Dear Laurence,

Your post is very stimulating. I need time to look at this possibility of relating black-hole physics and entanglement, and non-associativity. On the other hand, I don't consider that entanglement is a primary category in non-local/contextual questions. It may be that conformal arguments adapted to Grothendieck's approach may approach the subject you are talking about. I should say that I am not familiar enough with black-hole physics to have a motivated opinion I intend to read and understand this Maldacena-Susskind paper before discussing more with you on this topic. Meanwhile, may be you can have a look at recent papers by Frédéric Holweck and co-authors (we are now working together) about entanglement and algebraic geometry.

Thanks and best wishes,

Michel

The program of finding physics with [0, 1, ∞] can be found with the SL(2,C) group and the linear fractional transformation (LFT)

f(z) = (az b)/(cz d),

which has a correspondence with matrices of SL(2,C). The Mobius transformation or LFT is an automorphism group on the Argand plane, and this is equivalent to PSL(2,C). This projective linear group is then the automorphism group of C. If we let the constants a, b, c, d be points in C then the LFT

f(z) = [(z - z_1)/(z - z_2)][z_3 - z_2)/(z_3 - z_1)]

is for the identity f(z) = z a case where z_1 = 0, z_3 = 1, and z_2 = ∞. A matrix representation may be found by dividing through by z_i and taking the limit z_i --- > ∞.

From this comparatively simple example we may move up to SL(2,H) and SL(2,O). In the case of SL(2,O) ~ SO(9,1), there is an embedding of SO(9) ~ B_4. This in turn is defined with the short exact sequence

F_4: 1 --- > B_4 ---> F_{52/36} ---> OP^2 --- > 1

where the strange symbol in the middle means that the 52 dimensions of F_4 - the 36 dimensions of B_4 ~ SO(9) defines the OP^2 projective Fano plane or OP^2 ~ F_4/B_4.

The B_4 group is the SUSY group that Susskind employs with the holographic principle.

The group F_4 is a centralizer in the E_8, which means it commutes with the automorphism of E_8, which is G_2. We then have a somewhat Rococo form of the same construction. A projective form of SL(2,O), PSL(2,O), defines matrices ~ aut(O) ~ G_2 which map three points to [0, 1, ∞] with the action of the 7 elements in the Moufang plane. I think I can find this matrix in the near future.

Unfortunately I am moving shortly, so that is complicating plans to do much analysis. If I do this in the immediate future it will have to be in the next week.

Cheers LC

Dear Michel, and apologies if this does not apply to you. I have read and rated your essay and about 50 others. If you have not read, or did not rate my essay The Cloud of Unknowing please consider doing so. With best wishes.

Vladimir

Vladimir,

The rate is less important than comments you may have.

I wonder if you have specificremarks concerning my essay.

Thanks.

Michel

Dear Michel,

I have rated your essay on 10th of July with maximum rating and I would like to know whether you have rated mine. Please inform me in my thread.

Best,

Sreenath

4 days later

Dear Michel,

World contests FQXi - it contests new fundamental ideas, new deep meanings and new concepts. In your essay deep analysis in the basic strategy of Descartes's method of doubt, given new ideas, images, and conclusions. I especially liked the idea «dessin d'enfant».

Constructive ways to the truth may be different. One of them said Alexander Zenkin in the article "Science counterrevolution in mathematics":

«The truth should be drawn with the help of the cognitive computer visualization technology and should be presented to" an unlimited circle "of spectators in the form of color-musical cognitive images of its immanent essence.» Http://www.ccas. ru/alexzen/papers/ng-02/contr_rev.htm

Do you agree with Alexander Zenkin?

And the second question: Why the picture of the world of physicists poorer meanings than the picture of the world lyricists? http://www.youtube.com/watch?v=H3ho31QhjsY

I wish you success,

Vladimir

Dear Vladimir,

At the bottom of Zenkin's interview

http://www.ccas.ru/alexzen/papers/ng-02/contr_rev.htm

there is

"Drawing is a very useful tool against the uncertainty of words" - Leibniz.

Of course, this is exactly what Grothendieck did with his 'dessins d'enfants'.

And as I said in the post on your webpage, the underlying triangle O,1,\infty possibly relates to your cognitive triangle Δ-Logit.

I fully agree with Zonkin's view. I appreciate very much what Vladimir Arnold did for science (including a lot of geometrical ideas and drawings). I am not so surprised that he wrote

"the possessing a large influence mafia of "left-hemispheric mathematicians" has managed to eliminate the geometry from the mathematical education (at first in France, and then also in other countries), by replacing all informal part of this discipline by training in a formal manipulation by abstract concepts"

For many reasons, I really believe that 'the crisis in physics' will start unveil by the use of these dessins.

Your second question is much more difficult to answer. You know that Descartes studied music as well.

Thank you very much for your very positive feedback and the high rate you gave me.

Good luck for the final issue of the contest.

Michel

Michel,

I count myself fortunate to find your recent arXiv articles on Riemann conjecture and its quantum simulations.I try to make something similar but merely in the context of post - quantum cryptology. My initial result ( published in 1999 in France )is connected with introduction of periodic perfect numbers(Bull Sci math 1999,123,29-31),hence, new definitions of prime number theorem, cubic groups and quantum one-way function( Cryptology ePrint Archive, 653/2010 ) are arising. I had found that your attempt to formulate Riemann hypothesis as a property of the low temperature Kubo-Martin-Schwinger states is very original. Your last articles also suggest that beyond very popular Wheeler delusion there exist new world of unknown mathematics and unexpected physics.

best

Michael

Dear Michael,

I have not be able to get your 653/2010, may be you can send it to me.

I already checked that the fourth case in your conjecture is not perfect and the fifth case seems out of reach.

There is non-zero interesection between number theory and quantum information processing as you already noticed. May be the perfect numbers are important here, I don't know. Where do you connect your conjecture and RH?

'unknown mathematics and unexpected physics'; yes, a lot of interesting results to appear.

Best wishes,

Michel

Dear Michel

I think you highlighted the most important core issues that must be resolved in order to finally come to a genuine understanding of the universe and its inner workings in your opening quotes. It does seem that increasing knowledge about the details has brought increasing ignorance about the plan. I also think that we must abandon the notion that nothing can travel faster than the speed of light and discover 'what' and 'how' information of some sort or type is able to travel, if not instantaneously, then much, much faster than the speed of light.

I also must admit that as a non-scientist (Je suis an avocat) that some of the technical portions of your essay were beyond my comprehension. However, I think I understood the underlying premise of most of what you wrote and believe you made some creative and brilliant points, and thus, rated you highly. Thank you for your contribution.

Best,

Ralph

    Dear Ralph,

    Thank you for your appreciation, you are totally right that in quantum theory scientists neglected the plan and that much more can be gained by looking at the problem as a whole. Your idea of hardware/software somehow fits my approach. the dessins are the plans. More to come soon.

    I will also rate your essay so that it becomes more visible.

    Best regards,

    Michel

    Hello Michel

    Crikey! I had to do some work to understand your work as it might connect with mine.

    What I do like, and especially like, is your ability to work with interactions through graphs, and your clever ability to see that graphs (and perhaps all kinds of things) can have equivalent interpretations that look quite different to each other but emphasis different aspects. Is this not just what we see in our everyday world? From one perspective there are just physical objects, but from another there are mental objects as well, and so many anthropocentric perspectives - hot, far, large...

    Which form is the correct form? Is it It from Bit or the other way, or indeed some completely different way, or are there multiple interpretations (which is necessarily the case as touched on in my essay) none of which can be said to have priority (some people will recognise this as a solution to the mind body problem, but I'll leave that for next year's essay and my book 'The Armchair Universe' when it is finished).

    I have no problem with your argument, but pick out some aspects that lead to questions:

    Wheeler said:

    'We have clues, clues most of all in the writings of Bohr, but not answers ... Are billions upon billions of acts of observer-participancy the foundation of everything? We are about as far as we can today from knowing enough about the deeper machinery of the universe to answer this question. Increasing knowledge about detail has brought an increasing ignorance about the plan.'

    Lovely choice of quote. Seeking detail is to move on from unstable foundations (Hume, Kant, Popper) hoping the edifice will prove itself strong enough to compensate for the instability. Parmenides and Zeno stamp their feet! One must first find a foundation for change, and the idea that humankind is forever cut off from knowledge of reality is a flawed argument. First understand the machinery, and what brings the machinery that drives change, and so allows a universe that does not collapse under its own inconsistencies. That was my intent. And one wonders - how can the universe come full born, immediately following such complex rules. Whence spacetime? What is spacetime? These are the true foundational questions, of which It from Bit is a human-centered assumption.

    Bell says:

    'In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that a theory could not be Lorentz invariant.'

    This idea of Bell, and those who accept his argument, is very empiricist, though most will not see it. In a Harmony Set interpretation one might consider that what is really happening is that when two structures interact such that the polarity of one quantum of an entangled pair is realised, then, under equivalence, the totality of the system must be preserved. Given that in the Harmony Set a change is global, then automatically (without wanting to invent an entire 3-space physics to match this, but relying on the GPE) as a simple matter of equivalence to the pre-existing system the other photon will have the appropriate polarity. Otherwise the system would not comply with the GPE, which is absolutely impossible, at least from the point of Endpoint Skepticism (hence, absolutely for everyone else, as a matter of intellectual honesty). The only thing that might change the outcome would be if the evolving generation of new structure created a new localised variation that affected the result in some way (but this is a step too far for the present).

    The aspect that interests me, though I don't really see how you are connecting the concept, is your thought that a compatibility (i. e., commutativity) diagram of observables has a kind of engine that drives it: a dessin d'enfant (a child's drawing). This is a big cruncher for me, because I don't see how one has stepped across from the mathematician who is describing a connection (the same bother as with theories of physics) to an ontological force or power such as I attribute to the GPE. I wonder, if a dessin d'enfant is a bipartite graph embedded on an oriented surface, where did the surface originate, how did the surface find its orientation? These are, to me, the seriously foundational questions. This does not make your analysis at all incorrect. Unfortunately, under the GPE and its implied globalized bundling problem, not only does the universe collapse to a single minimally simple omnet, all of mathematics went down the tube with it. To develop the Harmony Set required that I reinvent a mathematics with it, and show how it aligns to contemporary mathematics, which it does, but only to up to a certain point. In doing so, infinities and limits and associated problems fall away. Of course there is a lot more work required here by me and others who might spend the time to understand this rather fascinating Harmony Set, and its implications.

    Apologies for the length of my response. This is the short version!

    Excellent effort,

    Best wishes,

    Stephen Anastasi

    Dear Stephen,

    As you gave a perfect summary of what I did, I don't have much to say.

    You write

    1. "not only does the universe collapse to a single minimally simple omnet, all of mathematics went down the tube with it.",

    The translation of this sentence would be the Belyi theorem (see the step 3 in my Sec. 2 giving the definition of a child's drawing) and the property that the child's drawing D itself is the preimage of the segment [0,1], that is D=f^-1([0,1]), where the Belyi function f corresponding to D is a rational function. All black vertices of D are the roots of the equation f(x)=0, the multiplicity of each root being equal to the degree of the corresponding vertex. Similarly, all white vertices are the roots of the quation f(x)=1. Inside each face, there exits a single pole, that is a root of the equation f(x)=\infty. Besides 0, 1 and \infty, there are no other critical value of f.

    Sorry about the technicalities.

    2. "the thought that a compatibility (i. e., commutativity) diagram of observables has a kind of engine that drives it: a dessin d'enfant (a child's drawing). "

    Yes, exactly. I leave you free to translate it in the GPE language. The point is that you can have many 'engines' for a given compatibility diagram, a kind of redundancy. For your example of the 3-simplex, e.g. the tetrahedron, I just checked that there are 6 distinct dessins/engines, for the 4-simplex, e.g. the 5-cell, there are 13 distinct dessins/engines that can be built with the cartographic group C2+ as the constructor [my equation(1)]. It would be interesting to understant what means this non-bijection in your approach.

    3. Orientabilty: we need an oriented surface like the Riemann sphere, or a torus, not a Möbius strip (that is not oriented). Thus the dessin is more than a graph and corresponds to a permutation group P with two generators, as given in my step 2 of Sec. 2.

    One needs to develop some familiarity with these concepts, then they become natural.

    I anticipate an unexpected and fascinating complementarity between your approach an the one based on Grothendieck's concepts.

    Thank you for your enthusiasm about this work.

    Michel

    Dear Michel

    Game with {0,1,Inf.} let me find out phenomenon of 18 degrees on the tangent plane.

    Could you please explain me reason of this effect. I see you are expert on this area.

    All the best

    Yuri

      Dear Yuri,

      Following your question on my page, I partially answered in my post above.

      "Yes, 20 vertices in the dodecahedron, a proposed model for the fluctuations of the cosmic microwave background (J. P. Luminet). I like Week's paper because it explains Klein's model of the platonic solids from the Riemann sphere

      http://arxiv.org/abs/math/0502566

      The 10 vertices of half a dodecahedron corresponds to your number 18=180/10 and you have it at the end of my essay as a model of the pentagram (or its complement: the Petersen graph) on the real projective plane."

      I don't know if one can encode your 18 degrees =180/10 on some representation of the pentagram. This would be fascinating. Neither the pentagram nor its complement graph can be seen as built from a 'dessin d'enfant' that needs to be drawn on an oriented surface, as I explain at the end of my essay. But the pentagram graph can also be represented as the Desargues configuration (not shown in the essay)

      http://en.wikipedia.org/wiki/Desargues_configuration

      Th

      e latter may be built/stabilized by a dessin d'enfant (in fact many do the job) on the Riemann sphere. When I go to them, in a next publication, I will think about your observation.

      Apart from the possible link to the Grothendieck's dessins, I found your observation very stimulating and will rate your essay accordingly.

      All the best,

      Michel

      Dear Michel and All,

      I am attaching the iDNASeries.bmp that I have envisioned and how it shows the DNA structure in its sequence.

      I give you all a cosmological iSeries which spans the entire numerical spectrum from -infinity through 0 to +infinity and the simple principle underlying it is sum of any two consecutive numbers is the next number in the series. 0 is the base seed and i can be any seed between 0 and infinity.

      iSeries always yields two sub semi series, each of which has 0 as a base seed and 2i as the first seed.

      One of the sub series is always defined by the equation

      Sn = 2 * Sn-1 + Sigma (i=2 to n) Sn-i

      where S0 = 0 and S1 = 2 * i

      the second sub series is always defined by the equation

      Sn = 3 * Sn-1 -Sn-2

      where S0 = 0 and S1 = 2 * i

      Division of consecutive numbers in each of these subseries always eventually converges on 2.168 which is the Square of 1.618.

      Union of these series always yields another series which is just a new iSeries of a 2i first seed and can be defined by the universal equation

      Sn = Sn-1 + Sn-2

      where S0 = 0 and S1 = 2*i

      Division of consecutive numbers in the merged series always eventually converges on 1.618 which happens to be the golden ratio "Phi".

      Fibonacci series is just a subset of the iSeries where the first seed or S1 =1.

      Examples

      starting iSeries governed by Sn = Sn-1 + Sn-2

      where i = 0.5, S0 = 0 and S1 = 0.5

      -27.5 17 -10.5 6.5 -4 2.5 -1.5 1 -.5 .5 0 .5 .5 1 1.5 2.5 4 6.5 10.5 17 27.5

      Sub series governed by Sn = 2 * Sn-1 + Sigma (i=2 to n) Sn-i

      where S0 = 0 and S1 = 2i = 1

      0 1 2 5 13 34 ...

      Sub series governed by Sn = 3 * Sn-1 - Sn-2

      where S0 = 0 and S1 = 2i = 1

      0 1 3 8 21 55 ...

      Merged series governed by Sn = Sn-1 + Sn-2 where S0 = 0 and S1 = 2i = 1

      0 1 1 2 3 5 8 13 21 34 55 ...... (Fibonacci series is a subset of iSeries)

      The above equations hold true for any value of I.

      As per Antony Ryan's suggestion, I searched google to see how Fibonacci type series can be used to explain Quantum Mechanics and General Relativity and found an interesting article.

      http://msel-naschie.com/pdf/The-Fibonacci-code-behind-super.pdf

      Now that I split the Fibonacci series in to two semi series, seems like each of the sub semi series corresponds to QM and GR and together they explain the Quantum Gravity. Seems like this duality is a commonality in nature once relativity takes effect or a series is kicked off from a basic singularity. The only commonality between the two series is at the base seed 0 (singularity) and first seed 1, which are the bits in our binary system.

      Its also interesting to see the singularity is in the base seed of zero and how it is all pervasive all through out the DNA structure in the attached image. I have been telling that I is that nothing which dwells in everything and this DNA structure seems to prove that notion. Singularity is right with in the duality. Absolute is right with in the relativity. This proves that both of these states of singularity and duality are interconnected and are the source of life.

      Love,

      Sridattadev.Attachment #1: 7_iDNASeries.bmp

      Hello Michel

      Richard Feynman in his Nobel Acceptance Speech (http://www.nobelprize.org/nobel_prizes/physics/laureates/1965/feynman-lecture.html)

      said: "It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms that are not apparently identical at first, but with a little mathematical fiddling you can show the relationship. And example of this is the Schrodinger equation and the Heisenberg formulation of quantum mechanics. I don't know why that is - it remains a mystery, but it was something I learned from experience. There is always another way to say the same thing that doesn't look at all like the way you said it before. I don't know what the reason for this is. I think it is somehow a representation of the simplicity of nature."

      I too believe in the simplicity of nature, and I am glad that Richard Feynman, a Nobel-winning famous physicist, also believe in the same thing I do, but I had come to my belief long before I knew about that particular statement.

      The belief that "Nature is simple" is however being expressed differently in my essay "Analogical Engine" linked to http://fqxi.org/community/forum/topic/1865 .

      Specifically though, I said "Planck constant is the Mother of All Dualities" and I put it schematically as: wave-particle ~ quantum-classical ~ gene-protein ~ analogy- reasoning ~ linear-nonlinear ~ connected-notconnected ~ computable-notcomputable ~ mind-body ~ Bit-It ~ variation-selection ~ freedom-determinism ... and so on.

      Taken two at a time, it can be read as "what quantum is to classical" is similar to (~) "what wave is to particle." You can choose any two from among the multitudes that can be found in our discourses.

      I could have put Schrodinger wave ontology-Heisenberg particle ontology duality in the list had it comes to my mind!

      Since "Nature is Analogical", we are free to probe nature in so many different ways. And you have touched some corners of it.

      Regards,

      Than Tin

      Dear Michel,

      A good essay. A bit technical though and as a result of my classical view of physics I still find remote influences difficult to digest. In this regard, being likely that you have a relational view of space, I have a question I will be grateful for an answer. I am asking other top scientists on this forum just for my enlightenment. Are you by chance suggesting that what decides whether a centrifugal force would act between two bodies in *constant relation*, would not be the bodies themselves, since they are at fixed distance to each other, nor the space in which they are located since it is a nothing, but by a distant sub-atomic particle light-years away in one of the fixed stars in whose reference frame the *constantly related* bodies are in circular motion as suggested by Mach's principle?

      You can reply me here or on my blogmy blog. And pardon my naive view of physics.

      Accept my best regards,

      Akinbo

        Dear Akimbo,

        First thank you for your kind interest. This post is a tentative response to your question having in mind your very pedagogical essay about monads.

        You: Monad - a fundamental unit of geometry; that of which there is no part;...

        i. extended objects, not further extensible or compressible.

        ii. they are fundamental and not a composite of other 'its'.

        iii. they are the fundamental units of geometry, both body and space.

        Me: The points of the geometries I am dealing with could perhaps be seen as monads. (e.g. the 7 points of the Fano plane in Fig. 1a. Then in Fig 1b the same points are extended as edges).

        You: monads are 'it' and their change between two alternate states is the 'bit'.

        Me: Agree. One edge in Fig. 2b is either black (bit 1) or white (bit 0).

        You: the two-valued attribute

        denoted by 0 and 1 must really occupy the deepest part of the basement!

        Me: Agree, but as two elements of a triple {0,1, \infty}.

        Stephen Anastasi: (above) "not only does the universe collapse to a single minimally simple omnet, all of mathematics went down the tube with it.",

        Me: The translation of this sentence would be the Belyi theorem (see the step 3 in my Sec. 2 giving the definition of a child's drawing) and the property that the child's drawing D itself is the preimage of the segment [0,1], that is D=f^-1([0,1]), where the Belyi function f corresponding to D is a rational function. All black vertices of D are the roots of the equation f(x)=0, the multiplicity of each root being equal to the degree of the corresponding vertex. Similarly, all white vertices are the roots of the quation f(x)=1. Inside each face, there exits a single pole, that is a root of the equation f(x)=\infty. Besides 0, 1 and \infty, there are no other critical value of f.

        Sorry about the technicalities.

        You: But what about the space then?

        Me: Although the model of dessins d'enfants may be applied differently, practically, in my essay, it corresponds to the (Heisenberg) space of quantum observables such as the Pauli spin matrices, or tensorial agregates of them. You would say that they cannot be monads in such a case! But they cannot be divided in the sense that the parties (let's say Alice, Bob and Charlie for the three-partite case, I used the Fano plane for this case) are linked once for all, whatever state they share, entangled or not. I don't know about Mach, I have to think more.

        I am sure that it does not dissolve your question, at least it gives you a hint, hopefully, of what this kind of maths may do.

        Please rate my essay if you like it.

        Best wishes,

        Michel

        Dear Michael your essay is very good

        The symmetry, the groups and their intimate relationship with the information; whose culmination, in regard to the observation process is the Bell theorem. His essay is technical for the average of the overall level of this competition. I especially liked your exposure on the geometric and topological aspects, which without doubt are directly connected to the concept of the information and its mathematical quantification.

        I think you'll agree with me that only by pure numbers generated by the ratios of the masses, fundamental constants, etc., only in this way will be possible to advance the unification of physics. Physicists have before their eyes a theory of strings that is already developed, so basic, in the foundations of quantum theory. I refer to model a rope in a box. In my work I have shown that a string compactified on seven dimensions, finding the probability for a dimension, a single string, it is the ratio of the Higgs boson mass in relation to the value of the Higgs vacuum. It is no coincidence that the geometry of the tetrahedron this closely related to the spins and the electric charges, because: no tetrahedral angle 1 = cos (spin 2), 1 tetrahedral angle cos = cos (spin 1/2), and so angle GUT unification = cos (spin 3/2). The sum of the cosines of all spins has, among others, this property: [SUM (cos (all spins)) / 2] ^ 2 x 246.221202 = ~ 127.2 GeV (Higgs boson mass). I am Going to more carefully read your essay, rate it certainly high. Thank you very much. Regards