Monday, January 18, 2021

Negentropy Maximization Principle and Second Law

Negentropy Maximization Principle (NMP) as the variational principle of consciousness replaces the  second law  and implies it for ordinary matter.  State function reduction (SFR) means a reduction of the entanglement for a  pair Sa-Sb of sub-system  Sa and its complement Sb in S.   Measurement cascade proceeding from long to short scales decomposes  at each step a system to a pair of unentangled subsystems is in question. NMP  as a variational principle of consciousness  states that negentropy gain in these reductions  is maximized and selects the pair Sa-Sb at given step.     

In adelic physics the  negentropy is sum N= -S1-S2 of real and various p-adic negentropies but p-adic negentropy can be positive so that  for non-trivial extensions of rationals one can have N>0. This kind of entanglement   is stable against NMP so that the process stops. One can assign positively colored emotions to this kind of entanglement and it distinguishes between living and inanimate matter and also between dark and ordinary matter.

An attractive idea is that NMP forces the system to peferom "big" state function reduction (BSFR) when system approaches cognitive fixed point. This would mean death of the conscious entity and its re-incarnation with an opposite arrow of time.

See the article Negentropy Maximization Principle and Second Law or the chapter Negentropy Maximization Principle.

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

Articles and other material related to TGD. 


Monday, January 11, 2021

Is genetic code part of fundamental physics in TGD framework?

Topological Geometrodynamics (TGD) leads to 3 basic realizations of the genetic code. Besides the chemical realization, there is a realization in terms of dark proton sequences (dark nuclei) with 3-proton state representing codon. Ordinary DNA strands would be accompanied by dark magnetic flux tubes carrying the dark proton triplets. Also RNA, amino-acids and tRNA would have dark proton analogs.

The third realization is in terms of dark photon triplets and involves the notion of bio-harmony modelled in terms of icosahedral and tetrahedral geometries with 3-chords of light assigned to the triangular faces of icosahedron and tetrahedron. 12-note scale is realized as a Hamiltonian cycle for icosahedron with the step between nearest neighbor vertices for the cycle realised as a quint scaling of frequency. The 3-chords correspond to the triangular faces of the icosahedron. Also tetrahedral realization of 4-note scale is necessary in order to obtain genetic code. DNA codons correspond to triangular faces and the orbit of a given triangle under the symmetries of the icosahedral harmony correspond to DNA codons coding for the amino acid assigned with the orbit. Vertebrate genetic code emerges as a prediction.

Codon corresponds to 6 bits: this is information in the usual computational sense. Bio-harmony codes for a mood: emotional information related to emotional intelligence. Bio-harmony would be a fundamental representation of emotional information realized already at the molecular level. Dark photon 3-chords and more generally, 3N-chords representing genes, would mediate interaction between various realizations.

Why both icosahedron and tetrahedron? Could this relate to the fact that the tesselations of a hyperbolic space H3 are in fundamental role in quantum TGD. There is one particular tesselation known as tedtrahedral-icosahedral honeycomb. Could the genetic code be realized at the level of fundamental physics as a tedrahedral-icosahedral tesselation of H3 emerging as a cognitive representation for space-time surfaces at the level of M8 and by M8-H duality also in H=M4× CP2. Biological realization could be only one particular realization.

It should be possible to unify all models of the genetic code to single model so that the codon as a dark proton triplet is assigned to a representation as an "active" triangle of icosahedron or tetrahedron containing at it vertices dark protons defining the same codon as the triangle as 3-chord for a given icosahedral harmony. Could these "activated" triangles be assigned with tetrahedral-icosahedral tesselation? Could genes correspond to sequences of these icosahedron-tetrahedron pairs at magnetic flux tubes defined dark generatic code.

See the article Is genetic code part of fundamental physics in TGD framework? or the chapter An Overall View about Models of Genetic Code and Bio-harmony .

Articles and other material related to TGD.

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

Saturday, December 26, 2020

Do galactic rotational spectra show a violation of Strong Equivalence Principle?

This comment was inspired by a popular article (see this) about a study of the effect of external gravitational fields to the rotation curves of galaxies. The title of the research article by Chae et al is "Testing the Strong Equivalence Principle: Detection of the External Field Effect in Rotationally Supported Galaxies". The claim is that the Strong Equivalence Principle (SEP) is slightly violated: the rotational velocities are slightly reduced in the region region of orbital radii, where they are predicted to be constant in CDM models.

SEP predicts that in the cold dark matter (CDM) scenario that the internal dynamics of the galaxy should not depend appreciably on even strong external gravitational fields so that rotational velocities should not change. The reason is that in CDM dark matter is concentrated around the galaxy: the only effects would be tidal forces plus the Newtonian acceleration of the galaxy which does not depend on its mass. The observations suggest that this is actually not the case, and this is seen as a support for MOND and in conflict with CDM and also with GRT if SEP is assumed.

In the TGD framework the flat velocity spectrum of distant stars around the galaxy is due to a long cosmic string carrying dark matter and energy containing tangles in which strings have thickened and partially decayed to ordinary matter. This also explains why galaxies form linear structures. These are not local objects so that SEP does not apply to them. Hence there need not be any actual violation of SEP. The long string as a non-local object would react to the external forces which its own mass and rotating stars would experience the net gravitational force caused by the environment as entities in empty space since there would be no cold dark matter present now.

There would be a strong dependence of the effects on the direction of external gravitational fields when they are caused by a single object rather than being an average effect of the environment. If the external gravitational field is in the direction of the string, there would be an acceleration to this direction since the cosmic string does not cause gravitational field in this direction. This would sharply distinguish between halo models and TGD predicting the possibility of free flows of matter along long strings. If the external gravitational field is transversal there would be smaller perturbation reducing the transverse radial gravitational force of the cosmic string and attracting it.

In the recent study, the effect of gravitational fields caused by the environment of the galaxy was studied. These fields represent the sum of environmental gravitational fields. The first estimate is that the gravitational attraction of the environment boils down to a radial central force transversal to the cosmic string weakening the gravitational force caused by the long string. This would give rise to the reduction of the effective value of string tension T and indeed reduce the rotational velocity (v2 ∝ TG). What about CDM model? Due to the presence of dark matter halo, the effect of external fields would be a considerably weaker tidal effect in the CDM model at the distances considered (near the boundary of the visible galaxy).

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

Articles and other material related to TGD.

Are mistletoes quantum energy thieves?

There was a thought provoking article in Quanta Magazine with the title "The mystery of mistletoe's missing genes. Various research groups have observed that the mitochondria of mistletoe miss large parts of their respiratory complex. There is article "Miniaturized mitogenome of the parasitic plant Viscum scurruloideum is extremely divergent and dynamic and has lost all NAD genes" by Skippington et al, article "Absence of Complex I Implicates Rearrangement of the Respiratory Chain in European Mistletoe" by Senkler et al, and article "Absence of Complex I Is Associated with Diminished Respiratory Chain Function in European Mistletoe" by Maclean et al.

Mitochondria serve as energy plants of the cell. The mitochondria of plants known as mistletoes are very small and many of the genes coding for the needed proteins are missing so that it seems that they cannot produce ATP appreciably. Somehow mistletoes however manage to get their metabolic energy. Mistletoes are parasites: could they be also metabolic energy parasites?

The respiratory complex I, which is the first one in the chain in which ATP is produced, seems to be missing in the mitochondria of mistletoe. This large protein has two catalytic functions. It catalyzes the transfer of protons against a field gradient through the mitochondrial membrane and the transfer of electrons from NADH to coenzyme Q10. Protons fall back and give their potential energy to the rotating shaft of APTPase resembling a turbine of a power plant. ATPase gives the energy to phosphorylize ADP to ATP. ATP transfers it to the end user as quantized metabolic currence, one might say. The production of ATP requires energy provided by the electrons transferred along the respiratory chain to acceptors, whose electronegativity (abilities to receive electrons) increases along the chain. As the electrons propagate along the chain, they lose energy originating from metabolites.

The idea that mistletoes could survive with a very little metabolic energy does not look attractive. One proposal mentioned in the article is that they could produce ATP by a much less effective method than usually - by a glycolysis burning sugar outside the mitochondria. This requires sugar: could mistletoes steal it from the host plant? Or could mistletoes get their ATP somehow from the host somehow receive the energy needed to transform the ADP of mistletoe to ATP from the host. Or could they get their energy as radiation by some mechanism difficult to imagine in the standard physics framework.

TGD indeed inspires the question whether mistletoes be more advanced energy criminals. Could they steal the metabolic energy by a mechanism that I have proposed to be a general mechanism of metabolism and called it quantum credit card or remote metabolism. They would effectively send negative energy to some system able to receive it. For this instance, in the transformation of ADP to ATP to get positive energy as a recoil. The energies involved would be around .5 eV which corresponds to metabolic energy quantum and IR energy. The model involves two ingredients. Zero energy ontology (ZEO) (see this) and the hierarchy of dark matter as eff=nh0 phases of ordinary matter (see this), which is a prediction of the number theoretic vision about TGD.

  1. In zero energy ontology (ZEO) quantum credit card mechanism would be possible by making a "big" state function reduction (BSFRs) changing the arrow of time for some part of the magnetic body (MB). This would mean dissipation with a reversed arrow of time. For a standard observer this looks like extracting energy from the environment. For instance, could the ATP of the host receive the negative energy signal sent by mistletoe ADP and transform to ADP. This would occur also normally but now in a much longer length scale. Could mistletoe send negative energy signals to the mitochondria of the host or even to the own leaves of mistletoe performing photosynthesis.

    ZEO solves the basic paradox of quantum measurement theory and has very profound implications for the understanding of living systems and self-organization in general. Dissipation with reversed arrow of time looks like self-organization and self-organized quantum criticality very difficult to understand in the standard ontology because criticality is by definition something unstable becomes possible since critical system as a repeller with a reversed arrow of time looks like an attractor for the observer with the standard arrow of time.

  2. Dark matter hierarchy as phases of ordinary matter (also photons) identified as heff=nh0 would make possible quantum coherence of dark photons in scale much longer than the wavelength of order 2 micrometers. Hence this process would be possible in scales considerably longer than cell length scales associated with the ordinary metabolism. The system needing energy would send a negative energy signal to ATP transforming it to ADP and get positive energy as a recoil. This could be like a ATP-ADP→ADP-ATP→... flip-flop transferring the energy of ATP over intercellular distances.

    If this picture is correct, something related to the ATP of the mistletoe should differ somehow from the ordinary ATP. The magnetic body (MB) of mistletoe MB might be this something. If it carries dark matter with a value of heff =nh0 higher than in the case of ordinary APT, the negative dark photons would have longer coherence length and they could transform to ordinary photons received by the ATP of the host. Quite generally, TGD view suggests that the increase of heff serving as a kind of universal IQ is responsible for big evolutionary leaps. For instance, the emergence of language is known to involve only a few genes, and the increase of heff for their MBs could be responsible for the evolution of language (see this).

We have written together with Reza Rastmanesh an article about the use of this mechanism by shock proteins in ordinary biology. They could extract thermal energy from the environment to reduce the local temperature in the case of heat shock and heat basic biomolecules by acting as ovens in the case of cold shock. They could also serve as heat engines for molecular motors.

See the article Homeostasis as self-organized quantum criticality . For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Friday, December 25, 2020

New evidence for zero energy ontology

There was an interesting popular article in Digital Journal with title "Scientists show future events decide what happens in the past". The research article by Truscott et al published in Nature Physics has the title "Wheeler's delayed-choice gedanken experiment with a single atom".

There were two grates - I would speak of gratings - A and B following A so that particles went through A first. B was removed and put back randomly. If both gratings were in place, the incoming He atoms chose one path through A and behaved like a particle. When only the grate A was in place, wave behaviour was observed.

What looks paradoxical is that the addition of B forced particle behavior although the incoming He atom was already gone through A and selected wave behavior. The geometric past of the particle was changed from wavelike to particle-like! As if state function reduction would change also the geometric past of particle and quantum states were superpositions of classical time evolutions rather than time=constant snapshots as in the ordinary ontology!

This is what zero energy ontology (ZEO) indeed postulates so that the findings can be seen as an additional experimental support for ZEO. In ZEO quantum states are superpositions of time evolutions and "big" (ordinary) state function reduction (BSFR) selects new superposition of classical histories with opposite arrow of time: the roles of cause and effect for classical time evolution are apparently changed. ZEO solves the basic paradox of the quantum measurement theory. Also the weird looking findings of Minev et al can be explained in terms of the time reversal occurring in BSFR(see this).

Effect precedes cause: here cone for instance explanation for the findings of Libet challenging free will: the neural activity preceding act of free will in geometric time will is caused by free will initiating a superposition of time reversed classical time evolutions in the geometric future of the brain! The geometric past is changed.

To avoid paradox, one must keep in mind that "small" state function reductions (SSFRs) give to the experienced time correlating but not identifiable with the geometric time. In the experiment, the BSFR corresponds to a removal or addition of a grating and changes what happened before the addition/removal of grate - "before" in the sense of geometric time. Removal/addition is in the sense of subjective time of the experimenter.

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

Articles and other material related to TGD.

Thursday, December 24, 2020

About the implications of the revised form of M8-H duality

A critical re-examination of M8-H duality hypothesis led to what might be called a brealthrough in the understanding of M8-H duality. Several intuitive beliefs turned out to be wrong at the level of details as precise calculation became possible. The improved understanding led to a construction of scattering amplitudes at M8 level as counterpart for momentum space representations of scattering amplitudes wheteras the earlier breakthrough was related to their construction at the level of H=M4× CP2 (see this).

Since the article grew rather long, I decided to divide it into two parts. Below are the absracts of these articles.

A critical re-examination of M8-H duality hypothesis: part I

This article is the first part of an article representing a critical re-examination of M8-H duality, which is one of the cornerstones of Topological Geometrodynamics (TGD). The original version of M8-H duality assumed that space-time surfaces in M8 can be identified as associative or co-associative surfaces. If the surface has associative tangent or normal space and contains a complex or co-complex surface, it can be mapped to a 4-surface in H=M4× CP2.

Later emerged the idea that octonionic analyticity realized in terms of real polynomials P algebraically continued to polynomials of complexified octonion could fulfill the dream. The vanishing of the real part ReQ(P) (imaginary part ImQ(P)) in the quaternionic sense would give rise to an associative (co-associative) space-time surface.

The realization of the general coordinate invariance motivated the notion of strong form of holography (SH) in H allowing realization of a weaker form of M8-H duality by assuming that associativity/co-associativity conditions are needed only at 2-D string world sheet and partonic 2-surfaces and possibly also at their light-like 3-orbits.

The outcome of the re-examination was a positive surprise. Although no interesting associative space-time surfaces are possible, every distribution of normal associative planes (co-associativity) is integrable. Another positive surprise was that Minkowski signature is the only possible option. Equivalently, the image of M4 as real co-associative sub-space of Oc (complex valued octonion norm squared is real valued for them) by an element of local G2,c or its subgroup SU(3,c) gives a real co-associative space-time surface. The conjecture is that the polynomials P determine these surfaces as roots of ReQ(P). These surfaces also possess co-complex 2-D sub-manifolds allowing the mapping to H to H by M8-H duality as a whole. SH would not be needed and would be replaced with number theoretic holography determining space-time surface from its roots and selection of real subspace of Oc characterizing the state of motion of a particle. The equations for ReQ(P)=0 reduce to simultaneous roots of ordinary real polynomials defined by the odd and even parts of P having interpretation as complex values of mass squared mapped to light-cone proper time constant surfaces in H.

Octonionic Dirac equation as analog of momentum space variant of ordinary Dirac equation forces the interpretation of M8 as an analog of momentum space and Uncertainty Principle forces to modify the map M4⊂ M8→ M4⊂ H from identification to inversion. Contrary to the earlier expectations the space-time surface in M8 would be analogous to Fermi ball and mass squared sections would correspond to Fermi spheres. This leads to the idea that the formulation of scattering amplitudes at M8 levels provides the counterpart of momentum space description of scattering whereas the formulation at the level of H provides the counterpart of space-time description.

See the article A critical re-examination of M8-H duality hypothesis: part I.

A critical re-examination of M8-H duality hypothesis: part II

This article is the second part of an article representing a critical re-examination of M8-H duality. This re-examination has yielded several surprises. The first surprise was that space-time surfaces in M8 must and can be co-associative so that they can be constructed also as as images of a map defined by local G2,c (octonionic automorphisms) transformation applied to co-associative sub-space M4 of complexified octonions Oc in which the complexified octonion norm squared reduces to the real M4 norm squared. An alternative manner to construct them would be as roots for the real part ReQ(P) of an octonionic algebraic continuation of a real polynomial P.

The outcome was an explicit solution expressing space-time surfaces in terms of ordinary roots of the real polynomial defining the octonionic polynomials. The equations for ReQ(P)=0 reduce to simultaneous roots of the real polynomials defined by the odd and even parts of P having interpretation as complex values of mass squared mapped to light-cone proper time constant surfaces in H.

The second surprise was that space-time surface in M8 can be mapped to H as a whole so that the strong form of holography (SH) is not needed at the level of H being replaced with much stronger number theoretic holography at the level of M8.

The third surprise was that octonionic Dirac equation as an analog of momentum space variant of ordinary Dirac equation forces the interpretation of M8 as an analog of momentum space and Uncertainty Principle forces to modify the map M4⊂ M8→ M4⊂ H from identification to inversion. One obtains both massless quarks and massive quarks corresponding to two different number-theoretically characterized phases.

This picture combined with zero energy ontology (ZEO) leads also to a view about the construction of the scattering amplitudes at the level of M8 as analog of momentum space description of scattering amplitudes in quantum field theories. Local G2,c element has properties suggesting a Yangian symmetry assignable to string world sheets and possibly also partonic 2-surfaces. The representation of Yangian algebra using quark oscillator operators would allow to construct zero energy states at representing the scattering amplitudes. The physically allowed momenta would naturally correspond to algebraic integers in the extension of rationals defined by P. The co-associative space-time surfaces (unlike generic ones) allow infinite-cognitive representations making possible the realization of momentum conservation and on-mass-shell conditions.

The new view about M8-H duality differs from the earlier one rather dramatically so that a summary of the differences is added to the end of paper.

See the article A critical re-examination of M8-H duality hypothesis: part II.

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

Articles and other material related to TGD.

Saturday, December 05, 2020

Breakthrough in understanding of M8-H duality

M8-H duality plays a crucial role in quantum TGD and this motivated a critical study of the basic assumptions involved leading to a surprisingly precise view realizing the most optimistic original vision. The notion of associativity as a number theoretical dynamical principle was however replaced with co-associativity.
  1. ReQ(o)=0 and ImQ(P)=0 allow M4 and its complement as associative/co-associative subspaces of Oc. The roots P=0 for the complexified octonionic polynomials satisfy two conditions X=0 and Y=0. They are 6-D brane-like entities X6c having real projection X6r ("real" means that the number theoretic complex valued octonion norm squared is real valued).

    Posing the condition ImQ(P)=0 gives a complex surface X2c at which the number theoretic norm squared defines complex norm squared, which is not physically acceptable. The real projection X2r with real norm is 2-D.

    The condition ReQ(P)=0 gives complex surface X3c which has 3-D real projection X3r, which should be completed to a real surface X4r by holography- perhaps by giving up the condition Y=0 and taking real projection X4r of the resulting 4-D surface X4c.

  2. The cold shower came as I learned that 4-D associative sub-manifolds of quaternion spaces are geodesic manifolds and thus trivial. Co-associativity is however possible since any distribution of associative normal spaces integrates to a sub-manifold. Typically these sub-manifolds are minimal surfaces, which conforms with the physical intuitions. Therefore the surface X4r given by holography should be co-associative. By the same argument space-time surface contains string world sheets and partonic 2-surfaces as co-complex surfaces.
  3. The key observation is that G2 as the automorphism group of octonions respects the co-associativity of the 4-D real sub-basis of octonions. Therefore a local G2 (or even G2,c ) gauge transformation applied to a 4-D co-associative sub-space Oc gives a co-associative four-surface as a real projection if the boundary conditions stating that X4r has as its ends surfaces X3r at X6r.

    An open question is whether this approach is equivalent to giving up Y=0 conditions so that octonion analyticity would correspond to G2 gauge transformation: this would realize the original idea about octonion analyticity. If this surface contains a co-complex 2-surface as a string world sheet, the conditions making possible to map X4r to H by M8-H duality are satisfied and there is no need for a separate holography in H. There is no objection against this option and it would replaces SH with much strong number theoretic holography fixing space-time region from the roots of a real polynomial. One could say that classical TGD is an exactly solvable theory.

  4. Remarkably, the group SU(3)c⊂ G2,c has interpretation as a complexified color group and the map defining space-time surface defines a trivial gauge field in SU(3)c wheras the connection in SU(3) is non-trivial. Color confinement could mean geometrically that SU(3)c reduces to SU(3) at large distances: could it be simpler!

    This picture conforms with the H-picture in which gluon gauge potentials are identified as color gauge potentials. Note that at QFT limit the gauge potentials are replaced by their sums over parallel space-time sheets to give gauge fields as the space-time sheets are approximated with a single region of Minkowski space.

  5. Minkowski signature turns out to be the only possible option for X4r. Also the phenomenological picture based on co-assiative space-time sheets, light-like 3-surfaces, string world sheets and partonic 2-surfaces, and wormhole contacts carrying monopole flux emerges.
See the chapter Breakthrough in understanding of M8-H duality or the article with the same title.


Wednesday, December 02, 2020

Ageing as approach of magnetic body and biological body to thermal equilibrium

There was an interesting a HREF="https://scitechdaily.com/researchers-solve-anti-aging-mystery-identify-gene-responsible-for-cellular-aging">article in Scitechdaily about ageing. The claim of the title of the article was that the gene responsible for ageing has been found.

The title of the article is somewhat misleading. David Sinclair emphasizes in this book Life Span that there is no gene for ageing. Rather, ageing can be understood as an outcome of the second law leading to molecular chaos at the level of DNA related molecules. He also emphasizes that epigenesis correspond to informtion processing in continuous degrees of freedom related to DNA geometry. In TGD these degrees of freedom would be associated with the magnetic body (MB) carrying dark matter as heff=nh0 phases of ordinary matter and responsible for control and induction of the coherence of the ordinary biomatter from its own long scale quantum coherence.

The gene expression changes since the epigenetic control mechanisms involving for instance methylation and acetylation cease to function properly. The number of non-expressed genes increases. A chaotic behavior in the conformational degrees of freedom of DNA paired with dark DNA at its MB.

One can of course argue that there could exist an ageing gene. If cells would not age it would not take a long time for metabolic resources to deplete. However, the second law can generously take care of ageing.

Living systems are however able to fight against ageing. This is a mystery from the point of view of standard physics. One could argue that metabolic energy feed is enough but living systems are also critical and even quantum critical systems able to remain so: this is like a ball getting again and again at the top of the needle. How is this possible?

Here the zero energy ontology, which is behind TGD based quantum theory comes at rescue: "big" (ordinary) state function (BSFR) for subsystems changes the arrow of time and dissipation looks like self-organization and self-organized quantum criticality becomes possible. Generalized thermodynamics also allows metabolism as an extraction of even thermal energy from surroundings. Stress proteins could do this and be near physiological temperature and also act as heaters of DNA and proteins in cold shock and as heat engines driving molecular motors. Time reversal would happen also in the de-differentiation to stem cells.

Ageing would be basically heat death in this framework. The MBs of information molecules like DNA controlling them must be at much lower temperature than the physiological temperature otherwise they would not be information molecules. Physiological temperature would be near the maximal temperature - Hagedorn temperature of the string-like flux tubes of MB. The MBs however approach thermal equilibrium with the environment. Eventually heat death results and leads to BSFR (death followed life in reversed time direction) at the level of the entire organism.

The shortening of telomeres is also related to ageing. In TGD framework, the sticky ends associated with them would correspond to the decrease of the electric field strength along DNA. The opposite charges would be associated with sticky ends at the ends of chromosome. This possible in TGD framework.

The strength of the longitudinal electric field would correlate with level of consciousness for DNA just as the electric field along body axis correlates with the level of consciousness for humans and animals - this was discovered by Becker long time ago. When the electric field weakens, the level of consciousness is reduced. When the direction of the field changes consciousness is lost.

Ageing would involve weakening of this electric field, the energy density of DNA (plus its magnetic body) would be reduced, and the DNA string would become "sloppy" and start to behave randomly. This is part of the ageing.

We wrote an article about this with Reza Rastmanesh: see this .

For background see the article The based view about dark matter at the level of molecular biology written together with Reza Rastmanesh.

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

Articles and other material related to TGD.