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RECENT POSTS IN THIS TOPIC

Michel Planat: on 8/15/15 at 9:57am UTC, wrote This essay is published as Mathematics 2015, 3, 746-757;...

Peter Jackson: on 4/24/15 at 15:13pm UTC, wrote Michel, Thanks for your post and comments on mine. I wrote a comprehensive...

Giacomo D'Ariano: on 4/23/15 at 1:13am UTC, wrote Dear Michel Nice story rich of erudite cases of study. The last example...

Yafet Sanchez Sanchez: on 4/23/15 at 1:09am UTC, wrote Dear Michel, I enjoyed your essay. I am still trying to grasp all the...

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Michel Planat: on 4/22/15 at 12:12pm UTC, wrote Dear Sylvia, Your paper really needs more comments than I was able to...

Sylvia Wenmackers: on 4/22/15 at 9:28am UTC, wrote Dear Michel Planat, To be honest, I generally don't like the dialogue...

Michel Planat: on 4/22/15 at 6:04am UTC, wrote Dear Ian, Thank you for going to my essay. I expect that my essay will not...


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FQXi FORUM
October 22, 2019

CATEGORY: Trick or Truth Essay Contest (2015) [back]
TOPIC: A moonshine dialogue in mathematical physics by Michel Planat [refresh]
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Author Michel Planat wrote on Mar. 4, 2015 @ 17:07 GMT
Essay Abstract

Phys and Math are two colleagues at the University of Saçenbon (Crefan Kingdom), dialoguing about the remarkable efficiency of mathematics for physics. They talk about the notches on the Ishango bone, the various uses of psi in maths and physics, they arrive at dessins d'enfants, moonshine concepts, Rademacher sums and their significance in the quantum world. You should not miss their eccentric proposal of relating Bell's theorem to the Baby Monster group. Their hyperbolic polygons show a considerable singularity/cusp structure that our modern age of computers is able to capture. Henri Poincaré would have been happy to see it.

Author Bio

Michel Planat is a senior scientist at FEMTO-ST/CNRS, Besançon, France. His present main interest is in fundamental problems of quantum information and their relationship to mathematics. He wrote about 120 refereed papers or book chapters.

Download Essay PDF File

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adel sadeq wrote on Mar. 4, 2015 @ 21:50 GMT
Dear Michel,

I want to ask you a hypothetical question since you are a very good mathematician.

Let's say a man is born in a MATRIX(movie). he grows up and knows nothing about real life. We will only teach him about mathematical facts. We will not even teach him geometry. Everything will be done in numbers.

If he learns the math, what would be your conclusion. Does math stands on its own or not?

Thanks. Good luck.

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Author Michel Planat replied on Mar. 5, 2015 @ 07:42 GMT
Dear Adel,

You had an entry on the subject at the FQXI contest "It From Bit or Bit From It?" with the title “Reality is nothing but a mathematical structure, literally” and you gave the impression that the laws of physics spontaneously emerge from quite natural mathematical structures that you can discover by intuition and play (let's say with the computer). Experimental mathematics is playing an increasing role in present day mathematics but it does not create the new ways that remain the privilege of a genius. For the existence of a genius I do not have an explanation but the social context seems important.

Trying to answer your question I would say that maths is the natural language for physics and that there is no alternative choice, the unity of maths fits that of physics because we simply do not have access to another real world, being part of the whole and a self-referencing observer (I agree with S. Hawking

at the end of my essay). May be the biggest open question is the mathematical structure of physical constants, or how they evolve (see Smolin's essay). Numbers are just part of the game, there is topology, category and so on.

Michel

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adel sadeq replied on Mar. 6, 2015 @ 03:12 GMT
Thanks Michel , my new essay should appear shortly. I expand on the results and provide very easy JavaScript programs to confirm the calculations. The Bohr atom and the electron mass simulation is all about the physical constants, however I cut on the discussion because I wanted to show the major results. I will elaborate in the comment, but basically the design is so strict that no room is available for "evolving"(I have all of Lee's books). and the major conclusion of the system is that TIME is emergent and not fundamental at all.

I do mention briefly how the system can be (must be) able to be converted to the usual mathematical formalism (connecting to endless mathematical concepts), which I do have the basic tries but not enough to show at this point.

Of course experiment is essential for confirmation.

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Mark A. Thomas wrote on Mar. 5, 2015 @ 20:03 GMT
"In the mysterious way the scales of the hidden monster flash iridescently from near impenetrable darkness"

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Author Michel Planat replied on Mar. 6, 2015 @ 18:19 GMT
For the information of readers of these posts , I put the link to your (coincidence) result seing the big number 3.377368...×10^38 as

relating the neutron mass and the Ramanujan constant.

http://mrob.com/pub/math/numbers-18.html#le038_337

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Mark A. Thomas replied on Mar. 6, 2015 @ 20:30 GMT
Professor Planat,

Thank you for your kindness.I am not meaning to distract away from your essay but I felt that the quote was appropriate concerning your exploration(s). Everyone is in the promotion game one way or another and I appreciate your reference to the coincidence I discovered. Actually if it is true then physics = mathematics at the nexus involving the Monster, modular functions, QCD and gravity. As it is a 'razor sharp' coincidence (or curio) it is so good that it might be considered an 'open problem'. I will leave it at that and if someone wants to view how exceptonal the coincidence is they may review my comments on it at http://vixra.freeforums.org/isospin-gravitational-coupling-c
onstant-and-ep-t386.html

I read your essay with great interest and although I did not comprehend some of the concepts I've come away from it with an increased sense of the use of dessins d'effants. Oh, and one last thing since I am here. The ratio is a QCD to gravity ratio and explicitly defines the 'gravitational coupling constant' on top of neutron star structure. Then it is a type of unification using non-abelian mathematics of gravity and QCD. Other definitions of the 'gravitational coupling constant' mix abelian and non-abelian math (i.e. proton and electron in same formula) which might be wrong, So it might be safer to say that the 'gravitational coupling constant' is not truly a measure of the weakness of gravity to the electromagnetic force (U1) but the measure of the weakness of gravity to the strong force (SU3).Because of the modular aspect of the coincidence involving 163 and the null vector relation of the Leech lattice this points directly to the Monster Group. Again look at Munafo's definition on his site.

Again Thank you, mark

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Member Alexei Grinbaum wrote on Mar. 6, 2015 @ 13:58 GMT
Bonjour Michel,

I like the idea that we should use new mathematics to better understand quantum theory, incl. contextuality and Bell inequalities. But your movement seems to be one-way, namely finding a place for the known physical structures within a broader mathematical framework. How about moving in the other direction: can your mathematical framework suggest something new about physics that we haven't discovered otherwise?

Bien cordialement,

Alexei

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Author Michel Planat replied on Mar. 6, 2015 @ 16:31 GMT
Dear Alexei,

The first point is to clarify the meaning of quantum observations in the general language of finite group theory including the sporadic groups, there are good signs that it is possible and that this also connects with attempts at understanding quantum gravity. Or may be both fields are totally distinct and it is just a coincidence that the same mathematical language is useful. As I am in a stage of collecting many singularity structures at the boundary of dessins d'enfants and finite/(possibly sporadic) groups, I cannot yet announce the new physical issues. I can only thanks the FQXI organizers for allowing me to present this unfinished work.

Michel

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Joe Fisher wrote on Mar. 6, 2015 @ 16:20 GMT
Dear Dr. Planat,

I quite enjoyed reading your essay.

Joe Fisher

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Author Michel Planat replied on Mar. 6, 2015 @ 16:37 GMT
Dear Joe,

Thanks, I know your quest of unicity and I am sure that there are enough particles in the Monster to satisfy your quest. More seriously, I also enjoyed writing it and will also read with great interest what you are writing this time.

Michel

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Ed Unverricht wrote on Mar. 7, 2015 @ 03:37 GMT
Dear Dr. Planat,

Great and interesting read with a unique format. You introduced a couple of groups and models that definitely inspire some thought.

I loved the wrap up in your conclusion:

Math: Do you think that our mathematics is the real world?

Phys: As a provisional response, I offer you a quote of Stephen Hawking from his lecture “Godel and the end of the universe” [27]: In the standard positivist approach to the philosophy of science, physical theories live rent free in a Platonic heaven of ideal mathematical models...

Regards and good luck,

Ed Unverricht

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Author Michel Planat replied on Mar. 7, 2015 @ 11:27 GMT
Ed,

Thank you for your appreciation. I am also inspired by your pictures of elementary particles. May be the singularity structure unveiled in finite groups may play a role for particles at a further stage. Best.

Michel

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Lawrence B Crowell wrote on Mar. 8, 2015 @ 13:44 GMT
I remember you from another one of these contests. If I remember you were advancing the Grothendieke cohomology of categories. You might look at my essay, for there is some informal overlap with this subject there. I think physical theories will be involved in the future with monoids, groupoids and categories.

I will read your essay as soon as possible. I am on travel right now, so it is a bit hard to read these.

Cheers LC

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Author Michel Planat wrote on Mar. 8, 2015 @ 14:25 GMT
Dear Lawrence,

I already red your essay when it appeared and still today. I found it more than excellent in the sense that I still need to think more about HOTT before my comment is useful. I intend to send you more in a couple of days with a special mention. I knew that you are away from your comments to Michael whose essay I also find very stimulating.

I will be glad to receive your appreciation when you are back, there is of course some overlap with you and Michael.

Best wishes,

Michel

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Jonathan J. Dickau wrote on Mar. 12, 2015 @ 20:06 GMT
Greetings my friend,

I started to read your paper last night, and came to realize it requires some undivided attention - which it will get later today. I can mention that I also came upon HOTT recently, and I find their idea of univalent foundations fascinating - rooted as it is in a constructivist ideal, but with a firm calculational proof-checking basis.

You might find interesting the paper of my friend Franklin Potter, as he is also enamored of the Monster group and has some wonderful ideas; though I have yet to read his paper, I am sure it is worth checking out. As an aside; I was looking at info for Weyl E8, which he mentions, and ended up downloading Borcherd's paper proving Monstrous Moonshine, just the other night.

So I am eager to read what you have to say, and I will comment after.

All the Best,

Jonathan

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Branko L Zivlak wrote on Mar. 13, 2015 @ 12:18 GMT
Dear Michel,

I think there is no doubt that the prime numbers have significance for physics.

It's interesting in groups which you use that you get big integers. In my work I get small integers not exceeding over 6.

Another important link between your and my work are series of a1, a2 where you are adding 1. To add one, I often have in my work, but not with integers. Let me try to explain: If you have a physical appearance that is in relation to your a1 (y = 4372 / x; otherwise we can write y = 4371 / x + 1 / x). That is happening as if 4372 is the limit of a process running in the segments of 1 / x to 4371 and this turns into another quality. For example attraction turns into repulsion. What is the physical meaning of integers a1, a2 is hard to say, but it is much easier to specify whole numbers (the exponents) 1-6 in the group of formula at the end of my essay.

Maybe you have not noticed my long answer to you on my site, because I have not put in the right place.

Best Regards,

Branko

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En Passant wrote on Mar. 13, 2015 @ 17:26 GMT
Dear Michel,

I may have misread what you have said in your essay, and in that case I hope that my comment will be taken with that proviso in mind (and ignored or corrected, as applicable or practical).

It seems to me that your view of the connection between mathematics and physics is that while there are obvious and pervasive parallels between the two, it is too difficult (or at least too early) to commit to a final and formal definition of the relationship.

Given your comprehensive knowledge of many areas of mathematics and related physics, this view merits thoughtful consideration by anyone interested in either subject (or their inter-relationship).

I chose not to take up specific issues which you mention as I am not sufficiently conversant in “your” subject, and instead focused on the “meta-message” conveyed by the essay as a whole. While reading your essay, it occurred to me that you may have an answer to certain questions that had intrigued me in the past, and if you permit, I would send you an email later to explore those issues (they are not strictly relevant to the concept motivating these essays, and so I prefer not to deal with it here).

Your essay receives my endorsement without reservation, and I will rate it over the weekend (favorably, of course).

I wish you continued success in your endeavors within FQXi, as well as in your academic work.

En

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Author Michel Planat replied on Mar. 13, 2015 @ 18:21 GMT
Dear En,

I am pleased that you liked my essay although it takes time to learn the details. I will be happy to reply to your emails on the questions you have in mind. I also posted an expanded message on your webpage. Thanks for reading me.

Michel

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Mark A. Thomas wrote on Mar. 13, 2015 @ 18:05 GMT
Quanta Magazine has a new article on moonshine titled "Mathematicians Chase Moonshine's Shadow" at link https://www.quantamagazine.org/20150312-mathematicians-chase
-moonshines-shadow/#comment-337039

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Lawrence B Crowell wrote on Mar. 15, 2015 @ 01:09 GMT
I intend to discuss this further, but your essay is a unique gift. I applaud your efforts. The connection between the Bell theorem and the Grothendiecke dessin d'enfant is most enlightening. You paper is definately a keeper, and I think you are onto something very deep. I give you the highest score on this.

Cheers LC

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Lawrence B Crowell replied on Mar. 15, 2015 @ 02:31 GMT
I gave you a 10 and put you up to 6.2, but not long after somebody gave you a 2. Too bad, I hope your paper sees favor with more people.

Cheers LC

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Author Michel Planat replied on Mar. 15, 2015 @ 09:53 GMT
Dear Lawrence,

Every scientist has his own way and velocity in going through the wonderful secrets of nature. At FQXi you already wrote many excellent essays like "Discrete time and Kleinian structures in Duality Between Spacetime and Particle Physics". I wonder if you already looked seriously at the concept of an orbifold? I see that it plays a role in the VOA associated to some sporadic groups. I also found http://arxiv.org/abs/math/0505431 for your topic of this year.

I appreciate much the impetus you gave to my essay. After my first participation I learned how it works and don't take care to much of the lazzy inappropriate votes. You received from me the best andorsement.

The goal is a continuing friendly discussion about the topics of mutual interest.

Best.

Michel

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Lawrence B Crowell replied on Mar. 15, 2015 @ 20:24 GMT
Dear Michel,

Of course I am aware of orbifolds with respect to superstring theory. The vertex operator algebra with partition function p(q) =tr q^N = Π_{N}1/(1 - q^n) is related to the Dedekind eta function. The trace results in the power [p(q)]^{24} In this there is a module or subalgebra of SL(2,Z), eg S(Z) ⊂SL(2,C), that forms a set of operators S(z)∂_z. This module or subgroup is...

view entire post


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Lawrence B Crowell wrote on Mar. 16, 2015 @ 22:05 GMT
Dear Michel,

A collaboration might be interesting. I have been pondering how it might be that Γ^+_0(5) is related to the tiling and permutation of links on AdS_5. The quotient SO(4,2)/SO(4,1) = AdS_5 is not an entanglement group, at least not as I know, but this might have some relationship to entanglement. This might be through the Γ^+_0(5). Particularly if this is related to Langlands in some way.

Cheers LC

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Jonathan J. Dickau wrote on Mar. 17, 2015 @ 00:26 GMT
This essay is excellent Michel..

You demonstrate well, how the very fundamentals of Math give rise to concepts and realities we know from Physics. I do think the Monster lurks behind a lot of orderly patterning that finds expression in the physical world; and I also affirm that it's not just too much Moonshine, that makes it look that way. A very high level discussion, but some humor too, which is nice.

The Monster made an appearance in my presentation at the 2nd Crisis in Cosmology Conference, in connection with my theory on the Mandelbrot Set and Cosmology, because of Witten's paper on 3-d gravity and BTZ Black Holes (which are 2-d) having a connection with the Monster group. But I feel strongly about the notion conveyed in my essay, that objects like the Mandelbrot Set and the Monster which arise from pure Math, must have some expression in real-world Physics.

All the Best,

Jonathan

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Torsten Asselmeyer-Maluga wrote on Mar. 18, 2015 @ 14:56 GMT
Bonjour Michel,

very thoughtful essay. I like your use of dessins d'enfants to understand quantum theory. Your essay demonstrates the necessity to look into other areas of math instaed of the obvious ones.

More comments after a second reading.

Best

Torsten

PS: I also used dessins d'enfants in my work.... Thanks for bringing it to my attention.

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Torsten Asselmeyer-Maluga wrote on Mar. 18, 2015 @ 18:07 GMT
Dear Michel,

in the last two years I went more deeply in hyperbolic geometric (hyperbolic 3-manifolds). Then I found many interesting relations to finite groups (of course much of it is also covered by a book of Kapovich "Hyperbolic 3-manifolds and discrete groups"). Together with my coauthor Jerzy, we calculated the partition function of a certain quantum field theory and found quasimodular behavior. Then we started to go into it more deeply and again found interesting relations to finite groups (Fuchsian groups). Then we managed to find a folaition of an exotic R^4 and this foliation is given by tessalation of a hyperbolic disk. Here, I found also your picture.

Your essay opened my eyes and it was like a missing link to fulfill another goal of us: to get a geometric description of quantum mechanics (right along your way).

For my there are many really deep thoughts in your essay and I certainly need moer time to grasp them.

Very good work,

Excited greetings

Torsten

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Jonathan J. Dickau wrote on Mar. 19, 2015 @ 05:38 GMT
Regarding Linas Vepstas and SL(2,Z)..

It was appreciated the link you sent to Linas' page the Modular Group and Fractals, and I agree there is a strong connection with other work, as you suggest. I guess you already know about the thesis of Tao Li, but I recently discovered this work following another thread, when I discovered the PhD thesis of Giulio Tiozzo, which you can find on his home page along with a link to other papers of interest.

All the Best,

Jonathan

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Torsten Asselmeyer-Maluga replied on Mar. 19, 2015 @ 10:54 GMT
Dear Jonathan,

many thanks for the links also from my side. I know very well the work of McMullen (and also used it to understand the quantum fluctuations of geometry).

Certainly I have to look in your essay, next point on my list.

Best

Torsten

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Author Michel Planat wrote on Mar. 19, 2015 @ 08:30 GMT
Dear Jonathan,

Thank you for the reference to Tiozzo's thesis.

It is interesting that what he defines as a quadratic interval looks the same as what we measure in the "superheterodyne calendar" of my paper [see Fig. 2 and eq. (17)] from continued fractions

http://empslocal.ex.ac.uk/people/staff/mrwatkin/zet
a/planat6.pdf

At least the starting point and the connection to Thurston's "quadratic minor lamination" is encouraging. I would also like to recognize a possible link to the f Farey fractions of hyperbolic polygons (tesselations of the upper-half plane, or of the conformally equivalent unit disk) that I mention in Sec. 3 of my essay.

We know what we have to work on. Thanks.

Michel

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Torsten Asselmeyer-Maluga wrote on Mar. 21, 2015 @ 00:27 GMT
Dear Michel,

thanks for your words.

You are absolutely right, this conclusion is strange. Actually I used the wrong tense and interschange math and physics. The corect statement is:

"the relation to math was mainly caused by the simple calculable problems in physics"

I think then it made more sense.

Thanks for the quote. Yes it is my intention. Our new paper about foliations of exotic R^4 gives also a relation to quantum field theory (we found a factor III_1 algebra which is typical for a QFT)

My remarks about dessins d'enfants were a little bit cryptic. A central point in the construction of the foliation is the embedding of a tree in a hyperbolic disk (here one has a Belyi pair i.e. a polynomial). A central point in the 4-manifold theory is the infinite tree giving a Casson handle. Of course one has finite subtrees. Here comes the dessins d'enfants into play: the embedding of these finite trees are described by this structure.

Currently we try to relate this Casson handle to Connes-Kreimer renormalization theory. If our feeling is true then the action of the absolute Galois group (central for the dessins d'enfants) must be related to the cosmic Galois group.

Of course the whole approach must be related to the interpretation of quantum mechanics too. Even in your essay you presented this relation. Certainly I have to go more deeply into your ideas.

Best

Torsten

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Torsten Asselmeyer-Maluga wrote on Mar. 21, 2015 @ 22:38 GMT
Dear Michel,

this brilliant essay needs more point. You got a 9 from me.

Torsten

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Author Michel Planat wrote on Mar. 22, 2015 @ 20:42 GMT
Thank you so much Torsten,

I started to read your book

http://www.maths.ed.ac.uk/~aar/papers/exoticsmooth.pdf

I am also doing mathematical experiments on 3-manifolds

http://magma.maths.usyd.edu.au/magma/handbook/tex


t/742

Another mathematical result of interest

"that every finitely presented group can be realized as the fundamental group of a 4-manifold"

http://mathoverflow.net/questions/30238/construct
ing-4-manif

olds-with-fundamental-group-with-a-given-presenta
tion

Of course, I just enter your field that I consider a pandora's box.

Best,

Michel

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James Lee Hoover wrote on Mar. 26, 2015 @ 16:16 GMT
Michel,

A fun but abstruse journey where symbolic characters guide us through the connective maze of math and physics.

"A mathematician is a blind man in a dark room looking for a black cat that isn't there." Schrodinger's Cat Thought Experiment? You connect math, physics and other disciplines in multiple meanings of PSI, the proposed 20,000 year link of math, graphical embedding and Riemann surfaces -- world sheet.

It seems to be a Rubrik"s Cube of learned references.

Quite clever.

Jim

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Author Michel Planat wrote on Mar. 26, 2015 @ 16:54 GMT
Dear James,

I happens that scientists like cats. Do you know Arnold's cat?

http://en.wikipedia.org/wiki/Arnold%27s_cat_map

It is also always a great pleasure to receive an agreement about a quite technical topic that many people may not be familiar with.

Thanks a lot.

Michel

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James Lee Hoover replied on Mar. 31, 2015 @ 20:20 GMT
Michel,

I returned to see whom I rated as I tend to rate some and not others. I find that I did yours on 3/26 and I subsequently found your comments.

The cat map reminds me of machinations of Euler's Identity which I reference in my essay and simulations I used to do in aerospace.

Jim

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Thomas Howard Ray wrote on Mar. 28, 2015 @ 11:59 GMT
Cher Michel,

What a fun essay! Because I share your interest in primes, modular arithmetic, and sphere packing -- with the attendant mysterious roles of numbers 12 and 24 -- you might be interested in this draft mishmash of research that I hope to develop someday if I live long enough.

To the current topic, while I agree with your mathematical interpretation of Bell's theorem, I think that adding a time parameter changes the game for physical applications, as explored in my essay here.

You get my highest mark just for the sheer exuberance of your exposition, and the passion that shines through the symbols.

All best,

Tom

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Patrick Tonin wrote on Mar. 28, 2015 @ 12:57 GMT
Bonjour Michel,

Another nice essay from you, although once again I did not understand everything, for lack of mathematical knowledge.

I also believe that numbers are at the root of everything, if you have time you can take a look at my essay, there are a few intriguing equations in it.

Et ça fait plaisir de voir d'autres Français sur ce forum !

A+,

Patrick

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Anonymous wrote on Mar. 29, 2015 @ 19:00 GMT
Dear Michel,

Very nice conversation between math and phys. The dialogue is captivating and full of interesting and deep connections. In particular, the connections between dessins d'enfant and Bell inequalities, and the moonshine group, are very intriguing. Good luck in the contest!

Best wishes,

Cristi Stoica

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Author Michel Planat wrote on Mar. 29, 2015 @ 20:46 GMT
Dear Christinel,

You are convinced that maths and physics are much related, as in Tegmark's thesis. I suggest you read Leifer's essay and in an another direction the multiverse essay of Laura Mersini-Houghton. As you worked in cosmology and QM, I would be glad to have your view about the multiverse as a possible way to connect these two separate fields. Myself I am quite innnocent on this subject. I am working at this essay by Laura.

I am also rating your essay now.

Thanks in advance.

Michel

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Jonathan J. Dickau wrote on Mar. 30, 2015 @ 04:58 GMT
Congratulations Michel,

Well deserved it is, that you have achieved one of the maxima in contest scoring trends, however fleeting or enduring that may be. I think perhaps it may be that the fact you have made the discussion fun, as well as appropriately mathematical, that makes people regard your work so highly.

I want you to know that I found it extraordinarily exhilarating, the period of research inspired by our discussions of the Dessins and the Misiurewicz points in M. I have never before found so much sheer elation from explorations in pure Mathematics, but I did relish the experience and must make time for more discussions and explorations.

I should thank you again for introducing me to Zvonkin, and reminding me to rediscover Peitgen. Also, the Maxima program has been most helpful; and who would have thought it is free? But as it turns out; I have had also the pleasure to meet one of its early developers. So little by little I learn.

All the Best,

Jonathan

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Member Tim Maudlin wrote on Mar. 30, 2015 @ 05:02 GMT
Dear Michel Planat,

I wonder if you could clarify your claim about Bell's inequality on p. 4 of your essay. You state that the sum of expectation values for the spin measurements you have in the diagram lead to the norm 2root(2), but of course one can only calculate an expectation value given the initial state of the pair of qubits. It is most usual to discuss these sorts of experiments done on singlet states, but for the singlet state the sum of expectation values for your experiments will be at most 2, which is within the bounds for a local theory. (This is because in the singlet state there is zero expected correlation between the outcome of x spin on one side and z spin on the other. As you have it written, the sum of expectation values is 0, but you can get 2 by relabeling.) So you evidently have some other state in mind, but you do not specify it.

This is important because any quantum state violating the inequality must be entangled. No product state will violate the inequality. I'm also not sure what you mean by "the proof of Bell's theorem does not mention entanglement". Bell's own proof, of course, does not mention entanglement, but predictions of violations of the inequality using the quantum formalism do require entangled states. And the derivation of the 2rt(2) bound, which is a property of quantum theory, will certainly require use of entangled states. So what is your comment about entanglement meant to say?

Any help on understanding what you have in mind here would be appreciated.

Regards,

Tim Maudlin

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Author Michel Planat wrote on Mar. 30, 2015 @ 09:29 GMT
Dear Tim Maudlin,

I know from your work that you have a strong acquaintance withh Bell's work (B). I arrived at Bell/CHSH inequality from my investigation of Kochen-Specker theorem for multiple qubits mainly through Mermin' treatise (my ref. [19]). At some stage, I observed that the commutation diagram for a set of four observables involved in the violation of the inequality is just a...

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Author Michel Planat wrote on Apr. 1, 2015 @ 08:08 GMT
Dear James,

Can you explain "The cat map reminds me of machinations of Euler's Identity" ? Before I passed to QM I worked a lot on chaos in relation to the understanding of 1/f noise that I finally saw as number theory in experiments. Thanks to you, this year, I realized that Euler's identity has to be kept in mind in relation to the Bloch sphere. As Riemann sphere R is just another representation (a la Felix Klein) of the Bloch sphere, Euler's identity also has a meaning in this context. I just gave a reference on Zivlak's blog. My today favorite objects correspond to three punctures on R or other Riemann surfaces with genus (dessins d'enfants). I spent some time seing them as the molecules of chemistry and biology with moderate success until now (unpublished work).

Cheers,

Michel

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James Lee Hoover wrote on Apr. 1, 2015 @ 17:47 GMT
Michel,

Maybe a stretch, but I was thinking of logarithmic spirals: In polar coordinates the logarithmic curve can be written as r = ae^b0. Logarithmic spirals occur everywhere in nature, from sea shells to galaxies, for example.

The dynamics of Euler's function. Then there are phase portraits of solutions: http://livetoad.org/Courses/Documents/ea8f/Notes/euler_formu
la.pdf

Jim

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Branko L Zivlak wrote on Apr. 2, 2015 @ 05:03 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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Joe Fisher wrote on Apr. 6, 2015 @ 15:39 GMT
Dear Michel,

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

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Author Michel Planat replied on Apr. 6, 2015 @ 15:56 GMT
Dear Joe,

As you already wrote me, and following my post on your blog you were not polite at all, I was prepared to reject your new post as inappropriate. But I would have been obliged to select the number 42 in the list. It turns out that the number 24 is found everywhere in my essay on moonshine and where the number 42 sould live I just did a misprint. Nobody yet detected the mistake but without knowing it you

arrived very close and gave me the opportunity to write this new post. Thanks.

Best,

Michel

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Torsten Asselmeyer-Maluga wrote on Apr. 9, 2015 @ 10:34 GMT
Dear Michel,

I think that we both have the same goal: to understand quantum mechanics from a geometrical point of view. At the end, our approaches will be converge.

BTW, there is a new Springer journal Quatum Studies

(they send me an email). Maybe interesting for you?

Best

Torsten

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Author Michel Planat wrote on Apr. 9, 2015 @ 11:40 GMT
Dear Torsten,

Yes: Quantum studies: mathematics and foundations.

The editor in chief Yakir Aharonow writes in the preface:

"Finally, there is the approach championed by Dirac and repeated successfully by Feynman and later by Freeman Dyson, namely “playing with equations” as Dirac puts it. This approach sometimes causes equations to reveal their secrets as in the Dirac equation. Dirac took this approach and created results that mathematicians and physicists are still digesting. Feynman, first with the Lagrangian approach to quantum mechanics, the so-called path integral approach, and later with QED and most of the subsequent papers he wrote, operated in this manner. The same could be said of what Dyson did when he “cleaned up ”QED into a methodology usable for calculations. Playing with the problems of quantum mechanics often leads to the creation of new mathematics."

and “Think, reconsider, explore, create deep questions, use paradoxes as a tool for understanding, and finally: publish in this journal!”

A priori this is a good journal for us. My own essay has quotes from Dirac and Dyson, and implicitely to Feynman that anticipated quantum information theory: "There's Plenty of Room at the Bottom" (in 1959). May be I can submit my Monstrous Quantum Theory and you?

Best,

Michel

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vincent douzal wrote on Apr. 11, 2015 @ 13:06 GMT
Dear Michel,

Reading your essay is challenging, if one tries to reach beyond the pleasant dialogue effect that makes you a heir of Plato, Galileo, Lewis Caroll, Donald Knuth (Surreal numbers), or even Leslie Lamport [1] for instance, and actually see all these objects you are uncovering.

As for me, I have no other option than to trust you (as is usually the case in science...

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Author Michel Planat replied on Apr. 15, 2015 @ 09:56 GMT
Dear Vincent,

I have not much to add to what you superbly wrote about my dialogue. When you write "that physics is by definition mathematical, therefore mathematics has to be efficient" I agree and we are quite close to "Science and Hypothesis" that you also quote at several places.

The group concept: absolutely yes in the Grothendieck's expanded meaning. Quantum groupoid (in Wise's essay): not sure and may be this can be falsified.

A remark: why is it so difficult to find the maths of biology (including at the basic level of DNA and proteins) ?

Why is maths so close to physics? Despite so many essays, I don't consider the mystery is lifted, may be the key is in neurophysiology, ant colonies, human sociology. I like Bach-y-Rita's work.

Thanks for your time.

Michel

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Lawrence B Crowell wrote on Apr. 12, 2015 @ 15:30 GMT
Dear Micheal,

I have been very busy with other work. It occurred to me that the dessin d'enfant for the simple y = x^3 is the same as the Dynkin diagram for the SO(8) group. It seems to me that one could easily build such constructions for the heterotic groups or for the sporadic groups with polytope realizations. These are in effect roots with Galois and abstract algebraic content. I was wondering if you had any insight into this.

Cheers LC

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Author Michel Planat replied on Apr. 13, 2015 @ 12:36 GMT
Dear Lawrence,

The Weyl group of the Dynkin diagram (DD) is not isomorphic to the (two-generator) permutation group P of DD (viewed as a dessin d'enfant). The Weyl group of SO(8) (or D4) has order 192 while its P is the cyclic group Z3. May be you have something else in mind. Incidently, four-qubit systems were found to be associated to a simple singularity of D4 in 1312.0639 [math-ph] by Holweck et al.

Best,

Michel

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Lawrence B Crowell replied on Apr. 13, 2015 @ 16:03 GMT
Dear Michael,

My point was not that there was an isomorphism, but that there might be some sort of relationship.

In addition I am wondering whether dessin d'enfant can be used to look at a general type of problem. You illustrate how Bell's theorem can be realized this way. I am interested in looking at whether this can be used to look at a general class of SLOCC groups. If they can't be found equivalent according to nilpotency on their Cartan subgroups then there is a polynomial invariant under that group which separates them.

Cheers LC

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Anonymous replied on Apr. 14, 2015 @ 15:38 GMT
Dear Lawrence,

This is the type of application we can discuss. Until now, I focused on dessins due to their relationship to quantum geometries and contextuality as in my [12] and [17], now I mentioned in the essay the link to most sporadic groups, there are plenty of other applications, some have to be discovered. Cheers.

Michel

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RJ Tang wrote on Apr. 13, 2015 @ 14:11 GMT
At it its core, math is about numbers. Natural number arises from counting orders and naming convention for the uniqueness of a places in a sequence. In that sense, the physical world is a book written in natural numbers.

Using an analogy, the English alphabet has 26 letters, and with the alphabet infinite books can be written. We examine the books and find that each book consists at least one of the five vowels, and each word is less than 100 letters long, and so forth.

We are puzzled by how a random book can be that way. But need not be so, if we realize that the rule of writing a book is quite simple although the end product is somewhat complex. We start with a letter, then a word, and then a passage, a chapter and so on. Each step has some simple but irreducible rules. This process masks the simple relationship between a book and the alphabet, if we simple look at them without the steps in between.

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Author Michel Planat wrote on Apr. 13, 2015 @ 16:18 GMT
Dear R. J. Tang,

Thanks for you post. The Monstrous Book I am reading has only two letters but infinitely many words that can be arranged in 97239461142009186000 chapters (coset classes). The number of symmetries in the Book is about 10^54. Some theoretical physics expect a better understanding of the physical world thanks to the Book. The physical world is also a human creation however.

Regards,

Michel

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Steven P Sax wrote on Apr. 14, 2015 @ 23:53 GMT
Dear Michel,

Thank you for a very enlightening and enjoyable essay! I really like how you combined rigorous analysis with a very entertaining narrative, and it's quite a thought provoking educational resource. It reminds me of genres along the lines of Flatterland. You presented a very intriguing discussion on Bell's theorem and the moonshine group, and your remark on self referencing was the perfect conclusion. I give this now the highest rating.

Thank you for your very stimulating comments and ideas on my essay (if you haven't yet rated my essay, I ask that you please take a moment to do that). I responded recently to your post and your comment inspires me to particularly revisit time entanglement and incompleteness from the perspective of gate dynamics. (And thank you for the time entanglement of connecting my past and present essays :) ) I look forward to seeing your further work and correspondence in the future. Take care,

Steve Sax

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Author Michel Planat wrote on Apr. 15, 2015 @ 08:15 GMT
Dear Steven,

I am glad that you found my reading of your excellent essay useful. Our discussion shows how much a 'correct' interpretation of what is going on in a physical experiment depends on the 'correct' maths. I am enthusiastic in your view that Goedel's incompleteness is (at least partially) related to the classical language and that the QM language is helpful on that matter, and similarly for the issue of self-reference.

As a clever physicist, I am sure you are also sensitive to the ongoing work about rubidium and the CNOT gate where entanglement between ligth and atoms has been established, e.g.

http://www.cos.gatech.edu/news/Researchers-Report-First-
Entanglement-between-Light-and-an-Optical-Atomic-Coherence

I am also happy that you were not frightened by my (may be too ambitious) topic and I thank you for your high mark. I already rated your essay highly at the time I studied it.

My best regards,

Michel

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Mohammed M. Khalil wrote on Apr. 15, 2015 @ 17:50 GMT
Dear Michel,

Wonderful essay! I enjoyed reading it very much, especially the part about Bell's theorem, and my rating reflects that.

Best of luck in the contest.

Mohammed

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Alma Ionescu wrote on Apr. 19, 2015 @ 13:36 GMT
Dear Michel,

This is a great presentation of a large web of new discoveries and conjectures that are a very exciting part of the Langlands program. For me, your essay is a powerful and comprehensive update about the current status of the direction and objectives of the program, something that isn't really easy to come by. I too think that these similarities are very promising for the future of physics, the tantalizing flavor of their existence being a strong motivation for current and near-future research. Hopefully time will show the true value of modular forms; I am sure they have a great deal to tell us.

Wish you best of luck in your research and in the contest!

Alma

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Author Michel Planat wrote on Apr. 19, 2015 @ 13:48 GMT
Dear Alma,

I spent a few hours this morning reading your essay and preparing a non trivial comment for you. You will have a very good comment and appreciation from me by the end of the day. May be this is an instance of distant entanglement between brains at least not a pure coincidence. My thoughts during the two hour fast walk I just had was about rivalry between the two hemispheres that you might be call Phys and Math., a kind of quantum superposition that collapses one side or the other depending on context.

Have a good afternoon.

Michel

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Alma Ionescu replied on Apr. 19, 2015 @ 16:15 GMT
Haha, I see! I think we were reading each other's essays at the same time. It is at the very least a nice and amusing coincidence :) I am impressed by and thankful for the time you spent reading my essay and I can't wait to hear your thoughts on it. I will post back to your page to let you know when I've answered.

Have a good afternoon too!

Alma

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Alma Ionescu replied on Apr. 20, 2015 @ 10:03 GMT
Dear Michel,

It brings me great joy that a scientist of your caliber has found things to appreciate in my essay. For your comment alone and it was well worth participating into this contest.

To me it is natural to speak about modular forms because in my opinion they are the Langlands program, first and foremost. The most famous achievement of the program lies with modular forms. I don't think they are forgotten, but probably very difficult even for skilled mathematicians. Moonshine is not often mentioned today much like the prime gap was not in focus before Zhang made his breakthrough.

I too find interesting the way humans are capable of working with complex categories instead of exhaustive search to push knowledge further. There are many things we don't understand in detail about how our minds and brains operate and to be honest, it wouldn't be very surprising if quantum effects were found at the scale at which neurons operate. Regarding knowledge itself, another essay in this contest made me think the other day about how new ideas are generated. If knowledge can be modeled as information points in a network, a new idea may be thought of as the minimum number of information points needed to deduce a new piece of the puzzle, as related to the complexity dimension of the concept that needs to be deduced and occurs as a phase transition. Since you considered the cognitive ability in your work, it would be of great interest to me to know your thoughts and your approach to the subject.

Many many thanks for your words! You made my day!

I realize I didn't include any contact information that is visible of my profile, so I am adding my personal address here alma.ionescu83@gmail.com

My warmest regards and my profound appreciation!

Alma

*I replied to you on my page and I am posting this on your page as well.

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Author Michel Planat replied on Apr. 20, 2015 @ 13:42 GMT
Dear Alma,

You essay and comments are insightful and you seem to be a charming person. I was also interested in Leifer's essay viewing the whole of knowledge as a scale-free network. Your idea of looking at possible phase transitions is developed in his Ref. [13], Sec. G, p. 63 where you can read that "the critical exponents of the phase transition equal the critical exponents of the infinite-dimensional percolation". On my side, in my Neuroquantology paper quant- ph/0403020, I wrote in the abstract "Time perception is shown to depend on the thermodynamics of a quantum algebra of number and phase operators already proposed for quantum computational tasks, and to evolve according to a Hamiltonian mimicking Fechner's law. The mathematics is Bost and Connes quantum model for prime numbers. The picture that emerges is a unique perception state above a critical temperature and plenty of them allowed below, which are parametrized by the symmetry group for the primitive roots of unity." We recently revisited the BC model in the context of Riemann hypothesis and quantum computation http://iopscience.iop.org/1751-8121/labtalk-article/45421. This is a good sign that a good mathematical theory may have many inequivalent applications.

Today I have in mind to approach the subject of cognition with the tools I am advocating in my essay, it may take a while. I already mentioned that rivalry between the two cerebral hemisphres looks like a qubit.

Thank you very much Alma for the stimulus you are giving me. My very best regards.

Michel

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Peter Jackson wrote on Apr. 20, 2015 @ 10:13 GMT
Bonjour Michel,

A wonderfully original, enjoyable, well written and possibly important essay. Now resorting to speed reading, and not a mathematician I infer the latter as much from your previous work as from the glimpses gained where I penetrated.

I consider the essay's high position to be well warranted and my score will support it. More important I hope I can persuade you to read my own, which I'm convinced identifies the confounding trick behind QM and the physical mechanism reproducing the complex plane/spherical co-ordinate complementarity and apparent non-local state reduction. A collaboration paper now expands on that 'quasi-classical' rationale (building from lst years essay) and I sincerely hope after the contest you'll be able to read, comment, advice and hopefully assist mathematically (I think I cited it in the essay).

I also identify a simple 'new' mathematical formalism in my essay which I hope you'll review.

Thank you, very well done, best wishes, and best of luck in the final judging.

Peter

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Author Michel Planat wrote on Apr. 20, 2015 @ 12:04 GMT
Dear Peter,

Thank you so much for your vote of strong confidence.

I already had a look at your essay prior to this post. I hope to be able to understand what you are doing more easily that some other respectable essays with a strong philosophical taste. Recently I red "John Bell and the Nature of the Quantum World" by Bertlmann himself and this should help me. You can expect my feedback by the end of the contest that is of course very close.

Best wishes,

Michel

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Peter Jackson replied on Apr. 24, 2015 @ 15:13 GMT
Michel,

Thanks for your post and comments on mine. I wrote a comprehensive reply, but it seems to be lost in cyberspace! So I posted the below to you;

Michel,

Strangely my comprehensive response appears to have vanished into cyberspace! Was it operator error, system failure, or some aliens overlooking us finding it too close to truth!! If I mislaid it and you find it do respond and advise. If lost, I'll try to sneak the other responses to you.

Essentially you need to read this, carefully and probably at least three times to remember it as it's a complex progression

Quasi-classical Entanglement, Superposition and Bell Inequalities.

I greatly look forward to your thoughts and questions. Best wishes

Peter

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Member Marc Séguin wrote on Apr. 21, 2015 @ 00:40 GMT
Dear Michel,

Yours is certainly a very eclectic essay, as you cover a lot of mathematical ground, some of which was completely new to me! The relationship between the Monster group, the j-function and sting theory is quite something, isn't it? As I argue in my essay, I believe that the only way to construct an explanation of reality that is self-contained is to somehow link the whole of mathematics (an infinite ensemble that taken as a whole contains zero information, like Borges' library) and the whole of physical existence. But the ever-puzzling question, "Why is our universe so lawful and so simple", is hard to answer within such a broad hypothesis of universal existence. There's clearly something missing, some process that empowers certain mathematical possibilities (and not others) to become actualized as physical realities. Could the monstrous moonshine conjecture be a hint at some convergent universal properties that physical universes share with particularly rich and fundamental mathematical structures? What if the ultimate answer to Life, the Universe and Everything is not 42, but 24? ;)

I really like the Frenkel quote, "Mathematics is not about studying boring and useless equations. It is about accessing a new way of thinking and understanding reality at a deeper level."

Let's push forward into the unknown!

Cheers,

Marc

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Author Michel Planat replied on Apr. 21, 2015 @ 09:29 GMT
Dear Mark,

Thank you for your kind comments. I doubt that the moonshine conjecture is useful for approaching MUH or your Maxiverse. It is just an amazing sporadic anomaly of our mathematical universe. But it may be useful to describe parts of our universe because the characters (the Fourier transform of the group) have the same number theoretical structure than modular forms (fonctions defined on the Poincaré upper-half plane). Within these structures, some have a non-local and contextual flavour that I am investigating at the moment.

Best,

Michel

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Armin Nikkhah Shirazi wrote on Apr. 21, 2015 @ 02:16 GMT
Dear Michel,

I found your dialogue to be a dizzyingly fast-paced voyage through many different areas of mathematics and physics which require a high sophistication to follow. It is good to be able to recognize novel connections between different areas of specialization, for then one is more likely to be able to approach a given problem from a new angle. Also the bigger one's toolbox, the greater the likelihood one will have just the right tool at hand when it is needed.

I had found out about the connection of the monster group to number theory via string theory concepts very recently, and not knowing much about it, it does seem rather unexpected. So perhaps there are other unexpected connections lurking in the back, waiting to be discovered by scientists who can connect fields that seem otherwise to be widely apart.

I wish you all the best in these endeavors,

Armin

PS. Since I saw that your essay had a major emphasis on quantum contextuality and non-locality, I am adding an additional response to your comment in my blog post regarding what I meant by "pseudo-nonlocality" (It is a very different concept from what most opponents of non-locality believe)

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Member Ian Durham wrote on Apr. 22, 2015 @ 02:09 GMT
Hi Michel,

I finally got a chance to read your essay today. Wow! It covered quite a broad spectrum of ideas. I need to digest them a bit. In fact, your essay is definitely one that I will most likely come back to. I think my primary criticism of it is that I didn't feel as if I understood the "big picture" – what was the point you were trying to get across? Or was it really just lots of little points?

Cheers,

Ian

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Author Michel Planat wrote on Apr. 22, 2015 @ 06:04 GMT
Dear Ian,

Thank you for going to my essay. I expect that my essay will not be red as a tree but as a surface with punctures, it is non local in some sense. I also hope a big picture is emerging, some points are ongoing research (as those pointed out in the abstract), some technical aspects may not be familiar to quantum physicists (e.g. modular forms and characters).

If you go to reference [17] just appearing in QIP, you can see that I cite a work of yours on the "order theoretic quantification of contextuality", meanwhile I also found another measure of geometrical contextuality that I am currently working on. A mathematician would say the Langlands program but I stay closer to physics.

Best,

Michel

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Member Sylvia Wenmackers wrote on Apr. 22, 2015 @ 09:28 GMT
Dear Michel Planat,

To be honest, I generally don't like the dialogue form (sorry!), but I do think that it requires a higher level of creativity to write such a text as compared to a monologue essay. In addition, this is only the second essay I read that has pictures, which also seems highly appropriate for a general audience. Although, some of your illustrations are quite advanced. ;-)

I think it is quite remarkable how you managed to get from the Ishango bone to weak measurements in QM in about 1 page! I also liked your selection of quotes. For instance, I didn't know the non-Darwin quote, but it's a nice one!

Best wishes,

Sylvia Wenmackers - Essay Children of the Cosmos

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Author Michel Planat replied on Apr. 22, 2015 @ 12:12 GMT
Dear Sylvia,

Your paper really needs more comments than I was able to deliver in such a short time left to us. I love your disclaimer. But I also enjoy concepts as the multiverse, the maxiverse, the megaverse, the babyverse, the monsterverse., everything chaotic, exotic, sporadic, anomalous probability distributions... With them it seems that we are are closer to the complexity of the world internal or external to us. Thank you for your read of my dialogue and your positive appreciation

Best wishes,

Michel

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Jonathan Khanlian wrote on Apr. 22, 2015 @ 16:54 GMT
I think you may like my Digital Physics movie essay which also talks about the primes. Here's a quote:

A Movie Quote from Khatchig: “A physicist looking at something that produced prime numbers in nature would probably use a formula like n/Log(n) to make predictions. They would say, ‘Look how statistically accurate the model is… We can get it so close to the right answer… Only off by two parts in a trillion… It has to be right!”

A “Real” Dedekind Cut Quote: “Just because the prime number theorem allows us to look at the primes in a statistical way, this doesn’t mean that the primes are generated probabilistically. In fact, we know the primes are only pseudorandom because there are deterministic processes such as Eratosthenes Sieveiii which will generate them. So how do physicists know that there isn’t some underlying pseudorandom process that could reproduce the results of quantum mechanics in a classical, deterministic way? Even if Bell’s Inequalityiv rules out local hidden variables, this doesn’t preclude determinism in general.”

Thanks,

Jon

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Yafet Erasmo Sanchez Sanchez wrote on Apr. 23, 2015 @ 01:09 GMT
Dear Michel,

I enjoyed your essay. I am still trying to grasp all the ideas you present as many of the mathematics and the physical concepts are new to me. Nevertheless, if I grasp one of the ideas correctly is that Phys and Math are trying to describe the quantum behaviour of matter using the language of algebraic geometry. This is a very fresh and innovative point of view.



Your essay make me think of the following Wittgenstein quote "The limits of my language means the limits of my world." because I believe that describing physical concepts in new mathematical language can only extend and enrich our understanding of our world.

Kind Regards,

Yafet

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Member Giacomo Mauro D'Ariano wrote on Apr. 23, 2015 @ 01:13 GMT
Dear Michel

Nice story rich of erudite cases of study. The last example from Dyson sets the difference from my mathematization of physics viewpoint and pure mathematics without physical interpretation (or physics as any possible mathematics): I definitely believe that the monster group will never have a physical interpretation in a theory (but I maybe wrong as Dyson).

My best wishes

Mauro

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Author Michel Planat wrote on Aug. 15, 2015 @ 09:57 GMT
This essay is published as

Mathematics 2015, 3, 746-757; doi:10.3390/math3030746

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