Condensation monads in higher categories

Very nice Perimeter talk on condensation monads: a higher dimensional categorical analogue of idempotents. Comments on Twitter.

Introduction to Quantum Gravity

Everyone will be able to learn quantum gravity. It is not at all difficult. But the mathematical details are important for technology. Here is a collection of introductory posts about the new theory, for the general reader.

Matter, Space and Time

Electrons, neutrinos and quarks as knot diagrams

Neutrinos and the CMB Sky

Coordinates and Polytopes

Number Theory for Physics

Category theory: from lattices to ribbons

Memories of the Star

I don’t remember exactly what year it was, that I first told Michael Rios about the modern Star. Probably 2014. 

I sent him a latex file, where I was looking at the symplectic Penrose map from the eight dimensional integers down into the plane. Then I wrote down the area of the pentagram, thinking about some work of Hodges, and explicitly mentioned the Star of David as the hexagonal analog. And I was putting quaternions in there too.

Of course I didn’t care much about the Lie algebras. They are less important than the category theory. And people tend to conveniently forget what I tell them. All the time. So when Piero Truini said to me, “You know, it was Mike who told me about the Star. I never realised”, I simply replied, “Yes, I know it was Mike. It had to be.” Piero didn’t understand what I meant. And there wasn’t really any point in trying to explain. People choose what they believe in. 

Back in 2010, when he asked me about the London moment anomaly, I said it was the neutrinos, with a precise numerical value. Of course, nobody told me about McCulloch’s work, or about anything else that was important, but it’s pretty obvious now that the cabal and the military knew about these things, although they did not understand the connection to neutrinos until they stole it from me in 2017.

Working Away

My next paper will probably have more of a moonshine feel to it! Plenty of work to do, even if the aliens arrive ...

Memories from Paris

Quantum Gravity Lesson 42

It was not the reals you wanted. Octonion multiplication was always about sets.

Quantum Gravity Lesson 41

Today we look once again at that 2/9 parameter in the Koide rest mass formula. We see how the central 6 points on the tetractys have a different origin to the remaining 21, when considering the basic simplex map from 81 paths to 27.

Quantum Gravity Lesson 40

A little introduction to the famous j-invariant, from some rough notes I passed around last year. Yes, we feature the golden ratio. I realised back in 2017 that it featured prominently in the defining polynomials, as noted here.

Memories

Over a year ago, I was playing with some nice diagrams associated to the magic star. But don’t forget, in quantum gravity, the Star of Remphan (and much evil) is always accompanied by pentagons (and love). 

Quantum Gravity Lesson 39

As some of you will remember, there are n^(n-2) parking functions. Here are the 16 parking functions on the pentagon, in terms of our standard X, Y, Z alphabet. This is a bit different to the 16 spinor degrees of freedom, but still out of the 27 paths on the tetractys simplex inside the 4-dit discrete cube.