PERFECTION STUDIES: CONTINUITY•SYMMETRY•HARMONY GOALS..April.2025
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Challenging Cosmological Paradigms…
by Bruce E. Camber
Abstract:
Ten (10) concepts provide access to deeper models for our scholarly-scientific community to examine the basic structure of things:
1. Geometry versus Big Bang (4 March 2025): A most basic geometrical structure remains unexplored. There are four hexagonal plates within every octahedron that are hypothesized to be the primary irrational numbers in action. Big bang cosmology has nothing to say. Plus, in these days of the James Webb Space Telescope, that theory is failing too many tests. We’ve got to relieve its pain and give it a rest.
2. Geometries of Quantum theory: Hypothesized is that five tetrahedral geometries with their 7.35+ degree gaps and the octahedral gap of 7.35+ degrees are the faces of quantum mechanics. (Gaps: January 2016, Tetrahedral; May 2022, Octahedral)
3. Endless Perfections versus Imperfections: Hypothesized are geometries of perfection. These are perfectly fitting geometries and numbers. The infinitesimal universe is an orderly place. Imperfections, probabilities, indeterminacy, and chaos become measurable when it is no longer too dense, too fast, and too small and five-tetrahedral clusters and five-octahedral clusters become systemic and quantum fluctuations begin. (On-going research)
4. Highly-integrated Universe Views versus Worldviews (11 December 2011): Hypothesized is that our base-2 mathematical outline and map of the universe in 202 notations from the Planck scale of the universe reflects a real reality.
5. Infinity versus space-time. Time is derivative. Hypothesized is that these 202 notations are always active and define the Now. The Now. (On-going research)
6. Spheres versus Particles as a Basic Building Block. We hypothesize that every moment of space-time and every particle and some hypothesized particles are defined by the complexifications and aggregations of infinitesimal spheres. (On-going research)
7. Simple Mathematics versus Mathematical Mysteries. Many mthematical experts have been working without a grid since the big bang cosmology became our standard. We hypothesize that all mathematics and science will readily tie into the 202 notational grid and expand our capacity to understand many current mathematical mysteries. (On-going research)
8. Size of the Universe: Knowable or Unknowable? Our hypothesis is that this outline of the universe in 202 base-2 notations will result in knowing our universe with ever more exacting numbers and geometries. (On-going research)
9. Majesty or Mystery of the Universe: The Majesty of the universe is its infinite variety within 18.5 tredecillion spheres per second, a cosmological constant, which grows our universe. We hypothesize that these notations are too small, too fast and too dense and that this packing of spheres is a perfection. (On-going research)
10. Knowable infinite versus the knowable finite. Our hypothesis is that infinity can be known through the continuity-symmetry-harmony of pi (π) and then by the deepest qualities of the other three irrationals, Phi (φ), the Square root of 2 (√2), and Euler’s number (e), and then by other irrational numbers, and the dimensionless constants. (On-going research)
Key words: Hexagonal plates, pi (π), phi (φ), the square root of 2 (√2), and Euler’s number (e), perfection, octahedron, tetrahedron, infinity…
URL: https://81018.com/big-ideas/
Introduction. This entire website, almost every page, is an exploration of one of these key points. This post reviews each concept and then directs you to key pages for more.
1. Geometry versus Big Bang: The Planck base units with geometries are a better place to start to build a model of the universe than the Big Bang itself. We impose base-2 notation on all those base units to begin to discern the continuity principles (order-time) and to look at all the data. Spheres, tetrahedrons and octahedrons, number theory, irrational numbers, space-time and infinity are all ignored within big bang cosmology. Within this study, they are the grounding. These are the basics.
The precedence of simple logic combined with experience tells us us that things always start simple. The sphere is most simple 3D object. Yet, that sphere encapsulates many complexities. An unexamined complexity is to start the four primary irrational numbers within the four intrinsic hexagonal plates within the octahedron. Now dubbed intimate incommensurables, we hypothesize that of the four hexagonal plates, the base plate is defined by pi (π) and each of other three define one of the intrinsic hexagonal plates that defines every octahedron which is inside every tetrahedron which is derivative of spheres.
Let’s explore these unexplored plates through several different thought experiments.
2. Geometries of Quantum theory: Ancient Greek philosopher and polymath, Aristotle, thought the tetrahedron could tessellate the universe. Given his place in our intellectual world, it was a mistake that prevailed for 1800 years. Though finally analyzed and documented in the 1400s, nothing more was said about it until 1926 when Dirk Struik, an MIT mathematician reviewed its history. Written in Dutch, the article did not receive much attention. In 2012 two scholar-mathematicians, one from Ann Arbor and other from Beijing, reviewed Struik’s article in detail and provided details about the natural gaps created by the tetrahedron. Though published by the American Mathematical Society, it has not been widely discussed or read. The implications are just too dramatic and affects so much of science and scientific history. Hypothesized is that these gap geometries are the basis for quantum fluctuations, quantum physics, and quantum theory. Gaps are first created by five tetrahedrons, then five octahedrons when the densities, sizes, and transaction speeds systemically support such an aggregation.
The net result is a quiet revolution. It’s disarming. Background…
3. Endless Infinitesimal Perfections versus Imperfections: Using base-2 notation, the universe is encapsulated within 202 notations. All notations build upon the prior notations. We are currently in the early part of Notation-202. The early notations, 1-50, are too dense, too fast, and too small for imperfections therefore we hypothesize geometries of perfection. Part of our universe is a highly-ordered place and today there are new studies of perfected states initiated by scholars at Berkeley and throughout the world. Imperfections, probabilities, indeterminacy, and chaos all have their place. In time, we will begin to learn just how these densities-rates-sizes of the expansion support quantum fluctuations. Yet, here we re-introduce the idea that there can be perfected states within space-time and that these perfected states may reach through all 202 notations.
The net result: Another revolution. Our earlier studies.
4. Highly-integrated Universe Views versus Worldviews: What is evolving is what I’ve called a highly-integrated model of the universe. It is hardly a worldview in any sense of the word. It’s a working model. A thought experiment. It starts simple and allows for the all the complexity that we see today. We hypothesize that each notation is always active and the time for the universe is always Now.
5. Infinity versus space-time: As a people, we have been plagued by the worst of fanaticism. Infinity is such a troublesome concept, some have said, “Just throw it out. Stop using it.” So, I have asked, “What is a concept?”
Infinity is a concept; and as a concept, it can be defined by what is given, observed, used in experiments, validated, and believed. The four primary irrational numbers are such examples. When we adopted the belief of Philip Davis (Brown) that a sphere was the most simple 3D object to be defined by the Planck base units, pi (π) naturally became our focus. Continuity-symmetry-harmony were obvious qualities; it begged question after question: How? What are the dynamics? Where does this all happen? Is there any affects with those endless numbers?
We hypothesized that infinity is defined by the irrational numbers with their never ending numbers. This is today’s work (March 2025).
Infinity is an important part of the puzzle. We welcome all things mathematically infinite.
6. Spheres as a Basic Building Block (versus particles and waves): Questions have been asked of scholars worldwide:
- Is the sphere the first thing to manifest as defined by Planck Time and Planck Length?
- Does it define a finite-infinite bridge?
- Is there any sphere stacking and packing on that bridge?
- Is the tetrahedron and octahedron manifest on that bridge?
- Are the four irrational numbers manifest within hexagonal plates on that bridge?
- Our questions continued: Within one second at a rate of one infinitesimal sphere per Planck base unit, do 185 tredecillion such spheres manifest every second?
- Might the Planck base units define the first units of length, time, mass and charge?
- Might this thing be a infinitesimal sphere?
- Does this expansion, a cosmological constant, explain dark matter and dark energy?
7. Simple Mathematics versus Mathematical Mysteries: I am a simple person with average abilities. My sliver of genius is my stubbornness. In 1970 when I began thinking about perfection and creativity, I came upon the concepts of continuity (time and order), symmetry (space and relations), and harmony (space-time and dynamics), but it went no further. It was “a good idea.” Though I had an intuition about geometries and was attracted to the Harvard’s Philomorphs and David Bohm’s writings, no logical path was found. It wasn’t until 2001 when we created the molds to manufacture thousands of clear plastic tetrahedrons and octahedrons did the basics of a model begin to shape. Then in December 2011 in the geometry classes in high school did we back into a base-2 progression, going down and down in size. We were re-discovering Planck base units and base-2 notation, and it was decided that that Planck Length was a good place to stop going smaller.
Unprecedented, we had mapped the universe from the start to this day in 202 notations. We thought it was a good STEM tool. It was, but it was also a revolution. Hypothesized is that exponentiation, especially base-2 notation, is a basic process by which the universe operates.
8. The Size of the Universe: Knowable or Unknowable? The people of this world, like Einstein, believe the universe goes on forever. It certainly seems so. Yet, within our configuration, we can begin to know this universe in exquisite detail, from the first notation and through each notation, right to the Now within Notation-202.
We have ignored so many details about our universe for so long, generations of scholars have had to be especially creative to intuit and fill in the gaps. The earliest foundations were still unknown. So, we now hypothesize that all notations, everything , everywhere, for all time, are on the grid and related. So much creativity we will be unleashed in a sea of explanations where so much work over the past couple of millennium will begin to get tied together, again, it will become a quiet revolution.
9. The Mystery or Majesty of the Universe: The Majesty of the universe is its infinite variety within 569 tredecillion spheres per second, a cosmological constant, which grows our universe. Too small, too fast and too dense, this packing of spheres is a perfection. The majesty of the universe is that we can know why it is as it is and begin to grasp all the reason for its unfolding in the way that it is. The mystery is within the new uniqueness as it unfolds, not the processes of unfolding. So, we hypothesize that these notations are too small, too fast and too dense; this packing of spheres is a perfection.
We will celebrate the mystery, but truly the majesty of the universe will be grasped by all.
10. The unknowable-and-knowable Infinite versus the knowable finite: Infinity is known through continuity-symmetry-harmony of pi (π) and the deepest qualities of the other three irrationals, Phi (φ), the Square root of 2 (√2), and Euler’s number (e). It is increasingly knowable. Those that say it’s unknowable have abandoned common sense. Two mathematical geniuses have defined the concepts of attractors and repellers. Heretofore, neither Steve Smale or John Milnor had seen our base-2 grid from the Planck base units, but their work along with all the work to measure gravitational waves open a duality electromagnetism and gravitation. Finally, I began thinking distinctions could be made between energy, charge, electromagnetism and gravitation. It will take awhile to get the words and concepts straight, but it seems we can with these new definitions of infinity that are deep within Phi (φ), the Square root of 2 (√2), and Euler’s number (e). Yes, our hypothesis is that Infinity can be known through the continuity-symmetry-harmony of pi (π), and then by deepest qualities of the other three irrationals, (φ), (√2), and (e) and then, more modestly by any of the irrationals and dimensionless constants.
More editing to come…
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Reading and re-reading
What is opened on the desk, on the shelves and on the floor.
I am always glad to circle back to Paul Davies, an acquaintance from the 1970s. He 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.” – Paul Davies, theoretical physicist, Arizona State University
Perfection studies at Berkeley. Boldly initiated in 2023, this would be a first — an institute focused on the concept of perfection. The following scholars presented papers at their March 2025 gathering: Toby Gee, Imperial College London; Tasho Kaletha, University of Michigan; Jacob Lurie, Institute for Advanced Study; Tomer Schlank, Hebrew University of Jerusalem; Karl Schwede, University of Utah; Naomi Sweeting, Princeton University; Alberto Vezzani, Università degli Studi di Milano, and Mingjia Zhang, Princeton University. Among the principal investigators at Berkeley are: Martin Olsson (director), Benjamin Antieau, Bhargav Bhatt, Kęstutis Česnavičius, Dustin Clausen, Pierre Colmez, Aise Johan de Jong, Peter Scholze (our correspondence). Matthew Emerton, Toby Gee, Jacob Lurie, Akhil Mathew, and Wiesława Nizioł. Links to key articles will be forthcoming.
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I asked myself, “Who within this world is aware of the four hexagonal plates intrinsic to the octahedron?” I had never done a search on various combinations of those words, yet now every time I did, our work came up in the first few listings and with the first few images. It wasn’t widely understood or discussed. Yet, I did find this listing by two chemistry professors in Dankook University. I immediately began searching for more of their work. It became obvious to me that the deeply intrinsic, four hexagonal plates within the first few notations was clearly seen in chemical structures in the 202nd notation.
Morphology-controlled synthesis of octahedron and hexagonal plate of Co3O4, Kim Myung-Jin and Huh Young-Duk, (Department of Chemistry, Dankook University, Gyeonggi-Do 448-701, Republic of Korea, 28), (University of California Irvine), Science Direct, Elsevier, February 2011
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Afterthoughts
Personal reflections.
I’ve said in many ways that we are all connected with everything we say, do, or think. Just that concept alone is enough to become a gentle soul, think twice, and walk softly. But it seems to go further and becomes the basis for ethics and values.
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Emails
There will be emails to many of our scholars about key points.
• 7 April 2025: George F. R. Ellis, Cape Town, South Africa
• 7 April 2025: David Gross, Santa Barbara, California
• 7 Apri 2025: Joseph Silk, Baltimore, Maryland and Paris, France
• 6 April 2025: Peter Woit, New York City, NY
• 5 April 2025: Martin Olsson, Berkeley, California
• 5 April 2025: Gustavo Turiaci, Seattle, Washington
• 4 April 2025: Frank Wilczek, Cambridge, Massachusetts
• 4 April 2025: Tim Tait, Irvine, California
• 3 April 2025: Peter Scholze, Berkeley and Bonn, Germany
• 27 March 2025: Jean-Pierre Serre, Alpes-Côte d’Azur, France
• 25 March 2025: Robert diSalle, London, Ontario, Canada
• 24 March 2025: Gerardus ‘t Hooft, Utrecht, Amsterdam, The Netherlands
• 24 March 2025: Kirsten Wickelgren, Durham, North Carolina
• 24 March 2025: Paul Davies, Phoenix, Arizona
• 19 March 2025: Huh Young-Duk, Gyeonggi, S. Korea
• 18 March 2025: Shabnam Akhtari, University Park, Pennsylvania
• 17 March 2025: Andrew Strominger, Cambridge, Massachusetts
• 15 March 2025: Martin Bojowald and others in College Park, Pennsylvania
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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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• This page became a homepage on 28 March 2025. We are still working on it.
• The last update was 8 April 2025.
• This page was initiated on 10 March 2025.
• The URL for this file: https://81018.com/big-ideas/
• The headline for this article: Concepts to relieve big bang cosmology
• First teaser* is: Radically inclusive concepts-and-ideas mark new beginnings.
*Or, wicket, kicker or eyebrow
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