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.

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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.

    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

    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.

    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

      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

      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

      For the information of readers of these posts , I put the link to your (coincidence) result seing the big number 3.377368...ﾃ--10^38 as

      relating the neutron mass and the Ramanujan constant.

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

      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-constant-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

      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

        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

        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

        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

        4 days later

        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

        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

        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

          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

          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