Status Updates From La forma dello spazio profo...

"The manifold, in other words, has to be like a torus rather than a sphere and have at least one hole. "
But what is the hole?? What space does it belong to?

https://en.wikipedia.org/wiki/Optic_c...

"These manifolds, they noticed, seemed to come in pairs in which the number of even-dimensional holes of one equaled the number of odd-dimensional holes of the other. "

"parity violation—the idea that the fundamental laws of nature distinguish between left and right and are not symmetric in this respect" Nice...so it is fundamental. Perhaps this is the "form of transcendence" relating monads to each other, or maybe just the dimension after "law": maybe w a complex eigenspace such that it aligns with the law when rotated

Basically, to set a Ricci curvature at zero is to to create tangent vector spaces that through their co-occurence approximate a condition of flat Euclidean space, which means that these vector spaces inside the non-euclidean object must make of the object a single element of a larger complex space through performing rotations that cancel each other.

Ricci-flat - the vector space associated with a certain curvature can avg zero in "curvature"

In the ball vase movement, the AdS constantly transforms into de-Sitter and vice-versa: dS becomes replaced with former AdS and AdS becomes replaced with former dS: former, past turns to a possibility of repetition and the latter, future possibilities actualize and narrow. Mass-gravity would then be possibilization of what has become actual and anti-gravity would be actualization of possibility.

The ball-vase movement between de-Sitter and anti-de Sitter hyper-surfaces could be achieved if the both of the hyper-surfaces had opposite directions of movement at the same time, which makes sense because as time moves towards singularity the possible states in anti-de-sitter space also become fewer. Time might as well be defined through restriction of possibilities.

Ok, so us being in de-Sitter space is better thought of as being in a positively curved hypersurface, and the Anti-de Sitter is the opposite, anti-gravity being bumps that create positive curvature in anti-de Sitter space. The poles would then be the black holes Ok, so I misunderstood some at first but look: WHAT IF the positively curved hypersurface moves into a vase surface like I said in a previous comment?

After you took a derivative of some world line you could group it along with associated world lines (that the world line is directly related to so as not to be arbitrary, "a system") and having grouped only those related ones together, you could form of them a vector space for studying that segment of Ads space. Question for antigravity would be: how to make state override time so that ads space attains positive curv

If our spacetime is a closed, definite de Sitter-space, it would have poles where its curvature would approximate Minkowski space. That would be an area with zero gravity just before adS-state universe. If you take derivatives of world lines, ie. the relation of the change in amount of three space coordinates to change in time, summary of the derivatives of all the world lines would be a state in adS space.

Another interesting thing about curvature is that both sides of its surface can move to opposite directions, shown by the fact that it can bend. Movement of the spacetime fabric means the world lines stretch instead of just curving. If space is dS, the other side is the ads, spacetime is finite and its curvature creates stretching. If anti de-Sitter space could be made positively curved at some point, anti gravity

Whats interesting about the idea of a curved spacetime object is the other side of the curvature: if a negative curvature caused by an object would be gravity, the positive curvature on the other side would be anti-gravity. But to create a positive curvature on this side, you should access the Calabi-Yau manifolds.

The problem with the idea of non-euclidean curvature as a full description of space is that the curvature has the other side, or else it's undefinable since there are no lines. And the other side has to be spatial to relate to the curvature, so the nature of space was not determined, only some object within a larger space. One way to make sense of it is if the curvature is accompanied by movement from parts of space

Imagine if the vase had a figure inside, a triangle. The triangle would turn from the inside of the vase, if the vase directed movement up first, to the outside, facing an upward moving matter, while itself being reversed, until it would turn back to be the outer moving matter while the other matter moved downwards. However, because both moved the same rate, the motion would appear continuous, esp with many figures

What kind of a movement is: a vase that keeps turning to a ball and back again without repeat movements before completion of the cycle? There's two opposite movements going on at the same time in such a rotation when its turning back to a vase, by some elements of the vase/ball displacing others yet allowing no unoccupied space.

It is an unfortunate fact that a postulated motion in space cannot be distinguished from quite different movements through space with corresponding changes to the object. Rather, there's some quotient of the space taken by the object in some fixed direction calculated from a definite time (because these differ). Object-space distinction collapses into a higher system with both in certain proportions.

Before reading any further, my take on "beyond spacetime": any fixed reference frame contains a problematical relation to what movement actually takes place, whether it be a straight movement or movements in depth with corresponding topological changes to the object. A straight motion can be rotation with changing size. The selection between these possibilities could be one dimension, distinct from world modality.