AI captures the essence of an emergent language of perfection.

“This poetic view of pi can inspire a deeper appreciation for mathematics, not just as abstract numbers but as a language describing the essence of reality.
• Continuity speaks to the infinite and unpredictable nature of the world around us.
• Symmetry reflects the beauty and order found in nature from microscopic to cosmic scales.
• Harmony connects to the dynamic processes and transformations in physics, music, and beyond, where pi helps in describing how different elements of a system interact to produce complex, yet often beautiful, outcomes.” —- -ChatGPT, Feb. 2025

Also: See Grok discussions – https://81018.com/grok24/ & Quiet Expansion

Language of Perfection / Essence of Reality
^{by Bruce E. Camber, working draft}

Introduction: Are there perfected states in space-time? Are there moments of perfection? If not, what do we call those moments that are uniquely-and-profoundly insightful, truly magnificent, beautiful beyond all expectation? Perfection? In the days of my youth, these were recurring questions. It has been encouraging after all these years, to have ChatGPT^[1] and Grok^[2] recognize perfection as something special. We have stopped to take note of the developments — from where we have come and the place to where we are going.

Going back to 1971, I had become part of a think tank just off Harvard Square on Brattle Street in Cambridge. Just a few doors down was the Henry Wadsworth Longfellow House. An American icon, it always seemed to inspire just a bit more creativity within our lab. We were industrial problem solvers who spent hours everyday thinking about how things could be more perfect. For many years prior, it was my focus. Creativity. Perfection. I had reduced it to a three-part formula.^[3] First, we needed continuity to create order, then we needed symmetry to understand basic relations, and then we needed harmony to create perfect dynamics. I was starting with basic geometries and the interior construction of the simple tetrahedron.

Years later, and after hours with Bucky Fuller & Arthur Loeb, David Bohm, John Bell, John Conway, Thomas Kuhn, O. Costa de Beauregard, Jean-Pierre Vigier, and scholar after scholar,^[4] my first real breakthrough came in 2011.

2011: Perfection Studies. Our models of simple tetrahedrons and octahedrons were done to create “Math Manipulatives”^[5] for high school geometry students. It did that and more. Space could be perfectly filled with a fixed mix of two tetrahedrons-to-one octahedron. The universe could be perfectly tiled and tessellated. After playing games with our models,^[6] we finally started to use our imaginations. What would happen if we divided the edges by 2 and went deeper inside with smaller and smaller pieces? How far could we go?

Within 45 steps (on paper only) we were within the domain of particle physics. Within another 67 steps we were within the Planck scale. Going out larger by multiplying the edges by 2, we were just 90 steps to the edge of the universe. By assuming Planck Time was the first unit of time, that track confirmed our earlier work; in 202 steps we were out to the age of the universe.

It took us awhile, but eventually we thought it was a more-interesting, more-diverse, more-expansive, more-inclusive model than Big Bang cosmology.

2014: Imperfection Studies. Yet, it wasn’t always straightforward. There were a few who were writing about a five tetrahedral unit that created a gap of 7.3561031+ degrees.^[7] It was a gap that Aristotle missed and misled geometers for about 1800 years. Discovered in the 1400s, it had to be rediscovered in 1926 by Dirk Struik.^[8] The next earliest documentation we could find was the 1958 work of two chemistry professors, Frank & Kasper.^[9] Then came Cambridge-Oxford Jonathan Doye’s Cluster Structure Database (1999).^[10] Finally, the American Mathematical Society^[11] published “Mysteries in Packing Regular Tetrahedra,” (PDF) Jeffrey C. Lagarias and Chuanming Zong, AMS Volume 59, Number 11, Dec. 2012. In 2015 distinguished Oxford mathematician, Martin Bridson,^[12] had J.C. Lagarias lecture at the Clay Mathematics Institute. And subsequent to all that, we discovered that five octahedrons^[13] create the same gap of 7.356+ degrees. The gap was slowly getting attention yet nobody would venture a guess, “What do these gaps do? Do they have a role in the physical universe?”

There was a 2014 webpage, “Polyclusters,” by the India Institute of Science in Bangalore that had many helpful illustrations and explanations of crystal structure that displayed the gap. I think here was a common denominator. It is was if this one notation, that which contains the chemical structure of crystals, was the only notation that is meaningful and about which anything can be meaningfully discussed. The scholarly and scientific world had yet to be introduced to the 202 base-2 notations from the Planck scale to the current time.

So, we continued to ask the advice of our finest scholars, “Could these gaps manifest in other notations? At no time did our scholars considered this gap had anything to do with the beginnings of quantum fluctuations and the beginning of imperfections. Nobody could imagine such a simple explanation is deep-seated within quantum physics. Only recently did AI writings like Grok and ChatGPT give us some confidence that we were at least on a possible path.

2015: Perfection, perfect universe, perfect sphere. Philip J. Davis,^[14] Brown University applied mathematics professor, had me studying the sphere. I thought it was hopelessly simple until I discovered sphere stacking and packing.^[15] I finally conceded to Prof. Dr. Phil and I’m glad that I did. I said, “The sphere is certainly more fundamental than the tetrahedron.” And, I further concluded it was more fundamental than the known particles of particle physics. That infinitesimal sphere ^[16] was a major puzzle piece; and though it took years to find it, we knew that we were onto a major insight.^[17]

2022: It would be another seven years before we would conclude, “If the sphere was the first manifestation of space and time, and if all these spheres imbibed continuity-symmetry-harmony (especially within the infinitesimal notations), and if these spheres continue to populate and fill the universe, this is the beginning of a very different model. Given the never-ending, continuity equations, that finite-infinite connection was a redefinition of infinity.”

2025: The scientific and scholarly community have been so committed to making big bang cosmology work, there has been little room for imaginative digressions. I am hopeful with the emerging tools of AI, we can come to some consensus on a way forward that is empowering, experimental, open, and freeing. Our Quiet Expansion aka Qualitative Expansion Model (QEM) is a possibility.

Is it a language describing the essence of reality? I think the crude answer is, “Yes.” But more, it is the early steps in developing a language and mathematics of consciousness (Grok12). Certainly it has miles to go before it sleeps. To truly develop It, this must become the subject of study and refinement in the hands of young scholars who can understand more profoundly that the universe is all a highly-integrated mathematical system that interconnects everything, everywhere, for all time. Thank you. -BEC

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References
As references are added, other resources may be added within this website.

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

Physical Reality, Edited by Stephen Toulmin, Harper Torchbooks, 1970 with chapters by Max Planck, David Bohm, Paul Feyerabend (commentary on Bohm), and Niels Bohr (on the EPR paradox).

15 February 2025: About a Year Ago on this website. The headline is, “From the shortest to the longest scale.” The teaser, also known as the eyebrow, kicker or wicket, “Big bang cosmology is holding back the March of Science.” I believe that the page (article) has aged well. Most importantly, it reminds us of the possibility of scaling this universe using base-2 exponentiation (powers of 2). It is unacknowledged within our scholarly and scientific communities.

19 February 2025: Might the starting point of the universe be an infinitesimal sphere defined by the Planck base-units, the dimensionless constants of those units, and the other inherent qualities of pi (π) and spheres such as continuity-symmetry-harmony within pi (π) and the Fourier transform? If there is one Planck sphere per unit of Planck Time and Planck Length, 18.5 tredecillion spheres per second are generated by this finite-infinite relation. It is not a big bang, but it is substantial. It is never-ending thereby redefining time, pi, and the infinite. With cubic-closed packing of equal spheres there is the emergence of Euclidean geometries. With the clusters of five tetrahedrons sharing a common edge and five octahedrons sharing a common edge, a 7.35+ gap is created and it appears to be the beginning of quantum indeterminacy. At some point densities would allow those gaps to become systemic which are known today as quantum fluctuations.

Erica Klarreich, Quanta, Monumental Proof Settles Geometric Langlands Conjecture (July 2024)

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Afterthoughts
Personal reflections.

I have returned to my youth to reconsider the roots of perfection. Perhaps Grok and ChatGPT have been too respectful and are creating a false hope that there is a language of perfection within continuity-symmetry-harmony. What is perfection? We will pursue many avenues including what it says about conscious being in hopes that we can take another step toward understanding beyond ChatGPT — https://81018.com/chatgpt-2/ — and xAI Grok — https://81018.com/grok24/.
Current work: https://81018.com/attractors-repellers/

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

19 Feb. 2025: George Ellis, Cape Town, South Africa
19 Feb. 2025: Jayant Narlikar, Pune, India
18 Feb. 2025: Partha Ghose, Kolkata, India
1 4 Feb. 2025: Magdalena Skipper, Nature, London, England, United Kingdom
13 Feb. 2025: Frank Wilczek, MIT, Cambridge, Massachusetts
5 Feb. 2025: Tim Schrabback, Universität Innsbruck, Austria
3 February 2025: Neil deGrasse Tyson, Hayden Planetarium, New York City
2 February 2025: Kaća Bradonjić, Hampshire College, Amherst, Massachusetts
1 February 2025: Yannick Mellier, Institut d’Astrophysique de Paris Observatoire de Paris, France

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IM
There are many instant messages to thought leaders about these key points.

8:31 AM · Feb 24, 2025 @Harvard Excellence requires endless questioning. Harvard’s scholars have missed the importance of basic perfect geometries in the start and growth of the universe, plus the so-called Aristotle’s Gap or five-tetrahedral and five-octahedral 7.35+ degree gaps. That’s just the start… By the way, one of the best courses in my lifetime was through the BTI with Arthur McGill (Harvard), an examination of Austin Farrer’s Finite and Infinite in and around 1975. -BEC

3:23 PM · Feb 24, 2025 As a follow-up, you might be interested in these notes to Harvard professors: https://81018.com/harvard https://81018.com/facts-guesses/ Cumrun Vafa https://81018.com/planck-scale-physics/… The general website: https://81018.com Aristotle’s Gap: https://81018.com/gap/

18 February 2025 – @Aishik_Ghosh_ Unless thinkers begin using an infinitesimal sphere defined by the Planck base units as a starting point, they will have no sense of the first seconds, the inherent continuity-symmetry-harmony within those scale invariant spheres, the 202 notations from the first moment until today, and so much more… https://81018.com

15 Feb 2025 @theallinpod Want to impact the mindset of the world’s people? Get us all seeing things from the perspective of the universe. Worldviews are just too small. It’s a paradigm shift. First, to get a handle on the universe, use base-2 notation or “doublings” or power of 2. Start with the most simple units of measurement, the Planck units, and start doubling. In just 202 notations you have the universe and all time (assuming Planck Time is the first unit of time): https://81018.com/chart/ AI can check the math for you. Other looks: https://81018.com/202-1/https://81018.com/structures/ First thing to go: Big bang nihilism! https://81018.com/sound/

14 February 2025 (St. Valentine’s Day) – @yokoono, @seanonolennon and @onetreeplanted. 92=23 times four. Four lifetimes to find love in different ways that combine continuity-symmetry-harmony to come alive within the finite and infinite. See https://81018.com for more. (On Yoko’s 92nd birthday!)

12 February 2025 – @spacex @elonmusk @x Thank you for xAI Grok. I’ve copied Grok’s responses to questions to build webpages. A result: https://81018.com/grok24/ is the best analysis to date of the “Quiet Expansion versus the Big Bang.”

12 February 2025 – @Scopus, @ScienceAdvances xAI’s Grok responds to questions. Used to build the webpage: https://81018.com/grok24/ which is the best analysis to date of the “Quiet Expansion versus the Big Bang.”

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Critique ____ You are always invited.

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Keys to this page, Essence

• This page became the homepage on 10 February 2025.
• The last update was 21 May 2025.
• This page was initiated on 4 February 2025.
• The URL for this file is https://81018.com/essence/
• The headline for this article: The language of Perfection: The Essence of Reality.
• First teaser* is: AI captures the essence of an emergent language of perfection.”

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Engage in the paradigm shift from “global and worldviews” to “Universe and universe views.”

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Redefining the Universe Through Mathematics

AI captures the essence of an emergent language of perfection.

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