During last years the understanding of the mathematical aspects of TGD and of its connection with the experimental world has developed rapidly. The material is scattered to 17 books about TGD and its applications and therefore it seems appropriate give an overall view about the developments as links (mostly) to blog postings containing links to homepage. In the article The latest progress in TGD I list blog links and also some homepage links to Quantum TGD, its applications to physics, to biology and to consciousness theory with the intention to give an overall view about the development of the ideas (I did not receive the final form of TGD from heaven and have been forced to work hardly for almost four decades!).

## 16 comments:

Hi Matti,

Congratulations with this incredible intelligent work.

Could you also make an extract for quick scanning?

I did it for my own ideas like this:

The result I try to describe :

1: Black holes are the same as Dark Matter, they all consume photons, even gravitons and the Higgs field, but REPEL Fermions due to their propeller shape. They produce electric charged plasma.

2: Dark Energy is the oscillating ( Casimir) energy of the Higgs Field equipped with a tetrahedron lattice structure with variable Planck length..

3: Quantum Gravity = Dual Push gravity= Attraction (Higgs-Casimir opposing Graviton push).

4: The Big Bang is a Splitting dark matter Big Bang Black Hole (BBBH), splitting into smaller Primordial Big Bang Spinters (PBBS) forming the Fractalic Lyman Alpha forest and evaporating partly into a zero mass energetic oscillating Higgs particle based Higgs field.

5: Dual PBBSs hotspots, produce central plasma concentration in electric Herbig Haro systems as a base for star formation in open star clusters as a start for Spiral Galaxies.

6: Spiral Galaxies will keep both Primordial Dark Matter Black Holes as Galaxy Anchor Black Holes (GABHs) at long distance.

7: After Galaxy Merging, these GABHs are the origin of

Galaxy- and Magnetic field complexity and distant dwarf galaxies .

8: Black Holes produce Plasma direct out of the Higgs field because two Higgs particles are convertible into symmetric electron and positron (or even dual quark-) propellers (by BH horizon fluctuations).

9: The chirality of the (spiralling) vacuum lattice is the origin our material universe. (propeller shaped positrons merge preferentially first with gluons to form (u) Quarks to form Hydrogen.

10: The first Supernovas produce medium sized Black Holes as the base for secondary Herbig Haro systems and open star clusters.

11: ALL Dark Matter Black Holes are supposed to be CHARGE SEPARATORS with internal positive charge and an external globular shell of negative charged Quark electron plasma.

12: The lightspeed is related to gravity fields like the earth with long extinction distances to adapt with the solar gravity field.

13. Quantum FFF Theory states that the raspberry shaped multiverse is symmetric and instant entangled down to the smallest quantum level. Also down to living and dying CATS in BOXES.

14 Large Primordial Big Bang Spinters (PBBS) are responsible for the creation of the Lyman Alpha forest structure and first spiral galaxy forming of the universe, but they seem to be also responsible for the implosion of the universe at the end in the form of Galaxy Anchor Black Holes (GABHs) located mainly outside galaxies. see: (Quasisoft Chandra sources)

If our material universes has a chiral oscillating Higgs field, then our material Right Handed DNA helix molecule could be explained.

However it also suggests that in our opposing ANTI-MATERIAL multiverse neighbour universe the DNA helix should have a LEFT HANDED spiral.

According to Max Tegmark: in an entangled multiverse we may ask: is there COPY PERSON over there, who is reading the same lines as I do?

If this COPY person is indeed living over there, then even our consciousness should be shared in a sort of DEMOCRATIC form,

Then we are not alone with our thoughts and doubts,see:

Democratic Free Will in the instant Entangled Multiverse.

One can imagine that there is a pool of standard mental images shared by many conscious entities.

Selve could sharing of mental images by entanglement of subselves defining mental images.

For us humans it is hard to imagine that we are entangled over the edge of our own universe (behind the horizon) and as such could have to deal with our opposite self at very long distance. http://vixra.org/pdf/1401.0071v2.pdf

In zero energy ontology one ends up with a strange problem. State function reductions occur as sequences at either boundary of causal diamond (CD). When the first reduction at opposite boundary happens, self dies and new is bor and its arrow of time is opposite. The simplest guess is that our life-time defines the increase of the size scale of CD during life cycle: something like 50-100 light years. Do I have shadow self in my geometric past at this distance? Some solar system? Better to add at least one ;-)!

In a CPT symmetric bubble multiverse, each wave function collapse thus human choices, should suffer instant entanglement over much more than 100 Light years.

(Time symmetry means only that the clock is running in the opposite way).

Ancient yogic texts advise meditation near waterfalls, rivers, and lakes. Carl Jung spoke for many in his description of lake scenery. "The lake stretched away and away in the distance. This expanse of water was an inconceivable pleasure to me, an incomparable splendour. At that time the idea became fixed in my mind that I must live near a lake; without water, I thought, nobody could live at all." The pleasure we derive from showers, saunas, swimming pools, ocean views and swimming in the sea testifies to the deep affinity that we feel for water. Perhaps an echo of our amniotic state in our mother's womb, and possibly related also to the image of the unconscious itself as an unfathomable ocean. --George , from Learn to Relax

--Stephen

https://en.wikipedia.org/wiki/Parton_%28particle_physics%29

this wikipedia article seems pretty decent to me, what do y'all think?

A parton distribution function within so called collinear factorization is defined as the probability density for finding a particle with a certain longitudinal momentum fraction x at resolution scale Q2. Because of the inherent non-perturbative nature of partons which can not be observed as free particles, parton densities cannot be fully obtained by perturbative QCD. Within QCD one can, however study variation of parton density with resolution scale provided by external probe. Such scale is for instance provided by a virtual photon with virtuality Q2 or by a jet. Due to the limitations in present lattice QCD calculations, the known parton distribution functions are instead obtained by fitting observables to experimental data.

Experimentally determined parton distribution functions are available from various groups worldwide. The major unpolarized data sets are ...

--Stephen

My ultimate conclusion is: The Big Bang did not produce instantly all the Fermions in the universes. Even now there is reason to assume that lots of Fermions are produced- in the form of charged plasma-globules by all BHs (see ball lightning fig B.) even by the largest primordial Big bang splinters located outside large galaxies.

https://www.academia.edu/11865245/New_Anode_Black_holes_are_Plasma_Producing_Charge_Splitters_by_a_Fermion_Repelling_Horizon

Would be quite different view from standard one in which inflaton fields decayed to elementary particles including fermions. My own view replaces inflation field with cosmic strings whose magnetic energy replacing the energy of inflaton fields decays.

The basic objection against your scenario is that horrible temperatures are required: temperature which considerable higher than rest mass (.5 Mev for electrons). How these black holes could be created if they are ball lightnings?

I understand that by fermion number conservation equal amounts of antifermions would be produced at the same time. Annihilations of photons with huge energies? For does the fermion or antifermion remain inside the blachole?

In the case of ball lightnings electrons and gammas in MeV range have been observed. They should not be there because electrons should dissipate their energy in atmosphere. TGD explanation is that they comes as dark electrons along magnetic flux tubes and accelerate freely in the voltage involved. I expected the production of fermion anti-fermion pairs from gamma rays is rather low.

Thanks Matti for your reaction.

Perhaps you may find those information on my flickr site:

https://www.flickr.com/photos/93308747@N05/?details=1

My approach is not math based but observation based, also for ball lightning.

I am an architect focusing on observation.

Speaking of firmeons, http://arxiv.org/abs/math-ph/0505041

Thank you. Interesting article I decided to Determinant of operator K(x,y) with continuous indices acting in the function space L^2 - now

functions on real line - is a subtle notion. One manner to disretize it is going to a discrete basis of eigenfunctions of some observables.

Ordinary determinant is defined in terms of N:th exterior power of cotangent space of N-dimensional space. Now one would have infinite exterior power o fHilbert space, call it Ext (in the case of WCW its cotangent bundle defined in terms of WCW gamma matrices).

Since single fermion state space can be identified as L^2 and the natural identification for Ext would be as the space of second quantized fermions. In TGD framework the WCW gamma matrices are indeed identified as Noether super charges of super-symplectic algebra expressible in terms of second quantizedfermions at string world sheets. WCW Kahler metric is fixed by sermonic anticommutation relations string world sheets.

One cannot overemphasise the importance of

Noether super charge interpretation: this is what leads to an explicit expression of WCW metric almost hopeless to deduce from defining formulate in terms of Kahler function. Kahler function itself is however easily expressed and Dirac determinant - very difficult to actually calculate- would correspond to exponent of Kahler action! The analog of AdS/CFT duality forced by huge generalization of conformal symmetries would make things calculable!

The article indeed demonstrates that one can express the norm of a local scaling operator (selected as an example) in three manners. A a norm in the space of configurations, as determinant in Hilbert space in the usual manner, and also has a determinant of an operator acting in sermonic Fock space.

The first expression of determinant is in terms of configurations of discrete points to which one can assign ordinary finite-D determinant of the restriction of projector K(x,y). In fermionic picture

this would correspond do many-fermion states localized to these points.

The localization of induced spinors to string world sheets indeed implies discretisation at partonic 2-surfaces.

A very delicate point relates to the ordering of the discrete points natural in 1-D case. What about ordering in higher-D case? No natural ordering exists. In TGD one expected product of determinants assignable with strings connecting partonic 2-surfaces so that effective 1-dimensionality is satisfied for each determinant in the finite product of them (and being basically due to the finite measurement resolution

realized by the structure of quantum states).

What about p-adicization? p-Adic numbers are not well-ordered: how to define determents? Is exponent of Kahler action well-defined. Now integral is problem. Even if generalisation of AdS/CFT applies one has 2-D integral- could some kind of residue integral make it well-defined? Can one define it by algebraic continuation?

http://people.sc.fsu.edu/~jburkardt/presentations/continuation_2014_fsu.pdf

I promise I didn't stumble upon that article just because it invokes the Lambert W function :) I only noticed that after thinking about the method for some unrelated reasons

the p-adic stuff is baffling to me

--croω

p-adic stuff is indeed baffling.

Norman Wildberger makes a very strong pure math case against modern "axiomatics" here: https://www.youtube.com/watch?v=rCDRCGjmaO8

... emphasizing that correct place to postulate axioms is at the level of generating natural numbers. And there are many ways to do that, not just Peano axioms - that very few actually know and think about, me including.

Spinoza's Ethics is perhaps the most consistently logical treatise on Absolute, and what are today called 'triangular numbers' is also a very natural and Pythagorean way to generate natural numbers. Combining these two ideas, we can start from Absolute (A) at the top of the triangle, and _share_ (not _divide_, in respect to Spinoza's argument against divisibility of Absolute) the 'metric' attributes of A into infinitely small (o) and infinitely large (ω) in the next row of the triangle. Finite attribute of A (1) emerges on third row, bounded by o and ω.

A

o ω

o 1 ω

o 1 1 ω ("2")

o 1 1 1 ω ("3")

etc.

In this approach we start number theory from 2D triangle instead of 1D line, and can immediately see the columns (c) and rows (r) of our number theory while also maintaining o and ω as attributes of any finite shape.

Also, it is immediately visible, that if we bend the number triangle and project the finite shapes of natural numbers starting from o, we get spiral line with border value ω (infinitely large completeness allowing any size), but if we project from ω, the infinitely small (0-dimension or dimensionless?) o's by their inherent character can't draw complete spiral and just "scatter" in any resolution.

This relation shows that the triangle approach is more general than the standard atomistic and reductionistic way of generating number theory from the smallest common denominator (cf. o = Planck scale norm), and giving o the value or symbol "1"; and we can see that the atomistic-reductionistic number theory is just subspace of the more wholesome triangular number theory.

It's quite strange feeling to address anonymous as having a 'me' (implied self) but do 'you' or 'you all' think any of the nonsense at https://oeis.org/A095861 is any sense relavant to this triangular proposition? I wonder wtf 'I' was thinking! Just exploring

--cr0w

Can't say yet definitively, but let's remain hopeful and trusting that there relevant connection. :)

This Gödelian contemplation came up:

https://www.youtube.com/watch?v=KXTJdryRueQ

We can at this stage of development of Spinozan Number Theory (aka between pals, croω ;)) state the basic Axiom:

Finite shapes and sizes can be neither infinitely large nor infinitely small, therefore any finite shape or form is by definition bounded by o and ω, or respectively ω and o. We give finite shape or form the symbol 1 and define that o < 1 < ω and ω > 1 > o.

We can interprete no-thing or "zero/0" as the blank space where we are formulating SNT, and at least tentatively give also following definition: 0 < o < 1 < ω < A.

Given above context, we could consistently, withing defined confines, substitute ω with a larger triangle than the row where ω manifests, and o with smaller triangle than the row where o manifests. For example we could write row labeled "2" in the following way:

1st column:

A

o ω

o 1 ω

2nd column:

1

3rd column:

1

4th column:

A

o ω

o 1 ω

o 1 1 ω

o 1 1 1 ω

= "2"

Substituting idea of 'infinitely small' with structure containing also symbol for 'infinitely large' may sound strange and unacceptable, but as we have been formally using so far only the "Archimedean" operators < >, we can continue believing in good hope that our number theory is consistent. If someone with better thinking skills can show that our number theory has at this stage or even earlier become inconsistent in the Gödelian sense, as argued in the linked lecture, we might need to rethink the whole - or not, if we set our goals lower.

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