Barish, Barry C.

Barry Clark Barish
Linde Professor of Physics Emeritus

California Institute of Technology,  Pasadena, California
UC Riverside
Director of the Global Design Effort, International Linear Collider

ArXiv: Search for gravitational waves from a long-lived remnant of the binary neutron star merger GW170817 (October 2018)
Nobel Prize 2017
Twitter (Nobel Prize)

From “5 Needed Breakthroughs”

  1. Understanding what is the dark energy in the universe? (We don’t even have a good idea here.)
  2. What is the dark matter? (This is the other big unknown, but at least we have some handles. We know it is non-baryonic and evidence points to either supersymmetric particles, or maybe axions. Perhaps it is neither.)
  3. What causes mass? (We have a very successful theory of particle physics, but the particles are massless. We need to understand the source of mass. The leading idea is that it is the Higgs mechanism, and we need to see if there is a Higgs particle or variant to make the next step. The Large Hadron Collider at CERN should answer this question.)
  4. Is the neutrino its own antiparticle? (This is a puzzle going back to Fermi and perhaps the next generation of experiments will resolve it by looking for neutrino-less double beta decay.)
  5. Is there ultimate unification of the forces of nature? (This is a long term intriguing simplification on our understanding of particles and fields, but present data does not support it. However, if there is a new symmetry in nature (supersymmetry) it could bring this unification.)
First email: 19 October 2018

Dear Prof. Dr. Barry C. Barish:

To begin to get a modest understanding of your work, I have started my own page of references, along with a copy of this note:

I found your work through a webpage from March 07, 2007 listing your five needed breakthroughs (just above). Although you might re-prioritize that list today, it seems that most respectable scientists would still agree with you just as it is.

We have just begun to address some of those questions. Although we have no pedigree, since December 2011 we have been studying an application of base-2 notation from the Planck base units to the age and size of the universe.

Such a simple concept renders rather surprising results:
• There are just over 202 doublings. Our working numbers:
• Too small to measure, the first 64 notations:
• We ask: Can this be where the answers to your questions are?
• The notations create a natural inflation:
• The first second emerges within the 143rd notation.
• The 202nd notation is 10.9816 billion years so we are just 2.8 billion years into it.

I thought you might find it all of interest. I don’t think it’s just poppycock… If it is, it seems we’ll have to re-examine the foundations of logic, mathematics, and integrity, and the concepts of continuity and symmetry?

Thank you.



This homepage is called a “how-to” page…

HOMEPAGESJUST PRIOR|1|2|3 |4|5|6|PI|8|9|10|11|12|13|14|15|16|17|187|19|20|21|22|23|24|25|ORIGINAL

Sphere to tetrahedron-octahedron couplet
Planckspheres, cubic-close packing, emergence†

The Emergence of the Universe

By Bruce Camber_  _*Inspiration for this page_ _And, Another Version of this homepage

This website is a study of a model of the universe based on an application of base-2 exponentiation (multiplying by 2 or doublings) that eventually encapsulates-and-relates everything, everywhere, for all time in just 202 notations. This model of the universe starts with Planck Length and Planck Time, the smallest possible measurements, and goes to the largest. It starts with the very first moment in time and goes to this very moment in time.

There has never been a mathematical model of the universe quite like it.

To get an intuitive sense of this model is difficult. Four sacred cows of science need to be reexamined; these are best summarized as continuity, symmetry, harmony and the finite-infinite relation. Continuity applies to the nature of time. Symmetries apply to the structure of space, focusing here particularly on the very small-scale. Harmony is a focus on the dynamics of perfection and imperfection whereby chaos, indeterminacy, creativity, free will and fluctuations all emerge. And, all three are the face of the finite-infinite relation. [1]

The dynamic image at the top of this article opens this analysis. The first sphere is the first instant of space and time with a very specific mass and charge. These numbers were all calculated by Max Planck in 1899 and have been studied in earnest since 2001 when Frank Wilczek wrote a three-part series, “Scaling Mt. Planck” for Physics Today. [2]  When he received his Nobel prize in 2004, these three articles took on the patina of authority.

The next step for scholarship was obvious, but everybody seems to be ignoring it.

The first moment of time is derivative, finite and discrete. Newton’s absolute space and time are sidelined to introduce a new scale of the universe that begins with Planck Length and Planck Time. The focus of that image, including the ellipsis (36 displayed), is the first emergence.” [3]

Seemingly out of nothing – no space, no time – it all starts with just one sphere, defined by the Planck base units and many dimensionless constants, that is followed by another sphere, then another and another…. For now, we’ll call these spheres, planckspheres. If these spheres could be observed — obviously much-much-too-fast-and-too-small to measure — perhaps this process might be described as a line or a string coming out of nowhere, literally defining space and time as it emerges. This is the beginning of time, and this first moment is still emerging, today, at this moment…. It is still creating space/time and the dynamics that are mass/energy (or charge). It is assumed that all four Planck units are inextricably interwoven throughout the 202 doublings [4] (or notations) that bring us to this very moment within this day.

In that light, our first principle is that our Universe begins and is sustained by the dynamics that are defined within Planck Length/Planck Time and Planck Mass/PlanckCharge. Given these are inextricably interwoven, one of our challenges is to loosen, then disentangle all the knots.

Be assured, this is not your daddy’s or your mommy’s sense of time. Here it is a rate of encoding and imprinting on a universe that has no past. It has no future. It is only right now. This instant. Everywhere, everything shares this same moment and this same infrastructure. [5] This first notation is always the same, yet it is always unique just like pi. Impenetrable, there is nothing smaller; and these spheres penetrate and sustain all things.

So, another principle is that time is not a measurement of duration but of processing speed.

Here is the operational nexus between the finite and the infinite. Here is the beginning of an integrated, mathematical model of the universe and a quiet expansion with a most-natural inflation. Here is our little universe displaying its deep-seated order; yet very quickly, it begins to reveal how disorder, chaos, uniqueness, and creativity emerge. [6] Those geometries are well-known and the dynamics within each manifestation are now being explored and will be discussed in subsequent homepages.

Doublings. In the second notation the most basic projective geometry begins to emerge and structure begins building on basic structures [7] that creates a logical continuum from the infinitesimally small scale structures right up to the 67th doubling where now things can, in some sense of the word, be measured by accelerators like CERN in Geneva, Switzerland.

One of the key purposes of this site is to chart a map that takes us right down into these assumed infinitesimal structures.

Academics and scholars have not adopted this model. Questions should be asked  first, about the jump or “quantum leap” from the CERN-scale to the Planck scale. 
To date, there appears to be no other attempt to define this exquisitely small space using a simple application of base-2 notation and a profound respect for the Planck base units. In this study Planck temperature is derivative of mass/charge; so to approach the Planck temperature value, it has been reverse ordered. Just for convenience, it is now started just one notation above the 202nd notation. The logic supporting such a positioning is still being formulated.

Can the deep nature of that “quantum leap” be calculated today using just the four Planck base units and doublings? Could the first doubling from Notation 1 to Notation 2 be the foundation for all doublings?  There are many different types and applications of doublings that have already been well-researched and defined. To learn a little about each, on one page within this site, these key types of doubling will be studied and further researched in light of the continuity equations from the first doubling to the 202nd doubling. [8] Hopefully period-doubling bifurcation, cellular division, double field theory and gauge-symmetry for T-duality-and-doubled geometry, and multiscale modeling and simulations will inform us.

What other kinds of doublings should be considered? The 64 doublings from the Planck scale to just under the CERN-scale (at the 67th doubling) have been well-enumerated through the study of geometric expansions, especially as outlined by the Wheat & Chessboard story. It begs the question, “Is there a logical progression by which numbers and geometries progress?” Does every kind of mathematics, geometry and logic build upon each other? [9]

Given recent scholarship within the studies of prime numbers, the question should also be asked, “What is the role of prime numbers in this expansion?” There are 45 prime numbers between notation 1 and 202; there are 19 primes from 1 and 67. Could each notation that is a prime open a path for more complex mathematics? That question is being pursued within the development of the following pages:

So, even as we study these possibilities, a simple stacking renders our first doubling and an infrastructure for all subsequent doublings. Our centerfold image at the top captures the dynamics of doublings. Cubic-close packing, both face-centered cubic (fcc) and hexagonal close-packed  (hcp), has a rich history beginning in-and-around the 1570s starting with the problem of stacking cannonballs on the deck of a ship. Today there are purely mathematical packing challenges as well as applications of atomic and crystallographic stacking and packing. By starting with planckspheres, this most-simple doubling application becomes discernible as the second,  third, and fourth doublings are assumed. Further, subsequent doublings are assumed right on up to 202nd doubling and the current time.  Yet, something unusual is captured within the 67th doubling, we begin to measure it. That length opens the possibilities of particle physics revealing the potential science of the first 64 steps. It begs the question; is this a logical continuum from the infinitesimally small scale structures up to those being measured by accelerators like CERN?

These planckspheres, a key element of the finite-infinite bridge, are defined by pi, the Planck base units, dimensionless constants and simple logic. Every finite-infinite discussion-and-debate should be re-examined. Though tedious,  it must be re-engaged.  There are too many fine scholars who are being torn up and their logic being shredded to not engage every idea that has been posited throughout human history. All of that is within the 202nd notation. The 197th notation takes us up to 343+ million years. Our first 196 notations open a deep study of the earliest cosmological epochs.

Could this model be in line with Neil Turok’s conclusions that the universe is in a perpetual state of starting? So, yes, I believe planckspheres and every form of emergence up to the 67th notation are keys.

Many people have asked, Why now?

Of course, the question must also be asked, “Is this model overly simplistic and naive?”  Yet, even if so, could this model of the early universe be closer to the truth than the big bang theory? I believe it is. Thank you. -BEC 



Endnotes and Footnotes:

(in process today, 29 June 2018)

[†]   This dynamic image was first introduced within this website on January 4, 2016 in an article about numbers, “Constructing the Universe from Scratch.” It has now become the center point within this analysis. In that initial article, the question was asked, “Which numbers come first and why? Which numbers are the most important to know and understand?” The image was also used within the following articles: Fabric of the Universe (November 20, 2017, just below point #4), Consider how symmetries within the first 67 notations actually create space (Sept. 17, 2017) and Symmetry: Circles-to-Spheres-to-Triangles-to-Tetrahedrons-to-Octahedrons (September 13, 2017.

[1]  The three faces of the finite-infinite relation extend our earlier discussions about David Hilbert’s understanding of infinity and Max Tegmark’s disdain for the word. Continuity-symmetry-harmony are the mathematical-scientific faces of infinity and each face is captured by the dynamics of pi and the emergence of lattice, tetrahedrons and octahedrons, and eventually complex structure.

[2]  Frank Wilczek wrote his three-part series, “Scaling Mt. Planck” for Physics Today, yet has not acknowledged that Planck base units are the best conceptual orientation to start constructing this universe. As a result of this analysis, we will ask him, “Why not?” To our knowledge, the writings within this website are the first to lift up Max Planck’s base units as the starting point for the universe. We are anxious to discover and understand any articles that analyze their place, power and conceptual richness.

[3]  “The first emergence” is a steady stream of planckspheres being uniquely created just like they were in the very first moment. Every notation has a unique function and every notation is evolving at the same time it continues to do what it has done. Here, perhaps are Neil Turok’s perpetual starts of the universe. Here everything, everywhere is built up and emergent from this fabric of the universe, called an aether and/or dark matter and dark energy, that gives this universe its isotropy and homogeneity.

[4]  The Planck base units and dimensionless constants are inextricably interwoven throughout the 202 doublings (or notations) are based on the “Plancksphere” and that analysis is just beginning. I googled the word, for example, on June 25, 2018 with those quotes and there are just nine results. Using two words, “Planck sphere” with the quotes, there are 320 results. And without the quotes there are just over four million combinations that come close. Such results suggest that this is a new or emergent science.

Within our dynamic image about sphere stacking, the tetrahedral-octahedral architecture begins to emerge. Here, the possibilities for getting things inextricably woven together become staggering. By the tenth doubling there are 134,217,728 scaling vertices with which to work. By the 20th notation it catapults to 1.4411519×1017 — there are no limits to the entanglement of strings and knots and yet-to-be-fathomed geometries to create. By the 64th notation those scaling vertices have jumped up to 6.2771017×1057  and the first particle has yet to emerge!

Unless this simple logic is mistaken, there is altogether too much potential to ignore these possibilities and this orientation any longer.

Also, it should be pointed out that Max Planck’s formula for light — you can see it on line 10 of the horizontally-scorlled chart of 202 notations is a special calculation that needs further study.  The fact that these doublings is a form of base-2 exponentiation suggests that our universe is not linear and just might best be defined by Euler’s identity, considered by many mathematicians and physicists to be the most beautiful of all equations.

[5]   Everywhere, everything for all time shares this same moment and this same infrastructure. There are many books and articles about the nature of time. Within this study, most have fallen short. Einstein and Planck opened the door to re-analyze Newton’s earlier conceptual frame of absolute space and time, yet nothing more compelling emerged. Newton continues to define our commonsense logic, but should it? If it is established that period-doubling bifurcation, cellular division, double field theory and doubled geometry, and multiscale modeling all share the same common denominator that starts at the Planck base units, absolute space and time can be placed on the historical shelf as a footnote within the imprinting on the sentience of this universe. More work needed…

[6]  Consider disorder, chaos, uniqueness, creativity and fluctuations. The scholarly community is increasingly confused with the terms, infinite, space and time.  David Hilbert’s simple analysis leaves much to be desired. The infinite can be understood as a logical construct where it is the foundation for continuity, symmetry and harmony. These three perfections should all be understood to be a scientific assertion about the nature of order, relations, and dynamics. The various manifestations of fluctuations can be experienced as disorder, chaos, uniqueness, creativity and human will. The geometry for fluctuations begins with the simple pentastar, a clustering of five tetrahedrons. The next base structure, the icosahedron, is a clustering of 20 tetrahedrons. The dynamics of each will be introduced within future homepages.

[7]  Structures begin building on basic structure.   There are two areas where our analysis is focused. The first is on a notation-by-notation analysis but progress is slow because there is so much mathematical logic to be learned. The other is basic geometries, quantum geometries and dynamic geometries.  Here, too, there is so much to learn and, of course, more to come

[8]  There can be strains of continuity within discontinuity. There can be strains of discontinuity within continuity.  The continuity equations from the first doubling to the 202nd doubling come from within a continuity that envelopes our physical universe, so here, too, there is more to come

[9]  There appears to be a rigorous academic study of the logical construction of concepts, geometries, and equations. Mathematics and geometries do build upon each other! These studies will become our studies and as quickly as possible, each will be integrated within our map of the universe. Yes, there is more to come

“In philosophy, systems theory, science, and art, emergence occurs when “the whole is greater than the sum of the parts,” meaning the whole has properties its parts do not have. These properties come about because of interactions among the parts.” -Wikipedia

This page was started on June 21, 2018 in South San Francisco while on our tour of America. On many occasions Hattie and I been challenged to look at the world and ourselves in new ways. Along our route, we’ve spent time engaging with people:

  • At John Hendrick’s retreat, Gateway Canyon Ranch, an hour south of Grand Junction, Colorado, we discovered his CuriosityStream retreat center. That got me thinking.
  • We were in the highly-overpriced Yellowstone Hotel in Wyoming where the National Park Service is attempting to create a Disney-like experience, highly-controlled-and-organized wilderness. That compressed conflict got me thinking.
  • On our drive to Bend, Oregon, I discovered the Simplot Don plant near Pocatello, Idaho and learned about fertilizers and growth and even that challenged my thinking.
  • In Bend, while visiting with friends, I was challenged again to understand why there is such disparity, both political and economic, within our world.
  • On to Portland, the land of inclusivity, two different sets of friends challenged me to see the world through their eyes. There is so much to process and process it we will until each becomes a homepage.

This homepage was simply to clarify the last three homepages:

Thanks again.


The next homepage builds from this page and from those past homes pages linked just above, and from a page written on July 23, 2016 entitled, Chaos-Order, Indeterminant-Determinant.

Your Small Group To Discuss The Nature of the Finite-Infinite Relation

Initiated: December 11, 2017  Updated: April 12, 2018   A work-in-progress

Convener-Presenter:  This could be you.

Purpose of this group. To develop a special graciousness and openness about life and beliefs, this group is for the people who want to get along with believers and non-believers. Can we find a deeper truth that holds up some new insights that will embrace both sides of an equation by focusing on the nature of the relation. We’ll engage the edges of scientific research and its implications for our current theories about the universe and its origins, and about who we are and the meaning and value of life.

Overview: One of the best sources for a study of the relation between the finite and infinite are the sacred texts within our religious traditions.  Many of us who grew up in the Christian tradition and like typical college students, we tend to reject the old to begin to self-actualize.  Then we begin studying at the limits and boundaries of our knowledge and the challenges can become so daunting, they get left in those undergraduate and graduate classrooms. Personally I went out as far as I could on the edges of physics, working with Bob Cohen, the chairman of Boston University’s physics department, and then with physicists from around the world. I began discovering there are conceptual overlaps between all the departments within the university. The most extreme appeared to be those who were religious and those who demonized all religions.

What can be more different that the texts within The Bible, both Old Testament and the New Testament, and most texts within the scientific community, that is between Genesis 1 and John 1 and Stephen Hawking’s big bang theory.  These sessions are designed to examine concepts within the sciences, philosophy, ethics, and mathematics to see how and where these overlap with concepts about eternity, infinity, light, and love. We start with an integrated view of the universe, and that begins to inform our understanding of the infinite and infinity.

Structure: This small group will have just nine gatherings, no longer than 90 minutes each. A goal for these sessions is to chart a way to empower people to create such a small group study.
• The first two sessions. We will re-examine cosmological models of the universe (2 weeks).
• The 3rd and 4th sessions:  We will explore various ways of approaching an understanding of the finite-infinite relation.
• The 5th and 6th sessions: We will explore a rather different understanding of light, a light that permeates and defines every notation and all of space and time.
• The 7th and 8th sessions.  We will explore the challenges to our understanding of basic concepts like space and time.  Both become finite and transaction oriented.
• The final session: Beyond the summaries, we will be searching for answers to the question, “What do we do now?”

Simple and small goals:  The first goal is to open the door to a very simple orientation to science and faith that (1) works with science and mathematics and (2) allows for, and possibly informs, religious beliefs. The next goal is to explore the entry points between the finite and infinite. Another goal is to explore the physics, philosophy, and psychology of light. If we have even limited success, we’ll all begin to shrink space and time and open up an intimacy with the universe.

Resources to start your own Study Group:

Promo sample to paste on bulletin boards: Please Update the dates, locations and people.
Update: PDF to be printed back-to-back after updating. It creates four 4.25×5.5 inch handouts.
Session 1Models of the Universe   Worksheet #1   S1a   S1b   S1c
Session 2: Models of the Universe
Session 3: Finite-Infinite: Continuity-Symmetry-Harmony
Session 4: Finite-Infinite: Order-Relations-Dynamics
Session 5: Light as defined by the Planck Length and Planck Time
Session 6: Light and time. Ten ways to reconsider the nature of time.
Session 7: Eight Key Ideas
Session 8: Planck Explains Einstein and Redefines Space-Time and Pi.
Session 9: “It’s a wrap.”
1. Always check the homepage of
2. Check for any prior homepages you may have missed.
3. Add to the dialogue: Comment, like, Tweet, Link


Richardson, Louise Mary

Louise Mary Richardson
Vice Chancellor
Oxford University


First email: Tue, Oct 31, 2017 at 3:49 PM

Reference:  Forward for Oxford University Press

Dear Prof. Dr. Vice Chancellor Louise Mary Richardson:

Sometimes even Tacitus is wrong. [1] Some age-old “truths” actually hold us back. Two powerful obfuscations came out of the other great British university, particularly from two of their Lucasian Professors [2]: Newton with his absolute space-and-time and Hawking with his big bang. [3]

Now, I have been reading What Terrorists Want: Understanding the Enemy. And, yes, we have been too slow to create counter narratives to the ideologues of terrorism. I would add that we have also been too slow to challenge conventional paradigms, especially when we find ourselves within circular arguments.

Now, we share a few common experiences. As a kid we would visit Aunt Nellie who worked in the Radcliffe Admissions office. My dad had been a sheet metal worker in the Harvard HVAC group and helped to keep the Mark I and II cooled down in the basement of the Cruft Lab on Oxford Street. While in high school I joined the SDS at Harvard before it was thrown off campus in 1964. By 1969 I was organizing national amendments to end the war in Vietnam with full-page ads in the New York Times and Wall Street Journal, and congressional conferences in Washington, D.C. on global priorities. There wasn’t anything we wouldn’t do.

But something fundamentally was missing.  My driving force was to understand scientific breakthroughs, creativity, and innovation. By 1971 I was onto the EPR paradox [4] and quickly found John Bell [5] at CERN labs. It became obvious that there was something very wrong with our notion of space and time, but we couldn’t break through Newton’s commonsense logic. Hawking was so hooked, the big bang seemed like the only logical choice among cosmological models. It wasn’t. [6] Then, after 100 years of being in an academic closet, the Planck units were re-discovered (2001). Then, in 2011, the first mathematically-integrated chart of the universe was made using the Planck units. Using base-2 from the first moment of physical time to the current time, there were only 202 notations.

That changes everything. Space-and-time are contained. And, now something more fundamental must emerge. Oxford should be on the forefront of understanding what that is. If I were able to assemble an Oxford team, among them would be Julian BarbourHarvey BrownArd LouisAlister McGrath, Jirina StoneRichard Swinburne, Roger Trigg, Keith Ward, I.A. Walmsley… and you.

May I follow-up this introduction?

Thank you.

Most sincerely,

Bruce Camber
Austin, Texas

[1]  We seem to settle in with concepts that actually become age-old truths, but these concepts are ultimately flawed. Of course, by and large Tacitus is right:  ‘Truth is confirmed by inspection and delay; falsehood by haste and uncertainty.’ You use the quote within the section, “Challenges” within the  Vice-Chancellor’s Oration 2017
[2] There are comments about the debate between Leibniz and Clarke (Sir Isaac Newton)  throughout the website,  For now, you might particularly engage the second point of this page:
[3] There are pages and copies of emails to Stephen Hawking about his Big Bang theory. Ostensibly the argument focuses on the texture of the first fraction of a second of the universe and whether there is “…an infinitely small, infinitely hot, infinitely dense point…”
[4] EPR Paradox, also known as the Einstein-Podolosky-Rosen thought experiment of 1935 opens the question about non-locality and quantum entanglement.
[5] Bell’s Inequality opens the discussion to the widest community within physics and these discussions lead to the conclusions of Nima Arkani-Hamed and Max Tegmark to stop using the concepts of space-time and infinity.
[6] All cosmological models are being called into question.

Just Eight Key Ideas

Center for Perfection StudiesThe Big BoardLittle Universe Project • USAUpdate: December 2017
Homepages:.Just Prior|1|2|3|4|5|6|7|8|9|10|11|12|13|14|15|16|17|18|19|20|Original

Concepts For A Simple Model Of The Universe

1. 202 base-2 notations (doublings, containers, clusters, domains, layers, sets and/or steps)
2. This Quiet Expansion Is A Natural Inflation. Here’s A Sampling.
3. The speed of light has variable speeds and there is a wide variegation of light.
4. Facelift for Space-time
5. Rebirth of the Finite-Infinite Studies
6. Incommensurables, transcendentals and irrational numbers get real.
7. Continuity-symmetry-harmony creates order, relations and dynamics!
8. A Place For Everything, Everywhere, Throughout All Time

Fabric-Space-Time1. These 202 base-2 notations easily encapsulate the universe.

Multiply by 2. Start with the smallest units of measurement, the Planck Time and Planck Length, multiply each by 2, then the result by 2, and continue right up to the largest possible measurements, the Age of the Universe and the Observable Universe. Though both are still constantly expanding, your result will quickly be a totally, mathematically-integrated model of the universe that includes everything, everywhere, for all time in just 202 notations.

Just one more time: Most scientists and scholars now believe that Planck Length and Planck Time are the very smallest possible measurements. If you double them, then double them over and over again, in just 202 doublings, you will have reached the size of our Universe and you will have gone from the beginning of time to this present moment in time.  It sounds impossible, but the math is the math.

•  Rather special. Though simple logic, simple math, it’s still just a model. As a challenge, take this model as a given, to explore in what ways it could be an outline for the initial structures of the universe. Also, if simple logic and math do not work from the Planck Scale to the CERN scale to the Large Scale Universe, then logic and math should not work anywhere. Continuity is continuity. Order is order.

Eventually we added Planck Charge and Planck Mass to our doublings and continued to study how the numbers and the inherent logic worked together.  We have been exploring this model since December 2011 and have discovered that it seems quite sustainable! No scientists or scholars have seriously challenged it. Of course, it is idiosyncratic and it does raise rather unusual questions. Notwithstanding, the universe within just 202 doublings (clusters, containers, domains, layers, notations, sets and/or steps), so far, actually does seem to cohere 1 (Footnotes/endnotes at bottom).

•  Sweet. By the 31st notation, Planck Mass has increased to 103 pounds. That may be an ideal weight for some, yet in this notation, space and time are still so small that science has always considered these values meaningless.  We do not. Though an entirely novel concept, we take it as a given that there was a time when the universe was just 103 pounds. Though necessarily defined by point free vertices, it already has more active ratios than our imaginations can grasp (1.23794×1027). It exceeded one million vertices by the eighth notation, one billion at the 11th, and one trillion at the 15th, and a quintillion vertices at the 17th notation.  To follow that quiet expansion, look at line 9 in the chart below.  More 1-67a

2. This Quiet Expansion is a Natural Inflation. Here’s a sampling.

•  In this model each notation is more than just a simple doubling. The next notation doubles in size and doubles in content and each notation it would appear is currently defining our universe. As we live with the model, grasping the first notation as the start of the universe and the current notation as our current moment in time, all the notations come alive as a process that gradually builds upon itself, every notation changing and growing because of the others. To think about this very different sense of space-time, I did a sampling of six of the notations somewhat evenly spaced across the 202 notations. Of course, these Planck scale doublings are all predictive numbers. Within these six notations that were sampled, each demonstrates a natural inflation that is a quiet expansion.  A sampling  Prime numbers...2

•  Being natural is good. If one were to wonder about the basis for bifurcation theory, chemical bonding, cellular development, and isotropy-and-homogeneity, we may have found a new opening to explore. Then, if one were ask about the source of this thrust, again I think we may have found another good opening to explore.

The alternative is not pretty, elegant, or logical. Any one of the many theories that use the big bang logic of infinitely dense and infinitely hot are incomplete, unnatural, and riddled with questions. Worse yet, the big bang philosophy and psychology have trashed our culture with a de facto nihilism and dystopia.  It is bad physics. It is bad mathematics. And, it’s bad psychology.

•  Sweet.  (1) The quiet expansion continues its doublings until finally at the 67th the folks at the CERN labs (Geneva) are able to pick up something and our core sciences start to evolve.  (2) Truly sweet is that this natural inflation approximates all the cosmological epochs that were defined by big bang theorists; however, in this model there is no bang.     (3) The 67 notations provides more than enough “room” for every possible system of mathematics to be applied. Remember the 64 doublings within the Checkerboard story!  More  And more...

3. Light has variable speeds and many faces.

Planck’s Equation

•  Planck Length divided by Planck Time equals the speed of light. And, as you might anticipate, with every doubling, that approximation of the speed of light naturally continues. See line 10 within the horizontally-scrolled chart. More

•  That is very special. Light, Time and Length are being redefined by each other and by Charge and Mass.3

Please take note that between the 143rd and 144th notation, the universe is finally one second old and Planck Length has grown to the size defined by the distance that light travels within that second.

Seasonal look at an equation that resets the universe.

It is simple math and simple logic yet it re-engages us to expand and begin to understand a rather extended spectrum of light, of course, well beyond the visible spectrum and well beyond where it has been defined to date.

This work has given new meaning to an old song (1977), “You light up my life.” The very final refrain goes something like this: “It can’t be wrong when it feels so right…” More

•  Sweet.  Here is the first time light, defined by another very simple mathematical formula, can be found within a simple mathematical progression. The formula from Planck predates Einstein’s!  More

4. Space-time is long overdue for a facelift.

•  The Gnarls and Knots of Space-and-Time. Definitively cast in stone in 1686 when Newton released his blockbuster, Principia, time-and-space took on an absolute frame of reference and this view became our commonsense worldview.  It became a realism (and naturalism) whereby our external reality is assumed to exist as it is given and experienced. Both concepts — space-and-time — have been problematic and now some really smart scholars want to throw them both out; we believe it would be better to redefine them in light of our model with its 202 notations. Here, the universe begins within the Planck Scale. Our challenge is to figure out how the universe evolved within those initial notations, and then how it continued to the 202nd notation and to this very second within our expanding universe.

•  It is a very special and rather non-intuitive challenge. There are so many people today who still affirm Newton. They unwittingly do so when one of them looks up into the clear, night skies, observing the panoply of stars, and says, “It goes on forever.” Those wrestling with this new model would say, “We are looking out at our expanding universe. It is still expanding within the 202nd doublings and has been for about 13.82 billion years.”  What happens is that no notation goes away and recedes into a past. Instead, each notation participates in the current definition of the universe and space-and-time, as the fabric of the universe, absorbs every imprint for all time-and-space.

•  Sweet. This new sense of space-time gives it a currency and vibrancy.  The universe has its own clock and as of 2013, the universe was 436 quadrillion, 117 trillion, 076 billion, 640 million  seconds (436,117,076,640,000,000) old.

Let’s turn on the clock.  There are about 31,556,952 seconds per year so at some time we will be adding at least four years of seconds, somewhere over 126 million additional seconds, to bring the total to the current time. A hundred years is just 3.1556 billion seconds. Extend that to 1000 years (31.556 billion seconds), a million years (31.556 trillion seconds), and a billion years (31.556 quadrillon seconds).  Our earth and solar system are approximately 4.5 to 4.6 billion years old.  The estimates for the Milky Way galaxy are about 13.7 billion years (yes, among the original galaxies formed).  Yet, none of it is old; it is all current. All the cosmological epochs are now understood to be ongoing processes of the universe.   More…

5. Let us try to rebirth finite-infinite studies.

 Science and mathematics have made great use the concept of the infinite; philosophers and theologians have as well.  Yet, over the years we have seen how these disciplines tend not to work very well together, especially those elitists among them, particularly among those religionists and theologians who too frequently don’t work well with anybody except their own.

It is no wonder that a few very bold scholars would like to throw out the concept of infinity. It has an awkward personality. It is too big for most of those yellow academic school buses.

•  We suggest a shakedown. First, let us shake out all the concepts that have anything to do with faith statements — these are too often argumentative, emotional, and sometimes even hostile. Within the quiet expansion model, there are several conceptual assumptions that begin to bind the finite and infinite in special-and-heretofore unexplored ways. These concepts include: continuity-order, symmetry-relations, and harmony-dynamics.  Though an unusual combinations of words, some element of each can be readily understood.

 We can do this. The word combinations may be a little gray, but we’ve all used each word at one time or another. Taken together and in this sequence, these words become very rare concepts because each reflects a face of the finite (our beingness, whether it is science, mathematics, psychology, philosophy or religion) and also a face of the infinite.  More   Foundations…   Ethics-and-values…

6. Incommensurables, transcendentals and irrational numbers

 Numbers. Perfect, unshakeable continuity occurs within numbers that are called incommensurables, transcendentals and the irrational. These numbers are never-ending and never-repeating. Our old friend, yes, a very dear friend of every circle and sphere, is Pi.  Its very close cousin is e, for Euler’s number.  Euler’s equation also defines the universe.  It is the heart of our exponential universe. Also, meet Pi once again.

•  Through our Looking Glass. Most looking glasses are mirrors. This looking glass can also be a magnifying glass. Isn’t it unusual that a number can seemingly go on forever without repeating itself and with no special pattern or repetition?  Doesn’t that define a certain kind of uniqueness?  …diversity?  Within this class of numbers there is a group that is also known as dimensionless constants.  There are quite a lot of them. Yet, in all the discussions about the many scholarly blogs, papers, articles and books, there does not appear to be any discussion about how these numbers must define some aspect of infinity.  Isn’t that an oversight? If we take it as a given within our new definition of infinity, this very special kind of continuity and order can also be understood as uniqueness and diversity. That’s rather special.

Now of all the scholars I know, perhaps Clifford Pickover or John Barrow have started a process of looking at infinity in this simpler way; we’ll be digging further into their scholarship. More…

But, for now, let’s see if we can take it one step further. Let us take as a given that these rather unique numbers (1) originate within the infinite, (2) tell us about the nature of the infinite, and (3) define the transformation between the finite and infinite.

•  That’s different and very sweet.  So, we now have an ordered-chaos and a discontinuous-continuity defining our finite universe.  The next step is to look at the symmetry/relations and harmony/dynamics.

7. Continuity-symmetry-harmony create order, relations and dynamics!

Sphere to tetrahedron-octahedron couplet
Creative Commons Share-Alike 2.5 Generic license

•   Pi leads the way. Leading the way out of the infinite is pi. Perfect equal circles, then spheres, then multiple spheres, then stacks of equal and doubled spheres. We are probably within the first ten notations or doublings.  And then, a radius discovers a radius and the first line is created. Then the radii begin discovering radii and lines and dimensionless, point free, vertices are created.  Vertices discover vertices and the first triangles are created. Triangles discover triangles and the first tetrahedron is created. Lines, vertices and triangles discover each other and then the first octahedron is created within the tetrahedron. And, quickly, hexagonal plates are discovered. Triangular plates are discovered.  And diversity begins to move into high gear in a perfectly simple, yet increasingly complex manner. Symmetries abound. Perfection is in the air. But the imperfect and asymmetrical are not far behind.  More…

•   Dynamics.  Euler’s number is somehow holding pi’s hand! The two are working those continuity and symmetry relations and are making a universe one step at a time. More…

•   That is a very special challenge. All shapes and forms and sizes and every manner of symmetry relations are being created. The pulse of energy known as Planck Charge creates a thrust, an energy, a direction, a motion, and soon our little universe is pulsing with activity.  More…

First, called the Planck Scale, it transmogrifies into what some call a Grand Unification.  Here is the first doubling. But for all intents and purposes, it is within a self-discovery mode. Yet, rather quickly (understatement), that self-discovery process organizes and begins what we call the Inflationary Processes right up to and including the 67th notation.  Now declared to be the Electroweak Processes, Planck Charge is huge. Planck Mass is huge. Planck Length has become manageable. Planck Time is still too small to be considered anything other than a placeholder.  More…

•   Sweet.  The rest of the cosmological epochs seem to follow rather naturally in line with the continued expansions (doublings and notations) of these Planck base units. Even Planck Temperature, which was placed at the top of the scale because everything begins simply, is now substantial enough to warm things up and to begin looking like our little universe.  More    And more…

8. A Place For Everything, Everywhere, Throughout All Time

•   The first 60 or so notations will never be observed by our machines. These domains are much too small to be picked up by our measuring devices. If there can be no validation by our machines, then we must rely on logic and mathematics. This special domain has a very special word to describe it; it’s call hypostatic. We actually create a real reality when shared by another. It is a really real reality when shared by many.  As more people adopt that structure, we press meaning and purpose into it.  Then we ask, “Is this helpful? Does it seem to describe a real reality for people within our time?”

•   Yes, this is very special challenge for all of us. Because everything, everywhere, for all time must be logically included on this grid — nothing is exempt —  we will hypostatize a place for philosophy, psychology, mathematics, quantum fluctuations, the cosmological constant, religions, the mind, consciousness, sleep, and qualities. More

•   So we have a bit of work to do.  And, we recognize that this work just started in December 2011 and it is still quite naive and young.  The initial goal was to give our high school students a very special chart to integrate Science, Technology, Engineering and Mathematics (also known as a STEM tool).  Today this project is known as the Big Board -little universe.

That was cool. But now, the real work begins. We know we are onto something and have opened a door that is worth exploring. We’ve begun to study some of the older problems within science with such names as inertial frame of reference, point processes, scalar fields and scalar field theory, and path integral formulation. Many of those subjects are listed on line 11 of our horizontally-scrolled chart.

We struggle with it all most everyday so your advice, insight, and help are most welcomed! Thank you.

Footnotes & Endnotes

1 Time: It is good to be reminded that the first second of the universe is between notation 143 and 144. The estimated 500 million years necessary for galaxy formation takes us up in between notations 197 and 198.

2 Number groups:  We will be studying every prime number as a possibility for a new mathematical system. The obvious, primes from 2 to 199 (3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197), prioritize themselves! The challenge will be to logically build the sequence of systems. It is anticipated that the work of Grothendieck and Langlands (IAS) will contain a few keys. More

3  Quantum fluctuations and imperfections.  We believe the geometry of imperfection begins with the pentastar and the pentastar gap.  Though possible within notations 1-to-40, simple logic suggests that these quantum geometries do not manifest until Systems (first column, eight row) begin organizing.  More

PS.  There may be more footnotes inserted in the forthcoming days. If you are observing changes in the post, it is because this post is edited every day. It will change, and undoubtedly grow a little longer.

Special Thanks

Friends from New Orleans came for a visit. Their two images have been in my mind’s eye as I worked on this page. I have been constantly asking myself, “Is there a way to write this up so they understand it?”   -BEC


We welcome visitors from Belgium, Brazil, Canada, Cambodia, China,  France, Germany, Honduras, the Netherlands, New Zealand, Portugal, Serbia, Singapore, South Africa and Turkey. Yes, all visitors to this site, we welcome you all.

Thumbs Up! Or, “Please Comment.”

We can only grow by helping each other with constructive criticism or reinforcement. A quick little “Thumbs Up” is helpful. If it is “Thumbs down” please send a comment. If you want to just use numbers, -1 for Do not understand, -2 for Confusing and -3 for Disagree.

Our most simple assumptions and insights for an alternative theory:

•  The finite-infinite relation can always be understood more profoundly.
•  The key numbers, functions and geometries recognized by our most-respected scholars all begin their work to define the finite-infinite relations within the very first moment that defines space, time and light.
•  Pi and Euler’s number are the first steps within this understanding and define the very beingness of the universe.
•  The Planck numbers are also part of these first steps and all subsequent steps. More…
•  Multiplying the Planck units by 2 over and over and over again creates a grid or a matrix within which to begin to understand numbers, functions and geometries. The principles of continuity and symmetry become penultimate. Though space-and-time-light are infinitesimal and thought to be meaningless, this is the beginning of a natural inflation and thrust of the universe.

The Finite and the Infinite

Most recent update: Sunday, 8 October 2017   Prior homepage  Next homepage   On Time

Stephen Hawking and Max Tegmark
Stephen Hawking – Max Tegmark

The relation between the Finite and the Infinite is rather hotly debated, mostly between people who equate the infinite with God and those who have no place for any kind of god. Yet, the infinite also creates conundrums within science. In 2014, MIT physicist, Max Tegmark advocated, “I’m betting that we also need to let go of it.” He wants to retire what he and others call an incorrect assumption – infinity. His friend, Stephen Hawking, opened that door with his 1983 No Boundary Proposal that holds that the universe has no beginning or end.1

“Not so fast y’all” as it is said along the banks of the Mississippi River in New Orleans. With these two thought leaders, Hawking and Tegmark, it should be acknowledged that both are being speculative and that their concepts are brilliantly incomplete.

In the Big Board-little universe model using base-2 notation from the Planck Time to the Age of the universe, the entire physical universe is contained within just over 200 notations that are highly-integrated and totally-predictive. Notations are also known as clusters, doublings, groups, sets or steps. Within the first second of the universe, there is more than enough “natural inflation” from the Planck Charge to get “things” going. As a result of studying and working with this model since December 2011, there are many-many facets to explore, however one of the most important is that this model logically suggests that time is derivative and that the finite and the infinite are perhaps best understood in terms of continuity, symmetry and harmony.

Continuity. Though an unusual way to define infinity, even with quantum indeterminacy, continuity throughout the universe is the bedrock of science, logic, and rational thought. Numbers clarify this continuity. If we were to carry our measurements out a billion places, the universe and its systems around us would still replicate day after day with utmost precision.

Within this model, continuity is more fundamental than time; it begets time. It is the initial condition of order.  More…


The complexity of a single molecule


Symmetry. The second face of the infinite is symmetry. Though so much of life is asymmetrical, the deepest examination of any physical thing begins to reveal deeper symmetries. Numbered relations define those symmetries, relations are created, and the universe appears to be tiled and tessellated deeply within every notation throughout the model. Here symmetry is more fundamental than space; it begets space.  More…

Harmony. Speculating, it is hypostatized that two symmetries begin interacting within a notation and then across notations, dynamics are created, and though not quite perfect, the interaction of the symmetries perfects the moment for the observer or for the notations involved. Therefore, we have moments of perfection within our experiences of the universe. More…

Our studies. At this point in our studies, there is not much more we can say about how the infinite defines the model and what the model says about the very nature of the infinite. These three insights, although reflective of the model, in part come out of a study of a moment of perfection in 1972,3 then from studies of the book, Finite and Infinite: A Philosophical Essay (Austin Farrer, Oxford, Dacre Press, Westminster, 1943), and from an application to a business model.4    More…

These three qualities became the bedrock for our model of the universe and for discussions about the shared nature of the finite and infinite.

What difference does it make? First, it is a clear contrast to the nihilism of big bang cosmology. Building in strength and popularity over the past 30 years, that nihilism has had a lot to do the fraying of our little world. So much is out of control and spinning apart. Money is not the issue. What we believe and how we believe is. Hope is. Charity is. Integrity is.

What is 5000 to 13.8 billion years?

The finite and infinite relation has been the focus of humanity for as long as we have been recording our ever-so-short history. In light of 13.8+ billion years, five thousand years of records is, of course, quite short. We’ve just begun to make sense of it all.

Today in history. The finite is usually associated with physical, limited things. The infinite is often capitalized and associated with godly things, the eternal and everlasting. To our knowledge, Max Tegmark is the first theoretical physicist who has suggested that the concept of the infinite be abandoned. His rationale is that it gets in the way. He cannot make it work for the science he wants to create. Within these many articles, we hope to convince him, Hawking, Guth and so many others to re-engage our simple definition of the infinite. It does not require a religion or religious beliefs. Notwithstanding, it also does not necessarily fly in the face of those who believe in a much more robustly-defined Infinite.

We can all begin to tolerate each other.

This is our simple introduction to a very large topic and we will return to this page often to expand its range and its depth.

1 A general introduction: See the prior homepage. Also, this Wikipedia article about the 1983 Hartle-Hawking State (wave function) provides even more information.
2 This construct was introduced within these pages at the end of the year, December 2015.
3 This construct goes back to work in 1972 at both Synectics Education Systems in Cambridge, Massachusetts and the Harvard Philomorphs with Arthur Loeb and Buckminster Fuller.
4 The original construct was used as the foundation of a business model for a weekly television series, Small Business School, that Bruce Camber and Hattie Bryant started in 1994. It aired on PBS-TV stations throughout the USA and on the Voice of America around the world for over 50 seasons (2012).


Related homepages:

Key references: Communications

A Quiet Expansion of the Universe


Most recent update: February 2018

A working draft for the scientific – academic communities. Or a shorter version for the general public.


Stephen Hawking rhetorically asked, “Where did the universe come from?” He continued, “The answer, as most people can tell you, is the big bang. Everything in existence, expanding exponentially in every direction, from an infinitely small, infinitely hot, infinitely dense point, creating a cosmos filled with energy and matter. But what does that really mean and where did it all begin?” Ref. [1] May 2016 PBS-TV series, Genius

As confident as Hawking appeared, the big bang is still just a theory. And, of course, there are other possibilities.

Within this post, we focus on a very simple model and nascent theory that has only been explored by a relatively small group of high school people and others within our extended community. We ask, “Is it possible that the universe began with an infinitesimally small length and time, and a relatively small charge and mass? Yes, we use those numbers defined by Max Planck in 1899, the Planck base units, to begin. In this model the universe is most simple and the opposite of  infinitely hot and infinitely dense.  Also, this structure becomes part of the ongoing structure of the universe. It supports the claim of Neil Turok and his colleagues that this universe is in a state of perpetually starting.

Our simple journey started in December 2011. In 2012 we began asking more-pointed questions about the first 67 of 202 notations. In 2013 we began our rather informal studies of the big bang theory. In 2014 we began to question it. Today, we are hoping the experts can tell us why using the powers of 2, doublings from the Planck scale to the Age of the Universe is not a proper outline for a model and theory. Having learned how idiosyncratic it is, we have many questions.

Universe View
Each epoch of the Big Bang has a corresponding set of notations. We question the first four epochs:
The Planck Epoch, the Grand Unification Epoch, and the Inflationary and Electroweak Epochs.
What is time? What is space?
What is finite? What is infinite?
Who was more correct, Newton or Leibniz?
The first four epochs of the big bang theory represent an infinitesimal amount of time within the QE model, surely not enough for the proposed events of those epochs.

Wilczek Wiki
In 2001 Frank Wilczek wrote a series of articles for Physics Today (link embedded here) about the Planck base units. Up until that point, this part of Planck’s work had been virtually ignored by the academic-and-scientific community (for over 100 years).

Might the mechanism for the doubling of a cell be a rather limited metaphor for the expansion of the universe? Could our universe be functionally based on the simplest mathematics, doubling both in size and in number up to this current notation and each step of the way? Is our universe, in fact, exponential (as in Euler’s equation), highly-ordered, and totally relational?

First principles. We postulate that the Planck scale is the unification of the four forces of nature with the unification of the Planck base units with those constants that define each unit, and that this unification, all defined as working ratios, is uniquely differentiated within each doubling throughout the entire 200+ steps from the first moment of creation to this moment, the current time and present day. It appears that all 202± steps are dynamic, actively participating in the current time and this definition of our universe. This postulation provides a working environment by which we hope to build a diversity of bridges from the Planck scale to all existing physical theories whereby each notation creates a very unique environment for predictive values.

We call this model the Quiet Expansion of the Universe, hereinafter, abbreviated QE.

We begin this study with the Planck Epoch, then attempt to justify reinterpreting the Grand Unification and Inflationary Epochs. The Electroweak Epoch begins the crossover which continues through the Quark Epoch and into the Hadron, Lepton and Electron Epochs. Thereafter, the QE will have so many bridges up from the Planck Epoch, it should become an expressway to the remaining epochs and all the useful definitions developed over the years within the big bang theory (hereinafter, abbreviated bbt).

The Planck base units. Further defined by the speed of light (or special relativity), the gravitational constant (or general relativity), the reduced Planck constant (or ħ or quantum mechanics), the Coulomb constant (or ε0 or electric charge or electromagnetism), and the Boltzmann constant (or kB or of temperature), all are bound within this Planck scale; and, herein it is proposed to be the foundations for a highly-ordered, totally-relational universe. The key to our model is multiplication by 2, starting with the Planck base units. A nexus of transformation between the finite and the infinite is defined by the crossing lines at “0” within the images on the right (just above Frank Wilczek).

We still have many questions. We have hopes and dreams. If the QE numbers can withstand the scrutiny of the academic and scientific communities, and we can begin to grasp the finite nature of space and time, and we can open a larger discussion about the nature of the finite-infinite relation, just maybe the bbt will recede and take a new role as an important chapter in academic as well as human history.

Our hope is that this posting will be able to stand the test of time; however, we full acknowledge that it is a “very rough first draft.”  Given the depth and breadth of the foundations upon which the big bang theory (bbt) currently rests, your comments while this posting is being refined, are most welcomed. If this embedded link does not open your email browser, my address is camber (at) 81018 (dot) com (or click on Contact (always within the navigation bar at the top).

Those pivotal Planck calculations were done between 1899 and 1905 by Max Planck. In December 2011 we were just beginning to learn about Planck and his calculations. We sought out experts and quickly found the work of Prof. Dr. Frank Wilczek (MIT).

Frank Wilczek. With very few exceptions, it was not until Wilczek began writing a series of articles in 2001, Scaling Mt. Planck, (Physics Today), did anybody think those Planck numbers amounted to anything more than numerology. It would take another ten years before we would come along, naively doing our thing with our geometries and simple doublings.

Though most academics are familiar with Kees Boeke’s 1957 work (Cosmic View) using base-10, we were not. Most all our academic contacts made quick reference to it, yet they were still surprised to see our chart from the Planck Length to the Observable Universe. Some asked, “Why haven’t we’ve seen this before now?” The others just thought it was more quantum mysticism  and numerology akin to Paul Dirac’s work with large numbers (link goes to a YouTube audio where Dirac explains it in his own words).

We are confident that the proponents of the big bang have never considered the first 67 notations defined within this Quiet Expansion model.

This simple work of multiplying the Planck units by 2, and then each result by 2, over and over and over again is a bit tedious. If you were to do it, in just over 200 steps you would emerge at the Age of the Universe and the Observable Universe. You can follow the progression in any one of several charts. A simple doubling is what cells do. Other processes like chemical bonding and bifurcation theory have analogous dynamics.

These 200+ doublings have at various points been called: (1) archetypes, (2) clusters, (3) containers, (4) domains, (5) groups, (6) layers, (7) notations, (8) ratios, (9) sets or (10) steps. We believe that each captures a face of the functionality within the notation. We recognize that these Planck base units can be computed in many different ways. Eventually, in order to refine results, the reduced Planck constant may be used. The various values of gravity (G) can be tested. Important at this time is consistency and equivalence of methodologies across all calculations within all 200+ notations. Our initial goal is to create a simple working model that outlines the general working parameters and boundary conditions to give us a platform. Now we begin looking at the key critical ratios throughout the model with a hope that we may discern natural groups and patterns that might help us to judge the veracity of the model itself.

The web page, Big Board-little universe, provides more background of our rather brief history.

Big-bang Theory Drowns Out Discussions

To learn as much as possible as quickly as possible, we’ve used Wikipedia’s summaries. Wikipedia’s goal is to represent the best current thinking of the thought leaders within the relevant scientific communities. The scientists who are most often quoted have lived within this theory throughout their professional careers. It is part of their intellectual being. Notwithstanding, we believe most all of their work can be absorbed within the QE. Questions are primarily raised about the Planck Epoch, the Grand Unification Epoch, the Inflationary Epoch and the Electroweak Epochs. Taken together, the first three “epochs” represent less than a fraction of a fraction of a second within the QE model. And, with just a few tweaks, we believe some of this work and all the work within the subsequent epochs can be readily integrated.

The writers within the Wikipedia community overlap with those within these scientific communities. Wikipedia, constantly in the process of refining their writing, provides several summaries of the History of the Universe. All work based on observations and measurements has a place within the QE model. Our guess is that the interpretation of those observations and measurements will become richer and more informative when the QE parameters and boundary conditions are engaged.

In 1970 there were truly competing theories about the beginning of the universe. By 1990 the bbt had become dominant. In 2011 our little group of high school geometry people began to explore the interior structures of the tetrahedron and octahedron. Then we found within our tilings and tessellations, and then all the simple doublings from the Planck base units to the Age of the Universe and to the Observable Universe. That continuum appeared so simple, we first engaged it as an excellent STEM (Science-Technology-Engineering-Mathematics) tool. Yet, with further study and thought, it also seemed to challenge some of our basic commonsense assumptions about nature (the back story). As we studied our new little model, the bbt continued to solidify its dominance within the general culture at the same time we started to question it. We began to believe that the actual physics of the first moments of creation might be better defined by the simple mathematics of a quiet expansion, especially those first 67 notations. These 67 have never been recognized as such and certainly have not been discussed within academia. The great minds throughout the ages have been unaware of the 202 doublings, especially those first 67 steps. So mysterious are the 67, we began more actively to think about them and to make some postulations about their place and purpose.

This is our first posting about this quiet expansion. It is a result of our naive, informal, and often idiosyncratic studies of the Planck base units, simple doublings, and an inherent geometry assumed (hypothesized, hypostatized, and/or imputed) to be within every scale (doubling, layer, notation, step, etc) throughout the universe. We have moved slowly. Having backed into the Planck base units from our simple exercises in geometry class, we were not at all sure of ourselves. So, after observing our results for a couple of years, we began asking the question, “Could this be a more-simple, more-inclusive model of the universe than the big bang theory?” Because we only have the beginnings of an outline of a model, we continued our quest and continued to ask more questions:

Who? What? Why?

When? Where? How?

Who: The history of the Big Bang Theory (bbt) is highly documented. It is an intellectual cornerstone within experimental and theoretical physics, cosmology, and astrophysics.

What: To challenge the bbt appears foolhardy at best. Yet, there are many, many reasons to challenge it, but most of all because (1) it is overly complex and confusing, (2) it is not very good philosophy, and (3) it is very poor psychology.

Why: The first three key parts of the bbt, involving substantially less than a trillionth of a second, are based on hunches and a need to shoehorn data to support the model.

Wikipedia says, “Planck scale is beyond current physical theories; it has no predictive value. The Planck epoch is assumed (or theorized) to have been dominated by quantum effects of gravity.”

We say that the Planck scale is the starting point for the initial six notations (de facto defined by the bbt) and that these notations are shared by everything, everywhere in the universe. Painfully aware of the limitations of our vocabulary, these first notations are considered to be archetypal forms, structure and substance. Archetypal is used in the sense of the original pattern or model by which all things of the same type are representations, the prototype, or a perfect example. For more, see all of 67 encapsulating notations (opens in a new window or tab).

Both models have made key assumptions. We believe the QE model is internally more consistent, imaginative, and stimulating.

This “Singularity” Is a Meeting Place of Converging Formulae, perhaps also known as a Modulus-or-Nexus of Transformation

Keys to this Quiet Expansion: More than the big bang theory‘s four forces of nature — gravity, electromagnetism, the strong force, and the weak force — within this Planck scale we assume these four are encapsulated within all four Planck base units and the constants that define them, and some manifestation of this unification is carried throughout all 202 notations. And, as we have noted, the Planck base units are defined by length, time, mass, and charge; and, these are further defined by the speed of light (or special relativity), the gravitational constant (or general relativity), the reduced Planck constant (or ħ or quantum mechanics), the Coulomb constant (or ε0 or electric charge or electromagnetism), and the Boltzmann constant (or kB or of temperature).

The Planck scale is not beyond logic, numbers, and conceptual integrity. Homogeneity, isotropy and simple logic rule. Yet, within the Quiet Expansion (QE) model, we have applied that simple logic somewhat arbitrarily by placing Planck Temperature at the top of the scale, just beyond the 202nd notation and then dividing by 2, it goes down approaching Absolute Zero. We are ready to adjust it at any time when a more integrative logic prevails! Also, we are increasingly finding a simple relational logic between the four original Planck base units. Notwithstanding, this logic will be constantly revisited throughout our ever-so-slow development of QE model.

Within the QE model, the Planck Charge, a Coulombs value, is taken as given. Within the big bang theory (bbt), the Planck Charge is ignored. The bbt value is as large as possible. Their measurement is given in GeV units, one billion electron volts. Add 1016 zeroes and you have quite a charge.

To begin to understand all these numbers and their correlations, questions are asked, “Are these all non-repeating, never-ending numbers like Pi? Are all numbers that are non-repeating and never-ending somehow part of the infinite yet also the beginning of quantum mechanics?” The suggestion has been made that we carry out each of the Planck numbers at least 10 decimal places, and if need be, 100 decimal places, and possibly even 1000 decimal places, to see if patterns can be discerned. We recognize that relative to other units of measurement, such as the SI base quantities, the values of the Planck units are approximations mostly due to uncertainty in the value of the gravitational constant (G).

The QE model holds that things are simple before complex and everything is related to everything. Imputed, hypostatized and/or hypothesized are pointfree vertices and simple geometries as the deep infrastructure that gives rise to the work on combinatorics, cellular automaton, cubic close packing, bifurcation theory (and the Feigenbaum’s constants), Langlands program, mereotopology (point-free geometry), the 80-known binary operations, and scalar field theory. Here are people working on theories and constructions of the simple, yet their concepts are anything but simple.

The exacting nature of the correlations between the multiples of the Planck base units is just being explored for the first time. But, to say the least, within the QE everything everywhere is related through simple mathematics.

Big Bang Theory (bbt)

Planck epoch

Planck time:

<10−43 seconds


Planck Temperature:

1032 Kelvin

First key bbt error

Planck Energy:

1019 GeV

Second bbt error

Grand Unification


<10−36 seconds~
1016 GeV

Third bbt error


Epoch and



<10−33 s to <10−32 seconds

1028 K to 1022 Kelvin

Expansion: 1026 meters

Editor: “Science Fiction”

Fourth bbt error~

Quark Epoch

>10−31 to

>10−12 seconds

1012 Kelvin

We sync the QE time to the bbt time. The temperature scale is now beginning to sync as well.

Hadron Epoch

10−6 seconds to

10−1 seconds

1010 Kelvin to

109 Kelvin

Lepton Epoch

1 second to

10 seconds

109 K

Note: QE temp higher

Photon Epoch


10 seconds to

103 seconds to

1013 seconds~

1011 Kelvin to

109 Kelvin to

103 Kelvin

10 MeV to 100 keV
Please note: We are actively seeking an expert in this area.



47 ka (47,000 years) to

10 Ga (10×109) years~

104 Kelvin to

4 Kelvin


380 ka (380,000 years)~

4000 Kelvin

Dark Ages

380 ka to 150 Ma (Mega-annus)

or 150 million years

4000 Kelvin to

60 Kelvin

Stelliferous Era

150 Ma (150 million years)

100 Gab (150 billion years)

60 Kelvin to 0.03 Kelvin


~150 Ma to

1 Ga (1 Billion)~

>60 K to 19 K

Galaxy formation

and evolution

1 Ga to 10 Ga

19 Kelvin to 4 Kelvin


dominated era

>10 Ga

Present time

13.8 Ga

2.7 Kelvin


Notations 0-6

Planck base units

Planck time:

5.39106×10−44 seconds

≈4.4×10-27 (K)

Temperature: Derivative

of the base units?

1.8×10-18 Coulombs

2.176×10-8 kilograms

1.61×10-35 meters

Notation 7 to 34

7: 6.901×10−42 (s)

31: 1.157×10−34 (s)

4.02×10-9 Coulombs

A simple natural inflation

Notation 35 – 40

35: 6.44×10-8 Coulombs

40: 2.06×10-6 (C)

35: 1.852×10-33 (s)

40: 5.927×10−32 (s)

Note: QE syncs to bbt time

2.42×10-17 (K)

35: 5.55×10-25 meters

40: 1.77×10-23 (m)

Notation 41-104

41: 1.18×10−31 seconds

104: 1.09×10−12 (s)

41: 4.84×10-17 Kelvin

104: 4.47×102 (K)

(Please note: 310K is equal to 98.33°F, 36.85° C. That’s special.

Notation 105142

105: 2.18×10−12 (s)

142: 3.0×10−1 (s)

105: 8.94×102 Kelvin

142: 6.14×1013 (K)

Notation 143147

143: 6.01×10−1 (s)

147: 9.61 (s)

143: 2.45×1014 Kelvin

147: 3.93×1015 (K)

Notation 147-154187

147: 9.6185 seconds
154: 1231.1 (s)
187: 1.05×1013 (s) or
or 320± thousand years
147: 3.932×1015 Kelvin
154: 5.03×1017 (K)
187: 4.32×1027 (K)
147: 3.346×1026 (C)
154: 4.28×1028 (C)
187: 3.67×1038 (C)

Notation 184– 201

Cosmology emerges!

184: 1,321,967,651,940 (s)

or 41,919.31 years

201: 10 billion years

184: 5.4×1026 Kelvin

201: 7.0×1031 (K)

Notation 187

10,575,741,215,500 (s)

320± thousand years

3.6×1038 (C)

4.3×1027 Kelvin

Notation 187-196

196: 171.2± million years

5,414,779,502,320,000 sec

2.2×1030 (K)

Approaching Planck Temperature

Notation 196-199

196: 171.2± million years

199: 1.27 billion years

Notation 196-199

196: 171.2± million years

199: 1.27 billion years


.Notation 199-202

199: 1.27 billion years

203+: Way-Distant future

7.08×1031 Kelvin

Notations 1-202

The dark-energy dominated era is being evaluated in light of the first 64 notations, the derivative natural of time, and homogeneity and isotropy.

Notation 202+

13.8 billion years

Planck Temperature

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