On reaching out to our world’s genius-scholars


An Integrated Structure of the Universe

by Bruce Camber   Working draft. Editing continues.  URL: https://81018.com/structure/

Introduction:  That final episode of The Big Bang Theory, the television series (2007-2019), is symbolic of Big Bang cosmology (bbc). Both have exhausted their storylines and now some of our world’s best scholars are raising new questions about the bbc and the need for an alternative theory grows.

This story is about how a rather unlikely group of high school people backed into developing a possible alternative.

The bbc begins infinitely hot. Our simple, mathematical model of the universe begins cold, close to absolute zero. Both cannot be right, so a few of us have had the audacity to think that our little model is more logical than today’s dominant theory. Our model is 100% mathematical, entirely predictive, a quiet expansion and a natural inflation.

Scaling Mt. Planck. In our high school geometry classes, we learned about the Planck base units. Most helpful was a series of three articles, Scaling Mt. Planck, written for Physics Today in 2001 by an MIT physicist and Nobel laureate, Frank Wilczek. He personally assured us that multiplying the Planck Length by 2 was OK. So, we continued with the others… over and over and over again. We added Planck Time, then Planck Mass and Planck Charge. That expanded chart, a radically different view of our universe, scales Mt. Planck to discover this entire universe can be contained within 202 base-2 notations.1 It starts with the smallest possible units of time and length and goes to the age and size of the universe right now.

Now, that’s a container! At the top of that scale within the 202nd notation we found Euler and his equations and they proclaimed, “This universe is exponential.”

The first 64 Notations.2 Although logically and mathematically well-defined, the first 64 Planck multiples are well below the thresholds of measurement by devices, instruments, or machines. It seemed an ideal place for the mathematics of Langlands programs and the physics of string theory. To begin to grasp the forms and functions within this domain, we started with the most basic expression of physicality imaginable, the sphere. And, the dynamics of that most simple sphere opened the way to an extensible model.

Max Planck discovered and mentored Albert Einstein but they did not truly engage Planck’s base units.

An extensible, mathematically-integrated model of the Universe.3 Yes, just a model, an outline, it starts at the very first moment of the universe at the Planck scale with four Planck base units and continues up rather comprehensively to this very day-and-second. Logic tells us that it includes everything, everywhere, throughout all time. Those Planck base units (and then each result) are doubling, even right now, today, within the 202nd notation; these numbers have inflated to the age of the universe, the size of the universe, the mass of the universe, and the total charge (Coulombs) of the universe. And, those numbers approximate numbers currently used within the scientific community. So we ask, “Isn’t that Euler’s equation?” and think, “Perhaps we have stumbled onto a most-logical, simple, and mathematically-integrated, deep-structure of the universe.”

“Maybe… Maybe not.” Our simple little model, at best, is questioned but mostly ignored.

People ask, “How could that be?” There are a few who think out loud, “That’s not right.” 4
But… it’s just mathematics and logic. It is what it is even if entirely idiosyncratic.

So, what does one do? I reach out to scholars with deep knowledge of logic, mathematics and the sciences. Quickly I’ve learned how profoundly invested we are in big bang cosmology (bbc). Not many scholars are willing to fly into those headwinds. Although some scholars do, the bbc is still a core belief of science today. Then, there are even fewer who will fly into the face of our commonsense understanding of time. There are a few who do; but it seems those who do, hold on to big bang cosmology. To do otherwise requires a better definition of infinity, space, time, mass and energy. And finally, in our increasingly narcissistic-nihilistic world, this new model is a profoundly relational view of the universe where everything is deeply-and-fundamentally related to everything.

To embrace our little model in its fullness is difficult. It is so different yet so simple, it is disconcerting and unsettling. And, the more it’s studied, the more unsettling it becomes. Yet, in the end, its simple logic and math may be the only reason this little model survives.

Let’s take a look:

Numbers: On Constructing the Universe From Scratch. 5  In January 2016, we started our study of the nature of numbers.  The most ubiquitous number, a keyway to so many other important numbers, is pi (π). It seems to follow that pi (always a dynamic number defining a relation) along with a few other similar numbers (more dimensionless constants) are most likely to create the very first instance of physicality. And, simple logic tells us that this first instance would render an infinitesimal circle-then-sphere defined by those Planck base units. Others have already been here (long before us). This primordial sphere has also been called a plancksphere. And, way back in 1955, John Wheeler called it quantum foam.

Let’s Go Over This One More Time. Defining the 202 notations was the first step. Being accurate was important. There are over 1000 numbers to check. Any mistake gets replicated quickly. Yet, in some measure, a simple validation in one place, validates the entire model. It is all so interconnected. Those first 64 notations, well below our tools and instruments to measure, were a red flag. What do those numbers represent? Because there is so much mystery and attention around dark energy and dark matter, it was easy to conclude, “That’s it.” And around all the mystery and questions about isotropy and homogeneity, we concluded, “Look at the continuities and symmetries in those first 64 doublings!”

Rolling Pi

Sphere to tetrahedron-octahedron couplet File:ComplexSinInATimeAxe.gif File:Circle cos sin.gif
Pi equals 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067…

Doublings: Sphere stacking 6 In that January 2016 exploration of numbers, we also learned about cubic-close packing (ccp). Though not generally associated with the infinitesimal, it is a mechanism for growth-and-inflation and for straight lines-and-Euclidean geometries. Known as sphere stacking, these dynamic images demonstrate that all-important first doubling function. It also begins to tile-and-tessellate the universe with those tetrahedral-octahedral couplets. It opens the historic studies of lattice structure as a direct analogy for string theory within infinitesimal structures. It seems to follow that it is a matrix for binary operations, scalar field theory, automorphic forms, hypergeometrics, and even information theory.

(Editor’s note: See line 11 in the horizontally-scrolled chart.)

First emerging within one of the earlier notations, once a density allows it, a five tetrahedral complex — here, called a pentastar — will necessarily emerge and the universe will have the potential to experience her first fluctuations. Other doubling functions also emerge. Geometries are key. Our prime numbers are a key.

Space, time, mass and charge.7  In this model, the four Planck base units appear to be equally and intimately part of light. There is more to learn about Einstein’s old equation, e=mc2 in light of Planck’s relatively unexplored equation about time, a length, and light:Planck Time

All are open for a deeper definition. If the 202 notations are taken as a given, not only is the light (electromagnetic) spectrum substantially extended, Planck Charge and Planck Mass are as well.

Notwithstanding, this model is mostly about the very-early universe.

It will take over 143 successive doublings to manifest the first second of time.  And, if all notations are active and now, each notation builds on the others, and each effects the very essence of all the others. The current notation, 202, requires 10.9816 billion years to come into its fullness. The sum of all prior notations is also 10.9816 billion years so if indeed the universe is between 13.7-to-14.1 billion years, we are only between 2.8-to-3.2 billion years into this notation. Perhaps the world’s Gaia hypothesis could be extended from the earth to the entire universe and all these notations. Relations become the primary real. The derivative sense of subjects and objects begins to be realized.

In this model all time has always been the Now.

Doublings continue.8 There is a natural thrust and there are now 202 doublings from our very first moment of time to this moment in time within the 202nd doubling. Just imagine all the sphere stacking and the tetrahedral-octahedral tiling and tessellations!  Nothing goes away; this base-2 outline of the universe includes all time, everything-everywhere, a living fabric of the universe.

It begs the question: From where do Planck units, light and dimensionless constants originate? 

To provide an answer, we advocate reopening the study of infinity.

Infinity.9 Although there are many who want to retire the concept, it has a long and pervasive role in our history and culture. Sometimes associated with God, we will also advocate for an expanded-yet-more-precise concept of infinity. Currently there are no definitions vis-a-vis the 202 notations and it seems that the definitions within Wikipedia, and the Oxford and Webster dictionaries, are all weak. A truly compelling definition based on the mathematics and logic of those 202 notations just might change our hearts. Perhaps with a little less arrogance and more openness, we might begin to spare ourselves from future religious wars.

In 1970 I was sure that there were perfected states within space and time, even in the face of quantum mechanics. I asked, “What are the qualities of a moment that intersect space and time perfectly?  What about continuity for time, symmetry for space, and harmony for that dynamic moment?” It was the beginning of my definition of infinity. I wasn’t concerned about religious dialogues; I was concerned about my personal experiences and scientific thought. And now, it seems to me that the finite-infinite relation could also be better known through all the dimensionless constants and these 202 notations.

That has become a foundational focus of this model.10

Continuity over discontinuity.  When we all begin to see and understand the Fourier Transform like Steven Strogatz (Cornell) does, the continuity of spheres will become the continuity of numbers, and both will become the continuity of everything such that we move towards unified theories of mathematics.

Symmetry over asymmetry. Structures become structures; this ether-aether-quintessence and grid-matrix actually dis-entangles the universe.

Harmony over the discordant or inharmonious. So many theorists have gotten so hung up on particles and waves without those first 64 notations! We can only truly discover Kepler’s harmony of the world when we uncover the potential harmony of the universe.

Ethical bridge is the finite-infinite bridge.11 Such dynamics, seemingly binding the finite and infinite across what appears to be an infinite number of bridges, opens a sense of the perfect, and a comparative judgment of the good and the better. Continuity, symmetry, and harmony may well be quantitative, yet there three together open the qualitative.

Can each statement be proven or disproven? 12 We don’t know. To get some guidance, we appeal to scholars — people like Emeritus Prof. Dr. Michael James Duff at Imperial College London and Dr. Gabriele Veneziano of CERN labs in Geneva, and so many others.

Since December 2011 that list is a who’s who of scholarship.

I am also asking younger scholars like Dr. Emily Nurse, whose work on the structure of atoms is helpful. She is affiliated with University College London, and also works with CERN’s Atlas Project and Fermilab Chicago.

The problem is that nobody is quite able to debunk this simple logic. And, there is so little truly academic history for this article, it begs the question,  “Why haven’t we seen it before now?”

Yes, to say that this model and structure is radically idiosyncratic is a bit of understatement. -BEC


Endnotes, Footnotes, References & Resources

Navigation Update:  To return to the referencing sentence, click on the footnote number!

1 Early years: This project formally started on December 19, 2011 in a New Orleans high school, within five geometry classes. The Big BANG Theory, the television series began in 2007!

• Stephen Hawking’s infinitely hot big bang: The early wrestlings
The Big Bang Theory (television): A little history
Questions about the big bang… even from friends of Stephen Hawking
• The geometry of our simple start: https://81018.com/tot/
• A story of our simple beginning: https://81018.com/home/
• The 202 notations:  https://81018.com/chart/

It’s a STEM tool! It’s Euler’s Universe! In December 2011, challenged by our high school geometry classes, we started with a 2″ tetrahedron and systematically went deeper inside of it. By dividing the edges by 2, connecting the new vertices, there are smaller tetrahedrons in each of the four corners and an octahedron in the middle. In 112 steps, we were within the Planck scale. We also went larger, multiplying the edges of our tetrahedron by 2. In just 90 steps we were out to the current age and size of the universe. We thought, “That’s unbelievable! A total of 202 steps (or base-2 notations or base-2 groups or Euler’s Universe) encapsulate the entire universe!”

“What a STEM tool!” And, for sure, Science-Technology-Engineering-Mathematics (STEM) come alive within this model, but I thought that it just may be much more.

Yes, we initially thought it was a compelling and complete STEM tool. And, it is! There are many places for technology and engineering inside the science and mathematics of this model.

Yet, it is more much more: https://81018.com/STEM/  As we shared it with others, we discovered it seemed too all-encompassing for most teachers to engage. It wasn’t in the textbooks or literature, so I tried writing about it: https://81018.com/planck-length-time/

The Planck Scale of the Universe. We looked for an expert who could tell us about the nature of the Planck units and found the work of Frank Wilczek. He had pulled Planck’s 1899 work out of the domain of numerology; and in December 2012, he assured us that we could multiply Planck’s numbers by 2. Although we already had had other luminous people advise us, Wilczek’s advice substantially opened this world for us. For much more: https://81018.com/Wilczek/

We asked, “Could the universe evolve from the Planck scale?

The more we looked at our chart, the more it appeared too ordered for a “big bang” to be anywhere. I concluded, “Our model is symphonic. It’s as beautiful as Euler’s formulas. It is an Euler equation! It even looks like it would jive and give rise to the FLRW metric!”

Physicist Stephon Alexander (Brown, Providence) was the first person I found who said in writing, “It’s either-or…” regarding the hot or cold start of this universe.

Scholar-Expert. Neil Turok is a most credible person to say, “The big bang theory is wrong.” He claims that it is as if “there is a perpetual state of big bangs.” Perhaps Notations 1-to-64 will some day qualify as the basis for their understanding of that perpetual state.

What others have said…

My summary of objections to the big bang is here. There is also a direct comparison with the big bang that tracks it by its epochs and our Quiet Expansion by notation.

2 The first 64 of the 202 notations: Physics has historically been focused on particles and waves. Here we introduce forms and functions that give rise to particles and waves.

Of course, from the viewpoint of waves and particles, these 64 doublings are too small for anything. Yet, if there is a more basic structure (and we posit an infinitesimal sphere that begins to evolve at the Planck scale), classic physics has already discounted it and their big bang blocks any view of it.

We have wrestled with the nature of these 64 notations from the very beginning. I have asked Robert Langlands and Edward Frenkel, “Is this a domain for a unified theory of mathematics?”  I have asked Ed Witten, Michael Duff, and Gabriele Veneziano, “Is this a domain for string theory?”

I call it a hypostatic domain to open all equations to the finite-infinite bridge.

The Sphere.  Also called a plancksphere, within cubic-close packing we found a simple doubling function and within the sphere itself, the Fourier transform opened the dynamics. That appeared to be enough to call this model extensible.

There is one thing we are sure of — our simple, little model will eventually be accepted or it will be put in its place.


Initially we thought we would discover that this work had been done by others but was hidden from easy public view. As the days turned to months, that idea was increasingly discounted. In our first year, many very smart people were puzzled and asked “Why haven’t we seen a base-2 model of the universe?” We quickly learned that in 1957 Kees Boeke created a limited base-10 model, but he had no causal efficacy for multiplying by 10 whereas we had actively begun thinking about base-2 and doubling functions throughout math and science to justify multiplying the Planck units by 2. Boeke didn’t start at the smallest units and didn’t go the the largest (especially following Planck Time). And, Boeke had no inherent geometry whereas our system started with a simple geometry. The rest of that story is here: https://81018.com/home/

• We expected, and still expect, that a red flag will be thrown out onto the field.  We are sure that there must be some fundamental piece of knowledge we are overlooking and we are very open to learn what that could be. Among all the scholars with whom we have communicated — https://81018.com/alphabetical/ — just one scholar told me that cosmology was just too complex to explain to a person like me with such a limited background and who could possibly think that our little construct could be meaningful: https://81018.com/andrei/

A third possibility is that we will discover why big bang cosmology is right. In 1980 when I left Boston University and formal academic studies, the big bang was gaining in popularity but at that time, it was not the only game in town. Fast forward to 2012, we began to wonder if our simple, little model could be an alternative to big bang cosmology, it was hard to believe that truly smart people could have overlooked something so simple. Then we learned more about Max Planck’s history and how the Planck base units were  a bit like Dirac’s numbers (“…bordering on numerology”), we began to appreciate that work Frank Wilczek  had done earlier. When Wilczek began to substantiate Planck’s 1899 work in 2001, big bang cosmology had already become the dominate theory. https://81018.com/Wilczek/


Sphere to tetrahedron-octahedron coupletI wrote to a friend: “If the Planck scale numbers for time, length, mass and charge manifest as a sphere, that sphere is defined by those numbers. From that first instant, I project that the universe continues to fill with these spheres and that defines the edge of the current expansion.

“The doubling is a little like stacking the cannonballs on the deck of the ship. The image I have been using was found in Wikipedia (#1 below). It provided a visual for both the manifestation and then doubling, and then the emergence of geometries. 

“What was going on inside the sphere so that the diameter or radius of each sphere “found” another?  I discovered and added two more dynamic images found within Fourier’s work:

1. https://upload.wikimedia.org/wikipedia/commons/2/28/Animated-HCP-Lattice-Thumbnail.gif
2. https://upload.wikimedia.org/wikipedia/commons/thumb/a/a5/ComplexSinInATimeAxe.gif
3. https://upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Circle_cos_sin.gif/450px-Circle_cos_sin.gif

“All three images are relatively new for me. Yet, it seems to me that here is a better beginning for Langlands (Unified theory of mathematics) as well as Witten (string theory), both at the Institute for Advanced Studies, Einstein’s old stomping grounds.”

Summary. The stacking of the sphere amounts to the doublings. Each sphere is defined by the Planck numbers, the three dynamics, and all the associated dynamics; and so, we have the start of our universe.

3 Model-Outline: So we backed into our little mathematically-integrated model of the universe that approximates 2202 and Euler’s equations. Some say, “So what?” To which I reply, “It’s mathematics. It has a form. It has a function. It has continuity. It coheres. Let’s study the numbers. If it’s wrong, it’s wrong; then let’s study the logic. There’ll always be more questions to ask: “Where, why and how is this logic going wrong? Where is it right?

4 Growing confidence: By 2015 I was actively analyzing the state of affairs within the politics of the sciences. The sciences had become a big business with billions of dollars per year at stake.

That prompted this initial analysis: So, what does one do? https://81018.com/why-now/

• I frequently write to those scholars with deep knowledge and who also project a sense of openness. https://81018.com/alphabetical/
• There are a few scholars who risk their reputations to take on big bang cosmology.
• There are many pages within this site that explore our commonsense understanding of time.  In October 2016, a simple summary page was introduced and it will now receive more attention.
Carolo Rovelli is rethinking the very nature of time through Loop Quantum Gravity (LQG). Richard Muller (Berkeley) writes about it within Now: The Physics of Time.
• Today’s abundance of narcissism leads to nihilism and that opens the door to dystopia.

5 You’ve heard it said, “Question everything.” So we ask, “What was the meaning of the Pythagoras statement, ‘Everything is number.'”

In the process of reviewing our Greek roots and and our understanding of numbers, in June 2016 I began working on an article, Numbers: On Constructing the Universe From Scratch and discovered that Pythagoras didn’t make that conclusion after all!

6 Might the simple concept of a doubling become a fundamental concept? Why not? When we looked at the history of stacking cannonballs, then at the work within cubic-close packing, we thought, “Wow, this is a powerful, primitive doubling function.”

The power of that analogy came alive. I thought, “Here is a necessary analogue, a fundamental building block that will be re-used and adapted over and over again throughout our radically-comprehensive, multiscale model: https://81018.com/stacking/

7 Space, time, mass and charge: A deeper definition of the basics will begin with the first 64 notations. To extend the definitions of these four basics, along with light and infinity, across 202 notations, gives us a much richer canvas upon which we can paint a deeper picture of the universe.

8 Doublings continue.  The concept of a natural thrust within Planck Charge, light, and the never-ending, never-repeating numbers has begun.

Our initial study is here: https://81018.com/thrust/ Still within its infancy when compared with the big bang cosmology, it all requires a new concept of time whereby each notation is constantly active and builds on all the others. Initial definitions of each of the 202 doublings are just that. Here the whole is constantly changing. It’ll be fascinating to watch how it becomes richer with our depth of knowledge from all the current research. Nothing will be lost except a small part of the bbc — the infinitely hot. Every observation, measurement, and every calculation and bit of math has a place.

9 Infinity, the infinite, and the finite-infinite relation. There isn’t a larger or more important discussion to have in these times.

While some academics like Max Tegmark of MIT want to abandon the use of the word infinity, it has a key place in the character of our thinking and believing. It needs to be defined better than it currently is within Wikipedia and especially dictionaries like Oxford and Webster.

I was 25 years old when I made my first attempt to define infinity within the domain of science and math and without consideration for religious grappling. It became the foundations for my understanding of infinity  — https://81018.com/infinity/ —  today.

10 Attempts to define things more deeply and widely. Perhaps that is deep and wide just like the universe. We don’t see the deepness, but we do see that it is ever so wide.

Continuity versus discontinuity. A deep nature of continuity yet to be integrated within dynamics of the earliest universe is how the Fourier Transform sets the cycle speeds, amplitudes and phase relations for every continuity equation. We have just begun this study as a result of a 2015 article by Steven Strogatz of Cornell and of our study of spheres. Ultimately we will want to walk these equations back into our study of infinity. We are now actively looking for young experts with active minds to be our consultants. The place of those notations defined by prime numbers — 18 within the first 64 notations — is part of our unified theory of mathematics  whereby all mathematical systems grow organically from this simple beginning.

Symmetry versus asymmetry. From the sphere to the tetrahedral-octahedral couplet, we can see how the universe could be tiled and tessellated and that this complex could have triggered the first attempts to imagine and attempt to define the ether (also known as the aether or quintessence). With continuity and symmetry as the primary definitions of the universe, entanglement and the very nature of the quantization is extended well beyond a photon and what has been thought to be a single quantum of light or electromagnetic energy. More…

Harmony versus the discordant or inharmonious. Is it possible to get substantially beyond the work of the de Broglie–Bohm theory to see how matter or form (not a particle as we know it today) and waves (function) have any status within the first sphere.  Consider the two faces of  its dynamics (Fourier Transform ). Perhaps the external is the first manifestation of gravity and the internal is the first manifestation of electrodynamics. There is so much to learn!

11 The basis for an ethical valuation emerges. 11 Such dynamics, seemingly binding the finite and infinite across the bridge, opens a sense of the perfect, the good and the better.

Continuity, symmetry, and harmony may well be quantitative, yet it opens the qualitative.

12 What’s next?  These documents are speculative in May 2019. I am hoping with each passing day, they’ll become less speculative and more suggestive and helpful. I recently appealed to Emeritus Prof. Dr. Michael James Duff at Imperial College London and Dr. Gabriele Veneziano of CERN labs in Geneva. Since December 2011 I have appealed to many, many people. Some are listed here. I have also appealed to younger scholars, people like Dr. Emily Nurse, whose chart about the structure of atoms is helpful; she is affiliated with University College London, and also works with CERN’s Atlas Project and Fermilab Chicago.

Challenge us. Coach us. We need all the help we can get.

History of this page:
• Privately-posted on April 27, 2019 @ 11 PM
• Publicly-posted on April 30, 2019 PM
• Most-active editing, April 27-28-29, 2019
• Endnotes, footnotes, references and resources, May 1-22, 2019.

Editor’s note on May 22, 2019 —

It’s getting close, yet I am still updating these endnotes, footnotes, references and resources. BTW, last weekend I went to my 50th college reunion at Wofford. I will assure you, time is real, but not in the ways we think. Everyone of us at the reunion picked up as if there was no time that separated us since our graduation day back in 1969.
It is all so fascinating.
Now, do you have any suggestions to improve this article? – Bruce aka BEC

Image: Our simple, little model doesn’t fit in.

It is out of sync with big bang cosmology.
It is out of sync with general science.
It is out of sync with popular culture.
Our simple model calls out for a deep respect
for logic and mathematics and a deeper definition
of infinity, finite-infinite, light, space, time, mass, and charge.

Subtitle: On reaching out to our world’s genius-scholars

There is always more work to do: