edanet
Sat, Jul 18, 2009
Nest for Newton - Sphidron & the Regge Calculus*
Don`t be Afraid Albert!
But, look at this picture below.

THE REGGE CALCULUS IS 0 EVERYWHERE
We found the corresponding physical phenomena in quantum gravitation theory.
Sphidron is an appropriate discrete geometrical model of it.

(Kan-a-Da, Ni >Al< Bertaba menet &it talalta)

The picture of the first sphidron relief (it is not spidron - i.e. without the letter "h" anymore), as it has no vertex at all, only bent edges and surfaces.

I am thinking about a new law of motion.

Picture from Mathworld.com

{image 6}

I quote Newton's 3 of them:

I. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.

(I'll have a little addition to it!)

II. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. Acceleration and force are vectors (as indicated by their symbols being displayed in slant bold font); in this law the direction of the force vector is the same as the direction of the acceleration vector.

(I'll have a little addition to it!)

III. For every action there is an equal and opposite reaction.

Ridiculous!!!

For example: You don't trust me, but I am deeply trusting you!
Or it is not a motion? Maybe not, "only a feeling"!

Let see! What "object means? A dead bone, or a concept? Or what on Earth? Am I an object? And you?
I can hardly imagine, but ... what "state of motion" means in this context? Is there anything in a state of motion, or is it an ever-changing state? Than, why "state"? What if ... a little soul or free will or a little god is living in every created creature? What if the statement what the Chasidim say, that JHV is in everything, but hidden by layers and spheres? What if in the middle of every spidronnest, there is a little invisible will? Or godess? A tiny one? And ... as we've seen, every stage of the deformation (I mean, spidron deformation) can take place without any outer impact, so HOW COME? Who can decide, which stage is valid in a certain moment? And ... what are the vertices of the classical nest do? Are they objects or only concepts? But anyway they are moving in a different way, that Newton tried to describe, as they are rotating or - in a better word - spiralling toward the center of the nest (or just to the opposite direction - without any restrictions (Limits are excluded in basic cases, but in case of sph(!)idrons the situation is much more interesting, because they can move unlimited!). The Regge calculus is constant everywhere on the surface. OK, maybe the acceleration of the points is decreasing during the deformation, but still, it is not a straight and even motion. Newton is speaking about "external forces", but how can we decide, whether a force or any impact is an external or an internal one? What is about the gravity itself, is it an external or an internal force?

He, Mr. Newton is speaking about straight vectors, though I don't believe that the direction of movement must be straight. Yes, you can say, every movement can be divided into 3 different and perpendicular straight vector, but, what if the the vector is the vector of slow spiralling fall down into the centre of the object, itself like you can see here on mour video http://www.youtube.com/watch?v=-GGCMDGpamA  ? As we saw in the remarks I took to law 1. the movement can be a spiralling one with a decreasing acceleration. So? What is the "truth"? The truth is that we must not say that the object is a dead bone, but we can suppose that there is a great and a beautiful freedom between the possible states of motions. And, if the mathematical "point" in reality is a rotating point, and a mathematical "line" is a rotating (around its axis) line, and a spiral and a circle and torus Check it on this video: http://www.youtube.com/watch?v=PjuWQCXQHSA  - thank you) and the sphere etc. are all moving "objects", we get a new type of physics. And it is a different one from Riemann's and Einstein's, because I can allow to have only two Euclidean dimension in an embedding third physical space. The number of physical dimensions can be increased infinitely with different parameters, like "time", "gravity", etc. but the 2D geometry works well only in 2D and the only way we can protect the validity of the embedding space from paradoxes, is to deform our 2d plane by logarithmic algorithms. That is what I showed up with Janos Erdos on the first page of the website: www.spidron.hu.

This circular disk is remaining circular from top view, during its deformation.
Look at this video: http://www.youtube.com/watch?v=2x5o1IpaFrM&NR=1  - It means, that, if we cut parts off, and we have - for example - a hexagon, a square, a triangle, or even Penrose tiles, we can tessellate the "plane" (I use "-s, because this kind of plane is a movable relief in reality) with moving, i.e. breathing polygons. What if we can build different Platonic and Archimedean solids from these polygons? All will have a breath? Certainly! That is what I am working with Jano Erdos and a little with Marc Pelletier, who understood in a moment, what I am talking about. So did Bori Cseh, who is a very smart woman.

... and ... WHAT IS ABOUT LOVE, Berta?

hugs,
d

{image 7}

Splatonics by Amina, Walt, Marc and Dani

Marc and Simon

*Regge calculus

In general relativity, Regge calculus is a formalism for producing simplicial approximations of spacetimes which are solutions to the Einstein field equation. The calculus was introduced by the Italian theoretician Tullio Regge in the early 1960s.

The starting point for Regge's work is the fact that every Lorentzian manifold admits a triangulation into simplices. Furthermore, the spacetime curvature can be expressed in terms of deficit angles associated with 2-faces where arrangements of 4-simplices meet. These 2-faces play the same role as the vertices where arrangements of triangles meet in a triangulation of a 2-manifold, which is easier to visualize. Here a vertex with a positive angular deficit represents a concentration of positive Gaussian curvature, whereas a vertex with a negative angular deficit represents a concentration of negative Gaussian curvature.

The deficit angles can be computed directly from the various edge lengths in the triangulation, which is equivalent to saying that the Riemann curvature tensor can be computed from the metric tensor of a Lorentzian manifold. Regge showed that the vacuum field equations can be reformulated as a restriction on these deficit angles. He then showed how this can be applied to evolve an initial spacelike hyperslice according to the vacuum field equation.

The result is that, starting with a triangulation of some spacelike hyperslice (which must itself satisfy a certain constraint equation), one can eventually obtain a simplicial approximation to a vacuum solution. This can be applied to difficult problems in numerical relativity such as simulating the collision of two black holes.

The elegant idea behind Regge Calculus has motivated the construction of further generalizations of this idea. In particular, Regge calculus has been adapted to study quantum gravity.

Sat, Jul 18, 2009  Permanent link

gamma     Sat, Jul 18, 2009  Permanent link
Ah you crazy artist! its just mechanics! People use math to build machines that draw paths! Some paths are very jittery - non smooth for differential equations in style of Newton. Pure vacuum possesses those laws. Extreme opposite are laws within matter or within networks. Tell us more about spidrons, they look amazing! I think these spidrons are fractal trees:
http://www.cgl.uwaterloo.ca/~csk/projects/spidron/
...Cayley trees:
http://demonstrations.wolfram.com/KCayleyTrees/
edanet     Sat, Jul 18, 2009  Permanent link
Crazy - hopefully, one of them

No it is not ONLY a stupid boring fractal (I was fed up with Benoit 15 years ago, though the 3D fractals are cool), it is an iterated sequence of triangles, no scalar symmetry in the embedding space, only locally in 2d geometry. That makes it much more interesting and that's why I started to speak in Newton's and other guy's discussions, like Einstein, Wolfram etc... Stupido Cupido

you can find a lot of them here: www.spidron.hu look Spidron Age animations!

Chokyyi or Xcuse me :o) Chokiiy!!! Do you love me? WoW

Unexpectedly - Wowww - I I LOVE YOU