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.