by Bruce Camber, April 2019, last update, May 5, 2021

Cubic-close packing (ccp) had its start back in 1587 with the work of Thomas Harriot. Johannes Kepler continued that work in 1611. Calculations were made to attempt to stack cannonballs on the deck of a ship most effectively. It became a more sophisticated study in the 20th century when it was applied to discern atomic-packing factors.

Our application brings ccp down into the Planck scale.

Defined by dimensionless constants, the sphere is projected to be the most simple structure and the first structure within space-time.

Before John Ralston called into question the veracity of Planck’s calculation for the Planck constant, we actually concurred with those people who have call it a plancksphere. Within the studies of ccp, particularly focusing on the functions within sphere-stacking, it is hypothesized to be the basis for all forms, structures, substances, qualities, relations, and systems (functions) and it is best understood within the very first notations of the first 64-notations out of the 202 that encapsulate our universe.

The deep dynamics of the sphere, ostensibly all the lines within this illustration (dynamic gif, above right) are being analyzed. Here begins the tetrahedral-octahedral tiling and tessellating of the universe. Here is where Aristotle failed. From one sphere to another and another, then within the internal dynamics of these spheres, triangles, tetrahedrons, octahedrons; and then plates of triangles, squares, and hexagonals begin interlocking all things for all time and all spaces.

Another image of the tetrahedron naturally filling space to create the octahedron came out of our high school geometry class many years before December 2011 when we went deep inside and down into the Planck scale.

Here are the first 67 notations. It is a huge domain of the infinitesimal. There are so many doublings, here we obviously find the essence of dark matter and dark energy. Here, too, is the basis of isotropy and homogeneity.

These additional images and references implicate the sphere as our first order of space-time business:

• https://81018.com/e8/  (April 2019) The specific dynamics of sphere stacking get the additional dynamics of the Fourier analysis. Insights by Steven Strogatz, a Cornell mathematician and an excellent physicist, helped. It seems that those dynamics are key elements of the even-larger dynamics of the finite-infinite relation and Planck’s formulas for light.
• https://81018.com/start/  (March 2019)
  Postulated as the basis of electromagnetism and gravity, every possible dynamic within the sphere will be studied. Every Fourier analysis becomes fundamental. The sine-cosine relation is a fundamental dynamic, uniquely pushing and pulling light. The image seems to jive with some of the current thinking within string theory. Of course, these postulations are stretched thinking, but probably less stretched than the ideation within big bang and multiverse work.  Within Notation-1 to Notation-67, a simple, logical foundation exists for all the mathematics of string theory and the Langlands programs. Yes, these concepts have been entertained in the past. Visit with David Bohm and Basil Hiley who wrote The Undivided Universe: An Ontological Interpretation of Quantum Theory (Routledge 1993). Bohm died in 1992; my last contact with him was in 1980, yet, we came to similar conclusions.
• https://81018.com/math/#Isotropy (November 2016)  This webpage was an earlier exploration of sphere-stacking, natural inflation and compactification.
• https://81018.com/sphere/ (March 2019) A companion page to 81018.com/start/
• https://81018.com/stacking/  (March 2019) Planckspheres stacked as high and wide and deep as our universe, the number count would be 67 notations greater than the estimated atoms that some have tried to address.
• https://81018.com/growth/
• https://81018.com/emergence/
• https://81018.com/plancksphere/
• https://81018.com/circles-spheres/

• https://81018.com/quantum-foam/

John Archibald Wheeler, a most distinguished Princeton physicist (1938-1975) and University of Texas-Austin (1976-1986), was seeking to define a fundamental unit within space-time. He conceived of a quantum foam (1955). It wasn’t small enough. Although the Planck numbers have a pre-history going back to 1881 with Irish physicist, George Johnstone Stoney, both Stoney’s and Max Planck’s 1899 work were largely ignored and remained in the background. In 1982 John Barrow introduced both the Planck numbers and the Stoney numbers but that paper did not ignite deeper studies.

When Frank Wilczek wrote the Climbing Mt. Planck I, Climbing Mt. Planck II, and in 2002 Climbing Mt. Planck III for Physics Today, interest in the Planck numbers began to spike.

For us, it all started here: https://81018.com/number/#Kepler

This image was discovered within Wikipedia when I was looking to discern the most fundamental number, and the meaning of that number as it is related to any given shape. Cubic-close packing, both face-centered cubic (fcc) and hexagonal close-packed (hcp), has a rich history beginning in-and-around the 1570s starting with the problem of stacking cannonballs on the deck of a ship. The display of the transformation from stacking to tetrahedrons and octahedron was the most compelling.

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This document was started on April 6, 2019 and was updated June 5, 2020.