From a sphere to many spheres to a tetrahedron

Excerpt from a posting titled,
On Constructing the Universe From Scratch

This animated illustration is from Wikipedia. It demonstrates how spheres generate lines (lattice), triangles, and then a tetrahedron. With that second layer of green spheres emerges the tetrahedral-octahedral couplet. The discipline, known as cubic close packing (ccp), deserves our attention.  “The Kepler conjecture states that this is the highest density that can be achieved by any arrangement of spheres, either regular or irregular. This conjecture was proven by T. C. Hales.” (Wikipedia)

Also see:
The horizontally-scrolled chart of all 201+ notation
Quiet Expansion of the Universe
An index of related postings
The homepage for this project

Sphere to tetrahedron-actahedron couplet
Attribution: I, Jonathunder
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Are the first 67 notations key missing links?

Could an integrated Universe View1 open new approaches to old academic questions? Because it redefines our understanding of space and time, it seems to open that possibility.

Sir Isaac Newton’s space and time became an absolute frame of reference2 and the basis of commonsense logic for well over 300 years. But, what if space and time are derivative, discrete and quantized? What if both have a specific beginning, the Planck Base Units, and today’s current time-length-mass-charge-temperature of the universe, or the Now, are always the endpoints? What if every notation is a highly-integrated part of the whole?

There are just over 200 base-2 exponential notations from the Planck Base Units to this moment, your “today.”  That range is best defined as the Age of the Universe.

Within our Universe View, also known as Universe Table and Big Board-little universe, the first 67 doublings cannot be measured at the singularity of the Planck base units. Planck time cannot even be measured at the 67th doubling. Though driven by a simple logic, simple mathematics, and very simple geometries, those first 67 doublings per se are not part of our observed universe and are currently not part of academic analyses.3

Given this situation, we advocate that the nature of space and time be reopened for scrutiny in light of these first 67 steps. Could these steps be the missing links that open real pathways to new insights into historic, impossibly-difficult and persistent, unanswered, academic questions that exist across all the disciplines? To open such a discussion, brief summaries and a few links will be provided within some of those large categories of human endeavor.  Eventually in-depth articles for each will be written and linked from here:

The longstanding goal of this article is to open the discussion to explore how these statements could be true and in what ways they are not true.

We invite you to join us to determine if and how these 67 notations just might be the infrastructure within which age-old questions can be addressed in new ways.

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Endnotes, Footnotes, and References:
1. We have begun building a bridge to the 68th notation, the place where things begin to be measured in space and time. We will be using all the current research at research labs such as CERN, and speculative work such as the Langlands programs and amplituhedrons. Pi, all the dimensionless constants, the physical constants, pure geometries, and numbers and ratios will all be used in new ways.

This article is our appeal for help.

2. Sir Isaac Newton’s space and time became an absolute frame of reference

3. Within those first 67 notations are a different set of building blocks for the universe. If we bring to bear all of the geometries (projective, analytic, combinatorial..), including the simplest geometries (cellular automaton and the platonic solids), a little bifurcation theory and the 80-known binary operations, perhaps we can begin to intuit how forms become structure, then substance, then qualities, relations and systems, increasingly-and-exquisitely complex with literally trillions-upon-trillions of possible combinations and expressions, right on up to the fermions, bosons, skyrmions and all combinations of elementary particles that make up the Standard Model (SM) and the SMPP for Standard Model for Particle Physics.

Much more to come: Entropic forces and causal determinacy

Tetrahedrons & Octahedrons

Tetrahedron

The text within the picture reads as follows:

Three levels of simple complexity:

1. Observe the tetrahedron in the bottom left corner.

2. Notice that it is enclosed in a larger tetrahedron. Right beside is
an octahedron, plus there is a tetrahedron in each of the other three corners. Every tetrahedron encloses four half-sized tetrahedrons and an octahedron.

3. Notice that our larger tetrahedron is enclosed by an even larger tetrahedron. This pattern repeats itself getting smaller and getting larger. Part of the complexity can be seen by observing the center octahedron. Notice the red, black and blue hexagonal plates. A white plate has been obscured.

For more, please follow this page on the website:
https://bblu.org/2014/12/01/tiling
“Tiling the Universe in 201+ Exponential Notations:
The Great Chain of Being”