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It From Bit or Bit From It? Essay Contest (2013)
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It from qubit: how to draw quantum contextuality by Michel Dr Planat
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Author Michel Planat wrote on Jun. 10, 2013 @ 17:28 GMT
Essay AbstractWheeler'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.
Author BioMichel 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.
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Joe Fisher wrote on Jun. 11, 2013 @ 16:42 GMT
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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Author Michel Planat replied on Jun. 12, 2013 @ 08:19 GMT
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
Philip Gibbs wrote on Jun. 12, 2013 @ 14:18 GMT
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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Author Michel Planat wrote on Jun. 12, 2013 @ 15:33 GMT
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
Philip Gibbs replied on Jun. 12, 2013 @ 15:42 GMT
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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Jochen Szangolies wrote on Jun. 13, 2013 @ 08:53 GMT
Dear Michel,
I've read your essay already when it appeared on the arXiv, and have since been waiting for a chance to comment on it. Having done some work on quantum contextuality myself, I was naturally very curious about your ideas, and though I'll need a bit more time to digest the mathematics, I must say I'm very intrigued.
From the title, I at first assumed you were going to...
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Dear Michel,
I've read your essay already when it appeared on the arXiv, and have since been waiting for a chance to comment on it. Having done some work on quantum contextuality myself, I was naturally very curious about your ideas, and though I'll need a bit more time to digest the mathematics, I must say I'm very intrigued.
From the title, I at first assumed you were going to consider the observation that the Lovasz theta function, a measure for a graph's Shannon capacity, gives the quantum violation of contextuality inequalities in at least some cases (something realized first, I think, by
Cabello and co-workers). But while you also talk about the Shannon capacity, to me at least the relationship seems not obvious.
First of all, I think your observation that "Wheeler's observer-participancy is contextual" is spot on: in fact, this is essentially the lesson of Bohr's complementarity---we cannot describe all our observations within one single classical picture, just as, in contextuality, we cannot give a single probability distribution (or truth-valuation) for all observables.
However, I think I've missed the main point, probably, which is the precise connection between the dessins and contextuality. Usual proofs of the Kochen-Specker theorem rely on finding a set of vectors in Hilbert space such that the associated graph is not 2-colorable, that is, one cannot find a truth valuation. What do the dessins tell you about this? (Apologies if it's obvious and I just haven't been paying attention.)
Also, on an unrelated note, since I know you've done some work on the black hole/qubit correspondence: in your opinion, does the correspondence tell us something 'deep' about nature, or is it just a mathematical curiosity? I used to be pretty skeptical, thinking that it's probably just based on the coincidence that the group SL(2,C) crops up in both context, but now that
entanglement is wormholes ;-), why not have qubits be black holes?
Cheers, and my best wishes for the contest,
Jochen
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Author Michel Planat wrote on Jun. 13, 2013 @ 10:00 GMT
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
Lawrence B Crowell wrote on Jun. 13, 2013 @ 15:19 GMT
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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Author Michel Planat wrote on Jun. 13, 2013 @ 17:12 GMT
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
Lawrence B Crowell replied on Jun. 14, 2013 @ 04:18 GMT
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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Author Michel Planat wrote on Jun. 14, 2013 @ 09:16 GMT
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
Jochen Szangolies replied on Jun. 14, 2013 @ 13:14 GMT
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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Lawrence B Crowell replied on Jun. 14, 2013 @ 14:14 GMT
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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Torsten Asselmeyer-Maluga wrote on Jun. 17, 2013 @ 10:43 GMT
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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Lawrence B Crowell wrote on Jun. 18, 2013 @ 15:51 GMT
Michel,
I reread your paper again this last Sunday. The desin d'enfant leads at the end to Mermin's pentagons. These are of course an aspect of the Kochen-Specker theorem. This is of course the main theorem on contextuality in QM. In my paper I discuss the quantum homotopies of associators at various dimensions, which are pentagonal systems. I copy this post on my essay blog page, so...
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Michel,
I reread your paper again this last Sunday. The desin d'enfant leads at the end to Mermin's pentagons. These are of course an aspect of the Kochen-Specker theorem. This is of course the main theorem on contextuality in QM. In my
paper I discuss the quantum homotopies of associators at various dimensions, which are pentagonal systems. I copy this post on my essay blog page, so you can respond to this there as well.
I notice you have considerable interest in the G_2 group, which is the automorphism of the E8 group. The F_4 group is a centralizer in E8, whereby G_2 action keep it fixed; the elements of F_4 and G_2 commute.
The Kochen-Specker theorem is connected with the F_4 group, or the 24 cell. The 117 projectors with the original KS theorem in 3-dim Hilbert space is simplified by considering a four dimensional Hilbert space, or a system of 4 qubits. This involves only 18 projector operators. The space 24-cells is a system of root vectors for the F_4 group. Each root vector is paired with its negative to define a line through the origin in 4d space. These 24 lines are the 24 rays of Peres. The root vectors are
1 (2,0,0,0) 2 (0,2,0,0) 3 (0,0,2,0) 4 (0,0,0,2)
5 (1,1,1,1) 6 (1,1,-1,-1) 7 (1,-1,1,-1) 8 (1,-1,-1,1)
9 (-1,1,1,1) 10 (1,-1,1,1) 11 (1,1,-1,1) 12 (1,1,1,-1)
13 (1,1,0,0) 14 (1,-1,0,0) 15 (0,0,1,1) 16 (0,0,1,-1)
17 (0,1,0,1) 18 (0,1,0,-1) 19 (1,0,1,0) 20 (1,0,-1,0)
21 (1,0,0,-1) 22 (1,0,0,1) 23 (0,1,-1,0) 24 (0,1,1,0)
(I hope this table works out here) Consider these as 24 quantum states |ψ_i>, properly normalized, in a 4 dimensionl Hilbert Space e.g. it might be a system of two qubits. For each state we can define a projection operator
P_i = |ψ_i)(ψ_i| --- I have to use parentheses because carrot signs fail in this blog.
P_i are are Hermitian operators with three eigenvlaues of 0 and one of 1. They can be considered as observables and we could set up an experimental system where we prepare states and measure these observables to check that they comply with the rules of quantum mechanics. There are sets of 4 operators which commute because the 4 rays they are based on are mutually orthogonal. An example would be the four operators P_1, P_2, P_3, P4.
Quantum mechanics tells us if we measure these commuting observables in any order we will end up with a state which is a common eigenvector i.e. one of the first four rays. The values of the observables will always be given by 1,0,0,0 in some order. This can be checked experimentally. There exist 36 sets of 4 different rays that are mutually orthogonal, but we just need 9 of them as follows:
{P2, P4, P19, P20}
{P10, P11, P21, P24}
{P7, P8, P13, P15}
{P2, P3, P21, P22}
{P6, P8, P17, P19}
{P11, P12, P14, P15}
{P6, P7, P22, P24}
{P3, P4, P13, P14}
{P10, P12, P17, P20}
At this point you need to check two things, firstly that each of these sets of 4 observables are mutually commuting because the rays are othogonal, secondly that there are 18 observables each of which appears in exactly two sets.
Now assume there is some hidden variable theory which explains this system and which reproduces all the predictions of quantum mechanics. At any given moment the system is in a definite state, and values for each of the 18 operators are determined. The values must be 0 or 1. with the rules they are equal to 1 for exactly one observable in each of the 9 sets, the other three values in each set will be 0. Consequently, there must be nine values set to one overall. This leads to a contradiction, for each observable appears twice so which ever observables have the value of 1 there will always be an even number of ones in total, and 9 is not even.
To add another ingredient into this mix I reference
, which illustrates how the Kochen-Specker result is an aspect of the 24-cell. The 24-cell has a number of representations. The full representation is the F_4 group with 1154 Hurwitz quaternions. The other is the B_4, which is the 16 cell Plus an 8-cell, and the other is D_4 which is three 8-cells. The more general automorphism is then F_4. The quotient between the 52 dimensional F_4 and the 36 dimensional so(9) ~ B_4 defines the short exact sequence
F_4/B_4:1 --> spin(9) --> F_{52\16} --> {\cal O}P^2 --> 1,
where F_{52\16} means F_4 restricted to 36 dimensions, which are the kernel of the map to the 16 dimensional Moufang or Cayley plane OP^2. The occurrence of 36 and 9 is no accident, and this is equivalent to the structure used to prove the KS theorem.
F_4 is the isometry group of the projective plane over the octonions. There are extensions to this where the bi-ocotonions CxO have the isometry group E_6, HxO has E_7 and OxO has E_8. This forms the basis of the "magic square." F_4 plays a prominent role in the bi-octonions, which is J^3(O) or the Jordan algebra as the automorphism which preserves the determinant of the Jordan matrix
The exceptional group G_2 is the automorphism on O, or equivalently that F_4xG_2 defines a centralizer on E_8. The fibration G_2 --> S^7 is completed with SO(8), where the three O's satisfy the triality condition in SO(8). The G_2 fixes a vector basis in S^7 according to the triality condition on vectors V \in J^3(O) and spinors θ in O, t:Vxθ_1xθ_2 --> R. The triality group is spin(8) and a subgroup spin(7) will fix a vector in V and a spinor in θ_1. To fix a vector in spin(7) the transitive action of spin(7) on the 7-sphere with spin(7)/G_2 = S^7 with dimensions
dim(G_2) = dim(spin(7)) - dim(S^7) = 21 - 7 = 14.
The G_2 group in a sense fixes a frame on the octonions, and has features similar to a gauge group. The double covering so(O) ~= so(8) and the inclusion g_2 \subset spin(8) determines the homomorphism g_2 hook--> spin(8) --> so(O). The 1-1 inclusion of g_2 in so(O) maps a 14 dimensional group into a 28 dimensional group. This construction is remarkably similar to the moduli space construction of Duff et al. .
Cheers LC
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Vladimir F. Tamari wrote on Jun. 19, 2013 @ 01:39 GMT
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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Lawrence B Crowell wrote on Jun. 19, 2013 @ 17:58 GMT
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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Hoang cao Hai wrote on Jun. 20, 2013 @ 19:17 GMT
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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Author Michel Planat replied on Jun. 21, 2013 @ 09:05 GMT
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
Jacek Safuta wrote on Jun. 21, 2013 @ 16:49 GMT
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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Author Michel Planat replied on Jun. 21, 2013 @ 19:46 GMT
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
Jacek Safuta replied on Jun. 22, 2013 @ 10:17 GMT
Thank you Michael,
I will keep checking Arxiv.
Regards
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Alexei Grinbaum wrote on Jun. 23, 2013 @ 10:08 GMT
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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Author Michel Planat replied on Jun. 23, 2013 @ 12:53 GMT
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
Cristinel Stoica wrote on Jun. 25, 2013 @ 08:19 GMT
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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Author Michel Planat wrote on Jun. 26, 2013 @ 19:15 GMT
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
Sreenath B N wrote on Jun. 27, 2013 @ 08:33 GMT
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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Satyavarapu Naga Parameswara Gupta wrote on Jun. 28, 2013 @ 02:09 GMT
Dear
Thank you for presenting your nice essay. I saw the abstract and will post my comments soon.
So you can produce material from your thinking. . . .
I am requesting you to go through my essay also. And I take this opportunity to say, to come to reality and base your arguments on experimental results.
I failed mainly because I worked against the main stream. The...
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Dear
Thank you for presenting your nice essay. I saw the abstract and will post my comments soon.
So you can produce material from your thinking. . . .
I am requesting you to go through my essay also. And I take this opportunity to say, to come to reality and base your arguments on experimental results.
I failed mainly because I worked against the main stream. The main stream community people want magic from science instead of realty especially in the subject of cosmology. We all know well that cosmology is a subject where speculations rule.
Hope to get your comments even directly to my mail ID also. . . .
Best
=snp
snp.gupta@gmail.com
http://vaksdynamicuniversemodel.b
logspot.com/
Pdf download:
http://fqxi.org/community/forum/topic/essay-downloa
d/1607/__details/Gupta_Vak_FQXi_TABLE_REF_Fi.pdf
Part of abstract:
- -Material objects are more fundamental- - is being proposed in this paper; It is well known that there is no mental experiment, which produced material. . . Similarly creation of matter from empty space as required in Steady State theory or in Bigbang is another such problem in the Cosmological counterpart. . . . In this paper we will see about CMB, how it is generated from stars and Galaxies around us. And here we show that NO Microwave background radiation was detected till now after excluding radiation from Stars and Galaxies. . . .
Some complements from FQXi community. . . . .
A
Anton Lorenz Vrba wrote on May. 4, 2013 @ 13:43 GMT
……. I do love your last two sentences - that is why I am coming back.
Author Satyavarapu Naga Parameswara Gupta replied on May. 6, 2013 @ 09:24 GMT
. . . . We should use our minds to down to earth realistic thinking. There is no point in wasting our brains in total imagination which are never realities. It is something like showing, mixing of cartoon characters with normal people in movies or people entering into Game-space in virtual reality games or Firing antimatter into a black hole!!!. It is sheer a madness of such concepts going on in many fields like science, mathematics, computer IT etc. . . .
B.
Francis V wrote on May. 11, 2013 @ 02:05 GMT
Well-presented argument about the absence of any explosion for a relic frequency to occur and the detail on collection of temperature data……
C
Robert Bennett wrote on May. 14, 2013 @ 18:26 GMT
"Material objects are more fundamental"..... in other words "IT from Bit" is true.
Author Satyavarapu Naga Parameswara Gupta replied on May. 14, 2013 @ 22:53 GMT
1. It is well known that there is no mental experiment, which produced material.
2. John Wheeler did not produce material from information.
3. Information describes material properties. But a mere description of material properties does not produce material.
4. There are Gods, Wizards, and Magicians, allegedly produced material from nowhere. But will that be a scientific experiment?
D
Hoang cao Hai wrote on Jun. 16, 2013 @ 16:22 GMT
It from bit - where are bit come from?
Author Satyavarapu Naga Parameswara Gupta replied on Jun. 17, 2013 @ 06:10 GMT
….And your question is like asking, -- which is first? Egg or Hen?— in other words Matter is first or Information is first? Is that so? In reality there is no way that Matter comes from information.
Matter is another form of Energy. Matter cannot be created from nothing. Any type of vacuum cannot produce matter. Matter is another form of energy. Energy is having many forms: Mechanical, Electrical, Heat, Magnetic and so on..
E
Antony Ryan wrote on Jun. 23, 2013 @ 22:08 GMT
…..Either way your abstract argument based empirical evidence is strong given that "a mere description of material properties does not produce material". While of course materials do give information.
I think you deserve a place in the final based on this alone. Concise - simple - but undeniable.
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JOSEPH E BRENNER wrote on Jun. 28, 2013 @ 06:41 GMT
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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Author Michel Planat replied on Jun. 28, 2013 @ 18:11 GMT
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
Sreenath B N wrote on Jun. 29, 2013 @ 18:01 GMT
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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Sreenath B N replied on Jul. 1, 2013 @ 14:49 GMT
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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Sreenath B N replied on Jul. 10, 2013 @ 06:09 GMT
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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Satyavarapu Naga Parameswara Gupta wrote on Jul. 1, 2013 @ 15:01 GMT
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
........................
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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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Member Giacomo Mauro D'Ariano wrote on Jul. 1, 2013 @ 23:38 GMT
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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Edwin Eugene Klingman wrote on Jul. 2, 2013 @ 20:35 GMT
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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Edwin Eugene Klingman replied on Jul. 5, 2013 @ 21:08 GMT
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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James Lee Hoover wrote on Jul. 3, 2013 @ 18:00 GMT
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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Dipak Kumar Bhunia wrote on Jul. 5, 2013 @ 13:17 GMT
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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Author Michel Planat replied on Jul. 5, 2013 @ 14:09 GMT
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
M. V. Vasilyeva wrote on Jul. 6, 2013 @ 04:04 GMT
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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john stephan selye wrote on Jul. 10, 2013 @ 14:50 GMT
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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Author Michel Planat replied on Jul. 10, 2013 @ 17:05 GMT
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
Armin Nikkhah Shirazi wrote on Jul. 11, 2013 @ 10:47 GMT
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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Author Michel Planat wrote on Jul. 11, 2013 @ 13:56 GMT
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
Member Ian Durham wrote on Jul. 11, 2013 @ 17:57 GMT
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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Author Michel Planat replied on Jul. 12, 2013 @ 06:14 GMT
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
Anonymous replied on Jul. 14, 2013 @ 02:55 GMT
Hi Michel,
Interesting. I'll have to think about that a bit.
Ian
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Lawrence B Crowell wrote on Jul. 14, 2013 @ 04:25 GMT
Dear Michel Planat,
I have been reading a paper by Maldacena and Susskind. This is a fairly bold paper that advances a pretty speculative idea. In keeping with my paper, which advances an associativity issue with quantum fields near the horizon , this seems to have a higher associator structure that is five fold. The most elementary is a three way associator (ab)c – a(bc) = [a,b,c],...
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Dear Michel Planat,
I have been reading a paper by Maldacena and Susskind. This is a fairly bold paper that advances a pretty speculative idea. In keeping with my paper, which advances an associativity issue with quantum fields near the horizon , this seems to have a higher associator structure that is five fold. The most elementary is a three way associator (ab)c – a(bc) = [a,b,c], that defines a fundamental form for a quantum homotopy but a five fold system is a second homotopy group, The fluctuations across the inner and outer horizons of a black hole results in a 5-fold associative system. This is also a pentagonal system for the Kochen-Specker theorem.
The Susskind-Maldacena paper requires there to exist two black holes with the same BPS charge and angular momentum. Even if such black hole pairs exist it is not clear how they become EPR pairs. In most standard QM systems it requires some sort of mutual interaction to establish an EPR pair. To argue that a black hole is an EPR pair with another it means there exist in the multiverse some other black hole with an identical quantum configuration. This demands a multiverse landscape, for it is probably not likely this exists within the observable universe.
The idea is interesting though. The odd thing about this idea, which has been making the rounds these days, is it makes some physical sense of the interior of a black hole. Maldacena and Susskind work with a Schwarschild black hole. There idea is there are entanglements between black holes through wormhole. This sort of multiply connected topology does exist with black holes. A BPS or rotating black hole has two event horizons at r_{+/-} = m +/- sqrt{m^2 – Q^2}, where Q can be either a gauge charge or angular momentum parameter. There are then two event horizons and three regions; region I being where r > r_+, region II where r_+ > r > r_-, and region III where r < r_-. These regions are timelike, spacelike and timelike respectively. The region III has been regarded as suspect, since the r_- event horizon has a pile up of UV divergent radiation or quantum fields that implies the horizon is physically singular. This region has been regarded as a sort of mathematical fiction. However, maybe this region does play some sort of physical role.
The Kerr black hole appears in the first diagram is attach. The second attachment is a Penrose diagram of the Kerr black hole. It is evident that upon leaving region I (the normal timelike universe) the observer enters region II which is shared by another black hole. The horizon is split so the observer may enter two III type regions. The ring singularity in region III is where x^2 + y^2 = Q^2. In this III region the geodesics around the ring are similar to the flow of a hurricane around the eye. Also the singularity is repulsive; you can’t reach it. In complex coordinates this singularity has a branch cut. If you make a complete orbit around the ring there is a branch cut which pops you into an identical copy of the III region as branch cuts link Riemann sheets of the complex plane. The interior region of a BH is naturally in a sense a sort of wormhole, and this approach might segue into this equivalency between wormhole multiple connectivity and entanglements. This interior region may physically play the role as an “entangler.”
The argument for a firewall associated with a black hole concerns entanglement swaps between states in region I and II. These states are H_h ∊ I for Hawking radiation, H_s ∊ I for states on or near the stretched horizon associated with r_+ and interior states H_n ∊ II for states near the horizon and H_s ∊ II on the singularity. In the Kerr-Newman metric this singularity is identified with r_-. Physically r_- is a region with UV divergent quantum fields. However, we may remove this as a singularity if this divergence is regulated in some manner. That of course is an open question. The singularity states H_s are split into H_r- for states in the region II near r_- and those in the core region H_{III}. We now have a 5-fold system of states.
I have argued that three quantum states along a null ray are an associated quantum system. If the middle state is very near the horizon and the horizon has a quantum uncertainty the entanglement between the three states is an associator system [a,b,c] = (ab)c – a(bc). In quantum homotopy this is a fundamental group π^1. A 5 fold system is a set of states in a permuting structure that gives π^2, and there is a higher system that defines the Stasheff polytope π^3, and it goes on from there. The five fold system is equivalent to the pentagonal arrangement of states in the Kochen-Specker theorem in four dimensions. The associator system is then a form of the KS theorem. The KS theorem in 4 dimensions is a result of a three color graph with pentagonal symmetry.
If there is then this sort of black hole entanglement that is equivalent to a worm hole it may then be of this nature. Again the interior region, if it is physically real, is such that an orbit around the singularity pops the geodesic into an equivalent spacetime. It is a form of the multiple sheets of the complex plane connected by a branch cut. The argument for spacetime would be rather difficult, for this is not an elementary conformal argument in two dimension, but four dimensions.
Lawrence B. Crowell
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attachments:
kerr_bh.jpg,
Penrose_diagram_for_Kerr.png
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Author Michel Planat replied on Jul. 15, 2013 @ 18:44 GMT
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
Lawrence B Crowell replied on Jul. 16, 2013 @ 04:20 GMT
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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Antony Ryan wrote on Jul. 14, 2013 @ 21:24 GMT
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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Author Michel Planat wrote on Jul. 15, 2013 @ 03:47 GMT
Dzar Antony,
I will certainly read it. Thank you for your interest and best wishes.
Michel
Vladimir F. Tamari wrote on Jul. 17, 2013 @ 01:40 GMT
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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Author Michel Planat wrote on Jul. 17, 2013 @ 06:05 GMT
Vladimir,
The rate is less important than comments you may have.
I wonder if you have specificremarks concerning my essay.
Thanks.
Michel
Sreenath B N wrote on Jul. 18, 2013 @ 03:33 GMT
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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Vladimir Rogozhin wrote on Jul. 22, 2013 @ 14:22 GMT
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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Author Michel Planat wrote on Jul. 22, 2013 @ 15:37 GMT
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
Michael Alexeevich Popov wrote on Jul. 23, 2013 @ 12:35 GMT
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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Author Michel Planat wrote on Jul. 23, 2013 @ 14:34 GMT
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
Ralph Waldo Walker III wrote on Jul. 23, 2013 @ 14:37 GMT
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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Author Michel Planat replied on Jul. 23, 2013 @ 15:05 GMT
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
Stephen James Anastasi wrote on Jul. 24, 2013 @ 12:34 GMT
Hello Michel
Crikey! I had to do some work to understand your work as it might connect with mine.
What I do like, and especially like, is your ability to work with interactions through graphs, and your clever ability to see that graphs (and perhaps all kinds of things) can have equivalent interpretations that look quite different to each other but emphasis different aspects. Is this...
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Hello Michel
Crikey! I had to do some work to understand your work as it might connect with mine.
What I do like, and especially like, is your ability to work with interactions through graphs, and your clever ability to see that graphs (and perhaps all kinds of things) can have equivalent interpretations that look quite different to each other but emphasis different aspects. Is this not just what we see in our everyday world? From one perspective there are just physical objects, but from another there are mental objects as well, and so many anthropocentric perspectives – hot, far, large…
Which form is the correct form? Is it It from Bit or the other way, or indeed some completely different way, or are there multiple interpretations (which is necessarily the case as touched on in my essay) none of which can be said to have priority (some people will recognise this as a solution to the mind body problem, but I’ll leave that for next year’s essay and my book ‘The Armchair Universe’ when it is finished).
I have no problem with your argument, but pick out some aspects that lead to questions:
Wheeler said:
‘We have clues, clues most of all in the writings of Bohr, but not answers ... Are billions upon billions of acts of observer-participancy the foundation of everything? We are about as far as we can today from knowing enough about the deeper machinery of the universe to answer this question. Increasing knowledge about detail has brought an increasing ignorance about the plan.’
Lovely choice of quote. Seeking detail is to move on from unstable foundations (Hume, Kant, Popper) hoping the edifice will prove itself strong enough to compensate for the instability. Parmenides and Zeno stamp their feet! One must first find a foundation for change, and the idea that humankind is forever cut off from knowledge of reality is a flawed argument. First understand the machinery, and what brings the machinery that drives change, and so allows a universe that does not collapse under its own inconsistencies. That was my intent. And one wonders – how can the universe come full born, immediately following such complex rules. Whence spacetime? What is spacetime? These are the true foundational questions, of which It from Bit is a human-centered assumption.
Bell says:
‘In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that a theory could not be Lorentz invariant.’
This idea of Bell, and those who accept his argument, is very empiricist, though most will not see it. In a Harmony Set interpretation one might consider that what is really happening is that when two structures interact such that the polarity of one quantum of an entangled pair is realised, then, under equivalence, the totality of the system must be preserved. Given that in the Harmony Set a change is global, then automatically (without wanting to invent an entire 3-space physics to match this, but relying on the GPE) as a simple matter of equivalence to the pre-existing system the other photon will have the appropriate polarity. Otherwise the system would not comply with the GPE, which is absolutely impossible, at least from the point of Endpoint Skepticism (hence, absolutely for everyone else, as a matter of intellectual honesty). The only thing that might change the outcome would be if the evolving generation of new structure created a new localised variation that affected the result in some way (but this is a step too far for the present).
The aspect that interests me, though I don’t really see how you are connecting the concept, is your thought that a compatibility (i. e., commutativity) diagram of observables has a kind of engine that drives it: a dessin d’enfant (a child’s drawing). This is a big cruncher for me, because I don’t see how one has stepped across from the mathematician who is describing a connection (the same bother as with theories of physics) to an ontological force or power such as I attribute to the GPE. I wonder, if a dessin d’enfant is a bipartite graph embedded on an oriented surface, where did the surface originate, how did the surface find its orientation? These are, to me, the seriously foundational questions. This does not make your analysis at all incorrect. Unfortunately, under the GPE and its implied globalized bundling problem, not only does the universe collapse to a single minimally simple omnet, all of mathematics went down the tube with it. To develop the Harmony Set required that I reinvent a mathematics with it, and show how it aligns to contemporary mathematics, which it does, but only to up to a certain point. In doing so, infinities and limits and associated problems fall away. Of course there is a lot more work required here by me and others who might spend the time to understand this rather fascinating Harmony Set, and its implications.
Apologies for the length of my response. This is the short version!
Excellent effort,
Best wishes,
Stephen Anastasi
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Author Michel Planat wrote on Jul. 24, 2013 @ 15:14 GMT
Dear Stephen,
As you gave a perfect summary of what I did, I don't have much to say.
You write
1. "not only does the universe collapse to a single minimally simple omnet, all of mathematics went down the tube with it.",
The translation of this sentence would be the Belyi theorem (see the step 3 in my Sec. 2 giving the definition of a child's drawing) and the property...
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Dear Stephen,
As you gave a perfect summary of what I did, I don't have much to say.
You write
1. "not only does the universe collapse to a single minimally simple omnet, all of mathematics went down the tube with it.",
The translation of this sentence would be the Belyi theorem (see the step 3 in my Sec. 2 giving the definition of a child's drawing) and the property that the child's drawing D itself is the preimage of the segment [0,1], that is D=f^-1([0,1]), where the Belyi function f corresponding to D is a rational function. All black vertices of D are the roots of the equation f(x)=0, the multiplicity of each root being equal to the degree of the corresponding vertex. Similarly, all white vertices are the roots of the quation f(x)=1. Inside each face, there exits a single pole, that is a root of the equation f(x)=\infty. Besides 0, 1 and \infty, there are no other critical value of f.
Sorry about the technicalities.
2. "the thought that a compatibility (i. e., commutativity) diagram of observables has a kind of engine that drives it: a dessin d’enfant (a child’s drawing). "
Yes, exactly. I leave you free to translate it in the GPE language. The point is that you can have many 'engines' for a given compatibility diagram, a kind of redundancy. For your example of the 3-simplex, e.g. the tetrahedron, I just checked that there are 6 distinct dessins/engines, for the 4-simplex, e.g. the 5-cell, there are 13 distinct dessins/engines that can be built with the cartographic group C2+ as the constructor [my equation(1)]. It would be interesting to understant what means this non-bijection in your approach.
3. Orientabilty: we need an oriented surface like the Riemann sphere, or a torus, not a Möbius strip (that is not oriented). Thus the dessin is more than a graph and corresponds to a permutation group P with two generators, as given in my step 2 of Sec. 2.
One needs to develop some familiarity with these concepts, then they become natural.
I anticipate an unexpected and fascinating complementarity between your approach an the one based on Grothendieck's concepts.
Thank you for your enthusiasm about this work.
Michel
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Yuri Danoyan wrote on Jul. 24, 2013 @ 16:01 GMT
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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Author Michel Planat replied on Jul. 24, 2013 @ 16:48 GMT
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
sridattadev kancharla wrote on Jul. 24, 2013 @ 18:00 GMT
Dear Michel and All,
I am attaching the iDNASeries.bmp that I have envisioned and how it shows the DNA structure in its sequence.
I give you all a cosmological iSeries which spans the entire numerical spectrum from -infinity through 0 to +infinity and the simple principle underlying it is sum of any two consecutive numbers is the next number in the series. 0 is the base seed and i...
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Dear Michel and All,
I am attaching the iDNASeries.bmp that I have envisioned and how it shows the DNA structure in its sequence.
I give you all a cosmological iSeries which spans the entire numerical spectrum from -infinity through 0 to +infinity and the simple principle underlying it is sum of any two consecutive numbers is the next number in the series. 0 is the base seed and i can be any seed between 0 and infinity.
iSeries always yields two sub semi series, each of which has 0 as a base seed and 2i as the first seed.
One of the sub series is always defined by the equation
Sn = 2 * Sn-1 + Sigma (i=2 to n) Sn-i
where S0 = 0 and S1 = 2 * i
the second sub series is always defined by the equation
Sn = 3 * Sn-1 -Sn-2
where S0 = 0 and S1 = 2 * i
Division of consecutive numbers in each of these subseries always eventually converges on 2.168 which is the Square of 1.618.
Union of these series always yields another series which is just a new iSeries of a 2i first seed and can be defined by the universal equation
Sn = Sn-1 + Sn-2
where S0 = 0 and S1 = 2*i
Division of consecutive numbers in the merged series always eventually converges on 1.618 which happens to be the golden ratio "Phi".
Fibonacci series is just a subset of the iSeries where the first seed or S1 =1.
Examples
starting iSeries governed by Sn = Sn-1 + Sn-2
where i = 0.5, S0 = 0 and S1 = 0.5
-27.5 17 -10.5 6.5 -4 2.5 -1.5 1 -.5 .5 0 .5 .5 1 1.5 2.5 4 6.5 10.5 17 27.5
Sub series governed by Sn = 2 * Sn-1 + Sigma (i=2 to n) Sn-i
where S0 = 0 and S1 = 2i = 1
0 1 2 5 13 34 ...
Sub series governed by Sn = 3 * Sn-1 - Sn-2
where S0 = 0 and S1 = 2i = 1
0 1 3 8 21 55 ...
Merged series governed by Sn = Sn-1 + Sn-2 where S0 = 0 and S1 = 2i = 1
0 1 1 2 3 5 8 13 21 34 55 ...... (Fibonacci series is a subset of iSeries)
The above equations hold true for any value of I.
As per Antony Ryan's suggestion, I searched google to see how Fibonacci type series can be used to explain Quantum Mechanics and General Relativity and found an interesting article.
http://msel-naschie.com/pdf/The-Fibonacci-code-behin
d-super.pdf
Now that I split the Fibonacci series in to two semi series, seems like each of the sub semi series corresponds to QM and GR and together they explain the Quantum Gravity. Seems like this duality is a commonality in nature once relativity takes effect or a series is kicked off from a basic singularity. The only commonality between the two series is at the base seed 0 (singularity) and first seed 1, which are the bits in our binary system.
Its also interesting to see the singularity is in the base seed of zero and how it is all pervasive all through out the DNA structure in the attached image. I have been telling that I is that nothing which dwells in everything and this DNA structure seems to prove that notion. Singularity is right with in the duality. Absolute is right with in the relativity. This proves that both of these states of singularity and duality are interconnected and are the source of life.
Love,
Sridattadev.
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attachments:
7_iDNASeries.bmp
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Than Tin wrote on Jul. 24, 2013 @ 23:47 GMT
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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Akinbo Ojo wrote on Jul. 25, 2013 @ 12:32 GMT
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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Author Michel Planat replied on Jul. 25, 2013 @ 15:03 GMT
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...
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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 'its'.
iii. they are the fundamental units of geometry, both body and space.
Me: The points of the geometries I am dealing with could perhaps be seen as monads. (e.g. the 7 points of the Fano plane in Fig. 1a. Then in Fig 1b the same points are extended as edges).
You: monads are 'it' and their change between two alternate states is the 'bit'.
Me: Agree. One edge in Fig. 2b is either black (bit 1) or white (bit 0).
You: the two-valued attribute
denoted by 0 and 1 must really occupy the deepest part of the basement!
Me: Agree, but as two elements of a triple {0,1, \infty}.
Stephen Anastasi: (above) "not only does the universe collapse to a single minimally simple omnet, all of mathematics went down the tube with it.",
Me: The translation of this sentence would be the Belyi theorem (see the step 3 in my Sec. 2 giving the definition of a child's drawing) and the property that the child's drawing D itself is the preimage of the segment [0,1], that is D=f^-1([0,1]), where the Belyi function f corresponding to D is a rational function. All black vertices of D are the roots of the equation f(x)=0, the multiplicity of each root being equal to the degree of the corresponding vertex. Similarly, all white vertices are the roots of the quation f(x)=1. Inside each face, there exits a single pole, that is a root of the equation f(x)=\infty. Besides 0, 1 and \infty, there are no other critical value of f.
Sorry about the technicalities.
You: But what about the space then?
Me: Although the model of dessins d'enfants may be applied differently, practically, in my essay, it corresponds to the (Heisenberg) space of quantum observables such as the Pauli spin matrices, or tensorial agregates of them. You would say that they cannot be monads in such a case! But they cannot be divided in the sense that the parties (let's say Alice, Bob and Charlie for the three-partite case, I used the Fano plane for this case) are linked once for all, whatever state they share, entangled or not. I don't know about Mach, I have to think more.
I am sure that it does not dissolve your question, at least it gives you a hint, hopefully, of what this kind of maths may do.
Please rate my essay if you like it.
Best wishes,
Michel
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Angel Garcés Doz wrote on Jul. 25, 2013 @ 19:41 GMT
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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Author Michel Planat replied on Jul. 26, 2013 @ 07:05 GMT
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
Peter Jackson wrote on Jul. 26, 2013 @ 14:18 GMT
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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Author Michel Planat wrote on Jul. 26, 2013 @ 15:36 GMT
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.
Peter Jackson wrote on Jul. 26, 2013 @ 17:38 GMT
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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Author Michel Planat wrote on Jul. 26, 2013 @ 19:37 GMT
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?
sridattadev kancharla wrote on Jul. 28, 2013 @ 22:36 GMT
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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Charles Raldo Card wrote on Jul. 29, 2013 @ 13:58 GMT
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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Jonathan J. Dickau wrote on Jul. 30, 2013 @ 00:34 GMT
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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Author Michel Planat replied on Jul. 30, 2013 @ 06:54 GMT
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
Jonathan J. Dickau replied on Jul. 30, 2013 @ 18:47 GMT
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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Author Michel Planat replied on Jul. 31, 2013 @ 08:25 GMT
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
Yutaka Shikano wrote on Jul. 31, 2013 @ 07:10 GMT
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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Author Michel Planat replied on Jul. 31, 2013 @ 07:27 GMT
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
Gordon Watson wrote on Jul. 31, 2013 @ 12:12 GMT
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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Author Michel Planat replied on Jul. 31, 2013 @ 13:34 GMT
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
Torsten Asselmeyer-Maluga wrote on Jul. 31, 2013 @ 12:55 GMT
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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Anonymous replied on Jul. 31, 2013 @ 14:13 GMT
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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Author Michel Planat replied on Aug. 1, 2013 @ 13:59 GMT
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
Akinbo Ojo wrote on Jul. 31, 2013 @ 14:55 GMT
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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Jonathan J. Dickau wrote on Jul. 31, 2013 @ 17:24 GMT
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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Hugh Matlock wrote on Aug. 1, 2013 @ 05:33 GMT
Hi Michel,
Your very interesting essay, taking us right to the foundations, raises some questions. You wrote:
> This implies the non-existence of the Belyi map and puts three-qubit contextuality on a qualitatively different footing when compared with the two-qubit case.
It seems that your quest to model 3-qubit contextuality has an unhappy ending in your essay. Do you thus...
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Hi Michel,
Your very interesting essay, taking us right to the foundations, raises some questions. You wrote:
> This implies the non-existence of the Belyi map and puts three-qubit contextuality on a qualitatively different footing when compared with the two-qubit case.
It seems that your quest to model 3-qubit contextuality has an unhappy ending in your essay. Do you thus conclude that (some? all?) mechanisms that explain contextuality for 2-qubit systems will not explain it for 3-qubit systems?
What avenues are you now taking to explore 3-qubit contextuality? (Yes, yes, I know I should read your recent papers... after the contest, please...) I am hoping there is another chapter to come in your story... with finally, a happy ending. I very much like the idea that you mention of lifting the Riemann sphere to S3 via the inverse Hopf Fibration. I will put some more comments about this on my blog.
> To find the corresponding Belyi map seems to be a challenging math problem.
My thought was there might be a possibility of easier results if we restrict white and black points to lie at
k-rational points: Consider Q(phi), the algebraic extension of the rationals by the golden ratio. These numbers are able to provide cartesian coordinates for
all the vertices of Platonic solids, and many other polytopes besides. These could be considered as k-rational points within larger fields, but also as a field on their own. (For such fields,
Falting's Theorem should apply and might possibly be useful.) But I was mainly wondering if anyone had looked at the techniques you describe with such k-rational points and fields in mind.
Anyway, if they prove useful, I imagined that such diagrams (living in S3?) you could call "Dessins d'Or"... and that they could lead you to a happy ending. A topic for next year's essay, perhaps?
Hugh
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Author Michel Planat replied on Aug. 1, 2013 @ 08:54 GMT
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
Angel Garcés Doz wrote on Aug. 1, 2013 @ 16:46 GMT
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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KoGuan Leo wrote on Aug. 2, 2013 @ 02:40 GMT
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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Author Michel Planat wrote on Aug. 2, 2013 @ 07:07 GMT
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
KoGuan Leo replied on Aug. 2, 2013 @ 09:09 GMT
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...
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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 stage. Let us perform! I am just a bumblebee Shakespearean actor performing in our shared magical Multiverse: Yes! No! Maybe!
If I may briefly make KQID simple. Forgive me for being respectfully boastful: First, 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 (Pythagoras complex triangles or Fu Xi's gua or Fibonacci numbers!) onto the 2D Minkowski Null geodesic and then instantaneously into the 3D in Lm, our Multiverse timeline to allows Existence to move around 360 degree and its arrows of time as you described below. New informations are created and distributed per 10^-1000 seconds. No information is ever deleted.. KQID is the only theory out there that can calculate the dark energy of our Multiverse ≤10^-153Pm/Pv and the minimum bits as the lower bound ≥ 10^153 bits in our Multiverse. KQID is the only theory that I knows here that proves bit = it, and KQID calculates Sun lights into Sun bits; calculates electron, proton and neutron in terms of bits; set up equivalent principle of bits with energy and matter. Therefore, Wheeler's it from bit and bit from it. Correct me if I am wrong. Furthermore, KQID is the only theory in this universe has the mechanism on how Holographic Principle works. Also answer the mother of all questions, the why, how and what Existence.
In short, answering the contest question of Wheeler's it from bit or bit from it. Pythagoras famously summarized: "All things are numbers." KQID rephrases it that all thing are one Qbit: Qbit is all things and all things are Qbit. Thus, Wheeler's it from bit and bit from it because bit = it and it = bit.
Thanks for taking the time to make a generous comment.
Best regards,
Leo KoGuan
I rather be a bumblebee poet than not to be.
I am buzzing my way to sing and praise Xuan Yuan Da Tong.
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Author Michel Planat replied on Aug. 2, 2013 @ 09:45 GMT
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
Hugh Matlock wrote on Aug. 3, 2013 @ 08:41 GMT
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
Hi Michel,
So it appears that the FQXI database has been reset and my comments have disappeared... I will add them back in. As I said before:
Your very interesting essay, taking us right to the foundations, raises some questions. You wrote:
> This implies the non-existence of the Belyi map and puts three-qubit contextuality on a qualitatively different footing when compared with the two-qubit case.
It seems that your quest to model 3-qubit contextuality has an unhappy ending in your essay. Do you thus conclude that (some? all?) mechanisms that explain contextuality for 2-qubit systems will not explain it for 3-qubit systems?
What avenues are you now taking to explore 3-qubit contextuality? (Yes, yes I know I should read your recent papers... after the contest, please...) I am hoping there is another chapter to come in your story... with finally, a happy ending. I do like the idea that you mention of lifting the Riemann sphere to S3 via the inverse Hopf Fibration. I will put some more comments about this on my blog.
> To find the corresponding Belyi map seems to be a challenging math problem.
My thought was there might be a possibility of easier results if we restrict white and black points to lie at
k-rational points:
Consider Q(phi), the algebraic extension of the rationals by the golden ratio. These numbers are able to provide cartesian coordinates for
all the vertices of Platonic solids, and many other polytopes besides. These could be considered as k-rational points within larger fields, but also as a field on their own. (For such fields,
Falting's Theorem should apply and might possibly be useful.) But I was mainly wondering if anyone had looked at the techniques you describe with such k-rational points and fields in mind.
Anyway, if they prove useful, I imagined that such diagrams (living in S3?) might be called "Dessins d'Or"... and eventually lead to a happy ending. Next year's essay, perhaps?
Hugh
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Hugh Matlock replied on Aug. 3, 2013 @ 22:19 GMT
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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Paul Borrill wrote on Aug. 4, 2013 @ 22:49 GMT
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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Author Michel Planat wrote on Aug. 5, 2013 @ 06:17 GMT
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
eAmazigh M. HANNOU wrote on Aug. 5, 2013 @ 22:39 GMT
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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Charles Raldo Card wrote on Aug. 6, 2013 @ 04:02 GMT
Late-in-the-Day Thoughts about the Essays I’ve Read
I am sending to you the following thoughts because I found your essay particularly well stated, insightful, and helpful, even though in certain respects we may significantly diverge in our viewpoints. Thank you! Lumping and sorting is a dangerous adventure; let me apologize in advance if I have significantly misread or misrepresented...
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Late-in-the-Day Thoughts about the Essays I’ve Read
I am sending to you the following thoughts because I found your essay particularly well stated, insightful, and helpful, even though in certain respects we may significantly diverge in our viewpoints. Thank you! Lumping and sorting is a dangerous adventure; let me apologize in advance if I have significantly misread or misrepresented your essay in what follows.
Of the nearly two hundred essays submitted to the competition, there seems to be a preponderance of sentiment for the ‘Bit-from-It” standpoint, though many excellent essays argue against this stance or advocate for a wider perspective on the whole issue. Joseph Brenner provided an excellent analysis of the various positions that might be taken with the topic, which he subsumes under the categories of ‘It-from-Bit’, ‘Bit-from-It’, and ‘It-and-Bit’.
Brenner himself supports the ‘Bit-from-It’ position of Julian Barbour as stated in his 2011 essay that gave impetus to the present competition. Others such as James Beichler, Sundance Bilson-Thompson, Agung Budiyono, and Olaf Dreyer have presented well-stated arguments that generally align with a ‘Bit-from-It’ position.
Various renderings of the contrary position, ‘It-from-Bit’, have received well-reasoned support from Stephen Anastasi, Paul Borrill, Luigi Foschini, Akinbo Ojo, and Jochen Szangolies. An allied category that was not included in Brenner’s analysis is ‘It-from-Qubit’, and valuable explorations of this general position were undertaken by Giacomo D’Ariano, Philip Gibbs, Michel Planat and Armin Shirazi.
The category of ‘It-and-Bit’ displays a great diversity of approaches which can be seen in the works of Mikalai Birukou, Kevin Knuth, Willard Mittelman, Georgina Parry, and Cristinel Stoica,.
It seems useful to discriminate among the various approaches to ‘It-and-Bit’ a subcategory that perhaps could be identified as ‘meaning circuits’, in a sense loosely associated with the phrase by J.A. Wheeler. Essays that reveal aspects of ‘meaning circuits’ are those of Howard Barnum, Hugh Matlock, Georgina Parry, Armin Shirazi, and in especially that of Alexei Grinbaum.
Proceeding from a phenomenological stance as developed by Husserl, Grinbaum asserts that the choice to be made of either ‘It from Bit’ or ‘Bit from It’ can be supplemented by considering ‘It from Bit’ and ‘Bit from It’. To do this, he presents an ‘epistemic loop’ by which physics and information are cyclically connected, essentially the same ‘loop’ as that which Wheeler represented with his ‘meaning circuit’. Depending on where one ‘cuts’ the loop, antecedent and precedent conditions are obtained which support an ‘It from Bit’ interpretation, or a ‘Bit from It’ interpretation, or, though not mentioned by Grinbaum, even an ‘It from Qubit’ interpretation. I’ll also point out that depending on where the cut is made, it can be seen as a ‘Cartesian cut’ between res extensa and res cogitans or as a ‘Heisenberg cut’ between the quantum system and the observer. The implications of this perspective are enormous for the present It/Bit debate! To quote Grinbaum: “The key to understanding the opposition between IT and BIT is in choosing a vantage point from which OR looks as good as AND. Then this opposition becomes unnecessary: the loop view simply dissolves it.” Grinbaum then goes on to point out that this epistemologically circular structure “…is not a logical disaster, rather it is a well-documented property of all foundational studies.”
However, Grinbaum maintains that it is mandatory to cut the loop; he claims that it is “…a logical necessity: it is logically impossible to describe the loop as a whole within one theory.” I will argue that in fact it is vital to preserve the loop as a whole and to revise our expectations of what we wish to accomplish by making the cut. In fact, the ongoing It/Bit debate has been sustained for decades by our inability to recognize the consequences that result from making such a cut. As a result, we have been unable to take up the task of studying the properties inherent in the circularity of the loop. Helpful in this regard would be an examination of the role of relations between various elements and aspects of the loop. To a certain extent the importance of the role of relations has already been well stated in the essays of Kevin Knuth, Carlo Rovelli, Cristinel Stoica, and Jochen Szangolies although without application to aspects that clearly arise from ‘circularity’. Gary Miller’s discussion of the role of patterns, drawn from various historical precedents in mathematics, philosophy, and psychology, provides the clearest hints of all competition submissions on how the holistic analysis of this essential circular structure might be able to proceed.
In my paper, I outlined Susan Carey’s assertion that a ‘conceptual leap’ is often required in the construction of a new scientific theory. Perhaps moving from a ‘linearized’ perspective of the structure of a scientific theory to one that is ‘circularized’ is just one further example of this kind of conceptual change.
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Margriet Anne O'Regan wrote on Aug. 6, 2013 @ 13:30 GMT
Hello Michel from Margriet O'Regan from DownUnder !
My research over the years has led me to believe that there are very few geometricians around ! So it's been great to encounter a few here in this essay arena - including Akinbo Ojo & you.
But it has confirmed my belief that few if any persons lay or expert alike, recognise & acknowledge REAL common, ordinary, everyday, garden...
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Hello Michel from Margriet O'Regan from DownUnder !
My research over the years has led me to believe that there are very few geometricians around ! So it's been great to encounter a few here in this essay arena - including Akinbo Ojo & you.
But it has confirmed my belief that few if any persons lay or expert alike, recognise & acknowledge REAL common, ordinary, everyday, garden variety geometrical objects lying all around (& in) us everywhere - rather than the abstract or hypothetical ones which exist only inside mathematicians & theoretical physicists' heads & textbooks !
My claim is not only that 'information' is the full set of geometrical objects present here in our universe but that they are all of the properly real ones present here.
My investigations have led me to believe that there are not any of these real geometrical objects in certain specific places or realms or domains. One of these domains in which no geometrical objects exist is the sub-sub-atomic realm down at the quantum level. I make this conclusion because geometrical objects are strictly 'surface dwelling' entities & do not, because they cannot, exist anywhere but on the surface of some one or another solid object. Whatever it is down there at the quantum level it has no surfaces - therefore no real information.
Space is another place where none of 'my' real geometrical objects exist. I do not believe that space-time itself is curved or warped. I believe that the light that is bent (lensed) around the sun is bent as it is due to the fact that it is passing through the Sun's heliopause & not responding to (non-existent) space-times curvature at all. Einstein did not know of such things as heliopauses or even our own Earth's magnetosphere - which does the same thing (bends light - just a little). The two spacecraft which are currently exiting our Solar system also have been affected by transitting the boundaries of the Sun's gigantic heliopause.
My belief in real geometrical objects gives me the personal advantage of not having to know the maths of 'deep' physics & even though I have read Penrose's 'The Road to Reality : A Complete Guide to the Laws of the Universe' I kind of let the equations 'wash through me' rather than working each out in detail.
And there was for me a very big reward at the end of his book as he confessed after more than one thousand pages of hard work, to not having found 'the answer' at all - not even close !! & that we'd not only better keep looking for it, but do so in significantly different directions from those we have previously taken.
Here is what he said :
On page 1025 in his last chapter ‘Where lies the road to reality ?'
‘It is certainly possible that there are many clues to Nature’s ways hidden in such (modern experimental) data even if we do not properly read them yet. Recall that Einstein’s general relativity was crucially based on his insight (the principle of equivalence) which had been implicit in observational data that had been around since (and before) the time of Galileo, but not full appreciated. The may well be other clues hidden in the immeasurably more extensive modern observations. Perhaps there are even ‘obvious’ ones, before our very eyes, that need to be twisted round and viewed from a different angle, so that a fundamentally new perspective may be obtained concerning the nature of physical reality.
Page 1027 and following.
What is reality ?
As the reader will gather from all this, I do not believe that we have yet found the true ‘road to reality’, despite the extraordinary progress that has been made over two and one half millennia, particularly in the last few centuries. Some fundamentally new insights are certainly needed, Yet, some readers may well still take the view that the road itself may be a mirage. True – so the might argue – we have been fortunate enough to stumble upon mathematical schemes that accord with Nature in remarkable ways, but the unity of Nature as a whole with some mathematical scheme can be no more than a ‘pipe dream’. Others might take the view that the very notion of a ‘physical reality’ with a truly objective nature, independent of how we might choose to look at it, is itself a pipe dream. . . . .
This is a question that has been posed for thousands of years . . . . .
On page 1045 Mr Penrose’s very last paragraph reads :
The spacetime singularities lying at cores of black holes are among the known (or presumed) objects in the universe about which the most profound mysteries remain – and which our present-day theories are powerless to describe. As we have seen ……. There are other deeply mysterious issues about which we have very little comprehension. It is quite likely that the 21st century will reveal even more wonderful insights than those that we have been blessed with in the 20th. But for this to happen, we shall need powerful new ideas, which will take us in directions significiantly different from those currently being pursued. Perhaps what we mainly need is some subtle change in perspective – something that we all have missed . . . .
Mr Penrose did not even mention real geometrical objects let alone consider them to be the (one & only) purveyors of information. So real geometrical objects are at least one of the things that he has 'missed' - nevertheless they are things that are 'before our very eyes' & it will take a rather significant change in perspective if mainstream physics is ever to acknowledge them !!!?
And yes, I can't help repeating what David Deutsch said :
‘I’m speaking to you now : Information starts as some kind of electrochemical signals in my brain, and then it gets converted into other signals in my nerves and then into sound waves and then into the vibrations of a microphone, mechanical vibrations, then into electricity and so on, and presumably will eventually go on the Internet, this something has been instantiated in radically different physical objects that obey different laws of physics. Yet in order to describe this process you have to refer to the thing that has remained unchanged through out the process, which is only the information rather than any obviously physical thing like energy or momentum.’
Answer : David Deutsch’s elusive ‘thing’ is geometric objects plain & simple.
Geometric objects are the only phenomena that can be & routinely are copied / transferred on to consecutive sequences of widely different physical objects – from medium to radically different physical medium to radically different physical medium to radically different physical medium - & yet retain their shape – at least this obtains as to certain mediums as on many others they fade quickly away. Which is why we ourselves choose our mediums with a very careful eye to their ability to carry information (in its native that is geometric form) on themselves with optimum stability.
I know it's late but here are my closing remarks !!!! Thank you for your patience !!! I make them because because I want to emphasize a distinction I did not sufficiently clarify in my essay.
My own investigations have led me to conclude that ‘information’ is NOT digits – no kind nor amount of them (including any that can be extracted from quantum phenomena!), nor how algorithmically-well they may be massaged & shunted through any device that uses them.
Unequivocally they – digits – make for wonderful COUNTING & CALCULATING assistants, witness our own now many & various, most excellent, counting, calculating devices BUT according to my investigations real thinking is an entirely different phenomenon from mere counting, calculating & computing.
For which phenomenon – real thinking – real information is required.
My own investigations led me to discover what I have come to believe real information is & as it so transpires it turns out to be an especially innocuous – not to omit almost entirely overlooked & massively understudied – phenomenon, none other than the sum total of geometrical objects otherwise quite really & quite properly present here in our universe. Not digits.
One grade (the secondary one) of geometrical-cum-informational objects lavishly present here in our cosmos, is comprised of all the countless trillions & trillions of left-over bump-marks still remaining on all previously impacted solid objects here in our universe – that is to say, all of the left-over dents, scratches, scars, vibrations & residues (just the shapes of residues – not their content!) (really) existing here in the universe.
Examples of some real geometrical objects of this secondary class in their native state are all of the craters on the Moon. Note that these craters are – in & of themselves – just shapes – just geometrical objects. And the reason they are, also one & at the same time, informational objects too, can be seen by the fact that each ‘tells a story’ – each advertises (literally) some items of information on its back – each relates a tale of not only what created it but when, where & how fast & from what angle the impacting object descended onto the Moon’s surface. Again, each literally carries some information on its back.
(Note : Not a digit in sight !!)
How we actually think – rather than just count, calculate & compute – with these strictly non-digital entities, specifically these geometrical-cum-informational objects, in precisely the way we do, please see my essay.
I did not make the distinction between computing with digits & real thinking with real information, sufficiently strongly in my essay.
This contest is such a wonderful ‘sharing’ – Wow – & open to amateurs like myself – Wow. How great is that !!! Thank you Foundational Questions Institute !!! What a great pleasure it has been to participate. What a joy to read, share & discuss with other entrants !!!
Margriet O’Regan
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Author Michel Planat replied on Aug. 6, 2013 @ 23:01 GMT
Thank you, Margriet, you are giving many questions to think about. It is always surprising that non academic thoughts can go so deep. My best wishes. Michel.
Jennifer L Nielsen wrote on Aug. 6, 2013 @ 13:56 GMT
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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Author Michel Planat replied on Aug. 6, 2013 @ 14:42 GMT
Thank you Jenneifer,
However I think to have proposed a few ways to do some progress about the understanding of quantum observations. More to be discussed in the future.
All the best,
Michel
Patrick Tonin wrote on Aug. 6, 2013 @ 14:40 GMT
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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Author Michel Planat replied on Aug. 6, 2013 @ 15:04 GMT
Dear Patrick,
Yes we can do some progress as you do as well. It is a matter of imagination, good reasoning and recognized shoulders.
Kind regards,
Michel
Angel Garcés Doz wrote on Aug. 6, 2013 @ 20:45 GMT
Good Look Dr Planat¡
Angel Garcés Doz
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Neil Bates wrote on Aug. 7, 2013 @ 01:03 GMT
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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Steven P Sax wrote on Aug. 7, 2013 @ 17:46 GMT
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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Author Michel Planat replied on Aug. 7, 2013 @ 19:15 GMT
Dear Steve,
I am delighted with your post. Thank you so much for your appreciation. Cheers.
Michel
Steven P Sax replied on Aug. 7, 2013 @ 19:29 GMT
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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Member Howard N Barnum wrote on Aug. 8, 2013 @ 00:06 GMT
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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Author Michel Planat wrote on Aug. 8, 2013 @ 07:29 GMT
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.
Jonathan J. Dickau wrote on Aug. 8, 2013 @ 23:48 GMT
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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Author Michel Planat wrote on Aug. 9, 2013 @ 06:01 GMT
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
Author Michel Planat wrote on Oct. 17, 2013 @ 06:42 GMT
Dear all,
An update of the ideas developed in the essay is in the paper
http://xxx.lanl.gov/abs/1310.4267
Michel
Branko L Zivlak wrote on Apr. 1, 2015 @ 19:20 GMT
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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