###### by Bruce Camber, April 2019

Cubic-close packing (ccp)^{1} had its start in year 1587 through 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 as a study of the problem of 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. We call it a plancksphere; and with ccp, particularly focusing on sphere-stacking, it is hypothesized to be the essence of dark matter and dark energy, and the basis of isotropy and homogeneity. The deep dynamics of the sphere, ostensibly all the lines within this illustration (dynamic gif just above) are being analyzed. These two additional images *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 with the help of Steven Strogatz, a Cornell mathematician and an excellent physicist. These 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, every possible dynamic within the sphere will be studied. The Fourier analyses become fundamental. The external sine-cosine is also a dynamic being considered in light of gravitation. 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 ideation within big bang and multiverse work. Notations 1-to-67 make a simple, logical foundation for all the mathematics of string theory and the Langlands programs.Those readers familiar with David Bohm and Basil Hiley’s work,*The Undivided Universe: An Ontological Interpretation of Quantum Theory,*Routledge 1993 will see that these concepts have been entertained in the past. Bohm died in 1992; my last contact with him was in 1980, yet, we have come to some of the same 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). Seeking to define the 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, but both Max Planck’s 1899 work 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. It wasn’t until 2001 when Frank Wilczek wrote the

*Climbing Mt. Planck*I, II, and III did the Planck numbers take deep roots. - https://81018.com/number/#Kepler
**It all started here!**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 a 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.