Can A Quiet Expansion Challenge the Big Bang?

Legacy: The first rough draft as of Sunday, June 12, 2016

Current work (still in process)

by Bruce Camber, New Orleans

History of the Universe Not too many people question the big bang theory (herein abbreviated bbt). We do. Back in September 2014 for the first time we publicly raised questions about the bbt.

The world-renown Cambridge University physicist, Stephen Hawking, is the leading spokesperson for the bbt. He has become a rock star among scientists because he has been so successful as its primary advocate.

Stephen Hawking
Stephen Hawking in the PBS-TV series, Genius, first aired in May 2016

Within his May 2016 PBS-TV series, Genius, he asks rhetorically, “Where did the universe come from? 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?” His confidence also exudes from his 1988, best-selling book, A Brief History of Time: From the Big Bang to Black Holes, and even from his foundational writing in 1973 (co-authored with Cambridge colleague, George F. R. Ellis) the highly-technical book, The Large Scale Structure of Space-Time.

Only a fool would dare challenge all this work over so many years.

So, such is life; each of us must sometime play the fool. With these facts and the basic premise established, this posting is a “rough draft.” It should become a first draft by July 4. 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) bblu (dot) org or go to the Contact page. There are many key images for the big bang theory such as this image above right. More images will be added over time. Most links related to the bbt go to Wikipedia pages. Images for our model, called a Quiet Expansion (QE), will be added soon.

The key to our model is multiplication by 2, starting with the Planck base units. Those pivotal Planck calculations were done in 1899 by Max Planck. Our simple work of multiplying them by 2, and then each result by 2, over and over and over again began in December 2011. We discovered that you readily emerge at the Age of the Universe and the Observable Universe, all in just 201 steps.

That is crazy, but true. It is called “base-2 exponential notation.” It’s what cells do. It’s a bit like chemical bonding. Bifurcation theory describes another element of its dynamic. In just 201 doublings, layers or groups, you can capture the entire universe in an entirely-ordered fashion! Beyond belief? Our web presence, Big Board-little universe, can provide more background about our rather brief history.

We’ve used the Wikipedia summaries of the big bang. Wikipedia appears to represent the current thinking of most within the relevant scientific communities. These scientists have lived within this theory throughout their professional careers. It is part of their intellectual being. We believe most all of their work can be absorbed within the QE. It is just from the starting point to the inflationary epoch — less than a fraction of a fraction of a second — are pointedly questioned. With a little-but-substantial tweak, we believe all the work on 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 based on the most current work of leading thinkers within the scientific community. The work that is based on observations has a place within the QE. Our guess is that those observations will become richer and more informative when the QE parameters and boundary conditions are engaged.

Are space-and-time unbounded or bounded? If bounded, is our universe a container universe? Are the Planck base units and all the dimensionless constants part of the definitions of the boundaries between the finite and the infinite?

Within the current bbt analysis gravitational waves arise from within their inflationary period. The bbt thought leaders ascribe a much faster-than-light expansion just after the big bang. And, that begs the question: What are the preconditions of superluminal events and motion? There haven’t been any answers since 1902 when Jacobus Kapteyn made his initial observations, since the 1983 “superluminal workshop” at Jodrell Bank Observatory, and since the subsequent studies of microquasars, their accretion disks and such phenomenon as magnetorotational instability. It is all a very special language, logic and reality; the observational results are well-defined; yet, we believe the most-penetrating conclusions are pending.

In 1970 there were 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 and that is when we found within our tilings and tessellations, just over 201 base-2 exponential notations 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 and 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 the first 67 notations. Those 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 201+ base-2 notations and those first 67 notations. So mysterious were the 67, we began more actively to think about them and to make some postulations about their place and purpose.

Our first posting about this Quiet Expansion is a result of our naive, informal, and often idiosyncratic studies of the Planck Base Units, base-2 exponential notation, 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 a high school 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 24 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 each of the four pages (24 columns) encapsulating notations 1-24 (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.

The key: More than just the bbt‘s four forces of nature within the Planck scale, we assume a certain unification of all five Planck base units and those constants that define them, and that this unification is carried through the entire 201+ notations to the current time and present day (until proven to be otherwise). The Planck base units are defined by length, time, mass, temperature and charge. These Planck units 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 followed a simple logic and placed the Planck Temperature at the top of the scale, just beyond the 201st notation and then it goes down, approaching Absolute Zero. We are increasingly finding a simple relational logic between the Planck base units. Of course, this logic will be revisited with every future analysis of the QE model. Within the QE model, the Planck Charge, a Coulombs value, is taken as it is given. Within the bbt, the Planck Charge is ignored and the bbt value is postulated to be as large as possible. Their measurement is given in GeV units, one billion electron volts. Add 1016 zeroes to it and you have a charge unlike any other! It is the penultimate, grand assumption that truly requires a leap of faith!

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 number 10 decimal places, and if need be, 100 decimal places, and possibly even 1000 decimal places, to see if patterns can be discerned.

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.
When: In the very beginning… Wikipedia says that the Planck epoch requires speculative proposals, a “New Physics” such as “…the Hartle–Hawking initial state, string landscape, string gas cosmology, and the ekpyrotic universe.” Each is a conceptually-rich, dense jungle of ideas. Cutting through that entanglement is only for the highly-motivated and academically astute. Most of us will just go on to the grand unification epoch, in search of a logical system that builds consistently upon itself. About the bbt model, Wikipedia simply says, “The three forces of the Standard Model are unified.” Of course, the QE goes much further, however, first consider a bbt problem. Electromagnetism, gravitation, weak nuclear interaction, and strong nuclear interaction are most often related to relations defined above the 65th notation.

Wikipedia says, “Cosmic inflation expands space by a factor of the order of 1026 over a time of the order of 10−33 to 10−32 seconds.[1] The universe is supercooled from about 1027 down to 1022 kelvins.[6] The Strong Nuclear Force becomes distinct from the Electroweak Force.” [1] (Our emphasis) First, consider that the Planck Temperature is 1.416 83×1032 Kelvin. The bbt totally skips the cooling from 1032 to 1027 Kelvin. It does not address what causes the cooling to 1022 Kelvin. Also, consider the amount of expansion and the short duration assumed in their statement above. To create that much space in that short of an interval would require light to travel so far beyond its normal speed, it would constitute the penultimate anomaly.

Also, because the bbt begins at the Planck Temperature, they truly need a supercooled concept. With the Quiet Expansion these temperatures are all superconducting being well below the superconducting transition temperatures. Perhaps the very concept of temperature will become better understood as a result of our struggles to define a different model of the universe.

About this inflationary epoch, Wikipedia says, “The forces of the Standard Model have separated, but energies are too high for quarks to coalesce into hadrons, instead forming a quark-gluon plasma. These are the highest energies directly observable in experiment in the Large Hadron Collider.”

Within the QE, if a quark-gluon plasma requires 1012 Kelvin, it is not possible until up around Notation 136 where the temperature is up to 1.92016×1012 Kelvin. Notation 136 is 4.6965×10-3 seconds from the singularity. One second is between Notations 143 and 144. Also, the Kelvin scale is counter-intuitive in many ways. The temperature of the Sun is about 5,778 K. Within the QE, that is expressed between Notations 107 and 108 (7.153178×103 K). The human temperature at 98.6 degrees Fahrenheit is 310.15 Kelvin which is between Notations 103 and 104 (4.47073×102 K). Also, at Notation 103 we find the Planck Length is now .163902142 millimeters or 1.63902142×10-4 meters or about the size of a human egg.

The exacting nature of the correlations between the multiples of the Planck base units is just being explored for the first time. Within the QE everything everywhere is related through simple mathematics.

In Wikipedia, their category experts say, “The physics of the electroweak epoch is less speculative and much better understood than the physics of previous periods of the early universe. The existence of W and Z bosons has been demonstrated, and other predictions of electroweak theory have been experimentally verified.”

Finally the the bbt gives us something that isn’t incomplete or highly speculative. Yet, even with such assurance, the logic of the bbt is difficult to follow. Again, within the QE model the only duration that would allow for W and Z bosons is about 30 notations away, somewhere around notation 65. There is just not enough “conceptual” space and time for elementary particles and their effects.

By the way, within this simple, highly-integrated progression, there is the first measurement that has a visceral meaning for us. At Notation 32 the mass of the universe is 93.48 kilograms or about 206 pounds. By Notation 40 it is up to 2.39×104 kilograms. The universe is bulking up quickly and it is creating space and time as it goes.

Also, consider this unusual concept: within every notation, the QE model aggregates base-8 pointfree vertices using scaling laws and dimensional analysis (recommended by Prof. Dr. Freeman Dyson). There are single line entries for both the base-2 and base-8 progressions within the horizontally-scrolled chart.

— most active edit area—

Big Bang Theory (bbt)

Planck epoch

Planck time:
<10−43 seconds
Planck Temperature:
1032 Kelvin
Planck Energy:
1019 GeV
First key bbt error


<10−36 seconds
1016 GeV

Inflationary epoch
Electroweak epoch

<10−33 s to <10−32 seconds
(QE syncs to bbt time.)
1028 K to 1022 Kelvin
Expansion: 1026 meters
Editor: “science fiction”
Second key bbt error

Quark epoch

Third error: >10−31 to
>10−12 seconds
1012 Kelvin
Notice there is a bbt/QE convergence

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-Nucleosynthesis

10 seconds to
103 seconds to
1013 seconds
<380 ka
1011 Kelvin to
109 Kelvin to
103 Kelvin
10 MeV to
100 keV


Matter-dominated era

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 Ga
(150 billion years)
60 Kelvin to
0.03 Kelvin


~150 Ma to
1 Ga
>60 K to
19 K

Galaxy formation and evolution

1 Ga to 10 Ga
19 Kelvin to 4 Kelvin

Dark-energy-dominated era

>10 Ga
<4 K

Present time

13.8 Ga
2.7 Kelvin

Quiet Expansion (QE)

Notations 0-24

0 = Planck base units

Planck time:
5.39106×10−44 seconds
Notation 1: 1.0782−43 s
Notation 24: 1.809×10−36 (s)
Notation 0: 1.416×1032 Kelvin
Notation 1: 4.4×10-27 (K)
Notation 24: 3.69×10-20 (K)
Notation 0: 1.8×10-18 Coulombs
Notation 1: 3.7×10-18
Notation 24: 3.14×10-11 (C)

Notations 25 to 31

Notation 25: 1.8×10−36 seconds
Notation 31: 1.157×10−34 (s)
Notation 25: 6.29×10-11 (C)
Notation 31: 4.02×10-9 (C)

Notations 32 to 40

Notation 32: 2.31×10−34 seconds
Notation 40: 5.927×10−32 (s)
Notation 32: 1.89×10-19 Kelvin
Notation 40: 2.42×10-17 (K)
Notation 32: 6.94×10-26 meters
Notation 40: 1.77×10-23 (m)
Notation 32: 8.05×10-9 Coulombs
Notation 40: 2.06×10-6 (C)

Notations 41 to 104

Notation 41: 1.18×10−31 seconds
Notation 104: 1.09×10−12 (s)
Notation 41: 4.84×10-17 Kelvin
Notation 104: 4.47×102 (K)
(310K = 98.33°F, 36.85° C)

Notation 105 to 142

Notation 105: 2.18×10−12 (s)
Notation 142: 3.0×10−1 (s)
Notation 105: 8.94×102 Kelvin
Notation 142: 6.14×1013 (K)

Notations 143 to 147

Notation 143: 6.01×10−1 (s)
Notation 147: 9.61 (s)
Notation 143: 2.45×1014 Kelvin
Notation 147: 3.93×1015 (K)

Notations 147 to 154 to
Notation 187

Notation 147: 9.6185 seconds
Notation 154: 1231.1 (s)
Notation 187: 1.05×1013 (s)
or 10,575,741,215,500 (s)
or 320± thousand years
Notation 147: 3.932×1015 Kelvin
Notation 154: 5.03×1017 (K)
Notation 187: 4.32×1027 (K)
Notation 147: 3.346×1026 (C)
Notation 154: 4.28×1028 (C)
Notation 187: 3.67×1038 (C)

Notations 184 to 201

Notation 184: 1,321,967,651,940 seconds or 41,919.31 years
Notation 201: 10 billion years
Notation 184: 5.4×1026 Kelvin
Notation 201: 7.0×1031 (K)

Notations 187

10,575,741,215,500 (s)
320± thousand years
Notation 187: 3.6×1038 (C)

Notations 187 to 196

Notations 187: 320,000+ years
Notation 196:
171.2± million years
5,414,779,502,320,000 seconds
Notations 187: 4.3×1027 Kelvin
Notations 196: 2.2×1030 (K)

Notations 187 to 204+

Notation 196:
171.2± million years
Notation 204+:
Distant future
Notations 196: 2.2×1030 (K)
Notation 204: 1.416×1032 (K)

Notations 187 to 189

Notation 187: 1.05×1013 seconds
or 320± thousand years to
Notation 189: 1.3± million years
Notation 187: 4.32×1027 Kelvin
Notation 189: 1.72×1028 (K)

Notations 187 to
Notation 201+

Notation 189: 1.3± million years
Notation 201: 10 billion years

Notations 187 to
Notation 201+

Notation 201: 10 billion years
Notation 201: 7.08×1031 Kelvin

Notation 201+

Notation 201: 13.8 billion years
Notation 201: 7.08×1031 Kelvin
At the 41st notation there are 10,633,823,966,279,326,983,230,456,482,242,756,608 pointfree vertices. The base-2 simple doublings could be aggregating structure as groups or sets. Defined by the Planck base units, in the range 41-to-60, we hypothesize that these are the domains for archetypal relations and systems. There are 549,755,813,888 base-2 pointfree vertices at Notation 41 and 5,070,602,400,912,917,605,986,812,821,504 at Notation 104.

The bbt’s Quark Epoch generalizes 63 of the QE notations, from 41 to 104. These notations within the QE model are foundational so perhaps this comparison to Quark Epoch is a key. Consider the estimated requirement for temperature. The bbt epochs can not begin until the temperature is cool enough. Given that temperature requirement, within the QE model, the Quark Epoch would not begin until up-and-around Notation 136 where the temperature has finally risen to 1.9201×1012 Kelvin. If that is the right range, as suggested by proponents of the bbt, less than a second has transpired, the universe has a diameter of about 874 square miles and a mass of about 1.896×1032 kilograms.

Within the QE model from around Notations 65 to 69 is the transition from the small scale to the human scale. This “human scale” is the middle third of the 201 notations, i.e. 67-to-134. Even though two-thirds of the way through the 201 doublings, less than a second has transpired from the start.

In the Quark Epoch the bbt and QE begin to cross paths and overlap. Wikipedia says, “Quarks are bound into hadrons. Over the hadron epoch, the process of baryogenesis results in an elimination of anti-hadrons (baryon asymmetry).” As noted within Wikipedia, some of these perceptions come directly out of the laboratory, such as CERN in Geneva, where this phenomenon has been observed. So, other than the improbable placement within the time/temperature curve, all processes herein after become readily integrated within the QE model. The bbt and QE have overlapped and begun to become simpatico.

A key question within the QE model is, “What is a notation?” Also known as a cluster, doubling, group, layer, set, and/or step, each word is perspectival and each notation is dynamic, always in the process of being defined, right up to the current time within the 201st notation. Each notation has an active role in defining who we are and what this universe is; and, each notation has an active role in defining all other notations. Today, right now, all of these notations activelyf define humanity or the human scale (67-to-134), must therefore be something like the archetypes of forms and functions (notations 1-to-67) that define our deeper beingness. The notations from 134-to-200 define our planetary and galactic systems and this is where most of the work of those physicists, cosmologist, and astrophysicists have worked.

In just a few more notations, between 142 and 143, the universe is at the one second mark. This measurement is most often used to determine the speed of light. Yet, as noted in earlier postings, within every notation, the Planck length divided by the multiple of the Planck Time renders an approximation of the speed of light. It is just commonsense when we see that the speed of light plays prominently in the definitions of Planck Length and Planck Time.

The question to be answered, “What is the meaning of temperature? …within the bbt? Within the QE model, we impute that it is the total temperature throughout the area defined by the notation (or cluster, container, domain, doubling, group, layer, or step). This measurement within the Hadron Epoch within the bbt is now lower than it is within the QE. There is a natural correlation between all these numbers within the QE simply because they start with the same definitional characteristics (the Planck base units) and the evolution of those numbers using base-2 exponential notation. The ratio of length to temperature renders .73322+ ratio. That result is currently being analyzed, space-to-temperature or kelvin per meters.

In 1972 George Ellis and Stephen Hawking began to explore the boundary conditions that define our universe between 10-13 centimeters (elementary particles) and 1028 cm, the assumed radius of the universe. They did not approach the Planck base units which would have expanded their range to 1.616199×10−35 meters (Planck Length) and then it would have tucked them in at about 5.1942×1025 meters according to current best guesses regarding the Age of the Universe.


With very few exceptions, it was not until Frank Wilczek (MIT) wrote a series of articles,
in 2001, Scaling Mt. Planck, (Physics Today), did anybody think these Planck numbers amounted to anything more than numerology. It would take another ten more years before we would come along, naively doing our thing with base-2 exponential notation, so we are confident that all the proponents of the big bang have not engaged our quiet expansion model.

Earlier it was observed that the big bang is not good philosophy and it is bad psychology. Philosophy is taken as a study of first principles and systems, the universals and constants that create the boundary conditions as well as the continuity equations that bind our universe together. Since 1972, especially with the very key question about the very nature of the first microseconds, the bbt has not progressed very far. Their Planck epoch is still mysterious. It is bad psychology for that very reason. It is so disjointed, so out of touch with anything human, it de facto promotes a certain form of nihilism.

Theories should have elegance, beauty, coherence, and simplicity. Children should be able
to begin to understand. And with the QE, children quickly begin to understand 2 times 2.
We just have to carry it out a few more places for them.


Disclaimer: Our charts and discussion are our first time to make a comparative analysis
between the big bang theory (herein abbreviated bbt) and our Quiet Expansion (QE).
Silly errors are inevitable. We are neophytes, not scholars, within these fields,
so please point out any of our failures with logic, math, and physics. We will be most grateful.

This ends the first story about two very different models of the universe. Of course, it is a story that is to be continued.



BruceCamber130Hi, my name is Bruce Camber and I would like to take you on a quick tour of our entire universe.

You will see everything, everywhere, throughout all time, in just 202 steps, notations, layers or domains. It is all so very simple, we’ve asked, “How could something this simple be ignored for so long?”

We thought there must be something wrong with our simple logic. Just by dividing an object in half, over and over and over again, we found the smallest possible unit of measurement of a length (the Planck Length) in just over 112 steps.

We multiplied this object by 2. Just 90 times and we were out to the largest measurement of a length (the Observable Universe). That’s a total of just over 202 steps from the smallest to the largest possible measurements in the universe.

We started this exploration back in December 2011.  When we couldn’t find it on the web, I began sending out emails to my smartest friends, “What’s wrong with this picture?”

We quickly learned of Kees Boeke’s 1957 work in a Dutch high school where they toured the Universe in just 40 quick jumps.  They had no geometry. They didn’t use those smallest and largest measurements as their container and they were multiplying by 10, just adding  zeroes.

We started with a geometry. We were multiplying and dividing by 2. Now that’s how cells divide. Our process is more natural, more lifelike, and most importantly, we get to see a much more granular universe.

Plus, those largest and smallest measurements are some of the most important numbers in science today.  They are called the Planck Base Units; they were formulated between  1899 and 1905 by Max Planck, a Nobel laureate in 1918, one of Einstein’s mentors, and the father of quantum theory.

Today, we have two primary charts.  This original from 2011 is based on the Planck Length.  It has been updated many times. And, now there is a comparative chart using all five  Planck Base Units.

Our project is to collect all our thoughts and writings from the past four years, consolidate and refine them for prime time for all the university scholars to come in to either take it apart or to attempt to incorporate it into the fabric of academic research today.

At the very least, the great physicist, Freeman Dyson, agreed with me that it would make an excellent STEM tool for our high school students to learn Science- Technology-Engineering-Mathematics.

If it challenges the Big Bang theory, so be it.  Let’s be intellectually honest and explore the most simple logic and most simple model of our universe. Called, The Big Board-little universe Project, we welcome you to join us.

Background Story: Big Board-little universe

Why you should say “Yes” when asked to do a favor…

Date:          December 28, 2011  (with small updates, March 24, 2013 )
From:         Bruce Camber
To:              Friends and family
Subject:     Big Board – little universe using base-2 exponential notation

Strange things can happen when invited to be a “guest lecturer” (essentially just an assistant for students) within five high school geometry classes and for the teacher who is part of the extended family.

Have you ever seen the entire universe mathematically related and notated on one chart? In studying the platonic solids and base-2 notation, it seemed to be an interesting task to do the simple base-2 math to create the picture on the far right of this page. That one was first printed at the Office Max in Harahan, Louisiana on December 17. It measured 24″ by 120″ but that was too big and awkward. Two smaller charts, 12″ by 60″ were created the next day, December 18, 2011 for the classroom discussions on December 19.

The ten foot board was cut about in half and the top section was put in the front of the class and the bottom section in the back. On the walls on the left and right were the two five foot charts. It seemed a bit enchanting.

There were five high school geometry classes that were challenged to see the universe using Plato’s five building blocks to visualize it all.  We used base-2 exponential  notation.  It was clearly more granular than base-ten.  One divides by 2 or multiplies by 2 instead  of by 10. There is a huge history of work done within the orders of magnitude that we could readily use. At first, we used an imaginary tetrahedron that was 1 meter on its side. Our actual models were 2.5 inches.  We divided that tetrahedron in half over and over again until we reached a measurement within the range of the Planck length, considered the smallest possible measurement. We then multiplied by two until that number was somewhere in the range of  “the edges of the observable universe.”  Where we expected thousands of steps in either direction, on our first pass we found as few as 105 notations (and as many as 118) going smaller and 91 going larger. We reduced it to a chart with a color wheel as the background, printed it up, and called it, Big Board – little universe  (Version displayed).

Not too much later, we decided to start at the Planck length and just multiply by two.  It worked out pretty well and kind of, sort of confirmed our earlier work.

It all started with Plato’s five basic solids and thoughts about  basic structure. Though most people do not give it much thought, it has been studied throughout time, probably starting with Pythagoras and picked up later by Plato.

For many of the students, this encounter was our second time to explore these five basic solids.  The very first time together in March 2011,  the students explored models using clear plastic tetrahedrons and octahedrons.  Both are pictured in the right column under the headings “…simplest parts.”  To go inside these models, essentially dividing them in half, requires a little finesse.  Simply divide each edge in half and that point becomes a new vertex. With the tetrahedron there are six edges and within the octahedron there are eight edges. Connect all the new vertices and you have the simplest internal structure.  Within the tetrahedron are four half-sized tetrahedra in each corner and an octahedron in the middle. Within the octahedron there are six half-sized octahedrons in each corner and a tetrahedron in each of the eight faces.

The students also made icosahedra out of 12 tetrahedrons.  It was quite a lot of fun.

The second time with these kids would be more of a challenge.  It would be the day just prior to their Christmas break.

The universe in 202.34 -to- 206 steps.   When we began finding simple math errors,  the number of notations increased from 206 to 215 (it became our fudge factor). Then a leading astrophysicist said, “There are 206 notations.”  Then on May 2, 2012, a NASA physicist made the calculation based on the results of the Baryon Oscillation Spectroscopic Survey (BOSS).  He reported 202.34 notations.  Looking under scientific notation and orders of magnitude,  we could only find bits and pieces of this work on the web.

An earlier history began with the study of perfected states in space time.
Sometime around 2002, at Princeton with geometer, John Conway, the discussion focused on the work of David Bohm, once a physicist from Birbeck College, University of London. “What is a point?  What is a line?  What is a plane vis-a-vis the triangle?  What is a tetrahedron?”   Bohm’s book, Fragmentation & Wholeness, raised key questions about the nature of structure and thought.  It occurred to me that I did not know what was perfectly and most simply enclosed by the tetrahedron.  What were its most simple number of internal parts?  Of course, John Conway, was amused by my simplicity.  We talked about the four tetrahedrons and the octahedron in the center.

I said, “We all should know these things as easily as we know 2 times 2.  The kids should be playing with tetrahedrons and octahedrons, not just blocks.”

“What is most simply and perfectly enclosed within the octahedron?” There are six octahedrons in each corner and the eight tetrahedrons within each face. Known by many,  it was not in our geometry textbook.  Professor Conway asked, “Now, why are you so hung up on the octahedron?”  Of course, I was at the beginning of this discovery process, talking to a person who had studied and developed conceptual richness throughout his lifetime.  I was taking baby steps, and was still surprised and delighted to find so much within both objects.  Also, at that time I had asked thousands of professionals — teachers, including geometry teachers,  architects, biologists, and chemists — and no one knew the answer that John Conway so  easily articulated.  It was not long thereafter that we began discovering communities of people in virtually every academic discipline who easily knew that answer and were shaping new discussions about facets of geometry we never imagined existed.

Of course, I blamed myself for getting hung up on the two most simple structures…  “You’re just too simple and easily get hung up on simple things.”

My family knows about this curious hang up of mine.  They have seen these models on my desk.  We made a pseudo-Rubik’s cube type of game out of the octahedron.  One of younger ones in the family is the geometry teacher in the family’s small private high school.  “Come in and introduce the kids to Plato’s five basic solids.”   That’s about my level.  In so many ways, those kids were actually more advanced than me.

During one of my days with them, we made icosahedrons with twenty tetrahedrons.  I called it squishy geometry, but told them that I have yet to find a good discussion about it under quantum geometry or imperfect geometries, “…but when I find it, I’ll, report in.”

At first, our dodecahedron was a simple paper thing.  We were trying to think of its simplest number of parts… “Could it be twelve odd objects coming into a center point, each with a pentagonal face and three triangular sides?”  It didn’t seem like it would readily be extensible.  On my desk was a “Chrysler logo”  made using five tetrahedrons.  There was always a gap — squishy geometry — but thought, “What would a pseudo-dodecahedron look like if it were made of twelve of those pentagonals (each made up of five tetrahedrons)?”  Very quickly we had  a model.  A few hours later we were filling it with Play Doh to see what was within it.  And just within, we found an icosahedron waiting.

Now that was fascinating to us, but, is it?  Is it common knowledge among all  the best-of-the-best within mathematics, chemistry, and physics?  We are still not sure.

In thinking about a sequel class to that earlier time together, we began focusing on exponential notation. Having learned a little about Base 2 notation  — my first time over these grounds — we put these pages up on this website to begin to share it with a wider audience:

If you find it of some interest, there are links to more background pages from both.

Can Plato’s five most basic objects in some way hold each progression together in a mathematical relation? Is it meaningful in any way?  We would all enjoy hearing from you.
Please drop us a note!  – BEC

202 base-2 notations from the Planck scale render a highly-integrated model of the universe

The Big Board–Little Universe Project, part of Center for Perfection StudiesUSA

Last update: 8 August 2017

IntroductionBig Board-little universe
In December 2011 two teachers and about 80 high school students rather naïvely began to explore a geometric progression that first went down in size to the Planck Length then reversed to go back up all the way to the Observable Universe (most links open a tab or window and go to an in-depth Wikipedia page).

The first chart to be developed, pictured on the left, measures 60×11 inches. It is a view of the entire universe and has just over 200 base-2 exponential notations (dividing or multiplying by 2, over and over again). Thinking that this simple math was already part of academic work, they began asking friends and family, “What is right or wrong within our logic for this model?” A two-year search did not uncover any references to base-2 and the Planck Length.* In that time, asking around locally and then globally, many people were puzzled and asked, “Why haven’t we seen a base-2 scale of the universe before now?”

An Integrated Universe View
Dubbed Big Board – little universe, this project started as a curiosity; today, it is an on-going study to analyze and develop the logic and potential links from their simple mathematics to all the current mathematics that define the universe, all its parts, everything from everywhere, and from the beginning of time to this very moment in time. Their hope is that this simple logic has simple links to real realities. Their standing invitation is, Open To Everyone, to help. This chart follows the progressions from the smallest to the largest possible measurement of a length. Subsequent charts engage the other Planck base units. With more questions than answers, this group is trying to grasp the logic flows in light of current academic-scientific research. Progress is slow.


Yes, on December 19, 2011 the geometry classes in a New Orleans high school were introduced to the chart on the left (Planck Length to the Observable Universe). In December 2014 they began to track Planck Time to the Age of the Universe. When they added the other the Planck base units to each maximum value, it seemed to call out for a horizontally-scrolled chart to follow each line of data more easily. Natural inflation becomes self-evident. And, that opened the way to question the big bang theory, especially the first four epochs — the Planck Epoch, the Grand Unification Epoch, the Inflationary Epoch, and Electroweak Epoch. In their search for answers about this model, questions abound.

This first chart is very early work.
Click on it, then click on it again to enlarge it

What’s next?
They ask, “Where are the informed critics to tell us where we are going wrong?” One rather brilliant, young physicist told them that the concept for this project is idiosyncratic. They quickly learned how right he was. Nobel laureates and scholars of the highest caliber were asked, “What is wrong with our picture? Where is our fallacy of misplaced concreteness?” The group is slowly analyzing the logic and developing their thoughts as web postings with the hope that somebody will say, “That’s wrong” and be able to tell them in what ways they have failed logically and mathematically.

The first 36 of 200+ notations of the horizontally-scrolled chartIf not wrong, the extension of their basic logic could begin to yield rather far-reaching results. For example, the Big Bang theory could get a special addendum, the first 67 notations. That would make it simple, symmetric (entirely relational), predictive, and totally other. The entire universe could get an infrastructure of geometries whereby many issues in physics, chemistry and biology could be redressed. The finite-infinite relation is opened for new inquiries. In this model of the universe, time-and-space are derivative of two quantitative qualities of infinity: continuity-and-symmetry. As a result, these derivative relations begin to have an inherent qualitative or value structure. If so, ethics and the studies of the Mind (the discernment of qualities) just might, for the first time in history, become part of a scientific-mathematical continuum. A trifurcated definition of the individual may emerge whereby people are simultaneously within the small scale, human scale, and large scale universe. Embracing a different sense of the nature of space and time by which both are localized by notation is surely enough; yet there will always be more. There are many working postings that have been written since their first chart; all of it needs constant updating. Many can be found through the top navigation bar option, INDEX.

Notes, lesson plans and posts (and all new posts) are being consolidated and linked from this homepage. Now called, The Big Board – little universe Project, it is a Science-Technology-Engineering-Mathematics (STEM) application. Secondary schools from around the world are being invited to join the exploration. Daily work on the topic is being researched, developed, and communicated through a sister website,

The earliest postings and blogs were done by Bruce Camber within a section of his website — That site supports a television series, Small Business School, that he and his wife, Hattie Bryant, started. It aired for 50 seasons on most PBS-TV stations throughout the USA and on thousands around the world via the Voice of America-TV affiliates.

Articles and blogs have been posted on WordPress, LinkedIn, Blogger, and Facebook (often those links open in new windows). An April 2012 article, formatted for and displayed within Wikipedia for a few weeks, was deleted on May 2, 2012 as “original research” by highly-specialized Wikipedia editors. Only then did this little group of teachers and students finally begin to believe that base-2 notation had not already been applied to the Planck base units. And, as they have grown in their analyses, it has become increasingly clear that this area of simple math and simple logic is a relatively new exploration and that notations 1-to-67 may be a key to unlock a new understanding of the nature of physical reality.

The challenge is to study the logic flow within their many charts, all based on the Planck base units, both up and down and across, to build on the question, “Is this logic simple and consistent? What does it imply about the nature of the universe?”

So, even now, there is much more to come. At the end of the year, 2015, a Lettermanesque Top Ten was added. In January 2016 an article, Constructing the Universe from Scratch, emerged. In April 2016 the horizontally-scrolled chart provided a better sense of the flow and of phase transitions. Still a “rough draft” this project has a long way to go! Bruce Camber says, “You are most welcome to add your comments, questions, ideas and insights!


* Footnote: In 1957 Kees Boeke did a very limited base-10 progression of just 40 steps. It became quite popular. In July 2014, physicists, Gerard ‘t Hooft and Stefan Vandoren wrote a scholarly update using base-10. Notwithstanding, base-2 is 3.3333+ times more granular than base-10 plus it mimics cellular reproduction and other naturally bifurcating processes in mathematics, physics, chemistry, biology, topology, botany, architecture, cellular automaton and information theory; it has a geometry; it has the Planck base units, and, it has a simple logic and so much more.


If you would like to contribute content to this site, please contact Bruce Camber
at camber – (at) – or click here for more contact information. Thank you.