Our eight original concepts help to explain the first second 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 September 2025
PAGES: Breakthrough!.|.REFERENCES | .RE-READING | EMAILS | IM |  CRITIQUE | Zzzz

An animated geometric representation showing a tetrahedron enclosing a cube, with various colored triangular faces and the symbol for pi (π) labeled.

Only Thought Experiments
and logic can go there.
by Bruce. E. Camber

Website Assessment by Al. This website is a domain for thought experiments and conjectures to analyze these eight key ideas and concepts. In 1998 we identified the four hexagonal plates. On 19 December 2011, we identified the 202 notations that encapsulate the universe. We’ve then asked hundreds of scholars for a critical assessment. In 2025, we asked AI for feedback. Grok, ChatGPT and Perplexity weighed in.[1] We can easily get others by asking each pointed questions. We started with the most visible like Google AI. Their edits and feedback are invaluable! It will be subject of analysis within our homepages to follow.

1. Fact: 202 Base-2 Notations from Planck scale to the Age of the Universe today. In 2011, when we first made that progression down to the Planck base units, we were following the geometries of tetrahedrons and octahedrons embedded perfectly within each other, smaller and smaller, until we were down at about the Planck Length. There were 112 steps. When we used the Planck Length as our base unit of measure, naturally it took 112 steps to get back to our classroom model. Surprisingly, it took only 90 additional steps to go out to the edge of the universe and the age of the universe. We were doing “base-2 exponential notation” and that the simple progression had, heretofore, never been made public.

We queried the best of well over 500 scholars from around the world. “Is it logical? Does it provide new insights?” Freeman Dyson and Frank Wilczek were two scholars who guided us in the early days of 2012 and 2013. Wilczek lifted Planck’s work up out of a nascent numerology. Dyson helped us to get comfortable with mathematical infinities. Brown University applied mathematics professor, Philip Davis, pointed us to the sphere from 2010-2018.

These are some of the hurdles we still have to get over:
a. These Planck base units are not “understood” within the academic community.
b. Exponential notation is not visceral within academia.
c. The first 143 notations define the first second. Most of the work that comes after the first second will stand. The foundations of the first second will be better-defined and understood.
d. Time’s mysteries still puzzle us. These are symptomatic of the many open questions today. The fundamentals — space-time, matter-energy, gravity-electromagnetism — all still harbor major puzzles within.
e. Neither the four primary irrational numbers nor the Planck base units and their dimensionless constants have ever been used in a model where each has a key contribution in the emergence of the universe. It begs questions about fundamentalities.

2. Fact: Mathematically, pi (π) puzzles us as well. On one hand it defines continuity, symmetry, and harmony, a perfection. There is a perfection within the never-ending numbers of pi. There are perfections within its symmetries and harmonies. Yet, there is a fundamental discontinuity and unknowns in what has become known as Aristotle’s gap. And, then to add to the unexpected and puzzling, each notation defines what amounts to a variable speed of light (VSL). Our simple geometries with Planck Time render equations to reconsider the nature of light, the nature of gaps, and the nature of perfection: https://81018.com/c/

All of it remains out of mainstream physics, yet there is an inherent logic to each that requires more careful study and general scrutiny.

3. A Simple Calculation. The expansion of the universe, approximately 18.5 tredecillion infinitesimal spheres/second, is based upon Planck base units assuming one Plancksphere per unit of Planck Time and Planck Length. It is a simple calculation based on simple logic. Although nobody has challenged it, we are pushing to have it challenged, studied, and reviewed.

When, and if that logic stands, or is reformulated, a quiet revolution will have begun.

4. Conjecture (Simple Logic). There is a deep-seated geometry, starting with Planck scale infinitesimal spheres, that populates the universe. This grid of infinitesimal spheres defined by Planck base units gives rise to every geometry. The 45 prime number notations between 2 and 199 are being studied for their functional complexities. First comes cubic-closed packing of equal spheres. Tetrahedrons are rendered. Octahedrons are necessarily part of the tetrahedron. The four hexagonal plates inherent within every octahedron are defined by the four irrational numbers. Each, like the continuity-symmetry-harmony of pi, stabilize these spheres and these connections between the infinite-to-finite conversions and transformations.

That first notation is loaded with values, constants, and equations.

Diagram illustrating the angle theta (θ) equal to 7.356 degrees in a geometric configuration where five tetrahedrons share an edge labeled AB.
A translucent geometric model composed of multiple triangular and quadrilateral faces arranged in a symmetrical design.

5. Conjecture: Five-tetrahedral & five-octahedral gaps are the setup for the earliest quantum fluctuations. However, the first fluctuations may not have happened until there is a trigger mechanism. There’s no precedence for fluctuations so what might account for a trigger mechanism is being explored. The academic community has ignored gap phenomenology. It was not perceived to be a key geometry when Aristotle’s mistake was first discovered in the 1400s. Rarely cited, in 1926, MIT mathematician, Dirk Struik, wrote a significant review of gap geometry. In 2012 Jeffrey Lagarias and Chaunming Zong built on Struik’s work and wrote a definitive article about the gaps. And then, in May 2022, I believe for the first time, we cited an octahedral gap and these two gaps were very much part of the icosahedral gap and dodecahedral gaps.

Since that time, we have been advocating that gap phenomenology be more carefully and more rigorously scrutinized and studied. These gaps need to be in the hands of scholars with their thought experiments and conjectures.


6. Conjecture: There is a domain of perfection where all geometries perfectly fill space. We have guessed that the 50th to 60th notations are the domain for systems theory. The most-basic forms-and-functions of the universe have emerged between Notations 1 and 50. All are described by disciplines within functional analysis. Yet, it is easy to make mistakes.

It seems that a well-order theory of the universe should start where there is real information; that is at the Planck base units. Another place to start is with the most-simple, most-basic structures of the universe: circles, spheres, tetrahedrons and octahedrons. Then, the four most-used irrational numbers also seem to be a good place to start. All four originate from within the endless numbers of infinity.

All these possible perfections, though known, are now being more actively explored.


7. Conjecture: The four irrational numbers manifest within the very first moment and further stabilize each infinitesimal sphere at the Planck scale and beyond.

In 1998 we uncovered four hexagonal plates inherent within all octahedrons. In July 2025 Grok dubbed this dynamic geometry, the “Planck Polyhedral Core” (PPC).

Four primary irrational numbers — Pi (π), Phi (φ), Square root of 2 (√2),  Euler’s number (e) — form infinitesimal hexagonal grids within every infinitesimal octahedron (which, of course, is within every infinitesimal tetrahedron, which is rendered by infinitesimal spheres). In March 2025, we began seeing how these all manifest. We have been working with pi (π) for years. It was time to put those four hexagonal plates and the four primary irrational numbers in new light.

An animated visualization of a geometric shape, featuring a cube surrounded by a tetrahedron, with colorful triangular faces indicating internal sections and the symbol 'π' labeled on one of the cube's faces.

The first digits:
Pi (π) = 3.141 592 653 5+
Phi (φ) = 1.618 033 988 7+
Square root of 2 (√2) = 1.414 213 562 3+
Euler’s number (e) = 2.718 281 828 4+
AI tools have given us some confidence to follow through.

8. Conjecture: “Infinity is within the finite as either continuity, symmetry or harmony.” Flying in the face of history’s finest logicians, we make this observation and conjecture — the fundamentals of infinity can be seen within the finite. These are all qualitative. For years we have had the feeling that academics had been limiting themselves. We had our old formula from 1972, but no structure. We had finally emerged with structures in 2011. We were slow to put the two together, to discern that continuity, symmetry and harmony were infinite and were the faces of infinity within the finite. Now we are extending that to include the qualities of the other three irrational, incommensurable numbers.

These concepts are the footings of our theory. There are well over 30 unique presuppositions that we are constantly exploring.

The following segments are based on feedback of our visitors.

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References
As references are added, other resources will also be added or linked from within this website.

[*] No less than 102 countries use short-scale:
— English-speaking: 64 countries
— Arabic-speaking countries: 22 countries
— Brazil and the former Soviet Union: 16 countries
Long-scale is currently used in most countries in continental Europe and most countries that are French-speaking, Spanish-speaking (except Puerto Rico and those countries where its primary influences are from an English-speaking country) and Portuguese-speaking countries, except for Brazil.

[1] Grok and ChatGPT and Perplexity:
Grok: https://81018.com/irrationals/
ChatGPT: https://81018.com/chatgpt-3/ More: https://81018.com/chatgpt-2/
Perplexity: https://81018.com/perplexity/

Grok and ChatGPT were the first AI platforms to analyze the 81018.com website. Other leading platforms like Google AI have been slow adopters, yet within a week’s time, Google AI became increasing less critical. Specific criticisms can be helpful counterpoint, so we are asking Google AI specific questions and we are studying the answers.

[2] Calculations. In 2019 and 2020, the first 60+ notations create a grid for disciplines currently identified within functional analyses. These deep and extensive studies are only on a grid that includes the Planck base units. Experimentally beyond the reach of standard measuring devices (and accelerators), we say that the first 60+ notations are a domain for thought experiments. Even Langlands programs could be included. Their work possibly describes some of the dynamics of the finite-infinite bridge within Notation-0.

[3] Fundamentality: “Which is more fundamental, the four primary irrational numbers along with the Planck base units, and its continuity-symmetry-harmony from the infinite to define the first moment of time  or general relativity, gravity, and quantum indeterminacy?”

[4] Basic challenges: Planck Second and to one second are Notation-1 to Notation-143.
— In 2025 a slightly revised version of the eight ideas became this homepage today.
— In August 2018, we compared our grid to the big bang grid.
–In November 2017 it became the first iteration of eight key ideas.
— In 2014, it began as these rough 15 key ideas.

[5] Editor’s note on September 2025:

In June 2025 it became increasingly clear that the website was in serious need of updating. That process started in earnest in July and it is still ongoing. We are making progress and the site is being tightened up. Some old files are finally being deleted. Thank you for your patience. All suggestions are welcomed. Thank you. -Bruce

Of course, there is more to come… September 2025

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Resources: Reading and re-reading
What is opened on the desk, on the shelves and on the floor.

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Afterthoughts
Personal reflections.

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Emails
There will be emails to many of our scholars about key points.

11 September 2025, Decatur, GA USA: Z. Merali
11 September 2025, Durham, England: Sophie Gibb
10 September 2025, Oxford, England: Subir Sarkar

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IM
There will also be many instant messages to thought leaders about these key points.

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Critique ____ You are always invited.

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Keys to this page, original

• This page became the homepage late on 23 August 2025.
It will be “under construction” for another week.
• The last update was 16 September 2025.
• This page was initiated on 8 August 2025.
• The URL for this file is https://81018.com/original/
• Headline: These original ideas and concepts render the universe just the way it is.
• First old headline is: Let us take them one-at-a-time.

A QR code with a design element displayed in the center, surrounded by a grid of black squares on a white background.

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