Is analysis as a cognitive process analogous to particle reaction?

The latest work with number theoretical aspects of M⁸-H duality (see this) was related to the question whether it allows and in fact implies Fourier analysis in number theoretical universal manner at the level of H= M⁴× CP₂.

The problem is that at the level of M⁸ analogous to momentum space polynomials define the space-time surfaces and number theoretically periodic functions are not a natural or even possible basis. At the level of H the space-time surfaces can be regarded orbits of 3-surfaces representing particles and are dynamical so that Fourier analysis is natural.

That this is the case, is suggested by the fact that M⁸-H duality maps normal spaces of space-time surface to points of CP₂. Normal space is essentially the velocity space for surface deformations normal to the surface, which define the dynamical degrees of freedom by general coordinate invariance. Therefore dynamics enters to the picture. It turns out that the conjecture finds support.

Consider now the topic of this posting. Number theoretic vision about TGD is forced by the need to to describe the correlates of cognition. It is not totally surprising that these considerations lead to new insights related to the notion of cognitive measurement involving a cascade of measurements in the group algebra of Galois group as a possible model for analysis as a cognitive process (see this, this and this).

1. The dimension n of the extension of rationals as the degree of the polynomial P=P_n1∘ P_n2∘ ... is the product of degrees of degrees n_i: n=∏_in_i and one has a hierarchy of Galois groups G_i associated with P_ni∘.... G_i+1 is a normal subgroup of G_i so that the coset space H_i=G_i/G_i+1 is a group of order n_i. The groups H_i are simple and do not have this kind of decomposition: simple finite groups appearing as building bricks of finite groups are classified. Simple groups are primes for finite groups.
2. The wave function in group algebra L(G) of Galois group G of P has a representation as an entangled state in the product of simple group algebras L(H_i). Since the Galois groups act on the space-time surfaces in M⁸ they do so also in H. One obtains wave functions in the space of space-time surfaces. G has decomposition to a product (not Cartesian in general) of simple groups. In the same manner, L(G) has a representation of entangled states assignable to L(H_i) (see this and this).

This picture leads to a model of cognitive processes as cascades of "small state function reductions" (SSFRs) analogous to "weak" measurements.

1. Cognitive measurement would reduce the entanglement between L(H₁) and L(H₂), the between L(H₂) and L(H₃) and so on. The outcome would be an unentangled product of wave functions in L(H_i) in the product L(H₁)× L(H₂)× .... This cascade of cognitive measurements has an interpretation as a quantum correlate for analysis as factorization of a Galois group to its prime factors defined by simple Galois groups. Similar interpretation applies in M⁴ degrees of freedom.
2. This decomposition could correspond to a replacement of P with a product ∏_i P_i of polynomials with degrees n= n₁n₂..., which is irreducible and defines a union of separate surfaces without any correlations. This process is very much analogous to analysis.
3. The analysis cannot occur for simple Galois groups associated with extensions having no decomposition to simpler extensions. They could be regarded as correlates for irreducible primal ideas. In Eastern philosophies the notion of state empty of thoughts could correspond to these cognitive states in which SSFRs cannot occur.
4. An analogous process should make sense also in the gravitational sector and would mean the splitting of K=n_A appearing as a factor n_gr=Kp to prime factors so that the sizes of CDs involved with the resulting structure would be reduced. Note that ep(1/K) is the root of e defining the trascdental infinite-D extension rationals which has finite dimension Kp for p-adic number field Q_p. This process would reduce to a simultaneous measurement cascade in hyperbolic and trigonometric Abelian extensions. The IR cutoffs having interpretation as coherence lengths would decrease in the process as expected. Nature would be performing ordinary prime factorization in the gravitational degrees of freedom.

This cognitive process would also have a geometric description.

1. For the algebraic EQs, the geometric description would be as a decay of n-sheeted 4-surface with respect to M⁴ to a union of n_i-sheeted 4-surfaces by SSFRs. This would take place for flux tubes mediating all kinds of interactions.

   In gravitational degrees of freedom, that is for trascendental EQs, the states with n_gr=Kp having bundles of Kp flux tubes would deca to flux tubes bundles of n_gr,i=K_ip, where K_i is a prime dividing K. The quantity log(K) would be conserved in the process and is analogous to the corresponding conserved quantity in arithmetic quantum field theories and relates to the notion of infinite prime inspired by TGD \citeallbvisionc.

2. This picture leads to ask whether one could speak of cognitive analogs of particle reactions representing interactions of "thought bubbles" i.e. space-time surfaces as correlates of cognition. The incoming and outgoing states would correspond to a Cartesian product of simple subgroups: G=∏^×_i H_i. In this composition the order of factors does not matter and the situation is analogous to a many particle system without interactions. The non-commutativity in general case leads to ask whether quantum groups might provide a natural description of the situation.

See the article Is M⁸-H duality consistent with Fourier analysis at the level of M⁴× CP₂? or the chapter Breakthrough in understanding of M⁸-H duality.

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

Articles and other material related to TGD. 


Is M8-H duality consistent with Fourier analysis at the level of M4× CP2?

Is M⁸-H duality consistent with Fourier analysis at the level of M⁴× CP₂? M⁸-H duality predicts that space-time surfaces as algebraic surfaces in complexified M⁸ (complexified octonions) determined by polynomials can be mapped to H=M⁴× CP₂.

The proposal (see this) is that the strong form of M⁸-H duality in M⁴ degrees of freedom is realized by the inversion map p^k∈ M⁴→ ℏ_eff×p^k/p². This conforms with the Uncertainty Principle. However, the polynomials do not involve periodic functions typically associated with the minimal space-time surfaces in H. Since M⁸ is analogous to momentum space, the periodicity is not needed.

In contrast to this, the representation of the space-time surfaces in H obey dynamics and the H-images of X⁴⊂ M⁸ should involve periodic functions and Fourier analysis for CP₂ coordinates as functions of M⁴ coordinates.

Neper number, and therefore trigonometric and exponential functions are p-adically very special. In particular, e^p is a p-adic number so that roots of e define finite-D extensions of p-adic numbers. As a consequence, Fourier analysis extended to allow exponential functions required in the case of Minkowskian signatures is a number theoretically universal concept making sense also for p-adic number fields.

The map of the tangent space of the space-time surface X⁴⊂ M⁸ to CP₂ involves the analog velocity missing at the level of M⁸ and brings in the dynamics of minimal surfaces. Therefore the expectation is that the expansion of CP₂ coordinates as exponential and trigonometric functions of M⁴ coordinates emerges naturally.

The possible physical interpretation of this picture is considered. The proposal is that the dimension of extension of rationals (EQ) resp. the dimension of the transcendental extension defined by roots of Neper number correspond to relatively small values of h_eff assignable to gauge interactions resp. to very large value of gravitational Planck constant ℏ_gr originally introduced by Nottale.

Also the connections with the quantum model for cognitive processes as cascades of cognitive measurements in the group algebra of Galois group (see this and this) and its counterpart for the transcendental extension defined by the root of e are considered. The geometrical picture suggests the interpretation of cognitive process as an analog of particle reaction emerges.

See the article Is M⁸-H duality consistent with Fourier analysis at the level of M⁴× CP₂? or the chapter Breakthrough in understanding of M⁸-H duality.

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

Articles and other material related to TGD.

Can one regard leptons as effectively local 3-quark composites?

The idea about leptons as local composites of 3 quarks (see this) is strongly suggested by the mathematical structure of TGD. Later it was realized that it is enough that leptons look like local composites  in scales longer than CP₂ scale defining the scale of the partonic 2-surface assignable to the particle.   

The proposal has profound consequences. One might say that SUSY  in the TGD sense has been   below our nose  for more than a century. The proposal could also solve matter-antimatter asymmetry since the twistor-lift of TGD predicts the analog of Kähler structure for Minkowski space and a small CP breaking,  which could make possible   a cosmological evolution in which quarks prefer to form baryons and antiquarks to form leptons. 

The basic objection is that the leptonic analog of Δ might emerge. One must explain why this state is at least experimentally absent and also develop a detailed model. In the article Can one regard leptons as effectively local 3-quark composites?  the construction of leptons as effectively local 3 quark states allowing effective description in terms of the   modes of leptonic spinor field in H=M⁴× CP₂ having H-chirality opposite to quark spinors is discussed in detail.

See the article Can one regard leptons as effectively local 3-quark composites? and the chapter The Recent View about SUSY in TGD Universe.

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

Articles and other material related to TGD. 


Quantum asymmetry between space and time

I received a link to a popular article about a test the proposal of Joan Vaccaro that if time reversal symmetry T were exact, our Universe would be radically different (thanks for Reza Rastmanesh and Gary Ehlenberg) For instance, wave functions would be wave packets in 4-D sense and conservation laws would be lost. Breaking of T would however come in rescue and give rise to the world in which we live. This proposal does not make sense in standard quantum theory but JV proposes a modification of path integral for single particle wave mechanism leading to the result.

I found that I could not understand anything about the popular article. I however found the article "Quantum asymmetry between space and time" by Joan Vaccaro. I tried to get grasp about the formula jungle of the article but became only confused. I expected clear logical arguments but I found none.

My comments are based mostly on the abstract of the article.

Asymmetry between time and space

[JV] An asymmetry exists between time and space in the sense that physical systems inevitably evolve over time, whereas there is no corresponding ubiquitous translation over space. The asymmetry, which is presumed to be elemental, is represented by equations of motion and conservation laws that operate differently over time and space.

My comments:

1. One might argue like JV does if one does not keep in mind that Lorentz invariance allows to distinguish between timelike and space-like directions and base the notion of causality on their properties.

   In Euclidian geometry there would be no such special choice of time coordinate. But also now field equations would define slicing of space-time to 3-D slices since initial values at them would fix the time solution. Now however the slices could be chosen in very manner manners - for instance 3-spheres rather than hyperplanes as in Minkowski space.

2. JV argues that there is an asymmetry in the quantum description of space and time in conventional quantum theory. The spatial coordinates of particle are treated as operators but time is not represented as an operator.

   The first mis-understanding is that the position of operator of particle is not space-time coordinate but specifies position of point-like particle in space time.

   The second mis-understanding is to think that the configuration space of the particle would be 4-D space-time. The configuration space of particle in non-relativistic wave mechanics is 3-space and time is the evolution parameter for unitary time evolution, not space-time coordinate. In the relativistic picture it could correspond to proper time along a world line.

   In quantum field theory (QFT) the spatial and temporal coordinates are in completely symmetric position. Wave mechanics is an approximation in which one considers only singlenon-relativistic particle. One should start from QFT or some more advanced to see whether the idea makes sense.

3. JV identifies subjective and geometric time as practically all colleagues do. In geometric time time evolution is determined by field equations and conservation laws. In TGD zero energy ontology (ZEO) does not identify these times and resolves the problems caused by identification of these two times. The counterpart of time evolution with respect to subjective time is sequence of small state function reductions.
4. The asymmetry between the two time directions appears in two manners.
   1. There is the thermo-dynamical arrow of time usually assumed to be the same always. In TGD both arrows are possible and the arrow changes in "big" (ordinary) state function reduction (BSFR). Subjective time correlates with geometric time but is not identical with it is closely related to the thermo-dynamical breaking of time reversal.
   2. The field equations (geometric time) have slightly broken time reflection symmetry T. This breaking is quite different from the generation of the thermo-dynamical arrow of time.

Could we give up the conservation laws and unitary time evolution and could the breaking of time reversal symmetry bring them back?

[JV] If, however, the asymmetry was found to be due to deeper causes, this conventional view of time evolution would need reworking. Here we show, using a sum-over-paths formalism, that a violation of time reversal (T) symmetry might be such a cause. If T symmetry is obeyed, then the formalism treats time and space symmetrically such that states of matter are localized both in space and in time.

In this case, equations of motion and conservation laws are undefined or inapplicable. However, if T symmetry is violated, then the same sum over paths formalism yields states that are localized in space and distributed without bound over time, creating an asymmetry between time and space. Moreover, the states satisfy an equation of motion (the Schrdinger equation) and conservation laws apply. This suggests that the timespace asymmetry is not elemental as currently presumed, and that T violation may have a deep connection with time evolution.

My comments:

1. JV is ready to give up symmetries and conservation laws altogether in the new definition of path integral but of course brings them implicitly in by choice of Hamiltonian and by using the basic concepts like momentum and energy which are lost if one does not have Poincare symmetry.

   What remains is an attempt to repair the horrible damage done. The hope is that the tiny breaking of T invariance would be capable of this feat.

2. Author uses a lot of formulas to show that T breaking can save the world. There are however ad hoc assumptions such as coarse graining and assumptions about the difference between Hamiltonian and time reversed Hamiltonian argued to lead to the basic formulas of standard quantum theory.

   The proposed formulas are based on single particle wave mechanics and do not generalize to the level of QFT. If one is really ready to throw away the basic conservation laws and therefore corresponding symmetries also the basic starting point formulas become non-sensible.

   Holistic mathematical thinking would help enormously the recent day theoretical physicists but it is given the label "philosophical" having the same emotional effect as "homeopathic" to the average colleague. What my colleague called formula disease has been the basic problem of theoretical physics for more than half century.

3. This modification of path integral formula looks rather implausible to me.
   1. Giving up the arrow of time in the sum over paths formalism breaks the interpretation as a representation for Hamiltonian time evolution (path integral is mathematically actually not well-defined and is meant to represent just Schroedinger equation).

      If there were no asymmetry between time and space, quantum states would be wave packets in 4-D sense rather in 3-D sense. This is of course complete nonsense and in conflict with conservation laws: an entire galaxy could appear from nothing and disappear. Author notices this but does not seem to worry about consequences. By the way, in TGD inspired theory of consciousnessthe mental image of the galaxy can do this but this does not mean the disappearance of the galaxy!

      The use of the wave mechanics which is not Lorentz invariant, hides the loss of Lorentz invariance implied by the formalism whereas ordinary Schrödinger equation as non-relativistic approximation of Dirac equation does not break Lorentz invariance in non-relativistic approximation.

   2. It is optimistically assumed that the tiny breaking of T symmetry could change the situation completely so that the predictions of the standard quantum theory would emerge. Somehow the extremely small breaking of T would bring back arrow of time and save conservation laws and unitary time evolution and we could be confident that our galaxy exists also to-morrow.

      Why the contributions to modified path integral for which time arrow is not fixed would magically interfere to zero by a tiny breaking of T invariance?

      The proposal seems to be in conflict with elementary particle physics. The view is that neutral kaon is a superposition of a state and its T mirror image and this means tiny T breaking. Neutrinos also break T symmetry slightly. In this framework all other particles would represent complete T breaking. Usually the interpretation is just the opposite. This does not make sense to me.

   3. The test for proposal would be based on the idea that neutrino from nuclear reaction defined flux diminishing as 1/r², r the distance from the reactor. This should somehow cause an effect on clocks proportional to 1/r² due to the incomplete destructive interference of the contributions breaking the ordinary picture. I do not understand the details for how this was thought to take place.

      The small T violation of neutrinos would affect the maximal T violation in environment and somehow affect the local physics and be visible as a modification of clock time - maybe by modification of the Hamiltonian modelling the clock. This is really confusing since just the small T violation is assumed to induce the selection of the arrow of time meaning maximal T violation!

To sum up, I am confused.

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

Articles and other material related to TGD.

A test for the quantum character of gravity as a test for quantum TGD

The following represents comments to a popular article describing a proposed experiment possibly conforming the quantum character of gravity. Thanks for the link to Gary Ehlenberg.

The proposal in idealized form is following.

1. One has two diamonds which are originally in superposition of two opposite spin directions.
2. One applies magnetic field with gradient. We know that in external magnetic field which is not constant, particle with spin is deflected to a direction which is opposite for opposite sping directions. If one has a superposition of spins then one would obtain superposition of deflected spin states with different spatial positions. The diamond can be said to be at two positions simultaneously. This is the key effect and leads to the question about whether and how it could be described in general relativity.

Consider now the situation in various approaches to quantum gravity.

1. The situation is problematic from the point of view of classical GRT since the gravitational fields created by the different spin components of superposition would have different distribution of mass. Classical GRT space-time determined by Einstein's equations would not be unique. In order to avoidthis one could argue that state function reduction (SFR) occurs immediatelyso that the spin is well-defined and space-time is unique. This looks very ugly but to my surprise Dyson takes this possibility seriously.
2. In quantum gravity based on GRTview it seems that one should allow superposition of space-times or at least of 3-spaces. The superposition of 3-geometries would conform with Wheelerian superspace view but leads to the problems with time and conservationlaws quite generally. Wheeler's superspace did not work mathematically.
3. In the description in terms of quantum gravitons one would give up the GRT picture altogether and string model view is something akin to this. Unfortunately, the attemptsto formulate quantum gravitation as a field theory in empty Minkowski space using Einstein's action fail. The divergences are horrible and renormalization is not possible. String models in turn try to get space-time by spontaneous compactification but this led to the landscape misery.

TGD based picture avoids the problems of these approaches.

1. In zero energy ontology (ZEO) the quantum states are superpositions of space-time surfaces : not superpositions of general 4-geometries making even not sense in standard QM or of 3-surfaces as they would be in generalization of Wheeler's superspace approach. The space-time surfaces would be preferred extremals of the action defining the theory and one obtains holography from general coordinate invariance: 3-surface determines space-time surface just as the point of Bohr orbit defines the Bohr orbit.
2. In this picture superposition of states with position of particle depending on spin direction corresponds to superposition of different space-time surfaces. Also the entanglement between various components of the state involving two spin superposed states of the two diamonds involved, is possible and generated in the time evolution. Entanglementwould have as a correlate magnetic flux tubes connecting the diamonds. One would have superposition of space-time surfaces corresponding to different flux tube lengths connecting spin states at various positions. Thereisno reason to expect that entanglement would not be generated. The expected positive outcome of the experiment could be seen as a proof of not only quantum character of gravitations but evidences for the superposition of space-time surfaces and ZEO.
3. Diamonds are rather large objects and the small value of Planck constant is the trouble in the standard approach. It might be possible to overcome this problem in TGD. TGD predicts that dark matter corresponds to phases of ordinary matter with arbitrarily large values of h_eff at MB glux tubes would have macroscopic quantum coherence in the scale of flux tube and could induce coherence of ordinary matter (diamonds) at their end as controllers of the ordinary matter. This would not be quantum coherence but would make visible the quantum coherence at the level of MB.

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

Articles and other material related to TGD. 


Oumuamua and TGD

The strange object known as Oumuamua (briefly O in the sequel) has gained a lot of attention. I have not had time to seriously check why O is so strange that Harward's top astronomer Avi Loeb regards it as evidence for alien life. Now I decided to do this and read a popular article describing the basic features of O. Wikipedia contains a more technical article about O.

O indeed has several strange features.

1. O had no tail as comets have: the tail is due to evaporation caused by the solar radiation. Artistic vision about O is as a long cylinder looking like rock. This vision is misleading since what was actually seen was a point-like object.
2. The reflectivity was highly varying and could be more than 10 times higher than for an average comet. From this it was deduced that O must have a shape of a cigar or a thin pancake. The spinning motion of O would be a tumbling characteristic for a rotor which rotates around a non-principal axis. This motion could explain the variations in reflectivity witha period of 7 hours.
3. O experiences a non-gravitational acceleration near Sun driving O away from Sun. Solar radiation pressure has been proposed as a reason. This would however suggest that solar light evaporates part of O:s mass and this causes a formation of a tail. No tail was observed.

   Could O have used an analog of a solar sail? The surface of the solar sail could have absorbed or perhaps even reflected the solar radiation and provided the momentum as a recoil to O. If the solar sail had a suitable shape, it perhaps prevented the radiation from reaching O itself and the formation of tail by evaporation. This shield mechanism would be somewhat similar to how the Earth's magnetic field shields life at the surface of Earth from the effects of cosmic rays and solar wind.

In the TGD framework the natural question is whether the magnetic body (MB) of O - having much larger size than O itself - could have served as a highly effective solar sail. Did the solar photons from the Sun give their energy and momentum to the MB of O? Did MB absorbthe photons and transform them to dark photons providing their energy for dark Bose-Einstein condensate of ions at the MB of O making it a primitive intelligent life form? Did solar light push MB away from the Sun and did O follow it?

A connection with the rotating magnet system studied by Godin and Roschin is suggestive. This system had strange features.

1. The system was accompanied by thin cylindrical magnetic walls in the direction of rotation axis.
2. As the rotation frequency approached 10 Hz (alpha frequency), the rotation started to accelerate and the system's effective weight either increased or decreased depending on the direction of rotation.
3. Also the air around the system was ionized and was cooled by a few degrees. This is not in accordance with thermodynamics.

In the TGD based model (see this) the system is regarded as a primitive life form.

1. The magnetic walls would correspond to the magnetic body (MB) of the system containing dark ions in TGD sense, in particular iron ions having very high value of h_eff=nh₀ and defining giving rise to cyclotron Bose-Einstein condensate to which the energy of the motor driving the system would have been stored. MB would have gained part of the energy feeded by the motor as analog of metabolic energy.
2. Eventually the system made a macroscopic state function reduction ("big" state function reduction (BSFR)). In TGD based theory of consciousness BSFR means what might be called death and reincarnation with an opposite arrow of time - this in a completely universal sense.
3. The time reversed dissipation by transformation of dark photons to ordinary photons looked for outsiders with the standard arrow of time like absorbing energy from the environment and causing the cooling. The energy and momentum of the photons would have caused effective loss of weight and accelerated rotation.

Could O be an analogous system? Elongated cigar shape would favor MB consisting of thin magnetic walls forming an ideal solar sail gathering the energy and momentum of solar photons by transforming them to dark photons of BE condensate. MB would have shielded O just like it shields life forms at Earth so that it O have avoided evaporation.

Is O a product of an advanced engineering or a primitive life form? It might be that the latter option is correct. As astronomer Avi Loeb suggests the interstellar space might be teeming these entities. If so, primitive life would populate the interstellar space.

See the article Time reversal and the anomalies of rotating magnetic systems or the chapter About Strange Effects Related to Rotating Magnetic Systems .

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

Articles and other material related to TGD.

How could the higher levels of MB use the brain to realize their free will?

The model proposed why predictions of events known to occur are better than those believed to be fictive (see this) assumes that the experienced long terms goals (in the recent case the goal of experimenter to perform the experiment) correspond to state function reductions (SFRs) that have already (with respect to subjective time) occurred at some higher layer of MB controlling the brain but that this subjective time corresponds to geometric time in the future of the participants and experimeters.

Neuroscience supports the view that frontal lobes are responsible for long term planning and decision making. They are involved also with the self model. This suggests that the highest layers of MB control frontal lobes. There would be a hierarchy of layers of MB having frontal lobes at the bottom.

Model for the coupling of MB with frontal lobes in terms of cognitive entanglement

A natural assumption is that the control of biological body by MB involves entanglement. Since frontal lobes are associated with high level cognition, this entanglement could be cognitive entanglement discussed in (see this). Cognitive entanglement is a hierarchical entanglemen between wave functions in hierarchy of sub-groups in the factorization of Galois group to a product G₁G₂...G_n of sub-groups reflecting directly the representation of extension as extension of extensions of .... of rationals.

What is special is that entanglement is directed like attention and hierarchical just like for the slaving hierarchy. The entanglement between states in group algebras of G₁ and G₂...G_n is directed from boss G₁ to slave G₂..G_n. Cognitive SFRs are cascades proceeding downwards and reducing entanglement. Negentropy Maximization Principle can however prevent the cognitive measurement cascade from proceeding down to G_n (see this) if it does not give rise to negentropy gain.

Long term goals could involve this kind of cognitive entanglement assignable to directed attention and motor actions as BSFRs at this layer of MB would produce what is experienced by the levels of the hierarchy with the standard arrow of time as a behavior with long termgoals. This would produce what could be regarded as analog of precognition (see this and identifiable as sensory perception of signals propagating to non-standard direction of time. Precognitive dreams would be an example of this.

What happens when frontal lobes are damaged?

This vision conforms with what happens when frontal lobes are damaged. Although intellectual abilities are not lost, long term planning is not possible and the patient loses the ability to initiate actions. Damage can also lead to idiot savant phenomenon. Although the person seems to lack conceptual thinking completely, he/she can possess miraculous looking mathematical skills (see this) or artistic gifts (see this). In some poorly understood sense idiot savants can be extremely intelligent.

Is the character of the cognitive entanglement changed or replaced with something totally different in these situations? TGD predicts two kinds of information related to two different representations of genetic code which relate to each other like function represented by its local values to its Fourier transform as a non-local and holistic representation (see this and this). The local representation of the genetic code is in terms of bits and using sequences of genetic codons as units of 6 bits. The second representation is in terms of 3-chords of light defining the allowed chords of a bio-harmony. Music expresses and induces emotions and bio-harmony would characterize a mood. Emotional intelligence would relate to this representation. Could it be that for idiot savants non-verbal emotional intelligence dominates.

The duality of these two representations of genetic code is highly analogous to the duality of momenta and position coordinates in wave mechanics. In quantum TGD this duality has as an analog M⁸-H duality (see this and this ) stating that space-time surfaces can be regarded as 4-surfaces in H=M⁴× CP₂ or in M⁸. M⁸-H duality relates these representations. H corresponds to ordinary differential geometric space-time representation involving also the notion of field. M⁸ identifiable as 8-D momentum space corresponds to non-local algebraic and number theoretic representation, which is non-local and holistic since the momenta are analogous to frequencies. Scattering amplitudes in particle physics provide an example of this representation.

Both representations can be used and it depends on the situation which representation is more appropriate. Could it be that for ordinary resp. emotional intelligence H resp. M⁸ representation is more appropriate? Could one exaggerate and say that not only idiot savants but also people in timeless meditative state and experiencing no separations (produced by cognitive SFRs), and maybe also children "live" in M⁸ whereas the ordinary people with their tight time schedules and busily performing comparisons "live" in H? Momentum eigenstates are delocalized.

Are meditative states labelled by finite simple groups?

What could be the counterpart of meditative state without cognition be at the level of cognitive representations? Could it correspond to a situation in which it is not possible to create separations as decompositions to unentangled system pairs by reducing the entanglement between the factors of the Galois group G?

This is certainly the case if G is simple, that is does not allow this factorization at all. Simple finite groups are the basic building bricks of finite groups: the classification theory for simple groups (see this) states that simple finite groups is cyclic and of prime order, alternating group consisting of even permutations of n objects, group of Lie type or one of the 26 sporadic groups or Tits group. The meditative states of pure consciousness would correspond to finite simple groups!

A question about possible classification of meditative states definitely raises eyebrows. But the power of mathematics is miraculous: if one agrees that thinking means SFRs (thought generates separations and comparisons) and that in meditative states thinking ceases, this is the conclusion.

Rather paradoxically, the "idiot savant state" would be cognitively irreducible in the same sense as the states of Hilbert space with prime dimension do not allow a representation as entangled states. They would represent elementary particles of cognition - fundamental ideas - from which more complexthoughts are composed by performing repeated extensions. The basic advice of meditative practices is to stop thinking: maybe this is indeed the manner to achieve the state of understanding.

See the article Why the outcome of an event would be more predictable if it is known to occur? (with Reza Rastmanesh) or the chapter About the nature of time.

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

Articles and other material related to TGD.

Why the outcome of an event would be more predictable if it is known to occur?

The experiments of Armor and Sackett demonstrate that the reliability of future predictions for events is better for real than for hypothetical events. This strange finding, if real, would be an anomaly analogous to Libet's findings about active aspects of consciousness challenging the notion of free will.

In this article it is argued that it is difficult to explain the finding in the physicalistic framework, and that the allowance of free will seems only to worsen the situation since precognition of acts of free will does not make sense. In the framework of Topological Geometrodynamics (TGD) zero energy ontology (ZEO) replaces the standard ontology of quantum theory. ZEO predicts that in "big" (ordinary) state function reductions (BSFRs) the arrow of time changes and that the identification of acts of free will identified as BSFRS is not in conflict with the determinism of classical physics as an exact part of quantum TGD. Also Libet's findings can be understood.

This suggests a model for the anomaly. The experiment would have already happened as BSFR ("already" is with respect to subjective time to be distinguished from geometric time) for a quantum system associated with the experimenters and participants. The knowledge that the event is actual inspires unconsciously the attempt to "remember" the personal performance in the experiment instead of only imagining it and this would explain the improved future predictions.

See the article Why the outcome of an event would be more predictable if it is known to occur? (with Reza Rastmanesh) or the chapter About the nature of time.

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

Articles and other material related to TGD. 


Time reversal and the anomalies of rotating magnetic systems

Free energy phenomena can be  defined as phenomena exhibiting   thermo-dynamical anomalies such as generation of gradients  rather than their disappearance. Concentration gradients can develop, electric fields as potential gradients can emerge  due to generation of  charge separations,   and  temperature gradients can be created.  The failure of  the second law in its standard form   also  manifests  itself as over-unity energy production,  cooling of the environment, and generation of structures rather than their decay characterizing self-organization.  

  The  general explanation of  these phenomena   would rely on the  change of the arrow of time in  ordinary ("big") state function reduction (BSFR) reversing the arrow of time  in the quantum measurement theory based on zero energy ontology (ZEO). This implies a new view about self-organization and also an explanation for self-organized (quantum) criticality.  BSFR would take place at the level of  the magnetic body (MB) carrying dark matter as h_eff=nh₀ phases and controlling ordinary matter, and BSFR would be macroscopic for large values of h_eff. 

In this article the anomalies in rotating magnetic systems  (RMSs)  discovered by Russian researchers Godin and Roschin are  discussed as  a particular free energy phenomenon. The time evolution of a rotating magnetic system (RMS) could be seen as an emergence  of a very simple life form receiving  and storing metabolic energy from the    motor driving the RMS, and liberating it at the moment of "death" as dark photons transformed to ordinary photons, whose counterparts in ordinary living matter are biophotons.  

See the article Time reversal and the anomalies of rotating magnetic systems or the chapter About Strange Effects Related to Rotating Magnetic Systems .

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

Articles and other material related to TGD. 


Aging from TGD point of view

The article "Aging from TGD point of view" written together with Reza Rastmanesh was inspired by the book "Lifespan" by Sinclair and LaPlante. The books proposed that aging is basically  caused by the approach to epigenetic  chaos. The book also proposesthat bio-information is not only associated with DNA and genetic code but the  conformational  degrees of DNA and these are crucial in epigenesis. This vision  serves as the starting point of   TGD (Topological Geometrodynamics) inspired view. 

Negentropy Maximization principle replacing in adelic physics second law but implying it for ordinary matter is the first key notion. Magnetic body (MB )carrying dark matter as h_eff=nh₀ phases of ordinary matter  implying quantum coherence in the scale characterized by h_eff represents the second key notion. MB is the controller of the dynamics and its quantum coherence induces the coherence  of ordinary biomatter as forced coherence rather than quantum coherence.  

 Zero energy ontology (ZEO) predicting the occurrence of time reversal in "big" (ordinary) state function reductions is the third key notion.   Time reversal forces generalization of thermodynamics and dissipation of a subsystem with a reversed arrow of time looks like self-organization from the point of view of the system. Also self-organized quantum criticality difficult to understand in ordinary thermodynamics becomes possible.

The basic idea is that at birth  the  MBs of information molecules are at very low temperature and gradually approach the  physiological temperature, which is near to Hagedorn temperature defining the maximal temperature of MB. This thermalization leads to epigenetic chaos implying that the flux tubes carrying dark DNA and therefore also  DNA become loopy. Also the control of methylation and other modifications and their reversals   crucial for epigenesis is lost. In particular, demethylation fails  and leads to hyper-methylation of the  promoter regions of genes. This leads to the failure of the control of genes coding for housekeeping  proteins and eventually the system suffers a crash down.

See the article Aging from TGD point of view or the chapter chapter with the same title.

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

Articles and other material related to TGD.