Funny things happen :)) Together with the two previous seemingly favorable comments, I've got two very small rates, probably 1. Maybe this is a coincidence, maybe somebody's playing, this is not the first time when this happens in this contest. Maybe Russian hackers? :))
Indra's Net - Holomorphic Fundamentalness by Cristinel Stoica
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 Kevin,
Thank you for reading my essay and for the comments. The central points of my essay were (1) to argue that there is a relativity of fundamentalness (even ontological), based on isomorphism/automorphisms of mathematical structures, and (2) to propose the holomorphic fundamentalness, which is illustrated by the metaphor of Indra's net - the whole is present completely in each part. The section about unification was meant to give an example which may turn out to be holomorphic, and indeed it was too short to properly explain the content of a 33 pages paper. I guess a proper explanation would be of the length of a book, just to explain how the Standard Model fits in that matrix without gaps or new predicted particles, and has the right symmetries, charges, colors etc, all this coming from a simple algebra. In the meantime I found some new directions to develop it and I am more convinced that as a bonus will be holomorphic. Making it holomorphic was not the reason I am working at it, but it seemed a nice bonus, as I thought holomorphic fundamentalness brings a fresh view on what is "fundamental".
Best regards,
Cristi
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
[deleted]
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
Dear Austin,
Thank you for the comments, especially for the description of the stages you experienced. As you may know, a theory is better when you don't need or eve can't change it to accommodate new data. This means it will make better and more exact predictions, without having to change something. It is difficult to obtain this "rigidity", and the main danger is, as you said, that it may be "too static". What would be the way to get the maximal rigidity? I think this is a unified holomorphic field, because holomorphic fields are indeed the most rigid ones. Among them there are others even more rigid, like the constant ones, these indeed would be too static. But are holomorphic fields too rigid? I think not, because while they can determine everything everywhere from the data at the field, there is no way to control or determine this data completely. This is because you explore it from within the field, and no measurements can give you the field as it is, because the operators don't commute. This "protects" the field from being "hacked".
You said "Today I saw the light and can imagine your timeless spaceless point or germ as the fundamental entities in my essay."
One of the surprising things at this contest was that although this idea of germs seems previously unused in physics, more readers told me it seems to be consistent with their own views. This is interesting, I'll have to check it in your essay. I like this "My model has universes within particles and particles within universes.". Good luck in the contest!
Best regards,
Cristi
Dear Andrew,
Thank you very much for reading and for commenting the ideas from my essay.
You wrote "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."
You've probably seen my comment to John Klauder's essay. The standard quantization procedure works very well, and I think geometric quantization is based on a geometric structure which is not only elegant, but contains relevant insights, so I think that it (or some version of it like enhanced quantization) may be on a good track. But there are some reasons why I am not completely satisfied with it. I'll just mention one, which is that it starts from a classical system, and applies some procedure to get a Hilbert space and hermitian operators for the classical observables, while the only thing we know is the other way around, that the world is fundamentally quantum, and the problem is to obtain the classical limit at a "macroscopic" level. The major justification of this procedure is that it gives very good predictions. This may be enough for most people, because physics is about getting the right predictions. This is why I was sympathetic with Klauder's quantization, because even if it still starts from a classical world, it seems to me to enhance this relation. But I just heard about his theory, and I didn't dive deep enough into it to seriously understand its consequences. So I was interested from the beginning to read your essay as an application of Klauder's quantization (this is in addition of wanting to read it because I'm interested in what you have to say about what is "fundamental").
Best regards,
Cristi
Hello Jonathan,
Thank you for the kind comments. You said "have long been a fan of the Indra's net metaphor ...", to me it happened the opposite: I had this idea of holomorphism long time ago together with the idea of the central role of Clifford algebras (others had the idea long before me, we differ by approaches), but only last year I heard about Indra's net which seems a suited metaphor to illustrate this. I answered Andrew on his page. I have your essay in my reading list too.
Best regards,
Cristi
If you do view my contest paper, it has reference#1
http://vixra.org/pdf/1709.0438v1.pdf
which has more wording on the relevant ideas wrt your mysical net than my highly-condensed contest paper. Figure A and pages 1 and 2 of the vixra paper show that I referred to braids (or universes) of three 4D colour dimensions and also referred to the braids as fibre optic cables. In some sense, these braids are analogous to fields whereas the jewels in the net are (to me, at least) analogous to particles.
To come clean, my earlier draft of the document referred to balls of wool rather than optic fibres and I even have carried some strands of red, green and blue wool in my brief case for several years. But I deleted reference to wool to avoid comments about wool-gathering, woolly ideas and dropped stitches in logic. A mystical net is a much more presentable analogy than a tangled, random hotch potch of three balls of wool.
My model is not mathematical but builds up SM particles using SM eigenvalues of fundamental properties. To do this one needs to gather the appropriate strands of coloured wool together, taking note to get the time directions of the strands correct, and tie them together using cotton to have the appropriate number and types of strands to make correct eigenvalues for whatever particle is being made. Repeat by making cotton ties for all particles in the block universe, or is that four block universes? In between particles we have strands of wool heading, as fields, forwards and backwards in time(s), to the next particle node, which demonstrates wave/particle/wave sequentiality. Likewise(?), in the mysical net the crystals reflect on each other.
Wrt free will, it all seems gridlocked to me with puritan predestination unfortunately predominating.
The cotton knots above imply particle decoherence to a point which to me seem like Penrose's CCC nodes, but for particles rather than universes. I wonder if the gridlock implies no free will across CCC cycles? That is, is the next CCC cycle already predetermined within the net?
In a way, these colour universes remind me of nearby galaxies in space but the colour universes are nearby (and interwoven) compactified universes. I suggested that our spacetime [say a brown universe] is emergent and the three colour universes are more fundamental, but that could be an observer effect and really they are all equal partners. In a red spacetime their particles could appear as interwoven strands of green, blue and brown wool and they could claim the red universe was emergent.
In a 16D block, is complex number algebra sufficient to allow analytic differentability to obtain probability amplitudes? Wrt being unhackable, distributing the mystical net data across four universes where each has its own 'spacetime' does seem a good way of protecting the data. One can only get probability densities in one's own (one of four) spacetime universe.
Best wishes
Austin
In this essay I am talking about holomorphic functions, which are known for the complex case for long time and have this property of containing in each point the complete information about the whole function. I illustrate this with "Indra's net" as a metaphor, about which I learned many years after I became interested in Clifford holomorphic functions in physics. It is not like I have a mystical idea and try to implement it, it just happens that the holomorphic functions do this, so the metaphor seems appropriate. I don't need to add wires and cables to connect everything artificially. The main point here is holomorphism, and I don't think you are interested in this in your papers. As for free-will, I started to discuss it when I tried to explain my views on quantum mechanics as not requiring collapse, and some people were worried that this will rob them of free-will. I think that whether one thinks QM is deterministic or not, it is independent on having or not free-will, and this is what I explain. I tried to explain previously that randomness isn't freedom, and anyway even if quantum mechanics is deterministic (and has to be if there is no collapse), this is not against one's freedom, because the initial conditions of the system are co-determined by future measurement setups [Flowing with a Frozen River]. Maybe this looks to you like predestination, but to me is not. If you read that reference, The Tao of It and Bit, and The universe remembers no wavefunction collapse you can see that my motivation is to keep Schrodinger's equation, which works, but to explain what we think is collapse without introducing discontinuous collapse in the time evolution (which would break Schrodinger's equation, conservation laws, and relativity). Then you will see that it has nothing to do with "predestination", but maybe it will appear so to people who believe that the state of the universe is completely defined from the beginning. This is not my position. We may disagree, but I felt I have to clarify :)
Best wishes,
Cristi
Just to clarify. I did say that at first I thought that your mystical net was an odd idea merely tacked on to your essay but somehow making it into the title. It took me five weeks to see how I could make it more prosaic by analogy to my own model. I personally am anti-mystic, anti-Tao-interpretation, anti-predestination, anti-theistic, anti-Bellist and anti everything which is not completely deterministic. Also I am anti the idea of having spacetime constructed of solid 'wires' just in the same way that I don't regard my path through spacetime as a continuous, solid wire. You introduced the mystic metaphor in this thread, not me.
Thanks greatly Cristi...
One thing of interest pops to mind. Following another thread; I found myself reading your paper on semi-regularizability of Schwarzschild singularities, and continuing the solution through the horizon. I immediately got excited to share that my model reveals a similar picture. Approaching the Misiurewicz point; a sequence of self-similar forms gets smaller in scale, and in reverse-mirror fashion reappear on the other side in increasing scale but in opposite phase!
This makes the Schwarzschild event horizon like a reverse mirror which mimics the information that strikes it but recreates it in opposite phase - which is what gives such a BH the appearance of a perfect black-body. One can make a circuit diagram analogy as well; the inverting feedback amplifier commonly used in op-amp circuits. The virtual ground or earth created by the amplitude null that appears at the summing junction would therefore appear like the Schwarzschild EH, as shown in the diagram attached.
All the Best,
JonathanAttachment #1: 2_MandelAmp2.jpg
Dear Jonathan,
That's interesting. One minor comment, actually my solution is continued analytically through the singularity, for the continuity through the horizon it just uses standard methods like Eddington-Finkelstein or Kruskal-Szekeres (it is irrelevant which one of them, because the atlas has different but compatible maps for horizon and singularity). The only difference between my solution and the standard Schwarzschild solution is that I use an atlas which differs only at the singularity by a singular coordinate transformation. But I think there are more differences between your solution and mine, yours involves fractals. Which makes me curious, how does this work?
Best regards,
Cristi
As i am not competent to enquire and seek further details on your excellent essay.But may i request you to see a manuscript i have just attached on my essay title ' Inconstancy of the Physical Constants.....' May i just request you to spare sometime to look at that manuscript as i desire your response to the same to continue my thinking in such a matter further!
Cristi,
Every essay contest, when I see your entry, it goes towards the top of my list, for you always have something enlightening to say. I know nothing about Indra's Net, will look into it for context here.
I wish you would have gotten into more detail on what your expectations were for holomorphic functions for Geometric Algebras over the field of complex numbers across dimensions.
My interest is Octonion Algebra, where there are seven complex subalgebras. If the Cauchy-Riemann equations were applied for all, every irrotational field component in their expected form would be identically zero, which just would not do if one wants to cover Electrodynamics and Gravitation with potential functions.
You mentioned to Geoffrey Dixon some apparent belief one would need non-associative Physics to justify use of a generally non-associative Algebra such as Octonion Algebra. I think he came back with the quip it is a feature and not a bug. This is true, and it is required to allow it to be a division algebra. Nature is not saying use Octonion Algebras only if you have non-associative physics, since really it spans multiplicative associative, non-associative, commutative and non-commutative properties intrinsically, and not only spans but precisely tells us how they play together in the greater whole of the full complement of basis products. Nature is more likely telling us Octonion analysis can go where essentially matrix based associative algebras like tensor and spinors can't go, with little to no limitations going the other way.
If you get a chance, look at my essay, it is called "Truth".
Rick
Hi Cristi,
"The entire state of the universe is therefore encoded in a single class of germs."
Is there a least germ? (There is, In Indra's Pearls.)
A wonderful, imaginative essay! My essay here.
All best,
Tom