In 1927 Prof. Dr. Georges Lemaître wrote that the universe started cold.


By Bruce Camber  Prior Homepage  Related Homepages: The First Three  References | Emails| Tweets


On June 29, 2020, a group of scholars from around the world 1 released a provocative article entitled, “The.First Three Seconds: A Review of Possible Expansion Histories of the Early Universe.”
In response to it, I have written this open letter to suggest another possibility for their “possible expansion” history. They say, “…there remains a gap in our understanding of cosmic history – a gap that spans the first few seconds.”

Open Letter:

To all 27 contributing authors:

And, to all scholars and budding scholars especially among the astrophysics community who affirm the basic foundations of the book, The First Three Minutes 2 by Steven Weinberg.3 (Basic Books, 1977) and to all who affirm the infinitely-hot big bang concept: 4

I have simple questions about your work to grasp the first few seconds:

• Is there a possible continuum from the Planck base units to the current time and size of the universe? We naively defined such a thing by applying base-2 or doublings to the Planck units to emerge with that chart of 202 notations.5

• Is an infinitesimal sphere the first manifestation of the Planck units and light (and other probable dimensionless constants) whereby continuity (never-ending, never repeating numbers), symmetry, and harmony manifest? Is this hypostatization a key finite-infinite relation? Here, two vertices and the never-ending, never-repeating numbers, create perfect circles and spheres. It’s a very simple idea.6

• Is sphere stacking a fundamental action of the universe starting with the Planck base units? When we engage all the work around sphere stacking since Kepler, it seems obvious that an answer is worth pursuing.7

• Is cubic-close packing of equal spheres a fundamental action for the expansion of the universe? Studying how it opens up the Fourier transform and Euclidean geometries, again it seems obvious that the question is worth pursuing.8

2011, high school geometry class 9 We chased the interiority of the tetrahedron (with its four “half-sized” tetrahedrons in each corner and the octahedron in the middle). Inside that octahedron are six “half-sized” octahedrons in each corner and eight tetrahedrons, one in each face. Additionally, the octahedron has four hexagonal plates, everything shares a common centerpoint, and there are also multiple  square and triangular tilings and tessellations. We went all the way down to the Planck Length in just 112 steps; and then, when we multiplied by 2 the next day, we were out to the size and age of the universe in approximately 90 steps.

There are a total of 202 notations, doublings or steps from Planck Time to this day.

It took me three years to realize that a base-2 expansion had not already been done. Of course, in 1957 in his Dutch high school Kees Boeke did a base-10 chart.10 Our base-2 model is a bit more granular and more natural, and it has a geometry, the Planck base units, dimensionless constants, spheres, sphere stacking, and cubic-close packing.

We have asked many scholars — 11 — about our chart. It is too idiosyncratic for most. Yet, it easily absorbs big bang cosmology and opens the first three seconds within 145 successive doublings starting with the Planck Length, Planck Time, Planck Mass and Planck Charge. For mathematicians those 145 doublings are a veritable playground to begin to define the structures of the earliest universe.
1. Perhaps you know of a scholar who might engage these numbers.
2. Perhaps you are that scholar.
3. If not, perhaps you can explain these numbers in a more compelling way than I have.

Thank you.
Bruce E. Camber

PS. Your article has become a basic challenge for me. All of your data must fit into our charts, somewhere, somehow and at some time. While working on other articles, I’ll continue to update this article by trying to incorporate your data while insisting that it works within the simple logic-and-flow of the base-2 numbers. Although that work will become another article, it will also be integrated within this article and with these key two charts: and  Thank you. -BEC

Endnotes and Footnotes

* Georges Lemaître. I was surprised to learn that in Lemaître’s first theory (1927) the universe started cold. Scholars like David Layzer and Anthony Aguirre have studied this fact, yet nobody has found Lemaître’s explanation for why he allowed his theory to change from starting cold to starting hot (yet perhaps not quite infinitely hot as Stephen Hawking suggested). Who convinced him to go from cold to hot? Is it the best concept? -BEC

Steven Weinberg may be able to help us.  In Chapter 4 of his book, The First Three Minutes, pages 77-100, Recipe for a Hot Universe, he begins his examination. Then on page 123, he suggests nucleosynthesis begins at the temperature of 109 degrees Kelvin.  Looking at our chart, that would be in the range Notations 126-to-128. The first second is within Notation-143. The first three minutes is within Notation-151.

Notations. The first 64 notations have received the most limited analysis and only within this website. The first year is between Notations 168-and-169. The first 1000 years — 31,556,952 seconds in a year and 31,556,952,000 seconds in a millennium is between Notations 178-and-179. Large-scale structure formation, 150 million to 300 million years, is within Notations 196-to-197.

Of course, Notation-0 is the Planck units and Notation-202 is the current notation defining the current time and expansion.

Planck’s calculation known as Planck Temperature does not seem to have a role.  Now we’ll continue this investigation from the viewpoint of the 27 co-authors of the article in question!


[1] The authors of the ArXiv article, The First Three Seconds. From the USA, UK, Sweden, Spain, Poland, Japan, Finland, France, Estonia, and Columbia, these folks write about the possible expansion of our earliest history of the very-early universe. The authors are:  1) Rouzbeh Allahverdi,  2).Mustafa.A..Amin, 3).Asher.Berlin,  4).Nicolás.Bernal, 5) Christian T. Byrnes, 6) M. Sten Delos, 7).Adrienne.L..Erickcek, 8)_Miguel_Escudero,  9).Daniel.G. .Figueroa, 10) Katherine Freese, 12).Tomohiro.Harada, 13).Dan.Hooper, 14) David I. Kaiser, 15).Tanvi Karwal, 16).Kazunori Kohri, 17).Gordan.Krnjaic, 18).Marek.Lewicki, 19) Kaloian D. Lozanov, 20).Vivian.Poulin, 21) Kuver Sinha, 22).Tristan.L..Smith, 23) Tomo Takahashi, 24) Tommi Tenkanen, 25).James.Unwin, 26).Ville.Vaskonen, and 27).Scott.Watson  (that link goes to a page of affiliations).

[2] The First Three Minutes. Back in 1979, I had a chance to talk with Steven Weinberg at Harvard about his book. In 2018, I wrote up this little summary about it. The article by these 27 scholars (PDF) is in light of Weinberg’s book. Their engagement of the “possible history” is from within big bang cosmology.

[3] Steven Weinberg. In 2018, I ended up in the greater Austin area, home of the University of Texas and the laboratory of Steven Weinberg. Forty years later, we did not meet again, but I did call and sent a few notes to re-introduce myself. I was hoping to find somebody in his group who could tell me why our logic was so wrong. I had finally realized that our model was profoundly idiosyncratic. I had stopped working on it with the high school students. We didn’t want them tainted by it in college! So, now, it just gets carried along here.

[4] Big Bang Cosmology. In the earliest stages of our work between 2012 and 2016, we very naively wrote to Stephen Hawking and Alan Guth (MIT) and other thought leaders who were advocating an infinitely-hot big bang. No real response. Even in 2016, Hawking was reminding us on public television, “The answer, as most people can tell you…”

Many highly-recognized scholars (foremost among them, Neil Turok) have written excellent articles about the weaknesses of the theory; that didn’t change the beliefs of those who had committed so much time and energy to it. Big bang cosmology just continued to dominate as it does even today. Personally, I had been quite perplexed. I decided that the big bang would continues to dominate because a viable alternative has not been affirmed. Understandably, an alternative from a high school geometry class is not acceptable. Yet, it seems to me, over these years, our simple, natural inflation described within our 2016 horizontally-scrolled chart just makes more sense.

[5] Our Chart of the Universe in 202 doublingsPlease go to Max Planck’s 1899 base units were largely ignored within academia until 2001 when Frank Wilczek wrote his three articles in Physics Today touting their place among the parameters we use to define the universe. Also, by 2001 the entrenchment of the big bang cosmology was further abetted by a hit television series.

I say, “Eventually, we will all get over this period in our history!”

[6] Circles, spheres, rotations, intervals, and more. There are no less than 64 notations before the first manifestations of particles. Notation-64 begins at 2.98×10-16 meters. It is a given that these Planck numbers define something with length, time, mass and charge. It appears from here that the most simple, basic thing that could define Notation-0 is an infinitesimal sphere.

As a result, we have begun a more formal study of spheres.

[7] Sphere Stacking. Can something so simple as sphere stacking be a key operation within this universe? Please visit our earlier pages about sphere stacking. There is so much important work within the domain that has been done by Thomas Hales and Maryna Viazovska.

[8] Cubic-close packing of equal spheres. Basic geometries and basic mathematical function, and most basic physics all get brought into the equations for beginning of this universe. Everything, everywhere for all time becomes highly ordered. Please visit our early pages — — where it is quite obvious Euclidean geometries and the Fourier transform come alive.

[9] High school physics and geometry.  Even within the very first page (2012) of this website we had begun questioning the need for an infinitely hot beginning. Of course, we were aware of Planck Temperature, but it seemed to be a derivative calculation and perhaps those kinds of calculations are always set at the top of the chart.  Also, it seemed that each notation was building on the prior notations and each needed those prior notations to be active. That called into question the very nature of time. Also, it was great fun to think that what we were learning in geometry about tetrahedrons and octahedrons (and in physics about the Fourier transform) had an immediate application within the start of the universe.

[10] Kees Boeke’s base-10 chart. Back in the early 1970s, I was working with MIT physicist, Phil Morrison, on a proposed budget for the Pentagon. We met in his home and on his coffee table was his book, The Powers of Ten. Both his book and related film, sponsored by IBM, were based on Kees Boeke’s little book, Cosmic View: The Universe in 40 Jumps. I was still active with a New York City group that actively proposed new concepts that could impact the quality of our life and an educational think-tank in Harvard Square (Cambridge) that focused on conceptual breakthroughs and paradigm shifts. Here, basic concepts were being shaped as first principles and theories.

[11] Asking Scholars Simple Questions. Though there are many groups of people, only notes to the most visible scholars are currently displayed — — and each listing opens a page of references to each scholar’s work as well as my notes, emails, and tweets. As this website moves forward, it will begin to include all the scholars who are listed as authors of a given paper.

References & Resources:

1. Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation”,  The Astrophysical Journal Supplement Series; Komatsu, E.; Smith, K. M.; Dunkley, J.; Bennett, C. L.; Gold, B.; Hinshaw, G.; Jarosik, N.; Larson, D.; Nolta, M. R.; Page, L.; Spergel, D. N.; Halpern, M.; Hill, R. S.; Kogut, A.; Limon, M.; Meyer, S. S.; Odegard, N.; Tucker, G. S.; Weiland, J. L.; Wollack, E.; Wright, E. L. (1 February 2011). 192 (2): 18. arXiv:1001.4538. Bibcode:2011ApJS..192…18K. doi:10.1088/0067-0049/192/2/18.

2a. A new type of isotropic cosmological models without singularity, A.A. Starobinsky, Physics Letters B, Volume 91, Issue 1, 24 March 1980, Pages 99-102  See footnotes. Screen Shot 2020-08-11 at 8.14.29 AM2b. Exploring cosmic origins with CORE: Survey requirements and mission design, 2018
2c. A.A. Starobinsky Resource page on this website

3. Emilio_Panarella, “Wave-particle duality” Proceedings Volume 5866, The Nature of Light: What Is a Photon?; (2005)


5. “There are theoretical motivations to consider physics beyond ΛCDM, such as the unknown nature of inflation, dark matter (DM), dark energy, and mechanisms to explain neutrino masses.”  Also, see: Beyond ΛCDM: Problems, solutions, and the road ahead (2016) and others.

6. Zeta function regularization, the multiplicative anomaly and the Wodzicki residue, E. Elizalde, L. Vanzo, S. Zerbini, ArXiv, January 1997  Email to Emilio Elizade on July 2020

7. The emergence of background geometry from quantum fluctuations, J. Ambjørn R. Janik, W. Westra, S. Zohren, Physics Letters B, Volume 641, Issue 1, 28 September 2006, pp 94-98

8. Inflation and String Cosmology, Andre Linde, July 20, 2001 



All 27 co-authors cited above will receive a personal email about this page. To date, Rouzbeh Allahverdi, Mustafa A. Amin, Asher Berlin, Nicolás Bernal, Christian T. Byrnes, M. Sten Delos, Adrienne L. Erickcek and Miguel Escudero Abenza have received an early version of the above note as an email.

August 11, 2020: Email to A.A. Starobinsky More…



7 August 2020, Vatican Observatory Foundation:  Dear friends, I have looked at David Layzer and Anthony Aguirre‘s work and there is now a Wikipedia entry, “Cold-big bang.” Could Lemaître’s super “primeval atom” actually be the most primitive of spheres? I have started to develop an answer online here:  Your comments would be most appreciated. Thank you. Warmly, -Bruce


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Key Dates for Open-Envelope

This article was initiated on Sunday, August 2, 2020.
The first time Open-Envelope was a homepage or top-level posting: August 2, 2020.
Last update: Wednesday, August 12, 2020

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The initial tagline: Open this envelope – There is a universe inside./