Primordial spheres defined by something like Planck’s base units…

Primordial spheres emerge.

a little working document by Bruce Camber, May 2021

These primordial, most-infinitesimal spheres emerge without a trace. Each is exponentially smaller than a neutrino and trillions of neutrinos pass through us every day. Yet, in an a most-understated manner — one sphere per unit of primordial time — it computes to an extraordinarily large number of spheres per second and as we shall see in section 7 of this analysis, that we might assume it is the approximate rate of expansion of our universe.

In 2012 for professional advice I turned to Philip Davis, a Brown University applied mathematician. He was one of the first scholars asked to help interpret our first chart. It had used just Planck Length and base-2 to encapsulate the universe. Phil had been the Chief of the Numerical Analysis Section of National Bureau of Standards (NBS) which in the 1980s became our National Institute of Standards & Technology (NIST). He had grown up in Lawrence, Massachusetts. the same place as Leonard Bernstein and the 1912 Bread and Roses Strike, one of the more important labor actions in American history. We had argued about the most simple possible three-dimensional object. He claimed the sphere. I claimed the tetrahedron. I granted him the two vertices of the sphere against the four vertices of the tetrahedron, but, “How do you build anything with just spheres?”

Phil pushed me beyond my study of Frank-Kasper phases to consider cubic-close packing of equal spheres. A Wikipedia illustration by Jonathunder was most convincing. On Tuesday, May 8, 2012, I gave in: “The sphere is more basic than the tetrahedron; it creates tetrahedrons!” By 2014, I was making my own prognostications about pi.

Scale invariant, pi takes it place within the infinitesimal. Whether we use Stoney’s numbers, Planck’s base units, or new calculations by mathematicians like John Ralston, these infinitesimal spheres will be the smallest possible and the most-densely packed (on the levels of a blackhole or neutron star), and still have all the Fourier dynamics of any sphere.


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