Chasing Moonshine's Shadow: The connection between Number Theory, Algebra, and String theory

Be forewarned, this article is long and complicated but also riveting. Tbh, I probably understood an eighth of the concepts put forth, but once I started reading I couldn't put my tablet down. The fact that people randomly discovered mathematical concepts over 100 years ago which they absolutely did not understand, but today are leading to what may be a major breakthrough in string theory, fascinates me. The fact that this discovery is also in a major and reputable scientific journal, and not from some of the more crackpot sites, is just icing on the cake. It sounds like we're on the cusp of something major here.

www.scientificamerican.com...

Moonshine’s shadows
In 1913, the English mathematician G. H. Hardy received a letter from an accounting clerk in Madras, India, describing some mathematical formulas he had discovered. Many of them were old hat, and some were flat-out wrong, but on the final page were three formulas that blew Hardy’s mind. “They must be true,” wrote Hardy, who promptly invited the clerk, Srinivasa Ramanujan, to England, “because, if they were not true, no one would have the imagination to invent them.” Ramanujan became famous for seemingly pulling mathematical relationships out of thin air, and he credited many of his discoveries to the goddess Namagiri, who appeared to him in visions, he said. His mathematical career was tragically brief, and in 1920, as he lay dying in India at age 32, he wrote Hardy another letter saying that he had discovered what he called “mock theta” functions, which entered into mathematics “beautifully.” Ramanujan listed 17 examples of these functions, but didn’t explain what they had in common. The question remained open for more than eight decades, until Sander Zwegers, then a graduate student of Zagier’s and now a professor at the University of Cologne in Germany, figured out in 2002 that they are all examples of what came to be known as mock modular forms.

Here's how the moonshine embedded in the sacred geometries of several world religions is related to the group mathematics of superstring theory and the geometry of the 421 polytope - the eight-dimensional polytope whose 240 vertices determine the 240 root vectors of E8, the exceptional Lie group in E8xE8 heterotic superstrings:
smphillips.8m.com...
In particular, study the miraculous moonshine to be found here

a reply to: Vdogg

String theory is way down a rabbit hole and needs to get back to the real axis. I am by no means an expert, but I have read quite a bit on it. Some books I thought were good, I've read 3-4 times. This finding doesn't sound, to me, like the one that leads to something testable because it's so damn abstract. I'm sure the coefficients matching stems from a real similarity, but it's hard to place a value on this "breakthrough".

These functions and models in the string theory domain are getting more and more complex as they struggle to find patterns. It seems there is a risk of tail chasing when looking for patterns in complex forms that match or resemble each other.

My takeaway? You never know what kind of person will bring the true breakthroughs. You never know what kind of person is going to teach you something that could save your life. It's the genius of the internet and places like ATS.

Very interesting post, F & S for it.

@ micpsi - seriously? God in math?? Funny...

Srinivasa Ramanujan was a gargantuan genius among geniuses. His incredible mental abilities were so towering as to be almost beyond belief. He was truly operating on another plane. What a drag he passed away so early in life; he probably had so much more to contribute. I guess the good die young...

Ramanujan’s contributions to many branches of mathematics are even more incredible in light of his background. During his youth it seems he was moved around a lot and passed between relatives quite a bit. Other than his exceptional mathematical skills, he was pretty much a failure at everything else in school. In math, though, he was light years ahead the rest and worthy of their respect and praise. In the end, a good formal education was not within his reach. For all intent and purpose he was a self-taught mathematician, obtaining various books/materials on the subject from his friends, or wherever, and consuming them with great ferocity. But having no formal (structured) education led to gaps in the scope of his overall knowledge. While he had a deep understanding of the mathematical concepts he taught himself, there were other major branches of mathematics he knew little about. I’ve read that while working a problem there were a couple instances when Ramanujan invented/derived his own method for getting from A to the solution at B, and in doing so had basically re-invented an already established methodology/discipline within mathematics. This innate ability of his has amazed and confounded many of the greatest mathematicians to this day.

The fact that Ramanujan had a very limited formal education, and was primarily self-taught, is a testament to the fact that his incredible genius and uncanny insight was the result of an innate, natural-born gift. The man was blessed, and way, WAY ahead of his time.

Great thread and link!!

PS: Can you imagine what a casual conversation between Ramanujan and Robert Langlands would be like? I can - INCOMPREHENSIBLE, but fascinating!

a reply to: netbound

I’ve read that while working a problem there were a couple instances when Ramanujan invented/derived his own method for getting from A to the solution at B, and in doing so had basically re-invented an already established methodology/discipline within mathematics.

As practiced by the Pythagorean inner circle, traditionally difficult math solutions were kept secret. Math tends to be more of an exact science than art so creative methodologies from outsiders like Ramanujan often did turn out to be reinventions.

Its possible string theory could trace back to the Greek Lyre similar to the one Hermes played or even earlier.
In the early 1900's scientists like Einstein could be quoted lamenting the loss of stringed instrumentals from the old country in modern music.

a reply to: Cauliflower
Yeah, you’re right. I guess you could say Pythagoras got the ball rolling that eventually led to M-Theory with his insights into the various relationships inherent in vibrating strings. Someone needs to tell Ed Witten about this!!

It’s easy to imagine Einstein missing the orchestral music of Brahms, Stravinsky and Wagner when faced with the modern music of his time. I really like Einstein. He respected and appreciated his predecessors. He approached nature from both a philosophical and scientific point of view. “Shut up and calculate” just wasn’t his style. His mind was one of humanity’s rarest treasures, in so many respects.

I’m sure over the ages that many deep, revealing truths have been lost in time, either hidden or simply forgotten, only to be resurrected later in one form or another and accepted as novel, ingenious solutions. I would also imagine that many ancient insights have been lost for all time. And so it goes, two steps forward and one back, on and on...

Although as humans we may lack the capacity to embrace it all, it seems our obligation to continue trying. It’s almost as though we owe it to someone...

a reply to: netbound

Someone needs to tell Ed Witten about this!!

Interesting link there, the Black Knight object.
So perhaps during the 1940's and 1950's there was an advance in physics made by the _ that is still classified.
Maybe he should have titled his book "the end of (fundamental) physics".
There still seem to be a lot physics theories around that resonate and conveniently explain different facets of observables.

Witten was also a fan of James Clerk Maxwell who among other things helped refine the metric system.
The Meter as a unit of length can potentially be traced back to the great pyramid location.

originally posted by: netbound
Srinivasa Ramanujan was a gargantuan genius among geniuses. His incredible mental abilities were so towering as to be almost beyond belief. He was truly operating on another plane. What a drag he passed away so early in life; he probably had so much more to contribute. I guess the good die young...

I've often caught myself wondering what would have happened if the Ramanujans of the world lived far into their primes. What inventions and/or revolutions have we missed out on because these great souls were stolen from us before their time? Hmm...You could make a pretty decent scifi movie off that concept.

Early death of talented mathematicians seems all too common, often under very strange circumstances.
Good example was the suicide of Yutaka Taniyama who committed suicide in 1958.

Taniyama was best known for conjecturing, in modern language, automorphic properties of L-functions of elliptic curves over any number field.

50 year later the NSA is using elliptic curve functions for cryptography.

en.wikipedia.org...

Maybe he got too close to solving Fermat's Last Theorem and went insane?