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


By Bruce Camber  Prior Homepage  Related Homepages: The First Three  Dark Matter & Energy


On June 29, 2020, a group of scholars from around the world 1 wrote a definitive article entitled, “The First Three Seconds: A Review of Possible Expansion Histories of the Early Universe.” To respond to it, this open letter suggests another possibility for their “possible expansion” history.

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 simple.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  square 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, 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 two charts: and  -BEC

Endnotes and Footnotes

* Georges Lemaître. I was surprised to learn that Lemaître’s first theory in 1927 had the universe starting 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 (yet perhaps not quite infinitely hot as Stephen Hawking suggested). Who convinced him to go from cold to hot? Is it the best concept?

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

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. About the possible expansion of our history of the 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.

[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 entirely from the point of view of 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. 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 how idiosyncratic our model is so I stopped working on it with the high school students. We didn’t want our students to be tainted by it in college! So, now, it gets carried along just here on the web.

[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. In 2016, Hawking was reminding us on public television.

Many highly-recognized scholars (foremost among them, Neil Turok) have written excellent articles about the weaknesses of the theory; they 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 have been quite perplexed. I decided that it 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 The Planck 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. 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, herein begins our 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. What’s not to love about it? Everything, everywhere for all time becomes coherent. It is too sweet. 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.

[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.

More to come on Thursday, August 6, 2020…



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 5, 2020

The Prior Homepage:
The URL for this page:
The initial tagline: Open this envelope – There is a universe inside.