Infinitesimal spheres stack, pack, then…

A geometric illustration of a quadrilateral pyramid with a hexagonal base, showing colored sections that represent angles and segments within the solid.

Revolutionary Operating System Sciences (ROSS)
From infinitesimal simplicity to universal complexity
by Bruce E. Camber

Emergent Work (July 2025). This is a most speculative page but given that you are here, let me please ask for a little patience as we explore our struggle to grasp the functions of this dynamic image.

First, the image debuted on this website on 9 July 2025 with two labels or names. I called it, ROSS,*and Grok had named it the Planck Polyhedral Core.

Early History. The four hexagonal plates were first identified in 1998. A game emerged in 1999. Even John Conway, in the Spring of 2001 within a personal day-long seminar, had no idea how these hexagonal plates manifest in space and time. Nobody had ideas. In 2021 I had been focused on the three faces of pi (π), as the first equation and the most diverse equation to bind three key facets of the sphere — continuity, symmetry, and harmony (Fourier’s transform).

Irrational Numbers (March 2025). Reviewing those pages and thinking about never-ending numbers, I asked Grok about the other three primary irrational numbers; their computations are also never-ending. In my mind’s eye, I could see how each had a pivotal role in the stabilizing the emergence of structure within the very earliest universe, i.e. right up to Notation-143, the first second.

It seemed as if the long-standing mystery about those four hexagonal plates might have a very practical application with the other primary irrational numbers. I had an intuition that all four plates were about to make their debut.

Graphics (June 2025). I talked with a most creative graphic designer, Ross Funderburk, about the challenge of making that image come to life. It was a geometric function that had no visual. He confidently said he could do it. I thought it could be a key image to identify our project and website, and it might quickly convey the deep-seated continuities, symmetries and harmonies within our universe.

Within a month we had a prototype and what you see here is the first generation.

Debut: 9 July 2025: This marks the first formal introduction of our “rotating hexagonals within an octahedron.” It was named the Planck Polyhedral Core by Grok. Secondary suggestions were Quantum Octahedral Seed and Base-2 Geometric Nexus. . Internally, with great appreciation for the work of our graphic designer,* I had named those four hexagonals within the octahedron, ROSS,* and forced fit an acronym: 1) Rotating Operating Systems: Simplicity-to-complexity, and 2) Revolutionary Operating Systems Science.

It is still early and we are open to ideas! Might you have a name for it?

Revolutionary Operating Systems Science. It is revolutionary. It is revolving. It is the result of the stacking and cubic-close packing of equal spheres (ccp). For me, it feels like a key element of a most simple operating system for science and mathematics. If spheres are being generated at about 18.5 tredecillion spheres per second, and cubic-close packing of equal spheres manifests as tetrahedrons and octahedrons, the four hexagonal plates all manifest virtually at the same time.

Observe the rotating image above. Watch the rotating plates through the four colors for the four irrational numbers–Pi (π)Euler’s number (e), the square root of 2 (√2), and the golden ratio (φ). Did you notice the emergence of an octahedron spinning on the left side of the image? To not have this phenomenon happen, I have to put my finger on the right-hand corner of the image and closely stay intentionally focused on that right-hand plate at the center line of the larger octahedron. An illusion? Misplaced concreteness? Or, an essential fact?

I done not think it is just an optical illusion. The rotation, I believe, is at the same time a switch (on-off), a gateway (in-out), a transference plate (yet to be defined), and a sequencer (numbering). I expect that there are many professional geometers and physicists who can define these with some finesse. This is a first pass on 16 July 2025, updated 20 July 2025, and then as a homepage on September 18.

Also, this has bearing on number theory. Our first discussion about it was in 2016. Our second discussion was a little more robust. The most recent is still evolving.

And, of course, this ideation is to be continued. Thank you. -BEC

* ROSS, our graphic designer, is Ross Funderburk: https://rossfunderburk.com