FE, FI, FO, FUM

You may think I am stupid to sell a cow (Standard Model Sacred Cow) for a handful of beans (four assorted finite groups, of orders 3, 8, 27 and 128), but you must understand these are mathemagic beans. If you just throw them out of the window, they will grow into a ginormous beanstalk, which you can climb up to get to the castles in the air where the Giants of Physics live.

I am working from an Arabic Ladybird book called “Sam wa’l fasuliya”, which I must have bought in London 30 years ago, judging by the fact that the price 60p is written upside down in the back of the book, presumably by someone who doesn’t know the difference between right-handed English books and left-handed Arabic books. Why Jack is called Sam, I don’t know, but fasuliya is a bean(stalk), that’s for sure. I suppose I thought this book would help me to learn Arabic, but it didn’t help much. So the text makes about as much sense to me as a string theory paper, and I’m reduced to looking at the pictures (experiments) to figure out what is going on in the story.

But at least I know which end of the book to start from. Apparently string theorists don’t realise that you are supposed to start at the beginning, that is the finite and discrete things, and work your way to the end, where the continuous stuff is. They read the book of nature as though it is a right-handed English book, when it is actually a left-handed Arabic book. If you start at the end, then you will see the picture of the Giant crashing to the ground under the force of gravity, and you won’t have any idea what the Giant was doing up in the clouds to begin with, or where the beanstalk came from.

You won’t have any idea about the electro-magic beans, or the weak force that caused them to germinate and send out shoots (neutrinos), or the strong force that creates the mass of the beanstalk, without apparently giving it any weight. Only at the very end of the story will you be able to understand where the weight comes from. When the magic beanstalk that leads to string theory is chopped down, gravity once again rules the world.

We don’t really want to look at all 24 pictures, do we? We do? OK, then. If you’re all sitting comfortably, I’ll begin. In the first picture, Sam is lying lazily on the floor, day-dreaming, while his mother is working hard at the housework. Let’s say Sam represents me, for the sake of argument. In the second picture, Sam is leaving home with the cow to sell. In the third picture, he sells the cow for a handful of (magic) beans. In the fourth picture his mother throws the beans out of the window in disgust, and despair at Sam’s stupidity.

In the fifth picture, the magic beanstalk has grown, and Sam is staring up at it in bewilderment. That’s roughly where we are today. Those four little tiny beans have grown up overnight into a passable resemblance to the entire Standard Model, when you would expect it to take fifty years of patient work in the garden to grow something this big. So shall we see what happens next?

In the sixth picture we assume Sam has climbed up the beanstalk, and we find him at the top looking out over a vast Landscape (of string theory, I presume), and standing on a road that leads straight off into the distance. In picture 7, he meets an old woman, who presumably directs him to the door of the Giant’s Castle, where he is greeted by the Giant’s wife in picture 8. In picture 9, Sam is bundled into the fireplace to hide from the Giant, who appears in picture 10. Here I see the words in Arabic on the opposite page: “FI, FU, FI, FUM”, but I prefer the version “FE, FI, FO, FUM” that I learnt first: Finite Energy, Finite Input, Finite Output, Finite Unified Model.

Next picture: the goose that lays the golden eggs. The Giant gets rich from all this gold, but it is still a stupid goose that gives him all this gold. I think this must be a metaphor for all the stupid research funding agencies that continue to fund string theory research despite the obvious fact that it is a castle in the air that will never stand up in the real world. In picture 12, Sam sees the goose lay a golden egg, and in picture 13 he’s either climbing down the beanstalk, or back up again to make another visit to the imaginary landscape of string theory. The goose doesn’t appear again, so perhaps it’s met its demise at this point. In picture 14, Sam is back at the Giant’s castle.

In picture 15, the Giant is gloating over his gold, but there’s no sign of any more golden eggs. In picture 16, Sam is carrying a large swagbag, presumably containing lots of the Giant’s gold, walking away from the castle. We have to assume he’s taken it home to his mother, because in the next picture he seems to be at home looking bored while his mother reads him a story, and next after that he is back on the road in the string theory landscape, and then he is hiding in the Giant’s castle again.

In picture 20 he steals the golden harp from under the nose of the sleeping Giant, who wakes up and chases him down the beanstalk in picture 21. In picture 22, Sam’s mother comes with an axe to chop down the beanstalk, and in picture 23 the Giant lies dead, having finally understood the force of gravity. And of course, in picture 24 they all lived happily ever after, as you can see from the smiles on their faces.

Well, as I said, we’re only on picture 5 out of 24, so there’s a long way to go before the String Theory Monster is dead, but if you want to know how those four mathemagical beans grew into that monstrous beanstalk, you can find out by reading my paper. I know there is zero chance that the arXiv will post it, since the last thing they want is people climbing up a beanstalk into their barren string theory landscape and stealing the goose that lays their golden eggs. So I’ll post it here at https://robwilson1.files.wordpress.com/2024/01/pgm2.pdf.

9 Responses to “FE, FI, FO, FUM”

  1. Robert A. Wilson Says:

    SAM = Silly Auld Me

  2. Robert A. Wilson Says:

    Did you ask, what sort of beans? They’re string beans, of course. Or string has-beens, perhaps.

  3. Robert A. Wilson Says:

    Arabic words have a tendency, as you know, to look like little tiny vibrating strings, especially if you look at them back-to-front or upside-down. So I think this must be where the idea for string theory originally came from. The fact that these “strings” are written in an alphabet of a finite number of discrete symbols seems never to have occurred to the string theorists who are trying to decipher a text written in Arabic without being able to read the language. In fact, many of them seem to think that Arabic is written like Chinese, which uses 2-dimensional “branes” rather than 1-dimensional “strings”. But in fact it is written like English, which uses “0-dimensional” letters. And Korean, which also uses letters, but looks like Chinese if you don’t know the alphabet.

  4. Robert A. Wilson Says:

    “The string-theorists’ song”

    Fe, fi, fo, fum,

    I smell the blood of a mathematician.

    Be he alive or be he dead,

    I’ll grind his bones to make my bread.

  5. Nige Cook Says:

    Thanks for uploading the paper https://robwilson1.files.wordpress.com/2024/01/pgm2.pdf which is precisely what I want. 

    “The full 4 × 4 quaternion matrix algebra can also be interpreted as a Clifford algebra for a 6-dimensional real space with signature (6, 0), (5, 1), (2, 4) or (1, 5).”

    What about (3,3)? Also, can be the 4 x 4 Dirac matrices be related to SU(4)? (There’s a 1985 old paper on this: https://inis.iaea.org/collection/NCLCollectionStore/_Public/20/080/20080752.pdf but it’s obscure.)

    The SM linking groups of 1, 2, and 3 basic charges, with combinations given by 1, (2^2) -1 and (3^2) – 1 matrices, respectively, doesn’t fit mathematically that well with Dirac’s original QED equation with four 4×4 matrices of spin and antimatter: problems come when reducing Dirac 4×4 matrices to 2×2 Pauli/SU(2) matrices, e.g. Dirac versus Majorana. Maybe Dirac’s 4×4 matrices should be expanded to 6×6, or the weak SU(2) matrices should be expanded to 4×4 like Dirac matrices or SU(4)? Part of the issue is that the importance chirality was only proved experimentally in 1957 by parity violation. There are dynamical reasons in physics why parity violation may be covered-up in electromagnetism (e.g. infinite self inductance preventing phenomena which would indicate it). I don’t think the mixing angles and SU(3) colour charges are problems; they are explained as emergent properties due to pair production phenomena when constrained by energy conservation in the dynamics of vacuum polarization (this dynamical and energy conservation is currently ignored by the mainstream).

    • Robert A. Wilson Says:

      Cl(4,2), Cl(3,3) and Cl(0,6) are 8×8 real matrices instead of 4×4 quaternion matrices. Both cases are plausible a priori, but only the quaternion case admits an action of the Gell-Mann and Pauli matrices in the `mixed’ form that I require.

      If you read my paper in detail, you will hopefully see the answers to your other questions as well. Dirac’s matrices are good enough for one generation, but need to be extended to 4×4 quaternion matrices to get the three generations. I first suggested this several years ago, but now I have better mathematics to explain *why* it has to be like this.

      Chirality is also explained in my paper as a non-invariance of the model under quaternion conjugation. Again, this cannot be explained with Standard Model complex matrices. And again, it is an obvious idea, that has been expressed before, but the difference is I now have better mathematics to explain *why* it must be like this.

      As far as I see it, there is no need to expand the Pauli matrices to a larger *group*, but there is a need to write them as 4×4 matrices. I identify four different copies of the Pauli matrices, playing four different roles: (1) non-relativistic spin, (2) mass-energy, (3) generation symmetry and (4) weak isospin, although I am not convinced I have explained them completely clearly or correctly.

      By changing small details in the Dirac matrices it is possible to use various different signatures of Clifford algebra – I don’t have any strong opinions about which is best at this stage. All I can say is that Spin(3,3) is the only one that definitely does not work.

      • Nige Cook Says:

        “I identify four different copies of the Pauli matrices, playing four different roles: (1) non-relativistic spin, (2) mass-energy, (3) generation symmetry and (4) weak isospin, although I am not convinced I have explained them completely clearly or correctly.”

        It should be possible to do that. If you look at the situation from the physical dynamics viewpoint, Dirac showed QED to require 4×4 matrices, which can be reduced (in various ways) to SU(2) 2×2 matrices. However, dogma held that QED was a U(1) Abelian theory, because no SU(2) Yang-Mills charge transfer gauge boson was ever observed in QED! However, if you look at Maxwell’s equations in a less superficial way, you see that there is a physical mechanism that blocks any charged, massless gauge boson Yang-Mills charge transfer term from working (i.e., the infinite magnetic self-inductance of charged, massless vector bosons). So QED can actually be a non-Abelian, Yang-Mills SU(2) theory after all!

    • Robert A. Wilson Says:

      I looked briefly at that 1985 paper, enough to find out what they do to get SU(4) from the Dirac matrices, and to see that there is nothing profound there. All they do is take the Lie algebra generated by the Dirac matrices and their non-identity products, which is 15-dimensional, and is obviously some real or complex form of SU(4), depending on what you do with the scalar multiplication by i. They just make a choice of scalar multiples that gives the compact real form. Mathematically, this is a triviality. What it means physically, I have no idea.

  6. Unification of particles and fundamental forces – Quantum field theory Says:

    […] (17 Jan 2024): Wilson has a mathematical paper up, linked at the end of his fairy tale post https://robwilson1.wordpress.com/2024/01/17/fe-fi-fo-fum/ My comment (in moderation queue there, copied below in case […]

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