A Qualitative Expansion Model for Everybody

Know our Qualitative Universe.
by Bruce E. Camber (Go to Version 2)

Abstract:
The history of science is of a constant search deeper-and-deeper inside and further-and-further outside. It seems Einstein’s foundation abides when he said, “… all these constructions and the laws connecting them can be arrived at by the principle of looking for the mathematically simplest concepts and the link between them.”^[*] More recently, Arizona astrophysicist, Paul Davies said, “We don’t know whether some of those constants are linked deep down. If we had a deeper theory, we’d find that they’re not actually independent of each other, but we don’t have that theory at the moment, we’ve just got all these numbers.”^[†] We nod to Einstein and say to Davies, “I think we have found a deeper theory and it opens a very different path and way.”

No singularities… The Qualitative Expansion Model (QEM) posits a universe beginning at the Planck scale (Length: approx 1.616 × 10^-35 m) with infinitesimal spheres, initially stacking and packing as tetrahedrons and octahedrons. Unlike Big Bang cosmology’s singular origin, QEM starts with a finite, ordered state, scaling deterministically across 202 base-2 notations to the present (~13.8 billion years). π’s continuity, symmetry, and harmony bridge the discrete and continuous, offering a singularity-free alternative. QEM’s sphere lattice at the Planck scale could be modeled using lattice gauge theory techniques. Gradient-based optimization might simulate the emergence of the 7.356° gap at the 60th notation, potentially revealing how geometries drive physical phenomena like curvature or forces.

2. Connect the dots. Enjoy the cosmic music. Assumed is the logic given within the qualities of pi (π) that is shaping every sphere. First there is the endless, never-repeating patterns of numbers (now confirmed over 200 trillion digits) imparts the initial order within the universe. Then there is the symmetry, a deep-seated relation. And, here we observe the dynamics within and throughout every sphere, best described as an archetypal harmony.

3. An initial analysis This expansion may begin with Notation-0, the first physical moment, but it’s not nothing. It’s necessarily three-dimensional. It’s qualitative. It’s quiet. And, it’s a very different start of the universe. The first moments are all archetypal. That’s logic. Yet, hypothesizing, we say Notation-1 to Notation-10 is for forms (like Langlands automorphic forms), Notation 11-20 is for structures (like strings), Notation 21-30 for substances (like [see functional analysis]), Notation 31-40 for qualities (like [see functional analysis]), Notations 41-50 for relations (like [see functional analysis]), and Notations 51-60 for systems (like [see functional analysis]).

4. Nothing like a little perfection It is all so small, fast and dense, there is no space or time for anything but perfectly fitting geometries. Here is a perfection within space-time. And then we hypothesize that this precedence carries it forward. There are a variety of perfections. New systems, relations, and qualities are introduced with every prime number. Substances now begin to morph as the periodic table of elements within Notations 80 and following. Features, functions, qualities and quantities, begin to morph within these first infinitesimals moments of space-time.

5. So much, so simple, so fast. Yes, this is all happening within the first second of the universe (which is within Notation-143), The first year is within Notation-169; the first 1000 years within Notation-179, the first million within Notation-189, and the first billion within Notation-199. That first second defines so much of the start of the universe. And, I think It still holds major surprises.

6. Imperfection We were introduced to a five-tetrahedral object in and around 1998-1999. It naturally evolved within our earliest model building activities. It created a natural gap. In 2001, early in our studies, we discovered the work of two chemists, F. C. Frank, and J. S. Kasper (1958). Then, we found the more recent work of academic geometers led by Jonathan Doye of Cambridge-Oxford geometry clusters study group (from 1997 to this day). Finally, in 2015 we discovered an in-depth study titled, Mysteries in Packing Regular Tetrahedra (PDF) by Jeffrey C. Lagarias and Chuanming Zong. We called this gap geometry, squishy geometry. Our models with that 7.356103172453456+ degree gap were indeed “squishable.” We also called it quantum geometry. It could also be called gap geometry. It was entirely unpredictable. So, quite naturally, we associated those models with quantum mechanics and began thinking about their place along the chart with 202 base-2 notations. It was very basic geometry.

In May 2022 we discovered five octahedrons created the same gap.

7. Infinite numbers and four finite plates Another puzzle became apparent at about the same time. We were studying our model of the octahedron with four smaller octahedrons, one in each corner, and eight tetrahedrons, one in each face. We noticed what looked like a hexagonal plate surrounding the center point. Then we noticed three other possible plates, all intersecting, and all around the center point. We asked ourselves how those plates might manifest within space-time. Though relying heavily on pi (π) and its continuity-symmetry-harmony to define the universe, we had not engaged the other three primary irrational numbers until we began thinking that if pi (π) defines the base plate, perhaps the other three define the three other plates. We began asking around the web.

8. Let a quiet and qualitative revolution begin Although Grok’s first response was to give us the standard answers, starting with the big bang, and then informing us about the limited success integrating the four primary irrational numbers, Grok did a thorough analysis about how the four numbers are related to the sphere. Then, Grok gave an even more thorough analysis when we associated them with the initial geometries intrinsic to the octahedron. We suggested that these function much like the stabilizing gyroscopes within a ship. Grok responded with a deep analysis of that possibility. It was the first real feedback about this model.

These all became our benchmarks for this model for the start and growth of our universe.

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References and footnotes. Qualitative Expansion Begins Quiet: This is a different model for the start of the universe. It’s not a big bang. [*] Einstein. Quote from Essays in Science, Philosophical Library, New York City, 1934 (translated from The World As I See It). [†] Davies, Miriam Frankel, The Conversation, Fundamental constants: Is the universe fine-tuned for life?, March 15, 2023

To continue with Grok: https://81018.com/grok-3/ Breakthrough: https://81018.com/breakthrough/ These are big ideas: https://81018.com/big-ideas/ Symphony of spheres: https://81018.com/spheres-symphony/ First index of related pages: https://81018.com/grok/ This page part of eight pages that begin with https://81018.com/qualitative-expansion/ This page is: https://81018.com/qualitative-universe/

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"One Sphere to the Standard Model to the universe: How Base-2 Geometry Generates Gauge Symmetries"

A Qualitative Expansion Model for Everybody

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