4th density geometry

[John G]

There’s a natural way to go from a string of n 0s and 1s to a point on an n-dimensional cube: Simply use the n bits as the coordinates of the point...

Then in 2018, it occurred to Huang to use a 200-year-old piece of mathematics called the Cauchy interlace theorem, which relates a matrix’s eigenvalues to those of a submatrix, making it potentially the perfect tool to study the relationship between a cube and a subset of its corners. Huang decided to request a grant from the National Science Foundation to explore this idea further.

Then last month, as he sat in a Madrid hotel writing his grant proposal, he suddenly realized that he could push this approach all the way to fruition simply by switching the signs of some of the numbers in his matrix.

I think it is possible to use the solution of conjecture for both geometric algebra and quantum graphity:

A model of spacetime where points are represented by nodes on a graph, connected by links that can be on or off*, indicating whether the two points are directly connected as if next to each other in spacetime**.

*(bits. 0 or 1)
**(a network with a matrix that tracks which points are connected and then examining a set of numbers called the matrix’s eigenvalues)

The quantum graphity idea is nice in that it has the idea of going from high to low energy as being a reduction in vertex connections. It's going from simplex physics to lattice spacetime physics. It's also nice for fitting with geometric algebra and looking at the individual bits. Ark uses Cauchy stress tensors on the cube for a bimetric gravity idea related to a 12x12x12 hint from the sessions.

 

[Ketone Cop]

BlueGazer quote from page 6, post #81 in this thread:

"Cool! But I was reading, and I think there's something else.

Laura said:
It came to my mind that perhaps Einstein, when you spoke about variable physicality, that Einstein was afraid when he understood that in his work. I thought about this and I think that Einstein determined that the future must be determined from the past and present, and when he found that he had a theory where the future was open, he dismissed it and was afraid. Is this a good guess that variable physicality, mathematically, means a theory where there is a freedom of choosing the future when past and present are given?

A: Yes.

Q: (A) Is it related to the fact that we should use higher order differential equations, not second order?

A: Yes. Einstein found that not only is the future open, but also the present and the past. Talk about scary!!

This is an excerpt from the Avengers Endgame movie:

RHODEY:

StarTrek. Terminator. Bill and Ted’sExcellent-

SMARTHULK:

WHY DOES EVERYONE THINK THIS? THAT’S NOT TRUE. IF YOU TRAVEL TO THE PAST, THEN THAT PAST HAS BECOME YOUR PRESENT, AND YOUR FORMER PRESENT HAS BECOME THE PAST, WHICH NOW CAN’T BE CHANGED BY YOUR NEW FUTURE!"

So...I'm not much of a mathematician, but I just read this article where physicists "prove" that time travel is possible, but that one can't change the past to influence the future (in terms of affecting major, world-shaping events):

ZeroHedge

ZeroHedge - On a long enough timeline, the survival rate for everyone drops to zero

www.zerohedge.com

I'm wondering what the reason is behind this research coming out at this particular time. It just seems awful convenient given the course of events lately that a main stream western university all of a sudden publishes this, when western governments all seem to be trying to push the world into a future that THEY are obviously envisioning for us. Is this just another way to brainwash people into accepting the "inevitable", when the C's have stated themselves that the future is always "open"?

Anyway, just musing and thought I'd post it here given that it's math based and you guys seem to be working on this question. Maybe you guys can find a flaw in their arguments! I mean, all theories are just that, right?!

 

[Bluegazer]

I'm wondering what the reason is behind this research coming out at this particular time. It just seems awful convenient given the course of events lately that a main stream western university all of a sudden publishes this, when western governments all seem to be trying to push the world into a future that THEY are obviously envisioning for us. Is this just another way to brainwash people into accepting the "inevitable", when the C's have stated themselves that the future is always "open"?

Anyway, just musing and thought I'd post it here given that it's math based and you guys seem to be working on this question. Maybe you guys can find a flaw in their arguments! I mean, all theories are just that, right?!

If there is a flaw in these arguments, it lies in what the C's have been saying since the beginning: Time does not exist.

In the same quote it is said: Einstein found that not only is the future open, but also the present and the past. Talk about scary!

This means that Einstein modified and/or hid his finding, creating what we know as the current theory of relativity.

The article looks more like a scientific gaslighing thing. They use relativity for masses. Never what Einstein discovered. You can travel in time but you can't modify anything. Well that is a paradox.

But in a variable universe, where you understand that conceptually all universes are possible and exist simultaneously, you have at hand all the possibilities of creation.

But as you so rightly point out, they're pushing for a result. If these scientists were to admit to variable physicality, none of this would be happening. And furthermore, admitting it implies that a hyperdimensional reality exists. And that things and those who are there...

If we can finally understand how the 4th density works, besides doing our internal work in our being, we will have the tools to change reality. But that change is a result of creating a new universe and moving there.

 

[woneill1701]

Time is an interesting creature...

IF SR is legit, then light does not experience either time or our physical “universe”.

Given that a photon of light is a wave function that traverses all possible paths through our universe “until” it encounters a suitable entity that can complete the transaction and absorb its energy, it means that a photon can be seen as a conjunction that unifies the “spacetime” emission of the photon with its absorption: Both emission and absorption of the photon exist at the exact same point in “spacetime” from the perspectives of the photon.

Where this is going is that our entire physical universe (Time/Space) exists as a set of simultaneous equations that solve the spacetime endpoints of the combined universe of photon wave functions.

Photons that emanated from the big bang are currently linking that point in spacetime to their (present/future) absorption as a singularity.

Knowing this, it is conceptually possible to share information back in “time” to the original emission point of the photon...

Meanwhile, our entire “spacetime” universe (past, present, future) exists as a self-consistent set of photon wave-function solutions...

An ever-present now...

The key is Heisenberg and his Uncertainty Principle, that allows our “time-localized” free-will to interact with the parameters of the wave equations, and change the entire photon wave-equation solution of the universe - past, present, future - as a single overall self-consistent solution...

 

[seiw83]

What You need to see that? This is 4 th dimension quality. Now you see/experience time linear. Todler don't see space 3d reality as newborn. How to newborn to 4d?

 

[woneill1701]

If I may, I have a question for those with better math than I: Is there a branch of math that specializes in succinctly defining the manifestation/representation of an N+/-1 (or N+/-2, etc.) dimensional entity/universe in an N dimensional space?

I’m trying to routinely deal with 1 and 2 dimensional entities in 3 dimensional space, and extend that to cover our 3 dimensional universe in a 4 or 5 dimensional space.

My favorite (Geometric Algebra) covers the geometry within an N dimensional entity/universe, but I’m trying to get to something different: the transform that would explain how a 4 dimensional observer would see/represent a 3 dimensional universe, and the inverse transform that would explain how a 4 dimensional entity/universe would be seen/represented by a 3 dimensional observer...

I’m looking for a generalized Transformational Geometry similar to Galilean and Lorentzian, but while they relate to transforms within an N-dimensional space, I am looking for something that does the same between N+/-n and N dimensional spaces...

Does such a specific branch of math currently exist?

 

[Guest 15258]

If I may, I have a question for those with better math than I: Is there a branch of math that specializes in succinctly defining the manifestation/representation of an N+/-1 (or N+/-2, etc.) dimensional entity/universe in an N dimensional space?

Sounds like you want manifolds, in particular sub-manifolds. This stuff is part of differential geometry. I know a little bit, but probably not enough to know what I'm talking about if I had to explain it.

To understand diff geo, you first need to know open sets, and I imagine knowing about compact sets would be helpful, basically you need to know a bit about real analysis and topology.

If you're looking for something simpler, then there are Linear subspaces, you only need linear algebra to understand these.

How are you going with physics and abstract algebra? I've thought a little bit about physics while walking my dogs but I haven't sat down and done anything.

 

[woneill1701]

Sounds like you want manifolds, in particular sub-manifolds. This stuff is part of differential geometry. I know a little bit, but probably not enough to know what I'm talking about if I had to explain it.

To understand diff geo, you first need to know open sets, and I imagine knowing about compact sets would be helpful, basically you need to know a bit about real analysis and topology.

If you're looking for something simpler, then there are Linear subspaces, you only need linear algebra to understand these.

How are you going with physics and abstract algebra? I've thought a little bit about physics while walking my dogs but I haven't sat down and done anything.

Thanks! Appreciated!

I used to know Differential Geometry from a Physics perspective (multivariate/vector calculus applied to curved 3D/Minkowski Spacetime) - but I've not used it in 30 years so it is beyond rusty. But the Differential Geometry I used to know would not help me here! (I'm not trying to represent one coordinate system in another curved space - e.g. translate between spherical and euclidian coordinate systems. I'm trying to bridge the gap between "Flatland" and 3D Land...)

I also got pretty proficient ~ 10 years ago in linear maths and vector spaces (was building electronics cad systems for fun and needed to use some pretty advanced stuff in the linear maths space...)

But, I think I'm looking for something probably closer to Topology...

I'll both explain and answer your question at the same time: I think I'm almost on the edge of being able to visualize the relationship between closed sub-universes with one set of dimensions - say ours with 3D - existing in a larger universe, say, with 8D.

Until this morning I couldn't conceptualize how a sub-universe could exist within one of larger dimension (e.g. 2D Flatland within our 3D) - but now I see them everywhere - based on hypercomplex numbers. (I finally figured out why they exist! They aren't just failed vectors! They were never vectors! They are SO much better! They define Universes, and vectors exist within those universes, obeying Geometric Algebra...)

What I am trying to get to now is to understand if there exists a branch of maths that could explain how a translation of a particle in the sub-universe that has components in the external universe, could generate a wave in another that extends through all of that sub-space...

I can actually see the transformation in my head but am trying to understand how to express it mathematically - or else I will sound like a typical pseudo-scientific idiot...

To make it real: An electron moving in 4D energy space generates an E/M wave that extends throughout all possible paths through our 3D space and does not experience time or the dimensions of our space. (But we in 3D Flatland CAN see it and we DO experience the wave taking time...)

Meanwhile, an electron physically moving in 3D Flatland space generates a <Gravity?> wave that extends throughout all possible paths in another external space, and those waves DO NOT experience time OR the dimensions of that space... (But I'm willing to bet that an observer in that space DOES experience time...)

I am trying to express the mathematical relationship that describes a translation between a 1 D movement in one universe into a wave in another. I see it happening, but I want to know mathematically why e=hc/λ...

It is not a bow-wave. The wave is the dimensional representation of the movement through the other dimension and automatically exists throughout all of the subSpace. But why a wave with a specific wavelength?

I see it, but cannot put it into words...

Meanwhile Time gets interesting, because it doesn't exist unless observed by consciousness existing within the world in which the wave exists... (It's not a Quantum Mechanics outcome that needs an observer to exist, it is Time itself that only exists if observed by consciousness...)

 

[Guest 15258]

Right, I think there is no time or space. I think it's just a manifestation of light.

If I recall correctly, and I doubt that I do. Ra said that at the beginning there's intelligent infinity. The first distortion toward intelligent energy is free will, the second distortion is love, and the third distortion is light.

If this is true then light is more fundamental than space and time. This makes sense to me if we observe space and time using light.

Suppose someone forgets that they're wearing a VR headset. They still perceive the virtual space, but does it really exist? Or is it only in their mind?

 

[woneill1701]

Interesting! I don't know Ra, but EVERYTHING we experience is based on an interaction with light (E/M Energy)... While matter has it's own wave function (and I more, and more think this is gravity), EVERYTHING we experience is the result of "energetic" interactions/exchanges between "our" sensory matter and that of the universe at large - facilitated by E/M waves.

I am forming a view of reality where all we actually experience is "light", and it is the interaction of our consciousness with this light that creates both space and time as we experience it.

If Lorentz holds, then a photon represents a spacetime singularity, meaning that sender and receiver share the same spacetime (and hence experience of the energy exchange) - forming the basis of a shared experiential reality - regardless of perceived distance/time...

All that matters is the experience of interactions with light.

The mind thing is interesting: For many years I studied NLP, which, at its heart, is based on Korzybski's General Semantics. The primary paradigm at play here is that our "experience" of the world at large is created inside our minds by the same part of the brain responsible for dreams. Our sensory apparatus (sight, sound, touch, taste, smell, etc.) feed this "dream engine" with sensory stimuli that our brain translates into a "real-world" experience from the perspective of being a human.

Except, it isn't! It's just an illusion inside our brain - an approximation based on its interpretation of the stimuli.

That is why we are vulnerable to optical illusions and a bunch of other anomalies...

The original Matrix film was the perfect analogy!

In 25 years of extreme testing of this paradigm, it has not failed me yet!

I realized that to understand the dimensions thing I need to master hypercomplex geometry and algebra. I need to fully understand the "shape" of the interactions where a single line for one observer translates to a surface for another. I do believe that everything we have ever been shown as a representation of "extra" dimensions is completely wrong! The universe is SO much simpler!

If I can find the maths I will show just how simple it is!

 

[woneill1701]

I need to fully understand the "shape" of the interactions where a single line for one observer translates to a surface for another.

If I can find the maths I will show just how simple it is!

The maths I need is projective geometry applied to hypercomplex numbers and giving a treatment similar - but different - to a Riemann Sphere, but for Complexes, Quaternions and Octonions, and allowing me to represent the interaction of 1, 3, and 7 dimensional (sub)spaces. I also need to understand what is so special about a Division Algebra that prevents Sedenions from being able to define a 15 dimensional universe/space...

And yes, I am saying that Complexes define a 1D space (not two), Quaternions define a 3D space (not 4), and Octonions define a 7D space (not 8) - they are Homogenious structures absent time.

(~20 years ago when I first jumped in to Geometric Algebra with nothing more than a basic understanding of simple (physics-based) Differential Geometry & Tensor Calculus, I tentatively mapped out all the physics that I knew to a 16D spacetime universe. I cannot remember how I did the mapping or exactly why it required 16 dimensions - but my limited math experience, belief in spacetime, and an inability to visualize how closed subspaces could exist in a larger dimensional universe prevented me from exploring that path... Now, with a better understanding of the role and meaning of hypercomplex numbers, Clifford algebra and projective geometry, I have a path to get back there - but this time with a solid foundation! )

 

[Bluegazer]

I think there is no time or space.

It may be that. A few days ago I read the following article in Thunderbolts.info

Space Is Not a Thing – The Thunderbolts Project™

www.thunderbolts.info

Relying on the misshapen theory of dark energy, astrophysicists believe that space, itself, is “stretching”. Although they point out that “…this new evidence suggests… that there is something fundamentally flawed in our current model of the universe.”

Indeed, to reify “space” into a physical form that can be modified—stretched, warped, or twisted—implies a serious misunderstanding. Space is not physical. Space is where physical objects exist. Space is defined as: “The unlimited or incalculably great three-dimensional realm or expanse in which all material objects are located and all events occur”. Space is a domain, not substance, since it is where substance exists. Therefore it has no existence, except as a method for defining the existence and position of things. To infer that space (and time) are a “fabric” is ludicrous.

We can only measure a space if we have an object A and an object B. If we only have object A and only that object, any measurement is impossible. Perhaps we can measure the volume of that object, but what if it is the only object in existence? What do we compare it to in order to measure that volume?

This fundamentally changes what we understand by gravity and mass.

Mass does not distort space by the action of gravity. It is the other way around, gravity brings mass into existence.

 

[Guest 15258]

Interesting! I don't know Ra, but EVERYTHING we experience is based on an interaction with light (E/M Energy)... While matter has it's own wave function (and I more, and more think this is gravity), EVERYTHING we experience is the result of "energetic" interactions/exchanges between "our" sensory matter and that of the universe at large - facilitated by E/M waves.

I am forming a view of reality where all we actually experience is "light", and it is the interaction of our consciousness with this light that creates both space and time as we experience it.

The Cs said that Ra was a precursor to their transmission. The website is L/L Research - Site Entry page.

Perhaps the way we interpret the world around us in terms of space and time is one way of interpreting the relationships and interactions light has with itself. And perhaps 4th density is another interpretation.

The maths I need is projective geometry applied to hypercomplex numbers and giving a treatment similar - but different - to a Riemann Sphere, but for Complexes, Quaternions and Octonions, and allowing me to represent the interaction of 1, 3, and 7 dimensional (sub)spaces. I also need to understand what is so special about a Division Algebra that prevents Sedenions from being able to define a 15 dimensional universe/space...

Sounds like maybe you want to generalize Mobius transformations to Clifford algebras in general. I don't know if this has been done before, and I think it must have something to do with Lie groups, kind of like how the Mobius transformations over C form the group PSL(2), but I really don't know.

I think a projective space over hypercomplex numbers would look just like projective space over Rn or Cn. You'd need to show that the vector multiplication is well defined when taking projections and I'd be surprised if it were. Still good stuff though, maths is interesting in its own right.

The complex numbers, Quarternions, Octonions and Sedenions are all built up from the Cayley–Dickson construction. By the time you get to the Sedenions, you've lost commutivity, distributivity, and associativity. The loss of associativity makes them insane and probably difficult to work with.

We can only measure a space if we have an object A and an object B. If we only have object A and only that object, any measurement is impossible. Perhaps we can measure the volume of that object, but what if it is the only object in existence? What do we compare it to in order to measure that volume?

This fundamentally changes what we understand by gravity and mass.

Mass does not distort space by the action of gravity. It is the other way around, gravity brings mass into existence.

Yeah, I'm wondering now if gravity is the way light interacts with itself. So two EM waves don't just pass through each other, but instead each one generates a potential for the other, which influences the way the other moves. This potential would be gravity.

Also, if you like general relativity, then perhaps you can think of gravity bending light, thus causing a perception of curved space, which really is curved space if there is no space. The curved space is then gravity, which in turn bends light. So there's a kind of triad.

 

[Guest 15258]

The complex numbers, Quarternions, Octonions and Sedenions are all built up from the Cayley–Dickson construction. By the time you get to the Sedenions, you've lost commutivity, distributivity, and associativity. The loss of associativity makes them insane and probably difficult to work with.

This is wrong. The Octonions aren't associative. The Sedenions aren't an alternative algebra, whatever that means.

 

[John G]

The maths I need is projective geometry applied to hypercomplex numbers and giving a treatment similar - but different - to a Riemann Sphere, but for Complexes, Quaternions and Octonions, and allowing me to represent the interaction of 1, 3, and 7 dimensional (sub)spaces. I also need to understand what is so special about a Division Algebra that prevents Sedenions from being able to define a 15 dimensional universe/space...

And yes, I am saying that Complexes define a 1D space (not two), Quaternions define a 3D space (not 4), and Octonions define a 7D space (not 8) - they are Homogenious structures absent time.

(~20 years ago when I first jumped in to Geometric Algebra with nothing more than a basic understanding of simple (physics-based) Differential Geometry & Tensor Calculus, I tentatively mapped out all the physics that I knew to a 16D spacetime universe. I cannot remember how I did the mapping or exactly why it required 16 dimensions - but my limited math experience, belief in spacetime, and an inability to visualize how closed subspaces could exist in a larger dimensional universe prevented me from exploring that path... Now, with a better understanding of the role and meaning of hypercomplex numbers, Clifford algebra and projective geometry, I have a path to get back there - but this time with a solid foundation! )

Tony Smith has this relationship to Sedenions:

Why not SEDENIONS?

to me, the useful part of the sedenion product is
not the full sedenion product,
but only the block diagonal part

OLx
ORx

of the SL sedenion left-multiplication matrix,
because
it represents the 16-dimensional full spinors of Cl(0,8)
and
it is equivalent to the direct sum OL + OR
of
octonion left-multiplication
and
octonion right-multiplication.


Sedenions may also be a good way to express
the structure of the last Hopf fibration
S7 --> S15 --> S8.
Since there are no Hopf fibrations other than
S0 --> S1 --> RP1 = Spin(2)/Spin(1)
S1 --> S3 --> S2 = CP1 = SU(2)/U(1) = Sp(1)/U(1) = Spin(3)/Spin(2)
S3 --> S7 --> S4 = HP1 = Sp(2)/(Sp(1)xSp(1)) = Spin(5)/Spin(4)
S7 --> S15 --> S8 = OP1 = Spin(9)/Spin(8)
sedenion structure may show why the sequence terminates.

Also,
it is possible that the sedenions may show the structure
of the 16-dimensional octonionic projective plane OP2 = F4/Spin(9)
and may also show
why there is no higher-dimensional octonionic projective space.