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**Branko Zivlak**: *on* 4/1/15 at 19:20pm UTC, wrote Dear Michel, From Maudlin's subquestion 1) „Which mathematical concepts...

**Michel Planat**: *on* 10/17/13 at 6:42am UTC, wrote Dear all, An update of the ideas developed in the essay is in the paper ...

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**Michel Planat**: *on* 8/7/13 at 19:15pm UTC, wrote Dear Steve, I am delighted with your post. Thank you so much for your...

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FQXi FORUM

August 3, 2021

CATEGORY:
It From Bit or Bit From It? Essay Contest (2013)
[back]

TOPIC: It from qubit: how to draw quantum contextuality by Michel Dr Planat [refresh]

TOPIC: It from qubit: how to draw quantum contextuality by Michel Dr Planat [refresh]

Wheeler's {\it observer-participancy} and the related {\it it from bit} credo refer to quantum non-locality and contextuality. The mystery of these concepts slightly starts unveiling if one encodes the (in)compatibilities between qubit observables in the relevant finite geometries. The main objective of this treatise is to outline another conceptual step forward by employing Grothendieck's {\it dessins d'enfants} to reveal the topological and (non)algebraic machinery underlying the measurement acts and their information content.

Michel Planat is a senior scientist at FEMTO-ST/CNRS, Besançon, France. His present main interest is in fundamental problems of quantum information and their relationship to mathematics. He wrote about 110 refereed papers or book chapters.

Mr Planat,

As I have carefully explained in my essay BITTERS, everything in the real Universe is unique, once.

Although I do not doubt that Wheeler’s yes/no binary code and Bell’s parameters and Mermin’s failing emerging EPR realty criterion and your ability to draw quantum contextuality out of nowhere could be important abstractly, they do not appear to me to be unique.

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As I have carefully explained in my essay BITTERS, everything in the real Universe is unique, once.

Although I do not doubt that Wheeler’s yes/no binary code and Bell’s parameters and Mermin’s failing emerging EPR realty criterion and your ability to draw quantum contextuality out of nowhere could be important abstractly, they do not appear to me to be unique.

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Joe,

Thank you for reading it. I also red yours. Yes, everything in the real world is unique and quantum mechanics tell us 'no-cloning'. But in my opinion physics can just explain the how, not the fine details of the existence. A step in the direction of explaining contexts is my approach through "dessins d'enfants' that drive the compatibilities of observables.

Michel

Thank you for reading it. I also red yours. Yes, everything in the real world is unique and quantum mechanics tell us 'no-cloning'. But in my opinion physics can just explain the how, not the fine details of the existence. A step in the direction of explaining contexts is my approach through "dessins d'enfants' that drive the compatibilities of observables.

Michel

Michel, it is good to see some new ideas from information theory being put to use in this contest. This is a mathematically very sophisticated and I was not familiar with the relationships around dessins d'enfants so it is very enlightening. I wonder how many times I will have to read it to fully appreciate it.

I included the Kochen-Specker Theorem in my essay last year so I have touched on some corners of these ideas before. It is remarkable how many concepts converge in the theory of qubits

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I included the Kochen-Specker Theorem in my essay last year so I have touched on some corners of these ideas before. It is remarkable how many concepts converge in the theory of qubits

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Dear Philip,

I am glad that you learned something. Apart from the Kochen-Specker theorem we have a few common interests: symmetries, the black-hole qubit analogy and number theory. May be you can have a look at my papers (e.g.in google scholar) containing the title 'Dedekind psi function'. Thank you again.

Michel

I am glad that you learned something. Apart from the Kochen-Specker theorem we have a few common interests: symmetries, the black-hole qubit analogy and number theory. May be you can have a look at my papers (e.g.in google scholar) containing the title 'Dedekind psi function'. Thank you again.

Michel

I recognised your name as author of http://arxiv.org/abs/1005.1997 which I looked at when I was looking at qubits http://arxiv.org/abs/1005.1997 . I should look at some others.

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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...

view entire post

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...

view entire post

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Dear Jochen,

Thank you for your post. I am familiar with your interesting papers on contextuality as well.

Concerning your main remark, I still do not fully understand the precise connection between Grothendieck's dessins and the finite geometries underlying the compatibility observables - Mermin's pentagram is one of the simplest objects displaying contextuality but there is more to come.

I agree that the black-hole/qubit correspondance is a toy model, I like it due to its link to string theory. I suggest you have a look at the work of my colleagues Peter Levay and Metod Saniga on this topic

http://xxx.lanl.gov/abs/0808.3849

An important object is the split Cayley hexagon that has 12096 automorphisms as the number of three-qubit pentagrams.

My best regards,

Michel

Thank you for your post. I am familiar with your interesting papers on contextuality as well.

Concerning your main remark, I still do not fully understand the precise connection between Grothendieck's dessins and the finite geometries underlying the compatibility observables - Mermin's pentagram is one of the simplest objects displaying contextuality but there is more to come.

I agree that the black-hole/qubit correspondance is a toy model, I like it due to its link to string theory. I suggest you have a look at the work of my colleagues Peter Levay and Metod Saniga on this topic

http://xxx.lanl.gov/abs/0808.3849

An important object is the split Cayley hexagon that has 12096 automorphisms as the number of three-qubit pentagrams.

My best regards,

Michel

Dear Michel Planat

I just read your superb essay. I will try to comment in greater detail later today after I have read your essay a second or third time. I have been concerned with the role of Cayley numbers, the projective Fano plane, Freudenthal cubic equation or determinant in quantum gravity. My essay I conjecture some role for octonions in quantum field theory or quantum gravity and its implication for nonlocality. This is in the second part of the essay after I illustrate a formal incompleteness of any causal scheme. Your essay hits on these issues within the context of nonlocality and the Bell-CHSH inequality.

What do you think of algebraic curves over [0, 1, ∞] and the Langlands program? This seems to suggest there are generalized Tanyama-Shimura theorems for curves on general surfaces such as K3xK3 that obey certain conditions or constraints, such as given by the Fano plane.

Cheers LC

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I just read your superb essay. I will try to comment in greater detail later today after I have read your essay a second or third time. I have been concerned with the role of Cayley numbers, the projective Fano plane, Freudenthal cubic equation or determinant in quantum gravity. My essay I conjecture some role for octonions in quantum field theory or quantum gravity and its implication for nonlocality. This is in the second part of the essay after I illustrate a formal incompleteness of any causal scheme. Your essay hits on these issues within the context of nonlocality and the Bell-CHSH inequality.

What do you think of algebraic curves over [0, 1, ∞] and the Langlands program? This seems to suggest there are generalized Tanyama-Shimura theorems for curves on general surfaces such as K3xK3 that obey certain conditions or constraints, such as given by the Fano plane.

Cheers LC

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Dear Lawrence,

I am delighted to read your opinion because I have liked your own essay and also thought at a connection between 'dessins d'enfants' and quantum logic. I intend to write you later on your topic. Now I am waiting for your extra remarks.

Unfortunately, at this stage, I am not able to say anything relevant about the connection between algebraic curves and the Langland's program, this is a difficult mathematical question and I am more focused on the occurence of algebraic curves in the realm of quantum physics. Of course Grothendieck had these questions in mind.

Cheers,

Michel

I am delighted to read your opinion because I have liked your own essay and also thought at a connection between 'dessins d'enfants' and quantum logic. I intend to write you later on your topic. Now I am waiting for your extra remarks.

Unfortunately, at this stage, I am not able to say anything relevant about the connection between algebraic curves and the Langland's program, this is a difficult mathematical question and I am more focused on the occurence of algebraic curves in the realm of quantum physics. Of course Grothendieck had these questions in mind.

Cheers,

Michel

If you have comments about my essay of course feel free to comment there. My take on logic is the modal logic of causality, which is used to argue that potentially the associative property is violated in some subtle manner with vacuum physics. I generally think that quantum mechanics is on the Cayley numbers 1, 2, 4, 8 complex or #2. QM may have states that are generated by quaternionic operators (standard physics actually) and further with uncertainty fluctuations of event horizons the ordering ambiguity of operators in an S-matrix channel is a nonassociative condition. My arguments tend to be rather physical at this point, having departed from the more metaphysical issue with modal logic.

It is curious that Grothendieck would comment on this dessins d‘enfant, for this does have the appearance of category theory of sorts, which was his area of mastery. In effect what appears possible is that a set of curves defined on [0, 1, ∞] with projective properties, such as with the projective Fano plane, are those which construct modular forms corresponding to curves or spaces of curves (orbits) on spaces of dimension 3, 4, 6 and 10, which are the Cayley numbers plus 2. The “plus 2” comes about because the “trivial case” with 0 is for Ricci flat spaces in two dimensions, T^2 torus, with elliptic curves that define points on them. This is of course the Tanyama-Shimura conjecture --- now proof by Wiles.

I guess that Grothendieck either completely disappeared or maybe he is dead by now. He was a brilliant but rather odd man.

Cheers LC

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It is curious that Grothendieck would comment on this dessins d‘enfant, for this does have the appearance of category theory of sorts, which was his area of mastery. In effect what appears possible is that a set of curves defined on [0, 1, ∞] with projective properties, such as with the projective Fano plane, are those which construct modular forms corresponding to curves or spaces of curves (orbits) on spaces of dimension 3, 4, 6 and 10, which are the Cayley numbers plus 2. The “plus 2” comes about because the “trivial case” with 0 is for Ricci flat spaces in two dimensions, T^2 torus, with elliptic curves that define points on them. This is of course the Tanyama-Shimura conjecture --- now proof by Wiles.

I guess that Grothendieck either completely disappeared or maybe he is dead by now. He was a brilliant but rather odd man.

Cheers LC

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You comments are very relevant and I should think more on them.

In my comments on your essay, I mention that G2 and thus the octonions relate to the contextuality for three qubits http://xxx.lanl.gov/abs/1212.2729

Yes, you may know this webpage

http://www.math.jussieu.fr/~leila/grothendieckcircle/

biographic.php

In my comments on your essay, I mention that G2 and thus the octonions relate to the contextuality for three qubits http://xxx.lanl.gov/abs/1212.2729

Yes, you may know this webpage

http://www.math.jussieu.fr/~leila/grothendieckcircle/

biographic.php

Just stumbling across this, the octonions are very relevant for three-qubit geometry in general: the state space is a 15-dimensional sphere, an S^8 with fiber S^7, i.e. the last Hopf fibration; likewise, two qubits are related to the second Hopf fibration, S^3 over base S^4, and of course the Bloch sphere is just S^2 fibered with the global phase S^1. What's intriguing is that the requisite maps can be used to characterize the entanglement in the state, as discussed in this paper by Barnevig and Chen.So in this sense, it's sort of natural to consider a 3-qubit state a 'octonionic spinor' (o_1,o_2), parametrizing the S^15 via the normalization |o_1|^2 + |o_2|^2 = 1.

Not sure if it's anything deep, but it's always struck me as a curious and perhaps interesting observation.

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Not sure if it's anything deep, but it's always struck me as a curious and perhaps interesting observation.

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I discuss the connnection to twistor theory on my page , which is a bi-spinor theory.

Thanks for the information on G_2. I discuss some of this on my page today. Duff has worked out connections between qubits, (2, 4, and 8)-qubits with C, H and O. I will read these papers on the E8 automorphism and comment later.

Cheers LC

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Thanks for the information on G_2. I discuss some of this on my page today. Duff has worked out connections between qubits, (2, 4, and 8)-qubits with C, H and O. I will read these papers on the E8 automorphism and comment later.

Cheers LC

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Dear Michel,

great essay. I like to see abstract methods like Dessins d’enfants. Additionally I wil also read your paper mentioned above. I also worked in quantum information theory around 2003 to 2006. There I remembered on a discussion withthe group in Karlsruhe (Prof Beth) about the uniqueness of te Hamiltonian representation of qubit operations. One member of the group thought about a decomposition of three or higher qubit operation using only 2-qubit interaction Hamiltonians. I have the feeling that this problem is connecetd with your three qubit problem above.

Then I was able to prove a No-Go theorem (using ideas about the non-parallelizability of spheres). We were not able to publish the paper. Everyboday told us that it is not interesting or trivial.

Here is the link:

http://arxiv.org/abs/quant-ph/0508029

Maybe you can use it....

I will also thought about the G_2.

More later

Best

Torsten

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great essay. I like to see abstract methods like Dessins d’enfants. Additionally I wil also read your paper mentioned above. I also worked in quantum information theory around 2003 to 2006. There I remembered on a discussion withthe group in Karlsruhe (Prof Beth) about the uniqueness of te Hamiltonian representation of qubit operations. One member of the group thought about a decomposition of three or higher qubit operation using only 2-qubit interaction Hamiltonians. I have the feeling that this problem is connecetd with your three qubit problem above.

Then I was able to prove a No-Go theorem (using ideas about the non-parallelizability of spheres). We were not able to publish the paper. Everyboday told us that it is not interesting or trivial.

Here is the link:

http://arxiv.org/abs/quant-ph/0508029

Maybe you can use it....

I will also thought about the G_2.

More later

Best

Torsten

report post as inappropriate

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...

view entire post

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...

view entire post

report post as inappropriate

Dear Michel,

I read your polished essay rather too quickly soon realizing its technicalities were beyond my understanding. As an artist I was fascinated by the concept of Dessin d'Enfent, but it soon became clear it was some sort of variant of network theory (?) - perhaps a causality map (?). It needs more study.

More importantly I feel that you base your paper on 'standard' quantum philosophy - that probability is at the base of everything, and that knowing Nature is observer-related. I and many other sans-culotte feel that these are derivative phenomena - that there is an absolute universe that explains all these phenomena without the 'weirdness' that has become the hallmark of the field. It is a long discussion, but my incomplete and qualitative Beautiful Universe Theory will explain why I have responded as I did to your paper.

With best wishes

Vladimir

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I read your polished essay rather too quickly soon realizing its technicalities were beyond my understanding. As an artist I was fascinated by the concept of Dessin d'Enfent, but it soon became clear it was some sort of variant of network theory (?) - perhaps a causality map (?). It needs more study.

More importantly I feel that you base your paper on 'standard' quantum philosophy - that probability is at the base of everything, and that knowing Nature is observer-related. I and many other sans-culotte feel that these are derivative phenomena - that there is an absolute universe that explains all these phenomena without the 'weirdness' that has become the hallmark of the field. It is a long discussion, but my incomplete and qualitative Beautiful Universe Theory will explain why I have responded as I did to your paper.

With best wishes

Vladimir

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Rdposted from my area

Michel,

I don’t have as much time this morning to expand on this, so I will just make this rather brief for now. I will try to expand on this later today or tomorrow.

The three-qubit entanglement corresponds to a BPS black hole. The four qubit entanglement is the case of an extremal black hole. I think there is an underlying relationship between functions of the form (ψ|ψ) = F(ψψψ), an elliptic curve with the cubic form corresponding to the 3-qubit, and the “bounding” Jacobian curve that defines a quartic for G(ψψψψ). This I think is some sort of cohomology.

The G2 I think defines a frame bundle on the E8 which defines the F4 condition for 18 rays in the spacetime version of Kochen-Specker.

As I said I should have more time later to discuss this in greater depth.

Cheers LC

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Michel,

I don’t have as much time this morning to expand on this, so I will just make this rather brief for now. I will try to expand on this later today or tomorrow.

The three-qubit entanglement corresponds to a BPS black hole. The four qubit entanglement is the case of an extremal black hole. I think there is an underlying relationship between functions of the form (ψ|ψ) = F(ψψψ), an elliptic curve with the cubic form corresponding to the 3-qubit, and the “bounding” Jacobian curve that defines a quartic for G(ψψψψ). This I think is some sort of cohomology.

The G2 I think defines a frame bundle on the E8 which defines the F4 condition for 18 rays in the spacetime version of Kochen-Specker.

As I said I should have more time later to discuss this in greater depth.

Cheers LC

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Dear Michel

Very nicely when you expressed in Mathematics but is concluded by Literature.

I understand your intent through: "They are Merely conventional signs!"

I also have the same opinion like that.

http://fqxi.org/community/forum/topic/1802

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Very nicely when you expressed in Mathematics but is concluded by Literature.

I understand your intent through: "They are Merely conventional signs!"

I also have the same opinion like that.

http://fqxi.org/community/forum/topic/1802

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Dear Hoang

Thank you, I will look at your essay.

Also Poincaré wrote in 1905 in "Science and hypothesis"

The fundamental propositions of geometry, for instance, Euclid’s

postulate, are only conventions, and it is quite as unreasonable

to ask if they are true or false as to ask if the metric system is true or false. Only, these conventions are convenient, and there are certain experiments which

prove it to us.

Michel

Thank you, I will look at your essay.

Also Poincaré wrote in 1905 in "Science and hypothesis"

The fundamental propositions of geometry, for instance, Euclid’s

postulate, are only conventions, and it is quite as unreasonable

to ask if they are true or false as to ask if the metric system is true or false. Only, these conventions are convenient, and there are certain experiments which

prove it to us.

Michel

Dear Michael,

Like Philips I was not familiar with the relationships around dessins d'enfants so also for me it is very enlightening. And I need time to understand it. This is one of the advantages of participation in the contest. I do not feel competent to comment all essays and not all of them are worth commenting.

Nice to learn something new and interesting.

My essay is much simpler and short.

Best regards

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Like Philips I was not familiar with the relationships around dessins d'enfants so also for me it is very enlightening. And I need time to understand it. This is one of the advantages of participation in the contest. I do not feel competent to comment all essays and not all of them are worth commenting.

Nice to learn something new and interesting.

My essay is much simpler and short.

Best regards

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Dear Jacek,

It is good that you learn something by reading me. There is more to come soon. Check Arxiv preprints. I will give a short comment on your own essay.

Best wishes.

Michel

It is good that you learn something by reading me. There is more to come soon. Check Arxiv preprints. I will give a short comment on your own essay.

Best wishes.

Michel

Cher Michel Planat,

Thank you for an interesting suggestion. Are you saying that this formalism will help us understand the difference between quantum and classical bounds of the Bell inequality, and if yes, then how?

Best regards,

Alexei Grinbaum

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Thank you for an interesting suggestion. Are you saying that this formalism will help us understand the difference between quantum and classical bounds of the Bell inequality, and if yes, then how?

Best regards,

Alexei Grinbaum

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Dear Alexei,

I thought that the section about the Cirelson's bound aas clear about that matter but may be I did not fully grasped your question. In general, I think that the introduction od dessins d'enfants may help to clarify the nature of Bell's inequalities and contextuality.

I will look at your essay next week, I am quite busy thesee days away from Besançon.

Best wishes,

Michel

I thought that the section about the Cirelson's bound aas clear about that matter but may be I did not fully grasped your question. In general, I think that the introduction od dessins d'enfants may help to clarify the nature of Bell's inequalities and contextuality.

I will look at your essay next week, I am quite busy thesee days away from Besançon.

Best wishes,

Michel

Dear Michel,

I returned from vacation, and left a reply to your comment on my essay's page.

You presented beautiful and surprising connections between dessins d'enfants and quantum observables, building on your 2004 conjecture suggesting a connection between the existence of mutually unbiased bases and the existence of projective planes. I understand from your reply to Jochen Szangolies's comment, that you "still do not fully understand the precise connection between Grothendieck's dessins and the finite geometries underlying the compatibility observables". With this in mind, do you have a geometric/topological interpretation of the Riemann surfaces arising from Grothendieck's dessins d'enfants? Are there possible configurations of quantum observables corresponding to higher dimensional varieties?

I look forward to see your forthcomming papers on this subject.

You may be interested in Florin Moldoveanu's approach to quantum mechanics, using the Grothendieck group.

Best regards,

Cristi Stoica

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I returned from vacation, and left a reply to your comment on my essay's page.

You presented beautiful and surprising connections between dessins d'enfants and quantum observables, building on your 2004 conjecture suggesting a connection between the existence of mutually unbiased bases and the existence of projective planes. I understand from your reply to Jochen Szangolies's comment, that you "still do not fully understand the precise connection between Grothendieck's dessins and the finite geometries underlying the compatibility observables". With this in mind, do you have a geometric/topological interpretation of the Riemann surfaces arising from Grothendieck's dessins d'enfants? Are there possible configurations of quantum observables corresponding to higher dimensional varieties?

I look forward to see your forthcomming papers on this subject.

You may be interested in Florin Moldoveanu's approach to quantum mechanics, using the Grothendieck group.

Best regards,

Cristi Stoica

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Dear Cristinel,

As I am away from home and quite busy this week I will answer your questions next week and will try to understand Moldoveanu's approach. Thank you for this important pointer.

My best regards,

Michel

As I am away from home and quite busy this week I will answer your questions next week and will try to understand Moldoveanu's approach. Thank you for this important pointer.

My best regards,

Michel

Dear Dr. Michel,

I have down loaded your essay and soon post my comments on it. Meanwhile, please, go through my essay and post your comments.

Regards and good luck in the contest.

Sreenath BN.

http://fqxi.org/community/forum/topic/1827

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I have down loaded your essay and soon post my comments on it. Meanwhile, please, go through my essay and post your comments.

Regards and good luck in the contest.

Sreenath BN.

http://fqxi.org/community/forum/topic/1827

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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...

view entire post

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...

view entire post

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Hello, Michel,

Thank you for this interesting essay. As you will see from mine, you are one of the people I critique as overweighting geometry at the expense of energy. The logic of Grothendieck, in my humble opinion, is not the dynamic logic of the universe. I hope we may communicate on this point.

Best regards,

Joseph

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Thank you for this interesting essay. As you will see from mine, you are one of the people I critique as overweighting geometry at the expense of energy. The logic of Grothendieck, in my humble opinion, is not the dynamic logic of the universe. I hope we may communicate on this point.

Best regards,

Joseph

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Dear Joseph,

First thank you for looking at my essay. I will discuss yours next week and will try to give you extensive comments. My geometrical view is not faith, it follows from the properties of (multiple) qubit observables. In the essay, I found that these (projective) geometries can, in many cases, be described from the action of Grothendieck's dessins d'enfants. The latter probably have deep physical meaning I am currently trying to establish. Of course, one can have other views about the nature of the universe and try to justify them. In Lewis Caroll tale, as well as in Poincaré's "Science and Hypothesis", it is a matter of conventions.

Best regards,

Michel

First thank you for looking at my essay. I will discuss yours next week and will try to give you extensive comments. My geometrical view is not faith, it follows from the properties of (multiple) qubit observables. In the essay, I found that these (projective) geometries can, in many cases, be described from the action of Grothendieck's dessins d'enfants. The latter probably have deep physical meaning I am currently trying to establish. Of course, one can have other views about the nature of the universe and try to justify them. In Lewis Caroll tale, as well as in Poincaré's "Science and Hypothesis", it is a matter of conventions.

Best regards,

Michel

Dear Dr. Michel,

Your essay is highly original and intriguing but at the same time it appears as if it is written for the experts in the field but not keeping general audience in the perspective. It is interesting to know how far the different geometric methods, you have followed in this article, are capable of solving other problems prevailing in QM. I congratulate you for producing such an innovative essay.

Sreenath

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Your essay is highly original and intriguing but at the same time it appears as if it is written for the experts in the field but not keeping general audience in the perspective. It is interesting to know how far the different geometric methods, you have followed in this article, are capable of solving other problems prevailing in QM. I congratulate you for producing such an innovative essay.

Sreenath

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Dear Dr. Michel,

I appreciate your kind comments. It is good to learn that we share some common basic views regarding the existence of knowledge.

Best regards,

Sreenath

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I appreciate your kind comments. It is good to learn that we share some common basic views regarding the existence of knowledge.

Best regards,

Sreenath

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Dear Dr. Michel,

I have rated your innovative essay with maximum honors and wish you best of luck in the essay contest.

Best regards,

Sreenath

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I have rated your innovative essay with maximum honors and wish you best of luck in the essay contest.

Best regards,

Sreenath

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Dear Michal,

Thank you once again for the questions you asked me on my essay. If you visit the FQXi page ,( at the beginning of the page)

http://fqxi.org/community/essay

........................

.....................

I. GOALS & INTENT

The goals of the Foundational Questions Institute's Essay Contest (the "Contest") are to:

^ Encourage and support rigorous, innovative, and influential thinking about foundational questions in physics and cosmology;

.............................................

They used a word 'innovative', that may mean they want more fundamental thinking and may not be a report on current research prepared for discovery channel viewers...

Best

=snp

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Thank you once again for the questions you asked me on my essay. If you visit the FQXi page ,( at the beginning of the page)

http://fqxi.org/community/essay

........................

.....................

I. GOALS & INTENT

The goals of the Foundational Questions Institute's Essay Contest (the "Contest") are to:

^ Encourage and support rigorous, innovative, and influential thinking about foundational questions in physics and cosmology;

.............................................

They used a word 'innovative', that may mean they want more fundamental thinking and may not be a report on current research prepared for discovery channel viewers...

Best

=snp

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Michal

nice essay and interesting ideas, even though I need more knowledge about your math, to understand the technical derivations. I like the one about CHSH.

Best wishes

Mauro

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nice essay and interesting ideas, even though I need more knowledge about your math, to understand the technical derivations. I like the one about CHSH.

Best wishes

Mauro

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Dear Michel Planat,

Having read your very interesting paper twice, I concluded that you would probably have little interest in mine. But after reading your comment on Stewart Heinrich's essay expressing your interest in the concept of self-awareness and the miraculous efficiency of mathematics for mimicking physical problems, both of which I address in my essay, I decided to invite you to read it and comment. I think it has little connection to your essay yet you may find a new perspective on these two topics.

Thank you for participating in this contest and good luck in the contest.

Best regards,

Edwin Eugene Klingman

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Having read your very interesting paper twice, I concluded that you would probably have little interest in mine. But after reading your comment on Stewart Heinrich's essay expressing your interest in the concept of self-awareness and the miraculous efficiency of mathematics for mimicking physical problems, both of which I address in my essay, I decided to invite you to read it and comment. I think it has little connection to your essay yet you may find a new perspective on these two topics.

Thank you for participating in this contest and good luck in the contest.

Best regards,

Edwin Eugene Klingman

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Dear Michel,

Thank you for reading my essay and commenting on it. I have had a chance to review the two papers you referenced there. The Riemann paper discusses the details of a specific partition function, which I find interesting as I base the applicability of the Born probability to my wave function model on the partition function. The other paper, on time perception is also interesting. I had not seen the Poincare discussion of the Continuum, and found that fascinating, as well as your connection. I am somewhat confused as to whether you are proposing the phase locking as the 'mechanism' of time perception or of the 'scaling' of time perception? I can understand how this could relate to scaling, but not perception as I understand it.

Thanks again for reading my essay. I hope it stimulates some ideas for you.

Best,

Edwin Eugene Klingman

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Thank you for reading my essay and commenting on it. I have had a chance to review the two papers you referenced there. The Riemann paper discusses the details of a specific partition function, which I find interesting as I base the applicability of the Born probability to my wave function model on the partition function. The other paper, on time perception is also interesting. I had not seen the Poincare discussion of the Continuum, and found that fascinating, as well as your connection. I am somewhat confused as to whether you are proposing the phase locking as the 'mechanism' of time perception or of the 'scaling' of time perception? I can understand how this could relate to scaling, but not perception as I understand it.

Thanks again for reading my essay. I hope it stimulates some ideas for you.

Best,

Edwin Eugene Klingman

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Michel,

If given the time and the wits to evaluate over 120 more entries, I have a month to try. My seemingly whimsical title, “It’s good to be the king,” is serious about our subject.

Jim

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If given the time and the wits to evaluate over 120 more entries, I have a month to try. My seemingly whimsical title, “It’s good to be the king,” is serious about our subject.

Jim

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Dear Dr. Michel Planat

Thanks and congratulations for your poetic qubits.

I am mere a learner of physics here who have huge interests to know the fundamentals in nature. I think that to resolve the issues like "quantum non-locality and contextuality' in your essay, why not we ask the nature in different ways? I invite you to read my submitted essay for a quite new approach of asking the nature.

With my regards

Dipak

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Thanks and congratulations for your poetic qubits.

I am mere a learner of physics here who have huge interests to know the fundamentals in nature. I think that to resolve the issues like "quantum non-locality and contextuality' in your essay, why not we ask the nature in different ways? I invite you to read my submitted essay for a quite new approach of asking the nature.

With my regards

Dipak

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Dear Kumar,

Thank you for reading my essay and inviting me to read yours.

Yes, I like to have some poetry and visualization when it is possible.

You tell us that each access to reality is digitized and I agree.

But it occurs in a different way in classical physics and quantum mechanics.

Myself I did measurements of the frequency of ultrasable clocks in the past; there I recovered the structure of rational numbers, you can easily google with the keyword "number theory and 1/f noise" and find my contributions. This is well in the spirit of what you are writing. Quantum physics is more seriously difficult in this respect in the sense that it undress in bits (the eigenvalues of qubit observables) and it is much more difficult to organize them. In addition the observer participates in the undressing as Wheeler explained.

Best wishes,

Michel

Thank you for reading my essay and inviting me to read yours.

Yes, I like to have some poetry and visualization when it is possible.

You tell us that each access to reality is digitized and I agree.

But it occurs in a different way in classical physics and quantum mechanics.

Myself I did measurements of the frequency of ultrasable clocks in the past; there I recovered the structure of rational numbers, you can easily google with the keyword "number theory and 1/f noise" and find my contributions. This is well in the spirit of what you are writing. Quantum physics is more seriously difficult in this respect in the sense that it undress in bits (the eigenvalues of qubit observables) and it is much more difficult to organize them. In addition the observer participates in the undressing as Wheeler explained.

Best wishes,

Michel

Dear Michel,

thank you for stopping by to comment on my essay. I was very much intrigued by your work and remember it from last year. It appears your presentation is more technical this year. I wish your interesting work reserves recognition is deserves among the specialists.

Best of luck :)

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thank you for stopping by to comment on my essay. I was very much intrigued by your work and remember it from last year. It appears your presentation is more technical this year. I wish your interesting work reserves recognition is deserves among the specialists.

Best of luck :)

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Dear Dr. Planat,

Your highly technical treatise was most absorbing, though in many parts I had difficulty following it. I will therefore state my comments along the broadest lines.

My view is that even if the emergence of random outcomes can be explained and contextualized in a variety of ways, the nature of information remains unchanged: It still defines the Observer's 'patch of reality' at any given moment, and continues to do so throughout evolution.

Even if we could describe the quantum world in perfect mathematical language, we would still have only described some small part of our Cosmos perfectly; and we would still be involved in our distinctive human Cosmos ... one that displays a continuous correlation between Bit and It over the course of evolution.

The observer does not interact with the whole field of reality regardless of how probabilities emerge, or how context affects them. Mathematics is the projection of the human mind on to the Cosmos - it will always be this, and it will always be entirely composed of Bits, thus keeping the Bit-It conundrum relevant to any definition of the Cosmos.

Though it is doubtless critical to investigate quantum reality as thoroughly as you do, I think we must also ask: 'Why do Bits 'match' Its so consistently at every instant of evolution – whatever their mathematics?' It would be interesting if the mathematics could be applied to the larger context of the perpetual Correlation of Bit to It.

As you can probably tell, this is one of the strands of my essay – which I think you would find interesting for the reasons I've stated.

Once again, yours is a very serious work, one with consequences; I am eager to hear your feedback, and wish you all the best.

John

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Your highly technical treatise was most absorbing, though in many parts I had difficulty following it. I will therefore state my comments along the broadest lines.

My view is that even if the emergence of random outcomes can be explained and contextualized in a variety of ways, the nature of information remains unchanged: It still defines the Observer's 'patch of reality' at any given moment, and continues to do so throughout evolution.

Even if we could describe the quantum world in perfect mathematical language, we would still have only described some small part of our Cosmos perfectly; and we would still be involved in our distinctive human Cosmos ... one that displays a continuous correlation between Bit and It over the course of evolution.

The observer does not interact with the whole field of reality regardless of how probabilities emerge, or how context affects them. Mathematics is the projection of the human mind on to the Cosmos - it will always be this, and it will always be entirely composed of Bits, thus keeping the Bit-It conundrum relevant to any definition of the Cosmos.

Though it is doubtless critical to investigate quantum reality as thoroughly as you do, I think we must also ask: 'Why do Bits 'match' Its so consistently at every instant of evolution – whatever their mathematics?' It would be interesting if the mathematics could be applied to the larger context of the perpetual Correlation of Bit to It.

As you can probably tell, this is one of the strands of my essay – which I think you would find interesting for the reasons I've stated.

Once again, yours is a very serious work, one with consequences; I am eager to hear your feedback, and wish you all the best.

John

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Dear John,

Thank you so much for taking the time to read my (too technical) essay and writing your long comment. It may be improved at a futher stage of the research.

I expect that the paradigm of the Riemann sphere rigidified at three points may ultimately be useful for understanding what you name " the perpetual correlation of bit to it" in some analogy with what Jean Piaget did for the child cognition with the paradigm of the real projective plane (that I also introduce at the end of my essay).

I already red your excellent essay and I will write separate comments for it.

My best regards,

Michel

Thank you so much for taking the time to read my (too technical) essay and writing your long comment. It may be improved at a futher stage of the research.

I expect that the paradigm of the Riemann sphere rigidified at three points may ultimately be useful for understanding what you name " the perpetual correlation of bit to it" in some analogy with what Jean Piaget did for the child cognition with the paradigm of the real projective plane (that I also introduce at the end of my essay).

I already red your excellent essay and I will write separate comments for it.

My best regards,

Michel

Dear Michel,

I think it is always good when someone examines the connection between ostensibly unrelated fields, finds certain parallels and then explores these to guide further research.

I am impressed by the fact that your approach permitted automating the search for proofs of Bell's theorem and related mathematical objects. I wonder if the different versions are sufficiently different from each other that this may also translate into differences in the difficulty of experimental set up. It seems that it might be useful to have a catalog/library of the objects found by your approach publicly available (perhaps even sortable by certain parameters), if only because it seems natural to assume that some versions may suggest certain deeper insights more readily than others.

At the conclusion it was not clear to me if you think that the dessin d'enfant for the Mermin Pentagram definitely does not exist or if this is still subject to further research. If it does not exist, how would you characterize the qualitative difference in contextuality between the two-qubit and three qubit case in terms of standard quantum mechanics?

All the best,

Armin

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I think it is always good when someone examines the connection between ostensibly unrelated fields, finds certain parallels and then explores these to guide further research.

I am impressed by the fact that your approach permitted automating the search for proofs of Bell's theorem and related mathematical objects. I wonder if the different versions are sufficiently different from each other that this may also translate into differences in the difficulty of experimental set up. It seems that it might be useful to have a catalog/library of the objects found by your approach publicly available (perhaps even sortable by certain parameters), if only because it seems natural to assume that some versions may suggest certain deeper insights more readily than others.

At the conclusion it was not clear to me if you think that the dessin d'enfant for the Mermin Pentagram definitely does not exist or if this is still subject to further research. If it does not exist, how would you characterize the qualitative difference in contextuality between the two-qubit and three qubit case in terms of standard quantum mechanics?

All the best,

Armin

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Dear Armin,

Yes, all proofs on non-locality and contextuality arising from the generalized Pauli group may be reached systematically. You can look at my/our recent papers on this subject from ArXiv.

The step towards dessins d'enfant is new. My essay is the first account of the relationship of finite geometries (contextual or not) and dessins. A publicly available catalog and, even better, all clues to reproduce my findings, will be given in the next paper.

I have some hints about why the Mermin's pentagram cannot be reproduced in this form (but the related Desargues configuration can be reproduced) and that constitutes a basic difference between two and three qubits first stated by Mermin himself.

An important fact is that several distinct dessins with different invariants give rise to the same geometry (as the Fano plane, the Mermin square or others), that is the absolute Galois group Gal(\bar(Q)/Q) is not enough to understand what is going on. Physically, it may have tremendous consequences regarding the link between the measurement space (here the Riemann sphere rigidified at three points) and the observable space (the finite geometry of compatible measurements). This should be distinguishable in measurements.

Thank you for your very relevant comments.

Best wishes.

Michel

Yes, all proofs on non-locality and contextuality arising from the generalized Pauli group may be reached systematically. You can look at my/our recent papers on this subject from ArXiv.

The step towards dessins d'enfant is new. My essay is the first account of the relationship of finite geometries (contextual or not) and dessins. A publicly available catalog and, even better, all clues to reproduce my findings, will be given in the next paper.

I have some hints about why the Mermin's pentagram cannot be reproduced in this form (but the related Desargues configuration can be reproduced) and that constitutes a basic difference between two and three qubits first stated by Mermin himself.

An important fact is that several distinct dessins with different invariants give rise to the same geometry (as the Fano plane, the Mermin square or others), that is the absolute Galois group Gal(\bar(Q)/Q) is not enough to understand what is going on. Physically, it may have tremendous consequences regarding the link between the measurement space (here the Riemann sphere rigidified at three points) and the observable space (the finite geometry of compatible measurements). This should be distinguishable in measurements.

Thank you for your very relevant comments.

Best wishes.

Michel

Hi Michel,

I had the same question as Armin regarding the Mermin pentagram so I will have to read your forthcoming works on this topic. If a dessin d'enfents does *not* exist for the Mermin pentagram, what, in your opinion, does this mean for contextuality and, more generally, the Kochen-Specker theorem?

Ian Durham

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I had the same question as Armin regarding the Mermin pentagram so I will have to read your forthcoming works on this topic. If a dessin d'enfents does *not* exist for the Mermin pentagram, what, in your opinion, does this mean for contextuality and, more generally, the Kochen-Specker theorem?

Ian Durham

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Dear Ian,

Excellent question left in abeyance in the paper, according to Belyi's theorem It means the lack on an algebraic curve associated to the pentagram. As there are 12096 three-qubit pentagrams it also means challenging questions for the whole finite geometry of operators.

Michel

Excellent question left in abeyance in the paper, according to Belyi's theorem It means the lack on an algebraic curve associated to the pentagram. As there are 12096 three-qubit pentagrams it also means challenging questions for the whole finite geometry of operators.

Michel

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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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],...

view entire post

attachments: kerr_bh.jpg, Penrose_diagram_for_Kerr.png

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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

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

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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

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Dear Michel,

Nice to see such an original idea around geometry - I've learned a lot from your essay. I appreciated how you utilised Mermin's pentagram and as above mentioned by Ian, think that it is interesting that it is unique with regard to Dessin d'enfents. I like anything relating to geometry an certainly anything we discover to be unique ought to be crying out for further study.

My essay is based around n-dimensional simplexes, entropy and the Fibonacci sequence around Black Holes. I hope you find the time to read it.

Best wishes & great work!

Antony

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Nice to see such an original idea around geometry - I've learned a lot from your essay. I appreciated how you utilised Mermin's pentagram and as above mentioned by Ian, think that it is interesting that it is unique with regard to Dessin d'enfents. I like anything relating to geometry an certainly anything we discover to be unique ought to be crying out for further study.

My essay is based around n-dimensional simplexes, entropy and the Fibonacci sequence around Black Holes. I hope you find the time to read it.

Best wishes & great work!

Antony

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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

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Vladimir

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Vladimir,

The rate is less important than comments you may have.

I wonder if you have specificremarks concerning my essay.

Thanks.

Michel

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

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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

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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

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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

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Dear Vladimir,

At the bottom of Zenkin's interview

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

tm

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

At the bottom of Zenkin's interview

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

tm

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

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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

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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

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

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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

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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

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...

view entire post

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...

view entire post

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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...

view entire post

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...

view entire post

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

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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

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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

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...

view entire post

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...

view entire post

attachments: 7_iDNASeries.bmp

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Hello Michel

Richard Feynman in his Nobel Acceptance Speech (http://www.nobelprize.org/nobel_prizes/physics/laureates/19

65/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

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Richard Feynman in his Nobel Acceptance Speech (http://www.nobelprize.org/nobel_prizes/physics/laureates/19

65/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

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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

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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

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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...

view entire post

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...

view entire post

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

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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

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Dear Angel,

Thank you for your interest. I agree that the tetrahedron may be a basic piece of

an unification model. I suspect that Klein's theory of invariants is related to your calculations. For the tetrahedron, the Belyi function is the cube of the ratio between the two invariants as given in Klein's book about the icosahedron (Dover, 1956, [5], p. 104). But we can discuss this by email when the competition ends. The tetrahedron may be seen as the 3-simplex, it can be driven in 6 distinct ways by a dessin d'enfant arising from the cartographic group (as I answer above to Stephen Anastasi), I wonder if one can attach some physical significance to these facts.

In what regards your essay, I find it extremely attractive because you are producing numbers that seem to correspond to mass ration in particle physics.

It would have to be organized in a more academic style but I don't worry at this stage. Your essay is also relevant to the topic of observer participancy. You know the sentence requoted in Wikipedia article about Preintuitionism

In fact Kronecker might be the most famous of the Pre-Intuitionists for his singular and often quoted phrase, "God made the natural numbers; all else is the work of man."

I am a fan of number theory and produced several papers on this topic.

I give you an extremely high rate to promote your research. I would like to understand the details of your calculations. My email is

michel.planat@femto-st.fr

Good luck,

Michel

Thank you for your interest. I agree that the tetrahedron may be a basic piece of

an unification model. I suspect that Klein's theory of invariants is related to your calculations. For the tetrahedron, the Belyi function is the cube of the ratio between the two invariants as given in Klein's book about the icosahedron (Dover, 1956, [5], p. 104). But we can discuss this by email when the competition ends. The tetrahedron may be seen as the 3-simplex, it can be driven in 6 distinct ways by a dessin d'enfant arising from the cartographic group (as I answer above to Stephen Anastasi), I wonder if one can attach some physical significance to these facts.

In what regards your essay, I find it extremely attractive because you are producing numbers that seem to correspond to mass ration in particle physics.

It would have to be organized in a more academic style but I don't worry at this stage. Your essay is also relevant to the topic of observer participancy. You know the sentence requoted in Wikipedia article about Preintuitionism

In fact Kronecker might be the most famous of the Pre-Intuitionists for his singular and often quoted phrase, "God made the natural numbers; all else is the work of man."

I am a fan of number theory and produced several papers on this topic.

I give you an extremely high rate to promote your research. I would like to understand the details of your calculations. My email is

michel.planat@femto-st.fr

Good luck,

Michel

Michel,

Thanks for your kind comments on my work, and helpful links, though I could make little sense of your arXiv papers (I'm sure my fault not yours).

I've now re-read your essay and have found some connections I didn't previously notice. I support PBR, but as it's consistent with the DFM's realist ontology, and still find a valid re-interpretation of Copenhagen. I understand you do too but on different grounds.

We think differently as I've eschewed the conventional 'shut up and calculate' era approach. I've found the belief in the power of manipulating symbols which are supposed to precisely represent nature's evolution is almost pagan mysticism. Can we formulate Kolmogorov complexity? I suggest a new 'stop and think' era is overdue. The McHarris essay on chaos is then more important than most realise.

Can a child's drawing of a curve represent the non-linear correspondence of a circle to a line? or explaining Borns' Rule by the DFM; a sphere to a plane? so a Bayesian cosine distribution which contains natures truths hidden BETWEEN the integers 0 and 1 inaccessible to our present mathematics?

You stand more chance than me of rationalising this in the language most with influence will understand so I hope you can. I also think your essay deserves to finish in the final placings so am pleased to assist.

Best wishes

Peter

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Thanks for your kind comments on my work, and helpful links, though I could make little sense of your arXiv papers (I'm sure my fault not yours).

I've now re-read your essay and have found some connections I didn't previously notice. I support PBR, but as it's consistent with the DFM's realist ontology, and still find a valid re-interpretation of Copenhagen. I understand you do too but on different grounds.

We think differently as I've eschewed the conventional 'shut up and calculate' era approach. I've found the belief in the power of manipulating symbols which are supposed to precisely represent nature's evolution is almost pagan mysticism. Can we formulate Kolmogorov complexity? I suggest a new 'stop and think' era is overdue. The McHarris essay on chaos is then more important than most realise.

Can a child's drawing of a curve represent the non-linear correspondence of a circle to a line? or explaining Borns' Rule by the DFM; a sphere to a plane? so a Bayesian cosine distribution which contains natures truths hidden BETWEEN the integers 0 and 1 inaccessible to our present mathematics?

You stand more chance than me of rationalising this in the language most with influence will understand so I hope you can. I also think your essay deserves to finish in the final placings so am pleased to assist.

Best wishes

Peter

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Dear Peter,

Thank you for helping me to float. Apart from several unfair votes this game is quite democratic at the level of exchanging deep thoughts and knowledge.

I still don't know what can ultimely be reached with this Grothendieck's dessins d'enfants. I try to extract them from the treasure trove of mathematics in the context of quantum paradoxes but I also had interesting feedbacks with a few philosophically oriented FQXi competitors, and you can find the tracks of these discussion above. The secret is in the understanding of the so-called Belyi theorem. I would have to tell more on this and display many examples to convey the beauty of the concept that has fascinated Grothendieck in his

http://en.wikipedia.org/wiki/Esquisse_d'un_Programme

Peter, I wish you not be overlooked this time.

Michel

ps: I realize that we are both born in 1951.

Thank you for helping me to float. Apart from several unfair votes this game is quite democratic at the level of exchanging deep thoughts and knowledge.

I still don't know what can ultimely be reached with this Grothendieck's dessins d'enfants. I try to extract them from the treasure trove of mathematics in the context of quantum paradoxes but I also had interesting feedbacks with a few philosophically oriented FQXi competitors, and you can find the tracks of these discussion above. The secret is in the understanding of the so-called Belyi theorem. I would have to tell more on this and display many examples to convey the beauty of the concept that has fascinated Grothendieck in his

http://en.wikipedia.org/wiki/Esquisse_d'un_Programme

Peter, I wish you not be overlooked this time.

Michel

ps: I realize that we are both born in 1951.

Michel,

I was October, and we could see France from our house in Royal Road. I have a yacht in Ramsgate Harbour and we often race over to the Dunes, Cote D'Opal, Normandy and Brittany.

Can you get any contact with Alain Aspect? He's ignored my letter advising of the theoretical explanation of the 'orbital asymmetries' he found. He discarded all that data (the vast majority) as no theory existed at the time!

If he is involved with the explanation he will look very good, but I think maybe not if he ignores it! What do you think?

Peter

PS. Yes, democracy is good, unfortunately power often corrupts and can ultimately prevail.

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I was October, and we could see France from our house in Royal Road. I have a yacht in Ramsgate Harbour and we often race over to the Dunes, Cote D'Opal, Normandy and Brittany.

Can you get any contact with Alain Aspect? He's ignored my letter advising of the theoretical explanation of the 'orbital asymmetries' he found. He discarded all that data (the vast majority) as no theory existed at the time!

If he is involved with the explanation he will look very good, but I think maybe not if he ignores it! What do you think?

Peter

PS. Yes, democracy is good, unfortunately power often corrupts and can ultimately prevail.

report post as inappropriate

Dear Peter,

May be Alain Aspect just forgot to answer. After his breakthrough experiment he was interested by other topics in quantum optics (Bose-Einstein condensates...). He is not a theoretician. He got the CNRS gold medal in 2005, I suspect that he will also win the Nobel Prize after Cohen Tannoudji and Serge Haroche.

Of course I met the three guys at conferences but they don't know me. I am not in the main stream and I don't try to be within it.

If you like, we can continue our exchange through the email

michel.planat@femto-st.fr

Best regards,

Michel

Do you speak some French?

May be Alain Aspect just forgot to answer. After his breakthrough experiment he was interested by other topics in quantum optics (Bose-Einstein condensates...). He is not a theoretician. He got the CNRS gold medal in 2005, I suspect that he will also win the Nobel Prize after Cohen Tannoudji and Serge Haroche.

Of course I met the three guys at conferences but they don't know me. I am not in the main stream and I don't try to be within it.

If you like, we can continue our exchange through the email

michel.planat@femto-st.fr

Best regards,

Michel

Do you speak some French?

Dear Michel,

Please see below statements and their implication in mathematics as you have posted a question in my thread about zero = I = infinity. I am using the symbol "~" to represent infinity.

If 0 x 0 = 0 is true, then 0 / 0 = 0 is also true

If 0 x 1 = 0 is true, then 0 / 0 = 1 is also true

If 0 x 2 = 0 is true, then 0 / 0 = 2 is also true

.

.

.

If 0 x i = 0 is true, then 0 / 0 = i is also true

.

.

.

If 0 x ~ = 0 is true, then 0 / 0 = ~ is also true

It seems that mathematics, the universal language, is also pointing to the absolute truth that 0 = 1 = 2 = i = ~, where "i" can be any number from zero to infinity. Any number on its own means absolutely nothing (zero) or itself (infinite or undefined). Only when compared to numbers before it or after it does it have a relative meaning. Theory of everything is that there is absolutely nothing but the self or i.

I have also explained that the universe is an iSphere and we humans are capable of interpreting it as a 4 dimensional 3Sphere manifold.

Love,

Sridattadev.

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Please see below statements and their implication in mathematics as you have posted a question in my thread about zero = I = infinity. I am using the symbol "~" to represent infinity.

If 0 x 0 = 0 is true, then 0 / 0 = 0 is also true

If 0 x 1 = 0 is true, then 0 / 0 = 1 is also true

If 0 x 2 = 0 is true, then 0 / 0 = 2 is also true

.

.

.

If 0 x i = 0 is true, then 0 / 0 = i is also true

.

.

.

If 0 x ~ = 0 is true, then 0 / 0 = ~ is also true

It seems that mathematics, the universal language, is also pointing to the absolute truth that 0 = 1 = 2 = i = ~, where "i" can be any number from zero to infinity. Any number on its own means absolutely nothing (zero) or itself (infinite or undefined). Only when compared to numbers before it or after it does it have a relative meaning. Theory of everything is that there is absolutely nothing but the self or i.

I have also explained that the universe is an iSphere and we humans are capable of interpreting it as a 4 dimensional 3Sphere manifold.

Love,

Sridattadev.

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Hi Michel,

Thank you for your excellent essay, which advances the discussion of the topics of quantum non-locality and contextuality, and thanks for your response with the references, which I will follow up shortly. Your work is highly relevant to my own and will be one of the most important of the competition for me. On Friday, July 26, I gave your essay a very high rating.

Sincerely,

Charles Card

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Thank you for your excellent essay, which advances the discussion of the topics of quantum non-locality and contextuality, and thanks for your response with the references, which I will follow up shortly. Your work is highly relevant to my own and will be one of the most important of the competition for me. On Friday, July 26, I gave your essay a very high rating.

Sincerely,

Charles Card

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Greetings Michel,

I have just given you a well deserved boost, after reading (or reviewing) your wonderful paper. As I understand it; the Dessins are contextual maps, showing the connections involved and the object-observer relationships. You state that the Fano plane is the smallest projective plane possible. I guess that means the octonions are the smallest irreducible representation of object and observer context. Anyhow; it was a very well written and fun introduction to a subject which could have been a lot less engaging. Your enthusiasm for your subject is infectious Michel, and you definitely portray the child-like playful explorer well.

Have Fun!

Jonathan

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I have just given you a well deserved boost, after reading (or reviewing) your wonderful paper. As I understand it; the Dessins are contextual maps, showing the connections involved and the object-observer relationships. You state that the Fano plane is the smallest projective plane possible. I guess that means the octonions are the smallest irreducible representation of object and observer context. Anyhow; it was a very well written and fun introduction to a subject which could have been a lot less engaging. Your enthusiasm for your subject is infectious Michel, and you definitely portray the child-like playful explorer well.

Have Fun!

Jonathan

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Dear Jonathan,

My best acknowledgements for the boost. I appreciate that the technicalities do not discourage you. I hope that the infection will propagate!

You are right that the octonions lurk around the examples I selected. Not all dessins are feature quantum contextuality. The simplest case given here is Mermin's square and can be seen as an archetype (in the language you use in your essay). The next case is Mermin's pentagram, there are 12096 of them with three qubits and 12096 is also the size of the automorphism group of G2(2) (related to the octonions as John Baez explains in his famous note). This is discussed in our recent papers on ArXiv.

My kind regards,

Michel

My best acknowledgements for the boost. I appreciate that the technicalities do not discourage you. I hope that the infection will propagate!

You are right that the octonions lurk around the examples I selected. Not all dessins are feature quantum contextuality. The simplest case given here is Mermin's square and can be seen as an archetype (in the language you use in your essay). The next case is Mermin's pentagram, there are 12096 of them with three qubits and 12096 is also the size of the automorphism group of G2(2) (related to the octonions as John Baez explains in his famous note). This is discussed in our recent papers on ArXiv.

My kind regards,

Michel

Thank you Michel!

I am pleased to help your wonderful essay rise higher. I expect that many more wonderful insights await, in the collection of your papers (or where you are an author) I have downloaded from arXiv. The overlooked importance of something small like the fundamental nature of the (0, 1, /infty) triple is seldom made known. I noticed you commented to this effect on Akinbo's essay site as well as in your own.

People are unaware that in an ab initio formulation, if we actually start at the very beginning and move forward from first principles, one can only know there is an extent; we can call it 1 but it could also be infinite as there is only nothing to compare it to. That is the rule for constructive geometers. In Ian Durham's essay; he makes the point that even knowing something is a unit, we still don't know how 'big' it is (e.g. - a bit or a trit). Perhaps ternary digits are more useful, after all.

But I like imagining that 1 is a nice balance point between 0 and infinity.

All the Best,

Jonathan

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I am pleased to help your wonderful essay rise higher. I expect that many more wonderful insights await, in the collection of your papers (or where you are an author) I have downloaded from arXiv. The overlooked importance of something small like the fundamental nature of the (0, 1, /infty) triple is seldom made known. I noticed you commented to this effect on Akinbo's essay site as well as in your own.

People are unaware that in an ab initio formulation, if we actually start at the very beginning and move forward from first principles, one can only know there is an extent; we can call it 1 but it could also be infinite as there is only nothing to compare it to. That is the rule for constructive geometers. In Ian Durham's essay; he makes the point that even knowing something is a unit, we still don't know how 'big' it is (e.g. - a bit or a trit). Perhaps ternary digits are more useful, after all.

But I like imagining that 1 is a nice balance point between 0 and infinity.

All the Best,

Jonathan

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Dear Jonathan,

As far as dessins d'enfants are concerned, the members of the triple (0, 1, /infty) have well defined meaning. Sorry that I just copy my earlier post:

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.

In experiments you will have 0 or 1 as the result of the experiment (in the single or multiple qubit context) but the unobserved \infty is needed in the explanation. The way the black points (bit 0) and white points (bit 1) ly on the dessin (a graph on the oriented surface such as the sphere S2, or a Riemann surface with holes) is such that sigma(0)*sigma(1)*sigma(infty)=id, where

sigma (0) is the permutation group attached to the black points 0 (how the edges incident on the black points rotate) and sigma (1) is the permutation group attached to the white point 1 (how the edges incident on the white points rotate).

It is still binary logic but in a more clever way (may be this has to do with Grothendieck's topos, I have not thought about this aspect).

Thanks again for your interest.

I intend to write you again about the Hopf fibrations.

My kind regards.

Michel

As far as dessins d'enfants are concerned, the members of the triple (0, 1, /infty) have well defined meaning. Sorry that I just copy my earlier post:

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.

In experiments you will have 0 or 1 as the result of the experiment (in the single or multiple qubit context) but the unobserved \infty is needed in the explanation. The way the black points (bit 0) and white points (bit 1) ly on the dessin (a graph on the oriented surface such as the sphere S2, or a Riemann surface with holes) is such that sigma(0)*sigma(1)*sigma(infty)=id, where

sigma (0) is the permutation group attached to the black points 0 (how the edges incident on the black points rotate) and sigma (1) is the permutation group attached to the white point 1 (how the edges incident on the white points rotate).

It is still binary logic but in a more clever way (may be this has to do with Grothendieck's topos, I have not thought about this aspect).

Thanks again for your interest.

I intend to write you again about the Hopf fibrations.

My kind regards.

Michel

Dear Michel,

Thank you so much for your essay. As far as I understand, in your essay, the conventional logic is used. When we use the different type logic, for example, topos http://arxiv.org/abs/quant-ph/0703060 , how to relate your approach? Also, the problem seems to be completely solved.

Best wishes,

Yutaka

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Thank you so much for your essay. As far as I understand, in your essay, the conventional logic is used. When we use the different type logic, for example, topos http://arxiv.org/abs/quant-ph/0703060 , how to relate your approach? Also, the problem seems to be completely solved.

Best wishes,

Yutaka

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Dear Yukata,

My essay don't refer to logic at all (although Grothendieck's topos may be hidden in it at some level).

Should I remind that Grothendieck introduced the concept of a topos.

It seems that you did not understand what my essay is about, but still scored it low, this is unfair.

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

I don't uderstand your sentence "the problem seems to be completely solved"!

Michel

My essay don't refer to logic at all (although Grothendieck's topos may be hidden in it at some level).

Should I remind that Grothendieck introduced the concept of a topos.

It seems that you did not understand what my essay is about, but still scored it low, this is unfair.

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

I don't uderstand your sentence "the problem seems to be completely solved"!

Michel

Dear Michel,

For completeness, I'm posting the following (slightly modified) response from my FQXi blog. Sorry to see that you are also the victim of some "unfair" voting. Regrettably, I scored many "ones" without the accompanying "critiques (the very reason that I entered, as spelt out in my essay).

Gordon

......

Dear Michel,

Many thanks for continuing the discussion. I hope we will get to do more of it in the future.

As for my acceptance (or otherwise) of COUNTERFACTUAL REASONING, let me offer the following proposition:

Perhaps the related problems are due to COUNTERFACTUAL TESTING!?

For example: In my Essay, referring to the CHSH Inequality -- page 7, equations (21)-(22) -- you will see that the inequality is based on a TRUISM (21). But we do NOT test the truism; rather, we test the best approximation that we can (22).

So, by this view, it is not counterfactual reasoning that's at fault. It's the failure, even the impossibility, of testing it.

Hence the question: Why should that impossibility be regarded as a valid strike against a rational local-realism?

Especially when QM fails to deliver in the same impossible context?

WHILE both theories deliver the same experimental outcomes!

Thus the need for further discussions continues.

With best regards; Gordon

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For completeness, I'm posting the following (slightly modified) response from my FQXi blog. Sorry to see that you are also the victim of some "unfair" voting. Regrettably, I scored many "ones" without the accompanying "critiques (the very reason that I entered, as spelt out in my essay).

Gordon

......

Dear Michel,

Many thanks for continuing the discussion. I hope we will get to do more of it in the future.

As for my acceptance (or otherwise) of COUNTERFACTUAL REASONING, let me offer the following proposition:

Perhaps the related problems are due to COUNTERFACTUAL TESTING!?

For example: In my Essay, referring to the CHSH Inequality -- page 7, equations (21)-(22) -- you will see that the inequality is based on a TRUISM (21). But we do NOT test the truism; rather, we test the best approximation that we can (22).

So, by this view, it is not counterfactual reasoning that's at fault. It's the failure, even the impossibility, of testing it.

Hence the question: Why should that impossibility be regarded as a valid strike against a rational local-realism?

Especially when QM fails to deliver in the same impossible context?

WHILE both theories deliver the same experimental outcomes!

Thus the need for further discussions continues.

With best regards; Gordon

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Dear Gordon,

Thank you for your continuing interest. I really appreciate your feedback at this time of the competition. We can certainly learn more from each other after the end of the contest. I will rate your essay highly, as it deserves, I would like to see you in the finalists, hopefully I will be too.

Concerning counterfactuality, as soon as a good theory of quantum observability is written, one will be able to check it as others assumpions in science. I claim that Grothendieck's approach with dessins d'enfants is an excellent starting point because it has all attributes of an archetype (read Dickau's essay) or a monad (read Ojo's essay) and other good ontological properties which I don't list here. Topos theory is not too far.

There are important essays here that pushed me to see the dessins d'enfants as "explicate imprints" of a more general (possibly spatio-temporal) algebraic geometry. I have in mind the Hopf fibrations as an excellent tool. For example you can lift S2 (the Riemann sphere) to S3 (the 3-sphere, i.e. the space of a single qubit (Jackson's intelligent qubit?), also the conformally compactified Minkowski space (see Matlock' essay and in relation to Bell's theorem Joy Christian 'realistic' approach).

Local/nonlocal arguments are insufficient, I think, mathematics should help in revealing the hidden machinary of the physical and ontological universe. May be this is Einstein's dream, not contradicting Wheeler, at the end of the day because we are, more or less, their children in knowledge.

Yes our discussion should live.

All the best,

Michel

Thank you for your continuing interest. I really appreciate your feedback at this time of the competition. We can certainly learn more from each other after the end of the contest. I will rate your essay highly, as it deserves, I would like to see you in the finalists, hopefully I will be too.

Concerning counterfactuality, as soon as a good theory of quantum observability is written, one will be able to check it as others assumpions in science. I claim that Grothendieck's approach with dessins d'enfants is an excellent starting point because it has all attributes of an archetype (read Dickau's essay) or a monad (read Ojo's essay) and other good ontological properties which I don't list here. Topos theory is not too far.

There are important essays here that pushed me to see the dessins d'enfants as "explicate imprints" of a more general (possibly spatio-temporal) algebraic geometry. I have in mind the Hopf fibrations as an excellent tool. For example you can lift S2 (the Riemann sphere) to S3 (the 3-sphere, i.e. the space of a single qubit (Jackson's intelligent qubit?), also the conformally compactified Minkowski space (see Matlock' essay and in relation to Bell's theorem Joy Christian 'realistic' approach).

Local/nonlocal arguments are insufficient, I think, mathematics should help in revealing the hidden machinary of the physical and ontological universe. May be this is Einstein's dream, not contradicting Wheeler, at the end of the day because we are, more or less, their children in knowledge.

Yes our discussion should live.

All the best,

Michel

Dear Michel,

yes, I read your essay but was on the vacation before I had the chance to write you. I like your geometric model very much (I rated your essay long ago with maximum score).

Now after a second reading I have some questions:

- You used the dessin d'enfants to visualize the contextuality. I understood the Mermin square but how did I see it in dessin d'enfant (Fig. 3b). Is it the number of half-edges (odd number) which produces the contradiction?

- Why is the transitive action so important? In case of a non-trivial orbit, you can check every point seperately.

One remark about the triple 0,1,infty: In the projective geometry, you always have the invariance w.r.t. the inversion operation. In the context of your model it means you have the operator and its inverse operator. Then 0 is related to infty and 1 is related to itself via inversion.

Thanks in advance for the answers.

Torsten

PS: Did you saw my post (June, 17) above?

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yes, I read your essay but was on the vacation before I had the chance to write you. I like your geometric model very much (I rated your essay long ago with maximum score).

Now after a second reading I have some questions:

- You used the dessin d'enfants to visualize the contextuality. I understood the Mermin square but how did I see it in dessin d'enfant (Fig. 3b). Is it the number of half-edges (odd number) which produces the contradiction?

- Why is the transitive action so important? In case of a non-trivial orbit, you can check every point seperately.

One remark about the triple 0,1,infty: In the projective geometry, you always have the invariance w.r.t. the inversion operation. In the context of your model it means you have the operator and its inverse operator. Then 0 is related to infty and 1 is related to itself via inversion.

Thanks in advance for the answers.

Torsten

PS: Did you saw my post (June, 17) above?

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Dear Torsten,

Thanks for your careful reading.

1) It is not straight to see the contradiction in the dessin of Fig. 3b, I failed to see it in general (for other contexts). Also there is not a single dessin leading to Mermin's square but many, why is it so? More work is necessary. This non-bijection is general for most geometries I have tried to reconstruct from the n-simplices to projective configurations such as Desargues, Cremona-Richmund (i.e. the doily W(2) of two-qubit commutatitivity) and others.

2) You are right that transitive action may not be a necessary condition. The geometry is constructed by having recourse to the stabilizer of each point in the permutation group relevant to the dessin.

3) Last remark, the geometry is of the projective type not the dessin. Here you have to refer to the theory that is well explained, for example in Lando and Zvonkin (my ref. [6]).

Torsten, please check that you vote was recorded.

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Thanks for your careful reading.

1) It is not straight to see the contradiction in the dessin of Fig. 3b, I failed to see it in general (for other contexts). Also there is not a single dessin leading to Mermin's square but many, why is it so? More work is necessary. This non-bijection is general for most geometries I have tried to reconstruct from the n-simplices to projective configurations such as Desargues, Cremona-Richmund (i.e. the doily W(2) of two-qubit commutatitivity) and others.

2) You are right that transitive action may not be a necessary condition. The geometry is constructed by having recourse to the stabilizer of each point in the permutation group relevant to the dessin.

3) Last remark, the geometry is of the projective type not the dessin. Here you have to refer to the theory that is well explained, for example in Lando and Zvonkin (my ref. [6]).

Torsten, please check that you vote was recorded.

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Dear Torsten (a copy is on your blog),

I am trying to better understand your deep essay but it turns out to be quite difficult accounting for my poor knowledge of differential geometry.

I have a naive question. The (first) Hopf fibration S^3 can be seen as the sphere bundle over the Riemann sphere S^2 with fiber S^1. Could you explain what is the sphere bundle S^2 x [0,1] that you associate to the gravitational interaction? May it be considered as some sort of lift from dessins d'enfants on S^2 to S^2 x S^0, and the latter object lives in circles on S^3, right?

I have in mind Matlock's essay as well.

All the best,

Michel

I am trying to better understand your deep essay but it turns out to be quite difficult accounting for my poor knowledge of differential geometry.

I have a naive question. The (first) Hopf fibration S^3 can be seen as the sphere bundle over the Riemann sphere S^2 with fiber S^1. Could you explain what is the sphere bundle S^2 x [0,1] that you associate to the gravitational interaction? May it be considered as some sort of lift from dessins d'enfants on S^2 to S^2 x S^0, and the latter object lives in circles on S^3, right?

I have in mind Matlock's essay as well.

All the best,

Michel

Thanks Michel for your message on my blog. My arguments are from a philosophical and classical perspective. It is possible that when viewed from your perspective we may well be saying something similar. I am not expert on the math involved in quantum theory.

Following additional insights gained from interacting with FQXi community members, perhaps you will find the the judgement in the case of Atomistic Enterprises Inc. vs. Plato & Ors, delivered on Jul. 28, 2013 @ 11:39 GMT easier to understand my thinking.

Best regards,

Akinbo

*I have already rated your essay so you may do likewise.

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Following additional insights gained from interacting with FQXi community members, perhaps you will find the the judgement in the case of Atomistic Enterprises Inc. vs. Plato & Ors, delivered on Jul. 28, 2013 @ 11:39 GMT easier to understand my thinking.

Best regards,

Akinbo

*I have already rated your essay so you may do likewise.

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Greetings Michel,

I enjoyed the last comments left on my essay space, and I eagerly await the next chapter on Hopf fibrations - which are already a subject of interest.

It appears the 'infection' has spread, but Dr. Planat is in!

Have Fun,

Jonathan

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I enjoyed the last comments left on my essay space, and I eagerly await the next chapter on Hopf fibrations - which are already a subject of interest.

It appears the 'infection' has spread, but Dr. Planat is in!

Have Fun,

Jonathan

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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...

view entire post

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...

view entire post

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Dear Hugh,

"different footing"

it is a matter of perspective, the pentagram possesses the same graph than the Desargues configuration that can be drawn in several ways. The non-bijection between drawings and geometries here (and elswhere) is something I am currently working at.

"avenues"

yes, our recent papers pointing out G2(2) and octonions (several comments in this blog) and more to come, including (with you?) the lift to S3.

"k-rational points"

excellent, we are preciselt talking about algebraic curves on the Riemann sphere (S2 say), after the lift we should keep the algebraic property.

"Dessins d'Or"

a lift to Orland circles, or Urland knots.

My kind regards,

Michel

"different footing"

it is a matter of perspective, the pentagram possesses the same graph than the Desargues configuration that can be drawn in several ways. The non-bijection between drawings and geometries here (and elswhere) is something I am currently working at.

"avenues"

yes, our recent papers pointing out G2(2) and octonions (several comments in this blog) and more to come, including (with you?) the lift to S3.

"k-rational points"

excellent, we are preciselt talking about algebraic curves on the Riemann sphere (S2 say), after the lift we should keep the algebraic property.

"Dessins d'Or"

a lift to Orland circles, or Urland knots.

My kind regards,

Michel

This test is the best that I have read and analyzed in this contest.Explains Dr Planat efficiently and deep map the graph theory applied to information processing, in quantum theory. In this analysis, both logically well argued, as mathematically demonstrated the clear and inevitable connection with the theory of graphs and maps permutations, with information theory.Certainly, from my humble point of view, a clear candidate to receive recognition for this contest.

Rate it all!!

Thanks Dr Planat

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Rate it all!!

Thanks Dr Planat

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Dear Michel,

I rated already your sophisticatedly serious essay on August 1st. Somehow, my comment accompanied with my vote is lost or not posted. I definitely agree that all interpretations must be contextual in its nature. Excellent work!

If I may say, KQID proposes contextuality through KQID Ouroboros Equations of Existence that combines Newton, Maxwell, Planck, Boltzmann, Lorentz,Einstein, Laundauer, Wheeler , Feynman, Ssusskind, Hooft, Wilczek, Bousso and others. The Ouroboros Equations mean each interpretation involves every beginning to every ending. Similarly, everything we do involve the Ouroboros action or totality of any action. Nature is such unbelievable phenomena that we are just now starting to peek into its secret that is shockingly simple in the beginning but infinitely complex in the ending that per KQID every absolute digital time ≤ 10^-1000seconds. Interestingly, the mechanism is also simple. See my essay Child of Qbit in time.

All the Best,

Leo KoGuan

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I rated already your sophisticatedly serious essay on August 1st. Somehow, my comment accompanied with my vote is lost or not posted. I definitely agree that all interpretations must be contextual in its nature. Excellent work!

If I may say, KQID proposes contextuality through KQID Ouroboros Equations of Existence that combines Newton, Maxwell, Planck, Boltzmann, Lorentz,Einstein, Laundauer, Wheeler , Feynman, Ssusskind, Hooft, Wilczek, Bousso and others. The Ouroboros Equations mean each interpretation involves every beginning to every ending. Similarly, everything we do involve the Ouroboros action or totality of any action. Nature is such unbelievable phenomena that we are just now starting to peek into its secret that is shockingly simple in the beginning but infinitely complex in the ending that per KQID every absolute digital time ≤ 10^-1000seconds. Interestingly, the mechanism is also simple. See my essay Child of Qbit in time.

All the Best,

Leo KoGuan

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Dear Leo KoGuan,

(copy of my response to you on my blog)

In my opinion, your essay belongs to the world of art, being a non-classical balance between old and modern concepts (trigrams and scientific equations), a superposition of religion and philosophy. It is well written and attractive. As we do not have access to the whole truth of the universe (may be you have), your approach is a possible opening.

Best regards,

Michel

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(copy of my response to you on my blog)

In my opinion, your essay belongs to the world of art, being a non-classical balance between old and modern concepts (trigrams and scientific equations), a superposition of religion and philosophy. It is well written and attractive. As we do not have access to the whole truth of the universe (may be you have), your approach is a possible opening.

Best regards,

Michel

Dear Michel,

Repost it here from my blog.

Absolute truth is relative as we are Qbit in finite form, thus we do have relative truth as a conscious observer as a meme ψI(CTE), bits-waves function of consciousness(C), time(T) and energy (E) = A + S. this meme ψI(CTE is us, amoeba, atom, our universe, our Multiverse and our God/s. we are Shakespearean actors in the Multiversal...

view entire post

Repost it here from my blog.

Absolute truth is relative as we are Qbit in finite form, thus we do have relative truth as a conscious observer as a meme ψI(CTE), bits-waves function of consciousness(C), time(T) and energy (E) = A + S. this meme ψI(CTE is us, amoeba, atom, our universe, our Multiverse and our God/s. we are Shakespearean actors in the Multiversal...

view entire post

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Dear Leo,

"KQID Qbit is (00,1,-1) which is singularity Qbit Multiverse in zeroth dimension at absolute zero temperature that computes and projects Einstein complex coordinates"

there is an analogy with Grotendieck's singularity triple (\infty,0,1) that is the building block of dessins d'enfant theory: very strange! You can see my response to Jonathan Dickau for details.

Where is the FAPAMA concept coming from in your frame? I mean who is the influencial thinker?

All the best,

Michel

"KQID Qbit is (00,1,-1) which is singularity Qbit Multiverse in zeroth dimension at absolute zero temperature that computes and projects Einstein complex coordinates"

there is an analogy with Grotendieck's singularity triple (\infty,0,1) that is the building block of dessins d'enfant theory: very strange! You can see my response to Jonathan Dickau for details.

Where is the FAPAMA concept coming from in your frame? I mean who is the influencial thinker?

All the best,

Michel

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...

view entire post

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...

view entire post

report post as inappropriate

I also saved a copy of your response, so I add it here:

--------------------------------------

Dear Hugh,

"different footing"

it is a matter of perspective, the pentagram possesses the same graph than the Desargues configuration that can be drawn in several ways. The non-bijection between drawings and geometries here (and elswhere) is something I am currently working at.

"avenues"

yes, our recent papers pointing out G2(2) and octonions (several comments in this blog) and more to come, including (with you?) the lift to S3.

"k-rational points"

excellent, we are preciselt talking about algebraic curves on the Riemann sphere (S2 say), after the lift we should keep the algebraic property.

"Dessins d'Or"

a lift to Orland circles, or Urland knots.

My kind regards,

Michel

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--------------------------------------

Dear Hugh,

"different footing"

it is a matter of perspective, the pentagram possesses the same graph than the Desargues configuration that can be drawn in several ways. The non-bijection between drawings and geometries here (and elswhere) is something I am currently working at.

"avenues"

yes, our recent papers pointing out G2(2) and octonions (several comments in this blog) and more to come, including (with you?) the lift to S3.

"k-rational points"

excellent, we are preciselt talking about algebraic curves on the Riemann sphere (S2 say), after the lift we should keep the algebraic property.

"Dessins d'Or"

a lift to Orland circles, or Urland knots.

My kind regards,

Michel

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Dear Michel - It took three readings of your paper before I understood it. However, I think it was worthwhile. There are some extraordinarily provocative ideas here, and as soon as the contest is over I plan to follow up and read your other publications.

I particularly enjoyed your recognition of bipartite graphs being at the heart of reality (a two-player) two qubit setup.

Introducing Grothendieck’s dessin d’enfant was a stroke of genius. A wonderful tool to cut to the heart of the matter and expose the underlying simplicity of our universe.

I was somewhat taken aback by the appearance of what appeared to be a random integer without reference in many places in your essay (e.g 12096 guys), until I realized that you were using the Magma software.

There may be an unfortunate spelling error in the first paragraph under 3.3. Mermin’s pentagram: If I am not mistaken “Peceptual” should be “Perceptual”. At first I thought it was some new word or concept in in projective geometry I was unfamiliar with, but then discovered I could not find the word in a web search.

All in all this is a great essay and I gave it very high marks. I look forward to following up on your other publications at a later time.

Good luck in the contest.

Kind regards, Paul

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I particularly enjoyed your recognition of bipartite graphs being at the heart of reality (a two-player) two qubit setup.

Introducing Grothendieck’s dessin d’enfant was a stroke of genius. A wonderful tool to cut to the heart of the matter and expose the underlying simplicity of our universe.

I was somewhat taken aback by the appearance of what appeared to be a random integer without reference in many places in your essay (e.g 12096 guys), until I realized that you were using the Magma software.

There may be an unfortunate spelling error in the first paragraph under 3.3. Mermin’s pentagram: If I am not mistaken “Peceptual” should be “Perceptual”. At first I thought it was some new word or concept in in projective geometry I was unfamiliar with, but then discovered I could not find the word in a web search.

All in all this is a great essay and I gave it very high marks. I look forward to following up on your other publications at a later time.

Good luck in the contest.

Kind regards, Paul

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Dear Paul,

Thank you for reading me. Let me briefly clarify a few points

* As an expert of time you may know that a bad clock, when phase-locked to a master clock, inherits the stability of the master.

* The dessins are bipartite, as you recognized. They have been applied to two-player operators (as in the Mermin square) and to three-player operators (as in the Fano plane). In the next stage of the research, I will show how to circumvent the "unhappy ending" with the three-player pentagram. The bipartite dessins can be applied to geometries underlying many player operators.

* The number 12096 is not a random one but is related to the number of symmetries in the split Cayley hexagon as you can read in my recent research (with coauthors).

* You are right, you should read "perceptual".

I now swithch and rate your essay.

Best wishes,

Michel

Thank you for reading me. Let me briefly clarify a few points

* As an expert of time you may know that a bad clock, when phase-locked to a master clock, inherits the stability of the master.

* The dessins are bipartite, as you recognized. They have been applied to two-player operators (as in the Mermin square) and to three-player operators (as in the Fano plane). In the next stage of the research, I will show how to circumvent the "unhappy ending" with the three-player pentagram. The bipartite dessins can be applied to geometries underlying many player operators.

* The number 12096 is not a random one but is related to the number of symmetries in the split Cayley hexagon as you can read in my recent research (with coauthors).

* You are right, you should read "perceptual".

I now swithch and rate your essay.

Best wishes,

Michel

Dear Michael,

We are at the end of this essay contest.

In conclusion, at the question to know if Information is more fundamental than Matter, there is a good reason to answer that Matter is made of an amazing mixture of eInfo and eEnergy, at the same time.

Matter is thus eInfo made with eEnergy rather than answer it is made with eEnergy and eInfo ; because eInfo is eEnergy, and the one does not go without the other one.

eEnergy and eInfo are the two basic Principles of the eUniverse. Nothing can exist if it is not eEnergy, and any object is eInfo, and therefore eEnergy.

And consequently our eReality is eInfo made with eEnergy. And the final verdict is : eReality is virtual, and virtuality is our fundamental eReality.

Good luck to the winners,

And see you soon, with good news on this topic, and the Theory of Everything.

Amazigh H.

I rated your essay.

Please visit My essay.

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We are at the end of this essay contest.

In conclusion, at the question to know if Information is more fundamental than Matter, there is a good reason to answer that Matter is made of an amazing mixture of eInfo and eEnergy, at the same time.

Matter is thus eInfo made with eEnergy rather than answer it is made with eEnergy and eInfo ; because eInfo is eEnergy, and the one does not go without the other one.

eEnergy and eInfo are the two basic Principles of the eUniverse. Nothing can exist if it is not eEnergy, and any object is eInfo, and therefore eEnergy.

And consequently our eReality is eInfo made with eEnergy. And the final verdict is : eReality is virtual, and virtuality is our fundamental eReality.

Good luck to the winners,

And see you soon, with good news on this topic, and the Theory of Everything.

Amazigh H.

I rated your essay.

Please visit My essay.

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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...

view entire post

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...

view entire post

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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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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...

view entire post

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Some fascinating ideas in here, and I much appreciated your reference to the Hunting of the Snark!

"We have clues, clues most of all in the writings of Bohr, but not

answer ... Are billions upon billions of acts of observer-participancy the foundation of everything? We are about as fas 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.."

And then are we back at the question as to what is an observation? :)

Cheers!

Jennifer

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"We have clues, clues most of all in the writings of Bohr, but not

answer ... Are billions upon billions of acts of observer-participancy the foundation of everything? We are about as fas 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.."

And then are we back at the question as to what is an observation? :)

Cheers!

Jennifer

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Bonjour Michel,

Merci pour vos commentaires sur mon blog !

Unfortunately I haven't got the academic level required to fully understand your essay but I think that we agree that the underlying structure of the Universe is much simpler than what we think.

Best of luck in the contest.

Patrick

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Merci pour vos commentaires sur mon blog !

Unfortunately I haven't got the academic level required to fully understand your essay but I think that we agree that the underlying structure of the Universe is much simpler than what we think.

Best of luck in the contest.

Patrick

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Michel - this is a fine interdisciplinary effort. Kudos for featuring a non house-hold name like Grothendieck in your presentation. It seems your are hinting that number theory should be a more prominent feature of this fundamental information science. Your graph concepts remind me of some efforts by David Finkelstein. These are crucial to representing the "tangle" of en-tangle-ment relations that must be understood to make sense of the contextual and interrelational nature of information in our universe. BTW that last line of the Lewis Carroll quote really gives pause. Cheers.

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Michel,

Thank you for contributing this essay to the project - it's an excellent mathematical approach to deeply understand measurement and information theory, and you accomplish it with sophistication, rigor, and passion. (I gave it the highest rating). I learned some interesting points about quantum contextuality, and especially liked the development of the dessins and Mermin's pentagram. I remember attending a lecture a long time ago by Mermin where he discussed some of these ideas, and your paper is a refreshing jumping point from that. Definitely I want to study this some more. Thanks again, and thanks for your comments on my page too,

Sincerely,

Steve Sax

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Thank you for contributing this essay to the project - it's an excellent mathematical approach to deeply understand measurement and information theory, and you accomplish it with sophistication, rigor, and passion. (I gave it the highest rating). I learned some interesting points about quantum contextuality, and especially liked the development of the dessins and Mermin's pentagram. I remember attending a lecture a long time ago by Mermin where he discussed some of these ideas, and your paper is a refreshing jumping point from that. Definitely I want to study this some more. Thanks again, and thanks for your comments on my page too,

Sincerely,

Steve Sax

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You are welcome, and thank you too :) Fyi, the page had problems accepting my voting at first, and I've been spending the last hour getting it to work (it was my browser apparently). But it now worked, and my vote (10) was just accepted, as you can now see. Again, it was a very informative and educational paper, and I'm glad to have read it.

Kindly, Steve

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Kindly, Steve

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Nice presentation of examples of contextuality proofs. A shortcoming of the essay was that I didn't see much presentation of their relation to the philosophical questions about it from bit, though, or what the particular implications of a dessins d'enfant-based proof might be for the nature of information and reality according to quantum theory. But an enjoyable presentation.

Howard

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Howard

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Dear Howard,

Thank you for your generous comment.

I agree that the philosophical issue of the toy (children-like) model of quantum observation is not discussed.

To be honest I felt too naive to treat it and I decided to restrict my presentation to very few but relevant

examples of contextuality, following Mermin's footsteps. I got a quite good feedback from a few philosophers

in this audience and I now have the feeling that Grothendieck's dessins d'enfants and the related algebraic curves

may help to clarify the it-bit duality.

The toy model is mathematical and I used it here to recover finite geometries such as the Fano plane and Mermin's

square. As mentioned a few times in my reply to posts, even Mermin's pentagram can be recovered but under a different

perspective (Desargues configuration). In this line of applications, the diagram/dessin comprises edges that are

quantum observables, the extremities 0 and 1 of the edges are the two allowed results of the multiple qubit experiment.

This reading of the toy model works as a "it from bit" approach. A more detailed meaning remains to be established,

possibly having in mind questions about counterfactuals, how come the quantum and thr related concepts you describe so nicely

in your own essay.

Thank you for your generous comment.

I agree that the philosophical issue of the toy (children-like) model of quantum observation is not discussed.

To be honest I felt too naive to treat it and I decided to restrict my presentation to very few but relevant

examples of contextuality, following Mermin's footsteps. I got a quite good feedback from a few philosophers

in this audience and I now have the feeling that Grothendieck's dessins d'enfants and the related algebraic curves

may help to clarify the it-bit duality.

The toy model is mathematical and I used it here to recover finite geometries such as the Fano plane and Mermin's

square. As mentioned a few times in my reply to posts, even Mermin's pentagram can be recovered but under a different

perspective (Desargues configuration). In this line of applications, the diagram/dessin comprises edges that are

quantum observables, the extremities 0 and 1 of the edges are the two allowed results of the multiple qubit experiment.

This reading of the toy model works as a "it from bit" approach. A more detailed meaning remains to be established,

possibly having in mind questions about counterfactuals, how come the quantum and thr related concepts you describe so nicely

in your own essay.

Congratulations Michel!

Your essay deserves to win a prize, and it was most excellent to 'meet' you on these forums. I wish you the best of luck in the finals.

Have Fun!

Jonathan

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Your essay deserves to win a prize, and it was most excellent to 'meet' you on these forums. I wish you the best of luck in the finals.

Have Fun!

Jonathan

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Dear Jonathan and friends,

I found a few noticeable quotes that may have to do with the spirit of this FQXI contest

Bohr

"What is that we human beings ultimately depend on? We depend on our words. We are suspended in language. Our task is to communicate experience and ideas to others."

Wheeler

"You can talk about people like Buddha, Jesus, Moses, Confucius, but the thing that convinced me that such people existed were the conversations with Bohr."

About his time working with Niels Bohr in Copenhagen.

Darwin

"In the long history of humankind (and animal kind, too) those who learned to collaborate and improvise most effectively have prevailed."

Darwin again

"I have called this principle, by which each slight variation, if useful, is preserved, by the term of Natural Selection."

Kind regards to all,

Michel

I found a few noticeable quotes that may have to do with the spirit of this FQXI contest

Bohr

"What is that we human beings ultimately depend on? We depend on our words. We are suspended in language. Our task is to communicate experience and ideas to others."

Wheeler

"You can talk about people like Buddha, Jesus, Moses, Confucius, but the thing that convinced me that such people existed were the conversations with Bohr."

About his time working with Niels Bohr in Copenhagen.

Darwin

"In the long history of humankind (and animal kind, too) those who learned to collaborate and improvise most effectively have prevailed."

Darwin again

"I have called this principle, by which each slight variation, if useful, is preserved, by the term of Natural Selection."

Kind regards to all,

Michel

Dear all,

An update of the ideas developed in the essay is in the paper

http://xxx.lanl.gov/abs/1310.4267

Michel

An update of the ideas developed in the essay is in the paper

http://xxx.lanl.gov/abs/1310.4267

Michel

Dear Michel,

From Maudlin's subquestion 1) „Which mathematical concepts seem naturally suited to describe features of the physical world, and what does their suitability Imply about the physical world?“

I suggest three main candidates for the mathematical concept:

bit (it was the subject of the competition FQXi 2013);

exp(x) (You know the unique features of this function);

Euler's identity.

There are other useful functions, but less importance.

Suitable use of pervious can to describe features of the physical World.

What are your main candidates?

Best Regards,

Branko Zivlak

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From Maudlin's subquestion 1) „Which mathematical concepts seem naturally suited to describe features of the physical world, and what does their suitability Imply about the physical world?“

I suggest three main candidates for the mathematical concept:

bit (it was the subject of the competition FQXi 2013);

exp(x) (You know the unique features of this function);

Euler's identity.

There are other useful functions, but less importance.

Suitable use of pervious can to describe features of the physical World.

What are your main candidates?

Best Regards,

Branko Zivlak

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