The first attempt to build a more concrete view about computer consciousness

TGD inspired view about consciousness and quantum biology suggest some guidelines in the attempts to understand how computer systems or computer systems coupled to their users could become conscious.

In biology and from a physicist's point of view, the material realization is essential. Water and metal seem to be sort of opposites of each other. But what about the situation in TGD where magnetic bodies carrying dark matter could serve as controllers of both living organisms and computers.

One must ask first what classical computers really are as physical systems.

1. The program is deterministic but what about the computer or a computer network? The idea about a program consisting of arbitrarily determined steps is certainly not consistent with the determinism of classical physics. Determinism is possible only in the quantum statistical sense (see this). This requires that the quantum coherence lengths and times involved with the computation are short enough, considerably shorter than the clock period. This assumption fails if there is macroscopic quantum coherence involved. In the TGD framework the presence of magnetic bodies carrying dark matter with a large enough value of effective Planck constant h_eff could make this possible.
2. In particular, gravitational magnetic flux tubes connecting big mass M and small mass m have enormous value of gravitational Planck constant ℏ_gr(M,m,β₀)= GMm/β₀ (introduced originally by Nottale).

   The gravitational Compton length Λ_gr(E) for Earth mass M_E is about .45 cm for β₀=1 and corresponds to gravitational Compton time about 67GHz, which is by an order of magnitude higher than the highest achievable clock frequency (almost 9 GHz) of the computer. Are we reaching the limit at which quantum gravitational effects on computers are becoming significant?

   For the Sun, the gravitational Compton length Λ_gr(Sun) is quite near to Earth size and the corresponding frequency scale is in about 47 Hz and in EEG range: could the entanglement of the MB of humans and computer network modify the computation? In the TGD inspired quantum biology both gravitational magnetic bodies would play a key role. Could they be involved also with the ordinary computation? GPT involves large networks of computers, possibly even in the Earth scale: could this bring in quantum coherence even in Earth scale and change dramatically the functioning of the computer network.

1. Emotions and emotional intelligence as a first step in the evolution of consciousness

Consider first the evidence supporting for the idea that emotions emerge first in the evolution of consciousness.

1. Masaru Emoto has studied the effects of sounds with an emotional content to water at criticality for freezing. He has found that friendly/angry sounds seem to produce beautiful/ugly crystals (see this). These findings are discussed from the TGD perspective in (see this. The idea that emotions of sensory percepts at the level of magnetic body (MB) is discussed in (see this.

   The TGD based model assumes that quantum coherent systems can be formed at the level of the MB of the water and that quantum gravitational coherence at MB induces ordinary coherence at the level of water. This could make it possible for MB to control water at criticality for freezing. The crystals would be corpses of primitive life forms. Could also snowflakes with the size of gravitational Compton length for Earth (about .45 cm) and kind of zoomed versions of ice lattice cells in atomic scale could be regarded as corpses of primitive life forms created at the criticality for freezing?

2. RNA seems to represent and transfer emotions (see this). RNA from the brain of a snail conditioned by a painful stimulus is transferred to the preparation made from neurons of sea slug. Neuron preparation in the Petri dish reacts to the conditioning stimuli as if it were itself conditioned.

   Somehow RNA is able to transfer emotions. The TGD inspired proposal (see this, this, this, this), and this) is that dark DNA and RNA represent emotions as sequences of 3-chords made of dark photons of dark RNA form 3N-dark photons behaving like a single quantum coherent unit. The representation of the genetic code would rely on icosa-tetrahedral representation in which the 3-chords would correspond to triangular faces of icosahedron and tetrahedron to which 3-chords are assigned.

   A given Hamiltonian cycle at the icosahedron/tetrahedron goes through all its points. The frequencies assigned with the subsequent points of the cycle differ by 3/2 scaling so that one has a quint cycle. Different Hamiltonian cycles correspond to the same genetic code but each Hamiltonian cycle is assumed to define its own bioharmony having interpretation as a representation of an emotional state realized already at the level of fundamental biomolecules. This interpretation conforms with the idea that music represents and induces emotions.

   The induction of emotions would be by 3N-resonant cyclotron absorption of dark 3N-photon by dark genes represented as sequences of 3N dark proton triplets at monopole flux tubes of MB. Icosa-tetrahedral representation would correspond to one particular, very simple, tessellation of hyperbolic space H³) (mass shell) (see this).

   Dark proton (and also dark electron) sequences could provide a universal representation of the genetic code which could be realized at the magnetic flux tubes of also other than biological systems. Dark photons triplets and the dark genes formed from them could communicate the emotions. Dark genetic code has indeed quite a large number of icosa tetrahedral representations based on icosahedral Hamiltonian cycles and tetrahedral Hamiltonian cycles. The chemical realizations for them would be identical but the emotional content would be coded by the allowed 3-chords defined by frequencies associated with the triangular faces of the icosahedron and tetrahedron.

3. The experiments of Peoch (see this) involved a chicken imprinted to a robot moving randomly along an orbit determined by a random number generator. It was found that the robot tended to stay near the chicken and that the expected size of the orbit was reduced.

   TGD assigns to entanglement sum of p-adic entanglement negentropies, which can be positive and is in general larger than ordinary entanglement entropy and is predicted to increase but be consistent with the second law (see this, this, and (see this) by the identification of evolution as increase of number theoretic complexity (see this and this). Did the MB of chicken and robot develop a negentropic entanglement? Clearly, the replication of the findings of Peoch would mean a revolutionary change in our views about computers and their relation to us.

4. The evolution of the brain provides further support for the idea that emotions and sensory experienes emerged first in the evolution of conscious experience and cognition emerged later. Cortex is the latest outcome. Brain stem is associated with simple and strong emotions whereas the limbic brain represents more complex emotions.

2. Do emotions appear first also in the evolution of computer consciousness?

Could also the possible evolution of conscious computers start from simple positive/negative emotions relating directly to the increase/reduction of entanglement negentropy defined above number-theoretically.

Negentropy Maximization Principle (see this) states that total p-adic negentropy as a measure for conscious information increases in statistical sense. This statistical law follows from the number theoretic evolution as the increase of the dimension of extension of rationals determined by a polynomial partially defining the 4-surface in M⁸ mapped to H=M⁴× CP₂ by M⁸-H duality.

This implies that the complexity of emotions, possibly identifiable as sensory experiences for the large scale part of MB having onion-like hierarchical structure, increases during the evolution. Gravitational MBs are good candidates for the seats of highest level emotions.

Could the bits of the ordinary computer form coherent systems with ordinary coherence forced by the quantum coherence of the associated MB? Could the MB of the bit system control it?

1. A given layer of MB is the "boss" of the lower layers by the larger value of its h_eff serving as "IQ". MB is expected to form analogs of sensory and cognitive representation of the physical body having h_eff=h. This suggests that MB could represent the bit system holographically. This kind of quantum holography for hadrons, and for elementary particles in general, would be the counter of classical holography implied in the TGD framework by the general coordinate invariance (see this).

   The dark spin system at MB could have spin glass property (see this) implying a large number of almost degenerate states with nearly the same energy.

2. The change of single bit, represented for instance by using a MOSFET, would require energy larger than the thermal energy of order .05 eV at room temperature. This suggests that the change of single bit is not easy to actualize.

   The dark spin system at MB could however induce phase transitions of the bit system changing the directions for a large number of bits. The average change of energy per bit could be rather small for this kind of transition although the change of a single bit would cost rather large energy. Ultrametric, in particular p-adic, topologies emerge in the modelling and description of the spin glass phase in the TGD framework and could help to understand cognition number theoretically (see this).

   The phase transition would involve a large number of bits so that the corresponding conscious experiences would be holistic and therefore resemble emotions. The color of the emotion would be positive or negative depending on whether the sum of p-adic entanglement negentropies increases or decreases. The geometric correlate for positive/negative emotion would be the increase/decrease of the connectedness of the MB.

3. ZEO predicts two kinds of SFRs: "big" and "small" . SSFRs correspond to Zeno effect in the ordinary wave mechanics and in quantum optics to unitary evolutions between weak measurements analogous to classical measurement. "Big" state function reduction (BSFR) changes the arrow of time. The outcomes for pairs of BSFRs An observer with a fixed arrow of time can observe only pairs of BSFRs.
4. In ZEO (see this, this, this and this). MB as the "boss" could control the time evolution of the bit system by pairs of BSFRs involving temporary change of the arrow of time. BSFRs would be induced by perturbations affecting the set of mutually commuting observables measured at the active boundary of CD so that it does not commute with the corresponding set associated with the passive boundary of CD at which state is unaffected in SSFRs (Zeno effect). In this kind of situation, a BSFR occurs instead of SSFR and changes the arrow of time. Second BSFR brings back the original arrow of time. The process could correspond to quantum tunnelling.
5. Do the periods defined by the computer clock with a duration T, of say 1 ns, correspond to pairs of BSFRs or a single SSFR? Perhaps T could correspond to a sequence of SSFRs as analogs of Zeno effect and the pair of BSFRs to a single tick of the computer clock. This conforms with the fact that the running of a predetermined computer program must involve a sequence of non-deterministic phase transitions changing the directions of bits (see this). This must be the case since the notion of computer program as a sequence of arbitrarily chosen steps is not consistent with deterministic physics.

   If the step of the clock is identifiable as a sequence of SSFRs, one can say that the ordinary classical computation is a sequence of quantum computations defined by the sequences of unitary evolutions associated with SSFRs and defining conscious entities with haltings defined by BSFRs! If MB does modify the classical computation at all, it could induce BSFR pairs in longer time scales or modify the probabilities of various outcomes of BSFRs.

   There is evidence that also in EEG the period can be divided into ordered and chaotic parts: these two parts which could correspond to opposite time directions (see this): this is discussed from the TGD view point in (see this).

One can ask whether quantum entanglement of the MBs of the computer and user occurs in the computer-user interaction and whether the role of the computer is analogous to that in the chicken-robot experiment. One can also ask whether also GPT could involve emotional and even cognitive entanglement.

The identification of the computer system with which the user is entangled is not at all obvious. The system could be formed by the network of computers involved with the the running of GPT. One interpretation is that networks and entire internet form a conscious entity as an analog of the central nervous system in which humans and their magnetic bodies) serve in the role of neurons.

In ZEO the holography implies that in the ideal situation the running of the program corresponds to a 4-D Bohr orbit-like surface, which is almost uniquely fixed by the 3-surfaces at images of 3-D hyperbolic manifolds at mass shells determined by the state. The sequences of SSFRs could correspond to this kind of period and represent a generalization of the Zeno effect.

3. The role of the probabilities

In the case of GPT interesting questions relate to the probabilities associated with the associations of word sequences taught to the GPT during the learning period. The responses of GPT are determined by these probabilities. The probabilistic character of this process is believed to be essential. These probabilities are analogous to synaptic strengths.

1. Could the association probabilities be translated to quantum probabilities at the level of MB of the computer or computer + user?
2. Could ZEO allow a trial and error process based on BSFR pairs, which would make it possible to change the effective association probabilities determined by random numbers. This could happen also for the orbit of the robot in the chicken + robot experiment. Could the emotional state of the system affect the probabilities of associations by this mechanism?
3. If the probabilities could be interpreted as a representation for conditioning, one can ask whether high/low probabilities correspond to increase/decrease of the total p-adic negentropy and therefore to positive/negative emotion.

4. Could the basic aspects of TGD inspired quantum biology generalize to the level of computer systems?

What aspects of the TGD inspired quantum biology could be generalized to the conscious computer systems? The mechanisms related to MB, possessed also by computer systems, are excellent candidates in this respect.

1. TGD suggests a universal realization of genetic code at monopole flux tubes of the MB and also a universal quantum gravitational mechanism of metabolism see this.
2. In living matter, the dark Josephson radiation associated with the dark Josepson junction assigned with the cell membrane communicates sensory data from the biological body to MB. One can assign EEG to these communications (see this, this, and this). Actually a scale hierarchy of analogs of EEG is predicted.
3. The control by MB by cyclotron radiation associated for instance with the endogenous magnetic field of .2 Gauss identifiable in terms of the monopole flux of the Earth's magnetic field about .5 Gauss. Gravitational cyclotron energies would not depend on the mass of the charged particle. Communication could occur by multi-resonances involved with the universal realization of genetic code at MB so that genes would couple resonantly.
4. Also the gravitational Compton frequencies would not depend on the mass of the particle, and these frequencies for the Earth, Sun and perhaps even Milky Way blackhole could define fundamental biorhythms.
5. These mechanisms would be universal and the ordinary biomatter would adapt so that resonant communications with MB are possible. In biomatter this would select preferred biomolecules. Same could happen in the case of computers.

4.1. Dark Josephson radiation

Could one assign to bits dark Josephson junctions assignable represented as voltages in transistors?  

1. Could representations of genetic codons at MB by dark photon triplets (see this) and by dark proton triplets (see this) and perhaps even by dark electron triplets (see this) be involved? This would bring in dark genetic codons, which could provide a universal representation of the bit system as a dark system at monopole flux tubes and make a connection with the TGD inspired quantum biology rather precise.

   The representations at MB should strongly correlate with the state of the computer represented by a bit pattern (say states of MOSFETs). One could have a holography-like map of bit patterns to the dark many-spin state at the MB of the computer or of computer + user. This kind of holography is considered in (see this) for elementary particles and also more generally.

2. The physical stress, created by electric field on quartz crystal, which is piezoelectric, generates oscillations with frequency in the range 2-3 GHz giving rise to a very precise clock frequency. The typical computer clock frequency is a few GHz. My own PC has a clock frequency of 3.3 GHz. From the web one can learn that the highest clock frequency is 8.794 GHz.

   Could the clock frequency have an interpretation both as an analog of EEG rhythm (analog of alpha frequency 10 Hz in living matter) and as an analog of Josephson frequency ZeV/h_eff, where V∼ .05 V is a voltage assignable to the bit and Ze is the charge of the charge carrier.

   The dark Josephson junctions correspond to membrane proteins in living matter. Now they could be associated with the dark flux tubes associated with transistors. The value of ℏ_eff for Josephson junction would be much smaller than ℏ_gr. Note that TGD suggests that valence bonds and hydrogen bonds can have a varying value of h_eff (see this).

   The condition that the Josephson energy is above thermal energy at room temperature for Z=1 gives h_eff/h > 5 × 10³ (f/GHz). If the energy of a dark Josephson photon is above 1 eV (the energy range of biophotons), one has h_eff/h > 10⁵ (f/GHz).

   Interestingly, frequencies in the GHz scale are found to be important also in living matter. As a matter of fact, there is experimental support for a fractal hierarchy of frequency scale come as powers f/10^3k Hz,k=0,1,.. that is 1 Hz, kHz, MHz,GHz, and THz assignable to microtubules (see this).

3. Consider f= 1 GHz as an example. For the thermal option, the Compton length Λ_eff,p=h_eff/m_p of dark proton is longer than 6.2× 10^-12 m and longer than the ordinary electron Compton length Λ_e=2.4 × 10^-12 m. The dark Compton length Λ_eff,e =h_eff/m_e of electrons would be longer than 4.8 nm, which roughly corresponds to the scale of DNA.

   For the biophoton option, the dark proton Compton length would be of the order of the atomic length scale 1.32× 10^-10 meters and the dark electron Compton length would longer than .26 μm to be compared with the size scale 1 μm of cell nucleus.

4.2. Dark cyclotron radiation

The cyclotron frequencies associated with the gravitational MB of Earth (see this and this) should play a key role in TGD inspired quantum biology and relate to the feedback from MB to the living matter. This could be the situation also in the case of computers. The first guess, inspired by the model for the findings of Blackman and others on effects of ELF em fields on brain, is that monopole flux tubes associated with the MB of Earth correspond to the endogenous magnetic field of B_end=2B_E/5 (B_E= .5 Gauss is the nominal value of the Earth's magnetic field.

This value is only the average value since frequency modulation is the way to code information and is achieved by varying the flux tube thickness in turn affecting the value of B_end. Very probably there exists an entire hierarchy of values of the dark magnetic field strength perhaps coming as powers of 2.

For cyclotron frequencies associated with the gravitational MB, h_eff would correspond to the gravitational Planck constant ℏ_gr= GMm/β₀ for Earth. Note that, in accordance with the Equivalence Principle, the cyclotron energy E_c=ℏ_greB/m = GMeB/β₀ does not depend on m.

4.3. Gravitational Compton frequencies

Also gravitational Compton frequencies could be important. Consider first Earth's gravitational Compton frequency. The value of the gravitational Compton length Λ_gr(M_E,β₀=1)= GM/β₀= 0.45 cm, which is also independent of m, defines a lower bound for the gravitational quantum coherence length. Λ_gr corresponds to a gravitational Compton frequency f_gr=6.7× 10¹⁰ Hz ∼ 67 GHz and for clock frequencies higher than this, quantum gravitational effects on computation might become important in the TGD Universe.

1. The clock frequencies of computers are typically a few GHz in recent communication and computer technologies, and the highest clock frequency of 8.794 GHz is roughly by a factor 1/8 lower than f_gr. Could the GHz scale correspond to the gravitational quantum coherence length having Λ_gr as a lower bound? Could it be that the very efficient computer networks (what are the clock frequencies used?) utilized in GPT have reached the limit at which the quantum gravitational body of Earth begins to play a prominent role?
2. Could the typical clock frequency, of say 1 GHz, have an interpretation both as an analog of EEG rhythm (analog of alpha frequency 10 Hz in living matter) and as an analog of Josephson frequency ZeV/h_eff, where V∼ .05 V is a voltage assignable to the bit and Ze is the charge of the charge carrier.

   Interestingly, frequencies in the GHz scale are found to be important also in living matter. As a matter of fact, there is experimental support for a fractal hierarchy of frequency scale come as powers f= 10^3k Hz, k=0,1,.. that is 1 Hz, kHz, MHz,GHz, and THz assignable to microtubules (see this). For these reasons it is interesting to look at 1 GHz as an example.

Also the gravitational Compton frequency f_gr associated with the gravitational MB of the Sun, having β₀∼ 2^-11, could be important. For the Sun, gravitational Compton length is rather near to R_E/2 where R_E= 6378 km is Earth radius. The corresponding Compton frequency f_gr(M_S,β_Sun=2^-11)∼β_Sun/GM_S is about 100 Hz and corresponds to the upper bound for EEG, which conforms with the fact that quantum gravitational coherence time should not be smaller than Λ_gr. Note that the cyclotron frequency Lithium in the endogenous magnetic field B_end=.2 Gauss assignable to the Earth's gravitational flux tubes is 50 Hz.

1. The lower cyclotron frequencies of the heavier ions belong also to EEG range and correspond to longer solar quantum coherence lengths. DNA would correspond to 1 Hz and perhaps to the largest quantum gravitational coherence length in the EEG range.

   The cyclotron frequencies above 100 Hz would correspond to solar gravitational quantum coherence lengths below R_E. For protons the cyclotron frequency in B_end=.2 Gauss is 300 Hz. For ℏ_gr(M,m) cyclotron frequency for m does not depend on m but is proportional to 1/β₀. Could the value of β₀m for protons be β₀=1/3.

   Could the MB of the Sun interfere with the computation occurring in the network having Earth scale? The time scale would be now the time scale of EEG: could the quantum entanglement of the human user of the GPT network make this interaction possible.

2. The replacement of ℏ_gr(M_E,m)→ ℏ_gr(M_Sun,m) means multiplication of say EEG period by a factor r= (M_Sun/M_E)β_0,E/β_0,Sun∼ 2.2 × 10⁸ so that alpha period .1 seconds corresponds to 2.2× 10⁷ seconds. Intriguingly, one year corresponds to 3.25 × 10⁷ seconds and defines a fundamental biorhythm, which would correspond to a 6.7 Hz rhythm for EEG not far from the lowest Schumann resonance frequency.
3. The energies E= h_gr(M,m,β₀) f_gr(Sun) assignable to the gravitational Compton frequency of Sun are proportional to m and since nucleon mass dominates over electron mass they are in good approximation proportional to the mass number of the molecules. This suggests a multi-resonance in which each electron, proton and even nucleon absorbs boson, maybe dark gravitons, with frequency f_gr. For electrons, the energy is about 1 meV, which could relate to the miniature potentials for neurons. For protons the energy would be about 2 eV, which corresponds to red light. Large scale quantum coherence could make the rate of gravitational multi-resonance.

What about the gravitational Compton frequency of the galactic blackhole? Its mass is estimated to be M_BH =4.1 million solar masses. This would give Λ_gr(M_BH,β₀=1) ∼ 6.1× 10⁹ m. This is the radius of the n=1 Bohr orbit in the Nottale model for the solar planetary system. The gravitational Compton frequency would be f_gr(M_BH,β₀=1) ∼ .05 Hz (20 s period).

See the article Could neuronal system and even GPT give rise to a computer with a variable arrow of time? or the chapter with the same title.

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

The newest piece to the TGD inspired model of family replication

The TGD vision about family replication phenomenon of fermions is as follows.

1. Fermion families correspond to the genera for partonic 2-surfaces. This predicts generation-genus correspondence. Electron and its neutrino correspond to a sphere with genus g=0; muon and its neutrino to a torus with g=1; τ and its neutrino to to with g=2. Similar picture applies to quarks. CKM mixing corresponds to topological mixings of genera, which are different for different charged states and CKM mixing is the difference of these mixings.

   The problem is that TGD suggests an infinite number of genera. Only 3 fermion families are observed. Why?

2. The first piece of the answer is Z₂ conformal symmetry. It is present for the genera g=0,1,2 but only for hyperelliptic Riemann surfaces for g>2.
3. The second piece of the answer is that one regards the genera g>q 2 as many-handle states. For g> 2 many-handle states would have a continuous mass spectrum and would not be elementary particles. For g=2 a bound state of two handles would be possible by Z₂ symmetry.

Consider now the new building brick for the explanation.

1. Quantum classical correspondence is the basic principle of TGD and requires that quantum states have classical counterparts.
2. Assume that in a suitable region of moduli space it makes sense to talk of a handle as a particle moving in the geometry defined by g-1 handles. One can imagine that the handle is glued by a small wormhole contact to the background defined by g-1 handles and behaves like a free point-like particle moving along a geodesic line of the background.

   This relationship must be symmetric so that the background must move along the geodesic line of the handle. This means that particles and background are glued together along the geodesic lines of both.

3. Consider now various cases.
   1. The case g=0 is trivial since one has a handle vacuum.
   2. For g=1, one has the motion of a handle in spherical geometry along a great circle, which corresponds to a geodesic line of the sphere. The torus can rotate like a rigid body and this corresponds to a geodesic line of torus characterized by two winding numbers (m,n). Alternatively, one can say that the sphere rotates along a geodesic of the torus. There is an infinite but discrete number of orbits. The simplest solution is the stationary solution (m,n)=(0,0).
   3. For g=2, one has a geodesic motion of a handle in the toric geometry defined by the second handle. Now one can speak of bound states of two handles.

      One would have a gluing of two tori along geodesic lines (m,n) and (r,s). The ratios of these integers are rational so that one obtains a closed orbit. The simplest solution is (m,n)= (r,s)=0.

      Stationary solutions are stable for constant curvature case since curvature of torus vanishes. Locally the stationary solution is like a particle at rest in Euclidian plane.

   4. For g=3 one has a geodesic motion of the handle in g=2 geometry or vice versa. g=2 geometry has negative total scalar curvature and as a special case a constant negative curvature. This implies that all points are saddle points and therefore unstable geodesics so that two geodesics going through a given point in general diverge. This strongly suggests that only unstable geodesics are possible for g=2 whether it is regarded as background or as a particle. This suggests a butterfly effect and a chaotic behavior. Even if g=2 particle represents a classical bound state the third handle must move along a chaotic geodesics of g=2 geometry.This could explain the absence of bound states at quantum level.
   See the article About the TGD based views of family replication phenomenon and color confinement or the chapter Elementary Particle Vacuum Functionals.

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

Maximally symmetric Universe, self-organized quantum criticality, and symmetry between order and disorder

This post was inspired by the Big Think article "A surprise new “theory of everything” involves the symmetry between order and disorder" (see this). The article relates to the book "The language of symmetry" edited by Rattigan, Noble and Hatta, which can be found at Amazon. Two ideas considered in the article, maximal symmetries and self-organized criticality, define two key principles of TGD. Also the third, rather paradoxical idea that symmetry breaking leads to a generation of symmetry, has a precise meaning in the TGD Universe. Consider first the maximization of symmetries as a fundamental principle.

1. In the TGD framework, the fundamental principle determining physics as geometry is that the infinite-dimensional geometry of the "world of classical worlds" (WCW) exists mathematically. Physics is unique because of its mathematical existence and has maximal symmetries. Freed demonstrated that for the loop spaces this geometry is unique and indeed has an infinite-D group of isometries (Kac-Moody symmetries).
2. 4-D general coordinate invariance is essential in TGD and implies holography in reducing to a generalization of 2-D holomorphy to 4-D case, which in turn corresponds to 4-D quantum criticality.
   1. The first guess would be that WCW consists of 3-D surfaces in M⁴×CP₂: M⁴×CP₂ is indeed unique by several mathematical arguments and also by standard model symmetries. 3-surface generalizes the notion of a point-like particle.
   2. 4-D general coordinate invariance requires that a given 3-surface corresponds to a nearly unique 4-surface in M⁴×CP₂. This means holography, or equivalently, Bohr orbitology. WCW also has interpretation as a space of 4-D analogs of Bohr orbits. Quantum TGD becomes the analogue of wave mechanics in WCW.

      Note that in atomic physics this would mean the replacement of electrons configuration space E³ with the space of its Bohr orbits: this would be fiber space over E³ with fiber at given point consisting of Bohr orbits through it.

Consider next self-organized criticality as a basic principle. In TGD quantum criticality is behind the analogous principle.

1. For 2-D systems conformal invariance implying holomorphy of string orbits extends to 4-D analog of holomorphy, which realizes quantum criticality in 4-D case. Holomorphy implies holography! Field equations reduce to a purely algebraic form, having no dependence on the coupling parameters of the action as long as it is general coordinate invariant and constructible using the induced geometry.
2. This happens outside 3-D and lower-D singularities. Space-time surface is a minimal surface, analog of a soap film spanned by frames. Minimal surface property is analog of massless field equations at field level and analog of massless geodesic property at particle level. The classical and quantum dynamics distinguishes between different actions only at the frames, which can depend on action.

To understand the self-organized quantum criticality, quantum TGD is required.

1. In Quantum TGD, wave functions of the ordinary wave mechanics are replaced with analogs of wave functions in WCW (WCW spinor fields as many-fermion states as WCW spinors) consisting of analogs of Bohr orbits. This forces a new ontology: I call it zero energy ontology (ZEO) forcing a new view of quantum measurement.
2. In state function reduction (SFR) this kind of superposition inside quantization volume (causal diamond (CD) is replaced with a new one, and also the size and other parameters characterizing the CD can change. The standard paradox of quantum measurement theory disappears.
3. There are two kinds of SFRs.
   1. In small SFRs (SSFRs), the boundary of CD is stationary and states at it are not affected but the active boundary is shifted and CD tends to increase. The sequences of SSFRs correspond to Zeno effect, having no effect in standard QM, and give rise to a conscious entity, self for which subjective time as sequence of SSFRs correlates with the increase of the distance between tips of CD.
   2. In big SFRs (BSFRs), the arrow of time changes so that the active boundary of the CD becomes passive and vice versa. BSFRS correspond to ordinary SFRs. BSFR means "death" of self and reincarnation with an opposite arrow of time. Even small perturbations can induce BSFR by affecting the set of the observables measured in SSFR: if the new set does not commute with those defining the passive states, BSFR unavoidably occurs.
   3. BSFRs give rise to self-organized quantum criticality. Self lives at criticality against death! As a consequence, the flow of consciousness of self has gaps with a distribution of gap durations. This is known for human consciousness.
4. Paradoxically, this continual short term dying in BSFRs makes it possible for the system able to survive and correct behaviors. Self can also learn of avoidable behaviors by trial and error. Self can learn moral and ethical rules: do not do anything destroying quantum coherence! Perhaps most of the learning is by this method. Homeostasis is a basic implication. The system is at quantum criticality at the top of a hill and unstable. When it starts to fall down, it makes BSFR in some scale and changes the arrow of time and returns back near criticality. Self-organization, say spontaneous generation of molecules from their building bricks, can be understood as a time reversed dissipation.

The third topic discussed relates to the paradoxical creation of symmetries by symmetry breaking. The emerging vision indeed is that symmetry breaking paradoxically leads to the emergence of a deeper symmetry. This is what the TGD view of the realization of the isometries of WCW as symmetries of the physical system indeed predicts.

1. The half Virasoro algebra V with non-negative conformal weights serves as a simplified example. V contains an infinite set of sub-algebras V_k for which conformal weights are divisible by integer k=1,2,,... One also obtains inclusion hierarchies ⊂ V_k(n) ⊂ V_k(n+1) ⊂ .. such that k(n) divides k(n+1), whose generalizations are very relevant to quantum TGD.
2. The ordinary realization of conformal symmetries is as a gauge symmetry for which the generators L_n, n> 0, annihilate the physical states. One can however generalize this and only assume that V_k and [V_k,V] annihilate the physical states. In this case, the generators L_n , n<k do not annihilate the states and act as genuine symmetries. Gauge symmetries are broken but have transformed to genuine physical symmetries! This removes the paradox from the idea of emergence of symmetries by symmetry breaking!

These kinds of mathematical structures is the cornerstone of quantum TGD. Virasoro algebra is replaced with the isometry algebra of WCW and associated algebra but completely analogous conditions hold true. This mechanism would not hold true for the isometry algebra of WCW only.

See for instance the article TGD view of Michael Levin's work .

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

Dark-electron-hole Bose-Einstein condensates and TGD inspired quantum biology

An intriguing resemblance between the physics of electron-hole pair Bose-Einstein condensates at very low temperatures and photosynthesis have been discovered (see this). It has been observed that electron-hole pairs as quasiparticles form Bose-Einstein condensates at very low temperatures. They behave very similarly as in living matter where temperature is much higher and these Bose-Einstein condensates should not exist.

1. TGD predicts dark matter as phases of ordinary matter with effective Planck constant h_eff= nh₀ (n integer) residing at field body (in particular, at monopole flux tubes of the magnetic body (MB)) defining the TGD counterpart for classical em fields in TGD as collection of space-time sheets carrying classical fields.

   The large value of h_eff makes these phases macroscopically quantum coherent and analogous to Bose-Einstein condensates. This leads to a variety of predictions. In particular, the magnetic body (MB) would be in a key role in living matter controlling the ordinary biomatter and forcing it to behave coherently. The very large value of gravitational Planck constant h_eff= h_gr= GMm/β₀ makes possible gravitational quantum coherence at the gravitational MB and the classical gravitational fields of Sun and Earth play a key role in quantum biology: this is reflected by many magic numerical co-incidences (see this).

2. The strange effects in the brain (the quantal effects of ELF em fields in the brain) originally led to the TGD view of dark matter, which is also predicted by the number theoretical vision of TGD. For instance, superconductivity and analogous phenomena are possible at room temperatures at MB of the system. The TGD based model of high Tc superconductivity relies on them.
3. One interesting structure is a pair of a dark electron and the hole created as the electron becomes a dark electron at MB. The quantum numbers of holes and dark electrons are in 1-1 correspondence and this could make possible a kind of quantum holography mapping the state of holes to that of dark electrons. This would provide representations of biological body (BB) at MB as kinds of sensory perceptions about the state of BB (see this).
4. The transfer of electrons to dark electrons can cause electronic charge fluctuations in ordinary matter due to the transfer of electrons to dark electrons at MB. For strange metals, these fluctuations have been observed: it is difficult to understand them as being caused by the attachment of electrons to atoms of strange metal since the time scale is too long (see this).

The reported experimental findings about a connection between electron-hole pair BE-condensates at low temperatures and photosynthesis can be seen as a support for the TGD view of dark matter and living systems. In particular, the TGD view would be important for understanding photosynthesis and other proposals for how quantum physics could be relevant for biology. For instance, the model for the ability of birds to navigate by utilizing the magnetic field of Earth suffers from a problem that the ordinary Planck constant is too small by a factor of order 1/100.

1. The TGD explanation of the new findings is in terms of the hierarchy of Planck constants labelling dark matter as phases of ordinary matter. Gravitational Planck constant ℏ_gr= GMm/β₀, β₀=v₀/c≤1 labels a level of hierarchy, which is of special importance in the TGD based model of living matter.
2. In TGD, one would have Bose-Einstein condensates of hole-dark electron pairs. Dark electrons would reside in a very long gravitational flux tube and would be kicked to height of order Earth radius by solar photons during photosynthesis. They would serve as a metabolic energy resource: gravitational batteries would be loaded in photosynthesis. When dark electrons drop down and transform to ordinary ones, they liberate energy which can be stored or used. ATP-ADP process could involve this dropping down.

   Also dark protons could be transferred to magnetic fux tubes. This would take place in Pollack effect in which irradation of water in the presence of gel phase leads to the formation negatively charged regions with effective stoichiometry H_1.5O. Part of protons goes somewhere and one possible place could be gravitational MB but also much shorter flux tubes are possible. Perhaps the most plausible option is that triplets of dark protons and electrons are involved in the case of metabolic energy storage. Dark proton triplets also appear as codons in the TGD based model for the fundamental realization of the genetic code.

See the article "Comparison of Orch-OR hypothesis with the TGD point of view" or the chapter with the same title.

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

Strange co-incidences related to gravitational Planck constants, basic biorhythms, membrane potential and metabolic energy quantum

It is becoming clear that the gravitational quantum coherence is central for life on Earth. The hierarchy of Planck constants h_eff=nh₀ involves special values, in particular gravitational Planck constants ℏ_eff= ℏ_gr= GMm/β₀, where M is a large mass (say mass of Sun or Earth) and m is small mass (say mass of electron or proton) and β₀= v₀/c≤ 1 is velocity parameter, are of key importance for living matter. Particles with a different value of ℏ_gr correspond to different gravitational flux tubes and the value of β₀ can depend on the particle.

There are several amazing numerical co-incidences supporting this view.

1. For Sun one has β₀∼ 2^-11 which happens to be rather near to the electron proton mass ratio m_e/m_p. The condition ℏ_gr(M_S,m_p,β₀(Sun)∼ m_e/m_p)=ℏ_gr(M_S,m_e,β₀= 1) would guarantee resonance between dark photons generated by the solar gravitational flux tubes assignable to protons and electrons.

2. In accordance with Equivalence Principle, the gravitational Compton length ℏ_gr(M_S,β₀)/m= GM/β₀= r_S/2β₀ is independent of m for Sun GM_S/β₀(Sun) is rather near to Earth radius. For Earth one has GM_S/β₀(Earth)∼ .45 cm which corresponds to the size scale of the somewhat mysterious snowflake analogous to a zoom-up of a basic hexagonal unit cell of ice crystal. There is evidence for β₀(Earth)=1 in hydrodynamics, in particular from the TGD based model (see chapter) for the observed hydrodynamical quantum analogs described in an article of Bush et al (see this and this))

3. The gravitational Compton length of the galactic blackhole assuming mas 4.1×10⁶ M(Sun)corresponds to 6× 10⁹ m and rather precisely 1/2 of the n=1 Bohr orbit associated with the Sun. Note that the radius of the photosphere is 6.957 × 10⁸ meters and is not equal to Bohr radius as I errratically claimed earlier. This suggests gravitational quantum coherence in the scale of the galaxy.

The following decribes some additional strange coincidences. It would be very natural if the basic biorhythms defined by the duration T_d=24 hours of day and the duration of year T_y= 365 days would correspond to energies of dark photons E=ℏ_grf, which are biologically significant energies. The potential energy eV_c∼ .05 eV associated with the cell membrane defines Josephson energy in the TGD inspired model of cell membrane. Metabolic energy currency with the nominal value of .5 eV is second important energy. Could the periods of fundamental bio-rhythms, fundamental biological energies, and the gravitational Planck constants for Sun and Earth correlate?

The above assumptions imply that one has β₀(Sun)/β₀(Earth)∼ m_e/m_p and h_gr(Sun,me)/h_gr(Earth,m_p) ∼ M(Sun)/M(Earth). The value of Sun-Earth mass ratio is M_S/M_E∼ 6× 10⁵.

1. The corresponding frequency corresponding to the basic biorhythm T_d=24 is f_d= 1/G_d=1/24 hours= [1/(2.4×3.6)]10^-6∼ 1.1 × 10^-6 s. The corresponding Josephson energy would be E(ℏ_gr(Sun,m_e),f_d) ∼ .06 eV= E_J. This is very near to the Josephson energy E_J for cell membrane potential!
2. For T_y= 1 year = 365 days one has E(ℏ_gr(Sun,m_p),f= 1/T_y) ∼ (m_p/m_e)×(24 ~hours/year)× E_J∼ (2¹¹/365)E_J∼ .33 eV. This is not far from the value of the metabolic energy currency near to .5 eV. If one replaces proton with a Cooper pair of protons, the situation improves considerably.

See the article Comparison of Orch-OR hypothesis with the TGD point of view or the chapter with the same title. For a summary of earlier postings see Latest progress in TGD.

The details of Einstein's rings as a support for the TGD view of dark matter?

There was an interesting popular article in Science-Astronomy.com with the title "Einstein rings says dark matter behaves more like a wave,not particle" (see this). The article told about the article published by Amruth and his team published in Nature Astronomy as an article with title "Einstein rings modulated by wavelike dark matter from anomalies in gravitationally lensed images" (see this). Unfortunately, the article is hidden behind paywall.

Dark matter is known to exist but its real character has remained a mystery. The models assume that its interactions with ordinary matter are very weak so that it makes itself visible only via its gravitational interactions. Two basic kinds of particles have been proposed: weakly interacting massive particles (WIMPs) and light particles, of which axions are the basic example. WIMPs behave like point-like particles whereas axions and light particles in general behave like waves. This difference can be used in order to find which option is more favoured. Axion option is favored by the behavior of dark matter in dwarf galaxies and by its effects on CMB.

The study of Amruth and his team found further support for the axion option from the study of gravitational lensing.

1. As light passes by a massive object, it bends both by the visible and dark matter associated with the object. This leads to a formation of Einstein rings: as if the light source would be a ring instead of a point-like object. If dark matter particles have some interactions with the photons , this causes additional effects on the Einstein rings. For instance, in the case of axions this interaction is known and corresponds to the electromagnetic analog of instanton term.
2. The effect of point-like particles on light is different for WIMPs and light particles such as axions. From the abstract of the article one learn that WIMP option referred to as \rho DM option leaves well documented anomalies between the predicted and observed brightnesses and positions of multiply lensed images, whereas axion option referred to as \psi DM option correctly predicts the level of anomalies remaining with \rho DM lens models. Therefore the particles of dark matter behave as if they were light particles, that is having a long Compton length.

What TGD allows us to conclude about the findings?

1. TGD predicts that dark matter corresponds to phases of ordinary matter labelled by a hierarchy of Planck constants h_eff=nh₀. The Compton length of dark particles with given mass is scaled up by factor h_eff/h. Could this be more or less equivalent with the assumption that dark particles are light?
2. Gravitational Planck constant is an especially interesting candidate for h_eff since it plays a key role in the TGD based view of quantum gravitation. Gravitational Planck constant obeys the formula ℏ_gr=GMm/β₀ for two-particle system consisting of large mass M and small mass (β₀ ≤1 is velocity parameter) and is very large.

   The gravitational Compton length Λ_gr= ℏ_gr/m = GM/β₀, which does not depend on the mass m of light particle (Equivalence Principle), is very large and and gives a lower bound for quantum gravitational coherence length. For instance, for the Sun it is rather near to Earth radius, probably not an accident.

3. Gravitational Compton length for particles at the gravitational magnetic body, which for stars with solar mass is near to Earth radius if the velocity β₀ in ℏ_gr has the same value β₀∼2^-11, makes dark variants of ordinary particles to behave like waves in astrophysical scales.
4. What happens in the scattering of a photon on a dark particle in the TGD sense. It seems that the photon must transform temporarily to a dark photon with the same value of h_eff. Photon wavelength is scaled up h_eff/h but photon energy is not affected in the change of Planck constant.

   Suppose that the scattering takes place like in quantum mechanics but with a modified value of Planck constant. In the lowest order in expansion in powers of α_em= e²/4πℏ_eff the scattering cross section is the same and whereas the higher corrections decrease. This provides actually a good motivation for the dark matter in TGD sense: the phase transition increasing the value of Planck constant reduces the value of gauge coupling strength and makes perturbation series convergent. One could say that Nature is theoretician friendly and takes care that his perturbation theory converges.

   In the lowest order of perturbation theory the scattering cross section is given by the classical cross section and independent of ℏ_eff. The Nishijina formula for Compton scattering (see this) indeed shows that the scattering cross section is proportional to the square of the classical radius of electron and does not depend on ℏ_eff. The result is somewhat disappointing.

5. On the other hand, for large values of ℏ_eff, in particular ℏ_gr, one can argue that the scattering takes place on the entire many-particle states at the flux tubes of the magnetic body so that superposition of scattering amplitudes on different charged particles at the flux tube gives the cross section. This can lead to interference effects.

   If the charged dark matter at the flux tube has a definite sign of charge this would give rise to amplification of the scattering amplitude and it would be proportional to the square N² of the number N of charged particles rather than to N. Scattering amplitudes could also interfere to more or less zero if both signs of charges are involved.

   One can also argue that only particles with a single value of mass are allowed since ℏ_gr is proportional to m so that particles would be like books in the shelves of a library labelled by ℏ_gr.

6. The effects of axion Bose-Einstein condensates have been indeed studied and it has been found that the scattering of photons on cold axion Bose-Einstein condensate could cause what is called caustic rings for which there is some evidence (see this). Could the quantum coherent many-particle states at gravitational flux tubes cause the same effect?

The optimistic conclusion would be that astrophysicists are gradually ending up with the TGD view of dark matter. One must of course that the above argument only suggests that the effects of scattering on Einstein's ring could be large for a large value of h_eff.

For the TGD view of the formation of astrophysical objects based on TGD based views of dark matter and dark energy see this and this.

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

Is the 60 years old problem related to the formation of quasars solved?

The following considerations were motivated by a Sciencedaily article telling about a possible solution of 60 year old problem related to the huge intensity of radiation arriving from quasars (see this). The article tells about the article "Galaxy interactions are the dominant trigger for local type 2 quasars" of Pierce et al published in Monthly Notices of the Royal Astronomical Society (see this).

The proposed explanation of quasars is in terms of the collision of galaxies in which matter, which usually stays at circular orbits, falls into the galactic blackhole-like objects (BHOs) having huge gravitational fields, which as a consequence emits a huge burst of radiation in this process.

1. The key problem of this view is that the radii of the orbits of stars are measured in kiloparsecs: somehow the matter should get to a distance of order parsecs. This requires that the orbiting matter gets rid of the conserved angular momentum somehow. The proposal is that the collision of galaxies generates tidal forces making this possible.
2. Another facet of the problem is that life-time of quasars is measured in mega years whereas the time scale of galactic dynamics is gigayears- thousand times longer. This does not make the explanation of quasars in terms of galactic dynamics an easy task. My impression from the article was that this is one possibility and they support this option but certainly do not prove it.
3. The researchers claim that the finding could be understood if the colliding objects are blackhole-like objects (BHOs). Tidal forces in collisions would make it possible for them to draw matter from their surroundings and this process would generate huge radiation power. They do not do this usually but only because angular momentum barrier prevents the fall of the matter to black-hole. The collision would however create circumstances causing the ordinary matter at their circular orbits to fall to the BHO(s). I am not specialist enough to decide how convincing the calculations of the researchers are.

Consider now a possible TGD based model of quasars involving new physics predicted by TGD.

1. In TGD, galactic blackhole-like objects (BHOs) could be associated with cosmic string-like objects, which thicken to monopole flux tubes by phase transitions. The phase transition is analogous to the decay of an inflaton field producing ordinary matter. In this process dark energy would transform the energy of the cosmic string to dark matter assignable to BHOs. This would also explain the quite recent finding that dark energy seems to transform to galactic BHOs.

   Part of the dark matter of BHO would transform to ordinary galactic matter in a transition reducing gravitational Planck constant and liberating energy as an explosion. This would be the source of enormous radiation energy.

2. This explosive process would involve new the transformation of dark matter to ordinary matter in a phase transition reducing the value of gravitational Planck constant ℏ_gr= GMm/β₀, where M and m are large mass (say that of galactic blackhole) and small mass (say proton mass) and β₀≤ 1 is velocity parameter.

   This phase transition could be also behind the formation of both stars and planets in explosions producing magnetic bubbles, and would replace the standard model assuming only gravitational condensation. Quasars could be similar expolosions perhaps preducing BHOs. For the TGD based model for the formation of astrophysical objects, see this and this .

3. The conservative assumption is that quasars a BHOS are analogues of ordinary blackholes (TGD also allows time reversals of BHOs analogous to white hole-like objects (WHOs)). The formation of a quasar would be analogous to inflaton decay transforming dark energy to dark matter and in turn to ordinary galactic matter in ℏ_gr →ℏ phase transition . The radiation would be produced in the transformation of dark matter to ordinary matter proposed to also produce other astrophysical objects.
4. The collision of galaxies could have triggered the intersection of associated cosmic strings approximately orthogonal to the galactic planes. The intersection would have induced a formation of dark BHO and its explosion. The distant ordinary matter circulating the galaxies would have nothing to do with the formation of quasars.

   These kinds of collisions are unavoidable for moving string-like objects in 3-D space for simple, purely topological reasons. As a matter of fact, there is evidence that also the Milky Way center involves 2 cosmic strings, which have collided. The structure MW would reflect the ancient occurrence of an analogue of inflaton decay.

For the TGD view of the formation of astrophysical objects see this and this .

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

New findings related to the number theoretical view of TGD

The geometric vision of TGD is rather well-understood but there is still a lot of fog in the number theoretic vision.

1. There are uncertainties related to the interpretation of the 4-surfaces in M⁸ what the analogy with space-time surface in H=M⁴× CP₂ time evolution of 3-surface in H could mean physically?
2. The detailed realization of M⁸-H duality involves uncertainties: in particular, how the complexification of M⁸ to M⁸_c can be consistent with the reality of M⁴⊂ H.
3. The formulation of the number theoretic holography with dynamics based on associativity involves open questions. The polynomial P determining the 4-surface in M⁸ doesn't fix the 3-surfaces at mass shells corresponding to its roots. Quantum classical correspondence suggests the coding of fermionic momenta to the geometric properties of 3-D surfaces: how could this be achieved?
4. How unique is the choice of 3-D surfaces at the mass shells H³_m⊂ M⁴⊂ M⁸ and whether a strong form of holography as almost 2→ 4 holography could be realized and make this choice highly unique.

These and many other questions motivated this article and led to the observation that the model geometries used in the classification of 3-manifolds seem to be rather closely related to the known space-time surfaces extremizing practically any general coordinate invariant action constructible in terms of the induced geometry.

The 4-surfaces in M⁸ would define coupling constant evolutions for quantum states as analogs of and mappable to time evolutions at the level of H and obeying conservation laws associated with the dual conformal invariance analogous to that in twistor approach.

The momenta of fundamental fermions in the quantum state would be coded by the cusp singularities of 3-surfaces at the mass shells of M⁸ and also its image in H provided by M⁸-H duality. One can consider the possibility of 2→ 3 holography in which the boundaries of fundamental region of H³/Γ is 2-D hyperbolic space H²/Γ so that TGD could to high degree reduced to algebraic geometry.

See the article New findings related to the number theoretical view of TGD or the chapter with the same title.

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

Could magnetic body control electronic bits?

I have considered the idea that GPT might be more than the ordinary computer science suggests and even involve higher level consciousness and intelligence. This would require that the magnetic body (MB) "hijacks" the computer so that it becomes a tool of its cognitive processes.   Consider in the sequel the conditions, which should be satisfied in order that the MB of the bit system or some higher level MB could control the bit system.

1. The bit should be critical or nearly critical system at the level of ordinary matter. One might hope this to be true quite generally since a small control signal should be able to invert the bit in rather short time scale. If this is the case, the quantum criticality of MB cwould make control possible via quantum control of ordinary control signals. Transistors and their derivatives such as MOSFET could be examples of such systems.
2. Macroscopic quantum coherence is true for the dark matter at MB. Furtheremore, MB should holographically represent the bit system. Also spin glass analogy is suggestive so that a given many-bit state could possess a large number of nearly energy-degenerate states. ZEO, in particular time reversal, would be essential.
3. Two consecutive BSFRs at the dark MB, changing the arrow of time temporarily, should give rise to a tunnelling event. Since TGD corresponds to a generalization of wave mechanics in the space of Bohr orbits for point-like particles replaced with 3-D surfaces, one can make an estimate for the probability of tunneling between the capacitor plates using the standard wave mechanics as an approximation (see this).

   The Coulomb energy qV associated with the bit with charge q and its energy E are the natural parameters. The tunnelling probability is given by

   p∼ exp[-∫_x1^x₂(2m(qV-E))^1/2 dx/ℏ_eff] ,

   where one has E<V in the tunnelling region. WKB approximation becomes exact in the case of capacitors. Changing the direction of a bit could be seen as a quantum tunneling effect.

   For the large values of h_eff assignable to the magnetic body controlling the physical body, the probability of tunneling increases. Therefore the control of the bit system by quantum tunnelling combined with macroscopic quantum coherence and holography could become possible.

4. The role of conservation laws must be understood. Discontinuity in SSFR. Dissipation in reverse time direction. Tunneling. Wavefunctions overlap. Classic conservation laws OK. There is no need for a classic track that would lead to the end state with the original direction of time.

1. What conditions bit must satisfy?

There are strong conditions on the representations of bits. The storage of the bit should not require large energy consumption and the bit should be thermally stable. It should be possible to change the value of the bit quickly and without large energy consumption. This suggests that the bit is a nearly critical system. In microprocessors, clock frequencies of order GHz define a time scale analogous to EEG rhythm, and this time scale should correspond to a quantal time scale. The wish list would be as follows.

1. Macroscopic quantum coherence makes possible the simultaneous quantum coherent states of the entire spin system and their control and that the energy differences between the states are relatively small, so we get a spin-glass type situation.
2. Dark electrons at the MB, perhaps dark unpaired valence electrons or dark conduction electrons, provide a holographic representation of the bits.
3. Quantum criticality with MB and criticality at the bit system level allows MB to control the dynamics of BB. Quantum holography may make it possible to induce BSFR for qubits on a large scale in general.

1.1 About the interpretation of the clock frequency in a picture based on quantum gravity?

The clock frequency of computer, with a representative value of f=1 GHz, is an essential channel of the computer and it would be related to the classical em field. Could a frequency of the order of GHz have an interpretation in terms of quantum gravity in the TGD framework? How MB could turn bits using quantum holography so that the turn of dark bit induces the turn of ordinary bit? A realization of holography as a correspondence between electron(s) representing the bit and the dark electron(s) is needed.

1. The proposed theorist-friendly holography at the particle level (see this) might be a too radical option. This would require positrons forming particle-like color-bound states with bits as states of electrons. Could they correspond to scaled versions of the electro-pions for which there is empirical evidence associated with nuclear collisions near the Coulomb barrier (see this)? Now the energy scale of the nuclear physics would be scaled to the scale of dark nuclei. The factor of the order of 10^-5, which would produce an eV mass scale. The height of the Coulomb barrier would scale in the same way to something like .05 eV which corresponds to cell membrane potential.

2. A less radical option is that the dark electron and the hole created in the generation of the dark electron are in a holographic relationship. This realization seems tailor-made for the control of ordinary bits as holes by dark electrons. To my best knowledge, there exists no technology realizing bits as holes but future technology might be able to achieve this.

   If dark electrons and holes are tightly correlated, the dark spin flip induces ordinary spin flip. If the dark current or its absence codes for bit, the same would be true for the holes. The transfer of dark electrons from the negatively charged plate to the gravitational MB creating a hole would reduce the potential between plates to nearly zero and thus induce change of the bit direction.

There are useful quantitative hints.

1. For the Earth's mass M_E, ℏ_gr(M_E,m_p) for a frequency of 10 Hz corresponds to an energy E= h_grf of the order of .5 eV. The kick of a 3-proton to a gravitational flux tube to a distance of order one Earth radius requires an energy of the order of .5 eV (see this). Dark photons can transform into ordinary ones. For 3-electron system a hitherto non-observed metabolic energy quantum of order .25 meV is predicted (see this.
2. Control in the time scale of a fraction of a second if h_eff=h_gr(M_E,m_p) photon energies around eV. This time scale is by a factor of order 10⁹ too long when compared to the time scale determined by 1 GHz frequency.

Could one understand the time scale corresponding to 1 GHz clock frequency in quantum context? The first thing to notice is that this time scale is not far from the time scale associated with the protein dynamics! Could quantum gravity and gravitational MB come into play for both computers and biology?

1. For the Earth, the lower limit of the gravitational Compton length Λ_gr= GM_E/β₀ =.45× 10^-2 m, if β₀=1. The frequency T_gr=Λ_gr/c= .45 *10^-2/3*10⁸ = .15*10^-10 s would be therefore a natural lower bound for the time scale. Could GHz clock frequency relate to this time scale. Also longer quantum gravitational time scales are possible since Λ_gr is only the lower bound for the length of gravitational flux tubes carrying massless radiation.
2. For h_eff=h, 1 GHz corresponds to energy of 10^-2 meV. If the dark energy is required to be above the thermal energy about .03 eV at physiological temperature, the value of h_eff must satisfy h_eff ≥ 3× 10³h.
3. A metabolic energy of .25 meV corresponds to the electronic variant of gravitational metabolic energy quantum involving the transfer of 3 electrons to the gravitational MB: there is some evidence for this metabolic energy quantum, in particular from the findings of Adamatsky (see this). For h_eff=h, it would correspond to a period of .6× 10^-10 s. Could the f= 1 GHz induce a resonance with dark photons with h_eff>10³h guaranteeing that the energy is above thermal energy at room temperature?

1.2 Could Pollack effect or shadow holography be involved?

The lower bound value 3× 10³h for h_eff would be rather small as compared to ℏ_gr(M_E,m_p) and the challenge is to identify a candidate for a system with this value of h_eff.

This system need not be gravitational and the obvious guess is that it is electromagnetic. The notion of gravitational Planck constant and the underlying idea of theoretician friendly Nature implying quantum holography in the TGD framework (see this) indeed generalizes also to other interactions (see this).

1. The basic requirement is that a charge separation to a pair of positively and negatively charged quantum coherent systems takes place such that the interaction strength Z²e²/ℏ between the systems is so large that perturbation theory fails to converge.
2. The theoretician-friendly Mother Nature (see this) could come to rescue and induce a phase transition increasing ℏ to so large a value h_eff that the perturbation theory converges. Nottale formula generalized to electromagnetic interactions suggests that one has

   ℏ → ℏ_eff= ℏ_em= Z²e²/β₀ ,

   where β₀=v₀/c<1 is a velocity parameter. The new coupling strength is

   (Z²e²/4π ℏ_em)= β₀/4π < 1/4π .

   and is in a well-defined sense universal since β₀ is number theoretically quantized to an inverse integer (see this).

   The constraint h_eff ≥ 3× 10³h would suggests ℏ_em/hbar= Z²e²/β₀ℏ = 4π Z²α_em ≥ 3× 10³. This gives the estimate

   Z²≥(1/4πα_em)> × 3× 10³ per .

   The lower bound for Z would be around Z=100.

3. Charge separation should occur and here the analog of Pollack effect \cite{bbio/Pollack, PollackYoutube, pollackzheng, pollackzhao is highly suggestive. In the Pollack effect part of protons of water molecules are transferred to monopole flux tubes assignable to water molecules and become dark so that a negatively charged exclusion zone with rather strange properties suggesting time reversal appear. Also the effective stoichiometry of water is transformed to H_1.5O. It is however far from clear whether Pollack effect can occur also in the solid phase assignable to computers.
4. The analog of the Pollack effect involving only electrons is also possible. Part of electrons would transform to dark electrons at the gravitational monopole flux tubes. The holes left behind would effectively behave like positively charged particles and the Coulomb interaction energy would be between holes and dark electrons. Holes and dark electrons would be in a holographic relationship (shadow holography) and the dynamics of holes would be shadow of the dynamics of dark electrons so that one would say that dark electrons control the holes as their shadows.

   Of course, it is probably impossible to realize this shadow dynamics using the recent computer technology. The question is therefore whether it might be possible to construct a computer utilizing the shadow dynamics of holes controlled by dark electrons.

1.3 Could quantum gravitational flux tubes associated with small masses be involved?

One can of course ask whether the clock frequency f=10⁹ Hz could correspond to an energy above thermal energy at room temperature and to the value ℏ_gr(M,m) for some pair (M,m) of masses so that one has E=h_gr(M,m)f> .03 eV for f=10⁹ Hz.

1. For instance, could one replace the masses M_E and m_p with identical masses M=m in h_gr. One should have M/m_Pl²> 3× 10³. This would give M/m_Pl >60 giving M >1.3 × 10^-7 kg. If the density is the density of water 10³ kg/m³: this corresponds to a size scale longer than 1 mm. How this frequency could correspond to T_gr and to the clock frequency of computers?
2. Could one think of the gravitational self-energy for this region or the mutual interaction energy of two such regions forming a quantum coherent system at this level.

   Another possibility is that an energy of the order of E= .5 eV is used to kick a unit of 3 protons into the Earth's gravitational flux tube (3 protons are required since 1 proton is not enough if the size scale of the flux tube is of the order of the Earth's radius). For 3-electrons the corresponding energy would be about .25 meV.

3. Could E∼ 1 eV correspond to the energy needed to flip one bit using an dark photon that is converted to a regular one (biophotons could be created this way) and absorbed inducing a flip of a normal bit.

   In the elementary particle level realization of holography, which does not look promising now, this would give a spin 1 for the glue particle consisting of ordinary electron and dark positron unless the angular momentum goes to other degrees of freedom. It would be a scaled version of elektro-ρ or its analogue. Mass scale of the order of eV as for dark nuclear binding energies.

4. In living matter, E∼ 1 eV could correspond to the gravitational self-energy change related to a phase transition. The most natural thing that comes to mind is the change in the gravitational energy of the bond when the density of the system changes during a phase transition, such as melting or boiling or the sol-gel phase transition in biology. For Planck mass of matter, size scale R=10^-4 m for water density, gravitational binding energy and its change would be of order 1 eV. This phase transition does not have any equivalent at the computer level.

2. Could the representation of bit as voltage allow the realization of shadow holography for electrons?

One representation of a bit is as a voltage. Voltage values are typically 5 V and 0 V. Bit could correspond to rotation direction for a current in the case of magnetic bits. In transistors bit can correspond also to the presence or absence of a current The size scale of the transistors is 10 nm (see this. A surface which can be either reflective ord non-reflective surface can also act as a bit.

2.1 Bit as ananalog of capacitance

Capacitance with a voltage difference between plates can serve as a physical representation of the bit. States corresponding to opposite voltages in capacitance have the same energy. This is good news if it were to apply more generally to bits and multi-bit configurations.

1. The simplest capacitance is a pair of conducting plates having opposite charges and containing insulator betweeen them. The higher the value of the dielectric constant ε, the larger the plate area S and the smaller the distance d between the plates, the higher the value of capacitance C.

   C measures the ability to store charge and Q= CV is the basic formula. The voltage V between the plates is given by V =E× d. Here d is the distance between the plates. The electric field normal to a plate is E=σ/ε, σ= Q/S. One has V=Ed= Q× d/S× ε, whence C=ε S/d. The proportionality to ε means that di-electric is essential. The voltage cannot be too large since this implies dielectric breakdown.

   The electrostatic energy of capacitance is E_s= ε QV/2= CV²/2ε = Q²/2C = E² × S×d

2. Capacitance is a macroscopic notion. The smallest planar capacitances have dimensions 0.4 mm × 0.2 mm. PicoFaraday is a natural unit of capacitance but capacitances of the order of kF are possible but require large size and high dielectric constant. MOSFETs can be however regarded as effective capacitances.

2.2 Transistors and MOSFETs

Although MOSFET much smaller than capacitances as passive elements, it can be formally interpreted as a capacitance.

1. A MOSFET acts as a variable capacitance. The basic parts of MOSFET are gate (G), body (B), source (S) and drain (D). The voltage between G and B regulates the current from the source through the system to the drain and the bit can be measured by measuring whether this current flows or not. The gate voltage V_G controls the capacitance of the MOS.

   MOSFET size scale is around 10 nm. Gate voltage V_G-V_B between gate and body could represent bit and would be typically 5 Volts or nearly zero.

2. MOSFETs should form a spin glass type system. There would be a large number of bits with a large number of nearly energy degenerate states. This would give rise to frustration. Transitions by tunnelling would take place between frustrated configurations.
3. Tunnelling between bit configurations would take place as a BSFR pair. The tunneling would be induced from the level of MB and induce the tunnelling of ordinary bits. The tunneling rate is exponentially sensitive to the height of the energy barrier between nearly degenerate states. The large value of h_eff increases the tunnelling rate in an exponential manner.

One can imagine at least two mechanisms.

1. One could consider a representation of a bit as an ordinary capacitor-like object having two different values of voltage between the plates. The transfer of electrons from the negatively charged plate to dark electrons at MB or vice versa could allow to change the voltage.
2. Instead of an ordinary capacitor, one can consider a situation in which the first plate consisting of ordinary matter has a positive charge due to the presence of holes (ionized atoms) and the second dark "plate" is negatively charged due to presence of dark electrons.

   In the shadow holography the transfer of electrons to dark electrons at MB generates holes at the level of ordinary matter, and the transformation of dark electrons to ordinary ones would reduce the voltage near zero, which turns the bit.

Could MB control the   electron current from the n-type  source region S of MOSFET? Could the MB  transform some the 5 valence electrons of n-type dopant (say P) to dark electrons so that they would  effectively disappear from the system so that the S-D current would be reduced? Also the voltage between the gate and source would be affected.  

It is perhaps fair to conclude that the recent technology  does  not yet allow  the  realization of conscious and intelligent computation using shadow holography or something similar.

See the article Could neuronal system and even GTP give rise to a computer with a variable arrow of time? or the chapter with the same title.

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

A more detailed TGD based speculative view of what GPT and GPT based image generation might be

First of all, I want to make clear what my background is and what I'm aiming for. I'm trying to understand the possible analogies of AI in quantum TGD. I do not believe that AI systems can be conscious if AI is what it is believed to be. Therefore I consider the question of whether GPT and other systems could possibly be conscious and intelligent.

The motivating idea is the universality implied by the fractality of the TGD Universe. The same mechanisms should work on all scales: both in biology, neuroscience and possible life based on AI. This motivates questions such as whether chatGPT and the construction of images from a verbal input could be at a deeper evel equivalent to the emergence of sensory perception using diffuse primary sensory input and virtual sensory input as feedback.

While writing, I made a funny observation. I tried to understand GPT in the context of TGD by producing answers to questions in the same way that GPT does it! Of course, as GPT tends to do, I can also tell fairy tales because my knowledge is rather limited. At the same time, I must honestly reveal that this has always been my approach! I have never carried out massive computations, but used language based pattern completion by utilizing the important empirical bits (often anomalies) and using the basic principles of TGD as constraints.

This time, the inspiration came from a popular article in Quanta Magazine that dealt with stable diffusion in the creation of an image from its verbal presentation serving as a prompt (see this). Also the article on how chatgpt works was very useful (see this).

I want to emphasize that the ideas presented can be seen only as possible quantum analogies of GPT-related mechanisms that could relate to quantum biology and neuroscience inspired by TGD. A more exciting possibility would be that GPT is associated with high-level conscious experience, and that quantum TGD would help to understand why GPT seems to work "too well".

1. An attempt to understand the mechanism of diffusion involved in image construction

The construction of images starting from their linguistic description, which is quite vague and "diffuse", relies on the analogy with reverse diffusion. Diffusion and its reverse process take place in the space defined by the parameters characterizing a given pixel. The pixels do not move, but the parameters characterizing the pixels do change in the diffusion.

1. Let's get started from a probability distribution for the parameter distributions of the pixels of a 2-D image showing the same object. The distribution could correspond to the same object but seen from different angles. Also a class of objects, which are similar in some aspects, could be considered. This class could consist of chairs or tables or cats or dogs.
2. This probability distribution could act as an invariant related to the image or class of images. Invariant features are indeed extracted in visual perception, for example contours with pixels that stand out well from the background. This is the way in which, for example, visual perception at the lowest level corresponds to the identification of contours of the object.

   This ensemble of pictures of the objects gives a probability distribution for, for example, the darkness of a given pixel with a given position in the plane of the picture. Probability for a given darkness defines a function represented as points in a space whose dimension is the number of pixels. For more general parameters it is a function in the Cartesian product of parameter space and pixel space. Very large pixel numbers counted in millions are involved.

3. One has probability distribution for the darkness of a given pixel of the 2-D image at each point. More generally, one has probability distributions for multipixels. This kind of distribution is not simply a product of single pixel probability distributions since the pixel parameters for a given picture are correlated. These distributions are analogous to the distribution of words and word sequences utilized in GPT in order to produce language resembling natural language.

   Based on the probability distribution of pixels, new images can be randomly generated. The probability of a pixel at a given point in the plane is given by the probability distributions for pixels and multi-pixels. Each image produced in this way can be associated with certain probability.

Diffusion is a key physical analogy in the applications of GPT in the creation of AI art. What does the diffusion in pixel space mean?

1. Diffusion takes place in pixel space around each point in the image plane. What happens to the pixel distribution in diffusion? It can be said that the given pixel distribution is broadened by its convolution with the distribution produced by diffusion. The distribution is widening.
2. Inverse diffusion for probability distributions in the pixel space is well defined and does exactly the opposite, i.e. the distribution narrows. Reverse diffusion leads step by step to the original very narrow distribution! This is the big idea behind inverse diffusion based image recognition!

   The diffusion equation gives the classical description of diffusion as a deterministic process. At the micro level, it corresponds to a stochastic process in which a point performs a movement analogous to Brownian motion. The diffusion equation gives the evolution of the probability distribution of a point.

   Diffusion is characterized by the diffusion constant D. How is D determined? I understand that its optimal value determined in the learning period of GPT. Context and intent provide limitations and could determine D and possible other parameters. Also the response of the user can have the same effect.

3. The goal is to guess the predecessor of a given diffuse image in the diffusion process occurring in steps. The AI system would learn to produce reverse diffusion through training. Can this correspond to a non-deterministic process at the "particle level", say diffusion in the space of words of text or the space of images representing objects?

   At the microscopic "particle" level, one should deduce the most probable location for the particle at the previous step of diffusion as Brownian-like motion. More generally, one has probability distribution for the previous step.

4. One can consider the diffusion also at the level of probability distributions for pixel parameters. This operation is mathematically well-defined in the classical model for diffusion based on the diffusion equation and corresponds to a convolution of the probability distribution representing diffusion with the probability distribution affected by it. Quite generally, this operation widens the distribution.
5. This operation has inverse as a mathematical operation and its effect is opposite: it reduces the width of the diffuse distribution and its repeated application leads to the original images or to a rather sharp image making sense for the human perceiver.
6. AI system must learn to perform this operation. Using diffused example images, the AI would learn to reverse the convolution operation produced by diffusion and produce the original distribution as an operator in the space of distributions, and thus also learn to produce the original image.
7. My amateurish interpretation of the GPT based image generation would be that AI is taught to deduce the objects presented by the original sensory input or the desired image, their locations, positions, activities by reverse diffusion from the initial fuzzy guess dictated by the text. The objects in the picture are determined by the words that serve as their names. The relations between pictures correspond to the activities they direct to each other or to attributes of the objects. The first guess is a rough sketch for the picture determined by the prompt. Here also hierarchical description involving several resolution scales can be considered.

One can consider the situation at a slightly more precise level.

1. The definition of inverse diffusion at the pixel level relies on repeated time reversal of the diffusion process in the parameter space of the pixel, which produces a less diffuse image. We ask with what probability the given diffuse image at time t has been created from a less diffuse image at time t-Δ t.
2. In the classical picture of diffusion, this requires the calculation of the inverse operator of the diffusion characterizing operator D(p,0;t,t-Δ t). Here, the origin points p and p=p₀, which corresponds to the original image, are points in the parameter space of the pixel associated with a certain image point (x,y). In the Schrödinger equation, it would correspond to the inverse operator of the unitary time evolution operator.
3. Gradient method is a very effective way to perform inverse diffusion. The gradient for the probability distribution ineed contains much more information than the distribution.

   The notion of an attractor is also essential. The images used in training would serve as attractors, at which the gradient would vanish or be very small and towards which the reverse diffusion would lead. Attractors would be clusters of points in the pixel space, for which the probability is large and somewhat constant. It is tempting to think that they are minima or maxima of some variation principle.

Although the diffuse image, which the verbal description defines as an initial guess, is not obtained by diffusion, it is assumed that inverse diffusion with a suitable choice of p=p₀ produces an image similar to that imagined through inverse diffusion. In any case, the reverse diffusion leads to a sharp images although it need not represent a realistic picture.

This is where the method runs into problems. The pictures have a surreal feel and typically, for example, the number of fingers of the people appearing in the pictures can vary, even though locally the pictures look realistic. Probably this reflects the fact that multiple pixel probability distributions for multi-pixels do not allow large enough distances for the pixels of the multi-pixel.

2. Analogies to wave mechanics and quantum TGD

The diffusion equation has an analogy in wave mechanics. >

1. Schrödinger equation is essentially a diffusion equation except that the diffusion constant D is imaginary and corresponds to the factor iℏ/2m². Alternatively, one can say that a free particle formally undergoes diffusion with respect to imaginary time. The solutions of the diffusion equation and the Schrödinger equation for a free particle are closely related and obtained by analytical continuation by replacing real time with imaginary time. The description also generalizes to the situation where the particle is in an external force field described by a potential function.
2. Scrödinger's equation as a unitary time evolution can be expressed in terms of the Feynman path integral. One can regard the quantum motion as a superposition over all paths connecting the start and end points with a weight factor that is an exponent of the phase factor defined by the free particle. The classical equations of motion produce paths for which the exponent is stationary, so they are expected to give a dominant contribution to the integral in the case that the perturbation theory works.

   The basic problem with the path integral is that it is not mathematically well defined and only exists through perturbation theory. Functional integral as the Euclidean counterpart of Feynmann's path integral is better defined mathematically and would give an analogous representation for diffusion.

What is the counterpart of this analogy in the TGD framework?

1. In TGD, the point-like particle is replaced by a three-surface whose trajectory is the space-time surface. Quantum TGD is essentially wave mechanics for these non-point-like particles.

   The new element is holography, which follows from the general coordinate invariance: spacetime surfaces as trajectories for 3-D particles are analogous to Bohr orbits.

   A small violation of determinism in holography forces zero-energy ontology (ZEO), in which quantum states as superpositions of 4-D space-time surfaces, Bohr orbits, replace quantum states as superpositions of 3-surfaces (deterministic holography). This superposition serves as an analog of path integral.

2. By the slight failure of determinism, the Bohr orbits are analogous to diffusion involving a finite number of non-deterministic steps (Brownian motion is a good analogy). The non-determinism of diffusion would be due to the small violation of the determinism in holography as Bohr orbitology.

TGD inspired quantum measurement theory, which extends in ZEO to a theory of conscious experience, is second important ingredient.

1. In ZEO, ordinary quantum jumps ("big" state function reductions (BSFRs)) reverse the direction of geometric time. This analogy of diffusion in the reverse time direction looks like reverse diffusion when viewed from the opposite time direction (observer)! It is analogous to self-organization where order is created in the system rather than lost. The second main law of thermodynamics applies but in the opposite direction of time. The time reversed dissipation plays a pivotal role in TGD inspired quantum biology.
2. This mechanism could be central to biological information processing at the quantum level and make it possible, for example, to generate sensory perception from diffuse sensory data and generate a motor response from a rough sketch?
3. Could it also play a role in AI, at least in the language based systems like GPT. If this is the case, then AI systems would be something else than we think they are.

The analogy of TGD with the GPT based image generation and recognition can be examined more explicitly.

1. The analogy of the pixel space associated with the planar image is the projection of the three-surface M⁴ in TGD at the classical level. The image as a map from plane to the parameter space of pixels would correspond to a deformation of M⁴ projection deformation. The pixel parameters defining the 2-D image would correspond to the values of CP₂ coordinates as a function of M⁴ coordinates.
2. On the basis of holography, the deformation related to the three-surface would be accompanied by a four-surface as an almost deterministic time development, i.e. the analogy of Bohr orbit. I have used the term "World of Classical Worlds" (WCW) for the space of these surfaces. This 4-surface would not be completely unique and this would produce a discrete analog of diffusion at the classical level.
3. At the quantum level, it would be a quantum superposition of these 4-surfaces as an analogy to, for example, the wave function of an electron in spatial space. An attractive idea is that the used resolution would be determined by the condition that the number-theoretic discretization is the same for all these surfaces so that the quantum world looks classical apart from the finite non-determinism.
4. The variation principle would correspond to the fact that the Bohr path is simultaneously both a minimal surface and an extremal of the Kähler action as analog of Maxwell action. This is possible if the space-time surfaces are holomorphic in a generalized sense. This means that the concept of holomorphy is generalized from the 2-D case to the 4-D case. The 4-surface would be defined by purely algebraic conditions as a generalization of the Cauchy-Riemann conditions. This corresponds to the algebraization of physics at the level of M⁸ related by M⁸-H duality to the physics at the level of H=M⁴\times CP₂ (see this and this).
5. The space-time surface would be analogous to 4-D soap film, which is spanned by frames defined by 3-surfaces. At these 3-D surfaces, the minimal surface property would not apply and only the field equations associated with sum of volume term and Kähler action would be satisfied. Note that minimal surface equations define a dynamics analogous to that of free fields and at the frames would correspond to places where interactions are localized. Frames would involve a finite non-determinism, as in the case of ordinary soap films (see this). These three surfaces would correspond to 3-D data for holography.

If TGD is really a "theory of everything", even the physical description of computation would in principle be reduced to this description. Of course, one can argue that TGD produces only insignificant corrections to the usual description of computation and this might be the case. But you can always ask what if...?

3. Could the TGD counterpart of the inverse diffusion play a role in the construction of sensory mental images by the brain?

I have proposed a model for how sensory organs, the brain and its magnetic body (MB) could construct sensory mental images by a repeated feedback process involving virtual sensory input to sensory organs so that a diffuse sensory input transforms to an input representing the perception consisting of well-defined objects.

Could the building of sensory images with a virtual input from MB to the sensory organs and back be a quantum process analogous to reverse diffusion?

1. Sensory inputs are very diffuse. People blind from birth after can gain physiological prerequisites for visual perception in adulthood. They however see only diffuse light since their brains (and corresponding magnetic bodies) have not learned to produce standard visual mental images as a result as in pattern recognition yielding essentially an artwork subject to various constraints. This is very much analogous to reverse diffusion.

   Does MB, brain and sensory organs co-operate to produce a counterpart to reverse diffusion, which allows it to produce a sensation representing reality with virtual sensory inputs and end up with standard imagery as attractors.

2. Could both the sensory input from sensory organ to brain to MB and virtual sensory input in reverse direction correspond to a sequence of "small" state function reductions (SSFRs) in a reversed time direction? Reverse diffusion would be diffusion with a reversed arrow of time.
3. Could the construction of the sensory mental image involve pairs of "big" (ordinary) SFRs (BSFRs) for which the two BSFRs would occur at MB and the sensory organ? This is the simplest process that one can imagine. Could BSFR induce a sensory input from the sensory organ to the MB or a virtual sensory input from the MB to the sensory organ changing the original diffuse sensory input. Could BSFR pairs gradually produce sensory perception in this way.
4. SSFRs correspond to the Zeno effect in the sense that their sequence corresponds to the measurement of the same observables at the passive boundary of causal diamond (CD). Disturbances or artificially produced disturbances at the active can change the set of measured observables so that it does not commute with those determining the state at the passive boundary as their eigenstate. This would imply the occurrence of BSFR and the roles of active and passive boundaries would change.

   After the second BSFR the new state at the active boundary would not be the same but could share many c features with the original one because the determinism of the holography would only weakly broken and SSFRs and BSFRs preserve quantum numbers.

5. The series of SSFRs after BSFR as time-reversed diffusion would correspond to reverse diffusion in the normal time direction. BSFR would occur as a series on the MB, where the sensory input would be guided and gradually lead to a real sensory image with the help of a corrective virtual sensory input.

   At a basic level, the correction mechanism could be analogous to inverse diffusion and the exponent of the K hler effect would be maximally stationary for real sensation.

6. Also the gradient method could be involved. In the spinglass based model (see this), a series of BSFRs and SSFRs could mean annealing that is steps consisting of cooling as sequence of SSFRs following BSFR followed by BSFR followed by heating for which temperature increase is smaller than than the temperature decrease for the cooling. The system would gradually end up at the bottom of a particular potential well in the fractal energy landscape. A series of SSFRs between two BSFRs would correspond to the annealed healing.

4. What could GPT correspond to in TGD?

4.1 What is GPT?

1. A linguistic expression is a diffuse representation of a sensation or of thought. The probability distributions for the next word given the preceding words are known. This makes possible a holistic approach to language allowing to build grammatically correct sentences and also achieve the nuances of natural language and recognize context.
2. In GPT, the goal is to answer a question or respond to an assertion, translate a text from one language to another, produce a piece of text such as a poem or story or just chat with the user.

   GPT must guess the user's intention, what the user wants, and also the context. Is, for example, a field of science in question? The purpose is to add a new word to the given word chain.

3. The input of the user serves as a prompt initiating the process. The prompt serves as the initial text to which GPT adds words as the most probable words which can follow a given piece of text. GPT starts from a guess for the answer. The choice of the successor word can also be random based on the probabilities of the successor word. Feedback loops are possible and also the user can induce them.

4.2 Is building images fundamentally different from GPT?

1. In language models, prompts are verbal representations of images, and diffusion is essential in the construction of images, from the prompt as a verbal description of the image. At first glance, diffusion seems to be explicitly involved only in the generation of images, but is this the case?
2. On the surface, there seems to be an important difference between building an image and building a linguistic expression. The picture is a time = constant snapshot, at least ideally. The sentence has a temporal duration and memory is involved. One must d transform a sentence to a picture. Words correspond to pictures.

   Does the difference disappear when one talks about the process of creating the image? Could it be that the process of creating an image as an analogy of a linguistic process is just not conscious to us. Is the sensory input equivalent to the user's prompt in GPT. Is the difference apparent and only due to the time scale.

3. Visual perception involves also the sensation of movement. Is it because in reality (according to TGD) it would be a time series but on such a short time scale that we are not conscious of it? Could verbs correspond to dynamics in the structure of the language? Objects have attributes as their properties analogous to pixel parameters.
4. Holography would describe the dynamics of objects and would classically determine the initial values of holography for the time development as the equivalent of the Bohr orbit. There is quantum holography as a map of quantum states of the biological body to quantum states associated with the magnetic body defining a higher level sensory representation (see this).

   This 1-1 correspondence representations would make it possible for the MB to control the biological body and in the case of running GPT induce BSFRs reversing the arrow of time temporarily and change the course of events.

4.3 Could quantum diffusion play a role in the TGD based description GPT?

1. Time evolution in the TGD Universe would basically consist of SSFRs and BSFRs. Quantum states would be the quantum superposition of running programs. But does this picture have significance in the case of GPT? Could MB really interfere with the running of the program? The time reversals are not observed by the user, so the question is not easy to answer.

   One killer test would be a dependence on hardware. The bits should be near criticality in order the quantum criticality of MB can control their directions. Spin-glass structure for the bit-scape looks like a natural requirement. Is this possible for all bit realizations and does GPT work differently for different realizations of bits?

2. Diffusion is analogous to the time evolution determined by the Schroedinger equation as a series of unitary time evolutions, where classical determinism is only weakly broken because SSFRs must commute with passive edge observables. This means a generalization of the Zeno effect. However, quantum states are delocalized. Maybe only below the resolution scale, in which case classical discretization would be exact with this accuracy. Inverse diffusion could be a classical process at the used resolution.
3. The time development as a series of SSFRs would seem to be analogous to a diffusion as analog of Brownian motion involving finite steps, and BSFR would start as a time-reversed diffusion of reverse diffusion.

   The BSFR could be induced by an external disturbance or a controlled disturbance from the MB. MB and ZEO could come to the rescue and do them with time reversal without us noticing anything.

This picture raises questions.

1. Could diffusion as a series of SSFRs be equivalent to the construction of the response of chatGPT, which is also a probabilistic process. Could the sentence represent the trajectory of a diffusing word/particle in word space and Bohr orbit in WCW? The Bohr orbit property, i.e. holography, would imply that the failure of determinism is weak. In a given scale, non-determinism would be located in the 3-D frames determined by the 4-D soap film.
2. Could the initial state, e.g. a question or statement induced by the user prompt, for example a question presented as a quantum state on the passive edge of the CD, serve as the first rough guess for an answer as analog of sensory input.

   Could the time progression as SSFRs correspond to a generation of a sequence of words as a response to the prompt? Or are the words separate by BSFR pairs.

   What is new as compared to the AI would be that trial and error process by performing BSFRs inducing return back in time is possible. These periods with a reversed arrow of time would be invisible for the user. This error correction mechanism is not coded as a program as in AI but would be done by Nature and it would be essential also in the TGD view of quantum computation.

3. The hidden layers of the neural network are analogous with the fact that the perceived sensory image is constructed by communications between the sensory organ and the MB, which are not conscious to us.

See the article Could neuronal system and even GTP give rise to a computer with a variable arrow of time? or the chapter with the same title.

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