Smooth, first minute, fluctuations, dark energy-matter, finite-infinite…

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Reason to believe ..
by B.E. Camber Working first draft
Go to an easier read: No links/notes

Abstract. Base-2 exponentiation symbolically begins with the Planck scale, the first possible moment in time, and in 202 doublings defines this current moment in time.[*] Base-2 groups diverse studies such as exponentiation, bifurcation theory, fractal geometries, and cellular growth. It’s becoming a working model based on simple logic, geometries, and algebra, initially based on spheres, tetrahedrons, and octahedrons. It begins with natural units and is driven by pi (π). Its 202 predictive, base-2 notations totally absorb big bang cosmology.[†] This mathematically-integrated view of the Universe addresses key issues that big bang cosmology cannot. Five examples follow.

I. Smoothness. The James Webb Space Telescope images have raised anxieties that the early universe is too smooth for our working understanding of the dynamics of big bang cosmology.[1] The transition from smooth to lumpy is not a problem within our 202 base-2 notations. In this model geometric gaps do not become systemic until later in the unfolding of the universe.[2] The earliest notations begin perfectly smooth because it starts with the most simple geometries that tile and tessellate this universe perfectly.[3]

II. Time: The first minute, first second, and first zeptosecond. The first minute of the universe is within Notations 149-150.[4] The first second is between Notation 143-and-144. Zeptoseconds (1×10-21) are between Notation 65-and-67. And, Notations 1-64 are opened for definition!

Eminent scholars, Sean Carroll [5] of John Hopkins and James Peebles [6] of Princeton (Nobel laureate, 2019, and a pioneer of cosmic microwave background radiation research) articulate the importance of defining the first minute of the universe. In June 2020 twenty-seven scholars wrote “The First Three Seconds: A Review of Possible Expansion Histories of the Early Universe” (arXiv:2006.16182 []). It focused on emergence, yet they were unable to define the first minutes of our universe.

The zeptosecond is on the cusp of quantum fluctuations. The first notations begin with the natural units that were defined by Max Planck in 1899 [7] and George Johnstone Stoney [8] in 1874. It is a natural grid. As each notation builds on the prior notations, the geometries, numbers and relations necessarily redefine the nature of time.[9] Those first 64 notations have been unwittingly defined by experts within Langlands programs, string theory, and like disciplines [10], but big bang cosmology hides any access to those first notations.

III. Quantum fluctuations and quantum physics. The study of a geometry of quantum fluctuations over the years has been limited.[11] A most-simple place to start is to recognize the tetrahedral gap that Aristotle did not see.[12] That gap is real. And, there are others that are ignored. Add to it our octahedral gap and then the icosahedral gaps.[13] Here are possibilities for fluctuations. Big bang cosmology has no simple geometry and certainly no geometry for chaos and indeterminacy. Our mathematically-integrated view of the Universe begins with the inherent geometries of doublings that perfectly tile and tessellate; plus, it has a geometry for fluctuations that is inherently indeterminant. One of our primary studies is to grasp the varieties of gaps and the probabilities for each manifestation within a given notation.

IV. A natural inflation and dark energy and dark matter. Dark matter and dark energy are below all possible thresholds of direct measurement. The indirect effects have been well-regarded since the work of Lord Kelvin (1884), Jacobus Kapteyn (1922), Jan Oort (1932) and Fritz Zwicky (1933). That mystery prevails.[14] Big bang cosmology blocks the view of both the geometries of perfection and of imperfection. Initially there are no gaps as spacetime is dynamically created. Within this mathematically-integrated view of the Universe, a natural inflation starts with the most simple infinitesimal sphere, sphere stacking, and cubic-close packing of equal spheres. Tetrahedrons and octahedrons naturally and smoothly tile and tessellate the earliest universe.

If taken as a given that one infinitesimal sphere is generated per unit of length and time, the rate would range from 539-to-4609 tredecillion spheres per second.[15] Of course, that range is established by Planck Time and Stoney Time.

V. Finite-infinite, quantitative-qualitative. Big bang cosmology has no finite-infinite relation and makes no distinction between the quantitative and the qualitative. It does not posit the smallest physical unit of spacetime. It makes no statements about pi (π), nor recognizes the essential faces of pi (π): continuity (ordering), symmetry (relating) and harmony (making dynamic).[16] Naturally, the ubiquitous dimensionless constant that generates the natural units for Planck and Stoney is pi (π). We hypothesize that these three faces of pi (π) define the qualitative and the infinite. Within big bang cosmology the Planck Epoch and a singularity are the baseline whereas within our mathematically-integrated view of the Universe, it is the simple perfections of the infinitesimal sphere, then spheres, and then tetrahedrons and octahedrons.

Thank you. -BEC


Endnotes & Footnotes
Most of these points, already have pages within this website, are linked from here.

[*] 202 predictive, base-2 notations. Initiated in 2011, this chart drives this model.

[†] Simple concepts: Spheres, tetrahedrons, octahedrons and doublings. This project began in 2011 in a New Orleans high school geometry class. Here’s an early assessment. Rather surprisingly, it readily absorbs big bang cosmology ( ).

[1] Smooth to lumpy. An early article, The Lumpy Universe, by a group within NASA’s Goddard Space Flight Center is written for students from 14 years old and up. The Imagine Team is an effort headed by Dr. Barbara Mattson and the segment, Imagine the Universe, addresses the current concerns within cosmology and astrophysics. It raises those issues that are pushing the scientific-academic community to re-imagine big bang cosmology.

Embedded links (URL):
Project Leader:

[2] Systemic gaps and fluctuations. Too dense and too fast to accommodate fluctuations, it is hypothesized that quantum fluctuations do not initially manifest until much later than the first minute which is within Notation-144. It is also hypothesized that these gaps, once systemic, will work back into prior notations and are currently at least within Notation-67. Further, it is hypothesized that there is also a geometry of gaps for consciousness and the mind.

[3] Tile and tessellate this universe with no gaps. Throughout mathematical and geometric history, tilings and tessellations have challenged the human mind. Kepler was the first to make it a systematic study (Harmonices Mundi). The simplest 3D tessellation is with the tetrahedron and octahedron. Within this model it shapes the first instant of the universe resulting first in a sphere, then a systematic expansion of spheres (see #15 below), sphere stacking, and then what is known as close-cubic packing of equal spheres. Here is the starting point within Notation-0.

[4] Notations 1-202: This chart of 202 notations began in 2011. It became a horizontally-scrolled chart in 2016. It may take several generations to fill out even the first level of notations. It may well take many more generations to tie all the notations together in a dynamic unit. Notwithstanding, elementary school children can (and have) effectively engaged the chart to see the order within our universe.

[5] Sean Carroll. He is listed among the scholars to whom we turn for insight and help. Based on the videos we have watched and from his writings, we readily speculate that Sean is a bit like Steven Weinberg. When Weinberg got impatient with a person with whom he disagreed, he would say, “Utter nonsense.” I suspect the response from Sean Carroll would be similar. Yet, we’ll continue to write to him!

[6] James Peebles. Of course, most Nobel laureates are swamped with correspondence. There are just too many people hoping to grab their attention. James Peebles is older now and still very active looking at astronomical phenomena that are “off the beaten track.” In that light, our strategy has been to catch him by surprise in hopes that he might rethink the concepts of space-time-and-infinity with us.

[7] Max Planck. There are current challenges to Max Planck’s base units yet the results of those challenges are still being evaluated. We are following the work of John Ralston, Espen Gaarder Haug, and Tim Palmer as each impacts our thinking about the Planck constant, the Planck base units, and the dimensionless constants.

[8] George Johnstone Stoney. Not many people pay attention to the scholarly work of Stoney. We do because we have been encouraging a deep review of all this work and the ISOCODATANPLNIST standards for all the units involved.

[9] Redefining Time. The most disconcerting notion to emerge from this work is to discover that in some manner of speaking all time is now. Although physicists like Carlo Rovelli, Max Tegmark, and Julian Barbour, claim time is an illusion, within the 202 notations linear time is associated with just that period of time experienced prior to sleep (when it is recompile into the whole). We say that time is exponential; time is an equation and all notations are always active.

[10] Langlands programs, string theory, and like disciplines. There are no less than nine disciplines currently, yet unwittingly, addressing these first 64 notations. None of their scholars has formally recognized the 202 notations and none are formally on the grid. They are further linked here: Langlands programs, string theory (including M-Theory, F-theory, type II and its offshoots), supersymmetry (SUSY), loop quantum gravity (LQG), causal dynamical triangulation (CDT), causal set theory(CST), field theories (QFT, CFT, LFT), spectral standard model (SSM), hypothetical particles, and a few more.

[11] Quantum fluctuations. A search on the words, “geometry of quantum fluctuations,” renders just ten results on October 5, 2022. There has been no geometry of fluctuations based on simple geometries of gaps. Our page, geometries, is our announcement of our intention to pursue this domain of study beginning with the geometries of gaps within the most simple structures.

[12] Aristotle’s blindspot. This history serves to remind us to be somewhat reserved about our conclusions. Life is short, but our words may well live on. Aristotle’s arrogance is all of us. Aristotle’s mistake is profoundly all of us.

[13] Gaps. The initial study of the five-octahedral gap was part of the /geometries/ efforts in May 2022 when we announced our intention to pursue this domain of study. We were even able to create a model of what we believe is the first five-octahedral gap — — that then coupled with the tetrahedral gaps — — becomes a new object — — which has been tentatively named, triantahedron, for a thirty-sided object. We’ll see if it works.

[14] Historical figures who first recognized dark energy-dark matter. Thousands of scholars have subsequently tried to explain the dark energy and dark matter. The big bang hides people’s access to answers. To say that it is the abundance of infinitesimal spheres below the boundaries of measurement is just an introductory overview and a direction for a more complete answer.

[15] 539-to-4609 tredecillion spheres per second. When I surveyed the initial formula in September 2021, it seemed simple and logical enough. Yet, to begin to imagine the emergence of 539 tredecillion spheres per second is simply beyond my grasp. This is the opening of a new domain of study. The range is a placeholder for more refined figures to come.

[16] Continuity-symmetry-harmony. The heart of this study began with simple geometries but backed into the infinitesimal sphere by backing into the very nature of pi (π) and finding the three faces of a perfected state in spacetime, continuity, symmetry, and harmony, all deeply inherent within pi. This is our essential story and it will be told and retold many more times to come.


References & Resources
As these references are studied, key references and resources will be added.

Reason to believe by Rod Stewart, Lyrics by Tim Hardin

If I listened long enough to you
I’d find a way to believe that it’s all true
Knowing that you lied straight-faced while I cried
Still, I look to find a reason to believe

Someone like you makes it hard to live without
Somebody else
Someone like you makes it easy to give
Never think about myself

If I gave you time to change my mind
I’d try to leave all the past behind
Knowing that you lied straight-faced while I cried
Still, I look to find a reason to believe

Please note: These are all the lyrics;
two paragraphs repeat. Life is fair;
it breaks everyone’s heart be it with
love or beliefs (ideas and concepts).

Diego Rapoport, The Geometry of Quantum Fluctuations II (Quantum Gravity and Ergodicity), in “Proceedings of the International Workshops on the Frontiers of Mathematics, Physics and Biology”, Monteroduni, Italy, August 1995 vol. 2, G. Tsagas (ed.), Hadronic Press and Ukraine Academy of Sciences, 1996

Two Questions:
(1) Is the smoothness of the JWST’s earliest universe a cause for concern? It seems some are concerned that it cannot be supported by big bang cosmology. Sean Carroll says, “…dark energy made the universe smooth out and accelerate, but it didn’t stick around for long.”
(2) Is the Guth-defined inflation cause for concern? Most of the old guard like ‘t Hooft, seem fine with the one-time exception that inflation was an expansion of space itself so extralogical assumptions apply.


This is a representative selection of our notes to scholars asking about the substance of this article.


There will also be many instant messages to thought leaders about the general thrust of this article.

10:08 AM · Oct 21, 2022 @FreelanceAstro @NYTimes @BBC @NPR @SciAm @QuantaMagazine @Undarkmag My note to you is really to all people who are exploring the edges of knowledge and our understanding. Isn’t simple better than complex?

1:35 PM · Oct 20, 2022 @GeraldoRivera @KellyannePolls @IvankaTrump Come on, Geraldo. You don’t have to incite folks with words like jingoism. You’re bigger than that. Little worldviews get little people saying little things. Get an integrated view of the universe. Be a leader:

2:04 PM · Oct 14, 2022 @GoryErika It will take a bold journalist to explore the “new physics” coming back with the images of smoothness from the James Webb Space Telescope. It is too radical for most: (Perhaps “after the big bang” will get redefined).

3:37 PM · Oct 9, 2022 @kanyewest The big bang theory (BBT) is coming down. It’s on a smooth decent on the JWST – James Webb Space Telescope – and within the deep continuity, symmetry and harmony of the universe. A BBT alternative working model is here: Give a shout for more. -BEC

8:43 AM · Oct 8, 2022 @NatashaBertrand Biden needs a new model of who he is and why he is. “The Biden Family” is not a model. A mathematically-integrated view of the universe is. Base-2 exponentiation (doublings) starting at the Planck base units is: is a simple start. All continuity equations!

Editor’s note: Continuity is the first principle of order. The second is symmetry whereby a relation is created. The third is harmony, where there are multiple symmetries within a dynamic moment. We need all three, but continuity will at least get us on a level playing field.



You are always invited.


Keys to this page, reason

• This page became the homepage on October 8, 2022. It is still under construction.
• The last update was October 17, 2022.
• This page was initiated on October 4, 2022.
• The URL for this file is
• The headline: Reason to believe (lyrics by Tim Hardin, sung by Rod Stewart).
• First byline: Anything that comes “after the big bang” will be damaged.
• Next byline: Smoothness, the first minute, fluctuations, dark energy-matter, finite-infinite….


Just as an aside, it appears that the adoption cycles of a major idea require no less than three generations and quantum theory is no exception. New theories have new truths but are not absolute truth and not “all truth for all time.”