# Ramon Llull Connected Ancient Wisdom to 21st Century Science

## Real Clifford Algebras with 8-Fold Periodicity Factoring.

So, changing notation from Llull(16) to Cl(16) etc, because mathematicians mostly use the term Clifford Algebra, named for William Kingdon Clifford, who, over 100 years ago, wrote about such Algebras, the factoring is

## So, consider each set of 8 Elements as an 8-dimensional Space.

### The Simplest Geometric Objects in the 8-dimensional Octonion Space are:

• 0-dimensional points (there is only 1 general type, involving none of the Basis Element directions)
• 1-dimensional line Subspaces (8 general types, one in each of the Basis Element directions 1, i, j, k, E, I, J, K)
• 2-dimensional plane Subspaces (28 general types, each in a Pair of Basis Element directions)
• 3-dimensional Subspaces (56 general types, each in a Triple of Basis Element directions)
• 4-dimensional Subspaces (70 general types, each in a Quadruple of Basis Element directions)
• 5-dimensional Subspaces (56 general types, each in a Quintuple of Basis Element directions)
• 6-dimensional Subspaces (28 general types, each in a Sextuple of Basis Element directions)
• 7-dimensional Subspaces (8 general types, each in a Septuple of Basis Element directions)
• 8-dimensional Space itself (there is only 1, involving the Octuple of all the Basis Element directions)

### Each of the 8 Elements is a Basis Element of the 8-Dimensional Space, one of which is represented by the Real Number 1 and 7 of which are represented by the 7 Octonion Imaginary Numbers i, j, k, E, I, J, K .

(The Octonion Imaginary Numbers i,j,k,E,I,J,K are generalizations of the Complex Imaginary Number i.)

## as shown by Llull in his V-wheel with two sets of 7 Elements and their Pair-lines.

### the Simplest Curved Geometric Objects in the 8-dimensional Octonion Space are:

• Circles, which are 1-dimensional Spheres S1
• 2-dimensional Spheres S2
• 3-dimensional Spheres S3
• 4-dimensional Spheres S4
• 5-dimensional Spheres S5
• 6-dimensional Spheres S6
• 7-dimensional Spheres S7

### A 3-dimensional example of Spin-Connection-With-Surroundings shows a cup held by a dancer in one hand. Rotating the cup by 360 degrees gets the arm (which is connected to the shoulder of the dancer) twisted, but turning the cup another 360 degrees gets the arm back straight:

• picture 1 is the start,
• picture 2 is 180 degrees,
• picture 3 is 360 degrees (note how the arm is twisted),
• picture 4 is 540 degrees,
• and picture 1 again is 720 degrees.

and

### the other 8 of which, because they look like mirror images of the first 8, are called -half-Spinors.

In the case of the 8-dimensional Octonionic Clifford Algebra Cl(8):

and

and

# Llull has described the basic ingredients for a high-energy (around Planck Energy) physics model with:

## 28 Spin(8) Pair-line Elements representing 28 Gauge Bosons

### The half-Spinor parts of the Llull Model already look realistic, by the correspondences:

• 1 = Neutrino
• i = Red Up Quark
• j = Green Up Quark
• k = Blue Up Quark
• E = Electron
• I = Red Down Quark
• J = Green Down Quark
• K = Blue Down Quark

and

and

# Llull's S-wheel and T-wheel show how to get our Spacetime and the Standard Model and Gravity.

## When that Quaternionic Structure is introduced, the 16x16 Real Matrix Algebra of Cl(8) is transformed into the 8x8 Quaternionic Matrix Algebra of Cl(2,6).

### and on the Fermion Particles and Antiparticles, which now come in 3 types, or generations:

• 1 - living in S1xS3 Physical Spacetime
• 2 - living in S1xS3 Physical Spacetime and CP2 Internal Symmetry Space
• 3 - living in CP2 Internal Symmetry Space

## To see the Gravity and its 15 Gauge Bosons, look at Llull's T-wheel.

### The 3+12 = 15 SU(2,2) = Spin(2,4) Conformal Group GraviPhoton Gauge Bosons act on 4-dimensional Physical Spacetime by:

• 4 Translations,
• 6 Lorentz Transformations,
• 4 Special Conformal Transformations and
• 1 Dilation.

## Using the Llullian Structures, you can construct a Lagrangian over 4-dimensional Physical Spacetime that allows you to calculate:

• • Me-neutrino = Mmu-neutrino = Mtau-neutrino = 0 (tree-level)
• Higher-order corrections give:
• Mneutrino1 = 0

Mneutrino2 = 9 x 10^(-3) eV

Mneutrino3 = 5.4 x 10^(-2) eV

Neutrino mixing matrix:

```                            nu_1          nu_2      nu_3

nu_e         0.87          0.50      0

nu_m        -0.35          0.61      0.71

nu_t         0.35         -0.61      0.71
```
• • Me = 0.5110 MeV
• • Md = Mu = 312.8 MeV (constituent quark mass)
• • Mmu = 104.8 MeV
• • Ms = 625 MeV (constituent quark mass)
• • Mc = 2.09 GeV (constituent quark mass)
• • Mtau = 1.88 GeV
• • Mb = 5.63 GeV (constituent quark mass)
• • Mt = 130 GeV (constituent Truth Quark mass) as the ground state of a 3-state T-quark - Higgs - Triviality Boundary System

### BHL state with Tquark mass = 218 +/- 3 GeV and Higgs mass = 239 +/- 3 GeV at the Triviality Bound - Vacuum Stability Critical Point.

and

```      d                    s                   b

u   0.975                0.222               0.00249 -0.00388i

c  -0.222 -0.000161i     0.974 -0.0000365i   0.0423

t   0.00698 -0.00378i   -0.0418 -0.00086i    0.999 ```

and

• • W+ mass = W- mass = 80.326 GeV
• • Z0 mass = 91.862 GeV
• • Higgs mass = 145.8 GeV
• • weak force - Higgs VEV = 252.5 GeV (assumed, since ratios are calculated)

as well as ratios of force strength constants:

• • Gravitational G = (Ggravity)(Mproton)^2 = 5 x 10^(-39) (assumed, since ratios are calculated)
• • electromagnetic fine structure constant = 1/137.03608
• • Gfermi = (Gweak)(Mproton)^2 = 1.02 x 10^(-5)
• • color force strength = 0.6286 (at 0.245 GeV) - perturbative QCD running gives
• • color force strength = 0.167 (at 5.3 GeV)
• • color force strength = 0.121 (at 34 GeV)
• • color force strength = 0.106 (at 91 GeV)

If Nonperturbative QCD and other things are taken into account, then the color force strength = 0.123 (at 91 GeV).

Dark Energy : Dark Matter : Ordinary Matter

Ratio

0.75 : 0.21 : 0.04

( for details of the physics model and the calculations, and for references and source material, see my web site at www.valdostamuseum.org/'hamsmith/ or mirror site at www.tony5m17h.net/ the contents of which are hereby incorporated herein by this parenthetical reference )

and

# Ramon Llull was a Nexus between Ancient Wisdom and a Unified Model of 21st Century Physics.

### Just as the practices of Divination had preserved in Africa

(and in the Mediterranean through 16-element Ilm al Raml,

and in China through the 64-element I Ching,

and in Japan through 128-element Futomani Book of Shinto Divination,

and in India through the 24+192 = 240-element First Sukt of the Rig Veda)

### the 78-Card Tarot Game/Divination

(and the common 52-Card Game Deck that descended from Tarot, which 52 Cards correspond to the 52-dimensional exceptional Lie Algebra F4 of which the 78-dimensional exceptional Lie Algebra E6 is a complexification)

### would spread throughout the Global Society that began to be formed in the 1400-1500s and so preserve Fundamental Details of the Ancient Wisdom seen by Ramon Llull.

( s=swords, w=wands, p=pentacles, c= cups and k=knave(page), j=Knight(Jack), K=King, Q=Queen, and

0=Fool, 1=Magician, 2=Popess, 3=Empress, 4=Emperor, 5=Pope, 6=Lovers, 7=Chariot, 8=Justice, 9=Hermit, 10=WheelofFate, 11=Strength, 12=HangedMan, 13=Death, 14=Temperance, 15=Devil, 16=Tower, 17=Star, 18=Moon, 19=Sun, 20=Judgment, 21=World)

• The 28 magenta 28 are the 28 Spin(8) adjoint bivectors of Cl(8).
• The 16 blue are the 8 vectors of Spin(8) and Cl(8) and their 8 dual/conjugates.
• The 32 red are the 16 spinors (8 +halfspinors and 8 -halfspinors) of Spin(8) and Cl(8) and their 16 dual/ conjugates.
• The 2 black are diagonal degrees of freedom in the 26-dim traceless J3(O)o part of the J3(O) Jordan algebra.

## Ramon Llull expressed what Einstein (in the New York Times Magazine on November 9, 1930 pp 1-4) called cosmic religious feeling:

### It is cosmic religious feeling that gives a man such strength. …".

Frank Dodd (Tony) Smith, Jr.

April 2007

( for further material and details, and for references and source material, see my web site at www.valdostamuseum.org/'hamsmith/ or mirror site at www.tony5m17h.net/ the contents of which are hereby incorporated herein by this parenthetical reference )