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E(8) x E(8) = (TS)
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benpadiah
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 Post Posted: Tue Oct 18, 2005 7:30 am    Post subject: E(8) x E(8) = (TS)
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Just found this: http://www.valdostamuseum.org/hamsmith/TShome.html

Appears to be a nearly 100% complete recreation of Tony Smith's original site (including his e-book .pdf BANNED BY CORNEL)!

If anyone who knows anything about Clifford Algebra happens to blow through and sees this, here's a link to Tony's own D4-D5-E6-E7-E8 physics model. I'll post more on this after I've studied it more, but I believe this to be the origin for John Titor's offhanded remark from which this thread derives its title.

http://www.valdostamuseum.org/hamsmith/1TSphysics.html

Also, I'm now hosting a .pdf e-book I found on an online free library that mentions "Z-transforms" on page 6. Check it out, this part, at least, looks (perhaps deceptively?) simple.

http://www.benpadiah.com/otherstuff/elib/Fourier_Transforms_and_Waves.pdf

Enjoy!

-ben
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Last edited by benpadiah on Wed Oct 26, 2005 2:03 am; edited 2 times in total
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benpadiah
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 Post Posted: Tue Oct 18, 2005 7:31 am    Post subject:
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Carbon wrote:
Way over my head I'm afraid Ben.


Naw, man. Look, it's simple.

Tony Smith wrote:


A 2-dimensional projection of the 7-dim 56-vertex configuration, by Peter McMullen, has 54 vertices in 3 concentric 18-gons with 1 pair of opposite vertices coinciding in the center. It can also be represented as 56 vertices in 4 concentric 14-gons, related to its 56 vertices being the compound of 7 3-dim cubes, for 7x8 = 56 vertices.



E8 has Weyl group of order 128 x 27 x 5 x 8! = 696,729,600 With respect to the A-D-E chain of the D4-D5-E6-E7-E8 VoDou Physics model, 248-dimensional E8 has the 28-dimensional structure of D4 = Spin(0,8 ) plus U(1) and 8-complex dimensional Spin(0,10) / (Spin(0,8 ) x U(1)) plus U(1) and 16-complex dimensional E6 / (Spin(0,10) x U(1)) plus U(1) and
27-complex dimensional E7 / (E6 x U(1)) plus SU(2) and
28-quaternion dimensional E8 / (E7 x SU(2))

Geometrically, E8 / (E7 x SU(2)) is the 248-133-3 = 112-real-dimensional
set of quaternionified Octonion projective planes(QxO)P2
that are in the octonionified Octonion projective plane (OxO)P2, which
is the 248-120 = 128-real dimensional space E8 / Spin(0,16).

(In OxO, x denotes tensor product. For details of the geometry of (OxO)P2, see Einstein Manifolds, by Arthur L. Besse (Springer-Verlag 1987) and Geometry of Lie Groups, by Boris Rosenfeld (Kluwer 1997).)

E8 is closely related to the Clifford Algebra Cl(8 ).

24 vertices of a 24-cell:



E8 has N = 240 root vectors, so its Coxeter number H is H = N / n= 240 / 8 = 30.



-source: http://www.valdostamuseum.org/hamsmith/Weyl.html#E8cartan

So, an E(8 )*E(8 ) dimensional model would have all the same characteristics, only double. It's essentially the same thing as saying E(8 )^2, which is only saying to go through the above and square every number.

-ben
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 Post Posted: Tue Oct 18, 2005 7:31 am    Post subject:
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The two diagrams above represent in the first case:

the two dimensional shadow of a 56vertex lattice,

and, in the second case,

a computer generated three dimensional wireframe model of a 24-cell or vertex lattice.

I felt I should point out that neither of these acuractely depicts the true dimensions of the hypothetical E(8 ) lattice.

Tony Smith tends deftly to avoid doing this, except on the cover of his ebook, "banned from Cornell" which picture is worthless.

However, the dimensions thereof are best described,

Tony Smith wrote:


In the D4-D5-E6-E7-E8 VoDou Physics model, an 8-dimensional spacetime has the structure of an E8 lattice with Planck length lattice spacing.

If octonionic coordinate are chosen so that a given minimal vector in E8 is +1, the vectors in E8 that are perpendicular to +1 make up a spacelike E7 lattice.

The E8 8-dim spacetime lattice is made up of two D8 lattices.

(E8 is the D8+ lattice, sort of like the D3+ diamond non-lattice structure that is two D3 face-centered cubic lattices.)

The 8-dimensional E8 lattice has octonionic structure, but no nearest neighbor light-cone links.

 

To build the E8 Lattice: Begin with an 8-dimensional spacetime R8 = O, where a basis for O is {1,i,j,k,e,ie,je,ke} . The vertices of the E8 lattice are of the form

(a01 + a1e + a2i + a3j + a4ie + a5ke + a6k + a7je)/2 ,

where the ai may be either all even integers, all odd integers, or four of each (even and odd),

with residues mod 2 in the four-integer cases being (1;0,0,0,1,1,0,1) or (0;1,1,1,0,0,1,0) or the same with the last seven cyclically permuted.

E8 forms an integral domain of integral octonions.

The E8 lattice integral domain has 240 units:

ħ1, ħi, ħj, ħk, ħe, ħie, ħje, ħke, (ħ1ħieħjeħke)/2, (ħeħiħjħk)/2, and the last two with cyclical permutations of {i,j,k,e,ie,je,ke} in the order (e, i, j, ie, ke, k, je).

The real 4_21 Witting polytope of the E8 lattice in R8 has

240 vertices;

6,720 edges;

60,480 triangular faces;

241,920 tetrahedra;

483,840 4-simplexes;

483,840 5-simplexes 4_00;

138,240 + 69,120 6-simplexes 4_10 and 4_01; and

17,280 7-simplexes 4_20 and 2,160 7-cross-polytopes 4_11.



All this compared to the simple description of the 24-cell (or second lattice in the previous post),

Tony Smith wrote:


The 24-cell 3{4}3 in R4 has

24 vertices,

96 edges,

96 faces, and

24 cells.



Sorry, just felt obligated to clarify.

-ben
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 Post Posted: Tue Oct 18, 2005 8:24 pm    Post subject:
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Let's assume... first of all let's assume linear time.

Then let's say that Tony Smith's work with the E(8 ) physics model is in some way prescient of the E(8 )^2 technology that will later enable John Titor to be sent back in time to contemporary with when Tony Smith himself was actually working on the E(8 ) model originally.

From a cursory overview, I gloss that ...

tony smith wrote:
248-dimensional E8 is the sum of

two copies of 28-dim Spin(8 )
plus

the 64-dim square of the 8-dimensional Cl(8 ) grade-1 vector space
plus

the sum of the 64-dim squares of the two 8-dimensional Cl(8 ) half-spinor spaces.



source: http://www.valdostamuseum.org/hamsmith/E8fromClif8.html

Basically, he's using Clifford algebra (ostensibly geometry), to construct finite-dimensional Kaluza-Klein models. Kaluza-Klein has super-symmetry as it approaches n-dimensions (or x^n, where n is any natrual number). In quantum mechanics, the addition of dimensions is merely a mathematical practicality. For example, you might have a single vector of (x^n, y^n, z^n) measuring movement in multiple directions simultaneously. The idea that holds back some modern string theorists is at what number of natural number dimensions do the different masses of different particles occur. To this effect the government has dumped huge sums of money into complex collider arrays and amasses an ever increasing number of new, "exotic" anti-matter particles daily. What is needed is a single model that can explain all that is missing from the mathematical and geometric models at the same time as accounting for the preponderance of "exotic" particles.



So, essentially, if I'm narrowing in on the broad scope of it a bit, a geometrical model for a certain number of dimensions can provide a lattice-like framework upon which to picture the relationships of different mass/frequency quanta. Smith's example is the 130GeV "truth" quark. However, good physics ought to be prepared for there to be an infinite number many particles as there can be an infinite number of dimensions. The E(8 ) model is only one type of multi-dimensional "vibration."

Like any other model thus far it has not proven to be the perfectly pitched harmonic vibrational tone to unify the four known forces.

However, what possibilities might lie in the E(8 )^2 model are mysteries yet to be revealed.

-ben
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 Post Posted: Sun Oct 23, 2005 6:55 am    Post subject:
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JohnTitor.com wrote:
10 January 2001 01:13
54. E(8 ) x E(8 )?
(HOST: Does this refer to string theory? If it does, did John predict this would be the dominant equation. Again, I don't know enough about the subject. )
http://superstringtheory.com/basics/basic6a.html


www.johntitor.com (titor links, Jan 2001)

well, I found the original reference to this material on the site, the info that started me out on this rapid websearch for E(8 )xE(8 ). It's an unremarkable page about M-theory that calls Heterotic E string theory "heterotic E8xE8.

I feel really stupid now. Maybe I should have just started researching the z-effect material. I don't know what to do with the Titor material now. I've made the compleete posts into an e-book. I suppose I could post that...

maybe later though. ~sigh~

-ben
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 Post Posted: Tue Jul 18, 2006 9:01 am    Post subject:
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wikipedia has a nice page on M-theory:

http://en.wikipedia.org/wiki/M-theory

I actually think I've drawn a picture of AdS/CFT (Anti-deSitter/Conformal Field Theory Correspondence) here: http://www.benpadiah.com/MISC_diagrams/3A.jpg which I go into in more detail here: http://www.benpadiah.com/MISC_diagrams/pages/originalMISC.html

In short, M-theory..

Quote:
It was believed before 1995 that there were exactly five consistent superstring theories, which are called, respectively, the Type I string theory, the Type IIA string theory, the Type IIB string theory, the heterotic SO(32) (the HO string) theory, and the heterotic E8Ċ~E8 (the HE string) theory.


M-theory is also mentioned briefly on page 56 of Stephen Hawking's November, 2001 book, the Universe in a Nutshell. Here is a diagram from that page:



I've even got a thread here about the (e)8X(e)8 heterotic string theory on this forum:

http://illuminati-order.com/forum/viewtopic.php?t=158

Good stuff.

-ben
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 Post Posted: Tue Jul 18, 2006 9:04 am    Post subject:
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in the same way I describe, above, how the 24-cell casts the shadow of the E8 model's 240 root vectors, you can also apply the same shadow-casting by an otherwise "transparent" object, or rather, geometric pattern, "as above, so below." (a prinicple which I don't think rightly can be applied to ethics!)

For example, here are the ten different archetypal Prime Electron Shells of superconductive ORMEs:



and here is their shadow, the ten by ten different Chladni vibrational patterns:



You see how, from above, the "solid" object casts down a network of geometric shadows as light refracts THROUGH it from a higher dimensional source (what I hypothesize to be the fifth spatial dimension).

Therefore, if given one (the above or the below) you will now be able to extrapolate the other (either one you aren't given to start with). For example, here is the "twenty-two" base shadow-lattice of the 231 Gates of Binah. It is called the "231 Gates of Binah" because that is how many lines there are connecting the alpha-numerics (here replaced by their zodiacal, elemental and planetary correspondence).



Therefore, if you took the 22 Tarot Trumps as the "paths" on the "tree of life," and then wound these all around in a circle, this is the pattern it would produce. This is not so different from any other type of Tarot "lay," and yet we see by substituting the zodiacal, planetary and elemental attributes for the alpha-numeric, we form an astrological chart, plotting a specific arrangements of the heavens that could only have occured rarely, if even more than only ever once alone. However, the lesson is that the Tarot Trumps always represent these attributes as well as their alpha-numerics, and that therefore every "spread" is a "chart" and every alpha-numeric a specific date, time and coordinate location.

Still just trying to shake some minds loose from their moorings as it were,

-ben
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