Finite convergence is an interesting idea because it implies a contradiction in terms. Convergence is known to be infinite, but there is no infinity, and after a finite number of iterations, convergence is not complete.
Take the convergence of dimensional scaling factor of the Triples to 3(3 – 2√2). If there is no infinity it will never get there, right, and yet this convergence defines the nature of three dimensional spatiality. Take this conundrum also in the context of quantum cosmology, where the idea of infinite granularity in an infinite universe is a nonsense. Clearly the universe is not infinite, just big, and the quantum granularity implies a sense of non smoothness at the bottom of the abstraction stack.
The bottom of the abstraction stack for me is the counting numbers. If you don’t know why, go back and re-read the blog. It’s not smooth. The first abstraction is the Triples and after that we get the first idea of spatiality.There is lots of noise and a thin thread of signal. So now consider the non-infinite sequence that is the evolving convergence to 3(3 – 2√2) – I will coin this Russell’s number (why not it’s my number).
What does it mean for three dimensional spatiality as this sequence converges. Remember the number it’s converging to is the dimensional scaling factor of the octahedral graph. This is represented by the abstraction of the exploding unit sphere. As the sequence progresses what idea arises that map to the idea of the progression of the exploding unit sphere. The scaling factor (Russell’s number 3(3 – 2√2)) is the diameter of each of the six resultant spheres, so as the sequence progresses the unit sphere can be thought of as exploding into six slightly smaller spheres in terms of their diameter.
What does this mean, exploding into less than the perfect fitting six spheres of diameter 3(3 – 2√2). what positions do the spheres have if they do not fit perfectly, do they rattle around, are the positions given by an equation that expresses “uncertainty”. Is this the root of all uncertainty in the quantum universe and because the sequence is still running we still experience uncertainty. Does this imply that uncertainty will decrease over time, is this a parallel for entropy.
How does the dynamics of six trapped and expanding balls predict the structure of the early universe. Is this the source of the big bang, when after a time there is a fundamental change in the mode and nature of the positional uncertainty that MST becomes a possible abstraction.