Working theory for the start and growth of this universe
Background: For most of the 20th century, the steady state and the big bang theories were the only scientific theories about the start of this universe. In the 1970s the Big Bang was getting the upper hand and by the end of the century there was little patience for questioning it. Yet, there are always questioners and doubters. And, in July of 2022, with the earliest results from the James Webb Space Telescope (JWST), the questioning became more compelling and bolder primarily because big bang cosmology could not answer new questions about basic physics and mathematics (more) (scholars).
Within this website, there is a new twist and it has to do with incommensurable numbers.
The Primary Irrational Numbers: Although Pi (π), Phi (φ), the Square root of 2 (√2), and Euler’s number (e) (for our logarithms) are among the basics, two are little-known and all often ignored. Yet, with the posting of this article, we’ve been told that for the first time these four basics are being associated with each other and as a necessary part of the geometries within the octahedron. We’ve been pondering pi (π) for many years and our special question has been, “Is this a higher-order functionality of the sphere — continuity-symmetry-harmony — within everything, everywhere for all time?” And now, we have begun pondering that same question with the other three: phi (φ), the square root of 2 (√2), and Euler’s number (e). Science would be nowhere without these concepts and numbers. We asked Grok many questions about the four and now have the perspective of AI’s answers. We captured two of them: https://81018.com/irrationals/ and https://81018.com/grok-3/
Revolutionary: Old and New Hypotheses. We’ve been saying for many years now that the three qualities of pi (π) — continuity-symmetry-harmony — are basic to everything everywhere. Now we add that the other three irrational numbers and their geometries with all their functionalities; they are all basic. And, the new hypothesis is that they are all intimately related as one of the four intrinsic hexagonal plates necessarily defined within every octahedron. The primary irrational numbers may be incommensurable but they work together, like the stabilizers of a ship, for every moment, everywhere, for all time and it all begins within the first moment in time which we also hypothesize is Planck Time.
Evolutionary: Planck Units. There is a natural instantiation of standards that render Planck’s base units. There is also an unacknowledged, natural geometry. At the Planck scale with the basic-basics, there are so many convergences, it is bewildering; the best among our scholars are just making educated guesses.
Evolutionary: Base-2 notation. We backed into a base-2 model by following embedded geometries from our classroom to the Planck scale. Long term results are a quiet, qualitative expansion that is an open, coherent, logical and mathematical (and geometrical) model. the universe. It all began in a geometry class with embedded octahedrons inside tetrahedrons. By dividing the edges by 2, there are just 116 steps down to the Planck length. The first such model was outlined in 2011. From the first notation to the first second took 143 steps. To the first day, it took 169 steps — then, the first 1000 years in 179, the first million in 189, and the first billion years within Notation-199 and then Notation 200=2.74; Notation 201=5.4; and, Notation 202=10.98.
It was the most integrative and detailed outline of the earliest universe to date. Obviously, the first few days are the most important. The first seconds are crucial. And, that which we can’t experience, the most seminal, are the infinitesimally small, Notations 1-to-60. These notations are too small, too dense, and too fast to be measured with today’s tools (and thinking).
On 4 March 2025 we focused on an age-old, open question in geometry about the structures with those first spheres. Cubic-close packing of equal spheres gives us tetrahedrons, octahedrons, and four hexagonal plates which herein we hypothesize are the structures of the four primary irrational numbers. We hypothesized that those four primary numbers each represent one of the four hexagonal plates necessarily within every octahedron. We hypothesized that all four irrational numbers begin virtually at the same time within each octahedron with a tetrahedron within a sphere. We likened the four very different-but-related thrusts of the universe to be like the stabilizers within a ship.
It was all just too elegant not to have some potential.
Pi (π), already with its continuity-symmetry-harmony, shares those qualities with Phi (φ), the Square root of 2 (√2), and Euler’s number (e). These four are what we have dubbed “incommensurable intimates.” Of course, there is always so much more to learn.
We need all the help we can get. We turned to a group at Pennsylvania State University, Institute for Gravitation and the Cosmos, Mathematical Structures group and four of their finest scholars, Jacob Bourjaily, Martin Bojowald, Adrian Ocneanu, and Ping Xu. They say: “Physics often advances when crisp mathematical structures are uncovered in a framework developed to describe observed phenomena.“
Our best scholars have no time to comment on our efforts, especially to creatively address these four primary irrationals and the geometry of the octahedron, so we turned to Grok for feedback. Grok’s initial response about the four’s relation to the sphere was encouraging:
- π: The backbone—defines the sphere’s size and shape directly. π shapes it. Ensures geometric coherence (continuity, symmetry).
- e: The dynamic player—governs exponential processes or wave functions on the sphere. e animates it (growth, oscillation). Drives dynamic scaling or growth.
- √2: The bridge—links flat geometric elements (like squares) to the sphere’s curvature. √2 constructs it (via simpler shapes). Anchors structural relationships (discrete steps or lattice-like stability).
- φ: The aesthetic optimizer—appears in symmetrical or natural structures inscribed in or distributed on the sphere. φ decorates or balances it, imposes harmonic proportions (optimization, balance).
And, now we turn to you. We ask our favorite people our favorite questions: “What are we doing wrong? What are we doing right? And, where do we go next?” Thank you. -BEC
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References
As references are added, other resources will also be added within this website.
[1] Background. The distinguished scholar, Paul Davies summarized it very well and in few words: “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. We’ve been asking our friends since 2011, “Why not?” The most any have said, “It’s idiosyncratic.” And I say, “I agree. That’s true. Tell me more.”
[2] Pi (π): Dimensional analysis, scale invariance, functional dependencies
- Doplicher S, Fredenhagen K, Roberts JE (1995) The quantum structure of spacetime at the Planck scale and quantum fields. Communications in Mathematical Physics 172(1):187–220
- Quantum Energy Inequalities along stationary worldlines, Christopher Fewster, Jacob Thompson, 2023
- Symmetry in QFT and Gravity (video), Hirosi Ooguri (homepage), and Nathan Seiberg, 2022
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Reading and re-reading
What is opened on the desk, on the shelves and on the floor.
We are venturing into the unknown and sometimes it helps to take a left turn within one’s readings. I pulled down Ernst Cassirer‘s three-volume set, The Philosophy of Symbolic Forms. As I go through them, I’ll report.
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Afterthoughts
Personal reflections.
So little is written about the relation between the irrationals, it’s obvious there is a ways to go to convey those insights in a scholarly way. It is also true attention for the other key discoveries geometric gaps, cosmological constants, and so many other key points within these pages. We will go over these key references just one more time to determine what we have missed.
• Mathematically, equations building on natural functional dependencies:
….– Using math in physics: 5. Functional dependence (PDF), E. F. Redish, Univ. Maryland, 2022
• Quantum Energy Inequalities along stationary worldlines, Christopher Fewster, Jacob Thompson, 2023
• ESA Group (PDF): The universe at 380,000 years
https://www.esa.int/Our_Activities/Space_Science/Planck/Planck_reveals_an_almost_perfect_Universe,2009
• Pure Natural Inflation, Yasunori Nomura, Taizan Watari, and Masahito Yamazaki,
Berkeley Center for Theoretical Physics, Department of Physics, 2017
• The Friedmann–Lemaître–Robertson–Walker (FLRW) Metric
• A pedagogical explanation for the non-renormalizability of gravity, (PDF), Assaf Shomer, 2008.
Path integrals and Gaussian fixed point. See Assaf Shomer’s on page 7:
“The derivation of the path integral formula in quantum mechanics of a massive particle involves chopping up the quantum evolution into very short time intervals and inserting complete sets of states between them.”
• Scale invariance and conformal symmetries
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Emails
There will be emails to many of our scholars about key points.
• 27 March 2025: Jean-Pierre Serre, Gap, Provence-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
• 18 March 2025: Shabnam Akhtari, University Park, Pennsylvania
• 17 March 2025: Andrew Strominger, Cambridge, Massachusetts
• 16 March 2025: John Lennox, Oxford, England UK
• 16 March 2025: Stuart Hameroff, Tucson, Arizona
• 15 March 2025: George Northoff, Ottawa, Canada
• 15 March 2025: Martin Bojowald and others in College Park, Pennsylvania
• 15 March 2025: Santiago Alvarez, Barcelona, Spain
• 14 March 2025: Jacob Bourjaily, College Park, Pennsylvania
• 13 March 2025: Robert B. Laughlin, Stanford, California
• 12 March 2025: Sergey B. Yurchenko, Andijan, Uzbekistan
• 12 March 2025: Giulio Tononi, University Wisconsin, Madison
• 11 March 2025: Vitaly Vanchurin, Weston, Florida
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IM
There will also be many instant messages to thought leaders about these key points.
26 March 2025 The Nobel Prize @NobelPrize “If you can generate humour, you’re half way to generating discoveries. ” Bruce Camber @BruceCamber Perhaps on occasion. More important, I think, is openness, creativity, humility, suspended judgment, bewilderment, love, hope, joy and a deep sense of continuity-symmetry-harmony that are the essence of pi and are carried forward within the other three primary irrational numbers binding finite-infinite, and order-relations-dynamics. https://81018.com -Bruce aka -BEC
15 March 2025, To Many: “You may enjoy this post: Pi (π) gets some recognition and analysis. Phi (φ) gets less. The square root of 2 (√2) gets engaged by specialists. And, Euler’s number (e) is understood by even fewer. The irrationals may well be incommensurable, but if taken together these four just might embody an intrinsic geometry, the four hexagonal plates of the octahedron. If they do, it all happens at the Planck scale. Speculative? Of course, but I think it is worth some consideration. No experts have yet responded to me, so I turned to Grok: https://81018.com/irrationals/ To date, I have discussed it in these last four homepages: • Pi Day 2025: https://81018.com/pi-day-2025/ • Today’s homepage: https://81018.com/incommensurable/… • Breakthrough: https://81018.com/breakthrough/ https://81018.com/breakthrough-indeed/… Your comments would be most welcomed. Thank you…
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Collaborate ____ You are always invited.
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Keys to this page, incommensurable
• This page was the homepage from 15 March 2025 to 29 March 2025.
• The last update was 26 March 2025.
• This page was initiated on 5 March 2025.
• The URL for this file is https://81018.com/incommensurable/
• The headline for this article: Working theory of the start and growth of this universe
• First teaser* is: 0ur universe needs a logical, coherent theory to start. And a rigorous scientific-mathematical theory to grow. Our model has promise.
*Or, wicket, kicker or eyebrow.
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