by Bruce Camber (July 18, 2022) The URL for this document: https://81018.com/gap-geometry/
If the Planck base units are meaningful, and that seems to be increasingly settled since Frank Wilczek’s 2001 articles in Physics Today, does it describe the starting point for spacetime? I have naively concluded that it does. When the efficacy of Planck’s constant was questioned by John Ralston, I dropped back to the 1874 work of George Johnstone Stoney and suggest the “actual numbers” are more symbolic yet in the range of a real reality.
So, from where does everything come?
I redefined infinity in light of three most basic facts of pi, and say, “continuity-symmetry-harmony.” The most controversial facets of infinity are considered personal. Of course, that may well be just too naive in light of the work of Hilbert, Gödel and Woodin.
Yet, if we can show from where imperfections originate, maybe we have something different. Assuming perfection is the sphere and pi, the first imperfections may well be geometric; and, Aristotle may have unwittingly missed that key mark; five tetrahedrons create a gap.
It seems nobody has ever formally recognized the five-octahedral gap. It is too simple. Constructions kits like ZomeTool and computer-aided design do not naturally calculate the gap. Neither can naturally create this object with the five-tetrahedral gap in the middle.
I think there is something to it.
That little cluster looks like it could function as a logic gate within computer programming. If we were to consider a twenty-tetrahedral icosahedron in place of a five-tetrahedral unit, complexity-and-possibility are multiplied.
Eventually we will further consider a Pentakis dodecahedron and combinations of all of the above.