John G
The Living Force
What makes sedenions really weird are zero-divisors as in you can multiply two non-zero numbers to get zero.This is wrong. The Octonions aren't associative. The Sedenions aren't an alternative algebra, whatever that means.
Back to the subject of Coral Castle:
The C's had said that everything is gravity. It makes sense that gravity would interact with itself.
And this is why geometry is important. After all, to measure space you need objects that can establish geometrical relationships, right? I'm thinking (and I think we're back to that in the end but in other words) that the manifestation of all that was, is and will be, is gravity interacting with itself, changing geometrical relationships. Nested geometries that go from the quantum to the cosmos.
woneill1701
Jedi
You have zeroed in on the best bit! The projections define hyper-surfaces that have the potential to extend throughout all space. This is how quantum mechanics exists...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.
How else can a photon traverse every single possible path through our entire universe? Think about the supposed size of our universe, yet a photon extends through its entirety and creates standing waves.
It is similar to a Riemann sphere, but not...
Unlike Kaluza-Klein, or String theory, you don’t need stupid ideas like microscopic rolled up dimensions. Each sub-space is closed and self consistent, but interactions with external dimensions project as surfaces and volumes - in both directions!
No wonder the ancients thought spheres were of the gods! They are!
woneill1701
Jedi
Thanks! I had checked out his site after re-reading through the Cs transcripts. But my math is still too primitive for me to be able to read his notation. Soon...
I had also checked out the stuff from Miles Matheson. He intuitively grasps that circles and spheres are mis-understood, and their conventional treatment broken, but he completely missed the mark by demanding that time/acceleration be incorporated into any circle...
But now I know where I’m going with this!
I can fit 1D and 3D subspaces into our universe and everything is consistent with Geometric Algebra.
I’m 90% locked in with our universe being Quaternionic (elipsoidal) inside an Octonionic one - and 10% on our universe being complex (spherical) in a Quaternionic one...
It is a question of why h (Planck’s constant) is the same in all directions...
I’m working, for now, without time - so all quantum wave functions are timeless, and photons are using E= hc/lambda - deriving the photon wave function purely spatially...
I can re-insert time later if it turns out to be necessary, but I doubt it will...
I’m just clawing my way through learning the language of maths while working 70 hours per week on my company - trying not to go bankrupt...
This is inspiring though!
John G
The Living Force
Conformal structures/Bounded Complex domains are Poincare disks/spheres/hyperspheres and the conformal metric could have projective structures as an affine connection and the Geometric algebra hodge dual structure (4-vectors as self dual) could give you Standard Model Yang-Mills structures.
woneill1701
Jedi
Ooooo.....
Thank you! Thank you! Thank you!
You just saved me years of reinventing the wheel!
I figured the maths was out there already, and I’m not surprised it was done by Poincare, but it struck me as weird that in every presentation on 1D and 2D, 3D entities they ignore these things and instead talk of points, lines, planes and volumes...
A point is actually 0D not 1D.
A 1D entity has a single dimensional value (say r), and if projected onto 1D is represented as a 1D hypersphere with perimeter thickness r. (e.g. A circle within a disk, with coincident centers at 0, and the radius of the circle given by its position in the 1D disk. Or, a line segment within a line, of length r, positioned at a point denoted by its 1D position from the origin, and orientation denoted by another 1D orientation- a 1D bi-vector...)
That same entity, when projected onto 2D is represented as a 2D hypersphere with radius r. (e.g. A circle within a ellipse at a position/orientation within the elipse given by 2D a bi-vector.)
Projected onto 3D is represented as a 3D hypersphere, again with radius r. (e.g A sphere within an ellipsoid at a position/orientation given by a 3D bi-vector...)
It all becomes so simple!
woneill1701
Jedi
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.
Vector multiplication within the projection would behave in accordance with “Geometric Algebra meets Quantum Mechanics”
- using the Hypercomplex number as the basis for the subspace (& its projection) is the reason why Geometric Algebra applies in the first place! The projected hypersphere is why QM exists the way it does...I’m not trying to invent a new universe; I’m just asking “why” things are the way they are already, and “how” can they be that way...
I'm not even going after Lorentz/Relativity (yet). I’m trying to understand how we can only experience 3 dimensions when there are clearly more (QM) - and how can a closed n dimensional space exist in a wider n+m dimensional universe.
Coming back and with an interesting article. Here we have related the light, the gravity, the spiders and the geometry of their webs. I will translate the article from Spanish and make it as short as possible.
es.gizmodo.com
Two spiders on the space station find a surprising trick to build webs without gravity
This article provides a series of clues that point to the direction of a geometric network that interacts with light and gravity. What if the same observable principle occurs at the quantum level? Can this be evidence of the close relationship between light and gravity?
Dos arañas en el espacio logran construir redes sin gravedad
Los experimentos en la Estación Espacial Internacional sugieren que las arañas pueden tejer telas de aspecto normal en el espacio; solo necesitan un recurso sorprendenteGeorge Dvorsky
es.gizmodo.com
Two spiders on the space station find a surprising trick to build webs without gravity
This article provides a series of clues that point to the direction of a geometric network that interacts with light and gravity. What if the same observable principle occurs at the quantum level? Can this be evidence of the close relationship between light and gravity?
ephemerality
The Force is Strong With This One
What's the current take about fractals in the geometry study of the work done so far? Could you guys shed some light on this?
Sorry it's only in beautiful french language
Le Cercle carré - Etude de la perception d'une forme mouvante | Canal U
Présentation de quelques illusions typiques et inédites de la perspective monoculaire. Etude expérimentale des conflits possibles entre ces illusions et la constance perceptive des grandeurs et des formes. Démonstration du rôle du mouvement dans la résolution de ces conflits.