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This is a voice narration of a seminar given at the Albert Einstein Institute, Potsdam on September 21, 2020. It describes the new theory of unification reported in arXiv:2009.05574

Keywords: Quantum Foundations; Trace Dynamics; Spontaneous Localisation; Non-commutative Geometry; Division Algebras; Octonions; Standard Model of Particle Physics; Unification; Gravitation: Connes Time; Spontaneous Quantum Gravity; Aikyon; String Theory; M-theory; Exceptional Lie Groups G2, F4; Quantum Measurement Problem; Quantum Determinism; Lorentz-Weak Symmetry; Lorentz Boson; Automorphism Invariance and Unification.

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It is very interesting, we search to explain this QG, many have tried in this logic with the geometrodynamics ,or strings , Branes, Mtheory , superstrings. I recognise several interesting mathematical tools with these geometrical algebras of Lie and the strings to rank the fields, but a thing important for me is that even if all this is relevant for the fields of our standard model, we cannot...

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It is very interesting, we search to explain this QG, many have tried in this logic with the geometrodynamics ,or strings , Branes, Mtheory , superstrings. I recognise several interesting mathematical tools with these geometrical algebras of Lie and the strings to rank the fields, but a thing important for me is that even if all this is relevant for the fields of our standard model, we cannot affirm what is the main philosophical origin of our universe and what are these foundamental mathematical and physical objects.I like the idea of strings begining with a 1D main cosmic field and after the 1D stings at this planck scales and so the maths correlated to create our topologies, geometries and matters, fields and properties. That said we cannot be sure about this generality , I understand what they have made to unify this GR and the QM, the thinkers have considered an infinite heat before the BB and after photons oscillating and vibrating differently due to these strings inside. But for me it is not the truth, my model also is an assumption I recognise it with these 3 main finite series of coded spheres, the vacuum space coded energetical and these two fuels, the cold dark matter and the photons, these series have the dirac large number and imply a superfluid because the space disappears when we apply a specific serie of volumes from the central biggest one, we have so 3 aethers , and at this moment we just consider the luminiferous one , that is why we cannot explain this QG for me and the unknowns, like this DM , the DE and the antimatter more the hard problem of consciousness, we must in fact unify all , not only the GR and the QM, wiclzek has had a good idea with the noise of gravitons but we must recognise that it is just also an assumption, the gravitons don t seem to be the quanta of gravitational waves for me, they are different and linked with the antimatter and this cold dark matter. I beleive strongly that this GR and strings have created a prison and now all they trty with the fields to explain these unknowns in changing the oscillations and in working on phases, but that does not solve the problems . I respect of course these attempts but since that the best thinkers work on this road, nobody has found the unknowns, there are reasons, all has been made in maths in fact but nothing, we just fractalise and explain deeper the actual fields . This QG does not seem to be an electromagnetic emergent force you know, it is the opposite it seems, the electronagnetism is emergent due to main codes in this space and this gravitation like main chief orchestra, it is an opposite reasoning in fact, that implies when we consider the 3V main series of 3D coded spheres an explaination concrete of this QG respecting the newtonian mechanics in changing so the distances and also it implies a fith force farer than these nuclear forces, that solve also the glueballs problem and the gap mass. In fact the photons are just a fuel permitting to observe due to light, they imply the electromagntic forces of our standard model and the life death, but they are not the primordial essence, the cold DM balance this heat and electromagnetism and the DE balance all this like an anti gravitational system and fruthermore explain the evolution, it is themeaning iof my spherisation. We can even extrapolate the future by predictions due to this DE and DM . We are still youngs at this universal scale, we shall have a probable expansion towards the maximum spherical volumes with a decceleration even after a time in the future and after we shall have a probable contraction towards the points of equilibriumm. I explain the generality of my model of spherisation and 3D spheres, like this you can see the idea general. In all case the waves particles duality isnot a problem and the transformations matters energy also can be explained, they are in motions oscillations rotations these finite series in a superfluid.I liked your video , it is a beautiful general work Tejinder, congrats and thanks for sharing it on this wonderful platform, Regards

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Member Tejinder Pal Singh replied on Oct. 10, 2020 @ 12:43 GMT

Thank you for your detailed response Steve. Regarding the main philosophical origin of the universe, as you rightly enquire - I do not know. But one thing I see, as we go to deeper layers of reality, physical universe and mathematical universe more and more become the same thing as each other.

Tejinder

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Steve Dufourny replied on Oct. 10, 2020 @ 13:05 GMT

You are welcome, I recognise also that I am not sure and I don t know also the truth, I just consider these spheres because it seems to me that they are foundamental seeing the nature around us and the universe made of cosmological spheres, I have ranked a little bit of all, animals, vegetals, minerals, maths, physics, biology, chemistry and in a book of biology I saw the hominid brains on a page and I have had this humble eureka ,we see a relative spherisation of brains , but I don t affirm that these foundamental objects are 3D spheres, I just consider them, I liked your videao like I told, congrats still, maybe you could be interested to discuss with the team of Klee Irwin working on these octonions also , they are good. Friendly

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Steve Agnew replied on Oct. 12, 2020 @ 15:53 GMT

Singh’s quantum matter gravity (QMG) unification of gravity and charge is a very exciting development and is especially so for me since QMG has many of the same puzzle pieces as does my quantum matter action universe puzzle. Basically, QMG defines aikyon particles as the generic aether of the universe and so QMG builds electrons, protons, neutrons, and all else with either fermion or boson...

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attachments: MatterActionCSL.jpg

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Greetings Professor Tejinder Singh,

I needed to do some research in addition to skimming your recent papers, but it is remarkable how much agreement I find with my recent body of work - since GR21 and in my lecture at FFP15 in Orihuela. What you call Connes time, and others refer to as Connes' "intrinsic time" I have treated as evolutive properties of non-commutative and non-associative algebras. I have been quoting Connes' statement "Noncommutative measure spaces evolve with time!" and other related comments for a while now.

So I think that your explanation of early universe dynamics is brilliant. And assuming the octonionic framework to explain Yang-Mills dynamics is likewise the right answer and a great insight. I think in the arena of Planck scale dynamics and Quantum Gravity, using the octonions is the only way to get past the obstruction. Nice though that you invoke the sedenions in order to obtain triality for 3 particle families. The sedenion sphere S15 fibrates uniquely yielding S7, S3, and S1 so it maps to the O, H, and C algebras. This makes decomposition almost automatic, along the lines you describe.

My findings relate to the Mandelbrot Set in the quaternion and octonion domain. There is an explicit representation of Cartan's G2 analogy in the form of M, when it is extended into higher dimensions. So my model implies a sort of modified DGP gravity cosmological scenario, with a 5-d --> 4-d transition, or perhaps more like cascading gravity - because the universe's origin or precursor state is higher-dimensional. How does your work treat the cosmological evolution of the universe, and the transition to the current era, given that you employ a similar set of assumptions?

Warm Regards,

Jonathan

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Jonathan J. Dickau replied on Oct. 14, 2020 @ 02:06 GMT

I should note here...

It is my conjecture that the Mandelbrot-G2 connection is non-trivial.

Best,

Jonathan

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Member Tejinder Pal Singh replied on Oct. 14, 2020 @ 04:49 GMT

Dear Jonathan,

Greetings and many thanks. I would like to know more about your work! Could you kindly point me to some references? Thanks.

It is thrilling to know that you also refer to Connes [intrinsic] time. So we are in perfect agreement then there is a 4+1 d spacetime, with the Connes time in the background. For me the Connes time is still there in today's universe, as if to say that the observed universe is a bubble which resulted from spontaneous localisation in a much larger aikyon `sea' and is now expanding back. Connes time belongs to the aikyon sea and hence is applicable to the expanding bubble also - it is perhaps the cosmological time.

I am still trying to sort out the cosmology - Dirac's large number hypothesis is all over the place! In his post above, Steve Agnew already foresees some of the things I was planning to say about length scales and Planck length.

Thanks for your interesting remarks about sedenions. The original idea for sedenions and triality and three fermion generations is due to Gillard and Gresnigt. Also, the connection with F4 and the exceptional Jordan algebra is fascinating. And now you mention the G2 - Mandelbrot connection! Amazing. I will look this up. You would also already know that G2 is related to spaces that have a 2-plectic geometry: I am exploring this in the context of my Lagrangian.

Once again, thanks for your insightful comments, and I look forward to knowing more about your work.

Tejinder

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Jonathan J. Dickau replied on Oct. 14, 2020 @ 15:28 GMT

Thanks so much Tejinder...

If the observed universe is a bubble; what if it is a ball rolling on the surface of a larger ball - which is the aikyon sea? This makes our universe the rolling ball in Cartan's G2 analogy, and this is the cosmology the Mandelbrot Set appears to suggest. Specifically; the cardioid portion of M relates to early universe dynamics, and the part showing features of present day Physics is the circular region centered at (-1, 0i), which is spherical in higher dimensions.

I have attached a diagram illustrating this idea. The associated cosmology is fascinating. The territory explored by Dvali, Gabadadze, and Porrati and the 5-d black hole to 4-d white hole model of Pourhasan, Afshordi, and Mann relate strongly to Cartan's rolling ball analogy for G2 - in my opinion. So I think there is perhaps a cosmological transition with your theory too. This could be ongoing as you say. The bubble we are in is unfolding by rolling across the aikyon 'sea.'

The key is understanding how localization enters the picture. I know about CSL but I use the metaphor of condensation in my work. This builds on a large body of work where gravitational horizons are like BEC formation. The model of Dvali and Gomez is a good example, but a very large number of researchers are exploring related territory. However; I also link this up to what happens at the high end of the dimensionality spectrum, because the octonions contain the quaternions, which contain the complex numbers, and the reals are a subset.

My most recent FQXi essay explores this angle in some detail.

More later,

Jonathan

attachments: G2MandelEversion.jpg

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ps Tejinder I have shared it in facebook

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I'm back for more Professor Singh...

I think it is delightful, and as I read more I am learning, that your approach is informed by a methodology that I began formulating about 20 years ago, and continued to sharpen since then. The idea is to look at the totality of all Maths with the Calculus of Variations as a guide. From this view; the maximal, minimal, and optimal cases all have a...

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I'm back for more Professor Singh...

I think it is delightful, and as I read more I am learning, that your approach is informed by a methodology that I began formulating about 20 years ago, and continued to sharpen since then. The idea is to look at the totality of all Maths with the Calculus of Variations as a guide. From this view; the maximal, minimal, and optimal cases all have a special significance. That statement is in accord with what Mary Boas said in her delightful book about Mathematical Methods for Physics. But seen in a larger context where the Maths drive and the Physics follows; this notion takes on a much greater significance.

This makes the exceptional Lie groups (E8, E7, E6, F4 & G2), the normed division algebras (Octonions, Quaternions, Complex numbers, and Reals), and structures like the Mandelbrot Set jump out as significant. If we examine the spheres in all dimensions; we find maxima of (hyper-) volume and (hyper-) surface area, as well as a minimum. And Maryna Viazovska and colleagues showed that E8 close packing is the tightest arrangement obtainable. And Giulio Tiozzo finished some of the last work of William Thurston by showing how the Mandelbrot Set maps the behavior of the quadratic function to all orders. So the whole landscape of Math is seen to be interconnected.

This results in a view of Physics where the core behavior of these Maths, like Alain Connes' view of Intrinsic Time as a feature of some higher-order algebras. Most people would not make the leap that working in octonionic space implies that we must use what you call Connes time to describe the evolution of the early universe - so I commend you and your colleagues for this insight. But it seems a lot of your program falls directly out of the Maths, if we take the view that Math came first, and that Physics was only possible because the Maths provided a road to the evolution of physical form and a pattern of regularities in its internal structure, when viewed as a whole.

Bravo!

Jonathan

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Jonathan J. Dickau replied on Oct. 26, 2020 @ 16:30 GMT

A little too long to show it all...

But the above missive shares a view that your Aikyon theory, professor Singh, appears to be the product of a kind of constructivist hyper-Platonism which I favor. That would be looking at the Totality of Maths through a Calculus of Variations perspective, informed by Philip Gibbs' Theory of Theories, to formulate a version of Tegmark's Mathematical Universe on steroids, such that the Maths set the tone, and the Physics is only possible because Mathematics as a whole has a congruent message.

All the Best,

Jonathan

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Jonathan J. Dickau replied on Oct. 26, 2020 @ 16:35 GMT

Whoops I meant to say...

This results in a view of Physics where the core behavior of these Maths, like Alain Connes' view of Intrinsic Time as a feature of some higher-order algebras becomes a driver of cosmological evolution.

More later,

Jonathan

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Steve Dufourny replied on Oct. 26, 2020 @ 16:44 GMT

Hi Jonathan, like I told , I love these geometrical alg of Lie and specially this E8 , I consider even them in my theory, but if I can , what if the fields and strings or points oscillating giving the topologies and geometries are not the primordial essence and that we have not only photons and this GR to unify the whole to reach this quantum gravitation, this tool is a good tool to better understand the fields of our standard model but that is all, what is all is just not true generally speaking about the main essence of feilds and that we have coded particles in a superfluidity and with 3 aethers superimposed, so that means that all the persons searching to explain this QG looses their time ? how are they going to accept this the thinkers ? hope their vanity can be humble if I am true , if not there is a big problem inside the sciences community. For the maths, we must be prudent we know that with the maths like main tool we can have odd extrapolations, the physics seems the main chief orchestra, the maths are a tool wich must be well utilised to help this physics for me,regards, bravo , cool to see french language

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Jonathan J. Dickau replied on Oct. 26, 2020 @ 21:19 GMT

Connes is a remarkable Frenchman...

The idea of Connes time is subtle. How can a measure space evolve with time? What property might provide this perspective? Non-commutativity is the answer. Imagine yourself in a spacesuit near the International Space Station floating in the void. If you are not spinning; it's easy to triangulate your position relative to the Earth and the ISS, and to roughly gauge the distance if you know the size of both objects.

If I give you a spin around your waist like a skater on the ice, then start you spinning end to end (head over heels) and then side to side (like in Leonardo's famous drawing of a man in a wheel), what happens to our ability to measure? We find that our own rolling motions (rolling, pitching and yawing to be precise) are the predominant input and they vary in cycles over time. So any measurements you make from that perspective will also be time varying.

Does this make sense?

Best,

Jonathan

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Steve Dufourny replied on Oct. 27, 2020 @ 13:09 GMT

Connes is the best for the non commutative analysis but it has not reached unfortunally this quantum gravitation, he has also probably forgotten to consider also the non associativitey and a different philosophy about the generality of the universe, but he is the best in this topic , I have learnt a lot in studying his papers on arxiv.

About what I explained, be frank Jonathan, what is for you the origin of our universe, the philosophy is important, I am curious , so I d like to have your general idea, do you consider the fields and so the points or strings and geonetrodynamics or geonetrical algebras for the ranklings of these fields, if yes, why and how can you be persuaded ?

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Jonathan J. Dickau replied on Oct. 27, 2020 @ 15:57 GMT

It all fits together Steve...

The optimal case for close-packing of spheres is why String Theory works in the dimensional spaces where it is effective. If you combine this with the notion that a minimal container is 2-dimensional (i.e. - a circle has in interior and an exterior), and it must persist in time, the reason for gravity to be quantum becomes obvious.

But in terms of geometrogenesis and geometrodynamics; the emergence of massive particles and of volumetric spaces coincides. So we end up with 5 10-d and one 26 dimensional String theories plus 11-d supergravity falling out of the compact arrangement of spheres and the need for there to be containers to have matter.

Simple,

Jonathan

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Steve Dufourny replied on Oct. 27, 2020 @ 16:17 GMT

Hi Jonathan, thanks for developing , I am understanding. I consider like you know that all is made of particles coded and 3 main systems of finite series of 3D spheres, in a kind of superfluid and so all is in contact. These spheres oscillate and with the two fuels, and the fact that they are in motions rotations oscillations, so that explains also the quantum fields these 3D spheres because they...

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Hi Jonathan, thanks for developing , I am understanding. I consider like you know that all is made of particles coded and 3 main systems of finite series of 3D spheres, in a kind of superfluid and so all is in contact. These spheres oscillate and with the two fuels, and the fact that they are in motions rotations oscillations, so that explains also the quantum fields these 3D spheres because they merge and we have the bosons , I beleive strongly that we don t need to have extradimensions, we live in a pure 3D at all scales and the 3D spheres cosmological and quant are ok with this idea, but I respect the strings theorists , they begin in 1D with strings inside the photons and after they are connected with a 1D main cosmic field and after they create the geometries, topologies, matters, fields, properties with the geometrical algebras mainly and the mathematical properties, but what I say simply is that if all the general philosophy of these strings, branes, superstrings, Mtheory is not the primordial essence, so all is generally false, it is just relevant for some rankings of fields , but I doubt personally that these strings are the answer begining in 1D towards 11D if my memory is correct, I prefer the coded particles , I don t know, maybe it is a fashion due to Witten or even a business, they have considered a kind of infinite heat and after only photons and after strings inside and after partitions like a music to create the reality, but frankly philosophically speaking there are many general problems with these strings , why we evolve for example ? there are reasons, the strings don t explain this evolution , and many other things. Some strings theorists consider a kind of god, others a kind of mathematical accident from this heat , but I have really difficulties to agree with this general idea that all comes from fields, the 3D coded spheres can explain all shapes with several mathematical tools also, I know that the strings are considered at universities but maybe they confound a good work of Witten about the fields giving him the field medal with the theory of strings, I can agree that there are several good things about the strings to better understand the QFT , but generally I don t agree like main cause of our universe and its correlated philosophy. That said a conjecture appears probably about these strings and the 3D coded spheres and these 3 main series, because they oscillate thes spheres. Maybe th secret to converge is to rank correctly all this and in considering only a pure 3D at all scales more a time evolution and these motions rotations and oscillations. I know that there is an enormous business around the strings and that Witten is supported, but it is always better to cooperate than compete after all, it exists this conjecture.

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Quantum mechanics and relativity. I never understood the issue physicists had with the unification of the two until today. I read about the issue of course but still didn't understand the problem. Listening to Brian Greene speak about the quantum approach to physics, I realized the big problem comes from the belief, as he stated, that all things are quantum and there is no distinction between what...

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Does ultraviolet behavior of quantum Yang – Mills theory with no instability indicates single particle theory that connects gravity with QM ?

The ultraviolet behavior of quantum Yang – Mills theory possess no instability as the separation between physical gluons becomes exceedingly smaller & smaller with increase in energy. Ultimately, at quantum length, in the limit of approaching the...

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Does ultraviolet behavior of quantum Yang – Mills theory with no instability indicates single particle theory that connects gravity with QM ?

The ultraviolet behavior of quantum Yang – Mills theory possess no instability as the separation between physical gluons becomes exceedingly smaller & smaller with increase in energy. Ultimately, at quantum length, in the limit of approaching the origin of field space, the dynamical variables, becomes so infinitesimal in magnitude that they effectively represent a single physical gluon G . At Gribov horizon, application of Gauss Divergence theorem to this single physical gluon G leads to singularities of color-Coulomb potential spread all over a spherical surface β at quantum length of physical gluon.

After acquiring additional degree of freedom in the form of free color-Coulomb potential at Gribov horizon, the gluon ‘G’ has the aforesaid spherical system β firmly attached to it. At Gribov horizon, the uncertainty principle forbids this spherical system β, of constant radius (h’/8π), to undergo any Lorentz – Fitzgerald contraction in laboratory inertial frame and rather, demands the motion of gluon ‘G’ to instantaneously drop to zero speed in the laboratory inertial reference frame. This sudden deceleration in the speed of gluon ‘G’ at Gribov horizon assigns an inertial mass to gluon ‘G’ in accordance with General Relativity theory. This inertial mass of gluon ‘G’ produces gravitational effect in its surroundings because of equivalence between inertial mass & gravitational mass in General Relativity theory.

For further details, please click the following link

https://www.researchgate.net/publication/346075636_Mathe

matical_Connection_between_Gravity_and_Standard_Model

Treatin
g the physical gluon as a point particle (of zero dimension) yields trivial UV fixed point for asymptotically free Quantum Yang Mills theory under flat space time assumption. However, the wave particle duality of any physical gluon entails to have non trivial UV fixed point at certain minimum Quantum length of the single physical gluon.

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Dear friends@FQXI,

My apologies for this long absence and for not taking part in the discussion of late. I have written a new paper on eigenvalues of the exceptional Jordan algebra. There arise a set of twelve curious eigenvalues from four cubic euations: perhaps these eigenvalues are telling us something about mass ratios of quarks and leptons:

https://www.tifr.res.in/~tpsingh/massratiosarxivdec7
2020.pdf

Maybe you can see a pattern in these remarkable eigenvalues. I also attach a table which could be useful.

Best wishes,

Tejinder

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Here is the link to the same paper [mass ratios]

Jordan Eigenvalues

The table does not get attached unfortunately: but it is only a list of known masses ande the eigenvalues.

Tejinder

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UPDATE January 7, 2021

A theoretical derivation of the low energy limiting value of the fine structure constant, from the algebra of the octonions, yields the value 1/137.04006

The fine structure constant from the algebra of the octonions

Best regards,

Tejinder

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Steve Dufourny replied on Jan. 7, 2021 @ 18:48 GMT

Hi Tejinder, It is a beautiful paper about the octonions and jordan works. You try to generalise this GR and QM and rank our standard model in considering an octonionic universe respecting so the fields and the general relativity. Like I said before , this kind of works is respectable and interesting to better understand our QFT, that said like I explained, we cannot affirm that this GR is the...

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Hi Tejinder, It is a beautiful paper about the octonions and jordan works. You try to generalise this GR and QM and rank our standard model in considering an octonionic universe respecting so the fields and the general relativity. Like I said before , this kind of works is respectable and interesting to better understand our QFT, that said like I explained, we cannot affirm that this GR is the only one piece of puzzle and that the fields are the origin of our universe. The string theorists and geometrodynamists forcus all on this with different maths and fractalise or extrapolate the dimensions like with the strings begining in 1D , after 10D for the bosonic strings or 26D or others in function of mathematical tools utilised. So they consider all that we have a 1D at this planck scale connected with this GR and a 1D cosmic field and the photons and oscillations vibrations inside. oK we understand this and even we can insert the kaluz Klein theory and the 5D, but what I try to explain is that this GR is probably not the rpimordial essence and the photons so also, they are just for me particles encoded in a the vaccuum giving us the electromagntism and the heat and they permit also to observe, because without light we don t observe. I like also the beauty of these E8 octonions and the play of persons in maths about them trying with the non commutativity to complete our standard model. But what I try to explain is that the points or strings and these extradimensions begining in 1D are just a general assumption. Of course they can permit with several symmetries and maths plays to explain better the bosonic fields, but the universe is not an octonionic universe, the fields are just emergent , what we must find is the main origin of this universe and I doubt it is from fields and oscillations of photons, we need to understand the vacuum , for me the main codes are there in the spacevacuum of this dark energy and these series of 3D spheres in my model after ar activated and becomes what they must become due to these photons encoded giving us the bosonic fields and the 3 main forces known and also the cold dark matter is encoded and permit to give the antiparticles and the gravitational quantum fields and also a fith force appears due to a serie of quantum BHs farer than our nuclear forces. I know that the thinkers are persuaded and have difficulties to change a line of reasoning but between us, I doubt that this universe has only created photons and that this GR is the only one piece, furthermore the dimensions can respect the pure 3D at all scales and this planck scale is just an assumption also due to maths, so it was the main problem to reach the quantum gravitation, utilise by curiosity and see the results the forces between these quantum BHs and the positrons , see what appears, the QG simply because we must consider not the protons and electrons, change the distances simply and respect the newtonian mechanics. See the calculations of the force. The problem of the majority of searchers is to consider only this GR , strings or geometrodynamics and also these E8 and fields like origin. It is the biggest error for me of thinkers, they turn in round in trying to explain the deep unknowns, but nothing, they just complete a litteö bit our standard model and its bosonic fields and they try just to complete this GR, they forget to think beyond the box. I liked your paper and I respect the maths utilised, I just explain that it is not sufficient to explain our unknowns. G c and h are not sufficient to explain this QG. Best regards, happy new year also.

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Steve Dufourny replied on Jan. 7, 2021 @ 20:59 GMT

Here is an idea for your works even if it is not my speciality about the octonions. The riemann hypotheisis for me is essential about the distribution of primes , and so the p adics analysis. The non commutativity and the hypotheisis of riemann become interesting if you consider the quasicrystals about the localisations and so the fractalisations of forces.Connes has worked about this , now consider also the hibert space , you shall see that several relevances appear when the order is considered but not the periodicity.The oscillations so in your octonions can be correlated.That can permit so to utilise the function of fields and the spectral analysis.Now insert the p adic numbers in these quasicrystals and mainly this E8 and also consider the non associativity for the subgroups ....Regards

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Member Tejinder Pal Singh replied on Jan. 9, 2021 @ 12:58 GMT

Thank you Steve, for your interesting suggestions. I am thinking them over.

Kind regards,

Tejinder

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Numbers, primes, riemann hypothesis, p adics analysis, spheres , Lie groups , quasicrystals, fields and particles , they all dance in a pure geometrical topological spherical truth ......

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An octonion is not a genuine number. An octonion is a set of numbers where each number has been assigned to a different category, and where each different category is said to be a different “dimension”. Octonions exist nowhere but the human imagination.

But there is NOTHING FUNDAMENTAL about the genuine numbers anyway. It is categories and relationships that are fundamental. This is just simple logic:

Relative mass and (single dimension) position are examples of real-world categories of information. Physicists represent these categories as variables, e.g. in the mathematical equations that represent the laws of nature.

You can potentially form genuine numbers out of mathematical relationships between such categories (when the numerator and denominator categories cancel out), but you can NEVER EVER form categories out of relationships between genuine numbers.

So it is categories and relationships that are essential and fundamental: clearly, genuine numbers are made out of categories/variables and relationships.

Once you have some genuine numbers, you can imagine an octonion number by assigning each number to a different category/ “dimension”.

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Steve Dufourny replied on Jan. 9, 2021 @ 12:56 GMT

Hi Lorraine, I can understand what you tell. Even if I don t agree with the fields like main origin and the octonions utilised to explain our unknowns. We must recognise that this E8 for example is a beautiful tool mathematical for its symmetries and others. When the numbers are inserted , the fields of our standard model, the non commutativity and even the non associativity, that becomes relevant for the ranking of fields and correlated particles , the dimensional analysis are not important for me, but the fractalisations of fields yes, this E8 is simply a good tool to improve our standard model not to reach the quantum gravitation because it lacks things , but to better understand our standard model yes. The p a dics analysis and the primes and this hypotheisis of riemann are utilised simply because there is a like partition wich could permit to correlate these fields in their fractalisations. It is mainly about hierarchies.

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Lorraine Ford replied on Jan. 9, 2021 @ 21:44 GMT

Steve, the points I’m making are that:

1) Octonions don’t exist: they are a complex human construction which requires human beings to perform a series of algorithmic steps to construct and utilise them. Physics is blind to algorithmic steps.

2) Categories and relationships are fundamental, but numbers are not fundamental.

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Jonathan J. Dickau replied on Jan. 9, 2021 @ 23:52 GMT

My dear Lorraine...

It is exactly as you say in point 2, with a caveat. So to restate things yet again; while categories and relationships are fundamental, REAL numbers are not.

This is precisely WHY the octonions are closer to the truth than the reals. The octonion algebra is a way to represent that everything starts out relational - having no constant or precise value - and by a process of reduction, we can arrive at stable quantities. If we view the imaginary dimensions of the octonions as rotations, then by fixing 4 of 7 axes we get the quaternions, by fixing 2 of their 3 axes we get the complex numbers, and by stopping the last rotation we obtain the reals.

It is BECAUSE your statement 2 is almost precisely true that your first statement falls apart Lorraine. It is only due to the fact that things are relational and not fixed to start with that we can arrive at a universe that is stably physical - while still having freedom of choice! It is the fact that variability is primal and constancy the result of variations that makes the octonions such a powerful tool. And while it is true they can be constructed; it is more nearly factual to say their self-existing properties were discovered.

All the Best,

Jonathan

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Jonathan J. Dickau replied on Jan. 10, 2021 @ 04:19 GMT

It is not unlimited...

But the real numbers are not the only valid algebra. One might consider extending things endlessly using a Cayley-Dickson construction but it turns out only 4 algebras are normed under division - which basically assures symmetry or makes certain operations reversible. The complex numbers have equal parts of constancy and variation, the quaternions have 3 times as much variation as constancy, and the octonions have 7 times as much.

But when variability greatly outweighs constancy; it makes sense things would become directional, cyclical, evolutive, sequential, and so on. Now Connes talks about all the really interesting stuff happening when the degrees of freedom approach infinity. So that's where it comes in that QM maps an infinite dimensional Hilbert space to a surface, and non-commutative geometry tells us about what happens in between.

All the Best,

Jonathan

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Steve Dufourny replied on Jan. 10, 2021 @ 13:56 GMT

Dear Lorraine, I beleive the same about the importance of these octonions, I don t beleive they are the truth , they are just a mathematical tool interesting to rank the fields of our standard model, that is all, the universe is not an octonionic universe where the fields are the truth in oscillating vibrating differently and the GR is not the onloy one piece of puzzle for me. The algorythmic steps like you tell seem important indeed , we have created the binar codes and the computing with the qubits and correlated algorythms, but for me the universe is more complex than this for the algorythms universal. I consider 3 main ethers and so qutrits and 3D spheres. If we want to create a universal quantum computer , so we must mimate this universe, I have seen that they work actually like the society D waves about the annealings computing, that could be relevant to consider the cold and heat and these 3 main primoridal series to reach this quantum computing but the complexity seems very difficult.

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Steve Dufourny replied on Jan. 10, 2021 @ 15:18 GMT

Dear Lorraine, if we take the meaning of algorythms, they are operations instructive finite to solve problems. It is so what we have in technologies now with the computing having created a basis and a specific structure, so we create roads to sove and adapt the solutions. But the actual algorythms utilised are different than our universal algorythmic mechanism. The universe has also created its basis and tools and the algorythms utilised with its own informations seem deeper than our actual system. All this becomes very philosophical in fact, we return about this origin of informations and what are our foundamental objects and why they create all this physicality with their properties, geometries, topologies and evolutive mechanism. The real difficulty is to mimate this universe in fact.Our actual algorytms are calculations numerical or non numerical permitting to solve the problems that we have created and it is function of the time and the complexity , the probabilities being essential also like the parallelisations. But like I said they are invented by us in function of our problems also invented like the basis of the system.We try in fact to detail our inventions and adaptations like a method to create a garden with all its steps to reach the aim. But what we don t know is this universe and its aim and its pure meaning , we are not in a problem like the rubbik cube if I can say, it is more than this and we must accept our limitations. That is why the AI can be created but not a conscious computer , maybe it is well like this after all. The ethic seems essential after all and we must be prudent maybe in playing with all this.But it is an other philosophical story.

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I might add that to construct octonions or to construct mathematical equations out of component parts, and the performance of mathematics itself, all require ALGORITHMIC STEPS. Poor old physics is completely blind to the algorithmic steps necessary to construct an equation or a universe. Physics seems to think that these things just miraculously happen, and that the necessary, “hidden”, algorithmic steps don’t have to be accounted for, and symbolically represented in detail.

And just like you can’t construct categories (like mass or charge) out of relationships between genuine numbers, you can’t derive algorithmic steps out of law of nature mathematical relationships. On the other hand, you CAN construct mathematical relationships using algorithmic steps: algorithmic steps are fundamental.

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Jonathan J. Dickau replied on Jan. 10, 2021 @ 04:40 GMT

We are looking for the way nature did it Lorraine...

Of course there are procedural or algorithmic steps to any process of creation or of observation. It appears observation and creation are two sides of the same coin, but we have yet to discern its true shape and size to the utmost. I've bet on the idea that all the Maths are true at once. Call me a hyper-Platonist, if you like. But people wonder 'how did we actually get here?'

I made some mathematical discoveries more than 30 years ago that set me on a path to discover why Math so drives Physics. Wolfram shares your idea that it's more algorithmic than mathematical. Tegmark favors the other view. Gerard 't Hooft would rather marry the algorithmic view with Physics. While I find it necessary to marry the mathematical and procedural view in a kind of process Physics.

But everyone wants to know the procedure nature used to create the cosmos.

All the Best,

Jonathan

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Steve Dufourny replied on Jan. 10, 2021 @ 20:58 GMT

It is not that we have a mathematical universe or an algorythmic one , it is that all is linked in a pure general physical and mathematical partition where the particles, the fields,the numbers, the algorythms dance together in harmony from a pure disorder and chaos. It is odd to separate all this because all is one simply under a specific universal logic. Ypou can tell all what you want, it is a simple fact and this partition is not known, we know a small so small part of puzzle, and for me personally it is the particles and their informations and codes wiuch distribute all

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I'd like to add this...

It is the fact that relations are more primal or fundamental than quantities that makes the octonions so exciting. When I spoke with Tevian Dray at GR21; what I verified with him is that things like size and distance or interior and exterior are relations instead of quantities, as we approach the Planck scale or the rim of a black hole. The geometry becomes first non-commutative and then non-associative, as we approach the universe's origin therefore.

This is precisely why Tejinder's work is so profound. It takes advantage of the fact that evolutive properties that arise in higher-order algebras are a causal agent that can explain early universe cosmology. Another example would be a background independent formulation called energetic causal sets, where from the barest of assumptions one can draw a fecund evolutive schema. I had the great pleasure to hear Lee Smolin lecture about this, and praise its simplicity to him afterward.

It truly fascinates me that there are evolutive properties inherent in the Maths. And I feel as though I've seen the world outside the cave, because I was the lucky guy who got to ask the right experts the right questions, to see the other side of the story. When I go to conferences and lectures by top experts; I feel as though I am in the company of the gods or the ancient philosophers, because they know so much more than I do - and only a true expert can answer the burning questions that fuel my romance with knowledge.

However at this point; I am fairly certain numbers can self-evolve in higher dimensions.

All the Best,

Jonathan

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Jonathan J. Dickau replied on Jan. 10, 2021 @ 03:59 GMT

What if Connes' intrinsic time is the main player?

If the canonical time evolution described by Connes is a property of a large class of systems; it may be a prime mover or driving force to create a sort of trend toward evolutivity. If "non-commutative measure spaces evolve with time!" as Connes suggests; there is an unseen evolutive property at work in a great variety of physically realizable settings. As Tevian and I discussed; it comes into play more often than most people in Physics realize.

I would have to point to the octonions as the example that epitomizes directed evolution in Maths. The process of multiplication in the octonions is best seen as a procedure or algorithm, but it is very much like a process of triangulation from every possible angle. From the inside looking out, and from the outside looking in, at every possible angle, is the root of projective geometry. This is embodied in the octonions, in the geometry of their algebra.

So if the intrinsic time of Connes manifests in evolutive properties that are universal to many higher-order systems; it MUST be significant somehow.

Have Fun!

Jonathan

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Steve Dufourny replied on Jan. 10, 2021 @ 11:36 GMT

Hi , all this is interesting indeed about the octonions but are you conscious that if the fields and the GR only are not the truth, so all the generality of these octonions is not sufficient ? the experts like you tell focus all on this , the problem is not their skillings , the problem is the generality philosophical.

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Steve Dufourny replied on Jan. 10, 2021 @ 11:37 GMT

it is not that we have higher dimensions, but other scales in fact and unknowns.

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Steve Dufourny replied on Jan. 10, 2021 @ 21:03 GMT

The maths are a tool Jonathan and we must be prudent in their interpretations, they permit indeed to prove rigorously the assumptions and theories in physics, but they can also imply assumptions themselves, let s take the multiverses or the whormholes or the reversibility of this time, they are due to maths, in fact the physics is the main chief orchestra, not the maths, and we have the same problem with the maths of strings and their extradimensions, they are just assumptions like even this planck scale.

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Jonathan J. Dickau replied on Jan. 11, 2021 @ 21:14 GMT

Ah the Planck scale...

It is where extensibility or extensiveness and uncertainty are equal. It is also indeterminate whether a given extent is space-like or time-like initially, because its precise definition is discovered in the direction of further evolution. This can be as you have said a kind of quasicrystal that becomes more ordered over time. The reason we can think of the Planck scale as self-evolving is because of uncertainty. We see that things including spacetime have to get bigger than a certain size to persist.

Best,

Jonathan

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Steve Dufourny replied on Jan. 12, 2021 @ 15:57 GMT

the palnck scale maybe does not really exist Jonathan and the GR is maybe not the only one piece of puzzle, so in trying to unify the GR and the QM, Gc and h with the fields, the thinkers turn in round in the philosophical prison simply for me, they forget now to think beyond the box. It is the reason why they cannot explain our unknowns simply. Wiclzek for example that I respect and like published the noise of gravitons like quanta of the gravitational waves, but it is just an assumption, the particles of gravitation are different that this, I was surprised in encoding his DM in our nuclei and in taking into account different distances , now make the calculations that I have explained, the QG appears simply , this weakest quantum force, it is not an emergent electromagnetic force, but the electromagnetism is emergent, it is totally different.

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To state the obvious, octonions are a hybrid, a human construction. They are not numbers, because they have been assigned categories/ dimensions. It’s very easy to see that numbers have no category/ dimension: you can easily construct numbers out of mathematical relationships between categories where the numerator and denominator categories cancel out, LEAVING NO CATEGORY. The whole point about numbers is that they have no category/ dimension. Categories/ dimensions are a different thing to numbers.

Something that we would describe as numbers really exists in the world; but octonions only exist in the human imagination. Yet we can represent both numbers and octonions as (e.g.) symbols on bits of paper, as though there were some similarity between them, but there isn’t.

Construction steps must be fully accounted for. Things don’t just miraculously “happen”. You can’t sweep construction steps under the carpet and pretend that they don’t exist. Mathematical equations only represent relationships, they do not represent algorithmic steps i.e. construction steps. Construction steps can only be represented algorithmically i.e. as IF, AND, OR, THEN, FOR…NEXT etc. Put a mathematical equation into a computer, and it will get you nowhere: it’s the behind the scenes IF, AND, OR, THEN, FOR…NEXT that does the work. Physics does not account for IF, AND, OR, THEN, FOR…NEXT: these are the algorithmic steps that cannot be derived from law of nature mathematical relationships.

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Jonathan J. Dickau replied on Jan. 10, 2021 @ 21:53 GMT

I'll explain why I think the truth is different...

The term 'imaginary' throws some people, or fools them into believing we have invented something unreal to account for a thing we don't understand. Imaginary numbers are the freedom to vary by a specified amount in a particular direction. If you put a weight on the end of a spring, there are real-valued quantities such as the stiffness and elasticity of the spring, the mass of the weight we use, the distance we can stretch the spring and have it return to its initial position, and so on.

The imaginary part is bound up in how far it goes above and below the midpoint, when you pull down the weight and release it. But it also results in a specific period of repetition, for the cycle of action, as the weight bobs up and down. The really tricky part, when you try to think of these things in pure Maths, is that the imaginary numbers are orthogonal to the reals. And furthermore; if you go to 3 imaginaries for the quaternions they are each orthogonal to the others, and likewise if you go to 7 imaginary dimensions for the octonions.

This makes most people's head hurt and think that it's all in their imagination, but imaginary does not mean unreal in this case.

All the Best,

Jonathan

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Jonathan J. Dickau replied on Jan. 10, 2021 @ 21:58 GMT

I am prompted to add...

When you use conditional statements in a program or sequence of steps; IF, AND, OR, THEN, FOR… NEXT are all ways to smuggle in the concept of time. They are based on a prior assumption of sequentiality. This is precisely what is seen to happen naturally or automatically with the octonions, if you believe in the work of T.P. Singh. So we don't have to sneak in time because it arises on its own.

Best,

Jonathan

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Lorraine Ford replied on Jan. 10, 2021 @ 22:17 GMT

Typical ignorant bullshit from Jonathan

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Stefan Weckbach replied on Jan. 10, 2021 @ 23:32 GMT

Jonathan,

if Octonions naturally or automatically can let arise time, then why not feed a computer with a bunch of Octonions and wait until the computer program starts to execute itself – without having to execute it? According to your statements that is impossible since we cannot use the conditionings like IF, AND, OR and so on, because according to you that would mean that we smuggled in time. So far, so good.

But consequently, Lee Smolin et al. - whom you have cited in some earlier posts here - unfortunately have smuggled into their numerical simulations exactly what they in the first place wanted to demonstrate with these simulations – namely time. They did it by using a computer. But if Smolin et al.'s brain would have the capacity to do the needed calculations “by hand” (hence, in the brain – let's call that “brain calculation”), they again would merely have smuggled in what they wanted to “prove” in the first place.

So, the simple and unspectacular logical truth about your claims is that already every “brain calculation” that uses “Octonions” to "deduce" something will smuggle in what it wants to “prove” in the first place – namely the “emergence” of time. And that is a “relatively meager” result – since it is just unspectacular good old circular reasoning.

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Rick Lockyer replied on Jan. 11, 2021 @ 03:51 GMT

‘It is very easy to see that numbers have no category/dimension” Now that is a prime example of more “ignorant bullshit”. 200+ years of complex NUMBERS.

Computer programming/algorithms and Octonion Algebra. There aren’t many people on the planet that know more about that combination than I do. One cannot effectively do anything meaningful with Octonions without a computer and...

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‘It is very easy to see that numbers have no category/dimension” Now that is a prime example of more “ignorant bullshit”. 200+ years of complex NUMBERS.

Computer programming/algorithms and Octonion Algebra. There aren’t many people on the planet that know more about that combination than I do. One cannot effectively do anything meaningful with Octonions without a computer and suitable software. I recognized that >25 years ago when I started development of my symbolic algebra software for Octonion Algebra. Several major iterations and three different programming languages later I have something that is actually quite good. I posted a simplistic version of it open source in the forum for my 2018 fqxi essay along with a sample program that cranks out and verifies the equivalence between the Octonion work-force equation and its companion form with outside differentiations, the Octonion equivalent of the divergence of the classical stress-energy-momentum tensor. This is classically used to integrate over some arbitrary volume with select outside differentials converting volume integrals to surface integrals leaving the mathematical description of the equations for the conservation of energy and momentum.

I mention this because it is a perfect example of how it is nuts to claim mathematics should take a back seat to algorithms, that somehow math is thus inferior. Coming up with the proper form for the Octonion Algebra work-force equation was not too bad, but the algebraic invariant portion has 192 differential product terms in each of eight dimensions, none with an outside differentiation. It would be excessively difficult to modify these terms such that you have nothing but outside differentiations on all product terms.

The sample program I gave shows both sides and proves after doing the outside differentiations on the SEM terms there is a perfect match with the work-force side. The ALGORITHM to produce the SEM terms was provided BY THE OCTONION ALGEBRA. It was created from all possible algebraic invariant quad products, as defined by the 16 different definitions for proper Octonion Algebra. It is quite ignorant for someone to think that Octonion Algebra is just in someone’s imagination when the form just referenced precisely covers Electrodynamics through its conservation equations while additionally providing another algebraically separate central force: gravity.

Anyone that has taken a numerical analysis programming course would clearly know the math drives the programmatic algorithm, not the other way around. The same math problem can be solved in a plethora of different programming languages. Computers, algorithms used in computer programming are nothing more than subordinate tools used to do something useful. They are totally a human manifestation. They are not fundamental like mathematics is.

We do not invent or “dream up” any mathematical principles, we discover them. They were there before us and will still be there when we are long gone. As for the popular notion of “emergence”, why bother?

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I'll admit I am a Platonist...

I share the view espoused by Plato, that ideals or archetypes of form exist apart from the material universe, and that nature somehow incorporates the perfect or ideal into the real forms we see around us. But it was Mathematics and not Plato's philosophy that convinced me. And like Rick Lockyer; I found a computer was essential to exploring some things, and provided unique but verifiable insights.

Rick is truthful and accurate in his statements that mathematicians discover the properties of Maths they explore, not invent them, and that the Maths dictate the program steps and their sequence inflexibly. If you are working in the octonions, the order and sequence terms are evaluated is strictly dictated by the algebra itself. So there is nothing to devise or invent, except how to carry the steps out.

In some ways; it's the repeatability factor that makes it impressive. It works the same on any computer with enough oomph. What that implies is that the Maths are the same for everyone, or in every setting, possibly even before the origin of the cosmos. That's where the Platonism comes in. I believe the Maths predate the universe and that's why Mathematics of itself can help shape the laws of nature, as we have come to know them.

All the Best,

Jonathan

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I speak as a person who studied Mathematics for 2 years at school, and for 3 years at university, and received a High Distinction for one of my Mathematics subjects. I also studied Physics and Information Science at university, and I was a computer programmer and analyst for more than 20 years.

Re Numbers:

What are real-world numbers? We are using number symbols to represent something about the real world, at a fundamental level. Clearly, numbers are nothing more than mathematical relationships between categories, where the numerator and denominator categories cancel out. There are no dimensions involved, except in the human imagination, which uses dimensions as a way of handing complex mathematical relationships.

Why doesn’t Rick Lockyer, who thinks he knows all about numbers, explain EXACTLY what a number is?

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Rick Lockyer replied on Jan. 12, 2021 @ 01:55 GMT

I would suggest you read the classic book by I.L. Kantor and A.S. Solodovnikov titled “Hypercomplex Numbers, An Elementary Introduction to Algebras”

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It was greeted with much skepticism...

When Tomita first began expounding the subject of Modular Hilbert Algebras, the Math community initially thought some of his ideas were crazy. But after Takesaki made a careful and thorough exposition of this topic; the rest of the world learned that Tomita's results are real and significant. This led to Alain Connes making Tomita-Takesaki theory the centerpiece of his PhD thesis!

So when Alain Connes wrote "Noncommutative measure spaces evolve with time!" in 'Noncommutative Geometry Year 2000,' he had been playing with these ideas for a while, but it was like a private obsession because it was pretty much a secret to the rest of the world, that algebras or geometric spaces could have intrinsic evolutive properties resulting in a canonical time evolution.

The 'intrinsic time' of Connes is therefore not an invention of the French Lion of Maths, but is instead a monumental discovery about autonomous patterns and dynamism in Mathematics first hinted at by Tomita, explained by Takesaki, and later greatly expanded on and put in geometric terms by Connes. This is still one of those mind-blowing ideas that turns the world inside-out, so it is unexpected..

And the development of these ideas has been very obscure before Tejinder Singh and his colleagues incorporated this notion into Aikyon theory. What makes the octonions an essential part of this story is that while the most exciting stuff happens when the degrees of freedom (dimensions) approach infinity; the octonions exhibit strong evolutive properties with only 8 dimensions!

All the Best,

Jonathan

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Steve Dufourny replied on Jan. 12, 2021 @ 15:53 GMT

Hi Jonathan, all this is interesting indeed , Connes we know him is the best for this non commutativity , and Tejinder has made a beautiful paper with these octonions, they are a good tool. But and there is a but lol, I repeat, we cannot confound the relevance of this tool to better understand our bosonic fields and the main origin of our reality, I repeat even if you are persuaded about your...

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Hi Jonathan, all this is interesting indeed , Connes we know him is the best for this non commutativity , and Tejinder has made a beautiful paper with these octonions, they are a good tool. But and there is a but lol, I repeat, we cannot confound the relevance of this tool to better understand our bosonic fields and the main origin of our reality, I repeat even if you are persuaded about your philosophy general of this universe. We are not sure thet the only one piec3 of puzzle is the GR and that the fields are the origin of our reality creating the topologies, geometries. I d like to have your general philosophy, please explain us, do you consider really that this infinite eternal consciousness for example is an infinite heat and that the photons and points or strings inside oscillating in 1D are the answer, be frank, develop your general idea please. I agree that the works of connes are interesting , the evolution in my model is essential and I don t consider that it comes from the maths but from coded particles , the time is irreversible on this entropical arrow of time and it is a thing emergent due to motions rotations of these particles for me, so why we must consider the fields and the maths of these octonions like the answer of our reality ? it is really a fashion in fact, I beleive that the thinkers have forgotten to consider the particles instead of fields, you know , the particles are not a problem, they are in contact explaining the fields and waves if we apply specific finite series of 3D spheres in begining with the biggest central volume and after we decrease tyhe volumes and increase the number with the dirac large number, now consider 3 main finite series coded, one for thje main codes, thje space vacuum and the two fuels that I explained , the photons and the cold dark matter and when they merge they create the electrm and gravitat fields, it is not a problem in this reasoning also to gfractalise the fields with the octonions if you want but the general philosophy is different about the origin. Why this fashion of fields ? explain me and please detail your answer. The einstein fields equations and his GR seems the problem and the works of witten it seems to me, it is really a prison now for me.

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Steve Dufourny replied on Jan. 12, 2021 @ 16:12 GMT

lol I have the feeling to fight alone against a lobby of fields like origin , apparently with my 3D coded spheres in a superfluid I am a problem , but it is not serious, I know that the persons have not thought about a so simple general universality, I know also that I irritate because I think differently and that the majority of thinkers have worked hard with these fields and this GR, I respect this, but like I said all is in contact and the fields and waves can be explained with my reasoning also, I don t understand why they want to insist on the fields creating our topologies and realities and with extradimensions to be frank. The universe is simple generally, and philosophically there is a lot of problems considering these fields, they don t really respect the evolution and the transformations of this E and the matters energy informations. This thing that we cannot define does not play at guitar for me you know, there is a problem philosophical considering the evolution I repeat and our evolutive consciousness, if we evolve and we are not perfect , there are reasons, if a thing can oscillate the photons to create the universe and that this thing is incredibly skilling, and when we see all these more than 10000 billions of galaxies, so frankly it is not a problem with oscillations to stop the sufferings and the lack of cosnciousness , so you see well that there is a problem with the oscillations vibrations. The universe is not mystical, it is a pure evolutive rational physicality with concrete laws, axioms, equations, why this infinite eternal consciousness has not created a perfect conscious universe and its lifes in a specific oscillation at the begining so ?

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Jonathan J. Dickau replied on Jan. 12, 2021 @ 16:19 GMT

Here are some missing pieces...

It turns out to be easy to coax automatic evolution out of infinite degrees of freedom and finitely reducible uncertainty alone. So in some ways; Tomita was just stating the obvious, or Connes was making plain something that should be apparent to Physics folks right away. The idea is that if you are working from an infinite range of variations, or infinite...

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Here are some missing pieces...

It turns out to be easy to coax automatic evolution out of infinite degrees of freedom and finitely reducible uncertainty alone. So in some ways; Tomita was just stating the obvious, or Connes was making plain something that should be apparent to Physics folks right away. The idea is that if you are working from an infinite range of variations, or infinite possibilities; pretty much anything is possible, ..almost! But nothing is quite actually real or truly possible without an evolutive process.

If we approach it from the Quantum-Mechanical view; some of this becomes possible to explicate simply. John Klauder eloquently explained at FFP15 that we can see Quantum Mechanics as a projection from an infinite dimensional Hilbert space onto a 2-d surface with specific well-defined properties. He went on to explain that we can obtain enhanced quantization by lifting the target space or varying it in ways that let us see hidden details. This is like constructing conformal field theories to fit the need.

We can relate this back to Connes' remarks that the really fun evolutive stuff happens when degrees of freedom become infinite but this must be mapped onto finite-dimensional spaces and relations. My guess is it does not happen all at once, but proceeds in stages respecting all possible forms up and down the dimensions. This expands on themes developed by my departed friend Ray Munroe - that both the simplest and most complex forms possible in Math inform Physics - informed by works of other departed friends, F.D. 'Tony' Smith and my Physics mentor Greg Kirk.

Bimetric Convergence is a term I have coined for a scenario where dimensionality is at first unconstrained, ranging from 0-d to infinite dimensions, and was both bottom-up and top-down limited - until cosmological transitions constrain the upper and lower limit of dimensions. The linked published paper explains a little better.

Best,

Jonathan

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As it turns out...

It does arise in General Relativity. Misner, Thorne, and Wheeler introduce this in chap. 16.3, which starts on pg. 388 in my copy. This regards factor ordering, curvature, non-commutativity, and the equivalence principle. Because some terms couple to curvature; we are told about exceptions or modifications to the "comma goes to semicolon rule" on pages 390 and 391, but Physics research in recent years shows there are additional modifications to add to the list.

The work that Rick Lockyer cited earlier speaks to precisely this concern! He fills in the blanks by showing one missing piece arises from the forced ordering of the octonions! So even GR experts MUST be acutely aware of non-commutative factors in their calculations - if they really know what they are doing. A lot of people take shortcuts Steve, or assume that certain things are true across the board. Translations in 3-space commute, but rotations do not.

Go Figure!

Jonathan

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Steve Dufourny replied on Jan. 12, 2021 @ 18:38 GMT

The big philosophical question will be , these 3D spheres , are they emergent or are they the choice foundamental of this universe jonathan ? all is there, they don t emerge for me from fields in 1D at this planck scale and connected with this cosmic field of this GR, no they are created coded at the primoridal essence of the universe. You see the difference now ? the topologies and geonetries are not due to fields for me and maths of strings or geonetrodynamics, no they are deformed spheres in 3D , it is totally different.If I am right it is the endo of strings and fields in fact , not the E8 because it can be utilised also with my finite series primoridal of 3D spheres.

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Jonathan J. Dickau replied on Jan. 12, 2021 @ 19:35 GMT

In my view...

They arise from the action of Lie group G2. I'm pretty sure E8 plays a part earlier on, but G2 supplies the piece you are looking for. Think on 'how does there come to be interiority/exteriority?' Then the place of the spheres in 3-d Physics becomes clear. We are used to a situation where size and distance are fixed or constant, but they might better be seen as relational at first, where a gauge setting mechanism is needed that gets supplied by cosmological transitions.

Early universe cosmology forces us to abandon some conventional assumptions entirely. There must always be some kind of determiner for fixed relations to arise.

Best,

Jonathan

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Steve Dufourny replied on Jan. 12, 2021 @ 20:22 GMT

I have discussed about this with several persons working with the octonions, the E8 and the G2. All this is interesting because it pexists probably a kind of conjecture about the fields or the 3D spheres like origin. The actual cosmology that we analyse is unfortunally limited, due to fact that we can only observe the photonic spacetime , the BB is an assumption and maybe we have a deeper logic...

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I have discussed about this with several persons working with the octonions, the E8 and the G2. All this is interesting because it pexists probably a kind of conjecture about the fields or the 3D spheres like origin. The actual cosmology that we analyse is unfortunally limited, due to fact that we can only observe the photonic spacetime , the BB is an assumption and maybe we have a deeper logic than this BB. I have studied also several papers about this inflation and BB cosmology and the GR. If I can , the shape of this universe seems a key , a sphere or not or a future sphere and why and how? I liked the explainations of Alan guth about this inflation. I consider personally an expansion of the space due to the multiplications of these finite primordial quantum series of 3D spheres having the dirac large number, the same I have calculated than our finite cosmological serie of 3D spheres. The singularity being this central cosmological sphere being a thing beyond our understanding, a kind of supermatter energy able to create all infornations with these finite quantum series having codes , this supermatter energy so is a matter energy possessing all the mendeleev table and the energies , and so the distribution of matters is in function of codes and the 3 series that I explained, the fuels permitting to activate the space vacuum.It is the DE , this spacevacuum Jonathan simply.See that that implies a logic that we cam predict seen the dark energy and dark matter disponible and the spherisation in my model, all can be unified in all humility and that can complete logically the standard model.I don t affirm that the universe is a sphere actually but it will be a sphere or is maybe allready a sphere, and that implies an acceleration decceleration towards the maximum volume spherical and after an acceleration decceleration towards the minimum balanced spherical volumes, it is a little bit this also the meaning of my model of spherisation, it is an evolution of this universe, see that at tghis quantum scales it evolves, that is why also this consciousness evolves, but it is an other story.

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Steve Dufourny replied on Jan. 13, 2021 @ 12:11 GMT

Jonathan, here is the general idea of my spherical geometrical algebras that I have invented and permitting to quantify this QG.

I have invented the Spherical geometrical algebras, correlated with the geometrical algebras of Clifford.

3 main finite primordial quantum series , having the same number finite than our cosmological finite serie of 3D spheres, I have calculated, it is the dirac large number.

---> space vaccuum main codes of the DE

--->photons , fuel 1 , implying in merging with the space the electromagnetic forces of the standard model and the heat.

---> cold dark matter ,fuel 2, implying the antiparticles the balanced cold and the antiparticles

General vectorial analysis, associativity, non associativity, commutativity, non commutativity, vectorial spaces, under vectorial spaces. Scalars , real numbers multiplication vectors , primes, p adics.

Utilisation and properties and 3D quantum spheres,

Tensors, matrix, torsors, vectors, complex numbers, spinors, quaternions , differential forms, volumes, densities, angles , sense of rotation, superimposinmgs, sortings, synchronisation....densities linked and life time and evolution. Rotations, phasis, imaginary numbers. Oscillations vibrations of 3D spheres, more the hopf fibrations on surfaces permitting to rank the quasiparticles. External and internal products ....rankings.

Symplectomorphims preserving the volumes for the deformations of 3D spherical volumes.

The number finite does not change ,

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This is how Connes explained it...

Time - in Noncommutative Geometry blog gives details of how time has an intrinsic evolution or arises automatically in NCG.

Heart Bit #1 - in Noncommutative Geometry blog explains how this gets to the heart of what non-commutative geometry is all about.

And it is further discussed and explained here at the n-Category Cafe:

Re: Alain Connes’ “Intrinsic Time” - QFT of Charged n-Particle: The Canonical 1-Particle - in n-Category Cafe blog features Connes' explanation in a discussion about how intrinsic time works in QM.

All the Best,

Jonathan

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Human beings are well known for extrapolating and interpolating ideas, and for creating fantasy scenarios in books and films. But many people seem to believe that mathematics and physics is exempt from this type of thing.

However, many mathematical ideas are clearly pure fantasy, e.g. some ideas about numbers. Number symbols can be used to represent something about the real world; the real world is what is important; the real world is most definitely not a fantasy scenario.

Seemingly, no-one can concisely explain WHAT a real-world number actually is, but then they try to claim a number can have some sort of dimensions.

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Jonathan J. Dickau replied on Jan. 13, 2021 @ 01:29 GMT

It is true humans are great fabricators...

It is sad, however, that many of those who dissemble with great apparent veracity are the ones who become the leaders in our society. It is too often the best fabricators and not the best thinkers making the important decisions.

Current events do so attest.

All the Best,

Jonathan

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Steve Dufourny replied on Jan. 13, 2021 @ 10:39 GMT

Hi to both of you,

Lorraine ,indeed the humans like to dream and imagine fantasies, they create, it is very well for the arts but we have this also inside the sciences community and mainly in maths and physics due to symmetries or others, and the psychology and the own encodings also create these things. That is why we have so many assumptions. But a sure thing after all is that only the...

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Hi to both of you,

Lorraine ,indeed the humans like to dream and imagine fantasies, they create, it is very well for the arts but we have this also inside the sciences community and mainly in maths and physics due to symmetries or others, and the psychology and the own encodings also create these things. That is why we have so many assumptions. But a sure thing after all is that only the proved laws, axioms, equations are accepted, implying that we must take into account just this pure rational determinisn after all. We can create, imagine but we cannot affirm our assumptions.

Jonathan, the world is not perfect like we know and like I said, we can rank the humans and their psychology, comportments, philosophies, ... the world is a system with specific parameters and the humans try to adapt themselves to this system, many plays a game and are not really conscious, all what they search is to be well and so the edcation permits to play and their skillings are utilised to reach the aims, many in the leaderships think they have successed their lifes because they win a lot of money, but they have forgotten foundamental parameters .This planet is surprising I must say and it is due to our past, our primitive instincs, our educations, we have not really understood the complementarity and the cooperation, of course it exists this cooperation but not globally, it is very sad because we could be so well generally on this earth. The project that I have created is for this, to harmomise the high spheres of power , that will permit to evolve better if we improve the main global system , that will reasure the humans mainly and they shall nourrish their minds with better informations. But I ask me if this UN wants to change or are they conscious really , maybe they accept this reality and are not really anxious about the future and the generality of lifes. I find this very odd knowing that these universal truths and this energetical potential are realities. But the hope exists still fortunally.

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Jonathan and Steve,

But what exactly is a number as opposed to: 1) categories (where mass and single dimension position are examples of categories); and 2) mathematical relationships?

I’m saying that numbers are nothing more than mathematical expressions/relationships between categories where the numerator and denominator categories cancel out, leaving something without a category. I’m saying that numbers have no dimension/ category; but, on the other hand, the human mind sometimes needs to use dimensions as a way of handing complex mathematical calculations.

I would like to hear other concise views about what exactly defines a real-world number.

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Steve Dufourny replied on Jan. 14, 2021 @ 18:07 GMT

Hi Lorraine, yes indeed they are mathematical expressions between categories, and they permit to rank in function of these categories becvause they are not identical , they permit to increase or decrease or others these categories. I don t beleive personally that we have extradimensions but a pure 3D where the numbers permit simply to categorize this 3D in function of the levels of properties.2 is bigger than 1 simply and the addition, multiplication, and others are tools permitting so to categorize better the different measurements and properties.The real world is what it is , a physicality with its physical and mathematical lwas, but the physics first for me and after the maths permitting to categorize like you say. So indeed we can rank and correlate, we have the Naturals, integers, rational numbers,irrationals, algebrics, trensciendentals, reals, imaginaries, complex and so we have groups and subgroups and correlations between them, it is just a tool for me, the primes are interesting that said and the p adics analysis. They are so generators and can be correlated with the physical properties when we converge of course.It is like this for the computing and the randomness and the generators simply. Regards

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Lorraine Ford replied on Jan. 14, 2021 @ 21:57 GMT

Thanks Steve

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What is a number in the 'real world'?

There is a profound difference between none and one of any quantity. And multiples of that yield a stable value, an integer. But one might also ask if the freedom to vary beyond a certain number is worth something. In the parlance of number theory; the freedom to vary in a specified direction finds its representation in an imaginary number.

It was found via the sums of squares problem that there can only be a certain number of imaginary dimensions in a sensible algebra - 1, 4, or 7 - corresponding to the complex, quaternion, and octonion algebras. This is simply an acknowledgement that it can be necessary to include more angles of rotation to represent the physical reality, but we are not free to insert any number as we like.

It is obvious that the freedom to vary is not worth as much as a specified value, as per 'a bird in the hand.' But even if it is only worth 1/4 as much, that means the freedom to vary becomes a 'this must vary' if we go to 3 or more dimensions of variation. However; that is my own interpretation of what Connes and others are talking about, and not the mainstream view.

But I think there is ample evidence that 'real world' extends at least to the quaternions, if the experience of aviators counts for squat.

Best,

Jonathan

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Jonathan J. Dickau replied on Jan. 15, 2021 @ 21:50 GMT

I find it interesting...

The sums of squares theorem was originally about real integers, and it led to the Hurwitz theorem being proved, So we find there are only 4 possible normed division algebras. It's all about being able to return to where you started.

Best,

JJD

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Lorraine Ford replied on Jan. 15, 2021 @ 22:46 GMT

Thanks Jonathan.

I would have thought that quaternions are just a convenient mathematical way of representing the world. The world is different to our symbolic representations of it: while we use time and energy to do calculations using pen and paper, or via computer, the world does it without using time and energy, and without any brain or computer infrastructure.

So I would think that perhaps there are no calculations going on in the real world, (and there is no Platonic realm which miraculously explains everything), there are merely relationships that exist. What we represent as numbers are also relationships (where the numerator and denominator categories cancel out). So, when a number-change event happens for a variable (from whatever cause), the law of nature relationships mean that other numbers automatically change, because numbers are merely relationships between categories, not calculated end-products.

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Georgina Woodward replied on Jan. 16, 2021 @ 04:24 GMT

Quaternions have a time dimension, so can represent change over time> I'd argue that that can be better used to represent the history of something happening in the World, like a flight. Rather than the material world. Each quaternion can represent a rotation and so change is built in. They are non commutative, so the importance of the sequence of happenings is inherent. (And they do not, in their favour, suffer from gimbal lock) However what has been ( unless still materially enduring) and what is are not both actual. Here is the same issue as when 4 dimensional Euclidean space is used to represent the material world. It does not make sense for there to be any kind of happening in the material world without energy. Time necessity is debatable. It can be regarded as an emergent concept, from material-spatial change.

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Re “change”:

What are the contributing factors that make a world? What we represent as variables/ categories of information (e.g. mass, position, charge), lawful relationships, and numbers are fundamental aspects needed to make a world.

But so is change of number/ assignment of new numbers to the variables a fundamental aspect needed to make a world. This is another aspect of the world that can’t be taken for granted. Things don’t just “happen”, numbers don’t just change for no reason.

A number is not an entity that changes itself. Law of nature relationships between categories “cause” number change for some numbers, but only because other numbers have changed. It’s these “other” numbers that are the problem.

Seemingly, a system must run down unless new numbers for the variables are continually input to the system.

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Georgina Woodward replied on Jan. 17, 2021 @ 05:05 GMT

Your list of what is needed to make a world is actually a list of what is useful to represent a world. Existence and energy are fundamental.. Whereas your numbers need input to make them change, energy throughout existence is change. Never destroyed just charging its type. Large changes can become smaller changes. Chaos theory shows small changes can lead to large changes. An isolated system or representation o such may run down. That is not necessarily so for many interacting systems; able to 'feed' off of each other.

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Georgina Woodward replied on Jan. 17, 2021 @ 05:10 GMT

That's not saying systems can endure eternally. Eventually they will decay or be destroyed; but also replaced by other systems.

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Jonathan J. Dickau replied on Jan. 20, 2021 @ 14:54 GMT

Let me turn this around...

The energetic component creates change and the material component observes or follows energetic activity. Georgina is correct to cast energy as the agent of change, while Lorraine's view that matter creates choice or exercises the freedom of choice needs further explanation.

Mass creates curvature in general and it has the effect of inducing the decoupling of wavefunction components in Continuous Spontaneous Localization, which is a feature of Tejinder's theory. That is; mass or gravity causes the quantum wavefunction to decohere through localization.

But the finite speed of light is also a result of the universe's curvature. If we turn Einstein's famous equation around; c^2 = E/m. Then look at what happens when the mass of the universe is 0, and we see that the speed of light is unbounded for a flat 2-d space devoid of matter, like we expect to see near the Planck scale.

So the presence of matter serves to slow down the communication between elements of space, by inserting time, or inducing a slowing of time through cosmic mass.

All the Best,

Jonathan

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No matter what the variables are, e.g. the energy or position variables, the laws of nature determine that the relationships between the numbers that apply to the variables always hold. But the lawful relationships don’t actually move the system forward.

The system of lawful relationships is static, the system of lawful relationships is not a perpetual motion machine. One number change “causes” other numbers to change due to fixed relationships, but that’s the finish of it: the numbers for the variables are now all in correct lawful relationship, and the world has ground to a halt.

What saves the system is free will/ agency which continually inputs new numbers to the variables, thereby driving the system forward.

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Jonathan J. Dickau replied on Jan. 20, 2021 @ 15:03 GMT

It is absolutely true Lorraine...

Energetic systems tend to run down. There is no perpetual motion, per se. It is an unavoidable consequence of the global asymmetry of the Mandelbrot Set that what you are saying must be true. It's written in the Maths as well as apparently being an inflexible law of Physics.

Best,

Jonathan

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Jonathan J. Dickau replied on Jan. 20, 2021 @ 15:06 GMT

The flip side of course is...

The action of the Mandelbrot Set under the Octonions tends to maximize choice for those who are in a position to make choices. So we can all be thankful that with hyper-dimensional super-determinism; we can all have optimally close to perfect freedom of choice.

Best,

Jonathan

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Jonathan J. Dickau replied on Jan. 20, 2021 @ 15:10 GMT

That is...

We have the optimal freedom to choose, if we have sufficient energy to exercise our choices by executing actions that adequately engender that choice.

JJD

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According to the paper linked in the article, Tejinder Singh's explanatory framework can be probed experimentally. By taking this as given, one can simply wait until there are some solid experimental results available for Singh's explanations (which are, in my opinion, interesting, but not mandatory).

Concerning the features of non-commutativity and non-associativity, I would like to add...

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According to the paper linked in the article, Tejinder Singh's explanatory framework can be probed experimentally. By taking this as given, one can simply wait until there are some solid experimental results available for Singh's explanations (which are, in my opinion, interesting, but not mandatory).

Concerning the features of non-commutativity and non-associativity, I would like to add that these features of sequentiality already occur in ordinary school-level algebra. For example, solving an equation that has one unknown constant left in the equation and one can obtain the value of that constant only by an auxiliary calculation means to first having to perform that auxiliary calculation before one is able to solve the main equation and obtain the result thereof. At first “obtaining” the main result and after that performing the auxiliary calculation (or even not at all performing that auxiliary calculation) does not make much sense to me. So in most cases one necessarily must obey a certain sequence in time to obtain the desired result of some main equation.

Whereas such mandatory steps in time can be neglected by human beings at will, for example by first painting a wall with the furniture left standing at the wall and after that part of the painting job removing the furniture and proceed to paint the left over areas of the wall (and not vice versa), hard science as physics – when considered as empirical – must obey certain steps in time to at all come to some reliable conclusions. “Possessing” the “result” before the needed calculations have actually been performed does and has only worked for a relatively small percentage of cases in history and surely there are many more cases where the obtained results had not been what one had believed them to be before having carried out the needed calculations – and more importantly before having carried out the needed experiments, and hence observations! I think the main issue here is that the hard sciences are really dependent on empirical research and experiments and not on beliefs. Beliefs are humanly, but what nature does must not necessarily be in accordance with human beliefs, history and even personal experience should tell us so.

And last - but not least - what would our craving for theories be without some nice humor... check out that nice and cute picture if you like, at

https://www.larecherche.fr/non-la-physique-ne-se-r%C3%A9du
it-pas-aux-maths

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Jonathan J. Dickau replied on Jan. 20, 2021 @ 18:38 GMT

Sometimes the result is a surprise...

When Benoit Mandelbrot first tried to print out plots of the Mandelbrot Set; he thought it was a computer glitch or some weird error, before verifying that the unusual warty shape was something persistent. It looks the same whoever probes it. Was it there before anyone did the calculations? What do you think?

There may be yet weirder stuff 'out there' but to find it you might need to imagine or think there is some 'result' worth pursuing, before you write the program to do all those difficult calculations. If he was still alive; I'd say ask Fokko du Cloux. Was E8 there already, before they began to probe it? Is it real or is it Memorex?

Best,

Jonathan

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Jonathan J. Dickau replied on Jan. 20, 2021 @ 18:55 GMT

Regarding possible experimental proof/disproof...

That should be interesting to see. But I would not count out an inexact match. The theory I've been developing for the last 20 years is not identical but it has perhaps 80% overlapping content or points in precise agreement - such as early universe evolution under the octonions in Connes' intrinsic time.

The biggest difference is the reductive mechanism, where I treat dimensional reduction as a process of condensation and Tejinder's group uses CSL. Astrophysical evidence is often ambiguous or inconclusive. So we could both be winners, if the evidence points the right way. And there could be room for adjustments.

In discussions with Gerard 't Hooft and with Aurelien Barrau I learned that predicting an exact fingerprint of what we would see if a theory is true can be quite tricky.

Best,

JJD

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Steve Dufourny replied on Jan. 20, 2021 @ 21:13 GMT

Hi , the predictions seem to follow harmonical partitions, but actually we have just a little bit understood our standard model and its bosonic fields and the QFT, we d be surprised if my reasoning is correct about the main codes of this vacuum and that the bosonic actual fields are just activated due to photons encoded, so the actual partitions and mathematical tools like this E8 consider these bosonic fields only , and it can be predictions of errors if that others encodings and codes have a deeper logic and that they don t follow the same partition .... so the results can be simply false and so the experiments are a lost of money if we are not sure about these predictions, there is an enormous philosophical problem for me actually inside the sciences community considering only these fields and this GR. They turn in round trying to go deeper but all this seems not true if my reasoning is correct about new partitions and fields due to different particles energetical encoded like this DM cold giving the quantum gravitation and the anti particles. The E8 is maybe beautiful but can imply an ocean of confusions and false predictions because the fields are emergent and not only correlated with these photons ....Think about this if I am right.

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To Steve, Rick, and All,

One can make an analogy in playing the Piano and learning the Octonions. There is a wealth of great Piano music written in keys with mainly black notes. I heard this in so many words from Vladimir Feltsman when auditing a Master Class, but it is also a well-known fact to composers - given the flexibility afforded. However it looks more complicated on paper. There is more to keep track of, in terms of where the black notes are added

One must add more and more sharps or flats, as one progresses around the circle of fifths to get to different key signatures. But there is a simplicity when playing on all or mostly black keys. So there is less to remember; if you know that you are starting and ending on a particular note. Working in the Octonions is similar because it allows a simplification due to the fact a higher-d algebra is a better fit to Physics.

All the Best,

Jonathan

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Jonathan J. Dickau replied on Jan. 21, 2021 @ 19:28 GMT

To explain further...

If one goes from playing in C on all white notes; one can go to the key of G then to D by adding sharps or to the key of F and then to Bb adding flats. But it gets more complicated in the middle, until you are playing on mainly black keys. Then it simplifies again in a higher order of progressions, in mostly black-noted keys.

Best,

Jonathan

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Steve Dufourny replied on Jan. 21, 2021 @ 20:17 GMT

Thanks for sharing Jonathan, I love the piano and guitar, I prefer to play at guitar the rock and blues mainly and jazz, but at piano I play mainly classic and jazz, I have in all humility many compositions , I love to improvise in fact , I take a gamut , and I play in function of my emotions and feelings of the moment , I love to accelerate and play quickly sometimes, the silences also are...

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Thanks for sharing Jonathan, I love the piano and guitar, I prefer to play at guitar the rock and blues mainly and jazz, but at piano I play mainly classic and jazz, I have in all humility many compositions , I love to improvise in fact , I take a gamut , and I play in function of my emotions and feelings of the moment , I love to accelerate and play quickly sometimes, the silences also are important. The music is fascinating in fact and the combinations are infinite in improvisations and never the same even with the time. The arts are important considering the creativity and the free will is correlated , that is why it is difficult to put the free will in algorythms, the consciousness also seeing the combinations and the parameters to take into account. The feelings and this universalism seems important at my opinion even when we create partitions in maths or physics, like if this consciousness permitted to converge towards this universal philosophy and its pure universal altruisn and uniqueness even considering the diversity of creations, the singularities become relevant. A melody at piano or guitar or others can be simple or complex but the most important is the harmony and the feelings , the arts permit to our minds to create things and express our heart, soul , mind, .... One of my favorites in classic is Vivaldi, when you listen the 4 seasons, wowww if you close the eyes you see the seasons and the nature. Bach is more mathematical but I love also , Mozart him are pure innocent creations of a child not polluted lol by the systems of adults, it is so pure and full of joy even. Others are more sad, or this or that . That depends of composers in fact. The same maybe for our partitions in sciences and maths, it is always after all in function of the education, the encodings, our evolution, our philosophy, our life , the environments, ....and its feelings. All roads don t go to Roma but towards this universal truth yes , and the diversity and our uniqueness are wonderfull after all, that is why the assymetries creating the unique things become relevant, and the complexity implies a kind of humility.

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Steve Dufourny replied on Jan. 21, 2021 @ 20:35 GMT

so Jonathan, in resume, it exists an universal partition of spheres , I am conviced and not from the octonions, they are just an instrument inside this partition for the fields and some gamuts where we improve or create , but the real universal music of 3D spheres considering these 3 finite series them are more more than this you know, I can understand that you love this E8 and octonions but see this universe and what is its essence primoridal, see well the nature around you and at all scales furthermore, see well what is the choice of this universe and see this complexity in the details. These spheres are fascinating. they can be deformed, don t forget, not need cosmic fields of this GR to create the topologies and geometries you know, the intrinsic codes in this space vacuum of these series of spheres are sufficient. Best Regards

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Steve Dufourny replied on Jan. 21, 2021 @ 21:08 GMT

we can go deeper in philosophy , we have all our assumptions that we don t affirm of course, we just discuss, I consider a kind of creator of this universe and I consider it like an infinite eternal consciousness and like you know this thing that we cannot define sends the imformations primoridal from the central cosmological sphere, it sends fionite coded series of spheres, a thing important in...

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we can go deeper in philosophy , we have all our assumptions that we don t affirm of course, we just discuss, I consider a kind of creator of this universe and I consider it like an infinite eternal consciousness and like you know this thing that we cannot define sends the imformations primoridal from the central cosmological sphere, it sends fionite coded series of spheres, a thing important in my model of spherisation iof that this thing is a kind of ether but without time, space, dimension, matter, it is a pure energy connected with all but in 0D , and this thing needs to transform and code the series finite, so the central sphere is essential in my model and it is there that the 3 other ethers become physical where we have only a pure 3D at all scales, like if it was the choice of this universe simply, a 0D ether of consciousness and 3 aethers in 3D , this thing cannot make miracles so with oscillations, we can just maybe feel it in meditation but it is an other story that I cannot really develop and answer or affrim. This mechanism proves that we evolve due to imformations continuing to be in evolution, see that this DM and DE disponible can explain the evolution and we can even predict generally the universe. We are still so youngs in fact and it is fascinating if the consciousness evolves and that the complexification of this biology is a reality, we create a kind of project Jonathan for me and we are tools , fractals of this infinity. There is nothing of odd or religious in all what I explain, we need a kind of transformator of this E , like a musician of spheres in fact and at this momment we don t know this partition of spheres, we just analyse a so small part, maybe 0,0000000001 percent of the secret of our standard model , so we must recognise that a TOE does not exist and probably in one million years on earth of evolutive sciences, it will be the same, we must be humble and when I read the name toe , lol that makes me laugh in fact. The same when the thinkers tell that we have only photons and this GR and strings inside oscillating vibrating like if this infinity that we name god played at guitar with these strings. You know , I have nothing agiant these octonions, but let s be logic, it is just a tool and we are I repeat so youngs at this universal scale, the complexity of series that I explain furthermore are not a problem, the problem is to know how they act really , and we know nothing about these spheres oscillating, vibrating, in motions rotations and in evolution.

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The steps that must be taken “between the lines” in order to make maths work are algorithmic steps.

Maths does not work all by itself. Similarly, Mandelbrot Sets don’t just “evolve”; mathematical iterations don’t just happen all by themselves.

Mathematicians and physicists are blind to the “between the lines” algorithmic steps that are necessary to make their equations work. What this means is that mathematicians and physicists are blind to a necessary aspect of the world.

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Jonathan J. Dickau replied on Jan. 22, 2021 @ 20:16 GMT

It was all there to start with Lorraine...

The mathematical structure is not something we invent or can alter. It has built in minima and maxima. The curious thing about the Mandelbrot Set is that only using the very simplest equation gets us the most complex object. If we add terms or go up in degree; we end up with something less interesting.

So sure; there have to be algorithmic steps to discover or uncover the structure that is inherent in the Maths. But this is precisely analogous to a procedure of triangulation used by navigators at sea to know where they are or find their way to distant lands. The Mandelbrot Maths are the same.

So your argument is that there is work to do, if we want to explore, and that we don't need to look beyond the real numbers because that is all unreal. It's like the people on the island in "Moana" arguing that everything they could ever need is already there; so why go exploring? The point is; there is really something there - out beyond the reef - worth finding.

All the Best,

Jonathan

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Jonathan J. Dickau replied on Jan. 22, 2021 @ 20:56 GMT

The Mandelbrot algorithm uses Pythagoras' formula...

The Pythagorean theorem uses a squaring operation, where a number is multiplied by itself. So the hypotenuse of a right triangle is obtained by c^2 = a^2 + b^2, where a and b are the legs joined by a right angle. When using complex numbers; the same letters a and b are employed, so a complex number is designated as a + bi where a is the real coefficient and b is the imaginary, and the two components are orthogonal as before.

So the complex numbers themselves are a triangulation in the Argand plane, the domain of the complex numbers. But then the Mandelbrot formula says we take the value for each location, multiply that number by itself, and then add back the location of our starting point - again and again to see what converges. And points that don't go to infinity; we say they are part of the Mandelbrot Set.

So this idea of multiplying something by itself and adding that to another value appears in both the Pythagoras and Mandelbrot formulae. So we are doing ranging operations on something by squaring and adding then comparing. This is a powerful generalization. It is also how we obtain dimensional estimation, in terms of distinguishing 2-d from 3-d and so on.

I have written and will explain that this is the key to symbolic thinking!

Best,

Jonathan

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Jonathan J. Dickau replied on Jan. 22, 2021 @ 21:09 GMT

Symbols are a projection...

A circle on the printed page has a wonderful regularity and uniformity. But it is seen in its entirety only from above. We can't tell if the circle is a cross-section of a cylinder or sphere, however, if we are assuming it is part of a larger (or higher-dimensional) figure. But humans are not born with the capacity to distinguish this. It generally develops around 2 1/2 years of age, according to the research of Judy DeLoache. So the capacity for dimensional estimation is what I think of as a gateway skill for other learning.

So we see that the circle is one of the earliest symbols to appear in petroglyphs all over the world. Is it the flattened image of the Sun or Moon? Some say it's a symbol for God. What about the reflection of the Moon in a pond? Does that seem like a gateway to another world to you? Maybe it did to the ones who first started making symbols. They even drew animals. They saw that they could make a flat representation of something 3-d and it opened up a whole new world. Go figure.

Best,

Jonathan

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The symbolic equations of mathematics and physics just sit there. They never move to the next line unless a person, or a computer program written by a person, makes them “move” by writing the next line. It’s the algorithmic steps taken by a person that makes them move.

It’s the same with the laws of nature and the numbers that apply its variables: they never move; the equations and numbers are not moving parts. Despite the delta symbols in the equations, the SYSTEM never moves forward unless new numbers for at least a few of the variables are input to the system. This input of new numbers can only be represented as algorithmic steps. IF, AND, OR, THEN represent some of the algorithmic steps that are a normal and natural part of the world.

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Jonathan J. Dickau replied on Jan. 22, 2021 @ 21:11 GMT

See the above comment...

Since symbols are only a projection or shadow of something higher-dimensional or deeper in its organizational level; they summarize something bigger than they are.

Best,

Jonathan

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Jonathan J. Dickau replied on Jan. 22, 2021 @ 21:34 GMT

You are right about equations that just sit there...

I particularly like Euler's identity e^ i pi = -1. The TeX version doesn't look right here either. Some formulae appear to be more deeply woven into the fabric of reality than others, however.

JJD

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A few basics about symbols:

Symbols were created by human beings for their own purposes. Symbols are not actual laws of nature, not actual numbers, and not actual algorithmic steps; but symbols that represent of law of nature relationships, numbers, and algorithmic steps are used by human beings to aid in understanding these aspects of the world. Symbols are a tool created by and used by human beings.

Symbols are nothing more than squiggles on bits of paper or screen: symbols that mean something to one person do not necessarily mean something to another person.

………………………

The use of symbols has allowed human beings to separate out the fundamental elements that make up the world, and it is clear that algorithmic steps are an entirely different, but normal and natural, fundamental aspect of the world:

Even when delta symbols are used in the symbolic equations, the system represented by a set of equations can never move forward unless new numbers are input to the system; this input of numbers can only be represented using algorithmic symbols.

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A brief tutorial is in order...

The inception of the cosmos is a tricky subject because it forces us to give up common assumptions in order to understand anything. We are talking about a condition where almost all of what surrounds us - that we take for granted - had not come into existence yet. And this means the context for the familiar rules of Math had not solidified either.

Things that work in the the normal way for 3-d don't apply if we don't have a 3-d universe yet. For something to be 0-d appears an impossibility, because it would need to possess (or imply the existence of) infinite energy. If it's only 1-d, then that implies it must be a dimension of time to persist. So this makes the lower limit of things that can have duration and spatial extent to 2-d.

But the conditions which set an upper limit to what the dimensionality was at the outset or origin of the universe require the existence of limited forms to appear first, so that the dimensions are constrained in some way cosmologically. This is why one cannot rule out the possibility for a higher-d origin, and why the dynamical properties of higher-d spaces remain a tantalizing explanation for the origin of time.

Best,

Jonathan

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Lorraine Ford replied on Jan. 25, 2021 @ 20:19 GMT

“Higher-d spaces” have NO “dynamical properties”. The equations of mathematics and physics just sit there. They never move to the next line unless a person, or a computer program written by a person, makes them “move” by writing the next line. It’s the algorithmic steps taken by a person that makes them move.

It’s the same with the laws of nature and the numbers that apply its variables: they never move; the equations and numbers are not moving parts. Despite the delta symbols in the equations, the SYSTEM never moves forward unless new numbers for at least a few of the variables are input to the system. This input of new numbers can only be represented as algorithmic steps.

IF, AND, OR, THEN are some of the algorithmic symbols that can be used to represent the cause of movement in the system.

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Steve Dufourny replied on Jan. 25, 2021 @ 20:52 GMT

Jonathan, if you consider an outside this physicality and let s assume like assumption that it is an infinite energy, let s tell an infinite eternal consciousness, it is an assumption I repeat, so this thing is and was before the physciality a 0D without time, space, dimension, matters, just a pure energy that we cannot define, so this thing has decided to create an universe, so imagine it has during an incredible long time transformed this E in a central main sphere and after all the information in a pure 3D are sent from there, we don t need extradimensions , just a 3D na a time of evolution to create this project that we name the universe, the problem of extradimension is not necessary, even for the time, the error comes form the non commutative time and the interpretation of the GR , it is just a thing that we observe due to photons, nothing of mystical. Lorraine is right for me in explaining also her points of vue, the humans complexify a simplicity wich is not necessary, sorry for the lobbies of octonions and strings, but it is a reality, the problem is philosophical.

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Steve Dufourny replied on Jan. 25, 2021 @ 21:01 GMT

Lorraine, I think we cannot change their works, they don t want I d say to change, they are persuaded about their extradimensions and their correlated philosophies with this GR and strings and octonions, in changing that implies that they are false and have lost their time during many years, and furthermore it is an industry, they convice the enterprises to make researchs with this lol, so we speak in the wind, because like all they are vanitious and are persuaded , me my theory I don t affirm it but I respect the pure determinism of motions of a pure 3D, them they invent mystical things to imply confusions frankly I tell me, it is a lobby and a philosophical prison simply. They play with the maths to see who will go the farer and who will find a toe unifying the QM and the GR, but what they have forgotten is that their philosphy , and their foundamental object is probably false , but never they shall accept and recognise this , I am a problem with my spheres and if you add the vanity and I am myself vanitious, so you understand the crisis inside this theoretical sciences community, they congratulate between themselves, the rest is not important for these strings theorists considering the fields and this GR like founda,mentals, we speak in the wind Lorraine.

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Some thoughtful attention is due here...

While 'only what can be constructed is definite' appears to be true for physical systems or the possible origins of a physical universe; the idea that Maths only arise because sentient being are there to construct it over-generalizes what is real. One does not have be be a hyper-Platonist to know that certain realities of Math are invariants. But even so; it's reasonable to say there is a dividing line between natural and invented Maths.

The real point at issue here is how to faithfully represent the real world as is is. Mostly; people have gotten caught up in convenient generalizations that hardened in place through the Einstellung effect so klunky solutions are hard to replace or displace with better models. But even so; things like Calabi-Yau spaces or Tensors are purpose-built Maths while the Octonions and the Mandelbrot Set are naturally-arising entities.

So there is some confusion in recent comments by Steve and Lorraine as to the naturalness of various Maths, and now Stefan appears to have fallen into the same trap. I also balked at the invocation of higher dimensions as a way to avoid certain limitations and achieve a higher level of organization, as it is done in String Theory, and earlier by Kaluza and Klein. It seems like an ad hoc solution, to just say the underlying reality has to be 10-d.

By comparison; there is a firmer basis to state that the 8-d Octonions predated us and are a necessary precursor to the 3-d Cosmos we inhabit today.

Best,

Jonathan

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Jonathan J. Dickau replied on Jan. 26, 2021 @ 19:32 GMT

To be specific...

If we allow for the possibility of higher dimensions at all; the Octonions have an important place in the order of things. And while it is easy to conjure dynamism from infinite-dimensional spaces; the octonions offer a strong directionality in a compact package.

So they were almost certainly put to use by nature, in the early universe and for the purpose of creating familiar forms - in some way. The real question is, if Strings are true, 'do the dynamical properties of Strings and Branes derive from the properties of the higher-d spaces they inhabit?'

That is to say; if Strings are an answer, they only work because the octonions function as nature intended. Any higher-d Physics whatsoever must hinge on the fact that the Octonion algebra really works, but only if calculational steps are taken in a specific order and sequence.

And that yields intrinsic time evolution as a bonus!

Best,

Jonathan

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Steve Dufourny replied on Jan. 26, 2021 @ 19:36 GMT

Hi jonathan, I love the humans, see how we are always persuaded lol , we compete with kindness , we are a little bit all vanitious and we defend our indeas after all, you imagine if all what I tell is true and that you are false, or the opposite for me, if the strings are proved, lol what a world, an institution these strings and E8 , thanks witten, lie and einstein lol they cannot think differently now. To be frank I love the maths and I know well the maths in all humility , I cannot stop to study them, what I try to explain is that it exists mathematical tools very important and they permit to prove and it exists tools in maths implying symmetries or infinities or this or that, if you take all the maths like they are , you create confusions considering the reality. That proves yes, but that implies also confusions and assumptions not proved. And if you consider also the philosophy, so you underatand better the crisis inside our community my dear friends. The maths tell that we have symmetries , so we have for example Whormhole and reversibilities of time, is it a reason to accept them ? the logic it is this also, we must be rational after all. Take care my friend the E8 fan :)

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Jonathan J. Dickau replied on Jan. 26, 2021 @ 20:10 GMT

Thanks Steve...

Even the wonders of a 3-d sphere are not fully or truly understood. And I was skeptical about higher dimensions, especially as part of physical reality. Somehow the idea of mystical realms of higher-d reality didn't bother me so much, but I did not place the two on the same footing. I even argued; 'why bother adding lots of extra dimensions, if it doesn't even get you more space?' I have since learned there is more value to garner.

I once wrote that perhaps the Sedenions are a useless distraction, and a bridge too far - being only of theoretical or instructional value as a point of reference. However if the universe was once a sphere - but in 16-d - then it has only 3 possible decompositions via fibration, with S15 yielding exactly the three algebras - the octonions, quaternions, and complex numbers. Almost too good to be true!

So while you hang out with 3-d spheres; I'll remember that the equation r = 1 yields the whole family of unit spheres - out to infinite dimensions - and not just a common circle or sphere. The simple equation holds more information than we readily see because we are mired in the 3-d reality that surrounds us, and we have forgotten that our origin is from mathematically distant places.

All the Best,

Jonathan

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You can’t just claim that something or other “moves”, or something or other has “dynamical properties”, and get away with it: movement needs to be represented with appropriate symbols.

If something or other in the world moves, there are various possible ways of representing it symbolically: 1) with word symbols (“it moves”); 2) with the symbols used by mathematics and physics; and 3) with algorithmic symbols.

In physics and mathematics, movement is represented by the delta symbol which is used to represent change of number for particular variables. In physics, if the numbers for some of the variables change, then the numbers for other variables will also change due to law of nature relationships. But there is no suggestion that numbers are entities that change and morph all by themselves; and there is no suggestion that laws of nature are entities that cause number change: laws of nature only “cause” number change via category relationships.

So, physics does not actually have a way of representing a genuine cause of, or reason for, number change. Physics does not actually have a way of representing genuine “dynamical properties”. THERE IS NO SUCH THING AS “DYNAMICAL PROPERTIES”.

The cause of, and the reasons for, number change can only be represented algorithmically e.g.:

IF the situation is such that (variable1= number1 AND variable2= number2) OR variable3= number3, THEN make variable4= number4.

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Georgina Woodward replied on Jan. 27, 2021 @ 02:23 GMT

"THERE IS NO SUCH THING AS “DYNAMICAL PROPERTIES”" Lorraine.

Movement is represented symbolically. For example; v is distance with direction over time. IF you were to plot V as T against distance from start point x, you will see number change aa t increases. Any equation that has v in it has motion built in; like momentum, angular momentum and kinetic energy. T, the time period for one cycle and represents the change occurring over that length of time.

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Jonathan J. Dickau replied on Jan. 27, 2021 @ 17:31 GMT

This question is only relevant because of what we have learned...

It wasn't until the 90s we found out cosmic expansion is accelerating. Perhaps the easiest way to explain this is to assert that empty space isn't just a void but instead has dynamical properties. This has a one to one correspondence with the intrinsic time idea of Alain Connes, arising from the Tomita-Takesaki theory of modular von Neumann algebras.

Simply put; a large class of mathematical spaces possess some inherent dynamism or the built-in capacity for dynamical evolution. The octonions are simply the most compact arrangement which preserves the strongly evolutive properties. This makes them the minimal case of those algebras one could call drivers. Rick Lockyer has often said that the octonions want or need to drive, and that this is how we can best understand their impact on Physics.

I've spoken with Tevian Dray face to face and corresponded with Cohl Furey and Geoff Dixon, so I know that what Tejinder and his colleagues have done is a major step forward, toward elucidating what octonionic Physics actually does for us. But one thing is for certain; it makes a complete non-issue of what the latest Scientific American labels a 'Cosmic Conundrum.' If space itself is dynamical; there is no conundrum. Problem solved.

Best,

Jonathan

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Jonathan J. Dickau replied on Jan. 27, 2021 @ 18:01 GMT

So the question remains...

Why is empty space dynamical? That is the real issue. It is senseless to imagine that reality adheres to a mathematical ideal where empty means devoid of form and without dynamical properties, when the actual spacetime we live in behaves differently. It deviates from what Lorraine would like it to be. Perhaps Euclidean geometry and Real-valued Math is inadequate.

One can posit the existence of dark matter and dark energy to explain some of the deviations from a mathematically perfect flatness or emptiness, and to explain the enormous discrepancy (>100 orders of magnitude) between the predictions of Quantum Field Theory and Relativity for the vacuum energy, but there is still a residual we can't explain by adding things. Some call it a Crisis in Cosmology.

The true answer is likely that spontaneous symmetry breaking is connected to continuous topological evolution, where the exact dimensionality of spacetime is changing or continues to evolve over time. So we are in a bubble that's mostly 3-d in nature, but because we are embedded in a larger form that includes higher and lower dimensional entities - D=3 is not a constant over cosmic time.

This allows the intrinsic time of Connes to play a part in the early universe.

Best,

Jonathan

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Steve Dufourny replied on Jan. 27, 2021 @ 18:16 GMT

Hi to both of you, the space does not really exists in logic Jonathan, the vacuum is made of particles coded, see now my reasoning with the 3 series of 3D spheres sent from the central cosmological sphere , so the space vacuum of this DE is coded and prossesses the main codes and it is like a super matter this central cosm sphere and in fact if we apply the same number than our cosmological finite series of spheres, we have the dirac large number, now consider that the central sphere is the biggest volume and after apply the decreasing of volumes and the increasing in number and see that the space does not really exists , we have particles in contact everywhere at all scales. Now when the two other series merge with it , the cold and heat, the gravitation and electromagntism, the photons and cold dark matter , they activate this space my friend, see that it permits to encircle the fields,waves and others.

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Jonathan J. Dickau replied on Jan. 27, 2021 @ 18:39 GMT

In my theory...

Early universe evolution happens under the octonions and makes use of Connes' intrinsic time as a driver toward forms or formation, as with Aikyon theory. In other words; intrinsic time is what drives things from an ambiguous state to specificity. But in my version; this causes the early universe to evolve toward a 5-dimensional volume, as a precursor or parent state to our current universe.

So the 3-d space we inhabit is part of a 4-d spacetime bubble evolving under the quaternions. We are in a ball riding on that 5-d ball, similar to the rolling ball analogy of Cartan for describing the octonion self symmetries. So our universe is a 4-d bubble on a 5-d sea (or a sphere on a higher-d sphere), in my theory.

In Aikyon theory the mechanism of Continuous Spontaneous Localization is what congeals our 4-d spacetime from the 8-d bulk. In my theory; this happens via condensation, but this results from our being inside-out from the prior universe that is left in a 5-d bubble.

I am seeing a phenomenology where spin was trapped in the spacetime fabric in the 5-d parent or precursor, so that torsion in the fabric took the place of tension in some braneworld theories. Thus a very high Weyl value occurred which opened a hole for a black hole - white hole bridge to form. This means that the CMB is the white hole residual from the prior cosmos.

Best,

Jonathan

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Steve Dufourny replied on Jan. 27, 2021 @ 18:48 GMT

In your theory wich is an assumption .....and in my theory wich is also an assumption the early universe has begun with a multiplication of these series 3D of spheres , and the time is not a problem you know , it is a problem when we analyse it only with this relativity that we observe, don t forget that it is about observations and in considering only photons, for me your error to all the...

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In your theory wich is an assumption .....and in my theory wich is also an assumption the early universe has begun with a multiplication of these series 3D of spheres , and the time is not a problem you know , it is a problem when we analyse it only with this relativity that we observe, don t forget that it is about observations and in considering only photons, for me your error to all the octonionists and strings theorists is there, you consider only this GR and the photons like the primoridal essence and after with KK or others you have created extradimensions, it is just a play of maths with the GR and in begining in 1D at this planck scale wich furthermore is a scale not proved and after you play with the tensors and fields of these photons oscillating and vibrating to explain our geometries and topologies, it is just a general assumption , the same for the early universe, we don t know what was this begining , even the BB with the CMB is an assumption even if we have some interesting datas cosmological. I can understand that you are fascinated by this E8 and the fields like origin and the works of connes, specially for the time, but don t forget my friend, all is an assumption , the E8 is just for me interesting to a little bit better understand these photons encoded in our nuclei giving the 3 known forces, don t hope to explain this quantum gravitation with these photons and field and E8, be sure, I have reached it in encoding this cold dark matter , we need a balance you know , that explains the antimatter , the quantum gravitation and furthermore the evolution with the DE disponible, we can even extrapolate the future of the universal sphere with acceleration decceleration towards the maximum spherical volume and after accel deccelleration towards the minimum balanced spherical volume continuing to evolve due to complexification of lifes and matters. The problem foundamental that I see in all humility is philosophical and ontological about your origin of this universe considering these fields , and the choice of foundamentaöl objects and also the fact to consider only the GR and SR . You can tell ball, sphere, hypersphere, 5D sphere or this, me I speak about 3D spheres cosmol and quant in an universal 3D sphere in evolution , it is not emergent these spheres, they are the foundamentals, don t confound. Friendly

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I can explain it this way...

People have it backwards. Or at least; the early universe reverses our common assumptions. So spatial extents are like the imaginary dimensions in the octonions or quaternions, which are degrees of freedom or directions of variability. Then, over the course of cosmological evolution; the possible becomes actual so there are definite spatial extents. And yet, for those definite extents to persistently exist; the enduring feature and real dimension is time.

This upends the common assumption that time is an emergent property, and replaces it with the notion that time is primal or foundational. The persistent existence of physical objects like particles in space requires the time dimension to be real. So in my version of Cosmology; that is the one essential element. And in fact; I assert that there must be a minimum time step associated with the cosmos' inception, and further speculate there is a 1/4 spin and possibly bosonic particle associated with that minimal time step.

Anyhow; if spatial extents are seen to arise from variability and the arrow of time originates from a minimal amount of definiteness; the origin of the universe is fairly easy to explain. Otherwise; we run into problems where various factors prevent 'something from nothing' to exist. But this reintroduces the idea of intrinsic time evolution, which only becomes a factor in higher-dimensional spaces, and brings into play higher order algebras like the octonions, where evolutive properties are a well-defined reality.

Best,

Jonathan

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Steve Dufourny replied on Jan. 27, 2021 @ 21:30 GMT

You repeat things like if you were obliged to defend your assumption, I repeat with respect , all is a general assumption like my reasoning and our vanity defending our ideas shall not change this reality. I am curious, why we exist and from what ontologically and philosophically ? do you consider a mathematical accident from an infinite heat ? or a kind of god playing at guitar with octonions ? or others, that needs deeper explainations Jonathan, we know the geometrical algebras of lie, clifford , hopf or others and the non commutativity of connes or others and the octonions, but why the fields like origin , detail please

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Steve Dufourny replied on Jan. 27, 2021 @ 21:32 GMT

recognise that you don t know the un knowns, nor the origin, nor the foundamental objects, nor the quantum gravitation, nor the gap mass problem, nor the DE and DM, nor the hard problem of consciousness and your octonions don t explain them, they are a general assumptions, it is just a tool to rank our quantum fields , and link with the einstein fields equations, that is all, since when you can affirm the origin of this universe my dear friend ?

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Steve Dufourny replied on Jan. 27, 2021 @ 21:34 GMT

Maybe the strings theorists and octonionists speak to god and beleive they have understood the project of this infinite eternal consciousness, you are in syncho with the 1D main field or what lol ?

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THERE IS NO SUCH THING AS “DYNAMICAL PROPERTIES” possessed by: 1) the system as whole; 2) the numbers that apply to the variables; 3) the categories of variable (like speed, position, energy or mass); or 4) the lawful relationships between the categories. There are NO symbols that represent the cause of number change in the whole of physics. A lot of people seem to have no idea that, in maths and physics, SYMBOLIC REPRESENTATION MATTERS.

The delta symbols, and the other symbols that represent law of nature relationships, represent the fact that IF the numbers for some of the variables change, then the numbers for other variables will also change due to law of nature relationships: the laws of nature only “cause” number change via category relationships.

A lot of people seem to have no idea that physics does not actually have a way of representing a genuine cause of, or reason for, number change.

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Georgina Woodward replied on Jan. 28, 2021 @ 03:11 GMT

Why do you consider speed, velocity and energy not to be dynamic?

The laws of nature are not the cause of change. Change happens that can be described by equations showing relationships between variables. Consistency of those relationships can lead to it being considered a law of nature. That's like saying its always like this (approximately) but not because of the identified law .How it is is different from why it is, as it is.

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How is reality dimensioned?

There is some discussion in the threads above on what a dimension actually is, in terms of measurable quantities like length, width, and height. This can be called size and distance measures. In a range from pea-sized to planet-sized, we can treat these quantities as constants - so Euclidean geometry holds and translations follow the Commutative law. And things can be treated as constantly and reliably three dimensional!

But we find we have to bend those laws to describe planetary motions accurately, and that this is increasingly true the farther out we go. So we have to deal with space itself being bendy and stretchy - which we call Relativity - and things get weirder when we include more and more of what's out there. Dark matter? Dark energy? Fractal distributions of matter in spacetime? Higher dimensions beyond the Hubble radius. Serious researchers explore all of this.

And if we go to the realm of the small instead of the large; do people imagine that reality is still 3-dimensional? We're talking about the space between or inside of sub-atomic particles, and what dimension it has. Anyone who has studied nuclear interactions knows it certainly behaves as though it is higher than 3-d there - in a quark-gluon plasma for example. This makes asymptotic freedom an automatically emergent property of higher-d spaces. No problem, if it makes things simpler.

The problem lies in the notion that because reality is reliably 3-d at common levels of scale; it is ever and always that way from the smallest to the largest scales in the universe, for all of time.

Best,

Jonathan

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Jonathan J. Dickau replied on Jan. 28, 2021 @ 17:24 GMT

I think people imagine it must be proved possible...

Many would preempt discussion about higher dimensions, using an 'early out' strategy, or claiming to be using 'Occam's razor' to avoid multiplying entities unnecessarily for crafting an explanation. I would counter that with making things as simple as they are - but no simpler! People have a tendency to look for an easy out, when trying to solve a hard problem. But that doesn't mean the easy answers are the best or correct ones.

Using the Ptolemaic system; astronomers in ancient times made some incredibly accurate measurements and determinations. But it was later seen as overly complicated to use epicycles and simpler to see things in 3-d with the Sun at the center, championed by Copernicus and Galileo and later perfected by Newton. So by going from a flat 2-d screen to a fully 3-d view of the heavens; we made things simpler! Thus adding one dimension replaced a host of epicycles.

Modern physicists would not be positing the existence of higher dimensions if they did not appear to already exist. They are searching for a way to see things differently - perhaps from a higher-d view - in order to explain things more simply, and to use fewer ad hoc assumptions or hokey mechanisms to make things come out right. Anyone can plug in known constants. We all want to find the magic formulas where by making just a few assumptions up front, we can derive results predicting something similar to what we observe.

All the Best,

Jonathan

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Jonathan J. Dickau replied on Jan. 28, 2021 @ 17:50 GMT

Let's set this out more formally...

Measurability is a familiar property possessed by only a subset of the full range of objects definable by Math or Physics principles. It is reasonable to assume from common experiences that ALL objects and spaces MUST have a well-defined metric, but this turns out to be untrue. With the caveats that we are talking about geometric objects and spaces that might be physically realizable; we can write the following relation:

$Smooth \supseteq Top \supseteq Meas$

Smooth objects and spaces are the largest class of figures here, then topological forms are the subset that has a surface, and measurable forms possess a metric which we can think of as grid lines marking distances on or across any surface. Then we see there is a relatively tight correspondence with the phases of matter; so we can write:

$Gas \supseteq Liquid \supseteq Solid$

I'll write next about how numbers fit into this picture.

Best,

Jonathan

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Jonathan J. Dickau replied on Jan. 28, 2021 @ 18:08 GMT

We can make a crisp relation here...

The normed division algebras follow an exact pattern.

$\mathbb{O} \supset \mathbb{H} \supset \mathbb{C} \supset \mathbb{R}$

We note that imaginary dimensions are the freedom to vary by a specified amount in a particular direction. The octonions have 7 imaginary components, the quaternions have 4, and the complex have 1. If we treat the 7 imaginaries of the Octonion algebra as rotations; we obtain the Quaternions by fixing 4 of 7 axes. Then we get the Complex numbers by fixing 2 of the remaining 3 axes. And the Reals are obtained by fixing or halting the remaining rotation, so the non-rotating extent lies only in a particular direction we assign to the reals.

Best,

Jonathan

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I'm replying to Georgina's hidden comment above...

On Jan 16 @ 19:21 GMT; Georgina commented Re: "What is a 'number' in the real world? "To be clearer: the start and end of a rotation do not co-exist but are together representing a happening. That represented rotation could be said to take time. Or the start and end can be said to belong to different configurations of existence. A quaternion can represent an important characteristic of existence, that it changes. They can also represent history but not uni-tenporal material existence."

That is a big Aha! You caught the gist of something important Georgina. Rotations are extents that happen in cycles. There is a time coordinate built in for cyclical actions of any kind. And crucially; the completion of any one cycle brings you to a new level, like an unfolding spiral, when looked at from the view of overall evolution. That is the exciting thing about the octonions, because the effect of evolutive properties is cumulative, such that completing a cycle leads to a new phase of action.

My very Best,

Jonathan

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Physics has NO dynamic elements, it merely has category relationships (laws of nature).

The delta symbols, and the other symbols that represent law of nature relationships, represent the fact that IF the numbers for some of the variables change, then the numbers for other variables will also change due to law of nature relationships: the laws of nature only “cause” number change via category relationships. This secondary number change (that occurs as a consequence of the original number change) does not occur “in time”, any more than it occurs “in mass” or it occurs “in position”: it is “instantaneous” BECAUSE the secondary number change is due to lawful relationship.

So physics has no explanation for the dynamic nature of the world i.e. physics has no explanation for any genuine number change. Genuine number change can only be represented algorithmically.

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Georgina Woodward replied on Jan. 28, 2021 @ 21:21 GMT

With constant non zero velocity of something the position of that something must change.

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Lorraine Ford replied on Jan. 28, 2021 @ 22:52 GMT

The equations of physics, that represent the laws of nature, represent the fact that IF the numbers for some of the variables change, then the numbers for other variables will change INSTANTANEOUSLY due to law of nature relationships.

“INSTANTANEOUSLY” because the physics equations that represent the laws of nature represent something that exists OUTSIDE the time, mass and position categories/ “dimensions”. This is because the physics equations that represent the laws of nature represent relationships BETWEEN the time, mass and position categories/ “dimensions”.

And that’s the finish of it: the physics equations that represent the laws of nature do not represent ongoing activities: the equations merely represent static relationships between categories/ “dimensions”.

So physics has no symbols that represent the true dynamic nature of the world. I.e. physics has no explanation for the original number change that caused the instantaneous number change for all the other numbers, and whereupon the whole system ground to a screeching halt.

Any genuine number change for a category/ variable can only be represented with algorithmic symbols.

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John R. Cox replied on Jan. 29, 2021 @ 00:30 GMT

Lorraine,

that is one of your best stated and concisely presented posts on the theme. Well said. I would agree with your final statement also, with the following qualification. All that precedes it argues for 'time taking time to act', or somewhat ambiguously; 2 (or more) dimensions of time whether linear or non-linear. So an algorithm would be necessary to state that light velocity is a measurable constant of that specific value because algebraically it is the result as a measurable definition, of a complex physical definition. And it should be axiomatic that whatever the defining reality of a physical phenomenon might be, any measurement definition is going to be a deconstruction and can at best be deemed an adequate approximation. best jrc

I'll add rather than post. While the algebraic result(s) obtain from derivatives, as the calculus was referred to early on, they are a static statement in form. And it is true enough that Newtonian Mechanics assume an instantaneous application of values, in practice, to the parameters explicit in any such form of 'physical' or 'natural' law. So in that sense an algorithmic procedure is required to express the dynamicism in operations describing any specific case of phenomenon exemplifying a said natural law. But the point is; that is precisely what is done with those laws. It is both parochial and naive to base an existential argument on what is notably a generic mathematical form of statement.

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dear all,

i have a question :why can not we unite electrostatic force with gravity?

and can we unite equation of gravity with equation of coulombs's law?

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Jonathan J. Dickau replied on Jan. 29, 2021 @ 14:13 GMT

Please note Prasad...

Rick Lockyer presented a framework referenced above, wherein the laws of electrodynamics elucidated by the octonions results in extra terms that are the equations for gravity. To me; this indicates that gravity is a residual of the other forces, an emergent property of spacetime, or a condensed form of electrodynamics.

Rick Lockyer has answered this question in the positive.

Best,

Jonathan

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Steve Dufourny replied on Jan. 29, 2021 @ 15:00 GMT

Jonathan, still an assumption, the problem and I insit is still to take into account the GR and the photonic space time and so you confound how we must consider this gravitation, it is not an emergent electromagnetic forces , einstein has created a new interpretation of the gravitation like a curvature of this photonic spacetime at HIGH VELOCITIES and for observations, and newton it was a force between all mass at SLOW VELOCITIES, so why you consider the GR to reach and quantify this quantum gravitation ??? in trying to unify G c and h , you see wel,l that we cannot renormalise in this reasoning , so why the people continues on this road ??? it is not like this that you shall reach this QG, you must respect this newtonian mechanics and forget a little bit this GR and fruthermore don t consider really this planck scale, and all will be easier dear thinker, do you understand that the GR is probably not the only one piece of puzzle, so you can utilise all the geom alg that you desire, that will not change you know. It is more than a prison and an institution this GR and E8 and strings frankly,

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Jonathan J. Dickau replied on Jan. 29, 2021 @ 17:12 GMT

It is true that...

If we don't look beyond the edge of our comfort zone; Newtonian mechanics works fine, there was no need for Relativity or Quantum Mechanics, and so on. If you never pick up a stone; it may be hard to imagine there are insects living underneath it. How could they get there? Did they burrow through solid rock? So in similar fashion; one can easily find excuses not to look at or even look for the evidence that reality has a hidden side, or uncomfortable contradictions.

It's certainly easier to deal with reality; if it all makes sense in the simplest and easiest way to explain it. Unfortunately; that is NOT a reality we actually live in. Instead; the idea that we COULD go back to the understanding people had in the 1890s. and everything would be OK, is a fantasy. Every advance in Electronics from the transistor forward depends on Quantum Mechanics working, in order to function at all. So it is a selective insanity to live in denial.

Or you could put away all the toys that conflict with your world-view, which means never using a computer or cell phone to write silly notes again. Without GR the Hubble's optics would still be fuzzy (and we wouldn't know why), and no GPS would be accurate enough to get you somewhere. I'd rather continue the conversation and be happy such devices DO function, but understand that if GR and QM were just hooey; they would not work.

All the Best,

Jonathan

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There might be several different ways of looking at time, but that doesn’t mean that there are actually several different time categories.

The time category can be seen as resulting from (e.g.) a relationship between the speed category and the distance category. This relationship can be transposed so that there are alternative ways of looking at it: the distance category can be seen as a relationship between the speed category and the time category; and/or the speed category can be seen as a relationship between the time category and the distance category. This way of looking at time can be symbolically represented as a mathematical relationship where time can go backwards and forwards.

In the above view, the time category can be thought of as deriving from a relationship between the speed category and the distance category.

But when people say "time is change", what they mean is that time is an algorithmically derived category of information: IF the numbers change for another variable, THEN add 1 (say) to the numbers for the time variable. In other words, the numbers for the time variable don’t change unless the numbers for other variables change. The algorithmic representation of time represents: 1) time as something that can only go forward; 2) time as knowledge that change has occurred, including knowledge of other categories of variable and knowledge of the numbers that apply to the variables.

In the above view, the time category can be thought of as deriving from knowledge.

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Lorraine Ford replied on Jan. 30, 2021 @ 22:33 GMT

I might add that there is no Platonic realm: everything that exists, only exists as a natural part of this world. Lawful relationships exist as a natural part of this world, but they don’t exist within time, any more than they exist within mass. Time is clearly a derivative category of information, derived from other categories of information. The time category might be somewhat fundamental, but it is not foundational.

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Lorraine Ford replied on Jan. 30, 2021 @ 23:22 GMT

There is much confusion about time.

The notion that lawful relationships between categories (like mass or time) do not exist inside those same categories (like mass or time) is basic to physics.

So change due to lawful relationship always occurs instantaneously, not “ALMOST instantaneously”, because the relationships do not exist inside time.

On the other hand, change that is NOT due to lawful relationship, i.e. change of number for a variable that can only be represented algorithmically, can be seen as introducing a time category.

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Stefan Weckbach replied on Jan. 31, 2021 @ 05:39 GMT

Thanks also to you Lorraine and also all other participants here for continuously bringing up interesting considerations.

Here are my thoughts on some issues about time.

A long standing question is whether time moves on continuously or discretely. If it does not move in a discrete fashion, then, at every instant of it, it needs some time for time to move, what then simply expresses our belief that time is something that has (or is) a movement along a certain direction, like an object in outer space with a well defined initial impulse represents.

However, by defining that object as “moving time”, we could also define that object to be at rest and another reference object as "moving time". Moreover, different objects have different velocities. Which one should we choose for a proper definition for the velocity of “time”? It gets not better by assuming that time behaves somewhat discretely, means for the case that Planck time is the fastest time physically possible and every speed that exceeds this measure must jump “from time to time”. If there are such jumps, they had to occur instantaneously by definition. If there are no such jumps, we are left with merely our conventional definitions of how much time it takes for time to accomplish a certain movement. If time emerges from something else, what should that something else be and how and with which ingredients does it - continuously? - spin together time?

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Tejinder, I work about a tool , the spherical geometrical topological algebras , here is the general idea

I work about the creations of a mathematical tool , the Spherical geometrical topological algebras, the persons shall can create what they want with these spheres. First we chose a serie of spheres , so we have an algorythm at the begining with the numbers, the volumes , it is an...

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Tejinder, I work about a tool , the spherical geometrical topological algebras , here is the general idea

I work about the creations of a mathematical tool , the Spherical geometrical topological algebras, the persons shall can create what they want with these spheres. First we chose a serie of spheres , so we have an algorythm at the begining with the numbers, the volumes , it is an operator for this serie chosen, after we can consider several series superimposed with an other multiplicator operation and we can even change the volumes and numbers if the utilisators desire it. We consider also an operator of motions and selectivity topological , if they want that all they are in motions they can , thay can even choose the specific topological spheres wich don t turn. We can with the operators of motions play so with the sens of rotations and the angles also. We create an operator for the oscillation vibrations on surfaces, like a hopf fibrations on these surfaces. We consider now an operator for the symplectomorphisms preserving the volumes and we add an operator of selectivity , we can like this deform the chosen topological spheres. We insert now an operator for the interactions of exchanges for the informations and when the series merge with informations and particles, so the volumes are preserved but the densities change, the operator is about this , the densities , they can change the number or the volumes if they want or not. We consider also an operator for the spinal and orbital motions, the angular moments in fact. After we consider an thermodynamical operation for the whole in playing with the cold and heat and we can insert an operator for the distribution of this thermo in the specifi series chosen of Spheres. The entropy is correlated . The general idea is there and we can superimpose many other operators and parameters.

The utilisators can create their series and their ideas , me I have considered 3 main finite series having the dirac large number begining with the central biggest volumes and after the primes around in decreasing the volumes and increasing the number, the space disappears.The main codes are in the serie of this space vacuum of this DE , the two others are the photons and the cold dark matter and when they merge they create the topologies, geometries , matters, fields, properties.

Regards

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Steve Dufourny replied on Jan. 31, 2021 @ 11:54 GMT

An other operator important is the time in function of motions and the lifetime correlated with the densities of volumes and the informations and the stability . We can also superimpose of course our equations in physics and some other mathematical tools.

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Steve Dufourny replied on Jan. 31, 2021 @ 12:17 GMT

of course we consider also the commutativity , non commutativity, the associativity, the non associativity like we want topologically speaking and the scalars, vectors, tensors also superimposed like we want ,

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Steve Dufourny replied on Jan. 31, 2021 @ 13:13 GMT

Well, there is a very important relevance about the non commutativity and the non computability when the angles and rotations of these spheres are taken into account.

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Mathematics is a dead thing: it is human beings that give life to mathematics.

Similarly, the mathematical equations of physics that represent law of nature relationships, do not represent the dynamic creativity of the world. No set of mathematical equations can represent a dynamic world. The use of the delta symbol in equations might be an attempt to represent a dynamic world, but it too can’t make the equations represent a dynamic world.

It’s only algorithmic symbols (together with equations) that can represent a dynamic world where the NUMBERS for the variables move/ change. It’s only algorithmic symbols that can represent the evaluation of a NUMBER situation for the variables.

Equations can never represent the evaluation of situations, and the response to situations: you need algorithmic symbols to represent this. What algorithmic symbols represent cannot be derived from, i.e. cannot be made to evolve out of, what equations represent. Algorithmic symbols represent a fundamental aspect of the world that can’t be represented with equations.

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John R. Cox replied on Feb. 1, 2021 @ 01:34 GMT

Lorraine,

An example of a particular algorithmic symbol, and how it represents an evaluation of a number situation would be useful. How would you algorithmically instruct a procedure to evaluate how many times you could divide a '1' by 'zero'. Seriously, jrc

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Steve Dufourny replied on Feb. 1, 2021 @ 11:23 GMT

Hi to both of you, it seems that Lorraine is right about these algorythms, now of course we utilise algorythms for our computers , and they follow a logic that we have invented to give us results and tools. The universe is of course more complex in its algorythms and it utilises foundamental objects and a main general philosophy, I beleive that these 3D spheres are the secret but the complexity of these spherical 3D algorythms aer so difficult to understand for us the humans . The numbers like Lorraine said are for the variables , changes, and are under a specifc partition wich is far beyond our understanding. These responses to situtations become so complex considering the free will and consciousness. Lorraine you speak about a very important point considering the creativity and others. Regards

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Lorraine Ford replied on Feb. 1, 2021 @ 22:56 GMT

I have given examples of algorithmic symbols in some of the above posts.

Algorithmic symbols are used to represent the evaluation of situations, where the situation in turn is symbolically represented as the numbers that apply to a set of variables; algorithmic symbols are also used to represent the response to this evaluation of a situation, where the response is also symbolically represented as the numbers that apply to a set of variables.

Equations can never represent the IF, AND, OR, THEN, ELSE evaluation of, and response to, situations. What algorithmic symbols represent cannot be derived from, i.e. cannot be made to evolve out of, what equations represent. Algorithmic symbols represent a fundamental aspect of the world that can’t be represented with equations.

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Dr. Singh, the voice of Cayley-Dickson algebras comes from their possible orientation variations. Look here for a description of the possible variations for Quaternions to Sedenions.

Rick

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Steve Dufourny replied on Feb. 1, 2021 @ 13:14 GMT

Yes these algebras are like the other interesting tools, they take the real numbers and after extyrapolate with the complexs the quaternions, the octonions and you tell so that that can be extrapolated for the sedenions, it is logic and so the properties of this 16D of sedenions being different, so you rank differently the propeties of numbers. The multiplications being interesting so the properties of fields can be analysed but it lacks the proof of the philosophical origin and the proof physically of dimensions correlated with this said physicality, these algebras, the quaternions, octonions, sedenions are of course relevant for several things but can also imply confusions. The problem is really the strings theory and the origin of the universe and the fact to consider that we come from specific osciilating vibrating strings at this planck scale.We could conjecture the pure 3D and rank and also SORT the fields and these properties of reals and complex numbers, a kind of logic universal could appear with the good sortings in respecting this pure 3D and take into account these foundamental mathematical and physical objects, the 3D spheres.

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Steve Dufourny replied on Feb. 1, 2021 @ 13:19 GMT

It is the basis the quaternions wich become relevant for the motions and the time, an octonion being two quaternions independent , so the sedenions being in the same logic of extrapolation, so we can consider the Lie E8 indeed or sedenions , but if we have not a main logic universal line of reasoning , so we just play in maths without really find the real universal correlated logic.

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Steve Dufourny replied on Feb. 1, 2021 @ 13:46 GMT

I am not against these mathematical tools for our fields and others, I just tell that of course the numbers have something to do with our physics , but it is the main philosophy of strings and the origin of our reality from the fields that I disagree like foundamental. I beleive that the problem is really philosophical, I repeat but the thinkers had not a deeper reasoning, so they have considered simply this BB from an infinite kind of heat that we cannot define , after with einstein they have inserted the GR , after with planck we have considered the scales and others, and after with witten , they have put strings in 1D at this planck scale inside these photonsconnected with a 1D main cosmic field of this infinite heat and after they have considered the numbers, the particles, the fields under specific partitions to create our topologies, geometries and propeties, but in fact we must be conscious that all this generality is an assumption, the same I recognise for my coded 3D finite series of Spheres. We must admit at my humble opinion that we have many limitations about all this, about the orgin of the universe and this BB too, about our foundamental objects and about the origin of this physicality. The maths of course and the numbers have something to do with the fields and particles but we must be prudent about our conclusions. It d be very odd to affirm to know the truth , when I have seen the name TOE I was surprised , how is it possible to utilise this ? that has no sense, we know nothing still, all rational wise thinkers accept this. I am persuaded and I don t affirm, it is not because I am persuaded that I am true, but there is like a conjecture between all this, the strings, the spheres, the geometrical algebras , that could permit us to better understand the origin philosophical of this universe. The poincare conjecture has something to do there, like the geometrization conjecture of Thurston also. But how ?

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Georgina and John,

You seemingly don’t have a background in maths, physics or computer science: you get everything very mixed up. You seem to get the thing mixed up with the symbolic representation of the thing.

ANY set of equations (even equations using the delta symbol) cannot represent a dynamic system.

The issue is that the equations of physics do not represent a dynamic world. The mathematical symbols/ equations that represent law of nature relationships imply only relationships: the equations do not imply a dynamic system; a dynamic system can only be represented with algorithmic symbols. Something that can only be represented with algorithmic symbols implies a quite different type of world.

It’s people who “fill the gaps” in mathematics; its people who give life to mathematics: but what people do can only be represented algorithmically.

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Jonathan J. Dickau replied on Feb. 3, 2021 @ 15:18 GMT

Let me try to parse this entry...

Mathematical Physics is the study of how Physics relations can be represented in Maths, and how Mathematics as a tool can show us features of physical reality that are well-represented by equations or other relations (>,, etc.). But there is ALWAYS a question of applicability, are OFTEN questions about how many terms are required to accurately model real systems, and so on.

The key piece here is the Calculus of Variations. Perhaps the best intro to this subject is found in Mary L. Boas' book on 'Mathematical Methods in the Phys. Sci.' (Chap 9 ~ pg. 383) which is an excellent text overall. She has already talked about Complex numbers and covered Ordinary Differential Equations by that point in the book, so it is sandwiched between the ordinary Calc and the intro to Tensors.

And the main point to make here is found right in the Intro. We can look to the Maths to show us the points of interest in C of V. It ALWAYS means something when the first derivative (rate of change) goes to zero, BUT we have to look at the Physics and the Geometry of the setup to determine whether it is a Minimum, Maximum, or Optimum value. So Mathematical Physics done correctly forces us to use both the Maths and the Physics parameters, to know what is real.

This brings us to the conclusive piece. Tevian Dray and Corrine Manogue developed the Vector Calculus Bridge project because of the PROFOUND difference between how multivariate analysis is approached by Math and Physics teachers, leading to massive confusion by students. There is an EXTREME gap between what is learned earlier on, and what comes after this point, SO it would be far better if the terminology and methodology was made consistent.

But the status quo is a bear.

Best,

Jonathan

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Jonathan J. Dickau replied on Feb. 3, 2021 @ 15:35 GMT

And respectfully Lorraine...

Your point is well-taken, in the sense there really IS a lot of confusion out there about which Maths are applicable to what Physics and so on. It is rampant and sometimes laughable. One really needs to work very hard to keep on point using only Maths that are applicable to the setting, but it gets ridiculous sometimes.

I remember reading an article with statistics by the Highway Safety Council that was a total joke. They concluded that it is safer driving in the city because the ratio of population to traffic deaths is lower. This is absurd of course. If it was a genuine commensurable stat; they would be comparing accidents vs. the traffic density. But they were way too stupid!!!

I remember talking about this example on the bus with B.G. Sidharth (head of the Institute for Applicable Maths) and Brian Josephson (discredited Nobel laureate) on the way to the Orihuela Playas. The conversation was almost like a 'can you top this?' contest at one point, where others on the bus got involved, and we all had silly stories about how Maths were used in absurd ways.

More later,

Jonathan

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Steve Dufourny replied on Feb. 3, 2021 @ 15:51 GMT

Maybe Jonathan, we must simply be prudent about the mathematical extrapolations, they permit to prove our assumptions but they can imply confusions indeed. For example what we measure seems the most important , but we must relativate our measures when we extrapolate them with our maths in considering a philosophy and choices about the foundamental objects. All seems there , the measures and how we extrapolate them , we have this problem with our fields that we measures wich are for me not a cause but an effect of a cause , if you utilise maths like this E8 for example in taking these fields , so you don t find the cause but you just extrapolate partitions of fields wich are probably not foundamental. We return about this philosophy general that we don t know about the origin. It is what we have like problem actually inside the theoretical sciences community considering only this GR and strings and geonetrical algebras, they try to explain things that we cannot measure with these fields like main origin, it is really a prison this GR and these photons only and strings. I insist but all seems a philosophical problem , not the tools probably but the essence primoridal chosen of the universe.

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Let me try something different...

I'm re-posting this entry because of faults in the TeX editor.

Regards,

Jonathan

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Jonathan J. Dickau replied on Feb. 4, 2021 @ 05:06 GMT

Let me try something different...

One of the points made by Georgina and echoed by John is that some Physics equations include terms like velocity that imply change. Lorraine has said that 'law of nature' equations in Physics are dead, or require input to create action; so I'll have a go at presenting something which tests this idea, and is already in my published works. So we'll use...

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Let me try something different...

One of the points made by Georgina and echoed by John is that some Physics equations include terms like velocity that imply change. Lorraine has said that 'law of nature' equations in Physics are dead, or require input to create action; so I'll have a go at presenting something which tests this idea, and is already in my published works. So we'll use Professor Einstein's famous equation, but switch things around by applying the framework of GR liberally.

Remember that in Relativity; it is the curvature of the spacetime fabric that represents or induces gravity. To be more specific; mass is what induces the fabric to curve, but then independent masses follow the curvature. However; in the very early universe, there are no free-floating particles but only a kind of quantum soup out of which the particles will later emerge. In addition; as we get very close to the Planck scale, the fabric is effectively 2-d and flat. This allows us to re-write Einstein's equation so that we are solving for c when the mass of the universe is zero.

$E = mc^2 \text{ becomes } c^2 = E/m \text{ where } m \rightarrow 0$

It works out nicely that the speed of light is unbounded for 2-d flat space where there are no massive particles in the universe yet. So there is a tendency for the Cosmos to expand outward beyond the speed of light, until the fabric of space becomes curved through the addition of mass to the universe by particle creation, in this scenario. Remember that some particles including photons, gravitons, and neutrinos are virtually massless. So it wasn't until after baryogenesis that more familiar and massive particles appeared.

This is one possible mechanism whereby one might derive early universe dynamism from simple Physics equations that appear dead, until you drop the human assumption that c has to be a constant. One could instead assert that it is the huge and largely unchanging mass of the universe that makes the speed of light appear to be a constant. But Georgina's assertion is correct in this instance, that because c is a velocity, that implies motion or change. If Einstein's equation is true; then the universe CAN self-evolve in the matter free regime before baryogenesis. Q.E.D.

Regards,

Jonathan

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Jonathan J. Dickau replied on Feb. 4, 2021 @ 19:32 GMT

Let's run with this a little...

In the context of a matter-free regime before baryogenesis; we are looking for a motivation or prescription for the evolution of form. We find that what is favored is geometrogenesis or the evolution and extrapolation of spacetime as a working entity. So we have a kind of Inflationary period, in the scenario above, but somewhat different from conventional inflation.

You can compare the above with research by Afshordi and Magueijo (arXiv:1603.03312 which has similar predictions but a slightly different basis. In terms of phenomenology; we reference something that bypasses conventional Inflationary Universe theories, in favor of what in a scenario like Tejinder's would be Octonionic Inflation.

So if we solve for the speed of light in the matter-free regime near the Planck scale using the re-work of Einstein's equation:

$c^2 = E/m \text{ where } m \rightarrow 0$

We also have the insight that; with the advent of massive particles during baryogenesis, the Inflationary epoch would come to an end, and the speed of light would come to take on a discrete value. So this provides an answer to the 'slow-roll' phenomenon that is a feature and requirement in conventional Inflationary models. However, it is as Steinhardt has pointed out; we are putting in adjustments as needed - in conventional Inflation - rather than as called for by the theory.

So other approaches might be better.

Bye for Now...

Jonathan

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Regarding the Large Number Hypothesis of Dirac...

It is reasonable to relate the above statements about c to Eddington's proposal that Dirac's relation is a consequence of the speed of light being related to a very large N which is the total number of charged particles in the universe - given as argued above that the particles created during baryogenesis carry the bulk of the weight of the universe.

So if we use the re-working of Einstein's equation above, to explain why the speed of light in the universe today has the value it does; we find that this also conveniently explains the LNH, at least in part. The idea is that the ratio of particle masses relates to the mass of the universe being a gauge-fixing quantity that sets the value of c and influences other constants.

Best,

Jonathan

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Jonathan J. Dickau replied on Feb. 4, 2021 @ 20:06 GMT

I wanted to mention...

Amitabha Ghosh has observed, various places in his writings, that the mass of the Cosmos is 'about right' to set the value of c to what is measured. But Dirac's observations certainly suggest that he had re-worked Einstein's equation as well, and pondered what the significance was of the curvature of the universe due to the mass in it, the relationship of this to particle masses, and so on.

It seems that modern researchers are very reluctant to flip things around, to look at them a different way, but this is how progress is made. I am reminded that the root word for 'think' is "tong" so the very process of thinking itself is related to being able to flip things around and look at them differently. This is exactly why people like Feynman have been helpful to the evolution of Physics.

More later,

Jonathan

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Steve Dufourny replied on Feb. 4, 2021 @ 20:08 GMT

Hi Jonathan, this number intrigues me a lot and there are many probable convergences, the ones like you explained and others also. Oddly I was surprised to have this number in calculating approximatelly the 3D cosmological spheres inside these more than 10000 , that is why I have considered also this number for the 3 quantum finite primordial series because I consider that there is a link , a choice of this universe for these cosmological and quantum 3D spheres ,the 3 series are the photons, the cold dark matter and the space vacuum of this DE. What I find relevant also is that if we begin with the central sphere the biggest volume, after we apply a serie around, 3 smaller, after 5 smaller around the 3 , and we continue, so see that the space in fact disappears and all is in contact so implying a superfluidity , that permits to explain the waves, the fields, the particles, when they merge the number does not change and the volumes also don t change, but the velocities, the densities and this and that yes.

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Jonathan J. Dickau replied on Feb. 4, 2021 @ 20:22 GMT

You may also find interesting a 3-d + 1 model Steve...

Something rather similar to what you have been talking about, but also inspired by the work of Connes is a paper by Aastrup and Grimstrup, called The Metric Nature of Matter. You can find it here:

arXiv:2008.09356

The thing is; while they show a nice emergent theory on a curved 3-d space; it arises from an infinite-dimensional Hilbert space and uses an infinite-dimensional Clifford algebra to derive the gauge group they utilize.

A nice way to get the Standard Model particles and a nearly-commutative space, in any case. It has some common elements to Tejinder's work, but is a different animal.

Best,

Jonathan

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The equations of physics that represent the laws of nature, including the equations with delta symbols, represent relationships between categories of variable. The equations do not represent movement or change.

The equations represent the fact that IF numbers for some of the variables change, the consequence is that the numbers for the other variables will change instantaneously i.e. the relationships always hold. This consequential change is merely due to relationship: there are no mini-computers or mini-people down there at the micro-level doing calculations. However, physicists doing experiments need to move and change in order to take measurements and do mathematical calculations representing (e.g.) predicted outcomes; these mathematical calculations represent what people do, they don’t represent the laws of nature.

The equations of physics that represent law of nature relationships represent a dead world: once the numbers for some of the variables change, the lawful relationships mean that the numbers for other variables change instantaneously, and the system comes to a halt.

The equations do not represent a cause for those original numbers changing. Equations that represent relationships can’t ever represent cause: only algorithmic statements can represent cause. This is what algorithmic statements look like: “IF variable1 = number1 OR variable2 = number2 THEN assign number3 to variable3” or even “assign number3 to variable3”.

The equations of physics that represent the law of nature relationships can’t represent our dynamic world. As well as the laws of nature, it is necessary to add something that can only be represented algorithmically, in order to represent a dynamic world.

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John R. Cox replied on Feb. 5, 2021 @ 15:53 GMT

So algorithmic statements look like the statements of procedures in math? For instance; the rules for multiplication of terms in distribution of a polynomial.

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Jonathan J. Dickau replied on Feb. 5, 2021 @ 16:06 GMT

From my experience...

Virtually ALL Physics equations represent change in some manner or fashion. But rightly framed; Physics equations are, by definition, an attempt to represent what is happening in nature. There will always be limitations, and a kind of trade-off between simplicity and accuracy, for any mathematical modeling process. But we have a sense that nature is executing its own process with mathematical precision, however it sometimes employs Maths we cannot readily fathom or discern.

Often the fact that the Physics Maths encode evolutive properties is hidden, due to an attempt at paucity in the symbology. In Functional Analysis, for example; the letters that would commonly represent variables now stand for functions of a given set of variables. And people often abbreviate the heck out of things, when using Maths like Tensor Calculus; so you have to know how to unpack the capital-lettered quantities (e.g. - the Christoffel symbols in GR) into equations of small-lettered variables, in order to attempt a solution.

But as I have tried to demonstrate above; even simple equations involving a quantity like c have implied dynamism or the capacity to encode change and changeability. In my opinion; the idea Physics equations do not represent action, motion, or change, falls apart. Instead; it is what Physics equations are all about. There is no 3rd party needed, nor an active agent as observer, because nature acting with mathematical precision upon itself is enough.

Best,

Jonathan

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Jonathan J. Dickau replied on Feb. 5, 2021 @ 16:22 GMT

And your comment above is astute John...

The rules for multiplication, when evaluating terms of a polynomial, are aptly related to this thread. The only difference is, that when you move from real-valued polynomials to equations with octonionic elements; the demands for precision and the degree of specificity grow along with the number of extra terms. It gets truly onerous and is too much for most people to bear. We need computers, and yes we need to program in the right sequence of operations. But the evidence is piling up that this is a calculation nature CAN handle.

Best to All,

Jonathan

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Despite the delta symbols, the equations of physics that symbolically represent the law of nature relationships do not represent movement or change or a dynamic system. The equations merely represent relationships.

Human beings need to move and change (expending time and energy) in order to e.g. solve equations, or do other mathematical procedures, but the laws of nature are not doing what human beings do: there are no mini-human beings or mini-computers down there at the micro-level doing calculations.

To symbolically represent any sort of movement or change, at the micro-level or the macro-level, you need to use algorithmic symbols.

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Jonathan J. Dickau replied on Feb. 6, 2021 @ 17:34 GMT

I can agree with your first paragraph Lorraine...

It's the second paragraph that gives me agita. Brian Whitworth is a prof in New Zealand who posited that; in order for there to be calculations, there must be a kind of computer outside reality, to make it so. He just finished his book on that subject. But I am wary as you seem to be, that we need an external computing apparatus to make the universe go. This was part of my motivation talking with Prof 't Hooft, who said 'the laws of nature do the calculation for us.'

This seems to be an unsatisfactory answer for you; so I will leave aside issues of where the calculation must take place in order to explore other areas which may flesh out the cross-section of our agreement and disagreement. There seem to be quite a few places where we agree, Lorraine. But I am taking up a contrary position because I see both sides as equally-weighted at this point. You appear to be entrenched, on the other hand, in a specific view of how things MUST play out, in order to be following the rules. I guess that's fair.

I have talked about how certain variables incorporate change or motion, so that even if they were a constant; it is a constant describing dynamism. Things like the speed of light or Planck's constant already include some dynamic elements, but I can see where it might arise that if these are natural relations which are mathematical; who or what is doing the Math? I guess that this is why some Physics equations include an i as well as an h or a c, but we should note that in some cases it should be i... because it could be j, k, I, J, K, or L instead.

Best,

Jonathan

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Jonathan J. Dickau replied on Feb. 6, 2021 @ 17:55 GMT

Sorry if my answer appears flippant...

I've been exploring the whole 'unreasonable effectiveness' thing for a long time, more than 30 years. My motivation was from the discovery of certain mathematical relations and wondering "why should that be true?" So it was only after many years of bitter experience trying to distance myself or to disprove what I had learned, and failing, that I came to accept that I'd found something worth pursuing. Then the real hard work started.

But if I hadn't spent such a long time clinging to views like your Lorraine, because it can't possibly be true that something dead like the Mandelbrot Set could have relevance to Physics; I would not be in a position to laugh about some of the things you have to say about what is or is not possible and realistic. To figure out ANY valid description of how we got here; one must be prepared to relax some assumptions in early universe cosmology, about what is physically-realistic.

It's a hard lesson to learn, but worth considering the experience of others.

Best,

Jonathan

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Jonathan,

Have you ever done a physics experiment in your entire life?

The symbols that physicists use to represent the world mean something to physicists (and others). The symbols that represent a law of nature relationship represent the relationship and nothing but the relationship. The symbols that represent laws of nature do not imply mathematical calculations or any sort of movement on the part of nature, or on the part of physicists.

Despite the delta symbols, the symbols that represent laws of nature merely imply relationship: the CONSEQUENCE that movement/ change of number for a variable V1 has on the numbers for the other variables in the relationship. The CAUSE of movement/ change of number for the variable V1, i.e. the dynamic aspect of the world, requires a different set of symbols.

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Lorraine Ford replied on Feb. 7, 2021 @ 00:01 GMT

The symbols that represent laws of nature imply relationship: the consequence that movement/ change of number for a variable V1 has on the numbers for the other variables in the relationship.

This change of number for the other variables is solely due to relationship, and it doesn’t occur in time, because lawful relationship does not exist in time any more than it exists in mass.

The CAUSE of movement/ change of number for the variable V1, i.e. the dynamic aspect of the world that is associated with time, requires a different set of symbols.

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Jonathan J. Dickau replied on Feb. 7, 2021 @ 16:59 GMT

I was really good at Physics experiments in High School Lorraine...

They made me the president of the Science Club, because not only was I careful and thorough (to eliminate possible sources of error); I also had lots of ideas about new experiments beyond what was in the textbooks. We did an experiment in plasma physics, after school, after a bunch of us had read about MHD and plasma discharge. I still have some of the apparatus we used. It's good we wore goggles and made multiples of some parts, because our first reaction chamber overheated, before we achieved a stable result.

But I will return later to talk about experiments that specifically relate to the work this thread is about. I think recent experiments claiming to disprove objective reality are flawed, because the apparatus does not satisfy requirements of geometric separability. I'm talking about the rules of projective geometry. I'll have to explain in detail later. And of course; it is relevant to this thread, because it has a connection to the theoretical framework for Aikyons. I'll say more when I have time to fully explicate.

Best,

Jonathan

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Steve Dufourny replied on Feb. 7, 2021 @ 17:54 GMT

Hi, you make me laugh both of you, we have had these experiments at school and universities and that must be precise in fact, it is what tell us Lorraine I believe, like the algorythmic universe and its symbols and mechanisms. Lol let s laugh, me I have not successed an experiment I have created a blue cloud in chemistry in all the university, the reaction was not ok apparently , I created acid acetyl salicilic lol but I have put sonething wrong probably, all they were smurfs in the university :)

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Jonathan,

I’m glad to hear that in the dim, distant past you have had SOME connection with the real world, the real world that physics represents with various symbols.

In order for people to communicate, there is no way to talk about, write about or represent the world except via written and spoken symbols: words, equations, numbers, algorithmic symbols. Although words and sentences can be interpreted in various ways, equations, numbers and algorithmic symbols have a more restricted meaning. The equations that physics uses to represent law of nature relationships have a restricted meaning: they represent static relationship and nothing but static relationship.

But, to represent the movement of the numbers that apply to the variables in the law of nature relationships, you need to use algorithmic symbols. You need to use algorithmic symbols to represent any change or movement on the part of people or on the part of nature.

This indicates that, as well as static lawful relationships, there exists aspects of the world that can only be symbolically represented with algorithmic symbols like IF, AND, OR, THEN, and ELSE.

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John R. Cox replied on Feb. 8, 2021 @ 02:34 GMT

Lorraine,

Variables in physical laws are not independent. It is the role of the analyst to select a particular empirical value in a real world application, but that value is of a parameter in that while the value might vary it will always be an element of a covariant relationship, and not something that will sometimes be part of a physical relationship and other times not. So it naturally...

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Lorraine,

Variables in physical laws are not independent. It is the role of the analyst to select a particular empirical value in a real world application, but that value is of a parameter in that while the value might vary it will always be an element of a covariant relationship, and not something that will sometimes be part of a physical relationship and other times not. So it naturally (in both the physical and mathematical sense) follows that the Algebraic expression of that measurable physical relationship is a derivative of the continuous function of general covariance of the constituent parameters.

If you write an algorithm to replicate Galileo's ramp experiment to derive the Inverse Square Law, you could start by (1) go to lumber yard (2) get 16 foot 2x10 and 32 feet of 3/4 inch half round and (3) build a ramp marked off in intervals to 5 meters and block one end up on some bricks...

The thing is that the function of changing the number of bricks changes the length of the y and x axes as well as the slope of the board, and coefficiently the number of ticks for the ball let roll to pass respective interval lines on the ramp. All of the variables are co-dependent and the resulting continuous function of what those values will be if only one is changed is not a static state. Only your choice of where you measure what when.

What algorithms have proven good at, is to plan out procedural steps to to find the continuous function from the form of the relationship and the algebraic equation. But you end up with the original form of continuous function from which the Algebraic physical law was derived.

I haven't gotten deep into algorithms, but in mathematical analysis, I would expect that such symbols as Bra-Ket notation play a role in sets of values of a parameter, such as distance. Rather than a 'delta', bracketing might be used for d,d' and if velocity is part of the function (in math, defined as 'a relationship') then perhaps it could be mapped as the bracketing of distance symbols followed by a / (slash) and a 't'. But you would have to make sure you don't use symbols in a manner that would be confused with other meaning in maths. I really couldn't say. It just isn't my bag. It IS Super Bowl Night and going my way, so I'm okay with whatever you are doing Down Under. Football is shaped like a prolate spheroid here. Good Luck, if you clash with conventional usage of terms, I'm sure people will let you know. :-) jrc

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Lorraine Ford replied on Feb. 9, 2021 @ 22:34 GMT

Jonathan,

I’m Australian. When I said: “I’m glad to hear that in the dim, distant past you have had SOME connection with the real world, the real world that physics represents with various symbols”,

I meant: I’m glad to hear that in the dim, distant past you have had SOME connection with the real world, the real world that physics represents with various symbols :)

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Jonathan J. Dickau replied on Feb. 12, 2021 @ 16:27 GMT

This is getting too silly Lorraine...

I have attempted to be entirely civil, but I am tempted to make a snarky comment here about how your remarks would be offensive if... It is better that you simply accept that getting a few slightly burned fingers in Chemistry class helped you learn just as my broken vessel in a plasma Physics experiment helped me to hone my skills and do things right a second time. We learned from our mistakes.

I am reminded of Doug Osheroff, who got the Nobel for his part in discovering superfluid liquid He 3. He was only a grad student at the time, but he actually performed the experiment that found the sweet spot. Hearing his life story; I'm the same kind of guy - the one who loves to take things apart to see how they work and then put them back together. So your exaggerated acclimation is way off base.

It's weird. Real world skills? I got top honors in Shop classes (Wood, Print, Metal, Electric) so I could have gone into the trades. I chose to become an elite Technician instead, so I still have lots of frequent flyer miles from jobs completed years ago, where the company sent me out (all over the US and sometimes abroad) to fix machines impossible to repair by other techs.

My Dad pushed me to become an Engineer. But I was told years later by an RPI professor that I was not like most of his students, who have an Engineering mentality, because I have the mind of a scientist. That led me to again become serious about Physics. And theoretical Physics appears to be my forte.

Best,

Jonathan

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Steve Dufourny replied on Feb. 12, 2021 @ 16:32 GMT

you are both relevant scientists and I suggest lol a beer from belgium to drink together , yep , they are the best , after this beer, you shall be in synchros :)

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Steve Dufourny replied on Feb. 12, 2021 @ 17:27 GMT

Ps Jonathan, you have nothing to prove to nobody in fact, we see that you search answers and that you are a general thinker. You learn the general works and you try to understand this universal puzzle. For this the philosophy, the maths, the general sciences are necessary and also the creativity to invent our own partitions in trying to desribe this universe with convergences. The imagination is important I believe, many are good in details but a few number are able to create innovative general partitions, tools. The sciences community we know it is the most vanitious community and mainly in theroretical physics, all we are persuaded to better understand the origin of the universe, the relativity, the foundamental objects , the maths , but in fact a sure thing is that even if we have encoded all these works and others, we are limited and we know nothing in fact simply, we must recognise this, if we know 0,0000000001 percent of the universe and its maths and physics, it is already well. We try to explain this consciousness like a competition inside this community, all they try to describe and be the best in the explaination but in fact it d be better to utilise this consciousness and the universal altruism at my humble opinion, the humans are so vanitious and think they are the centers of the universe and want to be special and recognised. That is why my project of global collaboration is not easy, the humans lack of humility and they prefer to be followed than to follow, the same for the researchs in theroretical physics, all they work mainly alone , it is odd all this. In all case, Lorraine and you you are different but both are interesting thinkers , and don t forget this beer together lol , take care

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Steve Dufourny replied on Feb. 11, 2021 @ 15:23 GMT

Hi Tejinder, it is of course a good extrapolation considering the eigenvalues and the reductions of jordan for the matrix and to arrive at the mass. If my theory is correct about these spheres, the blocks and reductions can be correlated with these spherical volumes and their motions oscillations, the aim being to find the correct partition and proportions. The densties of these volumes for me are essential because the volumes are preserved and if the series finite that I explained are a reality, so that becomes very relevant for the rankings or properties of particles, the 3D spheres. I d like that the thinkers focus also on this even if they have the habit to consider points , geometrodynamics or strings, the spheres can be interesting like foundamental objects, Thurston and Poincare d agree I think :)

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Lorraine Ford replied on Feb. 12, 2021 @ 22:13 GMT

A number that exists in the real world cannot be an entity, a Platonic entity, or a finished product (like 3.751, 147, or a number that approximates the square root of 3 over 32). A real-world number can only exist as a mathematical relationship, somewhat similar to the law of nature relationships that physics represents with equations, but a relationship where the numerator and denominator categories cancel out.

Clearly, categories and relationships are the fundamental things that underlie numbers: you can represent numbers as being derived from relationships between categories (like mass or position), but you can’t ever represent categories (like mass or position) as being derived from relationships between numbers.

Tejinder, you’ve got a whole lot of numbers displayed there. What do you think a number is? If we can send missions to Mars, surely we can say what it is we are representing with number symbols?

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Jonathan J. Dickau replied on Feb. 15, 2021 @ 20:37 GMT

I think you have the questions and answers reversed here Lorraine...

Tejinder is asking if, by making certain assumptions about numerical relationships and their geometric bases, we can derive the mass ratios between particles. Then the challenge is to see if the mathematical basis he proposes reproduces what we observe in the real world.

But it is much like positing or questioning the existence of God. One can only ask "If the Divine exists, what evidence would we see?" So I think the endeavor here is a bit more philosophical, rather than being dogmatic like a religion. By testing the outcome of certain assumptions we can gauge their veracity.

But I'd still like to grasp the Karolyhazy correction procedure better, and to understand why purely numerical assumptions fail.

Best,

Jonathan

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