Cubic-close packing (ccp) 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 when it was applied to discern atomic-packing factors.
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 basis for all structure-substance-and-function and it is best understood within the very first notations of the first 64-notations out of the 202 that so entirely 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.
Here is another image of the tetrahedron naturally filling space to create the octahedron. It came out of our high school geometry class many years before 2011 (when we backed down into the Planck scale).
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 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. Yes, these concepts have been entertained in the past. Visit with The Undivided Universe: An Ontological Interpretation of Quantum Theory, by David Bohm and Basil Hiley (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.
John Archibald Wheeler, a most distinguished Princeton physicist (1938-1975) and University of Texas-Austin (1976-1986).
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 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.
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.