A moonshine dialogue in mathematical physics by Michel Planat

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

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)

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

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

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

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

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