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RECENT POSTS IN THIS TOPIC

Steve Dufourny: on 1/27/21 at 18:48pm UTC, wrote In your theory wich is an assumption .....and in my theory wich is also an...

Jonathan Dickau: on 1/27/21 at 18:39pm UTC, wrote In my theory... Early universe evolution happens under the octonions and...

Steve Dufourny: on 1/27/21 at 18:16pm UTC, wrote Hi to both of you, the space does not really exists in logic Jonathan, the...

Jonathan Dickau: on 1/27/21 at 18:01pm UTC, wrote So the question remains... Why is empty space dynamical? That is the real...

Steve Dufourny: on 1/27/21 at 17:50pm UTC, wrote that must converge in logic Jonathan, there is like a conjecture between...

Jonathan Dickau: on 1/27/21 at 17:31pm UTC, wrote This question is only relevant because of what we have learned... It...

Steve Dufourny: on 1/27/21 at 17:29pm UTC, wrote my dear octonionic friend , lol you know you are persuaded, I am too, why...

Jonathan Dickau: on 1/27/21 at 17:14pm UTC, wrote It can be any natural process Steve... Humans or other living observers...


RECENT FORUM POSTS

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FQXi BLOGS
January 27, 2021

CATEGORY: Blog [back]
TOPIC: Towards the unification of the four fundamental forces by Tejinder Singh [refresh]
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Blogger Tejinder Singh wrote on Oct. 10, 2020 @ 07:01 GMT
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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Steve Dufourny wrote on Oct. 10, 2020 @ 12:06 GMT
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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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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Jonathan J. Dickau wrote on Oct. 14, 2020 @ 02:04 GMT
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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Steve Dufourny wrote on Oct. 14, 2020 @ 10:18 GMT
ps Tejinder I have shared it in facebook

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Jonathan J. Dickau wrote on Oct. 26, 2020 @ 16:24 GMT
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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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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ASHLEY j ANDERSON wrote on Nov. 11, 2020 @ 01:32 GMT
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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RAJAN DOGRA wrote on Dec. 8, 2020 @ 14:42 GMT
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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Member Tejinder Pal Singh wrote on Dec. 10, 2020 @ 15:33 GMT
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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Member Tejinder Pal Singh wrote on Dec. 10, 2020 @ 15:38 GMT
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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Member Tejinder Pal Singh wrote on Jan. 7, 2021 @ 08:26 GMT
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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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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Steve Dufourny wrote on Jan. 7, 2021 @ 21:08 GMT
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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Lorraine Ford wrote on Jan. 8, 2021 @ 21:28 GMT
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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Lorraine Ford wrote on Jan. 9, 2021 @ 21:20 GMT
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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Jonathan J. Dickau wrote on Jan. 10, 2021 @ 02:56 GMT
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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Lorraine Ford wrote on Jan. 10, 2021 @ 20:52 GMT
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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Jonathan J. Dickau wrote on Jan. 11, 2021 @ 20:24 GMT
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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Lorraine Ford wrote on Jan. 11, 2021 @ 21:45 GMT
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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Jonathan J. Dickau wrote on Jan. 12, 2021 @ 15:30 GMT
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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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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Jonathan J. Dickau wrote on Jan. 12, 2021 @ 17:05 GMT
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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Jonathan J. Dickau wrote on Jan. 12, 2021 @ 19:27 GMT
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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Lorraine Ford wrote on Jan. 12, 2021 @ 21:53 GMT
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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Lorraine Ford wrote on Jan. 13, 2021 @ 23:54 GMT
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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Jonathan J. Dickau wrote on Jan. 15, 2021 @ 19:57 GMT
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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Lorraine Ford wrote on Jan. 16, 2021 @ 21:52 GMT
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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Lorraine Ford wrote on Jan. 17, 2021 @ 21:49 GMT
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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Stefan Weckbach wrote on Jan. 18, 2021 @ 08:45 GMT
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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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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Jonathan J. Dickau wrote on Jan. 21, 2021 @ 19:14 GMT
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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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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Lorraine Ford wrote on Jan. 21, 2021 @ 23:14 GMT
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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Lorraine Ford wrote on Jan. 22, 2021 @ 21:00 GMT
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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Lorraine Ford wrote on Jan. 22, 2021 @ 22:19 GMT
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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Jonathan J. Dickau wrote on Jan. 25, 2021 @ 19:49 GMT
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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Jonathan J. Dickau wrote on Jan. 26, 2021 @ 19:17 GMT
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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Lorraine Ford wrote on Jan. 27, 2021 @ 01:32 GMT
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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