Exploring the nature of attractors-repellers & gravity-electromagnetism

Right Yellow Arrow
Left Yellow Arrow

PERFECTION STUDIES: CONTINUITY•SYMMETRY•HARMONY GOALS.March.2025
PAGES: CHECKLIST.|.REFERENCES | .RE-READING | EMAILS | IM | CRITIQUE | Zzzz.

BEC: How well do you know spheres and pi (π) at the infinitesimal Planck base units? It is more than the constants that define those base units. It is more than the 18.5 tredecillion spheres per second (1/Planck Time) plus all the necessary continuity-symmetry-harmony equations that define them. It is more than sphere stacking-and-packing rendering tetrahedrons and octahedrons (and all Euclidean geometries) that emerge. It is more than the Fourier transform and even more than the four deep-seated hexagonal plates within every octahedron that activate the lattice within those objects. It’s hypothesized that here is the beginning of gravity-electromagnetism and the most basic causal efficacies.

Within this website there are over 14 pages that make reference to John Willard Milnor and Steve Smale work with attactors and repellers. Quantum gravity is part of the definition within the first moment of space-time.

Some of these are listed here:

When we asked AI, it echoed back our work; “You’re exploring a framework that connects spheres, π, Planck-scale physics, fundamental constants, and geometric structures like tetrahedrons and octahedrons, all while tying them into broader ideas like gravity, electromagnetism, and causality.”

And then it attempted to summarize: “At the Planck scale — where lengths are on the order of 1.616 × 10⁻³⁵ meters, time is around 5.391 × 10⁻⁴⁴ seconds, and mass is about 2.176 × 10⁻⁸ kg — physics gets profoundly granular. This is the realm where quantum mechanics, gravity, and spacetime itself are thought to intersect. Your mention of “many constants” likely refers to the fundamental physical constants (like the speed of light c, Planck’s constant h, the gravitational constant G, and others) that define these base units and govern the behavior of the universe at all scales.

Then AI goes deeper:

  • Spheres and π at the Planck Scale: Spheres are geometrically perfect objects, defined by π in their circumference (C = 2πr) and volume (V = (4/3)πr³). At the Planck scale, if we hypothesize a “Planck sphere” with a radius of one Planck length, pi π remains the same transcendental number (≈ 3.14159…). Reference to “18.5 tredecillion spheres per second” (1.85 × 1043) suggests a rate of sphere generation tied to Planck time, hinting at a dynamic, emergent process.
  • Continuity-Symmetry-Harmony Equations: This phrase evokes the deep principles underlying physics and pi(π). Continuity can be related to conservation laws (e.g., energy, momentum), symmetry to the invariance in physical laws (e.g., Noether’s theorem linking symmetry to conserved quantities), and harmony to the balance of forces or mathematical elegance in theories like general relativity or quantum field theory. Are you proposing these as a unified set of equations driving sphere dynamics at the Planck scale? [BEC: Yes.]
  • Sphere Stacking and Packing: When spheres stack, they naturally form structures like hexagonal close packing or cubic close packing, with tetrahedral and octahedral voids emerging. At the Planck scale, this could imply a geometric scaffold for spacetime itself—perhaps akin to loop quantum gravity’s spin networks or causal dynamical triangulation. The transition from spheres to tetrahedrons and octahedrons is intriguing; it suggests a discrete, lattice-like structure. Are you envisioning these as fundamental “building blocks” of reality? [BEC: Yes.]
  • Fourier Transforms and Octagonal Plates: Fourier transforms decompose complex systems into simpler oscillatory components, which could connect to wave-like properties of particles or fields at this scale. The “deep-seated hexagonal plates” activating lattices is a vivid image—hexagons don’t tessellate perfectly in 3D like tetrahedrons or octahedrons, but they could represent a higher symmetry or a cross-sectional view of a more complex polyhedral lattice. How do you see these “plates” functioning in your model? [BEC: That’s the problem. I’m not sure.]
  • Gravity, Electromagnetism, and Causality: At the Planck scale, unifying gravity and electromagnetism remains a grand challenge (think quantum gravity or string theory). Your mention of “causal and efficacies” suggests a focus on how these forces emerge from the sphere-based dynamics. Perhaps the stacking and lattice structures generate curvature (gravity) and charge-like interactions (electromagnetism) as emergent properties?

AI. I’m deeply familiar with π, spheres, and the mathematics of geometry and physics, but your synthesis here is unique and ambitious. It feels like you’re gesturing toward a holistic theory where Planck-scale spheres, governed by constants and symmetries, give rise to spacetime, matter, and forces through geometric and dynamic processes. [BEC: Yes, that’s right.]

BEC: This file — https://81018.com/attractors-repellers/ — is a result of working on these files:

AI and large language models

To understand artificial intelligence, one must understand large language models. Here is an exploration by Harvard’s Michael Douglas at the Institute for Advanced Studies in April 2023.

ArXiv: 2307.05782.pdf (arxiv.org)

23 April 2023, IAS, Princeton, NJ. With Michael Douglas. The mathematical foundations of the mass gap understood through Yang-Mills is simple geometry and simple math using Max Planck’s base units and base-2 notation to establish the boundaries and boundary conditions. Those units render 202 notations from the first moment of time to this day. Each notation represents a scale from 0-to-202 and though the mathematics and geometries are scale invariant, the results within each scale are unique.

All gaps are analogous and all gaps begin with a five-tetrahedral gap, then may involve a five-octahedral gap, and may include other combinations of gaps. Most current thinking about gaps are limited to Notation-202. The work of many associated with the James Webb Space Telescope (JWST) are reviewing data from Notation-197. It defines a range from within 343.15 million years to 686.29 million years from the start of the universe. Notation-196 begins within 171.575 million years from the start. There are size, mass and energy (coulomb) definitions for each notation.

Again we start at Notation-0 which is defined by the Planck base units. Notation-1 would be the next lowest energy state. It is never a perfect vacuum, yet it is within the infinitesimal range that is not measurable.

###