The necessary Janus-face of pi-π and thus of all things*

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

Is pi (π) both finite and infinite?
by Bruce E. Camber (first draft)

James Webb Space Telescope1 (JWST): The JWST is challenging everyone who studies his/her/its findings. I predict that it will push the Standard Model of Cosmology2 well-beyond the formulations and justifications for big bang theories. Lemaître, Hawking, Guth3 and followers have had to ignore the most basic formula of science, pi (π), as well as the key dimensionless constants in order to make big bang cosmology appear to work.

An article, Standard Model of Cosmology Survives a Telescope’s Findings, by Rebecca Boyle4 was published on January 20, 2023 in Quanta Magazine.5 It focuses on the people and issues shaping this Standard Model. However, if we place all those issues within our 202 base-2 notations6 from Planck Time to this moment in time, our predictive, mathematical model would readily begin to absorb and transform the sense of logic within big bang thinking. The continuity equation from Planck Time to the current day is perhaps the most-basic continuity equation there is. The progression of numbers from the very-first moment of the universe to the very-first second7 of the universe is within our Notation-143[8] out of the 202. It is a “must-study” progression. It is a look at the earliest universe unlike any proposed. It has Planck units (numbers), geometries, logic, a built-in thrust9, and a host of studies10 yearning to be on that grid.

Penultimate grid.11 In this model key symmetry-and-harmonic functions, the essence of the finite-infinite transformation, give rise to a real cosmological constant that within Notation-0 emerges as an infinitesimal sphere. Assuming one Planck sphere per unit of Planck Time and Planck Length, within the first year )which is within Notation-169), the mathematics of this universe is already showing signs of greatness. Starting with Planck Mass at 2.176.470(51)×10-8 (kg), within just over one year our universe is already 1.628×1042 kg. As a comparison, our sun is estimated to be 1.989×1030 kg. Even with Jupiter, the sun is estimated to be 99.5% of the total weight of the Solar System. This expansion is clearly inflation. The entire Milky Way has been estimated (Sloan Digital Sky Survey). Currently it is thought to have a total mass of around 6×1042 kilograms. And, within the first year, the universe has densities in the range of neutron stars and blackholes. With just the first year, we can begin to understand why and how the universe is quite so large in 13.8 billion years.

This trajectory for the universe has a commonsense logic based on a simple mathematical progression that is emulated by nature everywhere.

From that first infinitesimal sphere, tetrahedrons and octahedrons naturally emerge. Fourier kicks in. Inherent harmonic functions of the Fourier transform should readily inspire because, yes, here is a place for Langlands programs and for string and M-theory, and loop quantum gravity and all the hypothetical particles. Here is a place of all those disciplines that are not on the grid. There’s even a place for Smale and Milnor with their attractors and repellers.

Here is a model of the earliest universe where our thinking is least developed. And, it offers a new challenge and opportunity. It’s a new opening of possibilities.

When the Boyle/Quanta article came out, I had been reflecting on the Scientific Method and how currently we all de facto assume the big bang. Of course, de jure is the counterpoint and I was particularly looking at pi and the dimensionless constants to provide foundations for natural law. It was increasingly clear that pi’s continuity-symmetry-harmony were descriptions of both the finite and infinite and de facto was finite and de jure was infinite. Although the Boyle article gives a passing reference to the big bang, that theory has nothing to do with the results of the JWST and it really doesn’t change any of the conclusions made by Boyle. She has given us an excellent introduction to some of the key challenges the JWST is making. It is not about the Standard Model. It is about the first microseconds and minutes and years and how the universe began so smoothly.

It is an article to which I will return and watch as a wonderful encapsulation of this moment in time.

Thank you. –BEC

Editor’s Note: Obviously this article was inspired by Rebecca Boyle and her article in Quanta Magazine. This homepage evolved from my note to her. -BEC



Endnotes & Footnotes
All these points already have pages within this website. Another 14 footnotes are being added…

[*] PI (π). In this website, pi (π) always has a face of the infinite and a face of the finite. When focused too much in either direction, we lose our bearings. For this posting, we had first named it, pi-pi, but quickly discovered there was a hip-hop recording named, Pi-Pi, by Milli Music, director, Shane Creative. Their recording of pi-pi opens with the lyrics, “Only you can bring the demon home.” So, here’s a viewer warning: drugs, sex, and darkness and nothing to do with circles or spheres was our first encounter with Pi-Pi. Our next, another recording named, Pi-Pi-Pi, is humorous and it is all about Pi Day and the circumference of the circle with a very light touch.

My work with pi (π) started in 1961 in high school. But it took a much later high school geometry class to begin the progression from the Planck units using base-2 that resulted in 202 notations. Those notations truly opened the discussion around the question, “What is the first thing to manifest in this universe?” After a false start, we’ve settle on an infinitesimal sphere defined by those Planck units. However, we are also open to using the Stoney units or new ISO units. Arguably, studies of pi began between 2500 to 5000 years ago. Euclid’s Elements was published around 300 BC. So with so much focused study over such a long period of time, of course, we think we have milked it dry. The opposite is true. We’re making slow progress to grasp its deepest, broadest, highest, most-comprehensive meaning.

[1] JWST. The James Webb Space Telescope is technically named for the head of NASA from 1961 to 1968. Huge progress was made during the Mercury, Gemini, and Apollo programs under his leadership. Yet, it could be argued that the array of sixteen hexagonal mirrors of this telescope is more like a she than a he. In the spirit of the time, I think the pronouns, he/she/it, are probably suitable. Wikipedia‘s summary of this work is an ongoing venture that is often updated with new information.

[2] Standard Model of Cosmology doesn’t care how the universe started. The more comprehensive it is the better. The more mathematical it is, the more compelling. If the model includes some of the key concepts of the big bang, yet not its time line or its place of importance, so much the better. The 202 base-2 notations do all that and so much more; so of course, we’ll come back to this footnote “for more” as we attempt to build a connection between the it and the Standard Model for Particle Physics.

[3] Lemaître, Hawking, Guth were the most pivotal thinkers to promulgate the big bang. Of course, Lemaître is long dead, and the very few who knew him are now close to the end of life. Hawking died on Pi Day, March 14, 2018. I can well-imagine he had had enough. Photo-op after photo-op, it is hard to be a celebrity and even consider doing serious science. Our infinitesimal sphere just may be a very good definition of Guth’s inflaton. It is creating the laws of physics as it populates the universe which based on either Planck‘s or Stoney’s base units could anywhere from 539-to-4605 tredecillion infinitesimal spheres per second… More to come.

[4] Standard Model of Cosmology Survives a Telescope’s Findings, R.Boyle, Quanta, Jan. 2013 Rebecca Boyle has written an excellent article. She gives the big bang passing acknowledgement yet focuses on the current tensions in cosmology created by the results of the JWST. The focus has to be on the results of real research. And, the focus is to answer the question, “How can the universe look like these images 330 million years from the start?” Although the base-2 expansion from a single infinitesimal sphere is dramatic, it is orderly and entirely geometrical and mathematical. It is consistent with the JWST’s findings… More to come. Standard Model of Cosmology Survives a Telescope’s Findings, by Rebecca Boyle

[5] Quanta Magazine Thomas Lin started the publication in 2012 and Quanta Magazine has already won the 2022 Pulitzer Prize in Explanatory Reporting and the 2020 National Magazine Award for General Excellence. The magazine is primarily sponsored by the Simons Foundation which is also responsible for the Flatiron Institute in NYC (Wiki), Simons Center for Geometry and Physics at Stony Brook, and hundreds of programs related to the advancement of scientific knowledge. James Simons used the power of mathematics to understand the markets and trading and made billions. His investment in Quanta Magazine is richly paying back.

[6] 202 base-2 notations. The horizontally-scrolled chart of 202 base-2 notations started in December 2011 with just Planck Length. That chart had somewhere around 202 notations. Not until we mapped it with Planck Time did we have a more definitive stopping point: 13.79 to 13.81 billion years. The 201st doubling has taken Planck Time, 5.391 16(13)×10-44 seconds, around 173,272,944,073,600,000 seconds or 5.4908 billion years. If we add up each notation up to the 201st notation, we are one unit of Planck Time shy of 10.98 billion years. Simple math tells us that just 2.8284 billion years has passed since the beginning of the 202nd notation (Calculation: 13.81 minus 10.9816 ≈ 2.8284). It is an important, hard-earned perspective. Our calculation for the UniverseClock helped us along that path. We are now challenged to exegete each notation! We quickly discovered how difficult that notational analysis can be: 0, 31, 64, 67, 101, 137, 143, 167, 197, 199 and 202.

There is a place for the big bang numbers but not until after the first few seconds.

[7] The very-first second. One might think that the very-first second of the universe is well understood. It’s not. Steven Weinberg within his 1977 book, The First Three Minutes, says on page 5, that “…one-hundredth of a second (is) the earliest we can speak with any confidence” and then adds with great aplomb that “the universe was about a hundred thousand million (1011) degrees Centigrade” as if he had observed it in the laboratory. Then there is a group of 27 scholars from around the world who titled their article, The First Three-Seconds. They didn’t get anywhere close to the first second. It is such a blindspot.

[8] Notation-143. Then, there is Notation-143, or the 143rd doubling of Planck Time, and we are well into the last third of our chart. Notations 1-67 are virtually unexplored and, to the best of our knowledge, had never been cited in our scholastic literature. We’ve called it the small-scale universe when perhaps The Infinitesimal Universe would be more appropriate. Notations 67-to-134 have been cited as the human-scale universe while Notations 135-to-202 have been cited as the large-scale universe. By that 143rd notation, on the first pass through, the core geometries, mathematics, and physics have been shaped by efficiencies and densities. There is no time or space for indeterminacy. In that first pass there is only perfection. It is the most efficient and the most simple. I can well-imagine those efficiencies become precedents and that perfection, currently called smoothness, readily defines the first 330 million years right up to and within Notation-197.

[9] Thrust in our universe. In September 2017, I took a stab at my first real article about the thrust in our universe. So now, over five years later, it is time to revisit that article and update it as much as possible. The major update would involve our understanding that the three facets of pi are each a Janus-face for the finite and the infinite. Another major update will include the continuity-symmetry-harmony functions that are abiding.

[10] Major studies not on the grid. I consider nine major studies not on the grid. I have written to Robert Langlands, Ed Frenkel, and others within Langlands programs. They have not yet acknowledged the 202 mathematical notations. Why not? It’s just math and logic. There is no philosophy. There are no agendas. It is either correct or not.

I have also written to people within string theory. None have acknowledged the 202 notations. Why not?

I believe people are naturally incrementalists. It is more comfortable. The Planck units were ostensibly ignored until 2001 and by that time Hawking-Guth-and-family had a choke hold on the theory about the start of the universe. With Hawking’s death, the choke hold has become somewhat more relaxed. With the JWST it’s time to breathe again. Of course, conformal-quantum-and-scalar field theories (CFT, QFT) have holds on all the old-timers within the industry. You can imagine that each night they are hoping that they may see a breakthrough before they die. Yet, although John Wheeler’s sense of simplicity was a good idea, for most of the nonagenarians, this base-2 model of 202 notations is just too simple. It is too obvious. Yet, prior to 2001 and Frank Wilczek’s three articles about the Planck scale, Planck’s numbers were aloofly small in a similar way that Dirac’s were aloofly big.

Perhaps a little more to come…

[11] Penultimate grid. The first infinitesimal sphere has been likened to Lemaître’s primeval atom and Guth’s inflaton. Both are hypothetical. Our very first infinitesimal sphere is a little less hypothetical because it has a geometry, a mathematics (an algebra), and a deep-and-abiding logic. The universe has to start with something to create space-time. Of course, our postulation that our universe is totally populated by such infinitesimal spheres is also hypothetical. Notwithstanding, this hypothetical penultimate grid warrants inspection. Although the finite-infinite transformations between the faces of continuity-symmetry-harmony (CSH) are assumed, our focus is on the finite. The finite is first defined by CSH, then defined by the Fourier transform, and the Poincaré sphere, and then the Poincaré homology sphere. Any and all types of spheres are included as potential spheres waiting for their mathematics to evolve (be possible, come out). This, of course, would include Smale and Milnor’s spheres, attractors and repellers.

In 1980 in Paris at the Institut Henri Poincaré, Jean-Pierre Vigier discussed (and I listened) the EPR paradox in light of the work of Alain Aspect in d’Orsay. Instead of infinitesimal spheres, Vigier had suggested using the metaphor of the dominos which was not instantaneous. Infinitesimal spheres with the packing densities suggested by the Planck-or-Stoney-or-ISO numbers, would be instantaneous. Mathematics and physics begin here.

Please note: Today, more of the linked words or expressions may still become a footnote. Today is indeed February 3, 2023.


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

•   The Friedmann–Lemaître–Robertson–Walker (FLRW) Metric
•  Path integrals and Gaussian fixed point. See Assaf Shomer’s on page 7: “The derivation of the path integral formula in quantum mechanics of a massive particle involves chopping up the quantum evolution into very short time intervals and inserting complete sets of states between them.”
•  Doplicher S, Fredenhagen K, Roberts JE (1995) The quantum structure of spacetime at the Planck scale and quantum fields. Communications in Mathematical Physics 172(1):187–220
•  Scale invariance and conformal symmetries


There will be emails to many of our scholars about the key points.

31 January 2023, Thomas Sumner, Simons Foundation
30 January 2023, Basil Hiley, University of London (UCL)
29 January 2023, Thomas Lin, Quanta Magazine
27 January 2023, Drew Harrell, Washington Post
26 January 2023, Carl Zimmer, New York Times
25 January 2023, James Sethna, Cornell
24 January 2023, Rebecca BoyleQuanta Magazine
23 January 2023, Rohan Naidu, MIT Pappalardo Fellow


There will also be many instant messages to thought leaders about the following key questions:

  1. Is it possible that the first instance of the universe is defined by Planck’s base units?
  2. Is it possible that the first manifestation of those base units is an infinitesimal sphere?
  3. Might the characteristics of pi describe those spheres?
  4. Might the Fourier Transform impart either electromagnetism or gravitation to each sphere?
  5. Is it possible that one sphere manifests per unit of length and time?
  6. If so, doesn’t that compute to 539 tredecillion spheres per second using Planck units and 4605 tredecillion units per second using Stoney time?
  7. Is it possible that the densities within the earliest notations are on the order of a blackhole?
  8. To create some sense of order with the generation of infinitesimal spheres, may we use base-2 notation?
  9. Using base-2 notation, are there 202 base-2 notations from Planck Time to the current time?
  10. Is the calculation significant at one second where that Planck Length multiple is a very close approximation of the distance light travels in that second?
  11. Is it significant that quantum fluctuations are measured within Notation-67? Notation-72 appears to be the limit of our abilities to measure a duration of time.
  12. Would these notations, 1-64, provide 64 possible redefinitions of a point-particle? (And, I would add a vertex.)

11:14 AM · Jan 31, 2023 @RBReich Everyone should find their creative thing that makes them happy and brings them joy and ask, “Is there a business in there?” Millions have. We call it small business and it enriches the soul and satisfies the heart and inspires the mind.

8:45 PM · Feb 1, 2023 @DrOsamaSiddique @Harvard_Law @UniofOxford @IGLP_HarvardLaw There is a type of natural law within pi (π) ( that also creates a mathematically-integrated view of the universe where value comes from its continuity-symmetry-harmony.


Participate       You are always invited.


Keys to this page, pi-π

• This page became the homepage on January 27, 2023 at about 8:42 PM.
• The last update was February 3, 2023 in the morning.
• This page was initiated on January 23, 2023 at 8:42 AM
• The URL for this file isπ/
• The headline for this article: Pi Defines the Finite and Infinite.
• First byline is: Filename changed to “pi-π” because pi-pi was already engaged.


On learning a little about the work of Carl Zimmer


First email: Sent within the form on his homepage, January 26, 2023 at 8:47 PM

Hi Carl, 

Most of us have bought into the Hawking-Guth version of the big bang theory. With the smoothness and early formations found by the James Webb Space Telescope, more questions are being raised by serious scholars. The problem has been that there has been no viable alternative. 

Our high school geometry classes strayed off the given curriculum back in 2011. We were having some fun with “embedded geometries.” Particularly, the tetrahedron enclosed four smaller tetrahedra in its four corners and an octahedron in the middle.

If you were to keep dividing those edges by 2, you can do a Zeno-like progression. In 45 steps, we were at the size of the fermions. In 67 more steps we were at the size of the Planck base units. If you multiply by 2, a rather robust geometric expansion occurs. In just 90 steps, we were out to the size and age of the universe.

As simple as it is, the universe encapsulated in 202 base-2 notations is just too much for most people to swallow. At first we were quite excited about the progression.

It seemed like the penultimate STEM tool. The kids loved it. So, that year it became a reference point, especially in our science and math classes. Then, I began sharing it with teachers around the area, and they asked for more source materials, we slowly realized that there were none. I got cautious. I don’t want the kids or other teachers going off with a half-baked concept. One of my scholarly acquaintances told me, “It’s idiosyncratic.” It was a dilemma so I pulled it back from the classes until we could get some readings from scholars. Freeman Dyson at the Institute for Advanced Studies cautioned me, but encouraged the exploration. Frank Wilczek, a 2004 Nobel laureate at MIT, did the same. In 2016 I decided to make a pointed study of it all. I had pages all around the web in free hosting sites. I consolidated those pages and just kept going:

Over the years, I aggregated new insights: Pi became the centerpoint. Its continuity, symmetry and harmony became a Janus face of the finite and infinite, and conceptually that opened it all up.

Interesting? Want to hear more?  Thank you for getting this far into these weeds!



Bruce E. Camber

On discovering the work of Rohan Naidu

Rohan Naidu, MIT, Cambridge, Massachusetts 02138

RE: Primary reference: Standard Model of Cosmology survives the James Webb Space Telescope
Homepage(s): Github, MIT Pappalardo Fellow, Twitter

First email: Jan 23, 2023 @ 6:39 PM Revised: January 25, 2023

Dear Rohan:

  1. Could we have vested too much in the wrong beginning? I think so.
  2. Could a natural inflation work if we start with something like Planck’s base units? It seems so.
  3. What would the very first moment look like?

My old mentor, Phil Davis, at Brown (and prior to that the head mathematician at NIST), loved the infinitesimal sphere. And, he convinced me it is the most logical place to start thinking about the start of the universe. 

Today, I’d say, “It’s the best possible start. It’s better than Lemaitre’s primeval atom.” Using Planck’s numbers, if we assume one sphere per unit of Planck Time, there would be about 539 tredecillion infinitesimal spheres per second. Our page about it: At that rate and with all the smoothness, 330 million years seems reasonable like a safe bet for large-scale structure formation:

I know how entirely idiosyncratic this construction is. Yet, I can hear the irascible nudge and savant, Murray Gell- Mann say, “Stop your whining and keep digging.”

Best wishes to you,



Asking questions of Yuxi Fu

Yuxi Fu, Shanghai Jiao Tong University, (C9) Shanghai, China

Homepages(s): Chinese Academy of Science, More to come
Publications (among many, these are a few documents): Thesis for Interaction (2021), A functional presentation of Pi calculus (2001), Symmetric π-calculus (1998)

References within this website:
(More come)

Third email: January 3, 2023 at 10:23 AM

Dear Prof. Dr. Yuxi Fu:

Thank you again for all your most thoughtful work. My working page about your work is now public: and there is a reference here:  Since sending the originals, small edits have been made to each document.

On my first visit to China, I was in Beijing to meet with steel manufacturing people and then down to Hong Kong to visit with family friends. In 2010 I had hoped to join my friend and the head of Boston University’s physics department when he donated his library to Tsinghua. More recently I had hoped to open a channel of communication with Andrew Chi-Chih Yao. I have had helpful exchanges with Chaunming Zong of Tianjin Center for Applied Mathematics (TCAM) and Xijia Wang of Hunan.

As the world continues to shrink and more and more scholarly work is shared, those shared insights and concepts will bring even more people together.  It is a very special time in the life of our little world. Moving from our very limited worldviews to a highly-integrated, mathematical view of the universe is important. It is common ground. Although big bang cosmology (bbc) is the de facto core concept of cosmology, when it begins to shift to foundationally more simple concepts, ostensibly those considered de jure, i.e. dimensionless constants like pi and our universal constants, we will all slowly shift and the solipsism of the bbc will begin to subside and a more gentle understanding of who we are and why will begin to emerge. 

Again, let me thank you for all your scholarly work.



PS. I have been spending time using Google Maps to visit your cities and have had a fine time exploring the ins-and-outs of neighborhoods around Shanghai Jiao Tong University as well as other schools within the C9. Most beautiful and most impressive. -BEC

Second email: December 28, 2022 at 3:54 PM

Dear Prof. Dr. Yuxi Fu:

In the Thesis for Interaction (2021) you open with a quote from David Deutsch who suggests that our current theories of computation are too abstract because that are based on “pure” logic and mathematics that has nothing to do with physical processes. I would challenge David on his definition of the very nature of physicality, “Are the Planck base units physical?” I think we would all agree that they are.

That begs the next question about nature of a “value-passing communication mechanism.” What might be some of the functional mechanisms for an information exchange communication?“, an initial discussion about which I found in Section 5, Conclusion and Variations, page 208, J. of Comput. Sci. & Tech. V1.13, 1998.

Today, right now, I am of the mind that the essence of information doesn’t exist in the finite; it is all contained with an infinite universe defined by continuity, symmetry and harmony. It doesn’t exist in the physicality of the computer, but in the mind of the participant or a dynamic equation. The finite-infinite relation is always and it is always dynamic. That would change the nature of the equations. Assuredly, the initial conditions would not be defined by big bang cosmology.

I’ll continue my path through your works and may change my mind, but wanted to again thank you for your work and for causing me to go over it all just one more time.

Warm regards,


First email: December 27, 2022 at 7:36 PM (lightly update)

Dear Prof. Dr. Yuxi Fu:

Your paper, Symmetric π-calculus from 1998, has come to my attention. It prompts me to ask you, “Could continuity, symmetry, and harmony be a proper description of the functional nature of pi?”  I am now studying the references within your website,

Years ago, I could see how it all might evolve from the most simple sphere:  I wondered, “Do the Planck base units define the first infinitesimal sphere? If so, is sphere stacking-and-packing a fundamental of physicality?”

If base-2 is applied, there are just 202 doublings to the approximate age and size of the universe and wave-particles-fluctuations are not measured until Notations-64 to Notation-67. The first second isn’t until Notation-143. So, of course, our chart of numbers is primarily a description of the very early universe. Is this interesting? Thank you.

Most sincerely,


PS. Along the way, we found a very interesting gap with five-octahedrons. Aristotle had failed to see the gap with five tetrahedrons! Nobody seems to be aware that five octahedrons create the same gap!  Even the commercial geometric construction sets and computer programs overlook these gaps!  -BEC

First principles make a difference.

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

“Science today is de facto within a conceptual framework
that is defined by a big bang theory. It is misleading us.”

by Bruce E. Camber

The Scientific Method: There was an argument about the title. The word, de facto, is for general concurrence. Yet, might it be better if science today is also required to grasp what is de jure or by law? The word, de facto, is “in fact” or “in effect” or actual practice. Within our model, continuity-symmetry-harmony define infinity and pi. It amounts to a conceptual counterpoint to de facto. Those three are inherently “de jure” or “by law” or “by right.” As a consequence, the scientific method may be logically required that as a result of “hypothesizing, testing, getting results, analyzing and synthesizing,” it also must explain how it is an extension of those natural laws inherent within continuity-symmetry-harmony.

Currently the focus of our academics has been dominated by big bang theories, especially within the scientific and scholarly communities. There is no law or right for big bang theories to be the abiding belief of the world’s scientific community when a more-rules based understanding of reality in fact appears to work better. Those who hold onto such a theory ignore rules that work in order to substitute de facto “rules” that ultimately do not. Although their substitutions are many, the primary one is Alan Guth’s inflation and the theoretical inflaton. I believe, albeit quite imaginative, that untested hypotheses will forever remain within an ever-growing domain of fantasy science.

Simple math, simple geometry, and simple logic work better.*

January 2023: For over eleven years I have asked scholars if continuity-symmetry-harmony are finite or infinite. Since 1972, unlike most, I have assumed the three are both finite and infinite.[1] If infinity (the infinite) is defined as continuity-symmetry-harmony, vestiges of all three dominate aspects of the finite. The three define pi. The three define aspects of space-and-time and all of the dimensionless constants. The finite side of the equation is quantitative and the infinite side of the equation is qualitative. It is not difficult. It tells us that the scientific method involves infinity and its inherent boundary conditions and parameters. There are over 30 presuppositions that opened these channels. Those all started with a few assumptions. More recently, these are becoming a checklist of what is necessary, de jure, to start and grow our universe.

The Big Bang does not qualify. There is no place for the Planck base units or their equivalent (Stoney units or ISO units), or for pi(π). There really is also no place or for the dimensionless constants or a finite-infinite relation. Big Bang theories ignore too many of the fundamentals of history and logic of scholarship.[2]

All research, every scholar who is in search of a deeper truth, engages our dimensionless constants and inherent presuppositions. Perhaps not articulated, these constants are part of our logic-and-thought structure and are necessarily always part of any research program. That’s de jure. If believed and accepted, research will never be quite the same because it will always be measured in light of pi and the other dimensionless constants and continuity-symmetry-harmony.

Thank you. -BEC


Endnotes & Footnotes
There may not be many because all these points already have pages within this website.

[*] Simple is better than complex. We’ve made it all too complex. In 1988, Richard Feynman asks, “What do you care what other people think?” The stakes are just too high. In a 1955 public address, The Value of Science, at the National Academy of Sciences, he said, “Throughout all the ages of our past, people have tried to fathom the meaning of life. They have realized that if some direction or meaning could be given to our actions, great human forces would be unleashed. The dream is to find the open channel.”

Come on. Let’s explore a few open channels.

  1. The 202 base-2 notations constitute an open channel.
  2. The faces of the finite and infinite defined by pi constitute an open channel.
  3. Yes, continuity-symmetry-harmony constitute an open channel.

Like fantasy football, fantasy science can be fun, but it doesn’t readily solve problems.

[1] Finite and infinite. Of course, David Hilbert, Kurt Gödel,  E.P. Wigner, or Max Tegmark do not the final words or concepts when it comes to infinity, and a finite-infinite relation. We’ve got a long way to go. First, it needs to be in the spotlight as an active investigation. Ignore the hocus-pocus. The pages around continuity-symmetry-harmony, I believe, are keys to our sanity. If the universe is fundamentally ordered, relational, and profoundly dynamic, let’s have some fun. Let’s break loose of all our stridency, know-it-all attitudes, and let everyone breath a bit more easily. Let’s harden up all the egg shells so we begin to grasp the depth and meaning of infinitesimal spheres!

[2] History, logic, and traditions of scholarship. In the 20 January 2023 issue of Quanta Magazine, journalist Rebecca Boyle’s lead story, “Standard Model of Cosmology Survives a Telescope’s Findings,” reports on the results coming in from the James Webb Space Telescope (JWST). Optimistically Boyle says, “The earliest of those confirmed galaxies shed its light 330 million years after the Big Bang, making it the new record-holder for the earliest known structure in the universe… How could stars ignite inside superheated clouds of gas so soon after the Big Bang? How could they hastily weave themselves into such huge gravitationally bound structures?”

The answer to her first question is that were no “super-heated clouds” and to her second question, “In the first second, space-time has already expanded to a size beyond our solar system.”

Cosmological constant: In our model of the Quiet Expansion, there is immediately a cosmological constant that is currently calculated in the range of 539.116 tredecillion planckspheres per second (Max Planck, 1899) and at about 4605 tredecillion spheres per second (using George Stoney’s calculations from 1874). The ISO has been invited to introduce a more recent calculation based on their current standards.

That first second is within Notation-143 using base-2 notation. It is possible to imagine that within the the first 330 million years stars would readily evolve from a very smooth, homogenous start.

Big Bang theories have truncated our creativity.

[3] There may be more to come based on your feedback or from scholars/celebrities.


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

Gerardus’t Hooft, In Search of the Ultimate Building Blocks, Cambridge University Press,1997. ‘tHooft is among the Nobel laureates who have inspired us.

Alain Aspect: In 1980 on a visit with Alain Aspect in d’Orsay, we never imagined it would take 42 years to be finally recognized with a Nobel Prize in Physics.

Rohan Abeyaratne, MIT and James K. Knowles, Caltech, Evolution of Phase Transitions: A Continuum Theory, July 2006


There will be emails to many of our scholars about these points.

26 January 2023, Carl Zimmer, New York Times
25 January 2023, James Sethna, Cornell
24 January 2023, Rebecca Boyle, Quanta Magazine
23 January 2023, Rohan Naidu, MIT Pappalardo Fellow


There will also be many instant messages to thought leaders about these.points.

11:52 AM · Jan 21, 2023 @katyperry At one time you said, “…be vulnerable, truthful, honest” and you genuinely struggled to put your deepest thoughts into words. Rebirth that old vision! Here’s our note:

7:20 AM · Jan 20, 2023 @PhysicsMagazine  @KatRWright @stevenstrogatz @JonathanDoye @Nature @NobelPrize Quasicrystals in a sand dune remind us, “Geometry is basic.” Five tetrahedral-and-octahedral gaps- – tell us, too. It’s all continuity-symmetry-harmony:



You are always invited.


Keys to this page, defacto

• This page become the homepage at the end of the day, January 21, 2023.
• The last update was on May 3, 2023.
• This page was initiated on December 30, 2022.
• The URL for this file is
• The headline for this article: Science today is de facto within a conceptual framework that is defined by Big Bang cosmology. It’s misleading us.
• First byline is: What’s best for the scientific method… de jure or de facto?.



Morning, December 30, 2022: Planck Temperature start and cold start tension equals flatness…

On-going right now and it is a major-major of the dynamics of the early universe.


9:48 PM · Jan 6, 2023 @maxdkozlov Take some guesses, Max. What if our basics are not basic enough and our foundations are not based on first principles but de facto assumptions? What if an exponential universe and we de facto still think linearly? We’re trying to break out:

10:00 PM · Jan 6, 2023 @Nature @russellfunk @dashunwang @yian_yin On the decline of disruptiveness: What if our basics are not basic enough and our foundations are not based on first principles? What if we live in an exponential universe and we de facto still think linearly? Let’s try to break out:

On following the work of IBM and CEO, Arvind Krishna

December 23, 2022 A level set.

Dear Dr. Arvind Krishna:

IBM boldly proclaims on its website, “We as a society need to implement scientific thinking at all scales.” The infinitesimal scale from the Planck units to particles, waves, and fluctuations is not part of that consideration. Within a base-2 model of the universe, it is the first 64 notations of the 202 that outline the universe. I believe it would be wise to consider those notations.

Please allow me to introduce myself. I have been a friend of IBM for many, many years.

A long time ago, 1982, perhaps 1983, our company was the #1 business partner in the USA and for that IBM awarded us a new red corvette! Thinking it would be a good award for best performance, it was as you might guess, an incendiary that almost got our three top salespeople! After hearing stories about “their week” with it, our hot rod was sold.

Also, long ago I made a short video for Lou Gerstner with the guidance of his immediate reports about small business. I also worked with the AS/400 division and Watson Labs.

Today, I write to advocate a concept —  transitioning from limited worldviews to a highly-integrated mathematical view of the universe that begins at the Planck scale. It is created by applying base-2 notation to the base units — If we accept that it defines the first moment in space-time, that chart comes up to this current point in time in just 202 notations.

Please consider how it deepens our understanding of continuity equations and symmetry relations. There should be applications within quantum computing. Watson and many others can use it. 

In 1992 the web was a paradigm shift. It disintermediated space and time. This is a paradigm shift as well. It redefines space and time.

We are a society that needs to implement scientific thinking at all scales. The infinitesimal scale from the Planck units to particles, waves, and fluctuations has not been considered. May I open that concept with you and your people? Thank you.

Most sincerely,


References & Resources:
“We as a society need to implement scientific thinking at all scales.”

“Science drives our research and scholarship. Now, more than ever, our society and culture depends on the strength of our commitment to practicing and upholding scientific thinking in all we do.” -Dr. Nariman Farvardin, President, Stevens Institute of Technology

9:16 AM · Dec 9, 2022  @IBM IBM proclaims, “We as a society need to implement scientific thinking at all scales.” See: Yet, the infinitesimal scale from the Planck units to particles, waves, and fluctuations has not been considered. Here’s an introduction:

Back on December 19, 2011…

Left Yellow Arrow
Right Yellow Arrow

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

Our Big Board-little universe chart began and
evolved as a highly-ordered Quiet Expansion.

by Bruce E. Camber, a first draft

Big Board - little universe was a Quiet Expansion of the universe, not from a big bang.

New Orleans: Five high school classes of students — mostly for geometry — were greeted with the chart on the left. It was huge, over seven feet high. Click on the image to see it! It is a mathematical map of the universe.

It didn’t take long for the students to get the knack of it. They were quickly going further and further inside new and unknown spaces. They quickly got smaller than a molecule, then a cell, and atom, and a particle.

Those students had been cajoled to go inside that tetrahedron and octahedron. In your mind’s eye you can do extraordinary things. Shrinking smaller and smaller is one of them. Dividing edges by 2 and connecting the new vertices is another.

Down through the DNA of biology and into the chemistries and its periodic table. Then very quickly we were into particles and waves and fluctuations. Our goal was to reach those natural units that Max Planck defined in 1899. We understood these were the the smallest possible units of space and time. We had come down 45 steps to the atom and then uncovered 67 more steps to those Planck units.

The first layer of the inside of a tetrahedron. There is so much to learn.
Four hexagonal plates are in every octahedron. Five octahedrons together sharing a common centerpoint creates a pivotal gap.

Encapsulated Tetrahedrons and octahedrons. All the way down smaller and smaller, each notation is active. It was difficult to discern the archetypal forms within a notation; yet, at Notation-0 it appears to be an infinitesimally-small, sphere.

We hypothesize that an infinitesimal sphere instantiates at Notation-0, the first space-time moment. The EOU within Notation-202 is the Edge of the Universe which is the current expansion of tredecillions of spheres per second.
From the Big Board - little universe chart from December 19, 2011
Eight Notations: Data from the larger cells, the egg within Notation-103 to the smaller at Notation-97.

Vibrant and dynamic, it appears to be the instantiation of the Planck base units and so much more.

From our magical observation deck, we could see those spheres stacking, with new functions with each doubling. From here we could readily look up the 112 steps back into the classroom. In just 90 additional magical doublings or steps or notations, we could see that we would be out to the edge of the universe watching the current expansion.

It happens so fast: Tredecillions of spheres per second. We’ve had to double check our numbers over and over again. In just over a second from Planck Time, we were out to Notation-143. In just over a year, Notation-169. And in just over 1000 years, Notation-179. A million years is just over Notation-189 and a billion years, just over 199. If we assume there is one infinitesimal sphere per unit of Planck Time and Planck Length, there are 539 tredecillion spheres per second. If we use Stoney’s numbers, there are 4605 spheres per second.

Here is our universe from the smallest to the largest in 202 steps or doublings or notations. It has its own special logic such that all notations are ongoing, interdependent, and forever.

What’s this all about? Yes, dynamic and logical, this model has numbers and geometries. It has the Planck units. It has a simple algebra; and it is constantly filling with infinitesimal spheres. It is the first time we could see the universe on one highly-ordered, fully-integrated chart. We searched online for experts to help us interpret our emergent model, but we couldn’t find such our chart in any textbook or anywhere on the web. So, we turned to the living scholars who would know. Many complimented our work and said something like, “Your chart uses base-2 exponential notation to parse the universe from the smallest to the largest possible measurements.”

Top to bottom: Five tetrahedrons over five octahedrons over five tetrahedrons

We learned that the work was unique. We also learned that the results did not jive with current cosmological theory. This model posits a very smooth, yet highly-integrated beginning of the universe. Here the geometries all fit together perfectly. These geometries tile-and-tessellate without gaps. Yet, we knew that a five-tetrahedral cluster made an object with a gap. Octahedral clusters do the same. Together they make a geometry that has not been discussed in any of the literature. We propose that it is a geometry of quantum fluctuations. It is squishy geometry.

Over our heads and inundated with new information. I consulted with old acquaintances who were scholars — John Conway, Phil Davis, Freeman Dyson, and Lisa Randall, Then we began learning through the work of new people like Frank Wilczek and Stephon Alexander. Work by Jeffery Lagarias and Chaunming Zong, Mysteries in Packing Regular Tetrahedra (PDF), was an indictment on the academic community. Aristotle’s mistake had been ignored and it continues to be ignored within academia. That’s a profound mistake and causes one to pause and ask, “What are some of our other profound mistakes?

Here’s my quick introduction to three:
1. Sphere-to-tetrahedron-octahedron dynamics: Cubic close packing of equal spheres: Scholars have focused on packing densities; very few have focused on the process by which tetrahedrons and octahedrons are created from sphere stacking.

2. Structures created by basic geometries. First, the octahedron within every tetrahedron is a key. The four interlocking hexagonal plates within every octahedron is another key. Those gaps created by clusters of five tetrahedral clusters and five octahedral clusters are also a key. The gaps created by clusters of twenty tetrahedrons (an icosahedron) are keys as well. It is all unfinished business, whereby we all, especially our scholars, should focus on the place and purpose of each gap. Are these gaps related to quantum fluctuations? That’s a major discussion.

3. The very nature of pi (π): I am no scholar but the mathematics of infinity seems to be a penultimate challenge. There are so few discussions of the place and importance of pi (π) and infinitesimal spheres. I believe that the open questions about the very nature of homogeneity and isotropy of the universe are keys and that Planck units or Stoney units (or the ISO’s equivalent units) will define an approximate rate of expansion so tredecillions of infinitesimal spheres per second fill the universe from the start through to the Now.

These three points are so idiosyncratic, it’ll take time to engage them, absorb them, then use them. It is, however, all very approachable with high school students. We even had our AP class of sixth grade savants get immersed in it; but once our graduates started circling back, we realized that it was too disruptive within the current curriculums. The only hope is within the special integrity of people like you. Might you have any advice for us? How do we proceed? Thank you.


PS. There were many new ideas and presuppositions that emerged along the way. Then, we organized them as a checklist to start and grow the universe. -BEC


Endnotes & Footnotes
Most of key points already have pages within this website; however, new footnotes may yet emerge.


References & Resources
Key references and resources will be added over time.

• All the webpages, week by week, going back to 2016.


A few of the emails to our many scholars.

• Martin Bridson, Oxford and Clay Institute, December 17, 2022
• Levent Alpoge, Harvard, Cambridge, Massachusetts, December 16, 2022
• Richard J. Fitzgerald, AIP and Univ. Texas-Austin, December 16, 2022
• Alan Guth, MIT, Cambridge, Massachusetts, December 13, 2022
• Gil Lonzarich, Cavendish Lab, Cambridge University, December 12, 2022
• Sankar Das Sarma, University of Maryland, December 11, 2022
• Ana Caraiani, Hausdorff Chair BonnImperial College London, Thurs, 8 Dec, 2022 8:43 AM
Orli Dahan, Tel-Hai College, Israel, 7 December 2022 @ 2:42 PM
Elizabeth Gibney, Nature magazine, Tues, Dec 6, 20227:57 PM


Often using Twitter. Criticized, now also using Parler. New IM will be added.


Participate…     You are always invited.


Keys to this page, December-19-2022

• This page became the homepage on Monday, December 19, 2022.
• The last update was 21 December 2022.
• This page was initiated on 18 December 2022.
• The URL for this file is
• The first headline for this article: An Alternate Point of View Evolved
Also: Our Big Board-little universe chart began and evolved as a Quiet Expansion, not a Big Bang.
• First byline is: Eleven years ago, from December 19, 2011 to December 19, 2022…

On following the work of Anna Ijjas

Anna Ijjas, Center for Cosmology and Particle Physics, New York University
726 Broadway, New York, NY, 10003

Articles: What if there was no big bang and we live in an ever-cycling universe?, New Scientist, August 2019; Pop Goes the Universe, Anna Ijjas, Paul J Steinhardt, Abraham Loeb, PMID: 28118351, DOI: 10.1038/scientificamerican0217-32
The philosopher of the Big Bounce (PDF), Big Bang or Big Bounce? Avoiding the Multiverse. A Conversation with Anna Ijjas, Jul 3, 2022
Homepage(s): CV, Falling Walls, Google Scholar

Most recent (third) email: 27 February 2023

Dear Prof. Dr. Anna Ijjas:

Is there a generally accepted definition of an inflaton or the inflaton field?

In my search, the closest thing is Wikipedia and we know that can be questioned. I don’t think there has been any consensus among those who use the term. I make reference to your work here:

Thank you.



PS. Is there any access to your 23 January 2023 presentation at the scientific meeting of the Royal Society, Probing the quantum origin of spacetime? Thank you. –BEC

Second email: 23 December 2022 @ 1:01 PM

Dear Prof. Dr. Anna Ijjas:

In preparation for your upcoming January 2023 talk, Probing the quantum origin of spacetime, for the Royal Society Scientific meeting, if you were to assume that those origins could involve the Planck base units and infinitesimal spheres, you might want to look at the potential role of pi (π) again:

Best wishes, 



First email: 23 December 2022 at 10:01 AM

Dear Prof. Dr. Anna Ijjas:

Lovely website — — great continuity, symmetry and harmony!

I watched with amazement as you, Paul Steinhardt and Avi Loeb knowingly stepped well out of line to challenge the orthodoxy of the day. There is no question that you are bold, courageous, and tenacious. I say, “Congratulations on a life well lived even though you have just started out!”

You’ve said, “There is no good evidence that our universe even had a beginning….” I think that’s a finite-infinite question. You can be like Max Tegmark (MIT) and desire to throw out the concept of the infinite. I think a simple redefinition is in order.

Pi (π) best captures that tension. And, I would argue that pi is an expression of the character of infinity and perfection. So, instead of collapsing in about 100 billion years, time is redefined, space is redefined, and we can refocus our attention on first principles and the foundations of the foundations:

I should forewarn you that this construction started in a high school!

Best wishes,




On following the work of Simon Singh

This page is in process. Simon is extraordinary in so many ways.

Homepage(s): Wikipedia

Reference page:

First documented email: 17 December 2022 at 11:18 PM

Dear Simon,

Even the most strident among us, scholars like Sean Carroll ( ), readily admit the first second is up for grabs. If we approach our little universe mathematically, there are just 202 base-2 notations from the first moment of time, symbolic Planck Time, to the current time, sometimes called, The Now. We have charted the numbers here:

We all should also be aware of Stoney’s Time. Planck is better known. I’ve asked the ISO to take a look at the discrepancy between them.

That first second is late; it’s within Notation 143 out of the 202. Just think what Sean Carroll and Alan Guth miss in those first notations. If these are dynamic, constant and always, they’ve missed the best part of the show.

A very simple introduction to this map of the universe starts here:
I hope it is not too idiosyncratic. If so… let’s work on it!



Time, a most problematic puzzle

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

It’s About Time…….
And how it holds values. ……
by Bruce E. Camber

A working-first draft

Abstract: Albert Einstein essentially said that time is an illusion.* Many other smart people have agreed with him. A person with a sense of history might say, “…since time immemorial…” when thinking of something from long ago that still affects us. There are many people who are familiar with the poetry of Ecclesiastes 3:1-8, “To everything there is a season…” where time has specific meanings; it’s all linear or chronos time. Throughout our history, there is also a special use of kairos, for the fullness of time, an intersectional time between the finite and infinite. And in that light, the faces of pi, continuity-symmetry-harmony, define a different time; here are the equations of time, always dynamic, always changing, and also always the same. It is the very definition of the infinite where time is recompiling, integrating, texturing, and making whole. And finally, today there are several major studies like loop quantum gravity and the spectral standard model where their scholarly advocates say, “All time is now.”†

The sanity within this world may well be conditioned by our understanding of the very nature of time. It’s about how this universe starts and we know that answers provided by big bang cosmology are incomplete and not quite satisfactory.

Introduction. Today all of science is de facto set within a conceptual framework that is defined by Big Bang cosmology.[1] Theoretically it is the start of everything yet those in the know readily admit that it has nothing to say about the first minutes of our universe.

The big bang theory began to get a singular hold on cosmology in the early 1980s. There were other theories but none were building consensus like the big bang and none had a de facto spokesperson like Stephen Hawking. Nevertheless, there were many scholars over the years who did not become believers.

Since 2011, we’ve been studying a simple base-2, mathematical progression from the Planck base units, particularly Planck Time until now, the current time. In that period we found ourselves agreeing more often with those who do not affirm a Big Bang theory.

In 2022 two key homepages emerged, Big bang versus Quiet Expansion: A Comparison and Hawking’s big bang theory has reached its limits. Always in process, along with this homepage, these three articles will continue to be worked and reworked until each is accepted within a respected publication. Communications (emails and instant messages) to each publication will be included here. Either this theory is on a better path or it’s not. If not a better path, there will be a fascinating discussion about the very nature of the continuity of numbers and equations that will have to be written. If it is a better path, we’ll try to get doctoral candidates and postdocs to engage all those numbers to tell us what they find.

The focus of this article is the nature of time. It seems that most big bang theorists cast time as linear even though Hawking said the universe is “…expanding exponentially in all directions…” They cannot and do not override their experience of personal-linear time, or chronos, or time measured by a clock. So, the net-net is that our commonsense view of time concludes that there are finite durations which are measured by clocks and, with a nod to Newton, that it goes on forever. There is chronos time and Sir Isaac Newton’s absolute time, “It’s finite and infinite at the same time.” That’s not easy and it doesn’t solve problems.

Our theory, the Quiet Expansion, casts time within an exponential framework. The essence of the Greek word, kairos, and the current leading advocates that all time is now, should become our centerpoint. Working within our larger model, the 202 base-2 notations from Planck Time until this moment, logic seem to be telling us that every notation is active and necessarily part of the ongoing definition of the universe, so in effect, we introduce a new equation within all the old debates about time.

Within this framework chronological time is limited to the waking hours of sentient beings within Notation-202. Time symmetry exists in all other respects and within all other notations; all time is now.[2]

The finite and infinite faces of time

I don’t think there is anybody else currently suggesting that linear time, chronos, is a subset of exponential time and that it is limited to sentient beings during their wake cycles and that unique experience is re-compiled during that sentient being’s sleep cycles. It is a peculiar sense of time. It needs critical review. Hopefully, there will be a lot of pressure put on it. To pre-release some of that pressure, these five prior homepages have looked into issues around big bang cosmology:

But all seven articles are not yet sensitive enough. Each new concept needs to be gone over again and again. There are too many new subtleties to grasp and integrate.

Our hope is that by adopting a radically different concept of time, unsolved problems in both physics and cosmology can be addressed in new ways. For example, concepts like dark energy and dark matter just might be defined by a heretofore unexamined grid — just a bit smaller than particle physics — this part of the overall grid of 202 doublings systemically continues for 64 notations, dividing by 2 each step of the way, down to Planck-scale physics. Particles and quantum fluctuations are observed in the range of Notations 67-to-64. Yet, within that grid, the speculation is that different kinds of hypothetical particles and quantum fluctuations may well be “observed” [3] down to about Notation-50.

A very different, yet-simple, understanding of the cosmological constant may slowly emerge whereby infinitesimal spheres are generated at rates symbolically defined by Planck Time (or Stoney Time or a new ISO Time). If we can assume that one infinitesimal sphere is generated per unit of the most Infinitesimal Time and Infinitesimal Length, that’d be a revolution unto itself! We’ve discussed the concept that it would be anywhere from 539-to-4605 tredecillion spheres per second constantly filling the universe from the very first instant.

Further, we may be able to assume that these 64 notations are the long-sought for bridge between quantum gravity and relativity theory. If so, it’s another obvious revolution.

Also, by recognizing an expanded role for pi, an entire domain of perfected states in space-time opens. These notations should also be the foundations for SUSY. We hypothesize that these new parameters also become the basis for valuations and ethics. There are more than enough domains, or notations, to include Langlands programs, strings, and the most active studies from causal dynamical triangulations (CDT), loop quantum gravity (LQG)causal set theory (CST), field theoriesspectral standard model (SSM), and all the hypothetical particles.

All can be redefined within that base-2 grid of 64 of the 202 notations.

Most importantly: The universe is opened up to an active finite-infinite relation, whereby continuity, symmetry and harmony, the primary functions of pi, have redefined what we can know about infinity.

Base-2 expansion of Planck Time. Taken to be a symbolic first moment of time, Planck Time goes out the 202 doublings to this very moment in time. Time has a mathematical structure of numbers and it has geometric structures of the simplest geometries (shapes) evolving from spheres and then from tetrahedrons and its octahedron, and then every possible geometric extension of them. In the 67 steps from Planck-scale physics to particle physics, the entire universe seems to share these building blocks. From the first moment of time to this very moment in time within a base-2 grid everything, everywhere, for all time is interrelated.

The universe is filled with the infinitesimal spheres defined by natural units such as the Planck base units and are initially best described by the stacking and packing of spheres (beginning with Kepler-Harriot) and then most-recently by scholars like Thomas Hales (Pittsburgh), then the cubic-close packing of equal spheres, and then the emergence of tetrahedrons and octahedrons and all the potential geometries.

That Planck scale physics defines the first moment of time. We can consider how these units are the manifestation of a finite-infinite relation whereby the continuity-symmetry-harmony of the sphere manifests through all space-time and mass-energy.

Time, profoundly personal

Kairos, the fullness of time. The scientific community has had justifiable reservations about engaging the concept of the infinite. Max Tegmark has been outspoken with his recommendation that it be retired completely from intellectual discourse. I have written to Max and to suggest that it would be better to redefine the nature of the infinite, especially in light of those facets of our reality that do not readily fit into what we generally consider to be finite, particularly continuity, symmetry, and harmony.

.That interstitial or intersectional place within Notation-0 is both finite and infinite [4]. It is quantitative and qualitative [5]. It is the basis of the fullness of time. It is the very nature of time defined as karios [6].

It is also opening up part of quantum computing and opening a spotlight on the concept of anyons. What is generated from observations can trick our eyes. What seems to have been generated from first principles, laws, and logic may not be basic enough. And, discerning the difference is not as straightforward as it seems.

So, of course, there will always be much more to come… Thank you. -BEC


Endnotes and Footnotes
Many of these points already have pages within this website.

[*] May 17, 20131:00 PM, National Public radio, Ira Flatow, Host of Science Friday:

To most of us, time is real: I’ve run out of time, I don’t have time, What time is it? But, not to most physicists. Albert Einstein once wrote: ‘People like us who believe in physics know that the distinction between past, present and future is only a stubbornly persistent illusion.’ Time, in other words, he said, is an illusion.’ Many physicists since have shared this view, that true reality is timeless.” 

– Flatow quoting from a letter to members of the Michele Besso family, 21 March 1955

[†] “All time is now.” Loop quantum gravity (LQG) expert, Carlo Rovelli, rekindles Einstein spirit when he says, “There is no such thing as past or future” and “Time is an illusion.” Notwithstanding, Rovelli and LQG have a ways to go before redefining time.

[1] A de facto weakness of our scientific method. The scientific method has historically been detached from a cosmological point of view. Afterall, it is a method of hypothesizing, predicting, measuring, testing, confirming, and synthesizing. Yet, in these days, the big bang theory casts a shadow over all of science and even its scientific method. Since becoming dominant in the last decades of the 20th century, it has become an arbiter of truth. It seems as though all of research must comply or, at least, not refute big bang orthodoxy. That is unfortunate.

[2] Time symmetry exists in all other respects and within all other notations. Of the great mysteries of life, consciousness-and-sleep are high on the list. The finite/infinite relation is perhaps at the top. Dark energy-dark matter, quantum fluctuations, blackholes are on most lists. We specially add perfections-in-space-time and a natural inflation-and-expansion to our list. There are so many unsolved mysteries. This definition of time may well open a door to re-address some of them.

[3] Observation, Measurement and the scientific method. To be science, it must be observed or measured. At Notation-67 we are on the edge of experimental observation and at Notation-64 we are on the edge of experimental measurement. The measuring devices begin to interfere with what is being measured. At Notation-50 we are within an ethereal zone where only logic and mathematics and geometries still stand. These first 50 notations are real. We know that because Planck units or Stoney units or ISO units give us the numbers from dimensionless constants and natural units. We can only trust that these calculations render meaningful albeit highly-symbolic numbers. These are our first calculations of space and time and although there may be three slightly different sets of numbers (Planck, Stoney, ISO), we should discover that when base-2 is applied and the whole numbers of our collective experience begin to emerge, say within that first second within Notation-143, the differences between the three sets of numbers are negligible. And, although I just wrote that sentence, I now know that it must be carefully checked out!

[4] Notation-0 is both finite and infinite. It is a Janus face. One side is physically (quantitatively) defined, the other side is qualitatively defined by universals, particularly, dimensionless constants set within continuity, symmetry, and harmony. David Hilbert’s work is being reviewed by scholars like Xijia Wang. The reach of symmetries is being examined by scholars like Yuxi Fu. So many scholars have danced within and throughout these issues. The Institute for Advanced Studies in Princeton have studied it as an art form! Eventually their scholars will begin to help us all move beyond Albert Einstein, Kurt Gödel, and David Hilbert.

[5] Quantitative and qualitative. Time has both numbers and values. Numbers objectify space-time. Values, the qualitative, personalize space-time and create memories. Those memories do not exist within the finite but the infinite. Our brains are localized within space-time; our minds are within continuity-symmetry-harmony and define who we are. To the degree that there is continuity-symmetry-harmony is the degree there is value.

[6] Confluence and karios. Always dynamic, the finite-infinite relation is exquisitely refined beyond all our sensibilities and imagination. The confluence of possibilities involves the perfect-imperfect, the hot-cold, the good-the bad, the light-the dark, asleep-awake… all the contrasts attempted to be captured by the writer of Ecclesiastes 3:1-8, and then even more, much more.

(still in process on January 16, 2023…)

More: The concept of anyons and fakeons.


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

  • Space-time as a causal set, Luca Bombelli, Joohan Lee, David Meyer, and Rafael D. Sorkin, Phys. Rev. Lett. 59, 521 , 3 August 1987
  • Neil Turok, appears to reaffirm the bang! Just a few years ago, he said that the universe acts like it is perpetually starting. Now, apparently he is trying to reconcile it with the strong CP problem and big bang cosmology. It’s a bit confusing. We’ll dig into his current work further.


Recent emails. There will be emails to many of our scholars about the key points.

• Thomas Callister Hales, Pittsburgh, December 30, 2022
• Yuxi Fu, Shanghai Jiao Tong University, December 27, 2022
• Benoit Estienne, Université Pierre et Marie Curie, December 17, 2022
• Damiano Anselmi, University of Pisa, December 17, 2022
• Martin Bridson, Oxford; Clay Institute, December 17, 2022
 Levent Alpoge, Harvard, Cambridge, December 16, 2022
• Richard J. Fitzgerald, AIP, December 16, 2022
• Alan Guth, MIT, Cambridge, Massachusetts, December 13, 2022
• Gil Lonzarich, Cavendish Lab, Cambridge University, December 12, 2022
• Sankar Das Sarma, University of Maryland, December 11, 20222
• Ana Caraiani, Hausdorff Chair BonnImperial College London, Thurs, 8 Dec, 8:43 AM
• Orli Dahan, Tel-Hai College, Israel, 7 December 2022 @ 2:42 PM
• Elizabeth Gibney, Nature magazine, Tues, Dec 6, 7:57 PM
• Pascal OeschObservatoire de Genève (Switzerland), December 4, 2022
• Salvatore Torquato, Princeton University, December 1, 2022
• Julia Collins, ECU, Joondalup, Australia, December 1, 2022
• Simon Singh, London, UK, December 1, 2022 (in process)
• Jonathan Doye, Oxford, UK, November 23, 2022 (follow-up)

Intersectional timeBlack Quantum Futurism Collective (Rasheedah Phillips + Camae Ayewa) Note: “I am just now starting to develop a paragraph with links to the BQF regarding their understanding of intersectional time. I am now searching for uses of the concept of intersectionality.” Also, see


There will also be many instant messages to thought leaders about the key points.

7:20 AM · Jan 20, 2023 @PhysicsMagazine @KatRWright @stevenstrogatz @JonathanDoye @Nature @NobelPrize Quasicrystals from a sand dune remind us, “Geometry is basic.” Five tetrahedral-and-octahedral gaps- – tell us, too. It’s continuity-symmetry-harmony:

10:54 AM · Jan 3, 2023 @zlj517 This is the time to redefine our understanding of time! I’m trying.
Real scholars in China are, too.
 We all need to celebrate the work
of Yuxi FuXijia WangAndrew Chi-Chih Yao, and Chaunming Zong:

2:11 PM · Jan 2, 2023 @geostylegeo Why not build from the simplest math and geometry with natural numbers by Planck, Stoney, and perhaps the ISO? If we apply base-2, there are just 202 notations (doublings) from the most simple to the age and size of the universe. Take a look:

6:35 PM · Dec 27, 2022 @howie_hua Howie Hua: You might be able to tell us what we’ve been doing wrong! We’re out of step with the mainline cosmology geeks. We just used base-2 from the Planck base units to encapsulate the universe in 202 notations. What’s wrong with that?

5:36 PM · Dec 12, 2022 @brianeno You’re in the groove of an all universe, everything, everywhere for all time which is the encapsulation of space and time using base-2 notation from the Planck base units. It’s not a trick. It’s continuity, symmetry and harmony in flow. More:

6:01 PM · Dec 3, 2022 @tedlieu If we are ever to reach some consensus for the future of this country, we need to break free of our little worldviews and adopt a highly-integrated view of the universe. This is a first: We need to grasp it all:

4:46 PM · Dec 3, 2022 @mtaibbi We are all wrapped up within our little worldviews that impairs judgment and logic. A highly integrated view of the universe sounds crazy but… apply base-2 to the Planck units, there are 202 notations from Planck Time to this day It opens logic.


Participate ….. You are always invited.


Keys to this page, all-time-is-now

• This page became the homepage on December 23, 2022.
 It still in process; it’s open for collaborations to improve it.
• The last update was January 21, 2023
• This page was initiated on November 24, 2022.
• The URL for this file:
• Prior homepage:
• The first headline for this article: All Time Is Now
• First byline is: Time is not what we think it is