In 1927 Georges Lemaître wrote that the universe started cold.




On June 29, 2020, twenty-seven scholars from around the world 1 released a rather provocative article, “The.First Three Seconds: A Review of Possible Expansion Histories of the Early Universe.” To respond to it, I have written this Open Letter to suggest a series of open questions. Real answers just might add to their possible expansion history. They readily admit in their article, “…there remains a gap in our understanding of cosmic history – a gap that spans the first few seconds.” Note: Well over two-thirds of the notations that define our universe occur within three seconds! So, yes, we have a lot to learn about that gap. There are 145 base-2 notations that define the gap from the Planck base units. Inviting Lemaître to answer, our first key question: Is it a hot or cold start?

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 this 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 Harriot and 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; at that moment in time, it was 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 — — 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. Every bit and byte 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

(Please note: Many links that follow will open a new window or tab outside of this site.)

* Georges Lemaître. I was surprised to learn that in Lemaître’s first theory (1927); the universe starts cold. Harvard scholars David Layzer and Anthony Aguirre have studied this concept, yet it appears that nobody has found Lemaître’s explanation for why he allowed his theory to change from starting cold to starting hot (yet perhaps not quite as infinitely hot as Stephen Hawking suggested). Who convinced him to go from cold to hot? What is the best concept? If you have been on this site for any time, you know that we worked with the concept that the universe started very cold. More

Big Bang Mythopoetics: See Weinberg’s The First Three Minutes. In Chapter 4: “Recipe for a Hot Start” (Basic Books, 1977, pp 77-99) Weinberg makes his highly-informed, educated guess about the big bang, both conceptually and historically. Inflation is still enigmatic. Cooling is problematic. And, the simplicity that he touts in his 1979 Nobel lecture is non-existent in his review of his “hot start” of the universe. An alternative view (of a high school teacher) finds the conditions for nucleosynthesis at the temperature of 109 degrees Kelvin is approximated in and around our Notation-137. That’s less than a second from the first moment. We need help to examine these numbers in light of the Quark-Gluon Plasma (QGP), aka quark soup, the Cosmic Microwave Background (CMB) radiation and isospin.

Weinberg had never seen a base-2 progression from the Planck units; and given his history, he would have immediately written it off as bit of silliness and crackpottery. It may well be, but I obviously don’t think so. However, I will remain open to learn why it is a bit of nonsense unless, of course, one of our scholars tells us, “It’s worth looking into.”

Notations. The first 64 notations out of 202 have received very-very limited analysis and it would seem only within this website to date. The first measurement of a length appears within Notation-67. Some might argue Notation-64, however, these are derivative numbers from ratio analyses, not an actual measurement per se. Notation-84 is currently the smallest measurement of a unit of time. The first three seconds appears within Notation-145. 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. The first million years is within Notation-189. Large-scale structure formation, 150 million to 300 million years, is within Notations 196-to-197.

Review. Notation-0 is the Planck units and Notation-202 is the current notation defining the current time and expansion. Planck’s calculation for temperature is still enigmatic and appears to have only a derivative role. Our mathematical model of the universe begins to capture the big bang at 1.8751×109 Kelvin (Notation-127) and surely within Notation-36 at 1.9201×1012 Kelvin. The universe is less than one-hundreth of second from its start and may have a diameter of 1750 miles. A natural inflation is generated by light, the Planck charge, and the mix of dimensionless constants. A natural symmetry is created within Notation-1 to Notation-201 because although “complete” they are still dynamic and “pushing up” Notation-202 where the very first sphere is possibly at the point of the current expansion.

So now this investigation continues. We will create a new page just for the viewpoints of the 27 co-authors of the article in question! We’ll have many questions for each!


[1] The authors of the ArXiv article, The First Three Seconds. These scholars come from the USA, UK, Sweden, Spain, Poland, Japan, India, Finland, France, Estonia, Columbia, China, and Bulgaria. They write about the possible expansion from within the first three seconds of the universe. Many of these authors are also representing their birth country. They came to study and stayed! Some countries are still being added. The scholars are:  1).Rouzbeh.Allahverdi,  2).Mustafa.Amin, 3).Asher.Berlin,  4).Nicolás.Bernal, 5) Christian T. Byrnes, 6) M. Sten Delos, 7).Adrienne.L..Erickcek, 8).Miguel.Escudero,  9).Daniel.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.Smith, 23) Tomo Takahashi, 24) Tommi Tenkanen, 25).James.Unwin, 26).Ville.Vaskonen, and 27).Scott.Watson  That prior link (six lines) goes to a page of affiliations with links to their working pages.

[2] The First Three Minutes. While working on a project at MIT back in 1979, I had a chance to visit with Steven Weinberg in his Lyman Lab office at Harvard. We talked about his book. Just recently, 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 living in the greater Austin area, home of the University of Texas (UT). In 1983 Steven Weinberg had moved his laboratory to UT, in part to work more closely with his mentor, John Wheeler.

Although I did not meet Weinberg again in Austin, I did call and I sent a few notes to re-introduce myself 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. We stop working on it with the high school students. I didn’t want them to be tainted by it in college! So, now, it just gets moved along here.

[4] Big Bang Cosmology. In the earliest stages of our work between 2011 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. With no real response, even in 2016, Hawking was reminding us on public television, “The answer, as most people can tell you, is the big bang…”

Many highly-recognized scholars (foremost among them, Neil Turok) have written excellent articles about the weaknesses of the theory. Even with Turok’s background, he didn’t change the beliefs of those who had committed so much time and energy to that infinitely-hot start.. Big bang cosmology just continued to dominate as it does even today. Finding it all quite perplexing, I decided that the big bang would continue to dominate because a viable alternative had 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 open this page: At Notation 0, the chart begins with Max Planck’s 1899 base units. These calculations 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. Yet, by 2001 the entrenchment of the big bang cosmology was further abetted by a hit television series. Most everybody was sure the big bang held all answers. Many scholars weren’t as convinced. Their work just didn’t fit well within that model.

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. We all recognize that the size of the neutrino is so small, we are all bombarded every day by billions and, of course, never thought about it. The infinitesimal sphere at Notation-0, when compared to the neutrino, is like the size of the atom compared to

As a result, I began a more formal study of spheres. I also began analyzing the many questions and a few answers about dark matter and dark energy.

[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 in our time by Thomas Hales and Maryna Viazovska.

[8] Cubic-close packing of equal spheres. Basic geometries, and basic mathematical functions, and the 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 geometry and physics.  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 stay 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 for more study:

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)

4. The Nature of Light: What is a Photon? edited by Chandra Roychoudhuri, A.F. Kracklauer, Kathy Creath

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.”  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 

9. Mythopoetic imagination as a source of critique and reconstruction: alternative storylines about our place in cosmos, Heikki Patomäki, Journal of Big History, III(4); 77 – 97. DOI

10. Freese, Katherine (2017) [1988]. “Status of dark matter in the universe”. The Fourteenth Marcel Grossmann Meeting. pp. 325–355. arXiv:1701.01840. doi:10.1142/9789813226609_0018. ISBN978-9813226593

11. Dark Matter, Jaan Einasto, ArXiv, 2010 (PDF)

12. Do electrons have third component of isospin? (Physics Stack Exchange 2017) John Wheeler is known to have said, “Only when we recognize how strange the universe is will we understand how simple it is.”



All 27 co-authors cited above received a personal email about this page. The first group included Rouzbeh Allahverdi, Mustafa A. Amin, Asher Berlin, Nicolás Bernal, Christian T. Byrnes, M. Sten Delos, Adrienne L. Erickcek and Miguel Escudero Abenza. Those emails became the basis for this “Open Letter.”

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

Monday, 17 August 2020: Another email to those cited just above and to  Daniel.G. Figueroa, Tomohiro.Harada, Dan Hooper, and Tanvi Karwal.

Tuesday, 18 August 2020: Finally, a  somewhat personal email went out to the rest of the co-authors: Kazunori Kohri,  Gordan Krnjaic, Marek Lewicki, KaloianLozanov, Vivian Poulin,  Kuver Sinha, Tristan Smith, Tomo Takahashi, Tommi Tenkanen, James Unwin,  Ville Vaskonen, and Scott Watson.  It went something like this: “Dear (Dr/Prof/ Name): Earlier this month I began working through your collective work with 26 others, The First Three Seconds; it is quite a look from so many perspectives. It seems that the definitive insights for the first three seconds will be discussed into eternity. I posted an entirely idiosyncratic “Open Letter” to you and your co-authors.

“As of today, it includes two direct references and links to you and your work:

“If you would like me to add or delete anything, I will gladly accommodate.

“A few years ago I was disappointed to read that Max Planck said, A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather… science advances one funeral at a time My hope is with the young. I’m 73. Notwithstanding, I don’t think Max Planck’s pessimism is well-placed. I think all of us can always be learning something new, even profound. And, I think we all have a ways to go before we sleep!

“I know what I have written is a stretch, yet I have also learned that even Hawking, Ellis, Guth, Linde… and thousands more, make many educated guesses. This base-2 concept just opens their time frame for the first three seconds so it becomes a mathematical domain with plenty of “room” to experiment with ideas. In the first three epochs of the big bang, not quite to the first second of the expansion of the universe, 143rd notations are created. So much is already happening, then this base-2 model readily begins to integrate all the following epochs of big bang cosmology, but not as epochs that start and finish, but as processes that go on forever. The first three epochs of big bang cosmology are within the first nanosecond and they appear to be, as Neil Turok says, perpetual processes.

“Again, let me thank you for your scholarship! I certainly wish you the best as you forge ahead!

“Most sincerely, Bruce PS. I continue to struggle with these issues within every new top-level post a/k/a homepage, which will remain the top-post for just a month, a week or sometimes, just for a day:”



7 August 2020, Vatican Observatory Foundation:
Dear friends,

I have looked at the work of David Layzer and Anthony Aguirre 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


Contact us with your comments and questions:


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: Saturday, October 8, 2022

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

Open Questions (Preserve):

What is happening at each doubling prior to particle physics which is between Notation-67 (first measurable unit of Length) and Notation-80 (first measurable unit of Time)?

In what ways does each notation change with the addition of the next notation?