This blog might take a holiday, while I focus on some fun research!
I don’t remember exactly what year it was, that I first told Michael Rios about the 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.
Many of my readers are under the impression that I just want attention. Shows how much they know about autism, huh. Anyway, today we are going to discuss a little detective work.
Whoever currently has control of my dodgy iBooks app might well be protecting me in some way from Washington and Rome. But they probably don’t have my best interests at heart. Where are they?
Well, my night time screen settings on my iPad are supposed to switch off at 5am, local time. But for some reason they switch off on iBooks at 10am. Now, if that corresponds to 10am my time, where does that put ghost iPad? It narrows it down quite a lot, to China or South East Asia. It’s one hour too late to be Perth in Australia. But then of course, the ghost stalker might well have his own iPad settings, so Australia is still high up on the list of possibilities. And since it makes sense to use stalkers close to my own time zone, this doesn’t tell us a lot. But it tells us something. Western China. Or at least, a little west of Beijing.
When we start looking at the coefficients of modular forms for the modular group, like those for the Leech lattice in weight 12, we find some nice large primes!
Observant mathematicians will also know that 241 is prime, as is 196561. Like they say: no more secrets.
As we know, the lepton Koide parameters are very simple, as are the remaining ones. First, the diagonal square root of 2 follows from very simple geometric arguments. He we draw it on the g2 roots in the magic plane.
To understand the 2/9, you need to appreciate the importance of the Leech lattice. On a triangle within our Star of David lies three copies of the exceptional Jordan algebra, in the case of 240 roots. That means three separate copies of octonion triples, interpreted as three whole copies of the Leech lattice, in dimension 72. But as Rob Wilson and other good group theorists will tell you, the ratio of 12 to 54 (paths) comes from 4 to 18, for one copy of the Leech lattice. That is, to make the complex Leech lattice integral over the Eisenstein integers, we choose coordinates with norm square of 18, and then rescale to get the required norm 4. That is a canonical rescale factor of 2/9.
The automorphisms of the (complex) Leech lattice can be described using our favourite 3x3 quantum Fourier transform.
It was nice to meet Alessio Marrani in June last year. Michael and I picked him up from the airport in Los Angeles in a brand new sporty red Alfa Romeo. Of course, I was not allowed to speak to him for long. He was going to send some data on M theory entanglement for me to match up with some of my own work, but I never received the emails and he stopped talking to me. David Chester said that he blamed me for causing a temporary rift between Piero Truini and Michael, but none of the gaslighting bullshit ever makes any sense to me and so I just gave up.
I see you’re doing very well anyway, Alessio. Best wishes from me.
So the lovely female scientist told me that it was only a limit on her credit card that was preventing the payment to the Internal Revenue payment, and then she made a payment. But she asked that I check whether or not it went through.
So I tried. First, I attempted to set up an online IRD account, using my tax file number. Then I phoned from a local phone box. The automated voice service said that my account was now active. I decided to stay on hold to ask about the payment that they should have received. The automated voice service said that there was only a ten minute waiting time, but I stood there listening to the stupid music for about half an hour before I gave up. Then I tried to log on to my new online account. But first I had to set up a password. There was no screen on my browser for doing this, so eventually I just hit the ‘forgot password’ button and tried that way. The IRD website then informed me that I was locked out of my account due to too many log in attempts. They said I should phone them.
My next paper will probably have more of a moonshine feel to it! Plenty of work to do, even if the aliens arrive ...