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November 2018

Associahedra Memories

When I spoke about associahedra and scattering amplitudes at ANU’s Morgan Phoa Workshop in 2006, nobody else was thinking along those lines, except Francis Brown, who was writing up his beautiful thesis. There was a mixed reaction from the mathematicians in the audience. Ross Street, as always, found the connection between category theory and modern physics fascinating. Michael Batanin was way ahead of everyone else with his new work on operads and higher dimensional ordinals. One algebraic geometer complained that he was not at all interested in physics, and I was far too modest at that time to tell him that he should pay attention. So many memories!

Quantum Gravity Lesson 1

Some of you may be wondering how Monster Moonshine gets a signature of (27,3) in higher Super Yang-Mills theories. Allow me to explain.

As we know, gauge groups and spacetimes are not fundamental in quantum gravity. Quantum mechanics tells us to start with a discrete set of measurement observables, and continuous things like complex Lie algebras are concretely built up as a limit of discrete geometries, much as SU(2) comes from the (universal for computation) B3 representation in the fusion category for Fibonacci anyons. Lattices for Lie algebras are a good place to find the essential discrete data. 

For E8, we saw that the 240 roots are given by two copies of Kapranov’s permutoassociahedron in dimension 3. Think of the ambient three dimensional vector space as a qutrit space, so that we take tensor products for total state spaces. Three qubits gives a 27 dimensional space, corresponding to three copies of the 240 roots. The 196560 points needed for the Leech lattice come from 720 (three times 240) times 273, where 273 is Rob Wilson’s octonion Leech lattice factor, equal to 1 + 16 + 256. We now think of this as a set of cubes (since polytopes are everywhere): one point, one 4-cube, and one 8-cube. It helps to look at these cubes as lifts of cubes in dimensions 3 and 7. As we have seen, the 3-cube carries Cohl Furey’s complex octonion charges for the Standard Model particles (negative charges), which we view as three ribbon strands in the anyon/dyon picture. (This is all published already). The full theory of course has a Langlands structure to it, with electric magnetic duality. Now you can probably figure out the missing details yourself. Look for thee time directions in the three qubits that label the cube, the anyons underlying leptons and quarks.  

Academia and Misogyny

You like to follow the man.

When the gossip says it was all his work, you figure it must be true. You shun the woman and mock her behind her back. You ignore the blatantly criminal censorship of her writing, and then call her paranoid. You tell people she only got a PhD because she slept with the boss. You spew hatred at her when she cries out about torture and abuse. 

But you see, your hellish error, your infinite foolishness, your misplaced anger ... it is all dismissed by one elementary, easily scientifically verifiable fact.

He is a clinical psychopath who enjoys abusing women.

Orwell’s New World

I have received two emails recently from Targeted Individual groups online, after years of battling Big Brother alone. They requested information. Like most emails I receive, they request  information. Given that I receive very, very few emails, it may be safely assumed that even these ones are an attempt to ruin my life in yet new ways. Or maybe Big Brother is pretending to care,   so that intelligent bystanders get the impression that something is actually being done. 

Only one thing will signal real change: give me that research fellowship.