Sphere-stacking may well be a most fundamental dynamic of the universe.

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 page to explore which numbers among all possible numbers are most important.

We know that all the mathematics that describe the sphere describe 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.

Forms emerge. Structures emerge. Functions emerge. Relations emerge.  There is substance. There is a quantity.  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.  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 and that octahedral-tetrahedral complex. It 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 a corresponding page about the dynamics.

Sphere to tetrahedron-octahedron couplet
External dynamics
Internal dynamics
E8 complexity

Other pages using this stacking image: [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], and [12].