Toy Model: The Emergence of Our Universe

Image of abstract geometric shapes representing continuity, symmetry, and harmony in a mathematical model of the universe.
A cosmic representation highlighting hyper-rationality, featuring spheres, octahedrons, and hexagonal plates, depicting continuity, symmetry, and harmony in an expansive geometric model of the universe.

PERFECTION STUDIES: CONTINUITY•SYMMETRY•HARMONY GOALS October 2025
PAGES: BEGIN.|.DISCUSSION | CONCLUSIONS | REFERENCES | CRITIQUE | KEYS

For just the very first second

By Bruce E. Camber (Revised Draft, October 2025)

Abstract
The first second of the universe remains poorly defined in mainstream cosmology, with limited consensus among scholars. This toy model proposes a playful yet structured framework using eight foundational mathematical concepts to describe the universe’s emergence. It starts with infinitesimal spheres and builds toward the observable cosmos, emphasizing geometry, natural units, and infinite qualities.

  1. First Sphere Manifests: An infinitesimal sphere, defined by Planck base units (or equivalents), emerges as the universe’s initial entity, encapsulating space-time via equations involving the speed of light (c), gravitational constant (G), reduced Planck constant (ℏ), and pi (π).
  2. First Actions: These spheres spin, stack, and pack, centers connecting, shaping tetrahedrons and then octahedrons—the geometric building blocks of the first temporal moment.
  3. Planck Base Units: These units delineate the inaugural instant of space-time, matter-energy, and fundamental forces like gravity and electromagnetism.
  4. Complexities of the First Moment: Octahedral structures reveal four hexagonal plates, hypothesized as the finite-infinite interface.
  5. 18.5 Tredecillion Spheres per Second: Generated at one per Planck time, this rate (18.5 × 1043 spheres/second) aligns with the Hubble constant (~71 km/s/Mpc), implying dense, flawless packing in early notations.
  6. 202 Notations Make the Universe: The cosmos is divided into 202 exponential doublings (notations), from Planck scales to the present, first charted in a 2011 high school geometry class.
  7. Pi (π) Shapes Our Universe: Pi embodies continuity, symmetry, and harmony from infinity, with other irrationals revealing additional facets.
  8. Quantum Fluctuations: Natural geometric gaps (e.g., 7.358+° naturally in clustered as five tetrahedrons or five octahedrons) initiate quantum indeterminacy.

Introduction

Our clocks and watches reinforce a Newtonian view of absolute space and time, which has long hindered a unified understanding of the universe’s origins. Religions offer moral principles, but science promises empirical foundations—yet it too struggles with first principles. This toy model challenges these paradigms by starting from basic geometries and natural units, aiming to bridge finite phenomena with infinite qualities. It critiques absolute space-time and invites playful exploration to redefine emergence.

Discussion

Toy Models in Context

This entire framework functions as a toy model: a simplified lens on “How did the universe begin?” It sidesteps the historical baggage of theories like the Big Bang, allowing analysis of core data and concepts in isolation. While speculative, it provides a stepwise path for humans and AI to test ideas without overwhelming complexity.

[1] The Primordial Sphere

Since 2016, our analyses have centered on pi (π) and spheres as foundational. By 2019, pi’s role expanded; in 2025, a polyhedral geometry emerged, linking finite and infinite realms via pi and three other irrationals (e, √2, φ). This sphere—immeasurably small yet definable—meets Archimedes’ criteria and qualifies as the first “particle.” It inhabits a hypostatic domain of forms, akin to automorphic structures, straddling the finite-infinite bridge and defining the first moment of spacetime.

[2] Spinning, Stacking, Packing, Centering, Triangulating

Everyday spheres (e.g., baseballs) are familiar, but celestial rotations (planets, stars) hint at deeper dynamics. Imagine Planck-scale spheres spinning at extraordinary rates—lab records reach 300 billion rpm, while neutron stars hit 716 revolutions/second. In this model, octahedral emissions create spinning spheres that stack, pack, discover abutting centers, then become archetypal tetrahedrons and octahedrons. Early notations (1-64) encompass spin states, forms, strings, geometries, substances, qualities, relations, and systems, leading to hypothetical particles by notation 50-60.

These domains embody “perfection,” with no room for imperfections until notations 64-67, where measurable fluctuations arise (as charted in our 2013 models).

[3] Planck Base Units

Introduced by Max Planck in 1899 and popularized by Frank Wilczek in 2001, these units—despite skepticism—offer a geometric foundation (tetrahedrons/octahedrons) with irrational complexities. They self-validate through relations like the speed of light, providing a testable base for our schema.

[4] Finite-Infinite Mechanism

This bridge, via octahedral hexagonal plates, applies irrationals (never-ending, never-repeating) to infuse continuity-symmetry-harmony. Generated infinitely but computed finitely, it echoes historical finite-infinite debates while introducing novel geometries.

[5] Tredecillion Spheres per Second

First calculated in 2021 (since verified across AI engines), one sphere per Planck time yields ~18.5 tredecillion/second, which in October 2025 converted to ~71 km/s/Mpc—matching observed Hubble values. This resonates with our geometries, potentially superseding general relativity and Friedmann-Lemaître-Robertson-Walker equations. ChatGPT builds upon Grok4. Then, DeepSeek opens it all up for a deeper examination. Also, it became time for a Lagrangian to slowly begin to emerge. We many of the AI platforms to help us with the Lagrangian.

[6] 202 Notations: Structuring the Universe

This 2011 discovery parses the universe into 202 doublings, each a potential cluster, domain, layer, or step. Early notations (0-143) span the first second; the full grid integrates scales seamlessly. Future work will refine these as multi-faceted platforms.

[7] Pi (π) and Irrational Shaping

Pi imparts infinite qualities to the finite universe, with e, √2, and φ adding layers. We urge scholarly societies to explore these hyper-rational facets.

[8] Origins of Quantum Fluctuations

Tying fluctuations to geometric gaps (e.g., in five tetrahedrons/octahedrons) adds texture without diminishing quantum physics’ validated status. It suggests dimensionality beyond current models.

Conclusions

Everybody wants a better theory; nobody wants to pay the price for a paradigm shift. This toy model offers a starting point: testable, geometric, and harmonious. It challenges us to validate its claims through math, simulations, and observations. If refined, it could unify scales and inspire new physics—let’s collaborate in order for it to evolve.

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References

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Critique

Does the sphere rate align with ΛCDM? Share your thoughts. Too esoteric?
How about our mission statement that reads like a manifesto? .

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KEY dates for this page:

• This page was started on 29 September 2025.
• The page became the homepage on 5 October 2025.
• The last update of this page was 22 October 2025.
• Headline: Toy Model Derivation of the Hubble Constant from Planck-Scale Dynamics

October 2025 • Perfection Studies • 81018.com • Est. 1972