Indra's Net - Holomorphic Fundamentalness by Cristinel Stoica

Hello Indra

Dare I say, 'Wow!' I think our work is strongly connected. The following detailed comments are provided to show the connection. My apologies if these are rather long. My question is, are the nodes in my Harmony Set the centres of your pearls?

Thoughts as I read through:

You say, 'Isomorphisms of mathematical structures will play a central role.' I agree. I agree because it follows directly from the general principle of equivalence (my essay, in which the GPE is 'the' fundamental) and argument by Kant, so it is philosophically acceptable to me. The issue then comes down to whether the mathematical structure with which one begins is fundamental and well-founded, or at least a trustworthy representation of reality.

You say, 'Could the world be made out of a small number of fundamental building blocks, by putting them together like we do with bricks when building a house?' I think, 'Absolutely.' It is these bricks that are the bones of my Harmony Set, derived from my principle of equivalence. Reading further it is surprising how closely your bricks seem to align to my own, though yours are derived as empiricist, while mine as rationalist. This is good.

You consider Euclid's and Hilbert's geometries. I have a significant problem with this (not your fault) because these geometries lead to a provably transfinite number of contradictions (let me know if you would like to see this). Riemann and Hilbert were also concerned about this. The problem must be embedded in the axioms, and no one has yet identified which and why, however the conclusion is that lines simply cannot be sets of points. For example, how many points cover the line? If you try this, the mathematics blows up. My work dissolves these problems and removes the need for axioms, but to do so is not part of this comment. I like your identification of automorphisms and find that my own work coincides with this.

My other concern as I reach the part on 'holographic fundamentalness' is that the connection between mathematics and physics has never been properly established, as shown by Wigner in his paper "The unreasonable effectiveness of mathematics in the natural sciences," available online, and also considered by other greats of mathematics and physics such as Einstein and von Neumann. My work provides a link but the Harmony Set is still quite basic, and points and lines are of a different nature, though they do produce a vector space. However, that's my work. I don't think this is fundamental to your next steps (having now read ahead).

You then identify that you are considering an ontological relativity, and I think, 'Yay! Someone who gets it! We are looking for mathematics that is fused to the underlying reality.' Then 'lo and behold' you identify equivalence as being somewhat at the centre of it all. Does it not then immediately occur to the writer that equivalence itself (symmetry, equivalence and all equivalent ideas) is the fundamental?

You then move into some high level mathematical physics which is essentially a literature review. Correct me if there is something new in that section. I note that my Harmony Set, raised into a 3-space topology (for which I have a basis, but not the detail yet) seems to produce at least some, possibly all, of the prerequisites for a Clifford algebra, but this would require a deal of work for me to connect the two. However, I will investigate this aspect, so you essay is valuable to me in this respect.

Indra's pearls do seem to be very similar to what I get if I rotate up my 1-space Harmony Set into a 3-space topology, at least as a skeleton (this is not in my essay). Rotating up the 1-space Harmony Set as mentioned does produce complex vectors as well, so I am getting a bit excited (though dreading the volume of extra maths that I will have to derive to show the holomorphism).

Now to the crunch. My model also had the 'problem' relating to it all happening at once, but if you follow the nature of evolution of the Harmony Set, the encoding within each pearl is evolving, and each step in the evolution is ontologically dependent on the previous state, so, while your description is quite reasonable, I would add to this in. You will note that this also gets around Parmenides' denial of change. Otherwise your proposal, as I read it, would be flawed for you need an ontological propagator, not an epistemological propagator (a la Feynman). Please, this is not really a criticism, because I like the treatment. I am just trying to add the missing part, which is in the essay that is precursor (https://fqxi.org/community/forum/topic/1904) to my present submission (https://fqxi.org/community/forum/topic/3041).

Finally, the entire universe being enfolded in a spaceless and timeless point is one solution to my Harmony Set. Some might call it the trivial solution, but that seems deflationary.

Fabulous paper. I rate it highly. If there was a book on this, your chapter would either be the chapter prior to or immediately after mine. You might consider my paper in the light of yours, and also my essay previous to this, which was in the It from Bit contest, which I think strongly relates. My question is whether the nodes in my Harmony Set are the centres of your pearls.

Hi Cristinel,

I really appreciate you commenting on my idea, after all you are the only customer so far:) This is a general response. The implementation of your program is hard to see and depends how much you delve, so I will address that desperately with details in the future.

Quick points. The reason that I say ill defined is because the point can go to infinity and hence it becomes uncalculable (the story is just a bit more involved but I wanted to keep it simple). As a matter of fact the first "l" that you see defined in my programs is the reminiscent of the size of the "universe" and it is just there because of the historic development, it is not needed. Because if I throw the numbers to size of it, it will make the particle to particle interaction inconsistent as I change the size of the universe. Meaning, all interaction in this setup lead to FINITE results (only particle to particle interaction). Also, I have tried all kinds of random other than uniform they do not lead to the consistent easy to interpret results that I get with uniform.

Although I know it is hard for people who have more than hundred essays to read, to really delve in some detail in my system by running the programs. However, I think still some time "maybe 15 min" should be taken to appreciate the system. Of course since I have not explained everything clearly it is easy to misunderstand. BUT I was hoping that people concentrate on the big picture i.e. the RESULTS that I have obtained and concentrate on the finer details later, and a lot of them do exist. Also many other results I have not shown.

Thank you for picking up on the bolded statement in my essay because this system represents it automatically without any fudging and it became apparent only after some development which was doing just what any generalization I was allowed to do.

Thank you again, I could not have asked for more. Comments are worth a thousand points.

Thanks again

If you switch the browser after running the program and switch back you will see a blank, it is calculating it will come back after finishing. The approximate timing and the mentioned issue and others are in the first textbox.

Your other points are well taken and I have already quickly mentioned them throughout the essays. As you know many mathematical systems are equivalent( Schrodinger, Heisenberg,path integral ..). Particularly, the system is linked to Geometric probability, Radon transforms ... etc, an ongoing program.

http://mathworld.wolfram.com/GeometricProbability.html

https://arxiv.org/pdf/quant-ph/0608251.pdf

Hi Cristi,

I enjoyed your essay very much. Excellent writing, wonderful concepts and sound conclusions. Using a game was effective to explain isomorphism and it made the reading more fun. It also made your essay more memorable for me because I showed the game to my wife, who is an avid Sudoku player, and challenged her to figure out the numbers that would sum up to 15.

Your discussion of holographic fundamentalness is spot-on. I wish I had learned geometric (Clifford) algebra in school. I tried to pick it up a few years ago after reading a paper by David Hestenes, which I recommend for your reading (if you haven't already - I noticed you referenced Hestenes and G Sobczyk.) "Oersted Medal Lecture 2002: Reforming the Mathematical Language of Physics." Am. J. Phys. 71.2 (2003): 104-121. I've forgotten too much to fully understand what you wrote in your essay, but I remember enough to say I think you are definitely onto something. Especially your suggestion that such a unification result in a single holomorphic field.

My approach to unification is much simpler than yours, and I took a sort of inside-out (or upside-down?) approach to conclude that motion serves to separate this holomorphic field in our percepption as space (S) and time (T), both of which are forms of motion:

In your words, "Our experience unfolds the germ, creating space and time, but the germ always remains enfolded, and we with our experiences, and spacetime itself, are always enfolded inside it."

In mine, "Physical form is the manifestation or perception we observe when motion separates the field into two coherent waves, S and T, one moving outward as a quantum particle wave function and the other moving inward as the collapse of the same wave function modulated with information. The surface boundary then is the holographic interference pattern forming the apparent surface of the volume in space."

I would appreciate it if you would read my essay at "A Simple Model For Integrating Quantum And Relativistic Physics with application to the evolution of consciousness by Theodore St. John" and tell me where I go wrong. I think that the concept you call the germ is what I refer to as simply an event (in the spirit of Alfred Whithead). You said in your notes "If we want to turn the picture upside-down and consider that our choices also determine the germ, then would it be possible that our local actions determine the germ..." I think that each germ is created in each moment, collapsed into events, so our actions are inherently part of the process of making the germ(s).

What little constructive criticism I can offer seems to make your point, as you say in the last sentence of Quantum holism section, about how "mathematics can offer more adequate notions of composability and reducibility than our classical intuition does". So here it is: You threw me off a little when you talked about "shapes", e.g. "If a particle can have two possible shapes, it can also have any superposition or linear combination of these shapes." I have never heard anyone refer to the shape of objects being described by the wave function, except perhaps as it relates to particle (localized) or wave (non-localized - expanded out in all directions), both of which would be spherical, or as the peaks and valleys in the solution that refer to probability amplitudes. I know you were talking about the shape of the wave because the previous sentence was "A single particle is a wave of various possible shapes." But the word "shape" formed a mental image of the object itself. I also had trouble with the "property of the particle" in the sentence "A property of a particle," you said, "like position or momentum, is well defined only for some of the shapes. For example no shape can have well defined position and momentum simultaneously." Position and momentum are not properties of the particle; they are dynamic variables and measurement of one of them changes the state of the wavefunction to the corresponding eigenvector. The state of the particle only changes in the sense that 'measurement of its position at a given instant in time' effectively means that it is stopped in that position, so the function describing it must be one that fits its current state.

Anyway, congratulations on an excellent essay!!

Ted

My link doesn't seem to work right in the text above. Maybe it's because I left a space in the link.

Try this.

"A Simple Model For Integrating Quantum And Relativistic Physics with application to the evolution of consciousness by Theodore St. John"

Dear Cristenel, Cristi,

I was very impressed by your essay esp in that it makes use of the algebraic group underlying QCD. I have also constructed a well-founded geometric approach to this same problem, with an emphasis on preserving causality at is most fundamental level.

I see that your approach generates one Std Model quark/lepton generation. This would seem to present a problem? I have also seen other similar approaches which produce four generations (or more?).

Thus I encourage you to read my essay https://fqxi.org/community/forum/topic/3092 which discusses only the most fundamental formulations, but with particle causality ensured by consistency with NBWF.

The algebraic group used is a subgroup of a cross product of two wreath products, which explicitly passes Seiberg's causality criteria. The essential mass/energy metrics are attributed to intrinsic _spatial_ variables of the quantum-geometric basis. It also has exactly three generations of SM fundamental particles! (which I didn't mention in the essay, but its in my older publications, cited)

I was most impressed by your expository writing skills, which would suggest that collaboration would be very productive.

Thus I downloaded your 2017 paper to better review its rigorous details.

best,

Wayne Lundberg

Dear Cristi,

Thank you for your interesting and insightful essay. It was a very enjoyable read, and I liked how you worked your way through various perspectives of geometry to Klein's Erlangen Program, which unifies geometries in a way. I still find it remarkable that such unifications, in description, are possible.

The section on Towards a Holomorphic Unification came fast and furious, as happens in an essay with a page limit. I would have liked to have seen this expanded to some degree with emphasis on the connections to the spirit of the essay. Clearly, at least another read is warranted and I will have to put some more thought into this, especially with the surprise of having geometric algebra taking a central role.

Thank you again for an excellent thoughtful essay.

Cheers

Kevin Knuth

Dear Cristinel Stoica

Just letting you know that I am making a start on reading of your essay, and hope that you might also take a glance over mine please? I look forward to the sharing of thoughtful opinion. Congratulations on your essay rating as it stands, and best of luck for the contest conclusion.

My essay is titled

"Darwinian Universal Fundamental Origin". It stands as a novel test for whether a natural organisational principle can serve a rationale, for emergence of complex systems of physics and cosmology. I will be interested to have my novel effort judged.

Thank you & kind regards

Steven Andresen

My goodness, what a wonderful essay and your writing style is impressive. I love your ideas about geometrical "laws", quantum holism and how you can relate them to particles of nature.

One major idea that is not discussed is the quantum property of monogamy (how system and subsystem relate to one another). If your model is holistic then the only way you can have "separate" subsystems is from holographic projections from the one whole system. And these holographic system can have 100% fidelity (since they are from holomorphic vectors as per your discussion page 4) and can have the appearance of "separate" yet be part of the whole.

Yes totally agree that the major issue is how "encoding is done" and your essay addresses that head-on.

I feel your model cannot support monogamy and monogamous behaviour at all. Since you cannot define a measure of monogamy with your "geometry" and as shown in my essay these concepts are the only ones that can have "holograms being a part and apart of the one holistic system".

And more serious problems arise -- you cannot have a "bird's eye view" of your model hence no independent truths can be established since you need the bird's eye to see the whole all at once so as to have objectivity in the first place.

Sometimes your beautiful writing makes seeing the ideas difficult. Can you tweet your model as to show "the whole" and "one small atom this can encode the whole" thru a holographic vector projection on a geometry.

After all there is only one whole holistic system that has internal holographic projections from your basic geometry.

If you have time see my essay where I took your route, and show that it is have monogamy when considered as one whole and is monogamous when considered as "many", by using the basic properties of complex numbers and the area of the imaginary unit. What is fundamental is the area of the imaginary unit" Enjoy

Dear Jouko Harri Tiainen,

Thank you for the comments. You said "I feel your model cannot support monogamy and monogamous behaviour at all. Since you cannot define a measure of monogamy with your "geometry"". I don't know what gave you this impression. Quantum monogamy is a consequence of quantum mechanics, is not some effect first observed in nature and unexplained by quantum mechanics, it is actually predicted by quantum mechanics, then observed. And my model doesn't leave outside quantum mechanics. In fact, Clifford algebras encode many maximally entangled qubits. You said "And more serious problems arise -- you cannot have a "bird's eye view" of your model". I don't understand why you say so or maybe what is your own view of what a bird's eye view is. I have the feeling that you don't get many of the points of my essay. You ask "can you tweet your model", this is funny, try and tweet a general holomorphic function. You seem to believe that holomorphy means that everything is contained in a short sequence of bits, but don't forget that a power series has an infinite number of coefficients, which themselves need infinite information to be specified. Holomorphic functions have encoded the complete information at each point, in the coefficients of the power series at that point, but this doesn't mean that you can encode the full universe in a tweet or even in all the books in the universe :)

Best regards,

Cristi

My thoughts on your essay have gone through three stages. Five weeks ago, I thought that the mystical net was an odd idea merely tacked on to your essay but somehow making it into the title. Later, I thought the net was relevant but too static, whereas today I realised that it was an excellent idea.

By too static I mean that I thought it as too perfect a fractal. That is fine for a perfect fractal which gives the same image wherever one zooms into the picture. But my own model at

https://fqxi.org/community/forum/topic/2982

has the universe starting out with perfect symmetry and then gradually losing symmetry and gaining entropy. I wondered how breakage of symmetry could be contained in the mystical net of timeless point(s).

Today I saw the light and can imagine your timeless spaceless point or germ as the fundamental entities in my essay. These are a 4D set of strong colour red dimensions, ditto for blue and for green and ditto for spin: making 16D in all. 4D blocks are used so as to allow colours and anticolours c.f. to matter and antimatter in a 4D spacetime block. Normal spacetime is emergent from the 16D and maybe uses the 4D of spin to add a topological twist to space. As in string theory, all these dimensions are compactified to one point which is observer dependent. An observer within the 16D could maybe observe the 16D-point as not compacted, so to call it a point or a universe depends on the observer.

So that is one point/germ but how does that one point lead to a myriad of jewels... In my model, the point/germ has four independent time dimensions in it, so a red brane can weave its way forwards in red-time but say backwards w.r.t. green-time. The time dimensions in the 16D are pretty mixed up. In this time-endless interweaving of dimension, snags of different dimensions get caught together as particles/fields. The single point or germ does not exist in spacetime but every particle lives in spacetime and every particle has its own contents of a snag of the 16D fundamental germ. So every particle contains the same jewel although contains different aspects of the jewel, eg having a red quality rather than an antired quality. In my model this can best be seen in the hexarks (which are sub-particles of preons where each hexark has a single polar attitude to each of the possible binary qualities of the germ).

My model has universes within particles and particles within universes. Despite, or perhaps because of, all the time dimensions in my model, there seems to be no place for free will.

quote

The relativity of fundamentalness implied by different axiomatizations and formulations is

just epistemological fundamentalness. But the examples from the quantum world seem to imply

that reality is holistic and there is a relativity of the ontology itself. Should we then take the

whole universe as ontologically fundamental? Should we consider that what is fundamental

are not the various sets of principles from which everything can be derived, but rather an

equivalence class of them? Or maybe it is possible that something more fundamental than

these exists?

end of quote

Cristi, this reasoning as to an equivalence class of principles, is exactly why I picked John Klauder's enhanced quantization for my bound put in the cosmological constant.

I would like it very much if you reviewed and commented on my essay, December 21, using this analogy to rate and review why I used John Klauders enhanced quantization.

Awaiting your reply. i.e. this is a very relevant insight.

Greetings Cristi,

I agree with the comment some others have made that your essay is impressive. I have long been a fan of the Indra's net metaphor, but you weave it into the whole fabric of Physics in a meaningful way. This is in some ways the kind of essay I wish I could write, if I was a little smarter and more learned in order to do the subject matter justice. That is to say you do that admirably; you explain yourself extremely well. I especially like the I-Ching characters used as binary numbers for the chapter headings - a correspondence first described by Leibniz. It will take at least one more reading to absorb all you are saying, but I will be back with more to say myself. I invite you to check out my essay when you get the chance.

I wanted to comment that I see Andy Beckwith's message/query above, and I noticed you already had high praise for John Klauder's essay. He and I both heard John Klauder's excellent talk at FFP15 and found his work inspiring. So I'm a little curious what you think of how Andy put that formalism to work, and if you feel it is relevant.

All the Best,

Jonathan