusses the theory of chemical bonds proposed by Prof. David Brown, which has turned out to be very successful. His article Another look at bonds and bonding is published in Structural Chemistry 31(1), 2019.

The bond theory of David Brown

The bond theory of David Brown is of special interest.

1. The theory involves the notion of electric flux as a purely classical element. The delocalization of valence electrons is of course a non-classical element and one can argue that this aspect is not well-understood in standard chemistry.

   In the TGD framework, the counterpart of electric flux is a flux tube carrying magnetic flux, which can be monopole flux. Thetube can also carry an electric flux and a simple modification of purely magneticflux tubes gives tubes carrying also an electric flux.

2. The key concept besides the notions of valence defined as the number N_v of valence electrons belonging to bonds, and the number of valence bonds N_b, is valence strength defined as N_v/N_b. The total electric flux is the sum of fluxes assignable to the bonds and equals to the total electric charge -N_ve of valence electrons.

   By flux conservation, the electric fluxes at the ends of a given bond are opposite and this gives a strong constraint on the model. This condition is new from the point of standard bond theory and is purely classical.

3. The configurations with minimum energy are expected to be symmetric. In this case, the electric fluxes for the bonds are expected to be identical and proportional to the common bond strength.
   1. An important implication of flux conservation in the symmetric case is that the valence strengths must be the same for bonded atoms. This condition excludes a large number of candidates.
   2. If N_b is larger than N_v the flux is fractional. This would represent an exotic situation. An interesting question, is whether the flux could correspond to a quark pair or two quark pairs possible in TGD framework in long scales: in this case the flux would be 1/3:rd or 2/3:rd of the flux associated with a single valence electron.
4. The model works for many kinds of bonds, and is claimed to work even for hydrogen bonds, and can be used to predict possible bonding structures. What is remarkable, that the notion of conserved electric flux assignable to chemical bonds resonates with the TGD view that non-trivial space-time topology behind the notion of flux tube is directly visible at the level of chemistry.

TGD view about chemical bonds

I remember the time when I realized that TGD suggests a description of the chemical bond in terms of the space-time topology. Could chemistry books be wrong, was the question, which I barely dared to articulate.

Gradually I learned that chemistry books do not really allow any deeper understanding of chemical bonds. One just says that they follow from Schodinger equation but computational complexity prevents proving this.

TGD indeed implies a revolution in chemistry. Some chemical bonds are accompanied by flux tubes carrying dark particles with effective Planck constant h_eff>h=6h₀. Valence electrons of the less electronegative atom would get to the flux tube and become dark. This leads to a model of valence bonds and the value of h_eff/h₀= n increases as one moves to the right along the row of the periodic table. This implies delocalization of the valence electrons to longer scale scaling like h_eff² for the Bohr model and this is essential for the delocalization. This delocalization would be essential for chemistry of valence bonds and for biochemistry in particular.

The article also mentions bonds without electrons. Hydrogen bond is of course an example of such: now it would be a proton that becomes dark and has h_eff>h. In water one could have a spectrum of h_eff values with various bond lengths and this would give water its very special properties. Even flux tubes without any particles but creating correlations and correlates of entanglement between atoms involved are possible.

Also h_eff<h bonds are possible. Randell Mills has found evidence for a variant of hydrogenfor which energies are scaled by factor 1/4: this would mean h_eff=h/2.

An interesting possibility is that in the past scaled down atoms with h_eff= h/2 have existed. Could they correspond to most of the dark matter, the primordial dark matter? The strange disappearance ofthe valence electrons of some transition metals in heating has been also known for decades: heating would provide the energy needed to increase h_e<>ff for valence electrons so that they become dark relative to us?

In biology metabolic energy would be used to increase h_eff, which serves as a kind of universal IQ as a measure of algebraic complexity.

For background, see this, this, and this .

For the topics discussed, see the article Revolution in chemistry.

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

Articles and other material related to TGD.

Has AI hit a dead end?

95 per cent of brain activity has been found to be fluctuations seemingly unrelated to conscious activities involving sensory perception, motor actions and cognition. In the neuroscience framework they are interpreted as noise. Since fluctuations are poison for deterministic computation, the finding poses a serious problem for model of the brain as a deterministic classical computer.

In this article the TGD based interpretation of the long range fluctuations as quantum fluctuations characterized by the value of the effective Planck constant h_eff=nh₀ labelling the phases of ordinary matter identified as dark matter and residing at magnetic body (MB) of the system is discussed. n has number theoretic interpretation and can be regarded as a universal IQ so that fluctuations are a prerequisite for intelligence. According to the TGD based view about neuroscience primary sensory percepts reside at the sensory organs which requires back and forth communications between brain and sensory organs to build sensory perceptions as standardized mental images. These communications must be fast and the proposal is that they use dark photon signals.

In this view nerve pulses do not represent signals inside the brain but act as neural relays at synaptic junctions making possible long range dark photon communications inside the brain. Part of the metabolic energy associated with the fluctuations could be used to the building of mental images in the proposed manner. Nerve pulse patterns generate Josephson radiation communicating sensory information to MB and also require metabolic energy. Dark cyclotron radiation from MB represents control signals to the brain. In both cases, long range fluctuations at brain level are involved.

See the article Has AI hit a dead end? or the chapter Artificial Intelligence, Natural Intelligence, and TGD

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

Articles and other material related to TGD.

Updated version of Expanding Earth Model

I wrote an updated version of the Expanding Earth Model (EEM)based on the assumption that during the Cambrian Explosion (CE) for about .5 billion years ago, the radius of Earth increased by factor 2.

The recent findings demonstrating that the Earth's mantle contains water and even pockets of fluid water plus a detailed discussion of various objections against EEM lead to an updated version of the model. The new key element is that the value of h_eff was h_eff=3h₀=h/2 at the atomic level before CE for Earth. Earth consisted of matter which would be dark relative to us. In CE the transition h_eff=3h₀=6h₀= h took place and induced scaling by a factor 2. This transition also initiated biological evolution.

The finding that Earth was already billions of years ago covered by water suggests that this water had h_eff=h so that it could leak almost freely into the interior of Earth and because of its darkness could have much lower temperature and pressure than the h_eff=h/2 matter around it. Therefore life could evolve in Mother Gaia's womb shielded from cosmic rays and meteoric bombardment.

See the article Updated version of Expanding Earth model or the chapter Expanding Earth Model and Pre-Cambrian Evolution of Continents, Climate, and Life.

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

Articles and other material related to TGD.

A chordate able to regenerate copies of it when dissected into 3 parts

The popular article Polycarpa mytiligera can regrow all of its organs if dissected into three pieces tells about  an extraordinary biological discovery.

The creature known as  Polycarpa mytiligera  is a marine animal commonly found in   Gulf of Eilat that is capable of regenerating its organs. The surprising discovery was that  the animal can regenerate all of its organs even when dissected into three fragments.

Such a high regenerative capacity has not been detected earlier  in a chordate animal that reproduces only by sexual reproduction. In the experiment, the researchers dissected specimens in a method that left part of the body without a nerve center, heart, and part of the digestive system. Not only did each part of the creature survive the dissection on its own, all of the organs regenerated in each of the three sections.

This is highly interesting challenge for TGD.  The information about the  full animal body  was needed for a full generation. How it was preserved in dissection? Was genetic information, as it is understood in standard biology, really enough to achieve  this? 

1.  In TGD inspired quantum biology magnetic body (MB) carrying dark matter as h_eff/h_0=n phases is the  key notion. h_eff is an effective Planck constant defining the scale of quantum coherence. n is dimension of extension of rationals defined by a polynomial defining space-time region,  and serves  as a measure for algebraic complexity and serves as a kind of IQ. MB with high IQ defined by n serves as  the master of the biological body (BB)  controlling it and receiving information from it. The layers of MB also define  abstracted representations of BB. 
2. If BB suffers damage, the information about BB is not lost at MB and  MB, which carries abstracted representations about BB and able to control BB, could  restore BB partially. Healing of wounds would be the basic example.  A more dramatic example about healing was discovered by Peoch:  the neurons of the  salamander brain can be shuffled like cards in a package but the animal recovers. 

   Indeed, since nothing happens to the MB of salamander or Polycarpa Mytilera,  recovery is in principle possible. The  new finding gives additional support for MB as a carrier of the biological information.

One can also make questions about  the recovery process itself. Could recovery be seen as a self-organization process of some kind? 

1. In the TGD framework, quantum measurement theory relies on zero energy ontology (ZEO)  and solves  its  basic problem. The basic prediction is that in the TGD counterparts of ordinary state function reductions ("big" SFRs or BSFRs) time reversal takes place.  In small SFRs (SSFRs) identifiable as analogs of "weak" measurements, the arrow of time is preserved. ZEO  makes it also  possible to understand why the Universe looks classical in all scales although BSFRs occur in all scales at the dark onion-like layers of MB controlling the lower layers with ordinary biomatter at the bottom of the hierarchy.
2.  Time reversed dissipation after BSFR looks like self-organization from the perspective of the outsider with a standard arrow of time, called it briefly O,  and would bea  basic self-organization process in living systems. In dissipation gradients disappear but in time-reversed dissipation they appear from the perspective of O.  
3. This  makes possible also self-organized quantum criticality (SOQC), which is impossible in standard thermodynamics because criticality by definition means instability. The change of the arrow of time changes the situation from the perspective of  O  since the  time reversed  system tends to approach the criticality. Homeostasis would rely  SOQC  rather than on extremely complex  deterministic control programs as in the computerism based picture. Change the arrow of time for a subsystem and let it happen. Very Buddhist approach to healing! 
4. The change of the arrow of time would be also central in the healing processes and also regeneration.
   For a summary of earlier postings see Latest progress in TGD.

   Articles and other material related to TGD.

AI research may have hit a dead end

I found a link to a very interesting article titled "Artificial intelligence research may have hit a dead end" followed by the comment "Misfired" neurons might be a brain feature, not a bug — and that's something AI research can't take into account" (see this).

Also Philip K. Dick's 1968 sci-fi novel, "Do Androids Dream of Electric Sheep?" is mentioned.  Would an intelligent robot  (if it were still a robot) dream?

AI models the brain as a deterministic computer. Computer does not dream:  it does just what  is needed to solve a highly specialized problem (just what a top  specialist does in his job;  computer is the  idol of every professional highflier). 

Computerism assumes  physicalism denying such things as genuine free will but this is not seen as a problem.  Also the mainstream  neuroscientist believes in physicalism. Some computational imperialists   even claim that physics reduces to computerism.

1. Is 95 per cent of brain activity mere noise?

What might be called neuroscience of fluctuations has however  led to a strange conclusion: 95 per cent of brain's activity and therefore metabolic energy seems to be used  to  generate fluctuations,  which in standard neuroscience represents noise.   Neuroscientists have routinely averaged out this "noise" and concentrated on the study of  what can be regarded as  motor actions and sensory input. These contributions seem to represent only ripples in a vast sea of activity.

[Amusingly, junk DNA corresponds to 95 per cent of DNA in the case of humans, as the article observes.]

By the way,  EEG is  still often regarded  as a mere noise. This  represents a similar puzzle: why the brain would use a lot of metabolic energy to send information to outer space: coding of information about contents of consciousness and brain state indeed requires a lot of metabolic energy.   To sum up, the brain seems to be diametrically opposite to a computer in the sense that spontaneous fluctuations are poison for a computer but food for the brain.

What article suggests  is that this 95 per cent could correspond to "dreaming"  that is  imagination. Ability to imagine  would give rise to intelligence rather than the property of being a dead automaton. Dreams would be freely associating cognitive fluctuations - whatever that might mean physically. Interestingly, it is mentioned that newborns dream twice as much as adults: they must learn. One can learn by imaging, not merely by doing all possible mistakes in the real world.

What can one say about these findings in the TGD framework?

2. Could fluctuations be induced by quantum fluctuations in quantum critical Universe of TGD?

Consider first the TGD interpretation of quantum fluctuations.

1.  TGD Universe is  quantal  in all scales. Zero energy ontology (ZEO) allows to overcome the basic objection that the universe looks classical in long scales: ZEO view about quantum jumps forces the Universe to look classical for  the outsider. The experiments of Minev et al indeed demonstrated this concretely.
2. TGD Universe is also quantum critical in all scales. Quantum criticality means that the system is maximally complex  and sensitive  for perturbations. Complexity means that the system is ideal for representing the  external world via sensory inputs. By criticality implying maximal sensitivity it is also an ideal sensory receptor  and motor instrument.
3. The basic characteristic of criticality are long range fluctuations. They are not random noise but highly correlated.  Could the fluctuation in  the brain correspond to quantum fluctuations. 

 Long range quantum fluctuations are not possible for the ordinary value of  Planck constant.  

 
1. Number theoretical view about TGD, generalizing ordinary physics of sensory experience to the physics of both sensory experience and cognition, leads to the prediction that there is infinite hierarchy of phases of ordinary matter  identifiable as dark matter and labelled by the values of effective Planck constant h_eff= nh₀, n is dimension for an extension of rationals defined by a polynomial determining space-time region.
2. The value of n serves as a measure for complexity and therefore defines a kind of IQ. The longer the scale of quantum fluctuations, the higher the value of n, and the larger the h_eff, and the longer the scale of quantum coherence. Fluctuations would make  the brain intelligent. Their  absence would make the brain a complete idiot - an ideal computer.
3. The higher the value of h_eff, the larger the energy of  the particle when other parameters are kept as constant. This means that intelligence requires metabolic energy feed to increase h_eff and keep its values the same, since h_eff tends to be spontaneously reduced.

One can however argue that since the brain consists of ordinary matter,  brain fluctuations cannot be quantal. 

1. In TGD they would be induced by quantum fluctuations at the level of  the magnetic body (MB) having a hierarchical onion-like structure. The dark matter would be ordinary particles with h_eff=nh₀ at MB and since h_eff/h₀ serves as a measure of IQ it would be higher for dark matter than for ordinary biomatter. MB containing dark matter would be the "boss" controlling the biological body (BB).  
2. The quantum coherence of MB would force ordinary coherence of ordinary biomatter as a forced coherence. Ordinary matter would be like soldiers  obeying the  orders and in this manner behaving apparently like a larger coherent unit.

MB would receive sensory input from BB and control it by using EEG realizes as dark photons. This would explain EEG and its probably existing scaled  variants.

3. TGD view about sensory perception, motor actions, and dreaming and imagination

The proposal of the article was that most of the brain activity goes to "dreaming". Dreaming, hallucinations,  and imagination are poorly understood notions in neuroscience.  TGD provides a rather detailed view about these notions.

1. What  distinguishes TGD from neuroscience is that sensory receptors are assumed to serve as carriers of sensory percepts. Zero energy ontology (ZEO)  providing a new view about time and memory makes it possible  to solve the basic objections related to  the phantom limb phenomenon: pain in  the phantom limb would be sensory memory.   
2. 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 a process to allow this and signals propagating with maximal signal velocity are suggestive.
3.  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/h₀=n) transforming to biophotons in an  energy conserving manner. 

   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 could be a 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. 

Returning to the original topic,  the natural question is following: How large fraction  of the 95 percent of brain activity goes to  feedback not present in the brain of the standard neuroscience? This would include  the construction of the feedback to sensory organs as  virtual sensory inputs to build standardized mental images. Dreams are a special case of this. There  is  also the virtual sensory input which does not reach sensory organs and gives rise to imagination, in particular internal speech.

 Similar picture applies to virtual  motor input and the construction of motor output as "standardized motor patterns" - this notion makes sense only in ZEO.  Note that the feedback loop could extend from brain to MB. 

There is also an interesting finding related to motor activities. In the experiments made for rats it is found that the spontaneous brain activity increases dramatically as the rat moves. This brings in mind a lecturer who moves forth and back  as he talks. This rhythmic motion could give rise to a brain/body rhythm  coupling the lecturer to a layer of MB with large h_eff. Its   quantum coherence of MB would induce ordinary coherence of BB in body scale and with large h_eff and raise the "IQ" of the lecture.  Thinking requires motion!

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

Articles and other material related to TGD. 


The notion of holography in TGD framework

Thanks to Bob Tang for the link to Sabine Hossenfelder's article about holography. I will not comment about the content of the link but about TGD view of holography.

What "Universe as a hologram" does really mean must be first defined. In pop physics this notion has remained very loose. In the following I summarize the TGD based view about what holography means in the geometric sense.

In TGD 3-D surfaces are basic objects and replace 3-space. Holography is not a new principle but reduces to general coordinate invariance.

1. "Ordinary" holography

General coordinate invariance in 4-D sense requires that they correspond to single 4-D surface-space-time - at which general coordinate transformations act. Space-time surface is like Bohr orbit, preferred extremal for the action defining the space-time surface.

This is nothing but holography in standard sense and leads to zero energy ontology (ZEO) meaning that quantum states are superpositions of 3-surfaces or equivalently, of 4-D surfaces.

[The alternative to ZEO would be path integral approach, which is mathematically ill-defined and makes no sense in TGD framework due to horrible divergence difficulties.]

ZEO has profound implications for quantum theory itself and solves the measurement problem and also implies that the arrow of time changes in "big" (ordinary) state function reductions as opposed to "small" SFRs ("weak" measurements). Also the question at which length scale quantum behavior transforms to classical, becomes obsolete.

2. Strong form of holography (SH)

Besides space-time-like 3-surfaces at the boundaries of causal diamond CD serving as ends of space-time surface (initial value problem) there are light-like surfaces at which the signatures of the metric changes from Minkowskian to Euclidian (boundary value problem). Euclidian regions correspond to fundamental particles from which elementary particles are made of.

If either space-like or light-like 3-surfaces are assumed to be enough as data for holography (initial value problem is equivalent with boundary value problem), the conclusion is that their interactions as partonic 2-surfaces are enough as data. This would give rise to a strong form of holography, SH.

Intuitive arguments suggest several alternative mathematical realizations for the holography for space-time surfaces in H=M⁴×CP₂. They should be equivalent.

1. Space-time surfaces are extremals of both volume action (minimal surfaces) having interpretation in terms of length scale dependent cosmological constant and of Kähler action. This double extremal property reduces the conditions to purely algebraic ones with no dependence on coupling parameters. This corresponds to the universality of quantum critical dynamics. Space-time surfaces are analogs of complex sub-manifolds of complex imbedding space.
2. Second realization is in terms of analogs of Kac-Moody and Virasoro gauge conditions for a sub-algebra of super-symplectic algebra (SSA) isomorphic with the entire SSA and acting as isometries of the "world of classical worlds" (WCW). SSA has non-negative conformal weights and generalizes Kac-Moody algebras in that there are two variables instead of single complex z coordinate: the complex coordinate z of sphere S²(to which light-one boundary reduces metrically) and light-like radial coordinate r of the light-cone boundary. Also the Kac-Moody type algebra assignable to isometries of H at light-like partonic orbits involve the counterparts of z and r. A huge generalization of symmetries of string theory is in question.

3. Number theoretic holography

M⁸-H duality leads to number theoretic holography, which is even more powerful than SH.

1. In complexified M⁸ - complexified octonions - space-time surface would be "roots" of octonionic polynomials guaranteeing that the normal space of space-time surface is associative/quaternionic. Associativity in this sense would fix the dynamics. These surfaces would be algebraic whereas at the level of H surfaces satisfy partial differential equations reducing to algebraic equations due to the complex surface analogy.
2. M⁸ would be analogous to momentum space and space-time surface in it analogous to Fermi ball. M⁸-H duality would generalize the q-p duality of wave mechanics having no generalization in quantum field theories and string models.
3. M⁸-H duality would map the 4-surfaces in M⁸ to H=M⁴× CP₂. Given region of space-time surface would be determined by the coefficients of a rational polynomial. Number theoretic holography would reduce the data to a finite number rational numbers - or n points of the space-time region (n is the degree of the polynomial). The polynomials would give rise to an evolutionary hierarchy with n as a measure for complexity and having interpretations in terms of effective Planck constant h_eff/h₀=n.

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

Articles and other material related to TGD. 


The rational and intuitive modes of problem solving from the TGD point of view

Reza Rastmanesh sent me a link to an article with title "The Impact of the Mode of Thought in Complex Decisions: Intuitive Decisions are Better". The following musings are inspired by this article.

As one learns from the article, it seems that problem solving and decision making rely on two basic approaches which correspond to right-left brain dichotomy.

1. Rational thinking in the ideal case error free provided the basic assumptions are correct and data are reliable. It is however mechanical and cannot lead to "eurekas". Computers can nowadays do it more reliably than humans. In mathematics Goedel's theorem tells that mere rational deduction is not enough for basic arithmetics: in a given axiomatic system there is an infinite number of non-provable truths.
2. Intuitive approach is less reliable but can be much faster, is holistic, based on affect rather than cold rationality, and can lead to new insights which only afterwards can be deduced but possibly only by adding some new basic assumption. In this case one can speak of a discovery.

What looks paradoxical is that besides induction of affective mood favoring intuitive problem solving, distraction is one way to induce intuitive thought. In TGD framework, the interpretation would be that distraction forces to give up the attempt to solve the problem at the level conscious to me - I am simply too stupid- , and delegates the problem to a higher level of the hierarchy (layers of magnetic body) representing higher level of abstraction (see this) and a more holistic view. This would make it possible to solve the problem.

A real life example about the connection with distraction is in order. In problem solving mood, I find that simple tasks of everyday life become difficult. I decide to do something, start to do this but decide to do also something at the same time, do it, and then realize that I do not remember what I had decided to do primarily, and even that I had decided to do something. I have seriously asked myself whether these are the first signs of dementia. The fact however is that this has been always the case - more or less.

My friends however tell me that there is no reason to worry, I am just what is called "absent minded professor". Perhaps I am indeed just absent minded - or almost permanently distracted - but certainly never a professor if this depends on colleagues.

I have many times experienced in real life that intuitive approach is more reliable than rational thinking when one must make decisions. I still find it difficult to confess that I have been cheated many times but I must do it now. I have felt from the beginning that this is happening but my rational mind has forced myself to believe that this is not the case. I have not wanted to insult the swindlers by somehow suggesting that I am not quite sure about their real motives.

Sleeping over night would be a basic example of this delegation of the problem to a higher intelligence. From personal experience sleeping over night is for me almost the only manner to get new ideas and solve problems which do not reduce to mere mechanical calculations. Often the problem and its solution pop up simultaneously during morning hours and going to the computer makes it possible to write out the details. The attempt to solve a problem by hard thinking later during the day does not lead anywhere.

An example about this relates to my own work. As some new idea has emerged, I have sometimes given it up after some rational thought. Later it has however turned out that the idea made sense after all but for different reasons that I had thought.

A concrete example relates to dark matter idenfied as h_eff=n×h₀≥h phases of ordinary matter at magnetic body in the recent TGD based model.The problem was the following.

Blackman and many others observed at seventies that ELF radiation in EEG range has strange effects on the behavior of vertebrates visible also physiologically. These effects looked quantal. This however does not make sense in standard quantum theory since energies are incredibly small and far below the thermal energies. For this reason mainstream refused to take the effects seriously and it was forgotten.

1. My first proposal was based on the notion of many-sheeted space-time. Perhaps the photons and ions responding to them were at space-time sheets at which the temperature is extremely low so that the thermal objection does not bite.
2. Then I entered a different idea. Perhaps the value of Planck constant varies and one has a very large value h_eff=n×h₀ of the effective Planck constant. n would correspond to the number of identical space-time sheets for the space-time surfaceas a covering space. This led to a nice theory and later I could deduce it from a number theoretic vision unifying real and various p-adic physics to adelic physics describing correlates of both sensory experience and cognition.

As I thought about this during last night, a question popped up. Could this original approach be correct after all? Could the h_eff approach be wrong? This would destroy 15 years of work: horrible! Or could these two approaches be consistent? This turned out to be the case!

1. The temperature at flux tubes and flux quanta of the magnetic body (MB) is in general below Hagedorn temperature T_H dictated by the flux tube thickness: the reason is that the number of geometric degrees of freedom is infinite. Flux tube behaves in good approximation like string and the notion of T_H emerged in string models. For instance, in living matter T_H corresponds to the physiological temperature, around 37 degrees Celsius for humans.
2. T_H is associated with dark matter with h_eff=n×h₀, and n is the number of space-time sheets of the covering. T_H characterizes n-sheeted structure. What is the temperature at a single sheet of covering?
3. Thermal energy is proportional to the temperature. For an n-sheeted structure one has by the additivity of thermal energy for different identical sheets T_H =n×T_H(sheet) implying

   T_H(sheet) =T_H/n.

   For the huge values of h_eff and thus of n, T(sheet)H(sheet) is indeed extremely small! The original explanation is consistent with the number theory based explanation! Trust your intuition! But be however cautious!

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

Articles and other material related to TGD.

Does muon's anomalous anomalous magnetic moment imply new physics?

Lepton universality predicts that the magnetic moments of leptons should be the same apart from the corrections due to different masses. Leptons have besides the magnetic moment predicted by Dirac equation also anomalous magnetic moment which is predicted to come from various radiative corrections.

The standard model predictions for the anomalous magnetic moments of the electron are a_e= (g_e-2)/2= .00115965218091 and a_μ =(g_μ-2)/2= .00116591804.

The anomalous magnetic moments of electron and muon differ by .1 per cent. This breaking of universality is however due to the different masses of electron and muon rather than different interactions.

1. The finding of the Fermilab experiment

The breaking of universality could also come from interactions and the Fermilab experiment (see this) and earlier experiments suggest this. The experiment shows that in the case of muon the magnetic moment differs by from the predicted: the deviation from the standard model prediction is 2.5×10^-4 per cent. This indicates that there might be interactions violating the lepton universality. Besides the problem with the muon's magnetic moment, which differs from that of the electron, there is also a second problem. The decays of B mesons seem to break universality of fermion interactions: indications for the breaking of universality have emerged during years so that this is not new.

The measurement result involves various sources of error and one can estimate the probability that the measurement outcome is due to this kind of random fluctuations. The number of standard deviations tells how far the measurement result is from the maximum of the probability distribution. The deviation is expressed using standard deviation as a unit. Standard deviation is essentially the width of the distribution. For instance, 4 standard deviations tells that the probability that the result is random fluctuation is .6 per cent. For 5 standard deviations from predicted is .0001 per cent and is regarded as the discovery limit.

2. Theoretical uncertainties

There are also theoretical uncertainties related to the calculation of magnetic moment. There are 3 contributions: electroweak, QCD, and hadronic contributions. The electroweak and QCD corrections are "easily" calculable. The hadronic contributions are difficult to estimate since perturbative QCD does not apply at the hadronic energies. There are groups which claim that their estimation of hadronic contributions produces a prediction consistent with the Fermilab finding and the earlier findings consistent with the Fermilab finding.

The prediction based on experimentally deduced R ratio characterizing the rate for the decay of a virtual photon  to  a qquark pair allows to estimate the hadronic contribution and gives a prediction for hadronic contributions which is in conflict with experimental findings. On the other hand, the calculations based on lattice QCD give a result consistent with the experimental value (see this). Should one trust experiment or theory?

3. Is a wider perspective needed?

To my opinion, one should see the problem from a bigger perspective than a question about how accurate the standard model is.

1. Standard Model does not explain fermion families. Also GUTs fail in this respect: the mass ratios of fermions vary in the range spanned by 11 orders of magnitude. This is not a small gauge symmetry breaking but something totally different: mass scale is the appropriate notion and p-adic length scale hypothesis provides it.
2. One must also challenge the belief that lattice QCD can describe low energy hadron physics. There might be much deeper problems than the inability to compute hadronic contributions to g-2. Perturbative QCD describes only high energy interactions and QCD might exist only in the perturbative sense.The fact is that low energy hadron physics is virtually existent. Saying this aloud of course irritates lattice QCD professionals but the reduction of QCD to thermodynamics in the Euclidian space-time looks to me implausible. There are deep problems with Wick rotation.

   For instance, massless dispersion relation E²-p²= 0 in M⁴ translates to E²+p² =0 in E⁴: massless fields disappear completely since one has only E=0,p=0 zero mode. There are similar problems with the massless Dirac equation. For the massive case the situation is not so bad as this. There is the strong CP problem caused by instantons and a problem with multiplication of spinor degrees of freedom since the 4-D cube has the topology of 4-torus and allows 16 spinor structures.

   Quarks explain only a few per cent of hadron mass just as ordinary matter explains only a few percent of mass in cosmology. Hadron physics might therefore involve something totally new and color interaction could differ from a genuine gauge interaction.

   4. What TGD can say about family replication phenomenon?

   In TGD framework, the topological explanation of family replication phenomenon identifying partonic 2-surfaces as fundamental building blocks of elementary particles provides the needed understanding and predicts 3 different fermion generations corresponding to 3 lowest general: sphere, torus, and sphere with two handles (see this).

   Conformal Z₂ symmetry for partonic 2-surfaces is present for the lowest 3 genera but not for the higher ones for which one must talk about many handle states with continuous mass spectrum. p-Adic thermodynamics allows to estimate the masses of new boson by simple scaling arguments and Mersenne prime hypothesis.

   In the TGD framework the two findings can be seen as indications for the failure of lepton universality. Besides 3 light fermion generations TGD also predicts 3 light generations for electroweak bosons, gluons, and Higgs. These generations are more massive than weak bosons and p-adic length scale hypothesis also allows to estimate their masses.

   The couplings of the lightest generations to the gauge bosons obey fermion universality (are identical) but the couplings of the 2 higher generations cannot do so since the charge matrices of 3 generations must be orthogonal to each other. This predicts breaking of fermion universality which in quantum field theory approximation comes from the loops coupling fermions to the 2 higher boson generations.

   This prediction is a test for TGD based topological view about family replication phenomenon in terms of the genus of partonic 2-surface: partonic 2-surface can be sphere, torus or sphere with two handles. TGD also explains why higher generations are experimentally absent.

   5. What does TGD say about low energy hadron physics?

   There is also the question about whether QCD catches all aspects of strong interactions. In TGD color magnetic flux tubes carry Kaehler magnetic energy and volume energy parametrized by length scale dependent cosmological constant so that a connection with cosmology indeed emerges. The reconnections of U-shaped flux tubes give rise to the TGD counterparts of meson exchanges of old-fashioned hadron physics. See this .

   Color group need not be a gauge group but analogous to a Kac-Moody group or Yangian group (only non-negative conformal weights). In TGD framework SU(3) at the level of M⁴xCP₂ is not a gauge symmetry but acts as isometries of CP₂ and fermions do not carry color as analog of spin but as angular momentum like quantum number. At the level of compelexified M₈ SU(3) is a subgroup of G₂ acting as octonion automorphism and defines Yangian replacing the local gauge group.

   For the TGD based model see this and this.

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

   Articles and other material related to TGD.

EEG and the structure of magnetosphere

Roughly 15 years  ago I proposed the idea that Earth's  magnetosphere (MS) could serve as a sensory canvas in the sense that biological systems, in particular the vertebrate brain, could have sensory representations realized at the "personal" magnetic body (MB)  closely associated with the MS of the Earth. EEG would make communications to  and control by MB possible. 

 At that time I did not yet  have  the idea about number theoretical realization of the  hierarchy of Planck constants h_eff=nh₀ in the framework of adelic physics fusing the physics of sensory experience and cognition. This hierarchy is crucial for understanding the basic aspects of living matter such as metabolism, coherence in long scales, correlates of cognition, and even evolution.

Also the concept of zero energy ontology (ZEO) forming now the basis of the quantum TGD was missing although there was already the about communication to past using negative energy signals. ZEO is now in a central role in the understanding of self-organization - not only the biological one. The new view about time predicting that time reversal occurs in ordinary state function reductions (SFRs) allows to understand homeostasis as self-organized quantum criticality. 

For these reasons it is interesting to consider the notion of sensory canvas from the new perspective. This article discusses besides  the earlier ideas about the MS  also the proposal that it is possible to associate EEG bands to the regions of MS via the correspondence between EEG   frequency with the distance of the region from Earth.   Also the idea  that the structure of MS could be a  fractal analog of the vertebrate body is tested quantitatively by comparing various scales involved.

See the article EEG and the structure of magnetosphere or the chapter with the same title.

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

Articles and other material related to TGD . 


Three alternative generalizations of Nottale's hypothesis in TGD framework

Nottale's gravitational Planc constant ℏ_gr= GMm/v₀ contains  the velocity parameter v₀ as the only parameter. In the perturbative expansion  of  the scattering amplitudes β₀=v₀/c appears  in the role of fine structure constant.    

There is however a problem.

1. The model  for the effects of ELF radiation on vertebrate brain  inspired by  a generalization of Nottale's hypothesis by replacing the total mass M in the case of Earth by M_D≈ 10^-4M_E suggests that in this case the dark particles involved couple only to a part of mass identifiable as dark mass M_D.
2.   Since only GM appears in the basic formulas, the  alternative option is that the value of G is reduced to G_D. This conforms with the fact that in the  TGD framework CP₂ length is the fundamental parameter  G is a prediction of the theory and therefore can vary. 
3. A further option is that the parameter β₀=v₀/c≤ 1 is variable and equals to β₀=1 or to a value not much smaller than 1, say β₀=1/2.

These three options are  critically discussed and compared. The cautious conclusion is that the the third option is the most plausible one.

See the article Three alternative generalizations of Nottale's hypothesis in TGD framework or the chapter About the Nottale's formula for h_gr and the relation between Planck length and CP₂ length.

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

Articles and other material related to TGD. 


Does Goedel's incompleteness theorem hold true for reals?

I have many times wondered whether the incompleteness theorem extends to real numbers, which are usually the stuff used by physics. There is a very nice discussion of this point here. Strongly recommended.

Real numbers and all algebraically closed number fields such as complex numbers and algebraic numbers are complete. All truths are provable. If physics is based on complex numbers or algebraic numbers, Goedel's theorem has no direct implications for physics.This however implies that integers cannot be characterized using the axiomatics of these number fields since if this were the case, Gdel's incompleteness theorem would not hold true for integer arithmetics. One can also say that Goedel numbers for unprovable theorems are not expressible as a natural number but are more general reals or complex numbers.

Since algebraic numbers are complete, a good guess is that algebraic numbers label all true statements about integer arithmetics and also about arithmetics of algebraic integers for extensions of rationals.

In TGD adelic physics definescorrelates for cognition. Adeles for the hierarchy labelled by algebraic extensions (perhaps also extensions involving roots of e since e^p is p-adic number). These are not complete and Goedel's incompleteness theorem applies to them. Only at the never achievable limit of algebraic numbers the system becomes complete. This would strongly suggest a generalization of Turing's view about computation by replacing integer arithmetics with a hierarchy of arithmetics of algebraic integers associated with extensions of rationals. See this article .

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

Articles and other material related to TGD.