Sphere-stacking: It appears to be a most fundamental dynamic of the universe.

(a dynamic image is building just below)

Sphere to tetrahedron-octahedron couplet

1. This dynamic image comes from a Wikipedia page entitled, Close-packing of equal spheres.  This image was first used within our posting to explore which numbers among all possible numbers are most important.

All the mathematics that describe the sphere also describe a range of primordial, dynamic relations. These are perhaps best characterized as a tension between the finite and infinite (the never-ending, never-repeating part of these dimensionless constants). The centerpoints to the circumference “discover” each other. The Fourier transform describes part of those dynamics. That string “discovers” another, and then another, and another, as millions-upon-billions upon trillions-upon-trillions of spheres are generated every second. Tetrahedrons and octahedrons readily follow.

Forms emerge. Structures emerge. Functions emerge. Relations emerge.  There is substance. There are quantities.  Then systems begin to emerge.

That simple witticism, “Everything starts simple before it becomes complex” echoes in the background. How simple can we get? Of course, the answer is “Very simple.”

2.  Within our chart of numbers, the first notation has actual numbers of time, length, mass and charge. Asked, “Is there any image that might capture or represent those numbers?”  After a few years of thinking about it, we decided that the sphere just might represent those numbers better than any other, especially in light of the dynamics being suggesting by this dynamic image.

3.  We were now being introduced to the field of study called “emergence.”

4.  If we follow the ellipsis within this image, we tile and tessellate the universe with spheres; an octahedral-tetrahedral complex becomes the fabric of the universe.

5. As this dynamic image became part of the story, there were more and more places to lift it up for its importance in the over all scheme of things.

6. It became part of our recognition of Pi Day.

7. With each year, it seems to become more important.

8. And now, there is an entire focus on the sphere with corresponding pages about the dynamics.

Sphere to tetrahedron-octahedron couplet




External dynamics


Internal dynamics


E8 complexity

A few of the other pages using this stacking image: [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], and [12].

This document was initiated on March 24, 2019. It will be subject to updates.