Dear Michel,

I've read your essay already when it appeared on the arXiv, and have since been waiting for a chance to comment on it. Having done some work on quantum contextuality myself, I was naturally very curious about your ideas, and though I'll need a bit more time to digest the mathematics, I must say I'm very intrigued.

From the title, I at first assumed you were going to...

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Dear Michel,

I've read your essay already when it appeared on the arXiv, and have since been waiting for a chance to comment on it. Having done some work on quantum contextuality myself, I was naturally very curious about your ideas, and though I'll need a bit more time to digest the mathematics, I must say I'm very intrigued.

From the title, I at first assumed you were going to consider the observation that the Lovasz theta function, a measure for a graph's Shannon capacity, gives the quantum violation of contextuality inequalities in at least some cases (something realized first, I think, by Cabello and co-workers). But while you also talk about the Shannon capacity, to me at least the relationship seems not obvious.

First of all, I think your observation that "Wheeler's observer-participancy is contextual" is spot on: in fact, this is essentially the lesson of Bohr's complementarity---we cannot describe all our observations within one single classical picture, just as, in contextuality, we cannot give a single probability distribution (or truth-valuation) for all observables.

However, I think I've missed the main point, probably, which is the precise connection between the dessins and contextuality. Usual proofs of the Kochen-Specker theorem rely on finding a set of vectors in Hilbert space such that the associated graph is not 2-colorable, that is, one cannot find a truth valuation. What do the dessins tell you about this? (Apologies if it's obvious and I just haven't been paying attention.)

Also, on an unrelated note, since I know you've done some work on the black hole/qubit correspondence: in your opinion, does the correspondence tell us something 'deep' about nature, or is it just a mathematical curiosity? I used to be pretty skeptical, thinking that it's probably just based on the coincidence that the group SL(2,C) crops up in both context, but now that entanglement is wormholes ;-), why not have qubits be black holes?

Cheers, and my best wishes for the contest,

Jochen

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Michel,

I reread your paper again this last Sunday. The desin d'enfant leads at the end to Mermin's pentagons. These are of course an aspect of the Kochen-Specker theorem. This is of course the main theorem on contextuality in QM. In my paper I discuss the quantum homotopies of associators at various dimensions, which are pentagonal systems. I copy this post on my essay blog page, so...

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Michel,

I reread your paper again this last Sunday. The desin d'enfant leads at the end to Mermin's pentagons. These are of course an aspect of the Kochen-Specker theorem. This is of course the main theorem on contextuality in QM. In my paper I discuss the quantum homotopies of associators at various dimensions, which are pentagonal systems. I copy this post on my essay blog page, so you can respond to this there as well.

I notice you have considerable interest in the G_2 group, which is the automorphism of the E8 group. The F_4 group is a centralizer in E8, whereby G_2 action keep it fixed; the elements of F_4 and G_2 commute.

The Kochen-Specker theorem is connected with the F_4 group, or the 24 cell. The 117 projectors with the original KS theorem in 3-dim Hilbert space is simplified by considering a four dimensional Hilbert space, or a system of 4 qubits. This involves only 18 projector operators. The space 24-cells is a system of root vectors for the F_4 group. Each root vector is paired with its negative to define a line through the origin in 4d space. These 24 lines are the 24 rays of Peres. The root vectors are

1 (2,0,0,0) 2 (0,2,0,0) 3 (0,0,2,0) 4 (0,0,0,2)

5 (1,1,1,1) 6 (1,1,-1,-1) 7 (1,-1,1,-1) 8 (1,-1,-1,1)

9 (-1,1,1,1) 10 (1,-1,1,1) 11 (1,1,-1,1) 12 (1,1,1,-1)

13 (1,1,0,0) 14 (1,-1,0,0) 15 (0,0,1,1) 16 (0,0,1,-1)

17 (0,1,0,1) 18 (0,1,0,-1) 19 (1,0,1,0) 20 (1,0,-1,0)

21 (1,0,0,-1) 22 (1,0,0,1) 23 (0,1,-1,0) 24 (0,1,1,0)

(I hope this table works out here) Consider these as 24 quantum states |ψ_i>, properly normalized, in a 4 dimensionl Hilbert Space e.g. it might be a system of two qubits. For each state we can define a projection operator

P_i = |ψ_i)(ψ_i| --- I have to use parentheses because carrot signs fail in this blog.

P_i are are Hermitian operators with three eigenvlaues of 0 and one of 1. They can be considered as observables and we could set up an experimental system where we prepare states and measure these observables to check that they comply with the rules of quantum mechanics. There are sets of 4 operators which commute because the 4 rays they are based on are mutually orthogonal. An example would be the four operators P_1, P_2, P_3, P4.

Quantum mechanics tells us if we measure these commuting observables in any order we will end up with a state which is a common eigenvector i.e. one of the first four rays. The values of the observables will always be given by 1,0,0,0 in some order. This can be checked experimentally. There exist 36 sets of 4 different rays that are mutually orthogonal, but we just need 9 of them as follows:

{P2, P4, P19, P20}

{P10, P11, P21, P24}

{P7, P8, P13, P15}

{P2, P3, P21, P22}

{P6, P8, P17, P19}

{P11, P12, P14, P15}

{P6, P7, P22, P24}

{P3, P4, P13, P14}

{P10, P12, P17, P20}

At this point you need to check two things, firstly that each of these sets of 4 observables are mutually commuting because the rays are othogonal, secondly that there are 18 observables each of which appears in exactly two sets.

Now assume there is some hidden variable theory which explains this system and which reproduces all the predictions of quantum mechanics. At any given moment the system is in a definite state, and values for each of the 18 operators are determined. The values must be 0 or 1. with the rules they are equal to 1 for exactly one observable in each of the 9 sets, the other three values in each set will be 0. Consequently, there must be nine values set to one overall. This leads to a contradiction, for each observable appears twice so which ever observables have the value of 1 there will always be an even number of ones in total, and 9 is not even.

To add another ingredient into this mix I reference , which illustrates how the Kochen-Specker result is an aspect of the 24-cell. The 24-cell has a number of representations. The full representation is the F_4 group with 1154 Hurwitz quaternions. The other is the B_4, which is the 16 cell Plus an 8-cell, and the other is D_4 which is three 8-cells. The more general automorphism is then F_4. The quotient between the 52 dimensional F_4 and the 36 dimensional so(9) ~ B_4 defines the short exact sequence

F_4/B_4:1 --> spin(9) --> F_{52\16} --> {\cal O}P^2 --> 1,

where F_{52\16} means F_4 restricted to 36 dimensions, which are the kernel of the map to the 16 dimensional Moufang or Cayley plane OP^2. The occurrence of 36 and 9 is no accident, and this is equivalent to the structure used to prove the KS theorem.

F_4 is the isometry group of the projective plane over the octonions. There are extensions to this where the bi-ocotonions CxO have the isometry group E_6, HxO has E_7 and OxO has E_8. This forms the basis of the "magic square." F_4 plays a prominent role in the bi-octonions, which is J^3(O) or the Jordan algebra as the automorphism which preserves the determinant of the Jordan matrix

The exceptional group G_2 is the automorphism on O, or equivalently that F_4xG_2 defines a centralizer on E_8. The fibration G_2 --> S^7 is completed with SO(8), where the three O's satisfy the triality condition in SO(8). The G_2 fixes a vector basis in S^7 according to the triality condition on vectors V \in J^3(O) and spinors θ in O, t:Vxθ_1xθ_2 --> R. The triality group is spin(8) and a subgroup spin(7) will fix a vector in V and a spinor in θ_1. To fix a vector in spin(7) the transitive action of spin(7) on the 7-sphere with spin(7)/G_2 = S^7 with dimensions

dim(G_2) = dim(spin(7)) - dim(S^7) = 21 - 7 = 14.

The G_2 group in a sense fixes a frame on the octonions, and has features similar to a gauge group. The double covering so(O) ~= so(8) and the inclusion g_2 \subset spin(8) determines the homomorphism g_2 hook--> spin(8) --> so(O). The 1-1 inclusion of g_2 in so(O) maps a 14 dimensional group into a 28 dimensional group. This construction is remarkably similar to the moduli space construction of Duff et al. .

Cheers LC

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Dear

Thank you for presenting your nice essay. I saw the abstract and will post my comments soon.

So you can produce material from your thinking. . . .

I am requesting you to go through my essay also. And I take this opportunity to say, to come to reality and base your arguments on experimental results.

I failed mainly because I worked against the main stream. The...

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Dear

Thank you for presenting your nice essay. I saw the abstract and will post my comments soon.

So you can produce material from your thinking. . . .

I am requesting you to go through my essay also. And I take this opportunity to say, to come to reality and base your arguments on experimental results.

I failed mainly because I worked against the main stream. The main stream community people want magic from science instead of realty especially in the subject of cosmology. We all know well that cosmology is a subject where speculations rule.

Hope to get your comments even directly to my mail ID also. . . .

Best

=snp

snp.gupta@gmail.com

http://vaksdynamicuniversemodel.b
logspot.com/

Pdf download:

http://fqxi.org/community/forum/topic/essay-downloa
d/1607/__details/Gupta_Vak_FQXi_TABLE_REF_Fi.pdf

Part of abstract:

- -Material objects are more fundamental- - is being proposed in this paper; It is well known that there is no mental experiment, which produced material. . . Similarly creation of matter from empty space as required in Steady State theory or in Bigbang is another such problem in the Cosmological counterpart. . . . In this paper we will see about CMB, how it is generated from stars and Galaxies around us. And here we show that NO Microwave background radiation was detected till now after excluding radiation from Stars and Galaxies. . . .

Some complements from FQXi community. . . . .

A

Anton Lorenz Vrba wrote on May. 4, 2013 @ 13:43 GMT

……. I do love your last two sentences - that is why I am coming back.

Author Satyavarapu Naga Parameswara Gupta replied on May. 6, 2013 @ 09:24 GMT

. . . . We should use our minds to down to earth realistic thinking. There is no point in wasting our brains in total imagination which are never realities. It is something like showing, mixing of cartoon characters with normal people in movies or people entering into Game-space in virtual reality games or Firing antimatter into a black hole!!!. It is sheer a madness of such concepts going on in many fields like science, mathematics, computer IT etc. . . .

B.

Francis V wrote on May. 11, 2013 @ 02:05 GMT

Well-presented argument about the absence of any explosion for a relic frequency to occur and the detail on collection of temperature data……

C

Robert Bennett wrote on May. 14, 2013 @ 18:26 GMT

"Material objects are more fundamental"..... in other words "IT from Bit" is true.

Author Satyavarapu Naga Parameswara Gupta replied on May. 14, 2013 @ 22:53 GMT

1. It is well known that there is no mental experiment, which produced material.

2. John Wheeler did not produce material from information.

3. Information describes material properties. But a mere description of material properties does not produce material.

4. There are Gods, Wizards, and Magicians, allegedly produced material from nowhere. But will that be a scientific experiment?

D

Hoang cao Hai wrote on Jun. 16, 2013 @ 16:22 GMT

It from bit - where are bit come from?

Author Satyavarapu Naga Parameswara Gupta replied on Jun. 17, 2013 @ 06:10 GMT

….And your question is like asking, -- which is first? Egg or Hen?— in other words Matter is first or Information is first? Is that so? In reality there is no way that Matter comes from information.

Matter is another form of Energy. Matter cannot be created from nothing. Any type of vacuum cannot produce matter. Matter is another form of energy. Energy is having many forms: Mechanical, Electrical, Heat, Magnetic and so on..

E

Antony Ryan wrote on Jun. 23, 2013 @ 22:08 GMT

…..Either way your abstract argument based empirical evidence is strong given that "a mere description of material properties does not produce material". While of course materials do give information.

I think you deserve a place in the final based on this alone. Concise - simple - but undeniable.

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Dear Michel Planat,

I have been reading a paper by Maldacena and Susskind. This is a fairly bold paper that advances a pretty speculative idea. In keeping with my paper, which advances an associativity issue with quantum fields near the horizon , this seems to have a higher associator structure that is five fold. The most elementary is a three way associator (ab)c – a(bc) = [a,b,c],...

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Dear Michel Planat,

I have been reading a paper by Maldacena and Susskind. This is a fairly bold paper that advances a pretty speculative idea. In keeping with my paper, which advances an associativity issue with quantum fields near the horizon , this seems to have a higher associator structure that is five fold. The most elementary is a three way associator (ab)c – a(bc) = [a,b,c], that defines a fundamental form for a quantum homotopy but a five fold system is a second homotopy group, The fluctuations across the inner and outer horizons of a black hole results in a 5-fold associative system. This is also a pentagonal system for the Kochen-Specker theorem.

The Susskind-Maldacena paper requires there to exist two black holes with the same BPS charge and angular momentum. Even if such black hole pairs exist it is not clear how they become EPR pairs. In most standard QM systems it requires some sort of mutual interaction to establish an EPR pair. To argue that a black hole is an EPR pair with another it means there exist in the multiverse some other black hole with an identical quantum configuration. This demands a multiverse landscape, for it is probably not likely this exists within the observable universe.

The idea is interesting though. The odd thing about this idea, which has been making the rounds these days, is it makes some physical sense of the interior of a black hole. Maldacena and Susskind work with a Schwarschild black hole. There idea is there are entanglements between black holes through wormhole. This sort of multiply connected topology does exist with black holes. A BPS or rotating black hole has two event horizons at r_{+/-} = m +/- sqrt{m^2 – Q^2}, where Q can be either a gauge charge or angular momentum parameter. There are then two event horizons and three regions; region I being where r > r_+, region II where r_+ > r > r_-, and region III where r < r_-. These regions are timelike, spacelike and timelike respectively. The region III has been regarded as suspect, since the r_- event horizon has a pile up of UV divergent radiation or quantum fields that implies the horizon is physically singular. This region has been regarded as a sort of mathematical fiction. However, maybe this region does play some sort of physical role.

The Kerr black hole appears in the first diagram is attach. The second attachment is a Penrose diagram of the Kerr black hole. It is evident that upon leaving region I (the normal timelike universe) the observer enters region II which is shared by another black hole. The horizon is split so the observer may enter two III type regions. The ring singularity in region III is where x^2 + y^2 = Q^2. In this III region the geodesics around the ring are similar to the flow of a hurricane around the eye. Also the singularity is repulsive; you can’t reach it. In complex coordinates this singularity has a branch cut. If you make a complete orbit around the ring there is a branch cut which pops you into an identical copy of the III region as branch cuts link Riemann sheets of the complex plane. The interior region of a BH is naturally in a sense a sort of wormhole, and this approach might segue into this equivalency between wormhole multiple connectivity and entanglements. This interior region may physically play the role as an “entangler.”

The argument for a firewall associated with a black hole concerns entanglement swaps between states in region I and II. These states are H_h ∊ I for Hawking radiation, H_s ∊ I for states on or near the stretched horizon associated with r_+ and interior states H_n ∊ II for states near the horizon and H_s ∊ II on the singularity. In the Kerr-Newman metric this singularity is identified with r_-. Physically r_- is a region with UV divergent quantum fields. However, we may remove this as a singularity if this divergence is regulated in some manner. That of course is an open question. The singularity states H_s are split into H_r- for states in the region II near r_- and those in the core region H_{III}. We now have a 5-fold system of states.

I have argued that three quantum states along a null ray are an associated quantum system. If the middle state is very near the horizon and the horizon has a quantum uncertainty the entanglement between the three states is an associator system [a,b,c] = (ab)c – a(bc). In quantum homotopy this is a fundamental group π^1. A 5 fold system is a set of states in a permuting structure that gives π^2, and there is a higher system that defines the Stasheff polytope π^3, and it goes on from there. The five fold system is equivalent to the pentagonal arrangement of states in the Kochen-Specker theorem in four dimensions. The associator system is then a form of the KS theorem. The KS theorem in 4 dimensions is a result of a three color graph with pentagonal symmetry.

If there is then this sort of black hole entanglement that is equivalent to a worm hole it may then be of this nature. Again the interior region, if it is physically real, is such that an orbit around the singularity pops the geodesic into an equivalent spacetime. It is a form of the multiple sheets of the complex plane connected by a branch cut. The argument for spacetime would be rather difficult, for this is not an elementary conformal argument in two dimension, but four dimensions.

Lawrence B. Crowell

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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...

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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

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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...

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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

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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...

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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-behin
d-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.

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Hi Michel,

Your very interesting essay, taking us right to the foundations, raises some questions. You wrote:

> This implies the non-existence of the Belyi map and puts three-qubit contextuality on a qualitatively different footing when compared with the two-qubit case.

It seems that your quest to model 3-qubit contextuality has an unhappy ending in your essay. Do you thus...

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Hi Michel,

Your very interesting essay, taking us right to the foundations, raises some questions. You wrote:

> This implies the non-existence of the Belyi map and puts three-qubit contextuality on a qualitatively different footing when compared with the two-qubit case.

It seems that your quest to model 3-qubit contextuality has an unhappy ending in your essay. Do you thus conclude that (some? all?) mechanisms that explain contextuality for 2-qubit systems will not explain it for 3-qubit systems?

What avenues are you now taking to explore 3-qubit contextuality? (Yes, yes, I know I should read your recent papers... after the contest, please...) I am hoping there is another chapter to come in your story... with finally, a happy ending. I very much like the idea that you mention of lifting the Riemann sphere to S3 via the inverse Hopf Fibration. I will put some more comments about this on my blog.

> To find the corresponding Belyi map seems to be a challenging math problem.

My thought was there might be a possibility of easier results if we restrict white and black points to lie at k-rational points: Consider Q(phi), the algebraic extension of the rationals by the golden ratio. These numbers are able to provide cartesian coordinates for all the vertices of Platonic solids, and many other polytopes besides. These could be considered as k-rational points within larger fields, but also as a field on their own. (For such fields, Falting's Theorem should apply and might possibly be useful.) But I was mainly wondering if anyone had looked at the techniques you describe with such k-rational points and fields in mind.

Anyway, if they prove useful, I imagined that such diagrams (living in S3?) you could call "Dessins d'Or"... and that they could lead you to a happy ending. A topic for next year's essay, perhaps?

Hugh

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Hi Michel,

So it appears that the FQXI database has been reset and my comments have disappeared... I will add them back in. As I said before:

Your very interesting essay, taking us right to the foundations, raises some questions. You wrote:

> This implies the non-existence of the Belyi map and puts three-qubit contextuality on a qualitatively different footing when compared...

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Hi Michel,

So it appears that the FQXI database has been reset and my comments have disappeared... I will add them back in. As I said before:

Your very interesting essay, taking us right to the foundations, raises some questions. You wrote:

> This implies the non-existence of the Belyi map and puts three-qubit contextuality on a qualitatively different footing when compared with the two-qubit case.

It seems that your quest to model 3-qubit contextuality has an unhappy ending in your essay. Do you thus conclude that (some? all?) mechanisms that explain contextuality for 2-qubit systems will not explain it for 3-qubit systems?

What avenues are you now taking to explore 3-qubit contextuality? (Yes, yes I know I should read your recent papers... after the contest, please...) I am hoping there is another chapter to come in your story... with finally, a happy ending. I do like the idea that you mention of lifting the Riemann sphere to S3 via the inverse Hopf Fibration. I will put some more comments about this on my blog.

> To find the corresponding Belyi map seems to be a challenging math problem.

My thought was there might be a possibility of easier results if we restrict white and black points to lie at k-rational points:

Consider Q(phi), the algebraic extension of the rationals by the golden ratio. These numbers are able to provide cartesian coordinates for all the vertices of Platonic solids, and many other polytopes besides. These could be considered as k-rational points within larger fields, but also as a field on their own. (For such fields, Falting's Theorem should apply and might possibly be useful.) But I was mainly wondering if anyone had looked at the techniques you describe with such k-rational points and fields in mind.

Anyway, if they prove useful, I imagined that such diagrams (living in S3?) might be called "Dessins d'Or"... and eventually lead to a happy ending. Next year's essay, perhaps?

Hugh

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Late-in-the-Day Thoughts about the Essays I’ve Read

I am sending to you the following thoughts because I found your essay particularly well stated, insightful, and helpful, even though in certain respects we may significantly diverge in our viewpoints. Thank you! Lumping and sorting is a dangerous adventure; let me apologize in advance if I have significantly misread or misrepresented...

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Late-in-the-Day Thoughts about the Essays I’ve Read

I am sending to you the following thoughts because I found your essay particularly well stated, insightful, and helpful, even though in certain respects we may significantly diverge in our viewpoints. Thank you! Lumping and sorting is a dangerous adventure; let me apologize in advance if I have significantly misread or misrepresented your essay in what follows.

Of the nearly two hundred essays submitted to the competition, there seems to be a preponderance of sentiment for the ‘Bit-from-It” standpoint, though many excellent essays argue against this stance or advocate for a wider perspective on the whole issue. Joseph Brenner provided an excellent analysis of the various positions that might be taken with the topic, which he subsumes under the categories of ‘It-from-Bit’, ‘Bit-from-It’, and ‘It-and-Bit’.

Brenner himself supports the ‘Bit-from-It’ position of Julian Barbour as stated in his 2011 essay that gave impetus to the present competition. Others such as James Beichler, Sundance Bilson-Thompson, Agung Budiyono, and Olaf Dreyer have presented well-stated arguments that generally align with a ‘Bit-from-It’ position.

Various renderings of the contrary position, ‘It-from-Bit’, have received well-reasoned support from Stephen Anastasi, Paul Borrill, Luigi Foschini, Akinbo Ojo, and Jochen Szangolies. An allied category that was not included in Brenner’s analysis is ‘It-from-Qubit’, and valuable explorations of this general position were undertaken by Giacomo D’Ariano, Philip Gibbs, Michel Planat and Armin Shirazi.

The category of ‘It-and-Bit’ displays a great diversity of approaches which can be seen in the works of Mikalai Birukou, Kevin Knuth, Willard Mittelman, Georgina Parry, and Cristinel Stoica,.

It seems useful to discriminate among the various approaches to ‘It-and-Bit’ a subcategory that perhaps could be identified as ‘meaning circuits’, in a sense loosely associated with the phrase by J.A. Wheeler. Essays that reveal aspects of ‘meaning circuits’ are those of Howard Barnum, Hugh Matlock, Georgina Parry, Armin Shirazi, and in especially that of Alexei Grinbaum.

Proceeding from a phenomenological stance as developed by Husserl, Grinbaum asserts that the choice to be made of either ‘It from Bit’ or ‘Bit from It’ can be supplemented by considering ‘It from Bit’ and ‘Bit from It’. To do this, he presents an ‘epistemic loop’ by which physics and information are cyclically connected, essentially the same ‘loop’ as that which Wheeler represented with his ‘meaning circuit’. Depending on where one ‘cuts’ the loop, antecedent and precedent conditions are obtained which support an ‘It from Bit’ interpretation, or a ‘Bit from It’ interpretation, or, though not mentioned by Grinbaum, even an ‘It from Qubit’ interpretation. I’ll also point out that depending on where the cut is made, it can be seen as a ‘Cartesian cut’ between res extensa and res cogitans or as a ‘Heisenberg cut’ between the quantum system and the observer. The implications of this perspective are enormous for the present It/Bit debate! To quote Grinbaum: “The key to understanding the opposition between IT and BIT is in choosing a vantage point from which OR looks as good as AND. Then this opposition becomes unnecessary: the loop view simply dissolves it.” Grinbaum then goes on to point out that this epistemologically circular structure “…is not a logical disaster, rather it is a well-documented property of all foundational studies.”

However, Grinbaum maintains that it is mandatory to cut the loop; he claims that it is “…a logical necessity: it is logically impossible to describe the loop as a whole within one theory.” I will argue that in fact it is vital to preserve the loop as a whole and to revise our expectations of what we wish to accomplish by making the cut. In fact, the ongoing It/Bit debate has been sustained for decades by our inability to recognize the consequences that result from making such a cut. As a result, we have been unable to take up the task of studying the properties inherent in the circularity of the loop. Helpful in this regard would be an examination of the role of relations between various elements and aspects of the loop. To a certain extent the importance of the role of relations has already been well stated in the essays of Kevin Knuth, Carlo Rovelli, Cristinel Stoica, and Jochen Szangolies although without application to aspects that clearly arise from ‘circularity’. Gary Miller’s discussion of the role of patterns, drawn from various historical precedents in mathematics, philosophy, and psychology, provides the clearest hints of all competition submissions on how the holistic analysis of this essential circular structure might be able to proceed.

In my paper, I outlined Susan Carey’s assertion that a ‘conceptual leap’ is often required in the construction of a new scientific theory. Perhaps moving from a ‘linearized’ perspective of the structure of a scientific theory to one that is ‘circularized’ is just one further example of this kind of conceptual change.

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Hello Michel from Margriet O'Regan from DownUnder !

My research over the years has led me to believe that there are very few geometricians around ! So it's been great to encounter a few here in this essay arena - including Akinbo Ojo & you.

But it has confirmed my belief that few if any persons lay or expert alike, recognise & acknowledge REAL common, ordinary, everyday, garden...

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Hello Michel from Margriet O'Regan from DownUnder !

My research over the years has led me to believe that there are very few geometricians around ! So it's been great to encounter a few here in this essay arena - including Akinbo Ojo & you.

But it has confirmed my belief that few if any persons lay or expert alike, recognise & acknowledge REAL common, ordinary, everyday, garden variety geometrical objects lying all around (& in) us everywhere - rather than the abstract or hypothetical ones which exist only inside mathematicians & theoretical physicists' heads & textbooks !

My claim is not only that 'information' is the full set of geometrical objects present here in our universe but that they are all of the properly real ones present here.

My investigations have led me to believe that there are not any of these real geometrical objects in certain specific places or realms or domains. One of these domains in which no geometrical objects exist is the sub-sub-atomic realm down at the quantum level. I make this conclusion because geometrical objects are strictly 'surface dwelling' entities & do not, because they cannot, exist anywhere but on the surface of some one or another solid object. Whatever it is down there at the quantum level it has no surfaces - therefore no real information.

Space is another place where none of 'my' real geometrical objects exist. I do not believe that space-time itself is curved or warped. I believe that the light that is bent (lensed) around the sun is bent as it is due to the fact that it is passing through the Sun's heliopause & not responding to (non-existent) space-times curvature at all. Einstein did not know of such things as heliopauses or even our own Earth's magnetosphere - which does the same thing (bends light - just a little). The two spacecraft which are currently exiting our Solar system also have been affected by transitting the boundaries of the Sun's gigantic heliopause.

My belief in real geometrical objects gives me the personal advantage of not having to know the maths of 'deep' physics & even though I have read Penrose's 'The Road to Reality : A Complete Guide to the Laws of the Universe' I kind of let the equations 'wash through me' rather than working each out in detail.

And there was for me a very big reward at the end of his book as he confessed after more than one thousand pages of hard work, to not having found 'the answer' at all - not even close !! & that we'd not only better keep looking for it, but do so in significantly different directions from those we have previously taken.

Here is what he said :

On page 1025 in his last chapter ‘Where lies the road to reality ?'

‘It is certainly possible that there are many clues to Nature’s ways hidden in such (modern experimental) data even if we do not properly read them yet. Recall that Einstein’s general relativity was crucially based on his insight (the principle of equivalence) which had been implicit in observational data that had been around since (and before) the time of Galileo, but not full appreciated. The may well be other clues hidden in the immeasurably more extensive modern observations. Perhaps there are even ‘obvious’ ones, before our very eyes, that need to be twisted round and viewed from a different angle, so that a fundamentally new perspective may be obtained concerning the nature of physical reality.

Page 1027 and following.

What is reality ?

As the reader will gather from all this, I do not believe that we have yet found the true ‘road to reality’, despite the extraordinary progress that has been made over two and one half millennia, particularly in the last few centuries. Some fundamentally new insights are certainly needed, Yet, some readers may well still take the view that the road itself may be a mirage. True – so the might argue – we have been fortunate enough to stumble upon mathematical schemes that accord with Nature in remarkable ways, but the unity of Nature as a whole with some mathematical scheme can be no more than a ‘pipe dream’. Others might take the view that the very notion of a ‘physical reality’ with a truly objective nature, independent of how we might choose to look at it, is itself a pipe dream. . . . .

This is a question that has been posed for thousands of years . . . . .

On page 1045 Mr Penrose’s very last paragraph reads :

The spacetime singularities lying at cores of black holes are among the known (or presumed) objects in the universe about which the most profound mysteries remain – and which our present-day theories are powerless to describe. As we have seen ……. There are other deeply mysterious issues about which we have very little comprehension. It is quite likely that the 21st century will reveal even more wonderful insights than those that we have been blessed with in the 20th. But for this to happen, we shall need powerful new ideas, which will take us in directions significiantly different from those currently being pursued. Perhaps what we mainly need is some subtle change in perspective – something that we all have missed . . . .

Mr Penrose did not even mention real geometrical objects let alone consider them to be the (one & only) purveyors of information. So real geometrical objects are at least one of the things that he has 'missed' - nevertheless they are things that are 'before our very eyes' & it will take a rather significant change in perspective if mainstream physics is ever to acknowledge them !!!?

And yes, I can't help repeating what David Deutsch said :

‘I’m speaking to you now : Information starts as some kind of electrochemical signals in my brain, and then it gets converted into other signals in my nerves and then into sound waves and then into the vibrations of a microphone, mechanical vibrations, then into electricity and so on, and presumably will eventually go on the Internet, this something has been instantiated in radically different physical objects that obey different laws of physics. Yet in order to describe this process you have to refer to the thing that has remained unchanged through out the process, which is only the information rather than any obviously physical thing like energy or momentum.’

Answer : David Deutsch’s elusive ‘thing’ is geometric objects plain & simple.

Geometric objects are the only phenomena that can be & routinely are copied / transferred on to consecutive sequences of widely different physical objects – from medium to radically different physical medium to radically different physical medium to radically different physical medium - & yet retain their shape – at least this obtains as to certain mediums as on many others they fade quickly away. Which is why we ourselves choose our mediums with a very careful eye to their ability to carry information (in its native that is geometric form) on themselves with optimum stability.

I know it's late but here are my closing remarks !!!! Thank you for your patience !!! I make them because because I want to emphasize a distinction I did not sufficiently clarify in my essay.

My own investigations have led me to conclude that ‘information’ is NOT digits – no kind nor amount of them (including any that can be extracted from quantum phenomena!), nor how algorithmically-well they may be massaged & shunted through any device that uses them.

Unequivocally they – digits – make for wonderful COUNTING & CALCULATING assistants, witness our own now many & various, most excellent, counting, calculating devices BUT according to my investigations real thinking is an entirely different phenomenon from mere counting, calculating & computing.

For which phenomenon – real thinking – real information is required.

My own investigations led me to discover what I have come to believe real information is & as it so transpires it turns out to be an especially innocuous – not to omit almost entirely overlooked & massively understudied – phenomenon, none other than the sum total of geometrical objects otherwise quite really & quite properly present here in our universe. Not digits.

One grade (the secondary one) of geometrical-cum-informational objects lavishly present here in our cosmos, is comprised of all the countless trillions & trillions of left-over bump-marks still remaining on all previously impacted solid objects here in our universe – that is to say, all of the left-over dents, scratches, scars, vibrations & residues (just the shapes of residues – not their content!) (really) existing here in the universe.

Examples of some real geometrical objects of this secondary class in their native state are all of the craters on the Moon. Note that these craters are – in & of themselves – just shapes – just geometrical objects. And the reason they are, also one & at the same time, informational objects too, can be seen by the fact that each ‘tells a story’ – each advertises (literally) some items of information on its back – each relates a tale of not only what created it but when, where & how fast & from what angle the impacting object descended onto the Moon’s surface. Again, each literally carries some information on its back.

(Note : Not a digit in sight !!)

How we actually think – rather than just count, calculate & compute – with these strictly non-digital entities, specifically these geometrical-cum-informational objects, in precisely the way we do, please see my essay.

I did not make the distinction between computing with digits & real thinking with real information, sufficiently strongly in my essay.

This contest is such a wonderful ‘sharing’ – Wow – & open to amateurs like myself – Wow. How great is that !!! Thank you Foundational Questions Institute !!! What a great pleasure it has been to participate. What a joy to read, share & discuss with other entrants !!!

Margriet O’Regan

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