4th density geometry

John G

The Living Force
Perhaps the inner torus has the opposite orientation to the outer torus as well.
IMO, I think here's the key. If we accept such a definition of the Cs, this must include both space and energy. And if it turns out to be so, for example, you can turn energy into mass.

A: Remember, you do have cycles but that does not necessarily mean cyclical. 3 Dimensional depiction of loop, seek hexagon for more. Geometric theory provides answers for key. Look to stellar windows. Octagon, hexagon, pentagon.
The part that I highlight in black, I think, is closely related, in part, to some discussions that arise from the theory of the electric universe.
With respect to octagons, exagons and pentagons, we have this: Saturn's hexagon - Wikipedia

In relation to this phenomenon, one could add and hand in hand with the stellar windows,
the formations we see in the birkeland currents:

Note that a spiral is circular in nature.

Within a birkeland current the following figure can be seen:


Perhaps here we have a relationship between geometry and electromagnetic and gravitational forces.

We must remember that the Cs mentioned that the stars and planets are windows.

It occurs to me that such a hypothetical individual is in wave mode, and when he wishes to materialize, the wave collapses.
Thornhill and EU have longitudinal photons which is the same math as conformal gravitons. I kind of have to be careful with "inner". For the Spheritorus, its 4D inner vs outer would be like with sides of a Mobius strip represent opposite orientations. For the S3 (3D depiction of loop) and S1 (time cycle acting space-like) of the spheritorus, the individual inner for each adds two dimensions giving you six (hexagon) where the insides represent complex numbers for stellar window-like wormhole math.
 

John G

The Living Force
Yep that's it. I first came across it via Tony Smith here:


GraviPhotons look like:
Virtual Covariant Conventional U(1) Photons, in that they have 4 Components, including Longitudina/Scalar Components; and
Vector Gravitons that can interact with the Imaginary Part of Complex Spacetime.
That "Complex" link above goes to a page where Tony mentions three of Ark's papers. The papers talk about SO(4,2) which adds the complex insides to the S3 and S1 of the spheritorus. It relates to this from the 12/19/98 session:

Q: (A) Okay, now, this is one thing. At some other point we were speaking about pentagons and hexagons and I tried to
be tricky and when it came to pentagons, I wrote a mathematical formula, a symbol for a pentagon, and then
there was the question of signs. We needed five signs. I asked you whether there should be four pluses and one
minus, or 3 pluses and two minus. The answer was that there should be 3 pluses and two minuses in a pentagon. Now,
what about a hexagon? What should I put in a hexagon? Three pluses and three minuses, or four pluses and two
minuses?
A: Four and two.
Thornhill mentions the longitudinal component here in a SOTT/Behind the Headlines interview:

 

Bluegazer

Jedi Master
Yep that's it. I first came across it via Tony Smith here:

http://tony5m17h.net/SegalConf.html
Weird, I want to access the site and I can't.

Thornhill mentions the longitudinal component here in a SOTT/Behind the Headlines interview:
Well, it looks like my intuition wasn't wrong. I didn't know about this interview! The only thing I regret is my lack of advanced mathematical knowledge. As you may have noticed I saw the parallelism in the geometric figure of the torus and the figures of the birkeland current and by association the idea came to my mind.

What strikes me today about the EU is the scalability. The effects can be seen on a microscopic/quantum scale as well as on a cosmic scale, i.e. the orders of magnitude. Geometric effects can be replicated and occur in both directions of the scale (topological effects?/ toroidal solenoids and their use as effective transmitters of electromagnetic waves??? / field geometry?)
 

John G

The Living Force
Weird, I want to access the site and I can't.
There's a mirror site here:

Well, it looks like my intuition wasn't wrong. I didn't know about this interview! The only thing I regret is my lack of advanced mathematical knowledge. As you may have noticed I saw the parallelism in the geometric figure of the torus and the figures of the birkeland current and by association the idea came to my mind.

What strikes me today about the EU is the scalability. The effects can be seen on a microscopic/quantum scale as well as on a cosmic scale, i.e. the orders of magnitude. Geometric effects can be replicated and occur in both directions of the scale (topological effects?/ toroidal solenoids and their use as effective transmitters of electromagnetic waves??? / field geometry?)
It is kind of a messy swiss cheese geometry of sorts. Tony talks a little about the Birkeland currents at different scales as being related to the conformal (complex) domains:


Within each Gravitationally Bound Domains there can exist Islands of Conformal Expansion in which all 15 generators of Conformal Spin(2,4) = SU(2,2) remain effective, like Puddles of Water (red) on an IceBerg (blue) floating in an Ocean of Water (red), so the overall structure of Our Universe in terms of Gravitationally Bound Domains (pennies, raisins, IceBergs) and Conformal Expanding Domains (balloon, cake, water) is quite complicated. To get some feeling for this structure, begin by considering Clusters of Galaxies to be the largest Gravitationally Bound Domains and then looking at the next level down in size, Galaxies...

If you look closely at the central star in the star-formation image above, you might see Birkeland Current Loops (image from thesurfaceofthesun.com web page) that look up close like Solar Coronal Loops (image from electric-cosmos.org/sun.htm web page).

Up close, Birkeland Current Loops are seen to have braided filament structure (Cygnus Loop image from antwrp.gsfc.nasa.gov.

The scale of Birkeland Current Loops extends beyond Stellar to Galactic (images, SOHO of Sun and NRAO of Fornax A from thunderbolts.info webpage, which said as to NGC "... a tiny but energy-dense plasmoid at the center of the galaxy ... Fornax A ... discharges energy along oppositely-directed Birkeland filaments (invisible in this image) into the radio lobes. Diffuse currents loop back from the lobes to the spiral arms, where their increasing density triggers star formation as they return to the central plasmoid. ..." ...).

The scale also extends down to Planetary, as is seen in the Jupiter-Io system (image from Anthony Peratt's book Physics of the Plasma Universe (Springer-Verlag 1992)).

The scale may also extend down to Asteroidal. According to a 17 September 1994 article by Jeff Hecht in the New Scientist: "... inclusions ... in chondrules ... in chondrites, the commonest meteorites ...[were]... heated ... to about 2000 kelvin at the birth of the solar system, 4.6 billion years ago. ...[possibly by]... Lightning ... and ... magnetic discharges ... laser tests ... to model the intense visible and infrared light expected near electric or magnetic discharges ... produced dark structures ... remarkably similar to .... inclusions found in chondrules ...".
 

susy7

Jedi Master
I'm more of a mathematician, but there are some excellent books, like Mirror Symmetry and Algebraic geometry by David A. Cox and Sheldon Katz and an excellent book J-holomorphic curves and Sympleptic Topology by Dusa MacDuff and Dietmar Salamon
 

John G

The Living Force
I'm more of a mathematician, but there are some excellent books, like Mirror Symmetry and Algebraic geometry by David A. Cox and Sheldon Katz and an excellent book J-holomorphic curves and Sympleptic Topology by Dusa MacDuff and Dietmar Salamon
Yeah the use of Hodge duals/theory/decomposition for the complex Kahler/Calabi-Yau manifolds is highly related to the complex Lie sphere geometry things I've been using here. Even that one vs zero bit duality I mentioned earlier is actually from Clifford algebra Hodge duals.
 

John G

The Living Force
IMO, I think here's the key. If we accept such a definition of the Cs, this must include both space and energy. And if it turns out to be so, for example, you can turn energy into mass.
This relates to this from the 12/19/98 session
Q: (A) Okay, at some point we were talking about a 3 dimensional matrix,
12x12x12. I was wondering where this 12 comes from, and I was thinking that 12 is
2x6 and I was supposed to be looking at hexagons, and a hexagon represents 6
dimensions, four pluses and two minuses. If I add to this 6 energies corresponding to
6 dimensions, then I have 12 dimensions, and this would account for number 12. Is
this correct?
A: Yes.
This relates to a more recent session where Ark talked about bimetric gravity. Ark on his blog mentions one metric is for the usual gravitational potential (potential energy per mass) and the other metric is for gravitational force (adds in the mass part over a distance).
 

Archaea

Padawan Learner
This relates to a more recent session where Ark talked about bimetric gravity. Ark mentions one metric is for the usual gravitational potential (potential energy per mass) and the other metric is for gravitational force (adds in the mass part over a distance).
I googled bimetric gravity and had a look at the Wikipedia page. It reminded me of something I was thinking about lately.

We have special relativity in position space, so it makes sense that there would be an analog in momentum space. (However, I don't think it'd be possible to get this working nicely with Fourier transformations and all that if you're using O(3,1) instead of O(4), not that I've tried.)

Is this the same thing as Ark's two metrics?

After thinking about your S3xS1 idea, seiw83's idea of a mirror dimension, looking at bluegazers pictures and thinking about inversions (composition of 3 orthogonal reflections in R3),

Crystal structure

*Inversion, which changes the sign of the coordinate of each point with respect to a center of symmetry or inversion point
I'm wondering whether it'd be possible to construct a 4-dim space where moving in any direction for some fixed length inverts the co-dim 1 hyperplane normal to the direction.

Basically you take a tesseract whose vertices are the 16 binary strings of length 4 (e.g. [0,1,1,0]) and identify each vertex with it's "dual" (i.e. flipping all the 1's to 0's and 0's to 1's, so, for example, we'd identify [0,1,1,0] with [1,0,0,1].) You get something that looks like,

4d6.png
Where the red lines travel though the 4th dimension and all have length 1.

Then you tessellate these things to construct a space.

If this works then this space would be non orientable.

I don't understand how 6-dim spaces relate to hexagons.
 

John G

The Living Force
I googled bimetric gravity and had a look at the Wikipedia page. It reminded me of something I was thinking about lately.

We have special relativity in position space, so it makes sense that there would be an analog in momentum space. (However, I don't think it'd be possible to get this working nicely with Fourier transformations and all that if you're using O(3,1) instead of O(4), not that I've tried.)

Is this the same thing as Ark's two metrics?
One metric is the standard 4x4 matrix and the other "metric" for Ark is a Cauchy stress tensor 4x4 matrix which combine for a 4x4x4 thing. This would relate to the Cs 12x12x12. How to get to 12? First would be get to 6 via a conformal transformation group. This doesn't add to the metric (related to the Cs hint of getting rid of pluses and minuses which Ark referred to as a sub-Riemannian metric). Sub-Riemannian metrics are always more dimensions than the underlying topological space. Getting up to 12 might involve what Ark right now is working on (related to a presentation he just gave for a conference which I assume was a virtual conference). Ark is working on "time" and that could mean a parallel transport proper time affine connection thing (perhaps preserving the the four volume for the stress tensor?). The affine one-form would be your free fall inertia/gravity momentum as well as a proper time thing.

After thinking about your S3xS1 idea, seiw83's idea of a mirror dimension, looking at bluegazers pictures and thinking about inversions (composition of 3 orthogonal reflections in R3),

Crystal structure



I'm wondering whether it'd be possible to construct a 4-dim space where moving in any direction for some fixed length inverts the co-dim 1 hyperplane normal to the direction.

Basically you take a tesseract whose vertices are the 16 binary strings of length 4 (e.g. [0,1,1,0]) and identify each vertex with it's "dual" (i.e. flipping all the 1's to 0's and 0's to 1's, so, for example, we'd identify [0,1,1,0] with [1,0,0,1].) You get something that looks like,

View attachment 38233
Where the red lines travel though the 4th dimension and all have length 1.

Then you tessellate these things to construct a space.

If this works then this space would be non orientable.
Yes that point reflection for 3D is orientation reversing. Reflection through a plane works too. The conformal/complex domain math makes all points equally close kind of via the multiple time-like "parallel" lines going everywhere so things like reflections can happen. The 4th dimension might kind of more supply reflection points than travel lines when it comes to what is "seen" at a given instant.
I don't understand how 6-dim spaces relate to hexagons.
Ark answered that this way:
Q: (A) In physics and mathematics we write a triangle to symbolize certain operations in three-dimensional space. One draws a square to symbolize wave equations in 4 dimensional space. One draws a pentagon to symbolize equations in 5th dimensional space, and a hexagon to symbolize equations in 6 dimensional space.
I've seen square diagrams for the two transverse plus longitudinal/time dimensions and I've seen triangle and one for the color and EM charge space.
 

Bluegazer

Jedi Master
After thinking about your S3xS1 idea, seiw83's idea of a mirror dimension, looking at bluegazers pictures and thinking about inversions (composition of 3 orthogonal reflections in R3)
It's possible that... :

Q: (A) Now, I want to come back to physics. We have this paper from the French guy Chardin, who speaks about anti-gravity and relates it to a double structure of the universe; that anti-matter is just located, not in our universe, but in another universe...

A: The two are exchangeable, much like an ion exchanger.

Q: (A) The two are exchangeable, but it's about us. We are apparently are made of matter rather than anti-matter, or there is another us that is made of anti-matter? I don't think that we are exchangeable. We are apparently living in a universe of matter rather than anti-matter.

A: Exchangeable.
Also, and in reference to a book I've mentioned in other threads:


The Poseidi found that in the realm beyond magnetism were yet other forces, superior and more intense of pulsation, forces operated by the mind. And Mind is of our Father, and is the constantly creating source of all things whatsoever. Were the perpetual vis a tergo of divine creation to cease for one instant, in that instant the Universe would cease to exist. Now wilt thou see the sublime beauty of the Atlan postulate not long since repeated: Incal malixetho. Axte Incal, axtuce mun. For down from His heights, marking the descent by forcefalls as a river marks declivities fin its bed by cataracts, comes this supreme power; comes far, oh! very far, adown its course to the cascades of magnetism, electricity, light, heat, sound, motion and far off where the bed of this Divine stream becomes nearly level, exhibits those little ripples of material differentiation which thou termest chemical elements, insisting on there being sixty−three, when there is but One.[...]Having given the basis thereof, now will I show a new philosophy:

I have said that the Atlans recognized Nature in its entirety to be Deity externalized. Their philosophy asserted that force moved, not in straight fines but in circles, that is, so as always to return into itself. If the dynamism operating the universe acts in circular progression, it follows that an infinity of increase in vibration possible to One Substance would be an untenable concept. There must be a point in the circle where extremes meet and run the round again, and this we find between cathodicity and magnetism. As vibration brought substance into the realm of light, it must carry it out. It does so. It conveys it into what the Poseidi termed Navaz, the Night−Side of Nature, where duality becomes manifest, cold opposing heat, darkness light, and where positive polarity opposes negative, all things antipodal. Cold is as much a substantial entity as heat, and darkness as light. There is a prism of seven colors in each white ray of light; there is also a septuple prism of black entities in the blackest gloom the night is as pregnant as the day.

The Poseid investigator thus became cognizant of wondrous forces of nature which he might bend to the uses of mankind. The secret was out, the discovery being that attraction of gravitation, the law of weight, had set over against it the repulsion by levitation; that the first belonged to the Light−Side of Nature, and the second to Navaz, the Night−Side; that vibration governed the darkness and the cold. Thus Poseid, like Job of old, knew the path to the house of darkness, and the treasures of the hail (cold). Through this wisdom Atlantis found it possible to adjust weight (positiveness) to lack of weight (negativeness) so evenly that no tug of war was manifest. This achievement meant much. It meant aerial navigation without wings or unwieldy gas−reservoirs, through taking advantage of repulsion by levitation opposed in overmatching strength to the attraction of gravitation. That vibration of the One Substance governed and composed all realms was a discovery which solved the problem of the conveyance of images of light, pictures of forms, as well as of sound and heat, just as the telephone thou knowest so well conveys images of sound, only In Poseid no wires or other sensible material connection was required in the use, at whatever distance, of either telephones or telephotes, nor even in caloriveyance, that is, heat−conduction.
Here we return to the matter of the prism. And apparently, if we take as valid what is exposed in the text, it would seem to infer that such a Night-Side of Nature is in fact the universe of antimatter. And hence the symmetry.
 

John G

The Living Force
And apparently, if we take as valid what is exposed in the text, it would seem to infer that such a Night-Side of Nature is in fact the universe of antimatter. And hence the symmetry.
The antimatter universe in the sessions got related to the no time, no space place where people get stuck for eons via Bermuda Triangle/Philadelphia Experiment kind of incidents. It relates to the sphere/torus/non-orientable portal geometry but it's kind of a wrong turn. Ark mentioned the ER=EPR idea in a blog post that relates wormholes to entanglement and it has some black hole/white hole math with spacetime-like coordinates that are different than ours. A white hole does time reversal math and antimatter can be modeled as time-reversed matter (an exchangeable kind of thing).
 

Bluegazer

Jedi Master
antimatter can be modeled as time-reversed matter (an exchangeable kind of thing).
But doesn't that make matter and antimatter belong to the same class? I mean, there's the apple, and there's the anti-apple. Both are apples and therefore are the same thing but in different ways (direction). If there is an interchangeability, then you can find a point in between. Cartesian axis mathematics for example (here I can do math! hehe).

On the X-axis where on your left you have the antimatter and on your right the matter, that antimatter has negative value and matter has positive value, if you do -1 plus 1 = 0

Could it be that being you matter, (i.e. your physical constitution or maybe also your own energy constitution) in a universe of antimatter where you are +1 the antimatter as environment works as -1 and therefore you are in a 0 state?

And that is very similar to the state described by the Cs and Laura in their event of the conflicting thought centers and the non-fluid state.

Whenever two opposing units of reality intersect, this causes what can be
referred to as friction, which, for an immeasurable amount of what you would
refer to as time, which is, of course, nonexistent, creates a nonexistence, or a
stopping of the movements of all functions. This is what we would know as
conflict. In between, or through any intersecting, opposite entities, we always
find zero time, zero movement, zero transference, zero exchange
It could be perhaps that when two opposing reality units intersect you get the entanglement mentioned in the EPR????

I get the impression that we're trying to see the wormhole outside, but that we're actually the bridge... i.e. our conscience makes the Rosen-Einstein bridge.

Isn't that what Ark is after by including consciousness in his mathematics? (It's either that or I read it wrong at some point.?)

I hope this doesn't go too far from the main topic... I just can't leave these questions in the inkwell.
 

John G

The Living Force
But doesn't that make matter and antimatter belong to the same class? I mean, there's the apple, and there's the anti-apple. Both are apples and therefore are the same thing but in different ways (direction). If there is an interchangeability, then you can find a point in between. Cartesian axis mathematics for example (here I can do math! hehe).
The photon is kind of the point in between.

On the X-axis where on your left you have the antimatter and on your right the matter, that antimatter has negative value and matter has positive value, if you do -1 plus 1 = 0

Could it be that being you matter, (i.e. your physical constitution or maybe also your own energy constitution) in a universe of antimatter where you are +1 the antimatter as environment works as -1 and therefore you are in a 0 state?
That could annihilate you into photons!

And that is very similar to the state described by the Cs and Laura in their event of the conflicting thought centers and the non-fluid state.

It could be perhaps that when two opposing reality units intersect you get the entanglement mentioned in the EPR????

I get the impression that we're trying to see the wormhole outside, but that we're actually the bridge... i.e. our conscience makes the Rosen-Einstein bridge.

Isn't that what Ark is after by including consciousness in his mathematics? (It's either that or I read it wrong at some point.?)

I hope this doesn't go too far from the main topic... I just can't leave these questions in the inkwell.
This is certainly on topic but it's a fairly flexible discussion even if it wasn't. Yes our consciousness is likely an ER bridge; one where the particles are kind of fully bridged to the point of being a single quantum state (superposition). Less fully bridged would be multiple states that depend on each other (entanglement).
 
It is time for me to re-ignite the fire that burned in me for Physics before my time at university snuffed it out...

I plan to re-learn Maths from scratch (high-scool level) but substituting the work of David Hestenes (Geometric Algebra) for Vectors.

I have a roadmap planned that will probably take about a year or so before I am back up to speed with SR, GR, Quantum Physics, and Electrodynamics using 3D Geometric Architecture as my core language.

Now I know that Geometric Algebra is a Clifford Algebra, but when I last tried to make the transition from straightforward 3D Geometry to the higher dimensions, I bounced off because I was unable to find any reading material that was understandable: Everything I could find was either Minkowski 4D Spacetime, Tensor-based, and aligned with GR/SR, or it was written in Greek/Hieroglyphics, and assuming I was a Math Post Grad...

Can anyone recommend a good book (or reading list) that would allow me to transition from my simplistic Undergrad Physics-based view of Geometry to being able to understand the Maths-based world of Geometry, and the Geometric relationship with Clifford Algebras?

I would prefer a simple, slow and laborious approach that I can slog through rather than anything at genius level...
 
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