International Advisory Committee

1. G. Ross (Oxford)

2. C. Savoy (Saclay)

3. G. Senjanovic (ICTP, Trieste)

4. F. Zwirner (Padua)

5. I. Antoniadis (Ecole Polytechnique)

6. M. Hirsch

7. R. Barbieri (Pisa)

8. J. Ellis (King’s College London and CERN)

9. H. P. Nilles (Bonn)

10. S. Pokorski (Warsaw)

11. M. Quiros (Barcelona)

Local Organizing Committee

  • O. Vives
  • S. Pastor
  • J.W.F. Valle
  • F. Botella
  • O. Vives
  • V. Mitsou

Big Bang versus Quiet Expansion:

Left Yellow Arrow
Right Yellow Arrow

Pages: Agree | Gravity| Hope | Hypostasis Mistakes | PI (π) | Questions | Sphere | STEM | Up

Logic and simple math open new paths to explore
Let Us Collaborate and Compare
Big bang theories have too many loose ends.
by Bruce E. Camber

Abstract: Big bang theories (BBT) start with a uniquely-unique singularity[*] that seems well-beyond human grasp. The BBT’s first minute is guesswork and extralogic. The Quiet Expansion starts with simple geometries of infinitesimal, scale-invariant spheres that generate tetrahedrons and octahedrons that are readily understood by primary school students. Big bang theories incorrectly explain the basis for various conditions of our universe today that obfuscate new research and discovery. The Quiet Expansion has a well-defined logic and mathematics to explain those same conditions. Plus, the big bang theories cannot address several open issues. The Quiet Expansion does. It has foundations to examine and begin to explain some of the most troubling issues within science today, i.e. dark energy and dark matter, Planck scale physics, quantum fluctuations, the cosmological constant, and the bridge between quantum gravity and relativity theory. It also recognizes an expanded role of pi, perfected states in space-time, all-natural grounds for valuations and ethics, and an always active finite-infinite relation, whereby continuity, symmetry and harmony are the primary functions of pi.[†]

An open, working document
A first draft for collaborations

There are nine key points, five of which are used to ground the big bang theory and four where it falls short. Unfortunately, the BBT concepts that instantiate those first five points actually obfuscate the four points that follow.

Big Bang Theory (BBT)Quiet Expansion (QE)
1. Nucleosynthesis1. Geometries of nucleosynthesis at the Planck scale
2. The abundances of the light elements2. The simple geometries of light elements
3. The CMB (or CMBR)3. The geometries and structure of the CMB
4. Large-scale structure4. Totally hierarchical, on-going, ever-changing
5. Hubble’s law5. Natural inflation and expansion
6. Doesn’t explain initial density perturbations 6. Geometries of quantum gravity density perturbation
7. Doesn’t explain flatness problem7. Pre-fluctuations: perfected states
8. Doesn’t explain horizon problem8. A very different cosmological constant
9. Doesn’t explain monopole problem9. The dynamic nature of finite-infinite equations

The scholar-theorists holding on to big bang theories are unaware of our Quiet Expansion (QE). They have not looked at a base-2 expansion of the Planck base units. They have not fully considered how Planck Time is logically and symbolically the first moment of time. They have not applied base-2 notation to follow it out the 202 doublings to this very moment in time.

I propose that we collaborate and do a few exercises together:
1. Go inside the simple tetrahedron. Observe its internal octahedron and four smaller internal tetrahedrons. This is the configuration in every tetrahedron and octahedron. Now, walk down inside 45 steps. You are in the range of particle physics. Continue to choose a tetrahedron and octahedron to go further inside. Walk back the next 67 steps into Planck-scale physics.

Now, go out by doubling those Planck units, over and over again. In 112 steps you will be back where you started. Continue an additional 90 steps. You will be observing the current expansion of the universe. Inj just 202 base-2 notations (also called doublings), the entire universe is infinitesimal spheres, a network or grid or matrix that encapsulates and interrelates everything, everywhere, for all time. Pythagoras, E.P. Wigner, Max Tegmark and so many others have been right all along — “It is all mathematics.”

2. Ponder Planck-scale physics. What does the first moment of time look like? Length, time, mass, and charge — consider how these units could be a manifestation of a finite-infinite relation whereby the continuity-symmetry-harmony of the sphere is what is manifest, and then manifests as space-time and mass-energy creating our universe as we know it.

3. Review the stacking and packing of spheres. Begin with Kepler-Harriot and cubic-close packing of equal spheres. See how tetrahedrons and octahedrons begin to manifest.

We propose that this is the beginning of an alternative theory, a real foundation that starts with pi, the most-simple geometries, and base-2 notation. This exercise began in our high school geometry classes in December 2011. Early in 2012 we began appealing to scholars, “What does it mean?” By August 3, 2014, we even asked Stephen Hawking. Nobody affirmed our work; yet more importantly, nobody denied it. It wasn’t idiotic; it was unprecedented. It was a new insight. It engaged old concepts in new ways. We studied spheres. We studied pi (π) . We studied Wilczek, Dyson, and Guth. We engaged hundreds of our living scholars about some facet of these problems:
1. Quantum fluctuations
2. Dark matter and dark energy
3. Homogeneous and isotropic
4. Natural inflation

Each year we chipped away at our little sculpture and asked, “How could we be so idiosyncratic and out of line with today’s scholarship?”

We also discovered many scholars who were at odds with the big bang. They were earnest. They were searching for truth. They had emerged with very sophisticated perspectives. When we discovered the 1999 conference at the Isaac Newton Institute of Cambridge University, the core prognosticators, which included Hawking, were challenged to rethink the Big Bang. It had been failing in too many ways. Yes, those deepest within the BBT are well aware of its shortcomings. Yet, no alternative theory has been compelling enough to convince enough of these scholars to abandon the big bang in order to create a concerted movement in a new direction.

It appears that the big bang will de facto remain in place until such an alternative is uncovered.

There may well be other pressures outside of the scholarly community.

Something curious happened over the summer of 2022. One of the leading critics of the BBT, Neil Turok, seems to have reaffirmed the bang! We all will need to be studying this article, The Big Bang As A Mirror: A Solution of the Strong CP Problem (2022). Having said that the universe acts like it is perpetually starting, it will be interesting to see what Latham BoyleMartin Teuscher, and Turok have to say when the strong CP problem is recast within the Quiet Expansion.


Conclusions. Somebody is wrong somewhere. If it is this work, it’ll be easy to say “Mea Culpa” as graciously as possible and to apologize to anyone we have offended. We always have so much to learn.

If we are closer to the truth than the big bang cosmology, It will be difficult for many scholars to admit that our leading scholars have been wrong for so long. It will be a difficult time for many. Yet, it’s important for our cultures to know the truth. Whatever the admission, these models will be constantly re-evaluated and more deeply engaged. One never knows, it may even open confessions in other areas of scholarship.

The big bang theory does not work. It fails the Kantian test; it does not answer the questions, “Where did I come from? Where am I going? What is the meaning and value of life?”

We can do better. We must do better.

Thank you. -BEC

More todayWant to help? Please drop me a quick note! – BEC

Endnotes and Footnotes
These points already have pages within this website.

[*] Singularities. This primary concept in big bang cosmology doesn’t work well. There is dimensionality down to the Planck scale. With this homepage, we will begin immediately reworking our page about singularities. We’ll be searching for the most insightful resources and experts to help us.

[†] Geometries and mathematics of fluctuations. The concept of a fluctuation is a primary unsolved problem in physics and we will begin reworking our page with the help of experts. More…

[1] Big bang nucleosynthesis (BBT). Requiring guesses and jiggering, the BBT hides the simple geometries that opened a path for us in 2011 to go down to the Planck scale. The BBT had never considered simple geometries and the de facto base-2 progression to the Planck or Stoney base units as a starting point. Within those first instants we find many keys. The BBT is locked into a one-of-a-kind inflation that lasts “…a millionth of a trillionth of a trillionth of a second.” In 2017 within Scientific American their editor said, “For physicist and cosmologist Alan Guth, one big question about the big bang remains: ‘What was it that banged?'”

We will answer that question several times over before the end of this article.

Quiet Expansion (QE). Within our nascent, emerging model known by many names but most affectionately as the Quiet Expansion (QE), that “…millionth of a trillionth of a trillionth of a second” has been parsed 98 times. That is, there are 98 doublings or base-2 notations from the Planck Time, each notation with a distinctive look and feel, and each within a progression of mathematics and geometry. Yes, those 98 doublings up until the first millionth of a trillionth of a trillionth of a second hold many never-imagined configurations and keys to start and grow our universe.

Inflation as described by Alan Guth and his collaborators is unique, highly-imaginative, and a one-of-a-kind event that requires extralogic. Within the QE, all 98 notations are active today and the entire universe is building on them right now. From notations 1-to-64, before the first particle, there is enough mathematics and geometry to lay foundations for nucleosynthesis. Within the QE’s numbers, geometries and functions, it is on-going. It is always on-going.

[2] The light element abundance. Helium and other light elements (deuterium, helium-3, beryllium) are believed to be created in the primordial Universe. The existence of these elements is used as a proof for the necessity of a very hot Universe, thus the BBT.

QE. Yet, the abundances of the light elements including all the elements of the periodic table are each uniquely pre-defined within a range of notations between Notation-67 and Notation-84 based on the Planck Length multiple. It’s all quite natural. That primordial hot universe is still with us. The same is true about the cosmic microwave background. If the Planck base units are taken as given (even while recognizing the disparity with Stoney’s base units from 1874), the universe starts very dense. There are many different approaches to try to figure out the approximate temperature. From Notations 1-to-64, the most basic forms and functions, structures, substances, qualities, relations, systems are shaped and continue to shape the universe this day and moment.

[3] The Cosmic Microwave Background Radiation (CMB or CMBR). It all begins with a measuring device, people doing the measuring, and a time stamp. The first was the Holmdel Horn Antenna (Penzias-Wilson, 1965). More recent surveys by Cosmic Background Explorer (COBE, John Mather – George Smoot, 1989), the Wilkinson Microwave Anisotropy Probe (WMAP, Charles Bennett, 2001-2012), and BICEP (Background Imaging of Cosmic Extragalactic Polarization) and Keck Observations (John O’Meara, 2022); all detail the CMBR and are used to justify the BBT.

QE. Notwithstanding, the black body, thermal radiation of the universe at a temperature of 2.73 Kelvin is readily supported by the QE within Notation-202 down to Notation-188. That includes this moment right now, and goes back around 13.79+ billion years to 375,000 years from the very beginning, the first moment of time. There are several factors involved with the heating and cooling, a function of the size, mass, and energy (coulombs) of the universe. Even if with an initial blast of light defined by the Planck Temperature, following the inverse square law, by the Notation-106 (4.37402×10-12 seconds), it would be in the range of 2.73 Kelvin. More fine-tuning can be done within the QE theory than can be done within the BBT.

[4] Large-scale structure. The BBT large-scale structure starts at the QE Notation-188.

QE. The QE large scale-structure begins with Notation-134. It is hierarchical, on-going, and ever-changing. All time is Now. There is no horizon problem. The Universe is in fact statistically homogeneous and isotropic because that is exactly how it unfolds. There is a rather different concept of the cosmological principle.[a][b][c] Where the BBT is guessing, our simple calculations are given using either the Planck or Stoney base units. Given we have only used the Planck numbers for our first-calculations, we expect adjustments. For example, there are 539 tredecillion infinitesimal spheres per second using the Planck base units and 4609 tredecillion using the Stoney base units. We have requested that the ISO render a judgement regarding the disparities between the Planck and Stoney numbers. Either way, within the QE model, the universe is dynamic, wholistic, intimate, and inclusive.

One might say that our universe is a huge, hyper-sensitive grid, one that some might think is overly sensitive, because it appears to respond to the thoughts, words and deeds of everyone as everything-everywhere becomes part of the face of the universe. Again, the big bang theory (BBT) hides and obfuscates these simple, very basic calculations of natural units and dimensionless constants.

The first and second laws of thermodynamics (you can’t create or destroy matter or energy) is relegated to Notation-202 where there is a directional, linear flow of time. Where primordial fluctuations within the BBT are considered density variations in the early universe, within the QE the seeds of all structure in the universe, the seeds of the large scale structure are given in the perfections (stability) within the earliest notations between 1-64. Within the QE theory, primordial fluctuations are imperfect geometries with gaps that have become systemic and have nothing to do with an inflationary paradigm or scale factors during inflation. More… a direct communication from George Ellis, I learned that Planck Temperature was not a consideration in 1972 when they jointly wrote The Large Scale Structure of Space-Time, CUP, (PDF), 1973.

[5] Hubbles’ law and redshift. The Big Bang theory de facto adopts the absolute time of Newtonian physics through the inflationary paradigm of Guth and associates.

The QE theory is more aligned with other studies, like Loop Quantum Gravity (LQG), that say there is only the current time. If true, the redshift is looking back within the current time. Thinking about it in terms of all notations being active might help. The concept may be unprecedented. It needs further examination because, if it abides, it changes everything. It immediately changes how we count galaxies. It doesn’t change the nature of the redshift; it changes the way we interpret it. Much moreHubble Natural inflation Expansion

[6] The initial conditions for structure formation and density perturbation. Within the big bang theory, structure is generally thought to arise through a growth of density perturbations which originate in the early universe. If smooth, the big bang theory is in trouble. There is no consistent logic upon which to build. Everybody realizes that the starting points for structure are still a mystery.

QE. At the first notation, the first doubling of our symbolic Planck base units, there are inherent geometries of quantum gravity. The initial condition is the infinitesimal sphere. There is a structure formation with-and-without density perturbations. It’s a radical departure. More to come

[7] Doesn’t explain the flatness problem. The BBT is stymied by its one-time event with no analogues anywhere in the universe. The density of matter and energy in the universe is determined by all the dimensionless constants. It is all very exacting mathematics. There is no flatness problem. The BBT doesn’t even have a guess at the type of structure or the advance of that structure. It is hidden in the mysteries of that so-called singularity.

QE. Each of the 202 notations is unique and a dynamic building block of the universe. It is all interrelated. The first sixty-four notations build successively from continuity, symmetries, and harmonies. Here is a domain that is pre-quantum fluctuations. Eventually our best postdocs will determine ways to test these assumptions. Probabilities will help to assume perfected states. The base-2 progressions for the density of matter and energy in the universe are close, perhaps closer than the current estimates. Again, this is territory for our best postdocs!

[8] The horizon problem. The horizon problem is the problem of determining why the Universe appears statistically homogeneous and isotropic in accordance with the cosmological principle.[a][b][c] It is a cosmological fine-tuning problem within the Big Bang model of the universe.

QE. The spatial distribution of matter in the universe is homogeneous and isotropic because the space, time, mass and coulombs are all doubling together within abiding and highly-interactive dependencies as already understood via-a-vis Einstein and Planck. More to come…

The horizon problem (also known as the homogeneity problem) is a cosmological fine-tuning problem within the Big Bang model of the universe. Fine-tuning is the backbone of the QE model.

[9] Doesn’t explain monopole problem. The BBT has nothing to say about the monopole problem. The scholars of nine most basic disciplines (below) will have much more to say about the monopole problem when they begin to accept the 202 notations, and the necessity of the finite-infinite relation.

QE: The monopole problem points to the infinite. That is, the primary foot of electromagnetism is within the infinite as understood to be continuity, symmetry, and harmony. At least the QE has a rationale that is consistent with its overall theory. It has everything to do with the concept of quantization which is being addressed by no less than these nine key disciplines: (1) Langlands programs, (2) string theories, (3) supersymmetry (SUSY), (4) loop quantum gravity (LQG), (5) causal dynamical triangulation (CDT), (6) causal set theory (CST), (7) field theories, (8) spectral standard model (SSM), and (9) all the hypothetical particles.

Even the best of us make mistakes.


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

Causal Dynamic Triangulation
A non-perturbative Lorentzian path integral for gravity (PDF), Ambjørn, Jurkiewicz, Loll, 2000
Scaling in four dimensional quantum gravity (PDF), Jan AmbjornJerzy Jurkiewicz (1995)

Strengths and weaknesses of the big bang cosmology, Narlikar, Jayant V., Astronomical Society of India, Bulletin (ISSN 0304-9523), vol. 20, no. 2, p. 1-12, March 1992
Strengths: The predictions of the expanding universe, the abundances of light nuclei, and the MW (microwave) background.
Weaknesses: Evidence for anomalous redshift, the age problem, the low abundances of helium, and the failure to find any feature in the microwave background as predicted by the theories of structure formation.

Day One Project (of the Federation of Atomic Scientist):
The team: Ryan Buscaglia: URL:

Follow-up of these key pages is on-going: (Cover-ups),


Recent emails. There will be emails to many of our scholars about this page.

• Pascal Oesch, Observatoire de Genève (Switzerland), December 4, 2022
• Salvatore Torquato, Princeton University, December 1, 2022
• Julia Collins, ECU, Joondalup, Australia, December 1, 2022
• Hugh David Politzer, Caltech, 29 November 2022
• Corrin Clarkson, NYU, NYC, NY Tuesday, November 29, 2022
• Sam Harris, NYC, November 29, 2022
• Dr. Oliver Janzer, ETH Zurich, November 28, 2022
• June Huh, Princeton, November 23, 2022
• Jonathan Doye, Oxford, UK, November 23, 2022
• Related email to Stephen Hawking in 2016


There will also be many instant messages to thought leaders about this page.

8:12 AM · Dec 1, 2022 @AyronJonesMusic Our problem as a people of many cultures and beliefs is our limited worldviews. A highly-integrated view of the universe is the beginning of wholeness, acceptance of diversity, and a bit of harmony: is a start on it. RU up for new lyrics? His album, Filthy, he says, “Where I’m from, the word ‘filthy’ is the highest compliment in the land. It’s being so good at what you do and who you are that it should be a sin.” Notwithstanding, we need new music with bigger lyrics.

2:25 PM · Nov 7, 2022 Geraint F. Lewis, @Cosmic_Horizons @Sydney_Uni Go inside the tetrahedron (divide the edges by 2, connect new vertices) and in 67 steps you’ll be at the Planck base units. Now multiply those units by 2, 202 times and you have the universe: A little math and geometry go a long way!


Participate You are always invited.


Keys to this page, parameters

• This page became the homepage on November 23, 2022.
It is very much under construction; it’s open for collaborations to improve it.
• The last update was November 24, 2022.
• This page was initiated on November 7, 2022.
• The URL for this file:
• Prior homepage:
• The headline for this article: Let’s Collaborate and Compare
• First byline is: Big bang versus Quiet Expansion



Still editing (and mostly deleting) these references from the prior homepage.

Hawking’s big bang theory has reached its limits:

Notations 0-to-201 are nonlocal. Locality is limited to each person’s unique space-and-time (universally recompiled within sleep – more to come).

Langlands programs and string and M theories need to be dropped into this base-2 container. Structure could easily be confused with points or vertices, but these have dimensional qualities, including qualities defined by the Fourier transform and attractors and repellers (Milnor and Smale).

Some editor needs to take my article for Foundational Questions Institute (FQXi) and help make it work for some one of our science publications.


Questions. Are quarks in the range of 10−18 meters? If so that would be in Notations 56-59. Are fermions within Notation-67? What else can be within to be in the range of the Planck base units (10−33 meters)? Are all the dimensionless constants? Are they on the cusp of the finite-infinite relation? Are these often misconstrued as vertices or points? Are simple doublings the most basic function in the universe? Does that circle of value and qualities extend to the Planck base units and out tot the current expansion?

Remember this Summary. This model is dynamic, wholistic, intimate, and inclusive. Here our universe is a huge, hyper-sensitive grid, one that some might think is overly sensitive, because it appears to respond to the thoughts, words and deeds of everyone as everything-everywhere becomes part of the face of the universe.

Key pages:


Max Planck Dr. John Mather, pi at its core drives our most significant formulas, foremost among them being that for the infinitesimal sphere.

Foundational Questions Institute Max Tegmark and Anthony Aguirre with financial help from the Templeton Foundation. Strengths and weaknesses of big bang theory by Jayant Narlikar,

Wikipedia Unsolved Problems. physics, mathematics, and astronomy, particularly cosmology. Cosmology and general relativity.

On learning about Matthew J. Strassler and his work…

Matt Strassler, Center for Fundamental Laws of Nature, Harvard University,
Cambridge, Massachusetts 02138

• Articles: Slow and steady. Nat. Phys. 15, 725 (2019) W boson mass too high?worrisome) link, 2022.
• ArXiv (46): The Duality Cascade, 2005 (latest work is from 2009)
• Homepage(s): Harvard, Facebook
• Publications: Bulk – A New Physics, 2016, …Singularity, 2014
• Twitter
• Wikipedia: Cascading gauge theory
• YouTube

Others related to Harvard: Randall, Georgi, Woodin, Elkies, Loeb (Avi), Holton, Schild, Ossiander

8 November 2022 at 2:30 PM

Dear Dr. Matthew J. Strassler:

Our page about your work — — is one of over 2000 pages-and-posts. In my daily monitoring of web activity, I’ll often re-visit a post that’s active the prior day which often prompts the question, “I wonder what (he/she) is up to today?” You’re recently part of that group, so today I revisited our page about your work and added a link to your March 21, 2014 article Did The Universe Really Begin With a Singularity?, as well as to your Facebook page.  And to be sure that we include your most recent work, W boson mass too high? is linked. 

I have three questions for you:

1. Do you have any interest in beefing up Cascading gauge theory Wikipedia listing?

2. Where is Wikipedia’s article about you? You are mentioned in the Cascading article. There’s a link to Igor Klebanov, but none to you. 

3. I have asked the ISO to consider the differences between the Planck base units and Stoney’s units. I then add, “It would also be helpful if there were a discussion about the possibilities of what is being manifest at that time. That is, given our understanding of dimensionless constants, could an infinitesimal sphere be defined by those basic units?”

Of course, your explanation of singularity is classic. It’ll be occupying our thought-space for a long time to come.

Thank you.

Most respectfully,


Second email: September 12, 2022 at 10:09 PM

Dear Dr. Matthew J. Strassler:

Yes, I rediscovered my note to you from June — — and then the more recent tweets. I thought you might not mind a question regarding your work in 2015 when you wrote about the data captured by the Planck satellite about the CMB. More recently the JWST results appear to show an even smoother earlier start. Some like Avi Loeb suggest that this smoothness may require a new physics.  

What do you think?

Just as a thought experiment, might we assume that it does require a new physics based on a domain from the Planck-scale to the electroweak scale. Some proposed The First Three Seconds, yet this domain is fractionally smaller yet. From the 2021 at the IPPP 23rd International Conference from the Planck Scale to Electroweak Scale, new insights were few. 

But, if we apply base-2 to the Planck base units, out of the 202 notations from Planck Time to this day, there are 64 notations that create a huge grid for that infinitesimal area and time. It is below the thresholds of direct measurement and might be be reserved for Langlands, strings, SUSY and a host of others. Might you comment? Thank you.

Warm regards,


September 10-11, 2022: Tweets

2:48 PM · Sep 10, 2022. Matt Strassler, a theoretical physicist studying particles and strings, tweeted, “So, the news from #Kharkiv is surprisingly good, but very worrying. This is not retreat, it is collapse. (Izium, already!) #Putin cannot tolerate more humiliation. I fear he will lash out.” 

9:16 AM · Sep 11, 2022, To which I replied, “You are right. The world needs to be giving him (Putin) an off ramps everyday. Let’s get creative!

Tweet: 3:00 PM · Jun 6, 2022, @MattStrassler Can you help us unfold this base-2 chart of the universe: The current homepage is my latest struggle with it all:

PS. I am going through your work within  inspireHEP.

First email: Jun 6, 2022, 4:50 PM

Dear Dr. Matthew J. Strassler:

I am sure you have a graduate student who could rather quickly bring your website,, up to speed. I think it is worth saving. 

At the divinity school (Harvard) back in 1977 with Arthur McGill, we focused on the Finite and Infinite relation through a slow reading of Austin Farrer’s book of that title. In trying to consider the fundamental laws of nature, it seems there should be some working assumptions about infinity. In my reading of your work, it is not clear to me what those assumptions might be. 

Have you articulated any such assumptions?

Beyond inSpireHEP, your ArXiv collection is a good resource. I am now working through your 2000 article with Joseph Polchinski. Excellent!

Warm regards, 

On following the work of Daniel Hooper…

Dan Hooper, Fermi National Laboratory
Wilson Street and Kirk Road, Batavia IL 60510-5011

ArXiv: Dan Hooper
TASI Lectures on Indirect Searches For Dark Matter (PDF), 2018)
Homepages: Chicago, LinkedIN
Podcast: Why This Universe? 
Publications: Books
Dark Cosmos: In Search of our Universe’s Missing Mass and Energy (2006)
Nature’s Blueprint; Supersymmetry and the Search for a Unified Theory of Matter and Force (2008)
At the Edge of Time: Exploring the Mysteries of Our Universe’s First Seconds (2019)
YouTube: Tedx Talk, Higgs Boson, 2012, On Time:

References within this website:

Second email: 31 January 2022 @ 4:30 PM

Dear Prof. Dr. Daniel Hooper:

I was visiting with some of our high school kids and we began talking about the Planck base units. We did a little thought experiment and used those units as a starting point for the basic structures of the universe knowing full-well that we were orders of magnitude smaller than anything defined within the Standard Model for Particle Physics. So, we began at the Planck scale with infinitesimal first particles that stacked and packed. It charts out nicely.

Even though a thought experiment, do you know if such a scenario has been logically explored?

It seemed to us that just maybe we could find a Langlands programs expert and string/M theory person and pull them into our first 64 of the 202 notations (base-2 doublings). Yes, there are 64 doublings before the Higgs and the particle zoo. Do you know anybody who has ever considered it?

Thank you.
Most sincerely,


First email: 18 August 2020 @ 5:55 PM

You are a scholar’s scholar. I really don’t know how you do it all! Articles, books, teaching, public lecture,* holding two post with all that administrative work, graduate students, doctoral dissertations… I am exhausted just looking over your shoulder!

Of your 227 articles in ArXiv, today I chose to read your singular work back in 2018, Life Versus Dark Energy. Earlier this month I began working through your collective work with 26 others, The First Three Seconds;  and because it’s a look from so many perspectives, it’s still quite open for discussion!
I posted an Open Letter to you and your co-authors and now that includes two direct references and linkst o you and your work:

If you would like me to add or delete anything, I am pleased to do so.

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 and even profound.

Now, I’ve backed into my studies of cosmology. Nine years ago, I was helping my nephew by taking his high school geometry classes (5)  to go inside a tetrahedron!  We used Zeno’s logic, dividing the edges in half, and kept going right back to Planck’s base units. It has been nine years now. Somewhere back near the beginning I started thinking that Lemaître’s cold start theory from 1927 should be examined more closely. The logic seemed to be pointing in that direction. Ever-so-slowly I am learning about our deep-seated biases about the very nature of time, the place of geometries, exponentiation, and, of course, Tegmark’s infinity…

I think we all have a ways to go before we finish

Thank you for your scholarship! I wish you well.

Most sincerely,


*Listening to your RI lecture on 10 February 2020. Great fun.  Nice confession at 26:42. “…you might be under the impression that we really understand a lot about our universe’s first fraction of a second…”  Thank you.

PS. I continue to struggle with these issues on every new top-level post a/k/a homepage, which remains for just a month, a week or even just a day:  –BEC


Questions-questions-questions: In search of continuity-symmetry-harmony

Left Yellow Arrow
Right Yellow Arrow

Pages: Blackhole.| C.|.Empower | Hope.|.Mistakes.|.PI (π).|.Redefine.|.Singularity | Sphere. |.TOE.|.Up

Let’s go over this one more time.
Are these the smallest calculations and the largest?
Is Planck Temperature within the very first instant?
by Bruce E. Camber

The smallest. The domain from the Planck scale to the Electroweak scale* is filled with mystery and unanswered questions. Although the Planck scale is widely accepted and its base units of length and time are generally considered to be the smallest, meaningful numbers of length and time, the equations that generate these numbers have not become the focus of our scholars. Nor has its ubiquitous pi. I have pressed our older scholars, people like James Peebles and Peter Higgs, “Why not?” I have pressed those who are just starting to move our conceptual boundaries, people like Malcolm Fairbarin and Isabel Garcia Garcia. There are so many movers-and-shakers (more just below) within specialized disciplines. Our list includes people with whom we have contacted over the years. These are the thinkers who constantly come up with new ideas and concepts to test and texture.

The largest. Certainly the current size of our expanding universe and the current age of the universe might be considered the largest possible numbers of length and time. So, it is a dynamic number and not an actual measurement. Yet, one might argue that the never-ending, never-repeating expansion of the numbers of pi could be larger yet. Dimensionless constants precede dimensional numbers. Building on our earlier work, we’ll continue to review the case based on causal sets and her cousins within those other systems within mathematics, geometry, physics, and cosmology that create continuity-symmetry-dynamics. [1]

Background: People like Pythagoras, E.P. Wigner and Max Tegmark (MIT) believe in numbers and geometries. If equations systemically cohere, the numbers are systemically really real.[2*] There are many of us who hold similar beliefs. We actually believe mathematics and geometries order and relate all things within the universe. And, within this site with our chart of the universe, we take it a step further; we believe that our base-2 exponential model defines and encapsulates everything, everywhere for all time, right on down to each hypothesized, infinitesimal sphere within the Planck scale. The mathematics defines a real reality and we need to begin to discern how it all works, and its implications for technology and our understanding of the key questions about life.

In that vein, there are many tetrahedral-octahedral paths through the honeycomb [2*] and each is really real. Dropping down by dividing by two, there are 112 base-2 steps from the desktop into the Planck-scale. Going out by multiplying by two, there are 90 base-2 steps to the age-and-size of the universe. Those 202 base-2 steps from the smallest to the largest are like pi, always changing and never-repeating. Although the numbers of pi, the 3.14159+ continue linearly, it is a most intimate part of our base-2 expansion. It defines every primordial sphere that has been filling this universe since the first instant at a rate perhaps anywhere from around 539 tredecillion (Planck Time) to around 4605 tredecillion (Stoney time) infinitesimal-primordial spheres per second. Possibly more symbolic than actual, those numbers of infinitesimal spheres per second are a challenge. [3]

Questions, questions, questions: Are these insights that could finally open the doors to the begin to grasp the hyper-interconnectivity of all things, everywhere, throughout all time? Who has similar insights? Who can help us understand the strengths and weaknesses of this thinking? [4]

Scholars and their focus

People, people, people: In 1975 a friend, Patricio Letelier, introduced me to the basic concepts within string theory as understood at that time. Today, people like Ed Witten, Nathan Seiberg, Stefan Vandoren and Dean Rickles are at the forefront of current work; and it is entirely obvious, something is missing.

In 2013 I was introduced to Langlands programs. My first contacts were Edward Frenkel and Robert Langlands. I continued my studies with the work of people like Ngô Bảo Châu, Vladimir Drinfeld, Stephen Gelbart, Laurent Lafforgue, Vincent Lafforgue, Gérard Laumon, Michael Rapoport and Andrew Wiles. How do we connect these programs to other dimensions of physics? Something is missing. Might Emil Artin’s work help?

Since 2015 I’ve also engaged people working within causal dynamical triangulation (CDT). Renate LollJan Ambjørn and Jerzy Jurkiewicz started those investigations. Fotini Markopoulou and Lee Smolin have tried to explain that work to the wider public. It has been said that it is an approach to quantum gravity that, like loop quantum gravity, is background independent. Although credited with many successes, physics is still splintered. Even within CDT something is missing.

How about causal set theory (CST)? It is the work of Rafael Sorkin, David Malament, Nick Huggett, James Owen Weatherall and Christian Wüthrich. Nick and Chris have been especially helpful. Yet, there are many others with insights. I’ll continue my studies of the work of colleagues like David P. Rideout, Graham Brightwell, and Ruth Gregory. Going back further, Luca Bombelli, Joohan Lee, and David Meyer contributed to the 1987 landmark article, Space-time as a causal set. It is all very compelling, but not compelling enough. Something is missing.

I continue to search. What about scalar field theory with Michael Peskin and Pierre Ramond? Right alongside is loop quantum gravity (LQG) and her thought leaders, Abhay Ashtekar, Carlo Rovelli, Jorge Pullin, and then, Jerzy Lewandowski, Francesca Vidotto, Israel Gelfand, Mark Naimark** and Irving Segal.

Also, I’ve looked into work on the spectral standard model, and particularly the work of Ali H. Chamseddine, Alain Connes and W.D. van Suijlekom. None have clearly broken through. [Please note: Those listed in gray type are deceased. We’re all dying; our pretensions are silly.]

So often, an article in publications like of Scientific American, Quanta Magazine, or Physics Today throws us a curve ball. In what group would you place those intrigued with the Moonshine Shadow? …mostly string theory? …number theorists? It’s real and it has another group of brilliant people like John McKay (1978), Don Zagier, Richard Borcherds, Shamit Kachru, John Duncan (Case Western Reserve), Miranda Cheng (NL), Jeffrey Harvey, Igor FrenkelJames Lepowsky, Arne Meurman, David Kaplan, Tohru Eguchi, Hirosi OoguriYuji Tachikawa, Sander Zwegers, Ken OnoMichael Griffin, and Terry Gannon. I thought, “Wouldn’t it be fun to have them all in one Zoom session? Martin Bridson could lead it!

Every scholar listed here knows that a radical paradigm shift is in order.

That it might be simple requires a bit of introspection about our essential nature, but that’s good. Let us all become a bit more introspective. [5]

Pi is much too plebeian for our leading thinkers. “Been there; done that.” Yet, I say, “Let’s go over this one more time. We’re missing something:”

  • Is pi the most simple relation?
  • Does it define the most simple thing?
  • Could that simple thing be a bedrock for all other things?

An infinitesimal sphere… I think so. And, I would like to encourage as many people as possible to reconsider pi. Perhaps Edward Burger, former mathematics professor at Williams College and once the president of Southwestern University (Georgetown, Texas), can help. His article begs the question,  Pi: The Most Important Number in the Universe?

Could pi be both the smallest possible number that literally defines the first moment of time that renders the first spheres that began stacking, and continues to stack, and interconnects everything everywhere for all time? Could it be the largest possible number because it continues to go steps beyond the size of the universe and the current time because it defines both!

** In this website if the words are a person and are in light gray, that person has died.


Question: If it is a quiet expansion up to the moment of the first possible physics for sound waves, who hears it?
Answer: We do not, we cannot, and we will never hear anything from these the earliest notations. It appears only possible within Notation-202.


Crisis of Confidence, The Gift of Openness

Confessions. On Monday, November 1, 2021, we started a new month and it was time to review old documents in light of today’s simple grasp of where we are. For some reason, the Planck Temperature was bothering me. So many brilliant people are still so profoundly committed to it.

It started bothering me so much I opened our horizontally-scrolled chart and followed the numbers up and down those 202 notations. Back and forth, back and forth, for some reason, the inverse square law jumped into my simple equation of state and I wondered, “Is that crazy? What is that first moment? Ex nihilo? If the inverse square law applied from Planck Temperature at Notation-0, within 100 notations, it would be within the range of the quark-gluon temperatures. Does that have any logical footing?”

In 2015 when we first began thinking about Planck Temperature, it was too difficult for me. I decided to put if off into the future. “We can deal with it later.” I put it in Notation-203 and divided by 2. By Notation-0 it was as close to absolute zero as it could possibly be.

Five years passed, and later came sooner than I expected. I had begun thinking, “Let’s see what those numbers would look like with Planck Temperature at the beginning (Notation-0). Obviously it would not double with the other numbers. Perhaps there is a justification to divide by 2. Maybe the inverse square law could be applied.”

I took the old chart, made a copy and began taking those numbers down from the hottest possible start.

Question. I asked myself, “Could some kind of extra logic or metalogic might help?”

I wrote a little about those thoughts within the prior homepage. With this paragraph and within the context of continuity equations from the smallest to the largest, we begin a process of peeling back the layers of ideation since about 2013 and 2014 as we wrestled with Planck Time, and then 2015 as we wrestled with Planck Mass and Planck Charge, and 2016 when we rather arbitrarily shelved Planck Temperature. “It will be at least 7 billion years before we need to explain its location.”

That was irrational. I was thinking about the duration of Notation-202 which is 10.98+ billion years. If the universe at Notation-202 is already 10.98 billion years, we’ve only had a small sampling of 3+ billion years that has defined this universe to date.

Within systems theory there has to be a rationale for every decision and this was one of the most important that I could make. Is it hot or is it cold? Of course, that’s extremely hot or extremely cold. The more I thought about it, the more that extremely-hot entry point and an inverse square law began to reveal glimmers of possibility. Where is light in all these equations? What is light? What are photons? If Planck Temperature decreases inversely — because there was so-very-little to hold such a temperature — might that open a path for a new inquiry?

So, let us re-explore the question, “Could that infinitely hot start have any cogency?” [6]

The temperature itself from the calculations of Max Planck would require much more study and reflection. So, yes, let’s continue to look at these numbers and progressions. Thank you. -BEC



* The range, Planck scale to the Electroweak scale. The prior homepage is about the 23rd conference (June 2021) to focus on that range, Planck scale to the Electroweak scale. It was coordinated by the Institute for Particle Physics Phenomenology of Durham University in England. Neither the conference nor IPPP has recognized the 64 base-2 notations from the Planck Scale to the Electroweak Scale. One of my reasons for focusing on this group of scholars is to invite their critical review. The essential question is, “Do we start our exploration of the infinitesimal from known particle-wave phenomenology or do we start with a hypothetical question about the most simple, infinitesimal structure that could define the first dynamic layers of space and time?”

Our focus is on pi and the 64 base-2 notations (out of the 202 that encapsulate everything, everywhere for all time).

[1] Scholars. People like James Peebles, Peter Higgs, Malcolm Fairbarin, Isabel Garcia Garcia, Max Tegmark, and over 60 other scholars who are listed and linked are among our world’s thought leaders living today. They are among the best of the best, the smartest of our smart. As a people, they do not come any better.

Could they all be assuming that they profoundly understand the very nature of pi? Would any of them dare go back and review it all just one more time? I don’t know, yet I will try to find out.

[2] Structure. If we know that the Planck Length and Planck Time are the smallest meaningful numbers of length and time, shouldn’t we ask, “Might a structure manifest within that time and length?” Why not start with the smallest numbers and assume these numbers are describing the smallest structure? Might the structure be a circle and/or a sphere? Isn’t there a lot we can still learn about spheres within the infinitesimal scale? When does the Fourier Transform begin? At what notation does sphere stacking begin? At what notation does infinitesimal cubic-close packing of equal spheres begin to generate the tetrahedron and then the octahedron? At which notation does that the five tetrahedral gap manifest and fluctuations begin? Can any of these ‘pure structures’ be more fundamental than quarks and neutrinos?”

[3] Epistemology. The earliest-known calculation of pi is found within the Rhind Papyrus from about 1650 BC. It appears to be the oldest and most-used equation in the world today. It permeates everything. If we allow pi and the sphere to permeate our thoughts, the first thing we discern is its continuity, then its symmetry, and finally its harmony and the Fourier transform. Are these the qualitative faces of the infinite that become the quantitative faces of the finite? Might we concur that here we begin to grasp the derivative nature of space-time and matter-energy? Are all those infinistirmal spheres, literally tredecillions per second, ostensibly the envisioned aether? Do we need to go over this one more time?

[4] Even More Questions. Why haven’t the folks within string and M-theory found their connection to particle physics? It’s been well over 50 years. Do the first 64 notations between the Planck scale and electroweak scale elude them? Just watch one of Leonard Susskind’s lectures. He is just too close to quarks, gluons, hadrons, protons and atoms, and he does not have any articulation of the length, weight (mass) scales from Planck to electroweak. Those 64 base-2 notations are a new universe of possibility.

We’ll continue this discussion with Susskind, Greene, and many of the other leading theorists. I have been particularly frustrated with the Langlands Program. They know they are in a mathematical, theoretical world. The 64-notations below possible thresholds of measurement provide a sweet entryway without getting into point particles and the limitations of two dimensions. Obviously, I am missing something (not unusual for me). Yet, just maybe they are missing those 64 base-2 steps out of the 202 base-2 doublings from the Planck scale. Yes, just maybe.

[5] Let us become a bit more introspective. My wife often tells me, “People can not be absurd to themselves.” That is, if you have spent your life defending an intellectual position, it is very difficult to change direction. 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.”

[6] The cogency of an extremely-hot start. Could there be a progression within laser thermodynamics that follows the path of Planck Temperature down into the range of 2.75 Kelvin? To search for an answer, perhaps it is time to re-engage the study of laser thermodynamics? Could there be two tracks, one that is a very stretched analogue of big bang progression but it is limited to a single flash at Notation-0 and it is the Planck Temperature, and then it decreases exponentially following the inverse square law? The other track is as we have intuited, an explosive number of infinitesimal spheres being generated at Notation 1. Then, it approximates our original chart with the temperature increasing exponentially from close to absolute zero. Does that earliest generation of temperature require differential equations between the two?


Editor’s notes: The most dynamic part of this page follows. These are the evolving endnotes/footnotes, references, emails, and instant messages. Your comments are most welcome.


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@malcfairbairn @FrancesVidotto and others: Pi is too plebeian for our leading thinkers, “Been there. Done that.” I say, “Let’s go over it one more time. We’re missing something.” Is pi the most simple relation? Does it define the most simple thing? Could that simple thing be a bedrock for all other things?

@USProgressives If things are ever to change fundamentally, we need to break free of our little worldviews and begin to engage an integrated view of our universe. We all think too small. We all fall short. We need to see the whole. A simple start is here:

@gary_zukav Just took your WuLi (next to Capra’s Tao) off the shelf. Checked your TOC for infinity, spheres, Planck Time. Studied with Bohm, Aspect, Bell… congrats on all you’ve done. Break though time: by dropping worldviews for integrated UniverseView!


Invitations and Collaborations

With whom do we collaborate? Of the thousands of people who visit this site every month, who among them might say, “May I help?” Our only thrust is that the foundations of this universe and life itself be seen in light of infinity and the continuity-symmetry-harmony that the infinite engenders. Please, talk to us. Thank you. -Bruce


Key dates for this document, questions-questions


A possible rapprochement with the naïvetés and simplicity of our youth

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Pages: Blackhole.| C.|.Empower | Hope.|.Mistakes.|.PI (π).|.Redefine.|.Singularity | Sphere. |.TOE.|.Up

Smallest to Largest
by Bruce E. Camber

Durham, UK (2021): Graduate students of the Institute for Particle Physics Phenomenology (IPPP Durham University) were substituting for Sir Peter Higgs. The question (above) for their audience is a major unsolved mystery.

At the IPPP 23rd International Conference from the Planck Scale to Electroweak Scale (June 2021), Prof. Dr. Malcolm Fairbairn of Kings College London presented “Dark Matter Hunting in 2021 – How do you look for something when you don’t know what it is?” His presentation raises key issues about the unsolved mysteries that have surrounded dark matter. On page 70, he challenges us all, “We are well into an era of using novel approaches to learn more about dark matter.”[1]

There were another 20 scholars with similar presentations; each focused on an open question within our smallest-scale universe. Those lectures need close scrutiny (see the endnotes below). The domain from the Planck scale to the Electroweak scale is filled with mystery and unanswered questions.

Princeton physicist and 2019 Nobel laureate James Peebles lifts up such questions as penultimates in physics and cosmology today.

All students are our sacred trust and treasure.

Thinking, learning, and seeing beyond. Students need to be challenged in every way. Yet, we also need to listen carefully to the ways they challenge us. Some of my most inspiring encounters have come from even younger students. In December 2011 and within all the naïvetés of a high school in the USA, we started exploring the infinitesimal. We had discovered a geometric and mathematical path through a tetrahedral-octahedral honeycomb.[2] It dropped down 112 base-2 steps into the Planck-scale. We also went out the 90 base-2 steps to the age-and-size of the universe. That is a total of 202 base-2 steps from the smallest to the largest. Yet, the first 64 base-2 steps stopped us cold. What could be so small? There are plenty of guesses, but nobody knew. And, we didn’t know what we didn’t know.[3]

We had a novel construct. By observing, thinking, and trying hard to be logical, over time we came to several radical conclusions: “That’s a quiet big bang. It’s a natural inflation. Perfectly smooth, it’s the basis for homogeneity-isotropy. Could it be dark matter and dark energy?”[4]

To say the least, we got a bit carried away! And, that is a problem. Nobody would touch it except the kids. [5]

What’s the smallest thing in the universe?

Our students’ response is quick, “An infinitesimal sphere, a little like Lemaître’s primordial atom.” Pushing back, “So what?” The retort is quick. “It’s defined by the Planck base units and there is one Planck sphere per Planck unit of time.” We had worked on the simple math so I asked,”What does that mean?” The answer is still baffling: “One Planck sphere per Planck unit of time computes to 539 tredecillion primordial spheres per second.” That’s a lot of spheres to track. We had our base-2 notation, a map encapsulating everything, everywhere for all time within 202 notations. It was a transformative surprise; it took us over two years to begin to accept the idea that is was a first. And as you’d expect, we were profoundly challenged by the multiplicity of issues it opens up.[6]

As crazy as it all seemed, we weren’t going to duck out. We learned to accept the idiosyncratic and to ask the experts for help. We continued on, but it could no longer be an extracurricular activity for our brightest seniors. They were going on to college and these concepts created too much tension. When I moved out of town, the lights on the project were turned down, yet I’ve continued to look for facts and to make some guesses… it’s a slowly-expanding history. [7]

Asked about the 539 tredecillion infinitesimal spheres per second, a few years before, we had examined questions about thrust and continue to pursue it focused on the infinitesimal thrust of numbers coming through pi and other dimensionless constants like light and Planck Charge.[8]

If Planck’s base units are symbolically the smallest, what could be the largest?

Discovering limits and a range. We became even more controversial. Built into our simple equations is an active finite-infinite relation. We say that only because these continuity equations are never-ending and never-repeating. Like pi (and with pi), all continue to expand.

Those numbers should be the most-dynamic and the largest numbers within each of the general categories within Notation-202 of our horizontal chart. [9]

By staying deep within pi and an ideal sphere, nothing finite is found. There is a sense of continuity, symmetry, and harmony. These simple perfections manifest within the finite yet are not themselves finite. These three are facets of the infinite. Historically the infinite has been defined in numerous other ways. Most are personal matters. We avoid such language and choose only to defer to continuities which manifest as order and is experienced as time, symmetries which manifest as relations and are experienced as space, and harmonies which manifest as dynamics and are experienced as space-time moments. Although still a series of abstractions, there are boundaries and boundary conditions, logic and structure, and the inherent-yet-quite-derivative mathematics and geometries.[10]

Reviews of the model anticipating our ten-year anniversary

Models of the Universe. The original chart followed the Planck Length (December 2011). Then we added Planck Time (2013-2014). Quite naturally we began adding Planck Mass and Planck Charge to our chart in 2015 and 2016. That’s when the extremely-hot Planck Temperature became an extremely-big challenge.

With time/length and mass/charge seemingly the Janus-face of each other, a cold-start seemed more logical than a truly off-the-charts hot start. The four basic Planck units were doubling. It would be truly idiotic if we projected that the temperature doubled with the other facets of the Planck base units. We decided to put that mystery up beyond the current time and we divided it by 2 to give us the results (numbers) in our very first horizontally-scrolled chart.

Review. Anticipating the tenth anniversary of our studies (yes, we formally started on December 19, 2011), it was a good time to re-engage all 1000+ numbers in that chart. For some unknown reason, the inverse square law forced its way into this ideation, “What if you start with Planck Temperature and with each notation the temperature is cut in half? Does that make any sense at all?”

“Be open. Think about it. Be open; be open.”

To get a sense of those numbers I began a new chart that actually begins with Planck Temperature at Notation-0. Instead of multiplying by 2, divide by 2. Though a bit more commensurate with Hawking-style big-bang thinking, it is still entirely idiosyncratic. The approach to absolute zero is too quick. So now we will place the approximate temperature of deep space within Notation-202 and attempt to discern how mathematically we get from Notation-0 to Notation-202. We are currently contemplating the working relation between all the prime-number bases keeping in mind that base-10 has 64-to-65 notations. How many notations using base-3? …base-5? …base-7 …base-11? We’ll do the numbers like we did with base-10.

The thought process went something like this: “Might the thrust required to generate the first infinitesimal sphere to create the first space/time and matter/energy moment require extreme temperature? Perhaps. Is it worth looking at it? Yes. Might the temperature drop by a half with each or the earliest notations with that very small mass? Maybe. Within the first second (Notation-143) as the number of spheres are increasing to 539 tredecillion infinitesimal spheres per second, there just may be some relatively new mathematics perhaps related to laser temperatures that may well be logical. Let’s explore it. It just might work.”

Can we be re-examining the four laws of thermodynamics (0,1,2,3)? Can we grasp the thermodynamics of laser physics? …its spontaneous fluorescence?  Might the inverse square law apply on the first notation? Might there be several different progressions down to the current, average temperature of the universe?


For many, it is all too simplistic. And, perhaps it is. Yet, just maybe it is the simplicity that was within John Wheeler’s dreams and the correlation between reality and numbers that E.P. Wigner so loved. It seems as if this idiosyncratic path is about to become quite a bit more idiosyncratic![11] Thank you.

Editor’s notes: The most dynamic part of this page follows. These are the evolving footnotes, references, emails, and instant messages. Your comments are most welcomed!

This page and the following sections will continue to be updated. A new homepage has been started and it will be released soon.



[1] Scholars. Durham University’s Institute for Particle Physics Phenomenology (IPPP) has achieved global recognition for her work and her graduate students. The seven pictured above are so good they stepped in for Sir Peter Higgs when he became too ill to make a public speech. The IPPP also hosted an event like the 23rd International Conference from the Planck Scale to Electroweak Scale (Planck 2021) where the focus was on some of the most-mysterious, open questions within the smallest scale of our universe. The intent of most conferences is to trigger new insights. That hope is especially true when considering the graduate students and postdocs. Our hope is also in those who make a presentation for a conference. There is nothing like a deadline! By making time fundamental, we experience its derivative nature.

From this 23rd conference, we now have access to the PDFs of the 21 scholars who’ve made a presentation where we can more readily ruminate about such things. Also, their references are always a great resource.

The primary reference to all related emails to these scholars will always be within this footnote:

These 21 scholars come from around the world. Although each focused on probabilities and possibilities, some are closer in spirit to the Fairbairn presentation which challenges us to stretch in new ways. In every instance, my focus is on the nature of that stretching.

In December 2011 we started working to understand the 202 base-2 notations from the Planck scale to the current time. We have come to believe that the first 64 base-2 notations from the Planck scale to what we’ve called the CERN-scale (or Electroweak scale) are the hidden keys to help unlock silos of information that keep the key domains of physics separated. It’s been ten years. There is nothing like a ten-year anniversary to prompt a more critical review.

[2] The tetrahedral-octahedral honeycomb. Not just a speculative vision, here are geometries that open many-many multiple paths to the Planck scale from that simple tetrahedron (sitting on a shelf in the classroom). To give something so simple a little panache, consider those paths to be a tunnel similar to the concept of an Einstein-Rosen bridge (or a wormhole). Though a real reality, not a virtual reality, we’re creating “Zeno goggles” that automatically divide space in half while proportionately and relativistically shrinking the observer.

You’ll observe and experience the 112 steps, going deeper and deeper within. We’ll slow you down as you get to Notation-20. You’ll observe how the tunnel options have gotten fewer and at Notation-10, you’ll observe the actual creation of the tetrahedron and octahedron between Notations 1-5. You’ll actually see the stacking of those 539 tredecillion infinitesimal spheres. Called cubic-close-packing of equal spheres, it’s brilliant. Then you’ll observe how those infinitesimal spheres are popping out of the Planck scale fabric of the universe. That’s a wow!

Seemingly instantly up at Notation-112 where we came in from the classroom, you’ll be given what we call, “Euler-2-exponential goggles.” Here you will see how every notation is multiplied by 2; and in just 90 steps, you will be out to the age-and-size of the universe, watching the current expansion. A show stopper, you’ll see and experience the universe from the smallest to the largest in just 202 steps, notations, sets, jumps… if you haven’t been to our old chart it may be a good time to go.

The new chart has risen!

We all need to look more deeply inside the tetrahedron and octahedron! We all should spend time deep inside the honeycomb. There is nothing simple about a honeycomb.

[3] What do any of us really know? Are things always simple before becoming complex? It seems to be true, all except around those issues coming out of the big bang theory as promoted by Hawking, Guth, and many others. Now, more recently Princeton’s Paul Steinhardt and his coterie have been getting some traction with their quest for a new kind of matter. Dan Shechtman (wiki) before him looked at the small-scale and got his Nobel prize in Chemistry in 2011 for his discovery of quasicrystals, the imperfect geometries based on five tetrahedrons sharing a common edge and lacking a translational symmetry. In our book, it is confined by notation and its respective Fibonacci sequence. Of course, outside of the 202 notations, that statement is meaningless or gobbledegook. The bottomline is arrogance impedes ideas and creativity. Remember Fairbairn‘s comment about “novel approaches.”

[4] Quiet start? Natural inflation? Perfectly smooth? Dark Matter and Energy? What if the universe starts very simply with Lemaître’s primordial atom? In 1927 Lemaître had suggested as much; it was his first idea, a cold-start. We’ve believe it was his best idea. At least 64 base-2 notations before all the complexification of a particle or a wave, here are the pure numbers of a sphere. A little like the Democritus atom, the conceptual study of a sphere is at least 1500 years older and here we are still learning about it! If we take off Planck’s quantum blinders, we might see his numbers more readily and see homogeneity-isotropy in a very different light. We have been fretting about dark matter since Fritz Swicky’s 1933 formal theorem inferring the existence of dark matter.

Dark energy didn’t come into focus until in 1968 the Hubble Space Telescope began collecting the detailed data. Interpreting it all is still up for grabs. With dark matter estimated to be 27% of the universe and dark energy as much as 68%, it is certainly the most enigmatic issue within science today.

Yet, the first 64 notations puts it all in a new light. Here there is a universe of mathematics and geometry that can not be measured with a physical measuring device of any kind. With all these open issues and with so many others that are ever-so-much more problematic, isn’t it time for a radical shift in our constructs for that first septillionth of a second. It sounds like an insanely short amount of time. Within mathematics, one tredecillionth of a second, and that range, a septillionth to a tredecillionth, is another universe unto itself.

[5] Always looking for the start. Fundamental change within our scientific belief systems is difficult. There are too many people, too much history, and way too much money involved with every major theory, whether right or wrong. Scientific research today is big business. Among those at the the top is CERN laboratories. Straddling the border of France and Switzerland, just outside of Geneva, CERN (Conseil Européen pour la Recherche Nucléaire) is a case study unto itself. Initially it involved twelve countries when it began in 1954. Today there are 23 member states, yet associations with virtually every country on the planet and well-over 100,000 research physicists around the world.

It is a very big business. As an organization, percolating out of the darkness and rubble of WWII, it had a bold start involving those twelve European nations. That start is well known. Yet most enigmatically and more importantly, even today the best of CERN are unsure about the first septillionth of a second at the very start of it all.

My first interactions with CERN folks started with Viki Weisskopf (MIT) and Lew Kowarski (Boston University). Weisskopf was Directeur-General from 1961-1965. Kowarski was the first to propose a laboratory for fundamental research; he was tasked with organizing and setting up it up with Raoul Dautry, Pierre Auger, Edoardo Amaldi and Niels Bohr. See: May 1952, Early beginnings

These were all people who understood the evolution of the first atomic weapon and how basic science can quickly become a Hiroshima or a General Electric. Any concepts that might upset these equations must be most compelling and be ready to face stiff, if not fierce, opposition. Yet, in time, the better concepts do rise. We think ours are straightforward.

[6] Redefining the first instant: Lemaître’s primordial atom, one Planck sphere per Planck unit of time. Those two basic assumptions opened the way to this simple calculation — 539 tredecillion primordial spheres per second.

It is Max Planck’s calculation for Planck Time extended to one second.

The results are beyond imagination. Even today, envisioning such numbers is an ongoing challenge. These numbers made their debut within this website in October 2020 and there are still many levels of error-correction yet to be done.

[7] Reaching out for critical feedback. In 1971 I became part of a think-tank on Brattle Street in Harvard Square in Cambridge. Part of the invention-research process was to suspend judgments and accept ideas as given. It wasn’t always easy to do. We are all naturally judgmental people. We are taught to look at new ideas critically. And, it is easy to fall into the trap of arrogance, “How can you be so stupid?” If only we could change that attitude to something like, “Let’s explore that idea and see where it takes us.” Idiosyncratic ideas are not always idiotic! Yet, it takes a bit of courage to approach our experts. So many of them ask, “How can you be so stupid?” After crawling back into our safety zone and hibernating for a bit, we eventually venture out again but with less ambitious goals. That’s why I enjoy the younger students. Some are still actively exploring imaginative ideas. Our goals as teachers should always be to explore such ideas thoroughly. In 2016, it was becoming clear to me that nobody was dealing with our numbers and the logic of base-2, doublings, spheres, stacking and so on. It was such a different paradigm. It was risky business for anyone with a high-standing within the community to come anywhere near it. Though I assured people that their responses would NOT be shared with the public, people were reluctant to be critical, so it became important to me to log my questions and develop a reference page to each scholar’s work. It is a very modest way to try to avoid becoming more of a nuisance and it helped to focus on their work as related to these efforts.

[8] Infinitesimal thrust of numbers coming through pi and all the all the dimensionless constants. Might it manifest as an inherent force within light and the Planck Charge? Might it be a manifestation of the intimate, immediate correlation with the continuity-symmetry-harmony of infinity? Might it be an ongoing, never-ending finite-infinite transformation? Might infinity be the source for the deepest nature of thrust and photons (force bosons)? Of course, we answer all four questions with a “Yes” and then ask, “What is this universe telling us?”

[9] Largest numbers. We are getting a grasp of the smallest numbers. We also can begin to grasp the very largest numbers that define our universe. These numbers give us some assurance that we are on the right path. The universe does, indeed, look more and more like it is base-2 exponential. Yet, again we asked, “In what ways is it also base-3 exponential? …base-5? …base-10? The largest numbers are not far from today’s actual numbers. Is that the roll of the prime numbers?

It all gives us clues and challenges us to fill in the mathematics and geometries.

[10] On infinity. In 1970, by asking questions about perfection in the face of quantum physics and Bell’s inequality equations, continuity-symmetry-harmony seemed like good abstractions. Building on each other, they were general enough yet have relatively specific scientific meaning. Eventually I asked if each could be a facet of the infinite. It didn’t go far because I could not discern a structure or a path from the infinite to the finite until 2011.

Those 202 notations have triggered new thoughts about very old concepts.

[11] From the old guard to the newest thinkers: From Wheeler dreams to Eugene P. Wigner’s extreme trust in numbers, we go to the likes of Tim N. Palmer, and others like Stephon Alexander, Espen Gaarder Haug, Ari Lehto, Ard Louis, Jirina Stone, Frank Wilczek, and Edward Zalta. It would be magical to have them all in a “Zoom-like” session to talk about this page. Yes, we can dream dreams like Wheeler.

With this ten-year review, we re-introduce Planck Temperature, no longer constantly pushing the boundaries out and getting closer to absolute zero, using the more traditional start at the Planck Temperature raises so many new questions for us. Every aspect of our mathematics will be pressed and stretched.

In a rather peculiar way, both models have the same results so that “the real model” of our universe, remains a mystery for another day. Thank you. -BEC


Please let us know if you would like to join us for a “Zoom-like” discussion about it all.

All eleven of these endnotes/footnotes above are being re-edited and textured.





Sir Peter Higgs, Edinburgh: Sunday, November 7, 2021. A quick note about the question the grad students asked their audience on the occasion of substituting for him when he became too ill to present his public lecture.

• Simon White, International Max Planck Research School on Astrophysics at the Ludwig Maximilians University Munich, has been at the forefront of a Cold Dark Matter paradigm. Because scholars like him have been working with cold concepts within a classic big bang model, I have been pushed to ask silly questions like, “Could there be a super-cooling from the Planck Temperature because that phenomena would most likely act like laser thermodynamics. Could the inverse square law apply?” Based on those flights of fancy, I just started another chart that starts with the Planck Temperature within Notation-0 and is divided by 2 to arrive at a radically reduced temperature for Notation-1. It is divided by 2 again for Notation-2. Because it is temperature assumed to be light and not an “infinitely-dense” singularity, but a very dense black light that within Notation-97 becomes visible light. If one Planck Sphere manifests per unit of Planck Time within thirty-one doublings, there are size is still an infinitesimal 3.470762×10-26 meters, the mass is just 103 pounds (46.79 Kilograms). So now we are asking, “What might the temperature be and why?” Within our first horizontally-scrolled chart, it is 4.73×10-18K. In the chart with Planck Temperature within Notation-0, it is 6.597×1022K. The Electroweak Scale requires an estimated temperature of 2×1012 Kelvin to create the Quark-Gluon Plasma (QGP). That’s an important benchmark. It requires 175 MeV per particle. We’ll need help to figure out which notation would be a logical place as another mechanism to force the review of possible mathematics and functions that may be at work.

Malcolm Fairbarin, Kings College London We have started a profile page to follow his work with the International Conferences from the Planck Scale to Electroweak Scale.

Marco Drewes, UC Louvain We will continue to study his work with the IPPP.

A note to the attendees of the IPPP June 2021 conference:

“I see that you were one of the participants in the Planck 2021 IPPP-Durham University conference. I am going through those papers now asking the questions, “What are the most special insights from those 21 scholars? How do we get beyond the Standard Model without getting too far beyond it?”

“Personally, I know that we’ve gone a bit too far because we started at the Planck scale and hypothesized that something like the concept like Lemaitre’s primordial sphere defines the very first moment. I am rather sure Malcolm Fairbarin (linked just above) thinks it is more idiosyncratic than it is a “novel approach.”

“If you would like to take a look, it’s posted here:

“We then applied base-2 notation at the Planck scale to find just 202 notations from Planck Time to this day.The numbers are fascinating — — but interpreting those numbers is not easy. Your comments and insights would be treasured.

“Surely more than a “novel approach.” Perhaps “idiosyncratic” is necessary today. Thank you.”

“Most sincerely,

From a student in Spain: Students ask us questions from schools around the world. Here is my response to a question from a biology student with a strong background in physics. He attends Complutense University of Madrid:

“Your English is excellent. Your references and links: Excellent. Your question, Do you know if Arkani-Hamed adopts something similar to Tegmark’s view as well?, is well placed. Those two are so cockily independent and aloof, they might disagree just to disagree. However, I think you nailed them. Like E.P. Wigner (pictured here), all the way back to Pythagoras (See – Theano, On Piety), they are all an inspiration to me. In my deepest being, I believe they are right and you’ll see throughout my work a deep belief in continuity-symmetry-harmony, the qualitative and infinite, always and profoundly giving rise to the finite.  Too much of our being is spent being arrogant. That doesn’t help anyone. Science and religion are full of arrogance so I try very hard to stay open. Any more thoughts and questions, I am all ears!  Thank you.  -Bruce”

In Process: Simons Foundation folks: Leonard Susskind – 2020 lecturer, Patrick Hayden – director, Brian Swingle lecturer – Chaos-Protected Locality, and Juan Maldacena – lecturer, and so many more


October 18, 2021: @BBCScienceNews@bbcnews@BBCNewsnight #RichardSharp Worldviews are incomplete; we all need a highly-integrated view of the universe. We’ve started here:

October 18, 2021: @MiddleEastEye @AlexandraPring Yes, true. Yet, even Gurnah’s work needs to be seen through a very different lens. We’ve all got to grow beyond our simple worldviews to fully integrated views of the universe. Sounds impossible… it’s not. We started here:
Abdulrazak Gurnah received the Nobel Prize in Literature in 2021.

Other communications are being reviewed from this period and may be added.


Invitations and Collaborations

With whom do we collaborate? You are among thousands of people who visited this page this site this month. Might you ask, “Can I help this effort?” The answer is, “Yes!” Our only thrust is that the foundations of this universe and life itself be seen in light of infinity and the continuity-symmetry-harmony that the infinite engenders. Please, talk to us. Thank you. -Bruce


Key dates for this document, smallest-largest

  • This document was started early on Monday morning, October 18, 2021.
  • First posted for collaborations, late evening, October 18, 2021
  • This page became the homepage, late on Tuesday, October 19, 2021
  • The URL:
  • Prior Homepage:
  • First Headline: The Smallest and the Largest
  • Second Headline: Smallest to largest
  • First Tagline: How do you answer, “What is the smallest thing in the Universe?”
  • Second tagline: A possible rapprochement with the naïvetés and simplicity of our youth
  • Another possible homepage:
  • The most recent update of this page: Monday, 21 March 2022


On following the work of Adrian Frederick Melhuish Smith…

Sir Adrian F. M. Smith, Director, Alan Turing Institute
President, The Royal Society, London

Books: Bayesian Theory and Applications: In Honor of Sir Adrian Smith, 2013
Bayesian Methods for Nonlinear Classification and Regression, 2002
Bayesian Theory, 2001
Aspects of Uncertainty: A Tribute to D. V. Lindley, 1994
Statistical Analysis of Finite Mixture Distributions, Wiley 1986

First Tweet: September 4, 2021 at 11:31 AM

@turinginst and @royalsociety As president of the Royal Society, Sir Adrian would do well to initiate a global discussion about Newton’s absolutes of space and time. He’d become a rock star. Let’s do it. Space-time is derivative and finite:

Editor’s note: Of course, that issue is debatable and that is the reason for the tweet. Sir Isaac Newton was the second president of the Royal Society. It is time for the Royal Society to become an even brighter intellectual beacon for the world.

First email: 31 August 2021 at 2:02 PM

Dear Prof. Dr. Sir Adrian Smith,

We have Planck Time on one side of us and somewhere around 13.81 billion years on the other. In between there are a finite number of seconds. Could that Planck Time be the first unit of time? What would it look like? …an infinitesimal sphere? Would the Fourier transform apply?

I am on your homepage:
You are an educator of the highest order, so I hope you do not mind my simple questions. I am flummoxed.

As a further backdrop for those questions, might we start at the Planck Scale, particularly Planck Time, and watch the flow of those units, apply base-2 to create an ordering-sorting mechanism, you discover that within just 202 base-2 notations, we are out to over 13.81 billion years. That renders a Planck-scale universe:  

Are those just numbers or are they meaningful? I think we can instantiate meaning:

Thank you.

Most sincerely,



Planck Constant

The four base units: Planck Length, Planck Time, Planck Mass and Planck Charge need to be studied and analyzed as carefully as possible. Perhaps most important is the Planck constant because it is involved in defining all four.

Planck Length. In 2011 my journey with Max Planck began in earnest through the Planck Length. Ultimately, it did not much matter what Max Planck’s calculation was for Planck Length, it was so small and we were so close to it, our system of going within using the tetrahedron and octahedron was more important than the actual numbers when our goal was just to get into the range of 10-35 meters.

Planck Constant. Fundamentally defining all four Planck units, the Planck Constant would appear pivotal to the entire system and our understanding of our base-2 mapping. In 2016 our base-2 numbers were placed on a horizontally-scrolled grid. Where Planck Length and Planck Time were most infinitesimal, Planck Mass and Planck Charge were larger than some current measurements of both.

Please note: There is a tension within academia about the usefulness of the Planck Constant. Several of these articles are just now being developed (5 April 2021).

Also see:

Universe before Planck time (PDF), T. Padmanabhan, Phys. Rev. D 28, 756, August 1983

Pattern of perturbations from a coherent quantum inflationary horizon

by Craig Hogan

It is proposed that if quantum states of space-time are coherent on null surfaces, holographic Planck-scale fluctuations of inflationary horizons dominate the formation of primordial scalar curvature perturbations. It is shown that the reduction of quantum states on nearly-spherical emergent horizon surfaces around each observer creates a distinctive pattern whose correlations in the angular domain differ from the standard quantum theory of inflation. Causal constraints are used in a semiclassical model to formulate candidate directional symmetries.” (PDF) Hogan

Expansion of the Universe: Approximately 539 tredecillion spheres/second

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Right Yellow Arrow


Tredecillions of spheres per second
One primordial sphere per primordial unit of time
PlanckTime: 5.3 ×10-44 seconds StoneyTime: 4.6×10-45 seconds
by Bruce E. Camber (the first draft)

If and only if we take the Planck units as a given, and if we assume one primordial sphere per Planck unit of time, then sequential, primordial spheres are generated faster than anything else in the physical universe. These spheres are also more dense than anything else in the physical universe.

This emergence at the Planck Scale is also defined by the Planck Length. Well below the thresholds for measurement, ostensibly they define a very different kind of blackhole. Here things are building and growing in number constantly.

Yes, it would seem that this is an excellent candidate for dark energy-dark matter.

How spheres begin to stack has everything to do with the mass-charge-density relations whereby as spheres stack, each sphere “discovers” others. Although the concept of sphere-stacking began with the 1611 Johannes Kepler discussions with Thomas Harriot, never have so many spheres been envisioned to emerge seemingly ex nihilo or from the infinite. We say these spheres emerge from the continuities, symmetries, and harmonies existent within the finite-infinite relation.

The finite-infinite relation is shrouded with history, religions, philosophies, mysticism, magic and more. In our constructions, the connection is through pi and then the other dimensionless constants. It is pi that opens access to the perfections of continuity, symmetry, and harmony.

Pi appears to be the first formula defined by continuity-symmetry-harmony that truly tells us something about the finite-infinite relation. The first qualities of that first sphere are the never-ending, always changing, always-the-same numbers, that define pi and manifest as continuity which creates order which is experienced as time.

Sphere to tetrahedron-octahedron couplet

The second quality of this most-infinitesimal sphere is its symmetries which create relations which are experienced as space.

There are college courses about the many types of symmetries involved.

For our purposes we focus on the most basic, cubic-close packing (ccp) of equal spheres and the creation of lines, tetrahedrons and octahedrons.

And, a third quality of this sphere is harmony which creates dynamics which creates a space-time moment defined by the Planck base units. This image takes pi and spheres and makes them dynamic, extending through time. It is called the Fourier Transform [3] and we are now researching possible faces of it and the harmonic functions uniquely created.

Within these three images, space-time and mass-charge become the Janus face of each other. Here, too, we should begin to see how electromagnetism and gravity have been yoked (through the spin states [direction and type] of the Fourier Transforms as also understood by Steve Smale and John Willard Milnor within their work on attractors and repellers).

Continuity, symmetry and harmony are conceptual words with exacting meanings within the infinitesimal scale. These words also are generalized observations that are applicable on the largest-possible scale. Yes, these words have applications from the most finite to the infinite and in so doing, create a de facto value structure for things.

Continuity, symmetry, and harmony are extended throughout the 202 base-2 notations that encapsulate everything, everywhere for all time. Yes, these three facets of any given moment lay the foundations for the expansion of the universe, the very nature of value, and the beginnings of economic theory.

Continuity, Symmetry, Harmony. Think of gold and silver coins. Think of fine homes, fine cars, fine clothes, and fine food. The first quality and value of each is that these things are the instantiation of continuity. Continuity establishes standards for the best of what is. It is not unpredictable. It transcends time (as it creates time).

Continuity is the beginning of value.

Now think of the people involved with the making, selling, and maintaining of all these fine things. Here are symmetries of many relations over time. All circles and spheres, here are affirmations, texturing, and imparting continuity. Every relation establishes, sustains and increases the inherent values.

Symmetry brings balance and stability and knowingness to value (continuity).

Now think about how those fine things bring joy, pleasure, and moments of perfection. As all the finer things are used or consumed, life is enlivened. There is a sense of a deep harmony and joy. The values created are experienced and confirmed and life is good. These are valuations that we yearn and strive for and though seemingly illusive, they are everywhere, just a bit deeper within.

Harmony opens the richest dynamics of life.

Conclusions: The three primary facets of life — continuity, symmetry, and harmony — coming from deep within pi, are the definition of the essential structure of the sphere, which ultimately give rise to very structures of our little universe. These facets manifest the deep nature of the finite and the infinite.

PS. What about quantum fluctuations? This link opens all references on this site.

*Relatively slow, the shortest measurable duration is currently a sextillionth of a second which runs from Notations-74 (1.01841×10-21 seconds) to Notations-77 (8.1472×10-21 seconds).


[1] An atom or any known particle. To grasp how small these spheres are, we apply base-2 notation to the Planck base units. The Planck units define these infinitesimal spheres. By applying base-2, we can account for all the spheres within natural groups. Most of it is quite straightforward, yet rather remarkable. It takes no less than 64 to 67 doublings before reaching the size of a neutrino and other elementary particles. The periodic table of elements ranges from about Notation-70 to Notation-80. Life comes alive between Notation-90 to Notation-103. The size of the earth and its environment come to manifest around Notation-144 where the Planck Time doubling has just passed one second. The size of our solar system manifests at about a light year within Notation-169. According to big bang cosmology, large structure formation requires 150 million years to begin. One million years manifests within Notation-189. One billion years manifests within Notation-199. Our current time is within Notation-202. To review these numbers, please see our horizontally-scrolled chart that we started to develop in 2016. It is still being developed! Notwithstanding, one can see that our infinitesimal sphere within Notation-1 is orders of magnitude smaller than a neutrino (and trillions upon trillions of neutrinos pass through us every day).


[2] The Planck base units, Part I. These Planck base units become solid gold (after 69 notations). My hope is that you’ll grasp their essence much faster than the academic-scientific community did. With few exceptions it took over 100 years to begin to understand Max Planck’s 1899 work. Here were units of time and space defined by four universal physical constants such that it was inconceivable that a smaller or shorter unit of time could exist. It is well worth the time to engage the Wikipedia accounts. My writing about these units has been on the job learning which will continue for my lifetime. There is that much more to learn.


[3] Other dimensionless constants. If these constants are dimensionless, where do they exist? Do these numbers exist only within themselves? There is so much to learn about dimensionless constants. Coming in two flavors, physical dimensionless constants and mathematical dimensionless constants, our all important Pi (π) is purely mathematical. Scholars work to define which constants are necessary for the Standard Model of Particle Physics (a)(b). Perhaps 31 is as good an answer as any in 2012. However, I believe we all have a huge amount of work to do to reconcile not just the 31 constants, but also the 300+ constants defined by NIST and the all those defined by Simon Plouffe (over a billion). This work is just getting started!


[4] Always the same and forever changing. The pure number and dimensionless constant, Pi (π), deserves its own day. Making pies and demonstrations are fun, yet this day should become a day that we all return to our foundations. It is here we can begin to grasp a bit of the perfection that is ours. How can something always be the same and be forever changing? That is the Great Enigma! We are all participating within it all the time. Life is a profound mystery that can actually be banal! It is everywhere within everything through all time.


[5] The very nature of time. For many years now, our leading scholars and scientists have been telling us that time is an illusion. We laughed at them. “Hardly true. Just take a look at my arrow of time. I look terrible, I’m 50 years beyond my prime. Only a fool makes such statements.” And then, I joined them. But my take on it is quite different. “I have 201 notations that are complete and symmetric; and, the current notation– that is Notation-202 — is directional. It is not an illusion; here time is directional, but only until you sleep. During sleep, all your uniqueness is recompiled into the universe. It is like throughout your waking hours, you are out mining gold — perfections of continuity, symmetry and harmony. And while you sleep, you make either a positive impact or a negative impact on the universe. It is a a rather novel, rough concept, but it is all that I have so far. Time provides part of the labeling of everything you do, think, believe, and process. I believe that is its most basic purpose. You uniquely label everything you do, think, believe, and process. Nothing is exempt.


[6] Unbelievably high. These prior studies of the emergence of structures, [1] [2] [3] [4] [5] [6] [7], and this overview make for a lot of reading, however, if we are going to join the crowd debunking the infinitely-hot big bang, we’ve got some work to do. Breaking free from a worldview that starts infinitely hot (big bang) where time and space go on forever (Newton’s absolutes) is not easy. Learning very large numbers to describe things that are infinitesimally small is not easy. Yet, once a person begins to be comfortable with those very large and very small numbers, one begins to grasp 539 tredecillion spheres per second, the expansion of the universe! That rate of expansion would be about the size contained within the current orbit of the International Space Station around the earth. This expansion would be quiet because these spheres are so much smaller than sound waves. It’d be deafeningly silent. Plus, this expansion begins superconductingly cold, not infinitely-hot. Yet, within just one second, the mass — 4.85×1034 kilograms — would be considered like a neutron star and the temperature would rise to support the quark-gluon plasma. The dark energy and dark matter experts should take a look. We may have a candidate here.

Consider a few simple calculations base on Planck Time, 5.39116(60)×10−44 second:
• 539,116,000,000,000,000,000,000,000,000,000,000,000,000,000 planckspheres/second
.. Read: 539.116 tredecillion or 539116000000000000000000000000000000000000000
• 436,117,076,900,000,000 seconds (approximately 13.82 billion years)
.. Read: 436 quadrillion, 117 trillion, 76 billion, 900 million seconds or 436117076900000000
• 4,361,170,769 times 5,391,247: 2.90655442×1013
• Add the eight zeros from seconds and 37 zeroes from the planckspheres per second
• Estimated total number of planckspheres in the universe: 2.90655442×1058 planckspheres

We’ll continue to check the math.


[7] Cannonballs on the deck of a ship. The best-known person to engage cubic-close packing of equal sphere is Johannes Kepler. We need to know his work and that of Thomas Harriot and a dozen other on the way to Thomas Hales in our day. Much more fundamental than the CCP that China proclaims, this ccp (1) (2) is a deep, fundamental process that evolves out of sphere stacking. It doesn’t get any more basic! And, with 539 tredecillion spheres expanding our universe every second, it is an image that our very finest cinematographic minds have not yet imagined.


[8] Creating relations which create space. The relation, a ratio also known as a formula, with continuity (time) is what is fundamentally real. Everything else is derivative. Creating relations with balance or love is the purest form. Those whose hearts bleeding the most for others, those who want everything for everybody, feel this fact even if they can not elucidate a concept around it. The problem is creating value to give to others takes away the possibility of that person creating their own unique value. I’ll come back to this footnote often; it needs to become a major discussion.


[9] Types of symmetries. Every symmetry is a key. We are just scratching the surface. Some geometers have been at it for decades; they know remarkable things about pi and symmetry. Yet when I ask them about the interiority of the octahedron and they can not tell me about those four hexagonal plates within, I know too much that is fundamental has been missed. We all need to be celebrating every honey bee in the world. Somehow they are in harmony with those hexagonal plates and everything that comes out of them has a deep hexagonality. We all need to know and experience every natural symmetry.


[10] Lines, tetrahedrons and octahedrons. Our earliest work was with points, lines, tetrahedrons and octahedrons. Even though we knew the sphere was important, we didn’t know what to do with it. It seemed rather removed from our basic building blocks. Then, cubic close packing of equal spheres showed up in a search. There is lattice generation. It changed everything. Yet, it still takes awhile to absorb; and to this day, there is still a lot to absorb and a lot more to learn.


[11] The Planck base units, Part II. We are all in search of an essential universe. Religious people of our world are often more stridently in search of what is essential. And, many are sure that they have what is most essential. Yet, until we understand more about the parts-whole relations, our talk is barely textured. We paint with such broad brushes, we often miss fine details that add to the majesty, the miracle, and the mystery of belief. All the dimensionless constants, both mathematical and physical, are the fine and extra-fine paint brushes. Until we know them, we don’t naturally use them. We can’t use them effectively. We may well use them unwittingly, but there is an art form, a perfection, within each of them. Here transformations may open new dynamics that have not even been imagined except for the most loving of our science fiction writers. Perhaps a new generation of artists-scholar-scientists can open ways to these dynamics and lead the way.


[12] The Fourier Transform. There are no less than six dynamics that naturally come with spheres. All can be applied to the Planck scale and to each notation thereafter.
Cubic-close packing of equal spheres: Though lifted up within this website first (2016), this image naturally builds on the next five dynamic images.
Sine-Cosine-Waves: We’ll all learn about the wave’s fundamental relationship to the circle.
Focus on Sine: We’re all going to learn a little trigonometry and calculus, too.
An all-natural polarization: An open metaphor and analogical construction (mimetic).
Lagrange points: All Lagrangians come home.


References & Resources

A More Simple Model: Six top postings, a summary overview
Worldviews to UniverseView
: Engage a Planck-scale Defined Universe.
The three
: Continuity-Symmetry-Harmony will take time to incubate.
: Change the Metaphor – Rewrite the History.
: One plancksphere/plancksecond, a natural-but-unorthodox expansion
First Instant
: Remember Pi, a primordial, constant, ever-changing, always the same
: Who am I? Who are you?


Communications: Emails & Instant Messaging

3:37 PM · Jan 30, 2021 @franlebowitz We all need a lift… outta the blues. We need a new view on life. Worldviews are too small. How about the universe? Here’s one for you: It’s real and it has pi, and spheres, and logic, and real moments of perfection. What’s not to love?

3:59 PM · Jan 31, 2021 @PNASNews Perhaps there’ll be a convergence here. We are starting at what we think is the first instant where Planck’s base units encounter pi and give us our first mathematical sphere: But at 539 tredecillion spheres per second, how are we going to sort things out?

4:43 PM · Jan 31, 2021· @walkingthedot You might enjoy this take on the first instant of the universe defined first by pi and the Planck base units. Gives the start of a full-blown view of the universe instead of little worldviews.

5:39 PM · Jan 31, 2021 @mthomps I’ll start working on a koan for the first instance of the universe with pi and Max Planck’s base units (Nobel, 1918, mentor of Einstein, began quantum theory). Basic, basics. Webpage: If you get there first, please let me know!

6:01 PM – Jan. 31, 2021 @SarahZielinskiWhy not start a different take on pi? What would be the most basic-basic use of pi? Could we start the universe? What if we were to use the Planck base units and add pi? I thought about it a bit: Perhaps it could add to the Pi Day discussions. Thanks. -Bruce Please Note: This little message was sent from within Sarah’s website from her comment page. She had written an article for Pi Day, March 14, 2011. Although the many links, i.e. the first to Pi’s history might best go to Wikipedia’s listing. There is also the book, the movie, a song, and a uniquely-focused, specialized website (with many more options).

1:14 PM · Feb 3, 2021· @ScienceWriters @SarahZielinski @sciencedirect @APSphysics @JAMA_current Pi Day is coming up. Here’s a different take on pi: “Pi is necessary for the start the universe!” Max Planck’s 1899 base units require pi (and the Fourier Transform) to get it all moving: Let’s go deeper with all the Pi Day discussions. Thanks. -Bruce


Afterthoughts. Like so many pages on this website, this is the first time we have so pointedly equated pi with the first sphere, the first moment of space-time, and continuity-symmetry-and-harmony. A sequel posting will be developed by merging this document with an earlier one titled, The First Instance of Our Universe. It also reflects the many other pages including:


Key Dates for this document, Tredecillion

  • This document was started on February 21, 2021.
  • First posted for collaborations: February 25, 2021 (Password protected)
  • The URL for this document is
  • First posted as a homepage: January 2, 2022
  • Prior homepage:
  • A related homepage:
  • First Tagline: Expansion of the Universe
  • Second Tagline: One PlanckSphere per PlanckTime
  • The last update of this page was on January 5, 2022.

In the beginning…

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First instance of the universe is still “in process.”
Pi (π) Shapes Our Universe
A Cold-Start becomes “QGP-Hot”
A Most-Simple Assist for Lemaître-Hawking-Guth Cosmology

by Bruce E. Camber Pi Postulations & More analysis


A different start of the universe is postulated so basic structure could be analyzed in light of the Planck base units. Can the most basic forms and functions within science logically and systematically unfold? (1).Here, the.progenitor of the circle and sphere, pi (π), has a pivotal role as one of our earliest working equations. (2).Pi.comes out of the seminal concepts of continuity, symmetry and harmony, simple perfections. (3).Spheres come alive and there is a rate of expansion. (4).Building on such concepts, Kepler and others give us sphere stacking and cubic-close packing of equal spheres. (5).Joseph.Fourier’s work on basic transformations (circa 1822) expands our understanding of pi and periodicity. (6) Our initial value formulation used the 1899 logic of Max Planck’s natural base units of length, time, mass and charge; these four numbers and all the dimensionless constants used to define them are fundamental. (7).To.create.order out of such a large number of spheres within the infinitesimal, we apply Euler’s base-2 notation. From PlanckTime to this day, there are just 202 notations. (8).The.first.64 notations are below the thresholds of direct measurements. In this model, these first 64 of the 202 are most foundational (superconductingly cold). (9) my laboratory for explorations. (10).Here let us engage causal set theory, causal dynamical triangulation, string theory, Langlands programs and so many other logically-constructed environments, too small to be measured, i.e. within the first 64 notations of this mathematical laboratory. -BEC


The infinitely-hot start of the big bang theory has key unanswered questions. In his 1927 reflections, Georges Lemaître advocated a cold-start, yet, by 1931 he had changed his mind and is now known for a rather-hot start. Max Planck’s 1899 calculation for Planck Temperature may have had something to do with that change, yet any explanation for this fundamental shift by Lemaître has yet to be discovered. [1] If Lemaître’s cold start had been adopted, I believe the fundamentality of pi would have been entertained in that process. Pi is a numerically-rich, universally-engaged, geometric, dimensionless constant; it is never-ending, never-repeating, invariant, irrational, and transcendental. These qualities are necessarily among the most fundamental processes that define our universe. The basic structure of the most-fundamental things tends to be spherical where the role of pi is pivotal. Herein, the hope of this article is to encourage a deeper analysis of the role of pi in shaping the first instant of the earliest universe.

Please note: We continue to build on this 2021 Pi Day article — Green Wall


Scale invariant, pi renders the qualities of continuity, symmetry, and harmony. First, there is the continuity of the never-ending and never-repeating numbers; there is also the continuity of all other dimensionless constants involved. Symmetry analysis begins within one of the five fundamental symmetry classes — dihedral, cyclic, tetrahedral, octahedral, and icosahedral. Each is a setting within which the dimensionless constants shape space-time, and mass-charge. Also, we assume Leibniz law of continuity and his transcendental law of homogeneity. The finite-infinite relation is a constant dynamic.

Harmonies of motion, symmetries extended through space-time, are described by the Fourier transforms. It is a new order and value for all numbers; everything-everywhere-for-all-time has deep-seated, dimensionless, dynamic relations. Subjects and objects are derivative and the relations are primarily real. The first dynamic moment is the face of continuity-symmetry-harmony and it captures the very nature of space-time, mass-charge, and electromagnetism-gravity. These fundamental expressions of reality are each Janus-faced, then each to the other.

Continuity, symmetry and harmony are conceptual words with exacting meanings within the infinitesimal scale. These words also are generalized observations that are applicable within the largest-possible scale. Yes, these words have applications from the most finite to the infinite and in so doing, create a de facto value structure for things.[2]


The “first manifestation of thingness” is the very first instance of space-and-time and mass-and-charge. These four faces of light are the fundamental shape within our universe and PlanckTime sets approximates an initial rate of expansion.

We had learned how the tetrahedron is derivative of the sphere, and that spheres stack and discover each other. A simple graphic helped us to grasp that phenomenon (below).

PlanckTime has been said to be the time it takes light to travel one PlanckLength. Here it is assumed to be one PlanckSphere* per PlanckSecond (a unit of PlanckTime). Here the very nature of light renders Planck’s calculation of a natural unit of time which is 5.39116×10−44 seconds. A simple calculation gives us a rate of expansion of 539.116 tredecillion planckspheres per second.**

Using base-2 to group those spheres, we find just 202 notations from PlanckTime to the current time. The more we engaged these numbers, the more every notation comes alive, fully interdependent with the others. The first 64 notations as such are relatively unknown and have hardly been explored. Those 64 notations are below the reaches of our measuring devices and most methodologies.

Quark-Gluon Plasma. For perspective, by Notation-136 the energy densities and temperatures are high enough for the Quark-Gluon Plasma (QGP) processes to begin. The numbers are there within our chart. The first second of the universe emerges between Notations-143-and-144. Each notation is being defined by a Planck-base unit multiple, by prior notations, and then by each subsequent notation.

Thinking about Lemaître’s primeval atom, Wheeler’s geon, and Pati-and-Salam’s preon, with the introduction of the first 64 notations, these can no longer be considered “point interactions” with no known extension. By the 64th notation, concepts like the preon and geon will have deep, rich textures and many extensions.

To help make the shift from the infinitely-hot Big Bang theory to include a Cold-Start UniverseView, consider this comparison, a simple chart. If so defined and understood, the PlanckSphere becomes the most essential, foundational unit that begins to quantize our universe. It provides immediate insights into the raison d’être and the very nature of homogeneity and isotropy, which taken as a whole is the aether, and measured as an effect, is dark matter and dark energy. [3]

* PlanckSphere: Not formally recognized, there are nevertheless many references to the word, Plancksphere, on the web (and within ArXiv).
** If this model is anywhere close to correct, this expansion of our universe is, for most people, a very different image, second-by-second. Consider the simple calculations:
539,116,000,000,000,000,000,000,000,000,000,000,000,000,000 planckspheres/second
.. Read: 539.116 tredecillion or 539116000000000000000000000000000000000000000
• 436,117,076,900,000,000 seconds (approximately 13.82 billion years)
.. Read: 436 quadrillion, 117 trillion, 76 billion, 900 million seconds or 436117076900000000
• 4,361,170,769 times 539,116 is equal to: 2.35117694×1015
• Add the eight zeros from seconds and 39 zeroes from the planckspheres per second
• Estimated total number of planckspheres in the universe: 2.35117694×1062 planckspheres


To review, although orders-of-magnitude smaller than an atom or any known particle such as the neutrino, that very-first infinitesimal sphere, is always “never-ending, never-repeating, always the same and forever changing.” Along with the inherent qualities of all other dimensionless constants, the very nature of continuity is redefined. It is a new order and value for all numbers; everything-everywhere-for-all-time has many dynamic relations.

Here, subjects-and-objects are derivative and the relations become primarily real.

Sphere to tetrahedron-octahedron couplet

That first dynamic moment is the face of continuity; it captures the very nature of time, space, mass and charge, and the first thing that happens is the spheres necessarily stack and begin creating dynamic relations. The earliest stacking is best described by cubic-close packing of equal spheres. Structure builds on structure.

Symmetry brings balance and stability and knowingness to values of continuity. [4]


Harmony opens the richest dynamics of the universe and of life.

Another quality of the sphere dynamics is a range of harmonies, Fourier pairs, symmetries in motion, each creating a space-time moment defined by the Planck base units, dimensionless constants, and a rich variegation of numbers. There are many faces and forms of the Fourier Transform. To associate these with the infinitesimal universe will empower many new insights about the nature of things and the very nature of life. More to come

The three primary facets of pi and of life — continuity, symmetry, and harmony — are the definition of the essential structure of the sphere which ultimately give rise to the very structures of our little universe and the deepest nature of both the finite and the infinite. I believe these three qualities define a perfection and a perfected state within space-time. Within the earliest notations there is a thrust of perfection. There is no room or time for imperfections. [5]


That first instant, defined by Planck’s four base units, are all so small, the first sphere is necessarily cold. From where would heat be generated? As each notation incorporates more units of Planck Charge – Planck Mass, there is a progression of forms, structures, substances, qualities, and systems. The initial guess is that systems begin to emerge around Notation-50 and one of the systems is the Mind. Here may be the first manifestation of what might be called ontic fluctuations, well prior to physical measurements, yet mental events that are not perfect, but discontinuous, asymmetrical, and not harmonious. What will be known as quantum fluctuations become measurable within Notation-64 to Notation-67. Of course, quantum fluctuations are not measurable until the advent of measuring devices within Notation-202. Thus, there is a domain of perfection from Notation-1 to those notations when and where ontic fluctuations begin. Yes, aspects of that perfection — continuity, symmetry, and harmony — are extended throughout the 202 base-2 notations that encapsulate everything, everywhere for all time.

This model is primarily about the infinitesimal universe. From the first instance with Notation-1 to Notation-144 includes the first second. The first year is within Notation-169, the first 1000 years is within Notation-179, the first million years is in Notation-189, and the first billion years is in Notation-199.

Today, Notation-1 to Notation-201 are fully symmetrical. Notation-202 contains the current time and will do so for another 7.9 billion years. Notation-202 is 10.89 billion years in duration. The sum total of all durations up to Notation-202 is also approximately 10.89 billion years. A simple calculation tells us that only a total of about 2.9 billion years of Notation-202 has been filed. There is what appears to be a flow of time experienced as time’s arrow. Within this model there is only one time, the Now. Our hypothesis is that the uniqueness of any moment-and-day is recompiled within the larger universe every time there is sleep. Of course, such a statement will be more deeply analyzed.[6]


To organize all this simple data — pi, spheres, continuity-symmetry-harmony, sphere stacking, cubic-close packing, the Fourier Transform, and an expansion rate of 539.116 tredecillion planckspheres per second — required a simple tool. Such a tool, introduced by Leonhard Euler in the 1700’s, is base-2 exponentiation. Those 539.116 tredecillion plancksphere (per seconds) could fill a circle slightly larger than the current low-earth, orbital paths, yet have a density of a neutron star that is orders of magnitude greater than the mass of the sun. If you can imagine that is happening every second, you have an image of a possible expansion of this universe.

The densities between Notation-2 and Notation 144 are unlike anything we can intuit. It would seem that such densities necessitate that the most simple symmetries emerge first. Nothing is by chance alone. No college course today imagines how symmetry groups flow within such densities and how cubic-close packing (ccp) occurs. We ask, “Do lines, tetrahedrons and octahedrons flow naturally within such density?” We are in search of scholars within the neutron-star disciplines who can help with these issues. [7]


Although not formally named by NIST, CODATA, BIPM, ISO or any other international governing body for scientific naming and standards, some refer* to that very first spherical unit as a PlanckSphere (10−44). There are six infinitesimal ranges that are yet to be named: 10−27, 10−30, 10−33, 10−36, 10−39 and  10−42. The 10−42 group includes 10−44 where that unit of time is currently informally referred as the PlanckSecond.  Reference:

Here Notation-1 through to Notation-64 (9.945379×10-25seconds) have no common name for time by which each is known. A naming convention has not been convened since 1991.** That’s a statement. This part of the scientific identity de facto has been deemed to be secondary, yet these may be the numbers necessary for deeper considerations of the proper definitions of dark matter and dark energy. Although dark matter and dark energy can be indirectly measured and we’ve known of their existence perhaps since Lord Kelvin (1884 lecture) or Poincare (1906 lecture), our lack of names for the infinitesimal does not facilitate discussion. We have reservoirs of infinitesimal data to couple with the growing reservoirs from large-scale CMB data. Names for these domains would help. So, as a result, we have become advocates that these high commissions name these six sets of numbers. [8]

* As of February 20, 2021, there are 1,420 online references to the “PlanckSphere.” Quotes are used to limit the search.
** Guide for the Use of the International System of Units (SI), Ambler Thompson and Barry N. Taylor, NIST Special Publication 811 2008 Edition, See Section 4.3, Decimal multiples and sub-multiples of SI units: SI prefixes, Table 5, p 7 PDF URL:


This lab will be more than an advocate for the clear recognition of this infinitesimal universe; it will be constantly refining our views of it. For example, we will continue to refine the work we did for the NASA SpaceApp innovation program to define a clock for the universe. We will continue to refine the horizontally-scrolled Chart of the Universe and our UniverseTable. But most importantly, we will continue to develop our understanding of the first 64 notations to bring dark energy and dark matter into the light. We will continue our understanding of how it all defines a new aether and renders a structure of homogeneity and isotropy. Yes, continuity-symmetry-harmony are three facets of any given moment and these lay the foundations for the expansion of the universe, the very nature of value, and the beginnings of economic theory. Some of our most important work will be interpreting this model as a value structure that inculcates aesthetics, ethics, morals, purpose and values.

Continuity is the beginning of value. Think of gold and silver coins and things made of these precious metals. Think of fine homes, fine cars, fine clothes, and fine food. The first quality and value of each is that these things are the instantiation of continuity. Each establishes standards for the best of what is. It is not unpredictable. It transcends time (as it creates time).

Now think of the people involved with the making, selling, and maintaining of all these fine things. Here are symmetries of many relations over time. All circles and spheres, here are affirmations, texturing, and imparting continuity. Every relation establishes, sustains and increases the inherent values. Symmetry brings balance and stability and knowingness to value.

Now think about how those fine things bring joy, pleasure, and moments of perfection. As all the finer things are used or consumed, life is enlivened and enriched. There is a sense of a deep harmony and joy. The values created are experienced and affirmed, and life is good. These are valuations that we yearn and strive for; and though seemingly illusive, they are everywhere, and always just a bit deeper within. Harmony opens the richest dynamics of life. [9]

10. Strings, Langlands, causal set theory, causal dynamical triangulation

Empowered by concepts at the edges of our knowledge, here our students will engage causal dynamical triangulation, causal set theory, scalar field theory, loop quantum gravity, string theory, Langlands programs, Spectral Standard Model… the cutting edge of research of the very nature of our universe. We’ll also begin to grasp the very nature of value. Returning to these roots to go over it just one more time, we want to see what we have missed in order to give us a more-complete picture of the structure of our emergent universe. Our three most general concepts — continuity-symmetry-harmony — render space-time and mass-charge as the Janus face of each other. Here, too, we believe that we’ll begin to grasp how it is that electromagnetism and gravity have also been yoked through the Fourier transforms. [10]

Our list of naive claims continues to grow and so this commentary will also grow.


Does pi have a role within emergence, especially the first moments and seconds of the universe?

Max Planck’s base units were ostensibly ignored for over 100 years. Today, we recognize their reality but those numbers radically change with just these four working assumptions:

  1. The four Planck base units manifest as a basic building block, an infinitesimal sphere many orders of magnitude smaller than a neutrino (64 base-2 notations). It is the first moment of spacetime.
  2. This sphere is also defined by pi and other dimensionless constants, then further defined by cubic-close packing of equal spheres and the Fourier Transform.
  3. Planck Time, 5.391 16(13)×10-44 seconds, defines a rate of expansion, one PlanckSphere per PlanckSecond renders 539.116 tredecillion units per second.
  4. Apply base-2 to that expansion; and, all those spheres and the universe are encapsulated within 202 notations. The first 64 are below the reaches of our measuring devices. Notation-1, the first moment in time, is that first sphere. The current time is within Notation-202. Those notations encapsulate everything, everywhere, for all time and our chart of those numbers provide a map to understand our universe.

We can begin to learn about a new aether, dark energy and dark matter, and the basis of homogeneity and isotropy which ultimately will help mitigate our inherent proclivity toward solipsism.

For Pi Day:


The three primary facets of pi and of life — continuity, symmetry, and harmony — are the definition of the essential structure of the sphere, which ultimately give rise to the very structures of our little universe. It all starts superconductingly cold. Yes, and, these facets manifest the deepest nature of the finite and the infinite.


Footnotes       (To return, click on the number inside the brackets.)

[1] Lemaître, Georges, 1927
• Aguirre, Anthony N. (10 April 2000). “The Cosmic Background Radiation in a Cold Big Bang”, The Astrophysical Journal. 533 (1): 1–18. Bibcode:2000ApJ…533….1A. doi:10.1086/308660. ArXiv.
D. Layzer and R. Hively, “Origin of the Microwave Background“, Astrophys. J.179, 361 (1973).[30] Ya. B. Zel’Dovich, Adv. Astron. Astrophys.3, 241(1965)
Odenwald, Sten, Quantum Physics, Knowledge in a nutshell, Arcturus Publishing Limited, 2020
P.J.E. Peebles and R. B. Partridge, Finding The Radiation from the Big Bang (PDF), January 9, 2007 (Note: 341 pages can be slow loading. -BEC)0
Simon D.M. White, Cold Dark Matter paradigm,

[2] Continuity, Symmetry & Harmony (at the top of most every homepage)
Dihedral, cyclic, tetrahedral, octahedral, and icosahedral
Law of continuity
Transcendental law of homogeneity

[3] “PlanckSphere” (or “Planck Sphere“): An unofficial word with a limited history — as of 23 February 2021, there were just 210 (or 1420) Wikipedia references. Until there is formal recognition of the word by some official international agency for naming conventions, we will attempt to update this footnote as often as possible. The concept of a most basic unit of the universe defined by something like Planck’s base units is essential. Planck’s base units have gained a level-and-status within the academic and scientific communities, many related words have followed. To date, there are no agreements about how these four Planck base units might manifest. Of the 1420 postings using the word, Planck Sphere, there is a wide range of implied definitions. We’ll continue our studies of the usage and update this footnote appropriately.

[4] Sphere stacking and packing: Cubic close-packing of equal spheres.
Johannes Kepler, Harmonices Mundi, Linz, 1619
Thomas Hales, A proof of the Kepler conjecture, Annals of Math. 162 (2005), no. 3, 1065–1185
Maryna Viazovska, The sphere packing problem in dimension 8, (PDF)
Jeffrey C. Lagarias and Chuanming Zong, Mysteries in Packing Regular Tetrahedra (PDF), AMS, Volume 59, Number 11, pp 1540-549 December 12, 2012
NOTE: Spheres, sphere stacking, and sphere packing have been profoundly studied. For our purposes, the two most important dynamics are (1) The dynamic image of spheres generating triangles, tetrahedrons, and then octahedrons and (2) dynamic images of the Fourier Transform. Both are derivative of pi.

[5] All things Fouriersymmetries in motion:
The role of symmetry in fundamental physics, David J. Gross, PNAS, December 10, 1996 93 (25) 14256-14259;
Fourier pairs: Grasping essential relations and dynamics

[6] Planck’s four base units: Three new roads to the Planck scale, Valerio Faraoni (Physics Department, Bishop’s University, 2600 College Street, Sherbrooke, Québec J1M 1Z7, Canada), American Journal of Physics, 85, 865 (2017);

[7] Base-2 exponentiation and Euler: This project got its start unwittingly doing a base-2 progression from a classroom tetrahedron inside the smaller octahedron within it, then into 112 successive steps back inside smaller and smaller octahedrons and tetrahedrons. We learned base-2 through geometry. It is how we learned about Euler and exponentiation. It was just a few months after that fateful day in class, December 19, 2011, when we began that I posted this article in Wikipedia. I was sure that our chart was already a STEM tool on the web somewhere, developed by different people, and that we only needed to find each other and pull our concepts together. It took four years to feel assured that we were outliers who had a very idiosyncratic view of cosmology.

[8] The Thresholds of Measurement: Since 2011 two measurement records for a unit of time have been broken by the Max-Planck-Institut für Quantenoptik in Garching, Germany. Prof. Dr. Ferenc Krausz group was able to measure an attosecond (10-18 seconds), then a femtosecond (10−15) and most recently a zeptosecond (10−21). It is still a long way to go to the Plancksecond 10−44). A hopeful glimmer on the horizon is the work of three doctoral candidates, Andrea Di Biagio (La Sapienza), Marios Christodoulou (Oxford), Pierre Martin-Dussaud (Aix-Marseille Univ, Université de Toulon) who are trying to formulate an experimental environment to determine time sequences as short as the shortest, the Plancksecond. They will also determine if time is ultimately discrete and digital.

[9] A Laboratory for the Infinitesimal: Three keys of the infinitesimal have not been explored:
The very first notation that is still generating one Plancksphere per Plancksecond
A domain of perfection from the first notation, perhaps to at least through Notation-50
A domain for the Mind and for Systems, perhaps from Notation-50 to Notation-60
Going back in time: Our earliest explorations (2011-2012)

[10] Out on the edges of our knowledge:
Causal dynamical triangulation: “…theorized by Renate Loll, Jan Ambjørn and Jerzy Jurkiewicz, and popularized by Fotini Markopoulou and Lee Smolin, is an approach to quantum gravity that like loop quantum gravity is background independent.”
Causal set theory: David P. Rideout, David Malament, Graham Brightwell, Ruth Gregory. Space-time as a causal set, Rafael Sorkin, Luca BombelliJoohan LeeDavid Meyer (1987) See also: Nick Huggett, James Owen Weatherall and Christian Wüthrich.
Scalar field theory: Michael Peskin, Pierre Ramond
Loop Quantum Gravity: Abhay Ashtekar, Carlo Rovelli, Jorge Pullin and Jerzy Lewandowski, Francesca Vidotto, Israel Gelfand, Mark Naimark, and Irving Segal
String theory and superstring theory: Witten, Dean Rickles
Langlands programs: Emil Artin, Ngô Bảo Châu, Vladimir Drinfeld, Edward Frenkel [1], Stephen Gelbart, Robert Langlands [1], Laurent Lafforgue, Vincent Lafforgue, Gérard Laumon, Michael Rapoport, Andrew Wiles
Spectral Standard Model: Ali H.Chamseddine, Alain Connes, W.D. van Suijlekom

Note: No page on this site is ever truly ready or complete. There are still just too many blanks to fill-in. Thank you for your understanding. The next page being developed is about the 539 tredecillion plancksphere per second. It will be building on this page as well as an earlier page about expansion.



• Orders of Magnitude Smaller Than Any Known Particle. In the prior posting, the size of things using base-2 notation from the Planck base units was explored. Planck Length and Planck Time are so infinitesimal spheres, the first 64 notations are difficult to conceive. Also, beyond imagination are the 539.116 tredecillion planckspheres by the first second between Notation 143 and Notation 144. The overall picture is reviewed in that prior posting, Notwithstanding, one can see that our infinitesimal sphere within Notation-1 is orders of magnitude smaller than a neutrino (and trillions upon trillions of neutrinos pass through us every day).

.Cubic-close packing of equal spheres: Though lifted up within this website first (2016), this image naturally builds on the next five dynamic images. Sine-Cosine-Waves: We’ll all learn about the wave’s fundamental relationship to the circle. Focus on Sine: We’re all going to learn a little trigonometry and calculus, too.An all-natural polarization: An open metaphor and analogical construction. Lagrange points: All Lagrangians come home.

Types of symmetries. Every symmetry is a key. We are just scratching the surface. Some geometers have been at it for decades; they know remarkable things about pi and symmetry. Yet when I ask them about the interiority of the octahedron and they can not tell me about those four hexagonal plates within, I know too much that is fundamental has already been missed. We all need to be celebrating every honey bee in the world.* Somehow they are in harmony with those hexagonal plates and everything that comes out of them has a deep hexagonality. We all need to know and experience every natural symmetry.

*Birds & the Bees: Our neighbors left a little package of honey at our door before they retreated back to their family home in North Carolina. It couldn’t have been more gracious and inspirational. I began to think about the bee, honey and the bee’s hexagonal containers. What other living thing naturally, automatically, instinctively constructs such a basic shape, a most-simple geometry, without thinking about it?

I wondered, “What bees are likely to give us the most pure honey of the world?”

I decided it would have to be in a remote place with the fewest number of humans (we rather naturally mess things up). I rediscovered the Mutiny on the Bounty (circa 1788) and the little island of Pitcairn in the South Pacific. They have honey! I also rediscovered the honey in New Zealand called Mānuka honey. Along with our neighbor’s gift from a little farm in Chocowinity (Happy Honey Bees), we will be having a blind taste testing of four (we’ll add a commercial brand from Florida). It should be fun, plus informative, plus inspirational. How do these bees know basic geometries? -BEC

PS. I’ll make up a taste-test rating sheet with ten questions and share that and the results of our first tests at a later date. The mānuka honey has arrived from New Zealand. Now, we are waiting for our Pitcairn honey to arrive! More later! -camber


References & Resources
A More Simple Model: Six top postings, a summary overview
Worldviews to UniverseView
: Engage a Planck-scale Defined Universe.
The three
: Continuity-Symmetry-Harmony will take time to incubate.
: Change the Metaphor – Rewrite the History.
: One plancksphere/plancksecond, a natural-but-unorthodox expansion
First Instant
: Remember Pi, a primordial, constant, ever-changing, always the same
: Who am I? Who are you?

Fine-Tuning, Complexity, and Life in the Multiverse, Mario Livio, Martin J. Rees, Jan. 2018 Two assumptions about the universe.
The emergent universe: inflationary cosmology with no singularity, George F R Ellis, Roy Maartens, IOP Publishing, Classical and Quantum Gravity, Volume 21, Number 1, November 2003
The Arrow of Time, David Layzer, Scientific American, December 1975.
Fourier Transform Pairs, A Listing, Peter Joseph Bevelacqua, 2010

The Uncanny Precision of the Spectral Action, A. H. Chamseddine and A. Connes, ArXiv, 2008

Research centers: Today, you can find people, their references-and-resources, in just seconds. So much is on the web. I just tweeted the following: @CKinstitute, @4pt0schools, @UCICove , @RichardSudek (UCI Beall Applied Innovation, Chief Innovation Officer & Executive Director, UC-Irvine within minutes the following:

“The biggest impediment to personal growth is a limited worldview. We live in the universe and need to see all things within that context. We’ve started on an integrated universe-view in a New Orleans high school: Today:


Communications: Emails & Instant Messaging
Fine-Tuning, Complexity, and Life in the Multiverse, Mario Livio, Martin J. Rees

4:01 PM March 1, 2021 An email sent to old contacts with whom I haven’t heard for awhile:
Quick questions. Have you ever thought:
1. Here we are 13.79 billion years of history and we barely know much about it, or think about it in order to context and understand our own time. Are we limiting ourselves?
2. Here we are in a splendid universe but we rarely think about it, we rarely think beyond our home’s bounds (or the country’s bounds during the evening news)! Do we need to expand?
3. What if we had an integrated view of the universe, everything, everywhere for all time that entirely encapsulates it all within 202 base-2 notations? Don’t you think that would give us a new perspective and it just might help us break free of our naturally solipsistic views of things? Don’t you think a highly integrated view of the universe could open questions we usually do not entertain? Might it give new insights to all the old, open questions about life (and physics and cosmology)? Might it help us get beyond worldviews with inherently limited points of view? Interesting? Thanks.

7 PM 21 March 2021 to Ben J. Green, Oxford:

Dear Prof. Dr. Ben Green:

  1. Have you ever considered Lematre’s 1927 model of a cold start with his primeval atoms?
  2. If not, why not?
  3. If so, might those primeval atoms be simple spheres defined by the Planck base units?
  4. If not, why not?
  5. If so, might Planck Time 5.39116×10-44 per second set a rate of expansion such that there are 539.116 tredecillion spheres per second?
  6. If not, why not?
  7. If so, might we apply base-2 notations simply to group these spheres in a logical progression whereby from Planck Time to the current time there are just 202 notations and the process is still active?
  8. If not, why not?
  9. If so, might we assume cubic-close packing of equal spheres whereby tetrahedrons and octahedrons are generated?

May I go on? If it is so entirely naive that I lost you with any one of these questions, I kindly ask that advise such. Thank you.

Instant Messages & Tweets

2:56 PM · Mar 18, 2021 @HarveyMasonjr Thank you for all you do to make this universe a better place. We’re all held down and back with little worldviews with no value equations. Solipsism is easy: We need values: We need an integrated view of the universe. Harvey Mason, Jr. is the CEO of the Grammy Awards.

11:28 PM · Feb 24, 2021 @tara_taylor How about expanding our understanding of pi? Could it be involved in the very first instance of space-time? Could be involved with the defining of a PlanckSphere generated from the Planck base units? is where we struggle for answers. -Bruce

6:46 PM · Feb 21, 2021 @RepKinzinger We all need a different vision of who we are and why. All our little worldviews tend to trample anything in the way. Globalism is too small. We need an integrated view of the universe so we can get grounded in the basics: is my simple start.

6:34 PM · Feb 23, 2021 @Gary_D_Cohn Possibly our most basic problem is our worldviews are too small and solipsistic when we need to have an integrated view of the universe. started in 2011 by applying base-2 to the Planck units to encapsulate the universe in 202 steps!

2:50 PM · Feb 25, 2021 @TrenaWilkerson Math should be engaged, not according to our world, but to the universe. Apply base-2 to Planck’s base units and we have a simple, mathematically-integrated view of the universe: Just 202 notations to consider. See chart: -BEC

3:59 PM · Feb 26, 2021 @FryRsquared Pi has to be more than the banality of so many Pi Day’s celebrations. Here’s a simple alternative: Puts Pi back at the beginning of it all. Here’s another:

@KurdistanRegion@IKRPresidentand 2 others A most important thing we can do is break free of our limited worldviews and adopt an integrated view of the universe. We’ll begin thinking about everything, everywhere for all time: is just a start, but start we must! The numbers:


Afterthoughts. Let us all begin to pointedly equate pi with the first sphere, the first moment of space-time, and continuity-symmetry-and-harmony. When pi is brought back to the first moment of space and time, everything changes.

More to come…


Key Dates for this document, Instance

  • This document was started on January 27, 2021.
  • First posted for collaborations: February 8, 2021
  • The URL:
  • The Prior Homepage:
  • Headline: Pi (π) Shapes Our Universe
  • Subheading or Subline: Cold-Start beats Infinitely-Hot Start
  • First Tagline: The first instance of the universe
  • Second subline: A Simple Alternative to Lemaître-Hawking-Guth Cosmology
  • The most recent update of this page: March 26, 2021