Concepts that just might change everything…

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Eight What-if Questions
by Bruce E. Camber
once in Positano, Italy

  1. What if we live in an exponential universe?
  2. What if the 202 base-2 notations are the most comprehensive-but-simple way to engage the universe from the very first instance?
  3. What if the first 64 notations are an unseen foundational fact?
  4. What if those first 64 notations define a new kind of blackhole?
  5. What if hypostatics grid everything, everywhere, for all time?
  6. What if a sphere is our most conceptually-rich starting point?
  7. What if pi becomes a key to grasp the finite-infinite relation?
  8. What if cubic-close packing (ccp) of equal spheres is a key function of the universe and a foundation of physics?

1 Exponentiation. The 202 base-2 notations are the result of a high school geometry lesson in 2011.1 Over time those eight key concepts above would emerge and be actively explored. Yet, each concept is out of step with today’s scholarship so we’ve asked our world’s leading scholars and their colleagues for their critical review.

It is difficult to get scholars to look at materials that originate in a high school geometry class. Early in the process, we thought it was a good STEM tool. It wasn’t. The concepts were too far outside the mainstream. Although this website provides some feedback, we are now in the process of creating a virtual reality platform of the major theories about the start of the universe and we will include this one so each of our eight key points above receives a larger audience.

Questions about an Exponential Universe. Who among all our scholars — including postdocs, graduate students, undergraduates — might be open to such a concept? Who is examining the domain from the Planck scale to the CERN-scale (or electroweak scale)? Might their concepts suggest an exponential universe?

This article is to answer these questions as succinctly and simply as possible. We build upon a concept that is analogous or similar to Planck Time or StoneyTime. Our primordial sphere is also analogous to Lemaître’s primordial atom.

In 1899 Max Planck first introduced his number for a natural unit of time based in part on fundamental physical constants. That calculation rendered 5.39116(13)×10-44 seconds. In some academic circles, it is the shortest, meaningful interval of time. Those calculations, however, use Planck’s constant and there is a growing group attempting to re-qualify Planck’s base units without the use of Planck’s constant. Yet, even with new numbers, the concept of base units of length, time, mass and charge (energy) stands.

George Johnstone Stoney did his initial calculations in 1874 for a lecture in Belfast.3 His number was similar, but shorter — 4.6054×10-45 seconds. We ask, ”What could possibly be rendered in such a short interval of time? What is the most simple thing?”

Eventually, the circle and sphere were studied.

Circles and spheres are each generated by just two vertices. So, yes, we began wrestling with the mysteries of pi and the nature of a circle and sphere. We’ve begun studying the types of Fourier transforms and quickly learned that we had to begin to grasp scale invariance and dimensionless constants more deeply.

Dynamic spheres open a radical concept. If we are correct and there is a range that begins somewhere around Planck and Stoney’s calculations, and if there is one infinitesimal sphere generated per that infinitesimal unit of time, we have an approximate rate of expansion of the universe. If we use Planck Time, it would be around 539 tredecillion spheres per second. If we use Stoney Time, it would be around 4605 tredecillion infinitesimal spheres per second.

Such numbers seem beyond the scope of imagination. Notwithstanding, if this picture is anywhere close to our real reality, the foundations of exponential notation are established.

Do a general search on ”We live in an exponential universe.” Many pages that are displayed originate from within this website. If our universe is exponential, then the seven concepts that follow are more true than false.

Many articles and this key chart contributed to this article:


2 Base-2 Units. Geometrically and mathematically the 202 base-2 notations are a fact. Here is the most comprehensive-but-simple way to engage the entire universe. From the very first unit of time to the current time, over 13.81 billion years, is within Notation 202.

That very first unit of time is a key that opens doors that have never before been recognized or observed. Of course, Planck, Stoney and in our time, John Ralston, have wrestled with that definition. Notwithstanding, it is a key challenge for our entire academic community throughout the world: Do such base units, defined in the manner of Planck, Stoney, or Ralston, conceptually encapsulate a very first moment of time? We say, “Yes, conceptually, here is the first instance of time.”

In 2011 we backed into the 202 base-2 notations; we certainly had not studied its ramifications. Also, although we had been trying to discern the most simple object, we were reluctant to embrace the circle and sphere. Although we knew about Max Planck’s work, we really had no real insights about Planck Time.

We didn’t even know that cubic-close packing of equal spheres generates tetrahedrons and octahedrons. We knew nothing about Langlands programs and automorphic forms. To say that our learning curve was rather steep is an understatement. Yet perhaps there were some hidden benefits within all of our naïveté.

As we studied and thought about the first 64 notations, we began to experience the stories about the “Wheat and Checkerboard.” What appeared to be an ”infinitesimal nothing” was beginning to look huge and totally dynamic. Then, it appeared even larger; base-2 notation seemed to be a good way to bring some order to it all. Here we had the makings of a geometrical-mathematical science that just might incorporate Langlands programs, string and M-theories, and other promising theories. It just might incorporate many disciplines that have never been on a grid. All the hypothetical particles of SUSY and our standard model of particles just might have a new home.

Obviously these infinitesimal spheres are being generated in a dramatically-explosive yet totally-unobserved-discrete manner. Our simple orientation to the universe was changing and as it did, there were more and more facets to be explored.

Base-2 notation is just an ordering mechanism; it has no causal efficacy. It is just a way to context reality. It logically includes all possible bases. Yes, any other base expansion can ride on top of base-2. In fact, any and all our mathematical formulations can functionally ride on a base-2 platform.

More references:

  1. The first-septillionth-of-a-second to start of the universe: Notations 1-to-64
  2. Built up with planckspheres: An introduction to nine overviews (pages)
  3. The Universe As Extended Planck Base Units
  4. 2015: Early reflections on base-2


3 Causality begins long before particles/waves. No less than 64 notations are all within scales smaller than particles and waves. Perhaps only geometries and mathematics are able to define these notations. The inherent continuity, symmetry and harmony of the sphere appear to give rise to the first dynamical moment.

We’ve been too particle and wave centric for much too long. These new concepts begin to break that logjam. Stymied with so many hypothetical particles, we know our foundational orientation is lacking and those first 64 notations just might challenge us appropriately.

Also, if the base units of Planck and Stoney are metaphorically or conceptually correct, let’s rethink the very beginnings of everything. Why not start very, very simply? If the deep nature of the circle and sphere are entered, the mystery of its continuity, symmetry, and harmony become boldly apparent. Though quantum physics has little to say about each, the evidence for all three is everywhere.

Many writers have suggested that our top-down investigations were missing too much and that we should start from the bottom-up. Yet, the questions must still be asked, “What are the core foundations upon which to build? What is fundamental?’ We answer, “The infinitesimal primordial sphere, the finite-infinite relation, and three finite-infinite functions within the primordial sphere (pi): continuity (order) – symmetry (relations) – harmony (dynamics). Those three finite-infinite functions become the basis for valuations. And valuations become the basis for ethics, and ultimately for morals. Taken altogether, we have the beginnings of the universe.

More references:

  1. From the bottom-up, not from the top-down
  2. Redefine Space, Time, And Infinity
  3. Simple, Logical Concepts
  4. From left to right, we can all be better and do better.


4 Complicate the concept of a blackhole. We agree; it’s a huge stretch. From Einstein to Hawking, the best of the best have been speculating about black holes.* Yet, given speculation is its cornerstone and given the first 64-notations, might there be another kind of blackhole?

Could there be a blackhole that is actually pushing out just below the scales of our measuring devices?

Given all the current anomalies within blackhole studies, it is beginning to look like it’s worth some consideration. Such a radical conclusion has not been entertained within the scholarly community — it has no precedent — but why not take a look? Those first 64 notations are below all our current thresholds of measurement. The time sequence is a bit over one quintillionth of a second. Our current commonsense logic tells us that it is too fast for anything; yet mathematically, it is a lifetime.

Recognizing how current black holes are seen as a sucking up everything, for many reasons, it may also be understood as being an essential foundation which cannot be measured by physical tools, yet, still be a real reality within space and time.

All of these references are recent documents and are still being developed:

  1. Blackhole: Turn the Blackhole Inside Out
  2. Hope: Our hope for you this day
  3. Redefine it all: Where do we go from here?
  4. Singularity: Never Quite Singular
  5. Sphere: First things first

*A consensus document, “Black holes, gravitational waves and fundamental physics: a roadmap”, over 100 authors, IOP Science, June 2019


5 Hypostatics. If quantum fluctuations and all things quantum are measured above the first 64 notations, might the first 64 notations be considered hypostatic. Dating as far back as Plato and Plotinus, the word means “that which stands under” or the essence, or the substance, or underlying reality or fundamental reality.

Might these infinitesimal units of time be called “hypostatic time” and that space becomes ”hypostatic space” and then, of course, hypostatic energy, and hypostatic mass?

The study of substances and a substantial essence was going on well before our current history, and well before what is considered to be the Common Era (CE). Within over 202 notations, this Common Era represents an extremely thin slice of the 10.98+ billion years of Notation-202.

Although the use of CE has been traced back to 1615 to Johannes Kepler, ”annus aerae nostrae vulgaris…”,[a][b]  one might rightly regard all of known human history to be an infinitesimal common era.

Within the perspective of this website, every event with the Common Era is current history, yet within what has become known as ”before the common era” (BCE), the Greeks surely began to wrestle with the concept of hypostasis. What could possibly be substance, essence, and that which stands under? In these days, we well understand how just numbers and geometries compute without particles and waves, as in genomic functions and the functions within artificial intelligence. Waves and particles are involved with the computing systems, but are not themselves that which is computed.

Yes, yes, of course, there will be more to come.

  1. Hypostatic structure starts between the finite and infinite
  2. Hypostatic Way of Learning & Knowing
  3. Perhaps a bit of perfection


6 The infinitesimal sphere appears to be the key. Lemaitre, like so many before him going all the way back to Democritus, called it a “primordial atom.” It is always a sphere. In this model, this sphere is defined by the smallest units of space and time yet it still has all the functionalities of any sphere.

The sphere has continuity and symmetry, and most importantly it has harmonics (dynamics).

An infinitesimal primordial sphere is our most conceptually-rich starting point. That sphere is postulated to be the first instance of space-time, matter-energy, and electromagnetism-gravity (each sphere is an attractor or repeller). It has its never-ending, never-repeating numbers of pi. It has all the symmetries of a sphere. And, it has all the harmonic functions of a sphere. And those three characteristics of pi represent the infinite within the finite.

  1. The first instance: Pi (π) Shapes Our Universe
  2. Power of Spheres, Circles and Pi (π)
  3. The Sphere: Is it the Most-Basic Building Block of our Universe?
  4. The primordial archetypal sphere
  5. Acknowledge infinity


7 Pi, our first clue about the nature of the infinite. Although religions of every kind claim to have an inside-and-direct track of information about the infinite, we will stay within mathematics, geometry, logic, and the foundations of physics. Notwithstanding, we will respect other people’s insights as currently stated.

Our belief and hope is that our information helps the philosophers, the religious, and the theologians to clarify their own beliefs, gesticulations, histories, and postulations.

David Hilbert was possibly just a bit too self-assured with his grasp of the rules of logic. How could he possibly know the depths of infinity such that he could discount some aspect of the infinite that readily manifests within and throughout the finite? Of course, this will be an ongoing subject of this website.

We all grow up within our family’s philosophical and theological orientations. As important as these orientations are to help socialize us, eventually we begin to learn about other traditions. Some of us attempt to build bridges and even to take the best from each tradition to create a new platform of understanding and for reflection. We are possibly thinking, “There has to be a way to respect other traditions without compromising your own or compromising one’s new platform of understanding.” People ask me, “What is your background? How does it influence you?” At the age of 10 in 1957, my mother and father encouraged me to explore and appreciate other traditions. By 1967 it was an avocation. By 1977 it was a vocation. In today’s world, the most dominant belief system is science and its most dominant philosophy is one of the many flavors of agnosticism and atheism. Our model engages them all. Our core belief is in order-continuity, relations-symmetries, and dynamics-harmonies. All are cornerstones of logic, rational thought, science, and our understanding of the infinite.

There are a few within our many cultures and religions who are desperately in search of a bridge of understanding that opens communications, an exchange of ideas, tolerance and trust. I continue to struggle with it all as evidenced within an invocation that I delivered at a birthday party for a friend in Positano, Italy, an event and place that inspired this page.*

Now, all these referenced documents were written over a nine-year period. I’ll be going every through each of them to create a more consistent message for today. Ultimately I believe the deeper truth is within the hyphen between the finite and infinite.

  1. Finite-Infinite: A Nexus of Transformations
  2. Finite-Infinite: We all so little understand the infinite
  3. Finite-Infinite: On more fully recognizing the infinite
  4. Finite-Infinite Bridge: A Nexus of Transformation


8 Cubic-close packing of equal spheres. None of the other current theories for the start of our universe invoke this simple function. The continuity-symmetry-harmony of the sphere are extended throughout those first 64 notations through a finite-infinite relation. Every one of the 202 notations defines a dynamic relation of this universe.

Here is a progressive, highly-relational flow where every thing is related to everything, everywhere, throughout time. We are foundationally and fundamentally related.

Yet, it appears that none of these notations are sacrosanct and all of them are constantly changing and none of them would ever be exempt from change. The first 64 notations, representing about 9.945379×10-25 seconds, is so far removed from any possible measurement, here is a new science and a new context for matter and energy (charge), and for gravity and electromagnetism. There is much more work that will be done on this last point. Essentially now that we have the foundations for the greatest diversity of geometries, formulations, and calculations; no part of science or the human experience is exempt, including the role of sleep (which only exists in Notation-202) and the nature of consciousness. And again, I repeat, continuity, symmetry, and harmony become the basis for valuations. And, valuations become the basis for ethics, and ultimately for morals.

  1. Cubic-close packing of equal spheres
  2. Cubic-close packing
  3. More to come…


Note: This document was started on September 19, 2021 in Positano, Italy overlooking the Amalfi coast; it’s truly an emboldening place! That eighth point has much more work. – BEC



[1] High school geometry lesson. The most wildly-speculative mind should be our high school kids, yet so many become passive, bored, and tired. What might happen within education if there was a growing crescendo of enthusiasm and creativity for scholarly work within each grade throughout our primary and secondary schools? What if by our senior year, the primary role of a teacher was to help context and interpret new ideas? That is the revolution these basic concepts should engender. Let us open up the box for creativity that is increasingly locked up with each passing year of education.

[2] Scholars. Who among us empowers the most insightful thinking, the most inclusive ethical understanding of things, and the most creativity? Those people are our best scholars. We’ve interacted with a few of them. Empowering people to discover their gifts and develop them is a high calling.

[3] George Johnstone Stoney. Our introduction to Stoney was through a short paper by John Barrow (enter the password: Stoney or go to Harvard’s UIRL). I believe Stoney should be acknowledged as the first to experiment with natural units.

[4] A consensus-driven article by 100+ scholars.  The corresponding author, Vitor Cardoso, had his work cut out for himself to get well over 128 signatures on this “roadmap” through the mysteries. When I find important documents like this one, I stop to write to a few of the key authors. Here are leading thinkers and just maybe, these are people who might examine the 202 notations, particularly the first 64 notations at the quark interface to matter where quantum mechanics begins its work.





14 October 2021: @zlj517 There is only one #Earth within the #Universe and China, the USA, Taiwan, and 195 other nations are an inalienable part of it. We have to grow beyond our simple worldviews for a comprehensive view of our universe: It is our key to the future. Note: Thi is just one of the many Chinese leaders to whom I have written. These people need to be hearing from us all. The concepts this leadership is using are still too tight and too limited.

12 October 2012: John L. Hennessy (Chairman), Sundar Pichai (CEO), Ruth Porat (CFO) of Alphabet You’ve been around idiosyncratic concepts; most are relatively complex. Simplicity is more difficult. In 2011 in a New Orleans high school geometry class, I had the kids chase smaller and smaller tetrahedrons and octahedrons by dividing the edges by 2, connecting the new vertices. We thought it was a great STEM tool. The page — — goes to is one of our early models. It takes 45 steps within to get to particle physics and another 67 to the Planck scale. If you were to multiply those tetrahedrons by 2,  in just 90 additional steps you’d be out to the approximate size and age of  the universe.  It is a model of the universe using base-2 exponential notation. In 1957 Kees Boeke did a base-10 model that became popular, but not functional. This model becomes functional:

9 October 2021: Ken Ono, a number theorist at Emory University, Michael Griffin of Brigham Young, Larry Rolen of Vanderbilt, and Don Zagier of the Max Planck Institute of Mathematics are closing in on the Riemann Hypothesis (Wikipedia). Their work is important because all numbers, all equations are being carried forward within base-2, yet the prime numbers open new possibilities. This group and so many other scholars (Langlands programs and M-Theory) also have a role.

8 October 2021: To the Princeton People: Paul Benacerraf and Paul Steinhardt

Riemann, Bernhard (1859), “Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse”, Monatsberichte der Berliner Akademie. In Gesammelte Werke, Teubner, Leipzig (1892), Reprinted by Dover, New York (1953). Original manuscript (with English translation). Reprinted in (Borwein et al. 2008) and (Edwards 1974)

“Let’s get a handle on the Riemann hypothesis. The Riemann zeta function  is made for base-2 notation. We will exegete his 1859 article “On the Number of Primes Less Than a Given Magnitude” in light of base-2 whereby base-3, base-5, and base-7 ride on top of base-2. All prime number notations — there are only 45 primes within the 202 notations — will be initially considered. Notation-199 is a prime-number notation. The next will be Notation-211; it’s assuredly a bit removed from our immediate considerations.

5 October 2021, A note into Pasadena’s ArtCenter College of Design to Heidrun Mumper-Drumm

Much more to come…


There are so many key words and key word combinations. Quite literally hundreds of instant messages will be sent to key thinkers around the world. Although it seems that we’ve become complacent about first principles and our starting points, we all wrestle with these questions every day.


October 12, 2021: @ChaseSupport @Chase We need to grow beyond all our old worldviews by starting over again with a highly-integrated view of the entire universe. Our model — — started in a high school. Continuity-symmetry-harmony become the bedrock of understanding. 

October 7, 2021: Joshua Rothman, @joshuarothman. Rationality is blocked by unexamined concepts that provide erroneous foundations. is a quick summary of what I think are the biggest. Here’s our different start: Newton’s absolute space and time is our biggest stumbling block.

October 5, 2021: @GuernseyCollege Guernsey, Guernsey, Guernsey — The only way we will ever manage equality-diversity-inclusion is to break free of limited worldviews and work on a mathematically-integrated view of the universe from the first moment of creation to this very day and time:

October 4, 2021: @xijinping_xi Three fallacies of Western thought became “commonsense” for the world: To break free of limited worldviews, we need a fully integrated view of the universe. A start: Mathematically:

October 4, 2021: @DrEugeniaCheng You’ve got all the right combinations from category theory to pi to infinity. Your music and cooking are a blessing. Now push it through Newton’s absolute space and time, and then through the infinitely-hot bang theory: begins to wrestle.

October 4, 2021: @BorisJohnson To right our little ship, Earth, we’ve got to take charge of Newton’s errors about “absolute” space and time and Hawking’s errors about an “infinitely-hot” big bang: Those errors have become the world’s commonsense!

October 3, 2021: @nickclegg [Facebook VP-Global Affairs] Nick – Let’s really empower leaders by breaking out of little worldviews. We need a fully integrated view of the universe to have depth and perspective and to unleash creativity: is just a beginning. Come on now. Life is short. Make it a work of art!

Communicate: China has become pivotal in our grasp of the transition from global perspectives to those perspectives that embrace the entire universe. Can cubic-close packing (ccp) become more pivotal than politics and parties to grasp the depths of our interconnectedness?

Politics is crazy. Desperation is in the air everywhere.



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


Key Dates for this document, Hypostasis

  • This document was started on Sunday, September 19, 2021 in Positano, Italy on the Amalfi Coast.
  • First posted for collaborations: September 20, 2021
  • This page became the homepage: October 6-7, 2021
  • The URL:
  • The Prior Homepage:
  • First Headline: Back to the Basics Second: Eight “What if…?” Questions
  • First Tagline: Concepts that change everything…
  • Another possible homepage: Password: Tredecillion
  • The most recent update of this page: 15 October 2021


For now, the end of this article…

The world wide web obviously connects the world. There are many much finer grids that interconnect literally everything, everywhere, for all time.

Prior Post|Claims|Endnotes-Footnotes|References|Emails|Tweets|Zzzzs

This Universe Is Planck-Scale Refined
What You Think Actually Makes A Difference

by Bruce E. Camber Related: The ThreeHistoryExpansionFirst InstantConsciousness

In 2011 our high school geometry class backed into a radically different model of the universe. We used base-2 notation to go from Planck Time to this day, the Now, all in just 202 doublings. We’ve been all these years working to grasp what it means. We’ve been searching for concepts that could support a highly-integrated, mathematical model of the universe. We have written to some of the world’s finest scholars for their objective criticism and advice.

A summary of our “progress” (or lack of it) year by year and to date:
: Our first-ever chart of the universe is 202 base-2 notations, a mathematical grid…
______By definition, this matrix includes everything, everywhere, for all time.
2012: 64 notations are smaller than particles. We explore dimensionless physical constants.
2013: All without that bang. Circles-spheres to straight lines, triangles, tetrahedrons and more…
2014: Planck Time to this very second, a Zeno-like progression of  tetrahedrons-octahedrons
2015: Mathematical chart of all five Planck units. Newton is challenged. Janus-faced space-time.
2016: Horizontally-scrolled chart. Infinitely-hot challenged with just a picosecond’s difference.
2017: Natural thrust. Natural inflation. It is 100% predictive and logical, but redefines time.
2018: Dark matter and dark energy, Homogeneity & isotropy. All notations are always active.
2019: Pi’s never-ending, never-repeating defines the infinite. There are domains for perfection.

2020: Pi defines ContinuitySymmetryHarmony, and these three define pi (circles and spheres). Here the relations become primarily real, not subjects and objects. These three are also the heart of the first principles of logic, mathematics, and science. Always highlighted at the top of each homepage, these three concepts also define the value chain, even a moment of perfection. The three define a face of the finite, the quantitative, and a face of the infinite, the qualitative. We’re closer to understanding something very different about the finite and the infinite.1

Results. Within our base-2, mathematical model of the universe these three most basic facets of reality define everything, everywhere for all time. Continuity-Symmetry-Harmony has no size restriction. From the Planck scale to the universe scale, cubic-close packing of equal spheres (ccp) is our first application for constructions. Kepler used it in 1611 to stack cannonballs on ships; today it’s for GPS and satellite communications, heart arrhythmia and atomic packing factors.2

On the other side of our equations, we hold onto too many mistaken concepts. Of three most-basic, historic errors, one was promoted by Aristotle, another by Newton, and the third by Hawking. These three have seriously limited our imaginations and clouded our vision. Although introduced within an earlier homepage, these big three need constant study:
Aristotle misled us about a key geometry that stymied science and our creativity for over 1800 years. He missed a basic gap that opens the way to quantum fluctuations.
Newton was sure that absolute space and time were the most fundamental facets of reality. The world.unwittingly followed; and his concepts became our commonsense. He rejected a more relational view and truncated the thinking of the world’s people and her emergent sciences.
Stephen Hawking, the symbolic leader of big bang cosmology, gave no ground to any competitive theory all while his big bang encouraged solipsism and gave us an excuse for our narcissism and nihilism, especially for the dystopians among us.

Result. Those three errors have placed an integrated view of our universe just beyond our reach. The three have also made us all feel rather inconsequential and our little world increasingly insensitive, abrasive and abusive. Everyone everywhere is on edge. Especially when we consider the processes of getting and holding onto power, even within a democratic state, from the left to the right, it has become altogether very nasty business.

Change is possible. There are much more inclusive perspectives of who we are. We can see ourselves within an intimate relation with the universe, within this world and with each other. What you think, say and do affects the quality of life throughout the universe.

For us, the most simple start to a basic change of our understanding has been this base-2 chart. Envision the Planck Scale, the smallest scale, necessarily the beginning of the universe, and it goes to the largest scale, the size of the universe as it is today, right now. In 2011 high school geometry classes backed into this model of just 202 steps. It has taken all this time to begin to understand it and to recognize its place and importance for our life together.

We have not been shy to invite people to study it and help us to understand it.


Twitter: A tweet went out to leaders of the Left and the Right within the USA:
@georgesoros @OpenSociety @Thomas1774Paine @maddow @Heritage @realDonaldTrump

“How can we all be so far off?”
Answer: Our worldviews are too limited. We’re missing the universe.

The universe can anchor us. It’ll give each of us perspective. See: It’s just a start.


We are moved to ask:
• What if the universe starts with the Planck base units, what might be the first “thing” created?
• What if the first thing created is a sphere defined by those Planck base units?
• What if there is an endless stream of spheres and the first functional activity is sphere stacking?
• What if sphere stacking opens cubic close packing of equal spheres and tetrahedrons and octahedrons are generated? Does Plato follow?
• What if the concept of infinity has been so tainted by philosophies, we miss its most simple definition — continuity creating order, symmetry creating relations, and harmony creating dynamics; and then we’d add, “Any personal and confessional definitions are not necessary here.”

And so we finally ask, “Is there a glimmer of truth to our simple what if questions? If so, does that glimmer change our approach to our most basic equations?”

Emails. There have also been many emails that review our struggles to understand something so simple. I write, “I hope you can help us grasp the scope of our model of the universe; it came out of a high school back in December 2011. Here are a few of our key documents:
Our history,
Our first chart,
Our current chart,
Our STEM perspective,
Our current homepage, (this page for now)

We had to stop using this model in our high school curriculum; we didn’t want to taint the students going to college with a model that had not yet been vetted. Of course, this model has a special logic, it’s simple, it has a natural inflation, and most importantly, it readily supports homogeneity and isotropy. Yet, it still needs to be vetted by scholars.

It still needs much deeper explorations, so we welcome your thoughts.

Here, space, time, finite and infinite are all actively redefined. Leading scholars from around the world have been earnestly calling for it since the turn of this century-and-millennium.

This view of the universe starts cold. It models Lemaître’s earlier 1927 theory. It starts with the Planck base units whereby the universe is fundamentally exponential. And, it is a model that has not yet been evaluated by the scholarly and scientific communities.

It’s time. Thumbs up or thumbs down? Can you help?


Endnotes and Footnotes

[1] The Finite-Infinite Relation. One of the most divisive issues throughout all the cultures of our world, we grasp three facets of pi: continuity-symmetry-harmony. From one perspective, these three are the best description of the qualitative and the infinite. From another perspective these three are the best description of the quantitative and the finite.

We say, “Continuity begets order begets numbers which beget time.”
Then,Symmetry begets relations which beget geometries which beget space.”
And then, Harmony begets dynamics which begets systems which begets space-time.”

That is a summary for logic, math and science. All other declarations about the infinite are considered personal statements, nothing more.


[2] GPS and satellite communications to heart arrhythmia to atomic packing. In 2015 Cornell mathematics professor, Steven Strogatz, opened up our understanding of pi. Obviously, something profound is going on inside every sphere. A strong spherical magnet is a better analogy than a soccer ball filled with air. Simple Pi became Most-Dynamic Pi. Its manifestations of the Fourier transform appear to work within everything, even something as personal as arrhythmia and as fundamental as atomic packing factors.

The Dynamics of Pi. These five dynamic images open the door to begin to grasp the internal and external activity of pi and the nature of the very dynamics of all that is. Each image opens a page of explanations.

Sphere to tetrahedron-octahedron coupletFile:Circle cos sin.gif

Poincaré, Poincaré polarization B, Poincare sphere Please note: Our speculative projection is that these five dynamics also describe the expansion of the universe. It is not closed, but it looks closed. It’s not flat, but could be described as flat.


References & Resources 



We have problems understanding each other and our universe. Arrogance slows us all down. We all can do better. This page URL is: The past ten homepages are also very closely related. Use the Left Yellow Arrow at the top to scroll back or choose from the listings on this page.

Reference links: There are ten scholars cited just above under References and Resources. Each will be linked to their own page on this site. Also, see David Tong of the Cambridge DAMTP and Hermann Nicolai of Max-Planck-Institut für Gravitationsphysik



22 September 2020: I just sent a tweet to a rather insensitive soul who has 2.8 million followers on Twitter today. I had never heard of him and I don’t recommend his vulgar work to anybody. His crudeness debases the human family. This is what I said to @DaBabyDaBaby: “Someday you’ll die like the rest of us; and, what will people say? What’s your legacy? Did you help us see the world in a new way? How about the universe? When you see yourself as part of the universe maybe you’ll start to understand.”

“Everything you do and say makes a difference.”

24 September 2020: @zoplaplace: What do we know? If space-and-time are derivative and quantized at the Planck scale and base-2 and cubic close packing of equal spheres are the most basic dynamic, we are all like your “dead” and “stupid” comments because we’ve blissfully ignored the rest of the universe.

28 September 2020: Magdalena Skipper, Editor-in-chief, Nature, @Magdalena Skipper:  I just started following you… surprised to see just 15.1K who do. Nature is such an historic and highly-influential, scientific magazine — so very important. In Jan. 2013 Geoff Brumfiel wrote “Shrunken Proton…” of 2010 research. It needs a sequel! “Point particles” are not small; the Planck scale has so much more to teach us:

28 September 2020: @gbrumfiel @Magda_Skipper Jan. 2013 your “Shrunken Proton…” (2010 research) needs a sequel! “Point particles” are not small. If the Planck scale is the start, there are 67 base-2 notations to your proton:



This section is for my Afterthoughts. As a start, the purpose of this section is to open the website up for deeper study. Click on the top yellow arrow on the left, and flip through each home page right through this summer (and all the way back into 2016). Each top level posting or homepage is an attempt to show if the universe starts cold. Within our little mathematical model, in less than a minute, it is hot enough to pick up on the big bang theory’s so-called epochs. In effect, the big bang is only wrong about its understanding of about a picosecond! Just look at this comparison and how the numbers quickly fall in line with each other.


Key Dates for this document, World

This article was initiated on Tuesday, September 22, 2020
World became a homepage on Thursday, September 24, 2020.
Last update: Friday, October 7, 2022
The Prior Homepage:
The URL for this page:
The initial tagline: Changing the course of our history from war and enslaving people to…
• This World Can Become A Nicer Place
• The reason we all have so many problems among nations and as a people:
• We Do Not Yet Grasp The Deeper Interconnections Within Our Universe.  
The universe is everything, everywhere, for all time. And, what you think, say, or do affects it all.

Four documents: Each is to help us grow beyond our little worldviews.

A Note from the Editor: This image floats around the web and has been used in many instances to describe quarks and/or “the smallest things within the physical universe.” To check on it, I used Google’s image search. In our model of 202 notations, this image might be applicable in the range from Notation 55 to Notation 65. Also, in 2018 it was this top level post. – BEC

The PDF for this document is World-October-2020.


This Shifting Paradigm Changes Our Perception Of Everything

Please Note: ALL LINKS will eventually be re-routed to this website,  That UPDATE is on-going. Many links currently go to back to the first postings within our website for our television series, Small Business School (1994-2012).  A weekly, half-hour, that show aired on PBS-TV stations around the country and Voice of America (VOA-TV) affiliates throughout the world.

An Integrated UniverseView: Beyond the WorldWideWeb & Worldviews

1.  The Universe is finite. That’s huge. It has measurable smallest units for space and time. It has measurable units for the largest dimensions of space and time, the Observable Universe and the Age of the Universe, respectively.  More

2. The Universe has an ethical bias. Yes, it certainly appear to be so! The theological among us have some very real work to do. Theology is informed by science and science is informed by theology.  When they disagree, one of them is wrong.  Those within radical Islam have much to learn from Allah (the Arabic word for “God”) and how science tells us so much about the Creator of all things.

3.  The Universe is smaller and more ordered than we think. In 201+ steps, you go from the smallest measurement to the very largest. Initially it sounded ridiculous and it seemed inconceivable.  Yet over time, it sinks in.

4.   The Universe is more connected than we think.   In fact, everything is related to everything, all within 201+ steps!  Seems impossible; it’s not.

5.  The Universe gets structure from space-and-time, but not its essence.  The structures go back to basic geometries that have become exquisitely complex (Also, see the reference just above). The essence of that structure comes from the infinite through our constants and universals which appear to be best engaged through the Planck Units.

We Can All Strive For A Higher Perfection, A Better Way

To our guests, our extended Small Business School family, and to all our first-time contacts, especially among editors and writers:

First, this Universe View is related to everything, everybody, every behavior and every thought. Some of the work actually began way back in the early 1970s.  Some of it came into focus with our old  television series from 1994 to 2012.  We all share the same first principles (linked from here). For us personally, it was a direct reflection of our faith and our belief that faith and science must cohere or one of them is wrong.

Second, we used those first principles in all that we have done. That’s how one knows the first principles work. Yet, eventually, those first principles inform in new ways.   It is not automatic.  It takes time.  But, there is always a next step. We can always improve on the initial conditions. That is the reason for this page.

Third, we all need to extend our principles globally, then extend them throughout the universe. That drove our work on the Big Board-little universe back in December 2011.  We can also now see how such principles just might become the core of a new small business revolution.

Now, with all these references, we now say, “Let’s get focused; there are great things to do to get us all on track for a brilliant future.”

Everything Starts Most Simply. Therefore, Might It Follow That The Planck Length Becomes The Next Big Thing?

Prepared and first posted on July 9, 2013 by Bruce Camber for five classes of high school geometry students and a sixth-grade class of scientific savants.

Propaedeutics: Let us analyze three very simple concepts taken from a high school geometry class, (1) the smallest-and-largest measurement of a length, (2) dividing and multiplying by 2, and (3) nested-embedded-and-meshed geometries. Though initially a simple thought exercise (hardly an experiment), our students quickly developed a larger vision to create a working framework to categorize and relate everything in the known universe. Though appearing quite naive and overly ambitious in its scope, the work began at the Planck Length and proceeded to the Observable Universe in somewhere over 201 base-2 exponential notations. That range of notations is examined and the unique place of the first sixty notations is reviewed. This simple mathematical progression and the related geometries, apparently heretofore not examined by the larger academic community, are the praxis; interpreting the meaning of it all is the theoria, and here we posit a very simple foundation to open those discussions. Along this path it seems we will learn how numbers are the function and geometries are the form, how each is the other’s Janus face, and perhaps even how time is derivative of number and space derivative of geometry.

Simple Embedded Geometries, The Initial Framework For A Question

Observing how the simplest geometric objects are readily embedded within each other, a high school geometry class [1] asked a similar question to that asked by Zeno (circa 430 BC) centuries earlier.2 “How many steps inside can we go before we can go no further?” The students had learned about the Planck Length, a conceptual limit of 1.616199(97)x10-35 meters. Using base-2 exponential notation, these students rather quickly discovered that it took just over 101 steps going within to get into the range of the Planck Length. For this exercise they followed just two geometrical objects, the simple tetrahedron and the octahedron. Within that tetrahedron is an octahedron perfectly enclosed within it. Also, within each corner are four half-sized tetrahedrons.

Illustration 1: The simple tetrahedron, the center triangle
being a face of an octahedron

We went inside again. At each notation or step we simply selected an object and divided the edges in half and connected the dots. Perfectly enclosed within the octahedron are six half-sized octahedrons in each of the six corners and eight half-sized tetrahedrons in each of the eight faces.

Illustration 2: An octahedron with its simplest internal parts.
Four pivotal hexagonal plates are outlined (red-white-blue-yellow); all surround the center point.

Selecting either a tetrahedron or octahedron, it would seem that one could divide-by-2 or multiply-by-2 each of the edges without limit. If we take the Planck Length as a given, it is not possible at the smallest scale. And, if we take the measurements of the Sloan Digital Sky Survey (SDSS III),  Baryon Oscillation Spectroscopic Survey (BOSS)3 as a given, there are also apparent limits within the large-scale universe — it is called the Observable Universe.

Also, observe how the total number of tetrahedrons and octahedrons increases at each doubling. At the next doubling there are a total of 10 octahedrons and 24 tetrahedrons. On the third doubling, there are 84 octahedrons and 176 tetrahedrons, and then on the fourth, 680 octahedrons and 1376 tetrahedrons. On the fifth step within, there are 10944 tetrahedrons and 5456 octahedrons. The numbers become astronomically large within 101 steps. It is more aggressive than the base-2 exponential notation used with the classic wheat and chessboard story4 which, of course, is only 64 steps or notations.

The following day we followed the simple math going out to the edges of the Observable Universe. There were somewhere between 101 to 105 steps (doublings or notations) to get out in the range of that exceeding large measurement, 1.03885326×1026 meters. By combining these results, we had the entire “known” universe, from the smallest to the largest measurements in 202.34+ (calculation by NASA’s Joe Kolecki) to 205.11+ (calculation by Jean-Pierre Luminet) notations5. At the same time the growth of the number of objects by multiplying or dividing became such a large number that it challenged our imaginations. We had to learn to become comfortable with numbers in new ways — both exceedingly large and exceedingly small, and the huge numbers of objects.

Not long into this exploration it was realized that to achieve a consistent framework for measurements, this simple model for our universe ought to begin with the Planck Length (ℓP). It was a very straightforward project to multiply by 2 from the ℓP to the edges of the Observable Universe (OU).

That model first became a rather long chart that was dubbed the Big Board – little universe.6 And then, sometime later we began converting it to a much smaller table7 (a working draft).

This simple construction raised questions about which we had no answers:
1. Planck Length. Why is the Planck Length the right place to start? Can it be multiplied by 2? What happens at each step?
2. The first 65 Notations. Although we initially started with a tetrahedron with edges of one meter, in just 50 notations, dividing by 2, we were in the range of the size of a proton.8 It would require another sixty-five steps within to get to the Planck Length. It begs the question, “What happens in each of those first 65 doublings from the Planck Length?”
3. Embedded Geometries. When we start at the human scale to go smaller by dividing by 2, the number of tetrahedrons and octahedrons at each notation are multiplied by 4 and 1 within the tetrahedron and by 8 and 6 within the octahedron. That results in an astronomical volume of tetrahedrons and octahedrons as we approach the size of a proton. What does it mean and what can we do with that information?

Starting at the Planck Length, a possible tetrahedron can manifest at the second doubling and an octahedron could manifest at the third doubling. Thereafter, growth is exponential, base-4 and base-1 within the tetrahedron and base-8 and base-6 within the octahedron. To begin to understand what these numbers, the simple math, and the geometry could possibly mean, we turned to the history of scholarship particularly focusing on the Planck Length.

Discussions about the meaning of the Planck Length.

Physics Today (MeadWilczek discussions).9 Though formulated in 1899 and 1900, the Planck Length received very little attention until C. Alden Mead in 1959 submitted a paper proposing that the Planck Length and Planck Time should “…play a more fundamental role in physics.” Though published in Physical Review in 1964, very little positive feedback was forthcoming. Frank Wilczek in that 2001 Physics Today article comments that “…C. Alden Mead’s discussion is the earliest that I am aware of.” He posited the Planck constants as real realities within experimental constructs whereby these constants became more than mathematical curiosities.

Frank Wilczek continued his analysis in several papers and books and he has personally encouraged the students and me to continue to focus on the Planck Length. We are.

The simple and the complex

A very simple logic suggests that things are always simple before they become complex. It seems that I adopted this idea while growing up as a child; my father would ask, “Is there an even more simple solution?” Complex solutions make us feel smarter and wiser, yet the opposite is most often true. When teaching students from ages 12 to 18, one must always start with the simplest new concepts and build on them slowly. Then, a good teacher might challenge the students to see something new, “If you can, find a more simple solution.”

Our class was basic science and mathematics, focusing on geometry. My assignment was to introduce the students to the five platonic solids. Yet, by our third time together, we were engaging the Planck Length. Is it a single point? Is it a vertex making the simplest space? What else could it be? Can it be more than just a physical measurement? Are we looking at point-free geometry? 10 Is this a pre-structure for group theory?11 Speculations quickly got out of hand.

We knew we would be coming back to those questions over and over again, so we went on. We had to assume that the measurement could be multiplied by 2. We attributed that doubling to the thrust of life.12 So, now we have two points, or two vertices, or a line, and a larger space of some kind. Prof. Dr. Freeman Dyson13 in a personal email suggests, “Since space has three dimensions, the number of points goes up by a factor eight, not two, when you double the scale.” We liked that idea; it would give us more breathing room. However, when we realized there would be an abundance of vertices, we decided to continue to multiply by two. We wanted to establish a simple platform using base-2 exponential notation especially because it seemed to mimic life’s cellular division and chemical bonding.

The first 60 doublings, layers, steps, or notations

Facts & Guesses. If taken-as-a-given, the Planck Length is a primary vertex and it can be multiplied by 2. The exponential progression of numbers becomes a simple fact. Guessing about the meaning of the progression is another thing. And to do so, we must hypothesize, possibly just hypostatize, the basic meanings and values. In our most far-reaching thoughts, this construct seems to open up possibilities to intuit an infrastructure or pre-structure that just might-could create a place for all that scholarship that doesn’t appear to have a grid and inherent matrix — philosophies, psychologies, thoughts and ideas throughout time. So herein we posit a simple fact and make our most speculative guesses:

  • Within the first ten doublings, there are over 1000 vertices. Perhaps we might think about Plato’s Eidos, the Forms.
  • Within twenty doublings, there are over a million vertices. What about Aristotle’s Ousia or Categories?
  • Within thirty steps, there are over a billion vertices. Perhaps we could hypostatize Substances, a fundamental layer that anticipates the table of elements or periodic table.
  • Within forty layers, there are over a trillion vertices. Might we intuit Qualities?
  • Within 50 doublings, there over a quadrillion vertices. How about layers for Primary Relations, the precursors of subjects and objects?
  • Between the 50th and 60th notation, still much smaller than the proton, there are over a quintillion vertices. Perhaps Systems and The Mind, and every possible manifestation of a mind, awaits its place within this ever-growing matrix or grid.
  • The simple mathematics for these notations, virtually the entire small-scale universe, appears to be the domain of elementary cellular automata going back to the 1940s work of John von Neumann, Nicholas Metropolis and Stanislaw Ulam, and the more recent work of John Conway and his Game of Life, and most recently the work of Stephen Wolfram and his research behind A New Kind of Science.

With so many vertices, one could build a diversity of constructions, then ask the question, “What does it mean?” Our exercise with the simplest math and simple concepts is the praxis. We have begun to turn to the history of scholarship to begin to deem the theoria and begin to see if any of our intuitions might somehow fit.

We knew our efforts were naive, surely a bit idiosyncratic (as physicist, John Baez14 had characterized them), but we were attempting to create a path that would take us from the simplest to the most complex. If we stayed with our simple math and simple geometries, we figured that we did not have to understand the dynamics of protons, fermions, scalar constraints and modes, gravitational fields, and so so much more. That could come later.

Although not studied per se, these 60 notations have been characterized throughout the years. Within the scientific age, it has been discussed as the luminiferous aether (ether).15 Published in 1887 by Michelson–Morley, their work put this theory to rest for about a century. Yet, over the years, the theories around an aether have been often revisited. The ancient Greek philosophers called it quintessence15 and that term has been adopted by today’s theorists for a form of dark energy.

Theories abound.

Oxford physicist-philosopher Roger Penrose16 calls it, Conformal Cyclic Cosmology made popular within his book, Cycles of Time. Frank Wilczek simply calls this domain, the Grid,17 and the most complete review of it is within his book, The Lightness of Being.

We know with just two years of work on this so-called Big Board – little universe chart and much less time on our compact table, we will be exploring those 60-to-65 initial steps most closely for years to come. This project will be in an early-stage development for a lifetime.

From Parameters to Boundaries and Boundary Conditions

This construction with its simple nested geometries and simple calculations (multiplying the Planck Length by 2 as few as 202.34 times to as many as 205.11 times) puts the entire universe in an mathematically ordered set and a geometrically homogeneous group. Although functionally interesting, quite simple and rather novel, is it useful?

Some of the students thought it was. This author thought it was. And, a few scholars with whom we have spoken encouraged us. So the issue now is to continue to build on it until it has some real practical philosophical, mathematical, and scientific applicability.

Taking our three simple parameters just as they have been given, (1) the Planck Length, (2) multiplication by 2 and (3) Plato’s simplest geometry, what more can we say about this simple construct? Let me go out on a limb here:

1. Parameters. These parameters have functions; each creates a simple order and that order creates continuity. The form is order and the function is “to create continuity or its antithesis, discontinuity.” As a side note, one could observe, that this simple parameter set is also the beginning of memory and intelligence.

2. Relations. The parameters all work together to form a simple relation. From four points, a potential tetrahedron, simple symmetries are introduced. With eight points, the third doubling, a potential simple octahedron could become manifest. All the parameters work together to provide a foundation for additional simple functions to manifest. The form is the relation and the function is “to make and break symmetries.”

3. Dynamics. Our simple parameters, now manifesting real relations that have the potential to be extended in time, create a foundation for dynamics, all dynamics. That is the form with the potential to become a category, and the function is to create various harmonies or   to create disproportion, imbalance, or disagreement. Dynamics open us to explore such concepts as periodicity, waves, cycles, frequency, fluctuations, and more. And, this third parameter set, dynamics-harmony, necessarily introduces our perception of time. With this additional parameter set we begin to intuit what might give rise to the fullness of any moment in time and of time itself. Also, perspectivally, these parameter sets, on one side, just might could summarize perfection or a perfected moment in time, and on the other side, imperfection or quantum physics.

Please note that our use of the double modal, might could, is a projection for future, intense analysis and interpretation. It is a common expression in the New Orleans area.

Perfections and Imperfections.

The first imperfection can occur very early within the notations (doublings-steps-vertices). With the first doubling there are two vertices (the smallest line or smallest-possible string). At the next doubling, there are four vertices; a perfect tetrahedron could be rendered. It is the simplest three-dimensional form defined by the fewest number of vertices and equal angles. There are other logical possibilities: (1) four vertices form a longer line or string, (2) four vertices form a jagged line or string of which various skewed triangles and polygons could be formed, (3) three vertices form a triangle that defines a plane with the fourth vertex forming an imperfect tetrahedron that opens the first three dimensions of space. Five vertices can be used to create two tetrahedrons with a common face. Six vertices could be used to create an octahedron or three abutting tetrahedrons (two faces are shared).

The third doubling renders eight vertices. With just seven of those vertices, a pentagonal cluster of five tetrahedrons can be inscribed (Illustration 3), however, there is a gap of about 7.36° (7° 21′) or less than 1.5° between each face.19 There are many other configurations of a five-tetrahedral construction that can be created with those seven vertices. These will be addressed in a separate article. For our discussions here, it seems that each suggests a necessarily imperfect construction. The parts only fit together by stretching them out of their simple perfection. One might speculate that the spaces created within these imperfections could also provide room for movement or fluctuations.

Illustration 3: The earliest analysis of these five regular tetrahedra sharing one edge appears to be the work of F. C. Frank and J.S. Kaspers in their 1959 analysis of complex alloy structures. (See footnote 19 for more details on this reference).

With all eight vertices, a rather simple-but-complex figure can be readily constructed with six tetrahedrons, three on either side of a rather-stretched pyramid filling an empty space between each group. This figure has many different manifestations using just eight vertices. Between seven and eight vertices is a key step in this simple evolution. Both figures can morph and change in many different ways, breaking-and-making perfect and imperfect constructions.

A few final flights of imagination

In one’s most speculative, intuitive moments, one “might-could” see these constructions as a way of engaging the current work with the Lie Group,20 yet here may begin a different approach to continuous transformations groups. Just by replicating these eight vertices, a tetrahedral-octahedral-tetrahedral (TOT) chain emerges.21 Here octahedrons and two tetrahedrons are perfectly aligned and a simple structure reaching from the smallest to the largest readily emerges and tiles the universe. Then, there is yet another very special hexagonal tiling application to be studied within the octahedron by observing how each of the four hexagonal plates interact with all congruent tetrahedrons.

Within the all the following notations simplicity begets complexity. Structures become diverse. And, grids of potential and a matrix of possibilities are unlocked.

Footnotes: (Work-in-progress)
1 Our Start DateMonday, December 19, 2011 Bruce Camber substituted for the geometry teacher within the John Curtis Christian High School, just up river from New Orleans. The concept of a Big Board – little universe developed within the context of these classes.

2 Zeno’s paradoxes, Zeno of Elea (ca. 490 BC – ca. 430 BC), a pre-Socratic Greek philosopher and member of the Eleatic School founded by Parmenides known for his paradoxes to understand the finite and infinite.

3 Base-2 Exponential notation: For most students, the wheat & chessboard example is their introduction to exponential notation. Wikipedia provides an overview.

4Most Precise Measurement of Scale of the Universe,” Jennifer Ouellette, Discover Magazine, April 6, 2012

Editor’s note: That page on the Discover Magazine site is no longer found. However, a report about the experimental work can be found on the site of the Sloan Digital Sky Survey (SDSS) using the Baryon Oscillation Spectroscopic Survey (BOSS).

5 Prof. Dr. Jean-Pierre Luminet, on Wednesday, July 17, 2013, wrote: “I tried to understand the discrepancy between my calculation and that of Joe Kolecki. The reason is simple. Joe took as a maximum length in the universe the so-called Hubble radius, whereas in cosmology the pertinent distance is the diameter of the observable universe (delimited by the particle horizon), now estimated to be 93 billion light years, namely 8.8 10^26 m. In my first calculation giving the result 206, I took the approximate 10^27 m, and for the Planck length 10^(-35) m instead of the exact 1.62 10^(-35) m. Thus the right calculation gives 8.8 10^26 m / 1.62 10^(-35) m = 5.5 10^(61) = 2^(205.1). Thus the number of steps is 205 instead of 206. You can quote my calculation in your website.” – Jean-Pierre Luminet, Directeur de recherches au CNRS, Laboratoire Univers et Théories (LUTH), Observatoire de Paris, 92195 Meudon Cedex

6 Big Board – little universe, a five foot by one foot chart that begins with the Planck Length and uses exponential notation to go to the width of a human hair in 102 steps and to the edges of the observable universe in 202.34-to-205.11 notations, or steps, or doublings.

7 Universe Table, ten columns by eleven rows, this table is made to be displayed on Smartphones and every other form of a computer. At the time of this writing, Version was posted..

8 Very large Numbers:  Taking just the octahedron, the calculation is: 665=3.8004172ex1050 octahedrons and 865= 5.0216814e58 tetrahedrons. Add to that, with the tetrahedrons at each step are four tetrahedrons: 465=1.3611295ex1039 and the additional octahedron within it at each step: 165=65

9 Frank Wilczek, the head of the Center for Theoretical Physics at MIT and a 2004 Nobel Laureate has a series of articles about the Planck Length within Physics Today. Called Scaling Mt. Planck, these are all well-worth the read. His book, The Lightness of Being, to date, is his most comprehensive summary.

10 Point-free geometry, a concept introduced by A. N. Whitehead in 1919/1920, was further refined in 1929 within his publication of the book, Process & Reality. More recent studies within mereotopology continue to extend Whitehead’s initial work.

11 Group Theory and Speculations: One might speculate that group theory, with its related subjects such as combinatorics, fields, representation theory, system theory and Lie transformation groups, all apply in some way to the transformation from one notation to the next. Yet, two transformations seem to beg for special attention. One is from the Human Scale to the Small Scale and the other from the Human Scale to the Large Scale. If there are 202.34-to-205.11 notations, our focus might turn to steps 67 to 69 at the small scale and 134 to 138 at the large scale universe. One’s speculations might could run ahead of one’s imaginative sensibilities. For example, at the transformation to the small scale, approximately in the range of the diameter of a proton, one could hypostatize that this is where the number of embedded geometries begins to contract to begin to approach the most-simple structure of the Planck Length. It would follow that within the small-scale all structures would necessarily be shared. Perhaps the proton is some kind of a boundary for individuation. That is, the closer one gets to the singularity of the Planck Length, the more those basic geometric structures within the notation are shared. Because this structure currently appears to be beyond the scope of measuring devices, we could refer to these notations as a hypostatic science, whereby hypotheses, though apparently impossible to test, are still not beyond the scope of imagination. Also, as the large scale is approached, somewhere between notations 134 to 138, there might be a concrescence that opens the way to even more speculative thinking. Though not very large — between 248 miles (notation 134) and- 3500 miles (notation 138) — it might appear to be silly, truly nonsensical, to begin the search for the Einstein-Rosen bridges or wormholes! That’s certainly science fiction. Yet, if we let an idea simmer for awhile, maybe workable insights might-could begin to emerge.

12 Purdue & NSF:  Although the term, Thrust of Life, is used within religious and philosophical studies, it is also the subject of continuous scientific study by groups such as the Center for Science for of Information (Purdue University) through funding from the National Science Foundation.

13 Freeman Dyson:  Personal email to me regarding multiplying the Planck Length by 2, he said: “Since space has three dimensions, the number of points goes up by a factor eight, not two, when you double the scale.” Certainly a cogent comment, however, given we have seemingly more than enough vertices, we decided on the first pass to continue to multiply by 2 to create an initial framework from which attempt to grasp what was important and functional.

14 Anonymous:  Personal email to me regarding the initial posting for Wikipedia, he said: “…it’s certainly an idiosyncratic view, not material for an encyclopedia.”  To which we say, “Thank you.”

15 The luminiferous aether was posited by many of the leading scientists of the 18th century, Sir Issac Newton (Optiks) being the most luminous. The Michael-Morley experiments of 1887 put the theory on hold such that the theory of relativity and quantum theory emerged. Yet, research to understand this abiding concept has not stopped. And, it appears that the editorial groups within Wikipedia are committed to updating that research.

16 Quintessence, the Fifth Element in Plato’s Timaeus, has been used interchangeably with the aether aether. It has a long philosophical history. That the word has been adopted in today’s discussion as one of the forms of dark energy tells us how important these physicists believe dark energy is.

17 Roger Penrose inspired the 1998 book, The Geometric Universe: Science, Geometry, and the Work of Roger Penrose. Surely Penrose is one of the world’s leading thinkers in mathematics and physics. He has been in the forefront of current research and theory since 1967, however, his work on Conformal Cyclic Cosmology is not based on simple mathematics or simple geometries. It is based on the historic and ongoing tensions within his disciplines. Though his book, Cycles of Time, written for the general population, it is brings all that history and tension with it.

18 Frank Wilczek has written extensively about the Planck length. He recognizes its signature importance within physics. When we approached him with our naive questions via email in December 2012, we did not expect an answer, but, we received one. It was tight, to the point, and challenged us to be more clear. Given he was such a world-renown expert on such matters, we were overjoyed to respond. The entire dialogue will go online at some time. He is a gracious, thoughtful thinker who does not suffer fools gladly. And because we believe, like he does, in beauty and simplicity, perhaps there will be a future dialogue that will further embolden us.

19 Frank, F. C.; Kasper, J. S. (1958), “Complex alloy structures regarded as sphere packings. I. Definitions and basic principles”, Acta Crystall. 11. and Frank, F. C.; Kasper, J. S. (1959), and “Complex alloy structures regarded as sphere packings. II. Analysis and classification of representative structures”, Acta Crystall. 12. This construct has been analyzed by the following:
(1) “A model metal potential exhibiting polytetrahedral clusters” by Jonathan P. K. Doye, University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom, J. Chem. Phys. 119, 1136 (2003) The compete article is also available at as a PDF:‎
(2) “Polyclusters” by the India Institute of Science in Bangalore has many helpful illustrations and explanations of crystal structure. PDF:
(3) “Mysteries in Packing Regular Tetrahedra” Jeffrey C. Lagarias and Chuanming Zong, a focused look at the history. To download:

20 The work of Sophus Lie (1842 – 1899), a Norwegian mathematician, not only opened the way to the theory of continuous transformation groups for all of mathematics, it has given us a pivot point within group theory by which to move our analysis from parameters to boundary conditions and on to transformations between each notation. We are hoping that we are diligent enough to become Sophus Lie scholars.

21New family of tilings of three-dimensional Euclidean space by tetrahedra and octahedra” John H. Conway, Yang Jiao, and Salvatore Torquato.

About the author(s)
In 1970 Bruce Camber began his initial studies of the 1935 Einstein-Podolsky-Rosen (EPR) thought experiment. In 1972 he was recruited by the Boston University School of Theology based on (1) his research of perfected states in space-time through work within a think tank in Cambridge, Massachusetts, (2) his work within the Boston University Department of Physics, Boston Colloquium for the Philosophy of Science, and (3) his work with Arthur Loeb (Harvard) and the Philomorphs. With introductions by Victor Weisskopf (MIT) and Lew Kowarski (BU), he went to CERN on two occasions, primarily to discuss the EPR paradox with John Bell. In 1979, he coordinated a project at MIT with the World Council of Churches to explore shared first principles between the major academic disciplines represented by 77 peer-selected, leading-living scholars. In 1980 he spent a semester with Olivier Costa de Beauregard and Jean-Pierre Vigier at the Institut Henri Poincaré focusing on the EPR tests of Alain Aspect at the Orsay-based Institut d’Optique. In 1994, following the death of another mentor, David Bohm, Camber re-engaged simple interior geometries based on several discussions with Bohm and his book, Fragmentation & Wholeness. In 1997 he made the molds to manufacture clear plastic models of the tetrahedron and octahedron. These models are used just above. In 2002, he spent a day with John Conway at Princeton to discuss the simplicity of the interior parts of the tetrahedron and octahedron. In 2011, he challenged a high school geometry class to use base-2 exponential notation to follow the interior structure of basic geometries from the Planck Length and to the edges of the Observable Universe. The first iteration of the Big Board-little universe was created. In September 2013, the first iteration of the Universe Table was created. In 2014, a values chart to enclose a moment of perfection extending from the chaotic to the good was introduced.

Initially on the web as:


The Resilience Project

27 October 2022 at about 1 PM

Pandemics call for a resilience we have yet to fully discover. It is a resilience of a deeper knowingness. This is not hype or wishful thinking: Everything, everywhere, for all time can be mathematically-and-geometrically mapped. Some scholars may recognize it as a scalar field theory. It is, but it is also much easier to grasp. Here’s the initial evidence: Here are more discussions: (most recent)

Some of those numbers may well be the start of scalar field theory but it is also the start of something much more and much easier to grasp. Max Planck (one of the prime movers of quantum theory, the Nobel laureate of 1918, and the one who discovered Einstein) calculated the smallest, meaningful units of space-and-time. Although Georges Lemaître thought a primeval atom would manifest, our best guess today is an infinitesimal sphere. If we apply Euler’s most simple exponential notation (base-2), in just 202 jumps or doublings or steps, we go from that start to this moment today. That bears repeating, “In just 202 jumps or doublings or steps, we go from the start of the universe to this moment today.” The notations build on each other and are always active. The universe acts organically. Everything is related to everything throughout all time. Everything you do, say, or think has an effect on our universe. Now, in 1874, physicist George Johnstone Stoney was the first to calculate these natural units. We have asked the International Standards Organization (ISO) to do an analysis to determine the efficacy of each and to advise us on the best possible numbers from what we have from Planck and Stoney. Yet, the resulting 202 notations will stand. That’s the nature of exponential notation. That Notation-202 spans over ten billion years (out of 13.81).

So here is a model of the universe that is the epitome of resilience. And, this model of the universe liberates us; it is wildly inclusive and empowering. And, it has a built-in valuation system and de facto ethics based on the three conditions of pi: continuity (begets order), symmetry (begets relations), and harmony (begets dynamics).

We may not know immediately how to deal with the next pandemic, but we know the answers are not far away.”
-Bruce Camber, The Resilience Project

Applied dimensionless constants are never dimensionless.

And, Singularities Are Never Quite Singular.
By Bruce E. Camber, August, 2021

Related pages on this website:

Let us extend the discussions started with the page, Calculations, which was written in 2015. This page is called: /singularities/

Not all “Singularities” are alike. Yet all singularities are a meeting place or a convergence of formulae, perhaps also known as a modulus-or-nexus of transformations between the finite and infinite.

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 ε or electric charge or electromagnetism), and the Boltzmann constant (or kB or  temperature).

The Planck scale is not beyond logic, numbers, and conceptual integrity. Simple logic and simple math rule. Homogeneity and isotropy are the results. 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 by 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.

Yes, this so-called “Singularity” Is a meeting place of converging formulae, that might also be known as a Modulus-or-Nexus of Transformation.

Much more to come…


Singularity Theorems and Their Consequences, José M. M. Senovilla, 1997

Why is the Matrix Model Correct? Nathan Seiberg, 1997

a little spacetime bibliography

Key Dates for this article, Singularities


The Mind, the Self, the Brain and Human Mystery

Left Yellow Arrow
Right Yellow Arrow



Just How Conscious Are We?

by Bruce E. Camber
Related: WorldThe ThreeHistoryExpansionFirst InstantConsciousnessMindPerfections


Within all our mappings of the brain, we still do not know where the mind is located. And, within all our mappings of the universe, we are still quite confused about where we are, why we are, who we are, and the meaning-purpose-and-value of life.

Perhaps we’ve been top down too long. Perhaps it is worth our time to try once again to start at “the most simple” and work up. In 1952 John A. Wheeler proposed the geon and quantum foam. Dozens of radical proposals followed. Scholars began to address a wide range of fundamental mysteries and now, many speculate on the nature of a more fundamental particle.*

What could possibly be the most basic thing? Of the many guesses throughout our history, most look a bit like Lemaître’s primeval atom of 1927. Might we assume a primordial sphere is the most basic thing, perhaps more like Plato’s Form, defining space and time? What more can we know about it? In 1899 Max Planck defined basic numbers, today called the Planck base units; these could define a sphere. Might it be considered a Plancksphere? If we apply base-2 notation (or doublings) to those units, in just 202 notations, literally everything, everywhere, for all time is encapsulated. It is a working outline of the universe that begins with the first instant and comes right up to this very day and current time.

The first 64 notations are a most-detailed map of heretofore unimagined places. And, rather surprisingly, within this map, it appears there could be a place along that continuum for the human mind and for all other minds (systems theory). Yet, these multiples of the Planck units of time and length are so infinitesimal; they cannot be measured. That which cannot be measured we call hypostatic. It must be approached through mathematics and logic alone.

Being entirely speculative, here Systems, as in systems theory, begins between Notation-50 to Notation-60 (out of the 201 symmetric notations). There is, however, an inherent challenge with this assumption. Historically human beings simply do not emerge until our asymmetric Notation-202.

Large-scale structure formations, all the stars and the galaxies, do not begin until Notation-191. We take as a given that the thin disk of our galaxy emerges within Notation 200. The earliest forms of life on Earth start within Notation 201 and begin their most earnest development only in Notation-202. Yet, both Planck and Wheeler would spread the mind over all 202 notations.

Notwithstanding, there is something about spacetime that makes all of it current within a given moment. How is it that the mind, if emergent within an earlier range like Notations 50-to-60, is current in our brain within Notation-202? That is our question. The answer to it will inform how the brain-mind connection works.


In December 2011 our first base-2 chart of the universe with 202 notations was introduced.
In May 2013 a more simple chart emerged; the first 67 notations just might define part of the continuum within which the Mind evolved.

Two of the greats of physics, Max Planck and John Wheeler,1 had advocated for all 202 notations! Planck said, “This mind is the matrix of all matter,” while Wheeler said, “…all things physical are information-theoretic in origin” and “…this is a participatory universe.”

Our mathematical model, by definition, not only contained everything, everywhere for all time, it uniquely identified and labeled every thought-word-and-deed with the numbers from those Planck base units. First, the continuum connects everything to everything. And, space-and-time labels everything, from the very first instant to this moment. Here is a radically relational model where everything is related to everything, everywhere, for all time. There are no barriers. And, here the work of systems theory helps to open up its dynamics.


How is it that the Mind is fundamentally a domain of all the notations, yet it may have unique structures within a range of the early notation such as 50-to-60, yet only manifest within Notation-202? Yes, according to Planck and Wheeler, the Mind is the core of all 202 notations.

Obviously our concepts of space and time are incomplete. In article after article we explore how Isaac Newton’s insight about absolute space and time is an overreach. Could our simple model of the universe comprised of 202 base-2 notations reopen the historic issues involved with brain-mind or mind-body problem? Might we gain new insights if were to study the issues in light of each of the 202 notations?

One of my early heroes was John Eccles. His work on synaptic functions (1963 Nobel Prize) was special; it opened up interstitial spaces. I’ve had three of his books, Understanding the Brain (McGraw-Hill, 1973), The Self and Its Brain (with Karl Popper, Springer, 1977) and The Human Mystery (Springer, 1979), on my book shelves since about 1979, yet never did Sir John answer the outstanding questions about the brain-mind connection. Nobody did.

Oxford’s Roger Penrose is another scholars’ scholar who engaged space-time and the mind-brain. Three of his books, The Emperor’s New Mind (Oxford, 1989), Shadows of the Mind (Oxford, 1994), and Cycles of Time (Knopf, 2010), are opened on my right. Two problems complicate the Penrose legacy. First, even though he pressed well beyond it, Penrose never really gave up on the infinitely-hot start of the universe. Also, though he acknowledges Max Planck and his numbers, at no time did the Planck base units become a starting point for the universe. Had he explored that kind of “what if” question, I think he would have begun to explore spheres, sphere stacking, and cubic-close packing. Scholars have been dancing around such concepts for years. Once reviewed, base-2 notation becomes the most simple means of expansion, and finally, we begin to realize that other models are possible and need to be explored.

Brain-mind discussions easily date back to Plato and just a bit more recently to leading scholars such as Leibniz, Locke, Berkeley, Hume, Kant, Hegel, Putnam, and Dennett.2 Most of these scholars did not have the advantage of knowing Planck’s base units. None had seen the universe encapsulated within 202 base-2 notations from the smallest to the largest. None had envisioned the structure of the first unit of time and how it would progress through to the current time, including this very second and instant.

III. Unimagined Structures

The Planck base units have not been fully respected. Of course, when engaging something new, our personal histories most often get in our way. Those scholars who have attempted to engage these units are preconditioned to think about particle structure and the infinitely hot. Thinking from scratch, the old tabula rasa, is difficult.

I think the qualities of pi, circles, and spheres give the three a special status among all things fundamental. The prior homepage focuses on it. To facilitate new explorations, let us assume the general structure of the 202 base-2 notations is correct, and the particular structure of the first instant, the primordial sphere, is also correct. Of course, both may be in some ways partially correct, yet we need to build this case, so we assume the place of both as a given in order to explore possible structures that connect the smallest to the largest.

The early days. Our first encounter with the Planck base units was in December 2011 within a high school geometry class in New Orleans. We were working on embedded geometries, particularly by going inside the tetrahedron and octahedron by dividing the edges of both by two and connecting those new vertices. When we discovered a dynamic image that helped us visualize how this tetrahedral-octahedral complex evolves out of spheres, it was an awakening. Infinitesimal numbers became meaningful. There was linkage to the universal sphere. Here was a gateway to infinity. The continuity-symmetry-harmony of pi and the sphere became the continuity-symmetry-harmony of infinity and the finite. Here was something more fundamental than space and time.

The Interstitial. Dimensionless constants exist, but nobody is quite sure where. Their qualities put them outside the finite and there is a sense that they are too particular to be infinite. So, imagine if you will, that there is a domain for transformation. It is definitely not finite and it is too specific to be infinite. In mathematics it is referred to as matrix transformations. Frank Wilczek and some filmmakers liked that concept, but the filmmakers soiled its metaphors and analogies, so now Wilczek prefers grid. I like all the words, including aether, ether and æther, interstitial, and nexus of transformation. There are many more. And, any and all of them that we find will be added within the References & Resources here.

Here is a domain of structureless structure. Here are (1) over 350 dimensionless constants, (2) the essence of light (continuity-symmetry-harmony), and (3) the essence of numbers and geometries. Here, on one side is the infinite and on the other side is the finite and in between is “the very different.” It is a kind of perfection. It is the opposite of miasma; it is the sweet, the enlivened, the creative, the veritable life-force of the particular.

Spheres become all shapes, sizes, and sorts. There is a lot of work to do to build up to the atomic scale and atomic-packing factors (APF) deep within Notation-67 to Notation-80. There is a lot of significant work to do to get to Notation-50 at 6.0701777×10-29 seconds, the beginning of a postulated notational range for The Mind. Notation-25 at 1.8090539×10-36 seconds is the earliest measurement for Hawking and those who want the universe to start infinitely hot. In our model an abundance of structures already manifests. Our 2016 chart only gives us an outline, yet I predict that string theory and Langlands programs will be keys to fill in the blanks.

Hardly a slow, thoughtful-and-prodigious start, as earlier noted, the universe begins with one plancksphere which becomes 539 tredecillion spheres per second.3 Stacking is immediate and penultimate. By Notations 6-7 and the 16 and then 32 spheres, cubic-close packing of equal spheres begins its processes. The dynamnic internality of the Fourier transform has begun. Notation-12 builds out immediately. The base-2 count is 1024; that concurrent base-8 expansion of 8,589,934,592 (8.589 billion) is being studied. Simple math tells us that the possibilities for complexity are already quite compelling.

Notation-25. By that 25th notation where most of the scholars and experts are talking about a singularity, the base-2 expansion has 8,388,608 units of something, perhaps spheres, maybe vertices; there may be even more possibilities. Yet, confirming the idea of other possibilities is the dimensional analysis, base-8 calculation of 4.722366×1021 units. Surely every possible mathematical combination can be tested. Then, all the internal dynamics of the primordial sphere open even more dynamical relations for connections.

And, that’s just the concrescence of possibilities within the first twenty-five notations!

Inside the Dynamics of Dynamics.4 Speaking only for myself, long-long ago, I was told, “If you open up a man’s head, balls fall out. All kinds of empty balls. Basketballs. Soccer balls. Tennis balls… and, yes, even that odd-shaped football.” It’s the power of suggestion all over again. Until recently, when I thought about a sphere, it was empty. Going forward, I’ll have no less than these six images (below) in mind. I’ll also see an entire universe, wall-to-wall, top-to-bottom, filled with the most infinitesimal spheres that are defined by the Planck base units filling everything, everywhere for all time. Of course, going inside these spheres, there can be no singularity. Here is a place defined by dimensionless constants that we can understand (and the billions I do not).

Sphere to tetrahedron-octahedron couplet
Sphere Stacking-Packing
File:Circle cos sin.gif
Lagrangian point

Attempting to be outrageously speculative, I project that these five Fourier-related procedures (above) may be a complete description of the first moments of gravity and electromagnetism. Two sets are all in the same family and it seems that A-and-B and C-and-D are Janus sisters.

The most radical image is Fourier-E which brings the Lagrange point of celestial mechanics down into the Planck scale. It is such a different idea; of course, we’ll be studying it further. We will consult with scholars to begin to determine which dynamics pulls in for gravity and which extends out for electromagnetism. Couple that image with the work introduced within Quanta Magazine (October 2020) where Emily Wolchover authored an article about the continued work of Chris Quigg (emeritus Fermilab) with Quanta’s very special enlivening of an earlier image that he postulated for particle physics.

It is the first image that I’ve seen within particle physics that has some metaphorical semblance to the dynamics within celestial mechanics.

You may have heard it said, “As above, so below.” A better expression in light of this work may be, “As within, so throughout.” One might readily conclude, “This universe is profoundly entangled!”


Time and again within these pages, the role of string theory and the Langlands programs has been touted. Here there is plenty of space and time to bring them into this picture.

Most speculative: Uniqueness and Prime Numbers.5 Among our most puzzling numbers are the prime numbers. From 1-to-202 there are 45 primes: 2, 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, 197, and 199. In this model where numbers and geometries are among the fundamentals, every combination of the two will need to be analyzed closely. Every function of a number has a role in this base-2 model. The hypothesis is that each prime opens up uniqueness — new dimensionless constants, new equations, and the possibility for new initial relations.

In that same spirit, might every “prime base extension” open yet other unique paths? A few of these primes bases may be worth exploring further. The limitation may be 13 given 13 times 13 is 169 and 17 times 17 is 289 . And though 14 times 14 is 196, wouldn’t it somehow been included within a base-2 or base-7 extension? Obviously we have many more questions than answers at this time.

Speculative Nodes: Every type of current, active network within our computing and communications networks has a direct analogical start within the infinitesimal. All need to be analyzed in light of our first 67 notations. We naturally hypothesize that there are multiple paths throughout the universe that make communications throughout all the nodes or notations such that certain types of information are transferred and communicated virtually instantaneously.


The shift away from absolute space and time will not be easy or intuitive. We’ve been Sir Isaac Newton’s children for much too long. Yet, shift we must. Typically the more simple solution is preferred by nature (and by our students). This model, however non-intuitive and complex it may seem, is simple, embarrassingly simple. Yet, it is still a very new conceptual frame of reference. There are many major parts of this puzzle that are missing. What happens as new spheres “push” older spheres forward? From just the numbers using the Planck base units, we can see that packing densities are in the range of Neutron stars within the earliest notations. That continuum, however, begins to approach our current density measurements within the first light year (Notation-169). So, what might be happening within Notation-170 as it starts? The first sphere of Notation-170, it is now building on all spheres. Because that first notation is so dynamic, there is a sense that it is perpetually starting (vis-a-vis Neil Turok), and there are dynamics that need closer examination. It’s building on all that went before — it doesn’t start over — and it would appear that the first sphere is the first within every notation and pushing out the expansion at this moment.

Everything, everywhere, for all time is connected.6 Nothing is exempt and deep within it all are infinitesimal spheres. We know information is communicated at the speed of light and there are only 202 notations, each like the nodes of a quantum computer where the connections from Notation-1 to Notation-202 would appear instantaneous. Within Notation-202, there are three-to-four billion years to this very moment since the coming of age of Notation-201. Thus, there are many possibilities for connections-and-switches to come within the day-hour-second-instance of any current moment. Yet, in the final analysis, I believe we will discover it would still appear to be virtually instantaneous.

Just how conscious are we? To be a bit diplomatic, the answer today it seems might be “…not as conscious as we could be.” Intelligence and consciousness may well go hand-and-glove; and to the degree we are actively integrating notations within our perceptions and analysis of any given moment, may well contribute to one’s grasp of the ubiquitous nature of the networking and intimacy of our real realities.

Is sleep the antithesis of consciousness?7 Within an earlier analysis, there were limited speculations that sleep was required to recompile our unique data sets within the total systems of the universe. Our capacity for storing and processing data is limited to, and commensurate with, our wakefulness. Sleep regenerates our capacities to absorb a new arrow of time. That’s the general direction to begin to grasp the essence of sleep and our deep requirements for continuity, symmetry and harmony.

Quite obviously, we need to continue to explore it and sleep on it. More is coming.

Sexuality.8 A key driver of our beingness is our sexuality, yet not much has been said about it within this site. That fact has to change. The power of two is conceptually fundamental within this model. Base-2 and doublings drive this website. In our life — all our experiences — two often become three and the transition from one to two to three is a dynamic that must be studied much more pointedly and in the near future.

Here we are, now nine years thinking about these things and it is obvious, there is so much more work to be done. Our cultures are in a frenzy, profoundly confused, and no grounding within continuity, symmetry and harmony. That all needs to be deeply examined and this footnote will remain open for years to come.

Concluding thoughts this January 2021:
There is no question about it; this is a very unusual theory. Nevertheless, since we backed into making our first chart, a simple continuum from the smallest thing to the largest, it has increasingly fascinated us. None of our scholarly friends has discounted it. Perhaps some one of them will. It could happen. Notwithstanding, we are increasingly confident that it is not a waste of their time to explore it more pointedly. At the very least, we can learn more about logic and systems, space and time, and possibly a finite-infinite relation.

We need help and it is my hope that our best scholars can help us. Thank you.BEC

Please note: I welcome your direct input. Thanks. -Bruce

Footnotes and Endnotes

Introduction. Less than 100,000 people in this world have visited this website. This section is supposed to be for those who are feeling a bit lost. unfortunately, these footnote and not simple and fully explanatory. more work will be done. Our concepts and language need more clarification. the hope is that our first-time visitors will feel comfortable here.

*A Few Key References Only Appearing Within the Preface:
* Preons: 1974 Abdus Salam and Jogesh Pati. On the edge of the explosion of possibilities, a Grand Unified Theory took guts to propose. Yet, particles and waves have consistently failed to get us over that last hurdle.
* Unsolved problems in physics and astrophysics. The editors of Wikipedia include academic scholars who know well the limitations of their knowledge. Several of these people within the physics and astrophysics communities keep working lists of unsolved and unresolved problems. Each is well-worth our time to reflect on our own limits of knowledge within general physics/quantum physics, cosmology and general relativity, quantum gravity, high-energy physics/particle physics, astronomy and astrophysics, nuclear physics, atomic, molecular and optical physics, fluid dynamics, condensed matter physics, and plasma physics.
* Postulations about new particles. It all hit the wall in 2018 at CERN with the diphoton results. Infinite divisibility has a limit. Any and all postulated particles based on a hunch, something observed yet untethered function, will have a new life if-and-when this model gains credibility.
* Plato’s Forms. The Wikipedia review of the issues with Plato’s forms is quite helpful.

Systems Theory: A formal study within philosophy, one might arguably say that the discipline got its start with Ludwig von Bertalanffy in 1934 with his introduction of a mathematical model for an organism’s growth over time. A consistent conclusion of systems theory is that “the whole is greater than the sum of its parts.” At no time has systems theory acknowledged the first 64 notations of the 202 that encapsulate everything, everywhere, for all time. When systems theory begins to adopt the first 64 notations of the 202 base-2 model of the universe from Planck Time to this current instant, as a fundamental operational part of our reality, the discipline will begin to understand how it appears that the whole is greater than the sum of its parts. Also, until systems theory full engages the dimensionless constants and a transformation nexus from the finite to the infinite, it will be incomplete. And, until the infinite is understood to be the deepest nature of the sphere and the value of pi defining (1) continuities-creating-order, (2) symmetries-creating-relations, and (3) harmonies creating dynamics, it will also be incomplete.

Systems theory and the work to define a relational database. The two have much in common including discrete mathematics, bit-string physics, pregeometries, a spectrum for the fine structure constant, database normalization, and object-relational portfolio management. Among others at this time, David McGoveran and H. Pierre Noyes had been pushing the soul of this work.

[1] Scholars: Although these links stay within this website, I think it is especially important that we engage Max Planck and John Wheeler. Their concept of The Mind was far-reaching in their time. Neither knew about the 202 notations from the Planck base units to the current time. I think it is interesting to know that Planck’s matrix was conceptually adopted by Frank Wilczek who ultimately liberated Planck’s numbers from a Dirac-like numerology. However, Planck’s matrix became Wilczek’s grid primarily because the movie, The Matrix, soiled the concept. Wheeler, with his it from bits, had a more natural foundation for his information-theoretic theory, yet he still didn’t break free of Newton’s absolutes and the infinitely-hot start.

[2] Our best thinkers about the Brain-Mind: The scholars whose work we studied in school and graduate school included Leibniz, Locke, Berkeley, Hume, Kant, and Hegel. I had the privilege to get to know Hilary Putnam as a friend and to know of Daniel Dennett and his work as a leading-scholars’ scholar (he had little patience for the rest of us).

[3] 539 tredecillion spheres per second. Planck Time is the shortest duration possible. If one plancksphere is generated every plancksecond, we have a rate of expansion. The other Planck units define the textures. I can only guess that when Planck invited Einstein to visit, he was hoping they could talk about these incredulous numbers. Of course, Einstein had his own agenda. And you can see in the pictures of them together, Max Planck appears to defer to others. His numbers were virtually ignored throughout his lifetime. So, let us accommodate Max. To begin, Planck Time is uncomfortably short for most of us. That it would render 539,1247 tredecillion spheres per second stretches credulity but perhaps less than the kind of inflation suggested by Alan Guth and the infinitely-hot beginning.

Those 539.1247 tredecillion spheres just might be a very good approximation for the current expansion. It would account for dark energy and dark matter, and it would free us from the constraints of a model that lacks integrity — i.e. the continuity, symmetry, and harmony of pi (and light).

[4] The Dynamics of Dynamics. This block of five dynamic images will now start appearing somewhere in most of the future articles unless some good scholar explains why these can not be applied to the Planck scale. The journalism and the people of Quanta Magazine, particularly Emily Wolchover, are among the best within our time. They surely stirred the pot with Chris Quigg (emeritus Fermilab).

As Within, So Throughout is our challenge to see how celestial dynamics are a manifestation of infinitesimal-spherical dynamics and why-when-and-how scale invariance works.

[5] Prime Numbers: There is a clue within our current, dominate use of prime numbers for encryption. Identities are unique beyond the DNA-level and even the atomic level. Identity goes deep inside the informational level between Notation-1 and Notation-64 (perhaps particles and their sub-particles manifest after, i.e. Notation-65 to Notation-75). Every notation adds more unique identity to everything-everywhere-throughout-all-time. It appears that every prime provides a branch for additional uniqueness whereby a new dimensional constant has its first expression. It also seems that these primes– 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61 — provide new branches that gives rise to programming, networks, information processing, and database structure. Turing, Von Neumann,Wolfram and so many others have roles.

[6] The concept, “Everything, everywhere, for all time.” It is used often within these pages. The logic must be reviewed. If Planck Time is the shortest possible interval and Planck Length the shortest possible distance, doesn’t that make the two the very first unit of space-time? If so, what does it look like? If pi is the most-ubiquitous, most-simple dimensionless constant, doesn’t the circle-sphere follow? If the circle-sphere follows, and the first one is manifest at the Planck base units at a rate of one plancksphere per plancksecond, doesn’t it follow that 539 tredecillion spheres per second are generated, all with unique identities that are constantly expanding with data? Doesn’t that look a bit like the Akasha in various historic traditions?

If we can answer in the positive, we have a new theoretical model of the universe.

In 1994 while thinking about the role of creativity, valuation, product development, marketing and sales, this model was inadvertently being developed whereby the transition from notation to notation were the nodes within computer and communications networks. As within, so throughout.

[7] A difficult discussion, let me put something down here just to get it going. The ever-present question, “What is sleep” It is part of the question of the directionality of time. There is the uniqueness of the constant labeling and relabeling of everything-everywhere-for-all-time, yet that is part of the dynamics. It is never a fixed point. The only thing that feels fixed is our own identity. Yet, that identity is…

[8] Sexuality Why is a male a male and a female a female? Is it just DNA? What are the building blocks? Do we choose our physical sexuality? Is it within the earliest notations like 40-50, just before consciousness and systems? Is by luck alone? How is it related to consciousness? … to death? …to a lifetime?

There is so much more to discern. There are so many open issues… This universe has a palette of possibilities far greater than the panoply of colors, sounds, smells, tastes, textures, and attitudes that we currently identify.


References & Resources

Every paragraph and every sentence could have a reference. Yet, the references here are reminders to return to the work of these scholars and to think more deeply about their constructs of reality. EACH HAVE BEEN PART OF THE AUTHOR’S PAGES IN CONSTRUCTING THIS ARTICLE.

Conformal Treatment of Infinity, Penrose, in Relativity Groups and Topology: the 1963 Les Houches Lectures, and The conformal approach to asymptotic analysis, Jean-Philippe Nicolas, 2015

Symmetry, Transactions, and the Mechanism of Wave Function Collapse, John Gleason Cramer and Carver Andress Mead, August 2020

Robert Edward Williams: The geometrical foundation of natural structure: a source book of design, Dover, 1979 The Integration of Universal ConstantsEudaemon Press · 2009

Victor J. Stenger, The Comprehensible Cosmos, Where Do the Laws of Physics Come From? Prometheus, 2006

BrainMind: Harvard, MIT, Stanford, Oxford

Marilyn Ferguson – Wikipedia

Theory of multiple intelligences Howard Gardner, William Damon

Matrix-transformations ( )

Brian Josephson, Life, Extended Mind, and Fundamental Physics

Annual Report 2019 | The Lindau Nobel Laureate Meetings


Dark Energy-Dark Matter – Wolchover 2017

The Hidden Meaning of Planck’s Constant, Robert L. Oldershaw, Universal Journal of Physics and Application 1(2): 88-92, 2013

Multimessenger constraints on the neutron-star equation of state and the Hubble constant , Tim Dietrich, Michael W. Coughlin, Peter T. H. Pang, Mattia Bulla, Jack Heinzel, Lina Issa, Ingo Tews and Sarah Antier, 18 December 2020, Science. DOI: 10.1126/science.abb4317


Emails (3 of many)

Most emails go to scholars who really know something about the issues involved here. Their problems are like our problem; they, too, get set in their ways. They have their own belief systems and they are naturally sticking to them. Nobody wittingly will be absurd to themselves. So as politely as possible, these emails invite their help to look at our data and their data in new ways.

Josh Sokol, Tuesday, January 13, 2021: Josh just won a fellow to explore the dark skies. I start a tweet to him that said, “Perhaps visits to Pitcairn and Tristan da Cunha are in order! Congratulations!” I’m searching your work in Quanta Magazine: In January 2017 I made a reference to you and I am trying to discern why: I’ll get back to you!”

Lee Smolin, Thursday, December 30, 2020 @ 7:15 PM: Questions about the very nature of time

Anton Zeilinger, Saturday, January 2, 2021 @ Ostensibly my questions are, “Is the first moment of space-time defined by the Planck base units?” If so, would an infinitesimal sphere be the first manifestation given pi’s abundance within the dimensionless constants? And, if so, would the rate of expansion be defined by Planck Time (which would render about 539 tredecillion spheres per second)?


Tweets (3 of many)

Links to tweets that might challenge people to engage an integrated view of the universe and not just the world that is in front of them…

11:25 AM · January 13, 2021 @skdh (SabineHossenfelder): You are brilliant, a lightbulb for the sun. Our favorites, Kepler and Wilczek, play their violins as we contemplate pi over an Italian dinner. Yes, that simple pi with its deep continuity, those ubiquitous symmetries, and never-ending harmonies, and ask, “Is that all there is…” My editorial note: Sabine’s book, Lost in Math, is indeed, quite brilliant, but all our complexity within mathematics and physics leads back to pi and the sphere. Add the Planck base units, and apply a bit of base-2 exponentiation, and you have yourself a most-simple beginning of a model of the universe.

10:43 AM · Dec 16, 2020 @AriSchulman Ari – Our little worldviews get in the way of an integrated view of the entire universe – everything, everywhere, for all time in just 202 base-2 notations from the Planck units to today. A start: Chart: So what would you do with it?

11:21 AM · Dec 16, 2020 @R_Allbritton@YousefAlOtaiba1 and @IsraelinUSA Excellent. Notwithstanding, our little worldviews hold us back and the radical rifts between right-and-left grow. To begin to heal, help us transition to an integrated view of the universe. A start, Base-2 from the Planck scale to today in just 202 steps! Robert Allbritton is the Chairman/founder of Politico.



Afterthoughts. Now a full nine years of thinking about our little model that begins with numbers calculated in and around 1899, I am still rather earnestly pleading with our foremost, leading living scholars, “What are we doing wrong?” Only a few acknowledge the question; and like the first scholar to respond in 2012, one word answers are of very little help. We know how entirely idiosyncratic this model is, but is it idiotic? If so, why? We will continue our search for answers — a reason to believe or not to believe — just as long as we can. -BEC


Key Dates for conscious

  • This document was started on December 14, 2020.
  • First posted for collaborations: December 15, 2020.
  • The URL for this document is
  • The Prior Homepage:
  • First Tagline: The Mind, the Self, the Brain and the Human Mystery
  • The last update of this page was on March 23, 2023.

Update and include before completed:

Potentially a highly-integrated model of the universe


Four Key Missing Pieces from Our Puzzle

by Bruce Camber  WORKING draft: December 2019

Introduction: The scholarly community has not openly asked the question, “Are there logical, sequential, relational structures that begin at the Planck scale and go up to the CERN-scale of measurement?” If we apply base-2 (doublings) to the Planck scale, there are at least 64 doublings to get to that particle-wave scale. Then, there are 138 more doublings to go on out to the age and size of the universe. That work was done in December 2011 within a New Orleans high school,. Geometry students structurally encapsulated “everything, everywhere, for all time” within 202 base-2 notations. That resulted in a chart that does the following: (1) Mathematically confirms the speed of light based on Max Planck’s 1899 calculations for the base units of length and time, (2) Opens an actual range to define dark energy and dark matter, (3) Opens homogeneity and isotropy for deeper study whereby conceptual silos of information can be manipulated, particularly including string theory, Langlands programs, and a substantial range of theoretical objects from axions to branes to preons (and most other hypotheticals), and (4) Redefines space-time and matter-energy; all are derivative and finite. Here is a new understanding of emergence; it is the simple beginning of an integrated-and-unified theory of mathematics of the infinitesimal structure of the universe.

Navigation. This article is a compilation of the last five articles for this website. There is easy access to those articles, first by clicking on the yellow arrows to the left and right (and just above the title), or by clicking on the underlined text just above the title.

Logic. The universe is a mathematical, highly-integrated system. There are several layers of simple logic that hold this construct together and gives it a certain veracity that is lacking in many of our more speculative theories about the origins of the universe held by experts and thought leaders within cosmology, theoretical physics, and astrophysics. There is something quite refreshing about starting simple and building from “the smallest possible” infinitesimal units of space, time, matter and energy.

Process. Over the next few years, these pages will be strengthened (and parts substantially rewritten). Experts (scholars) will be consulted. Hopefully there will be many helpful discussions about these four points.

Four conceptual frames of reference

1. The Speed of Light. Based on universal physical constants, in 1899 Max Planck discerned the values for Planck Length and Planck Time. The equation for time included the statement that Planck Length divided by Planck Time equals the speed of light. Ostensibly he was right. Also, if you multiply Planck Time and Planck Length by 2, over and over again, between the 143rd and 144th doubling, you could stop at one second to see that the length figure is the distance light travels in one second.

Simple mathematics defines relations that represent the deep order within the universe. If, indeed, it all begins with a simple doubling, we could be inspired to boldly say, “The universe is exponential.”  Of course, this is a most simple validation of an experimental definition of the speed of light. Within this website, we will continue to examine simple formulas that use the speed of light. Our first and the most basic formula, the one that Max Planck grasped in 1899, is: “Planck Length divided by Planck Time is equal to the speed of light.”

Light, time and length appear inextricably woven. So, in what ways is the very essence of light both time and length? In this relational model where the ratios are primary, the effects, a very specific time duration and a length, are both derivative. So, this question, from this rather different perspective, is well-worth our time to grasp more richly and fundamentally.

For example, that result between the 143rd and 144th notations works within every other notation (see line 10 within the chart) and it gives us encouragement that our chart and emerging model of the universe is worth our time to explore further even though there has been no scholarly validation of it. Because the implications and ramifications are a bit overwhelming, perhaps for that reason alone, there has also been no scholar who has told us why or how these numbers are wrong.

If this model is not wrong, because the chart is so simple and so comprehensive, our metaphors for life could begin to change once it is acknowledged. As this model absorbs most of the big bang epochs as defined by scholars and the flow as defined by our natural inflation, we have slowly come to realize that, “Everything is related to everything.”

So, we will continue to study all formulas that use the speed of light and continue to add to the simple facts that we have found in each notation within this emergence of our universe. And, we will continue to invite others to help explain these numbers. To that end, much of our work is focused on STEM tools and curriculum to help others participate.

With every article, we’ll always push to go even deeper. We need to get beyond our basic understanding of our simple chart. For example, let us try to bring in Einstein’s best-known formula ( e=mc2 ).  The next steps

2. The structure of dark energy and dark matter. To date, the academic community does not recognize any “…logical, sequential, relational structures that begin at the Planck scale and go up to the CERN-scale of measurement.” To date, our exploration of the emergence of functionalities within each of the first 64 notations starts with an infinitesimal sphere.

Through simple doublings, it has been shown how a simple tetrahedral-octahedral couplet is  generated. One can readily see how simple basic infinitesimal geometries can emerge and then begin to complexify. The first sphere, for now, is known as a plancksphere. Our on-going analysis considers how it is a finite-infinite bridge and how tiling-and-tessellating of the universe logically begins right here. Some have called it a fabric of the universe. There is well-established mathematics to show how each notation could readily create multiple fabrics functionally expanding earlier concepts of the aether and fields within fields, right up to a specific convergence where particles and waves begin to emerge between notations 64, 65, 66, and 67.

Having begun to identify forms/functions within sphere stacking and period doubling of equal spheres, the earliest work of Henri Poincare, and the more current work of Mitchell Feigenbaum, Ari Lehto (Finland), and Charles Tresser (IBM) are engaged.

David Hilbert. Within earlier scholarly work, in-and-around 1920 David Hilbert and Stefan Banach (developed functional analysis like the Fourier Transform) began to define vector spaces and function spaces. At this stage in our efforts, we ask a lot of questions: When and how do these morph? What is the functional relational between reciprocal spaces and Fourier spaces? Could these simple doubling functions open up the work of Henri Poincaré and his sections, periodic orbits, and state space?”

Hypothesized within these earliest notations is a place for all known mathematical systems to begin to emerge and to have each naturally build on the systems that birthed its essential structures.

We can’t measure any of it. We might confirm all of it.

Yes, although well-below the thresholds of direct measurement, I believe our mathematical devices, intuitions, and logic can, and will, create ways to confirm its reality and how-and-where it is included within the base-2 model. Today we start with the first notations; we have numbers generated from the Planck logic and these numbers are all being verified scientifically, logically, and mathematically.

That finite-infinite bridge may be defined by stretching the logic of existing scholarly studies already well-known and well-defined within their information silos. Though the work with subspace-hypercyclic operators” is currently just beyond my reach, I have a hunch that this work could help us to understand the roles of pi and the other dimensionless constants within this model that work both within the finite and infinite.  The next steps…

3. Homogeneity and isotropy. There are conceptual silos of information everywhere within our scholarly world. Two of the more fundamental studies are string theory within theoretical physics and the Langlands programs within mathematics. Neither has easily fit in with the current foundations of knowledge, yet both are very robust studies. Neither starts simply, yet both use the first principles of continuity (order) and symmetry (relations). So, those first 64 notations of the 202 could provide the necessary bandwidth to build the relational bridges.

In our preliminary studies, the first ten notations were for fundamental forms. Both string theory and Langlands engage specialized concepts of forms. In much the same way, both proceed with structures, substances, qualities, relations and systems. These are also the foundations for homogeneity and isotropy.

As simplicity becomes increasingly complex, all sorts and flavors of what are currently consider theoretical objects emerge. Things like axions, branes, and gravitons-and-gravitinos have had years of work to define them, but no place to go within a grid so all are still considered hypothetical. The currently-recognized grid that starts with particles and waves is just too limiting. Here the grid is huge — no less than 64 doublings of the Planck base units.

Unlike the Big Bang inflationary cosmology there is no need to project (as MIT’s inflationary universe scholar, Alan Guth, did) an infinitesimally short period of exponential growth to smooth out any and all irregularities from their infinitely hot start. Our first 64 notations  start cold and these are that exponential growth. It has smoothness (continuity and symmetry) right from the start.

Of course, within the base-2 model, chaos must come at some point before the 67th notation. Also known as quantum fluctuations, perhaps the five-star tetrahedral cluster with its pentastar gap is the source whereby the imperfect fitting creates a new domain for creativity, chance, randomness, and, yes, even free will.

Also, as a result of engaging these first 67 notations since 2011, I believe that the homogeneity-and-isotropy within our universe reflects the very nature of the infinite while chance, randomness, creativity, and free will reflects the very nature of the finite. If the instantiation of that five-star cluster is a marker, I suspect it is not a static location, but actually floats within a range of notations. The next steps...

4. Space-time, matter-energy as derivative of light. There is a continuum of light that starts simply defined as the speed of light, c, and then another at c2.  Suprasets, c3, c4, c5 and beyond are used in the definitions of the Planck base units. Hopefully our scholars will be the ones who will lead us into these areas. Important for all of us is to grasp the finite, derivative, and necessary relations between these four basics, the first faces of physicality.

Of course, within the world of our scholars, that is a heretical statement. More common among them would be comments  like Frank Wilczek’s summary, “Because Newtonian space is infinite and homogeouous (sic),  Earth and its surface are not special places.” He says this on page 5 in his book, Lightness of Being, Basic Books, 2008. The “(sic)” reference just above is to the relatively easy misspelling, “homogeouous” for homogeneous. In this emergent model of the universe, space is derivative and every place is special, i.e. uniquely defined.  The next steps


Building on prior homepages:
(1) Bridge (2) Formulas (3) Map the Universe (4) Bottom-up (5) Transformation


Endnotes & Footnotes

1 The Speed of Light. The electromagnetic spectrum is a well-understood facet of light. We’ve added time and length as two more facets. How about Einstein’s work on mass and energy? Within this chart, it appears that it is instantaneously multiplied by itself, mass and energy manifest as a third and fourth face of light. These four facets are part of the entire spectrum of 202 notations whereas we suspect electromagnetism, as we currently understand it, does not reach much below the 67th notation. Theoretically, the dimensionless constants, the Fourier transform, and close cubic packing do.

We’ll keep raising questions. The range for visible light is very small. The electromagnetic spectrum reaches beyond that ultraviolet light on the short side of visible light and possibly beyond what we understand are ultra-short gamma waves. The long radio waves not only reach the 202nd notation, these are also a facet of light. References/resources

2 Dark Matter and Dark Energy. To make progress, we have to bare our limitations and ask for help.  Although I find the logic within this base-2 model to be compelling enough to continue to dig deeper after all these years (since 2011), it is risky business.  So many fundamental questions have not been answered.  The most fundamental: Is the universe finite or infinite?

We don’t know so we split the difference and say it is a closed-but-flexible universe that continues to expand with a rather magical fabric that weaves between the finite and infinite with literally innumerable relations that bind the two. On the “other side” of the current expansion is the infinite which is defined by continuity, symmetry and harmony. Now, as a quick reminder, all the metaphors and mysteries of personal belief are left to the believers. We only ask them, “Do those three concepts in any way help to define our understanding infinite?”

Computations. Dark matter and dark energy are not understood. First, consider the range. Scholars currently estimate that dark matter is anywhere from 25% to 95% of all matter. For those who suggest 25%, we will need to aggregate those earliest notations,   0-to-64 for all 202 notations.  Each begins with the “same”  4.01495×1011 kilograms. We’ll get some help to see how close that calculation comes to  25% of our calculation within the chart of  1.399×1052 kilograms for the mass of the universe or to the higher figure, 1.5 × 1053 kilograms, used online in many places. Then, for those who calculate as high as 95% of the universe, it would suggest that all matter prior to the current notation, 202, essentially goes dark. Given the pivotal role of dark matter and dark energy within physics and cosmology and for the rest of us to understand the meaning and value of life, as of this article, much more intense work will be done here. References/resources…

3 Homogeneity and isotropy.  Assumed by most of the scholarly community, these two seminal words bind our universe as a single system. Notwithstanding, there is no currently-recognized cosmology that starts with and then builds upon those two concepts.

The essence of homogeneity and isotropy is continuity and symmetry and that is the very foundation of our model that starts with the Planck base units and encapsulates the universe in just 202 base-2 notations. Here the cosmological constant are those continuity equations  that cross the finite-infinite bridge to open the way for all the dimensionless constants. It is good to have the 31 identified by Wilczek and Aguirre, Rees, Tegmark (W-ART) as a starting point. They are clear to say that all necessary for the standard models of particle physics and cosmology (ArXiv PDF: page 2, Table 1), yet they are top-down particle-wave physicists.  With their 31 as a goal, it seems that it might be much more interesting to use them to build basic forms, then structures, that are purely mathematical yet begin to manifest with infinitesimal values for time and  length and very small values for mass and charge. We will continue to try to encourage bottom-up construction and not top-down thinking. References/resources…

4 Space, time, matter-energy and the finite-infinite. Since the advent of dimensional analysis, renormalization, and cutoff regularization, the concept of infinity has been less of a problem for scholars. But, it is no secret that each works around the problems of infinity. After awhile, it is easy to stop looking at each result to ask, “What does this tell us about the very nature of infinity? What does it tell us about the four Planck base units?”  The deeper inherent assumptions pulls us back into homogeneity and isotropy and that  the universe is a result of continuity, symmetry and harmonics.  It has an active and constant role with all things dimensionless. It part of the definition of light and as such is intimate with space-time and mass-charge. All four values are a reflection of the speed of light.  More to come..  References/resources…

 …on getting inside equations    More to come…._


Building on prior homepages:
(1) Bridge (2) Formulas (3) Map the Universe (4) Bottom-up (5) Transformation


References & Resources

(very  rough draft includes hunches and notes)

1. The Nature of Light.  On Absolute Units: Choices

Building on: (1) Bridge (2) Formulas (3) Map the Universe (4) Bottom-up (5) Transformation

2. The Nature of Dark Energy and Dark Matter.

Dark Energy is thought to be… to be continued…

fields within fields: physics and mathematics


Building on: (1) Bridge2 (2) Formulas #3 (3) Map the Universe10 (4) Bottom-up (4) Transformation


3. The Nature of Homogeneity and Isotropy.

The Friedmann–Lemaître–Robertson–Walker (FLRW) metric starts with the assumption of homogeneity and isotropy of space.

From the Planck scale to particles-and-waves, a hypostatic domain

and harmony (dynamics) of the infinite are transformed as


Building on: (1) Bridge (2) Formulas (3) Map the Universe (4) Bottom-up (5) Transformation


4. The Nature of Space-Time and Matter-Energy.

Regularization, Renormalization, and Dimensional Analysis (PDF): Dimensional Regularization Meets Freshman E&M ∗ Fredrick Olness & Randall Scalise Department of Physics, Southern Methodist University, Dallas, TX 75275-0175, U.S.A. (Dated: August 22, 2017)

How To Think About QFTs David Morrissey March 20, 2019 (PDF)

Base-2 chart of the universe

The intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower-dimensional subspace, called the Poincaré section, transversal to the flow of the system.

Then, that those two numbers have an internal relation that is necessarily related to light, has nothing to do with doublings. Or, does it?

Multiply by 2 works. In every one of the 202 notations, it approximates the speed of light. Mathematically Confirmed it take shape with many different faces from a simple notation, a step, an interval, a group, a set, a category, a shape, First, each notation is a group, first related by the mathematics of base-2 and then by inherent geometries.

The arrow and flow of time are limited to those 202 notations. To grasp the very nature of time.

First Steps of Quantum Gravity and the Planck Values, by Gennady Gorelik

In each case, a mathematical function called the Lagrangian is a function of the generalized coordinates, their time derivatives, and time, and contains the information about the dynamics of the system.

Evolution of Phase Transitions

A Continuum Theory. Rohan Abeyaratne,

T. Jacobson, S. Liberati and D. Mattingly, “Astrophysical bounds on
Planck suppressed Lorentz violation,” Lect. Notes Phys. 669 (2005)

S. Doplicher, K. Fredenhagen and J. E. Roberts, “The Quantum struc-
ture of space-time at the Planck scale and quantum fields,” Commun.

Math. Phys. 172 (1995) 187.
In particle physics, preons are point particles, conceived of as sub-components of quarks, and leptons. The word was coined by Jogesh Pati and Abdus Salam, in 1974.

A group is a set, G, together with an operation • (called the group law of G) that combines any two elements a and b to form another element, denoted ab or ab. To qualify as a group, the set and operation, (G, •), must satisfy four requirements known as the group axioms:[5]

For all a, b in G, the result of the operation, ab, is also in G.[b]
For all a, b and c in G, (ab) • c = a • (bc).
Identity element
There exists an element e in G such that, for every element a in G, the equation ea = ae = a holds. Such an element is unique (see below), and thus one speaks of the identity element.
Inverse element
For each a in G, there exists an element b in G, commonly denoted a−1 (or −a, if the operation is denoted “+”), such that ab = ba = e, where e is the identity element.


2.17643109 × 1059 m7 / s7

Rapid progress in the understanding of superconductivity gained momentum in the mid-1950s. It began with the 1948 paper, “On the Problem of the Molecular Theory of Superconductivity”, [1] where Fritz London proposed that the phenomenological London equations may be consequences of the coherence of a quantum state. In 1953, Brian Pippard, motivated by penetration experiments, proposed that this would modify the London equations via a new scale parameter called the coherence length. John Bardeen then argued in the 1955 paper, “Theory of the Meissner Effect in Superconductors”,[2] that such a modification naturally occurs in a theory with an energy gap. The key ingredient was Leon Cooper’s calculation of the bound states of electrons subject to an attractive force in his 1956 paper, “Bound Electron Pairs in a Degenerate Fermi Gas”.[3]

Initiated in private on Thursday, November 21, 2019
Public Access For Insiders; No Direct Links: Friday, November 22, 2019
Most active editing: November 21 – December 6, 2019

A first draft homepage: Not yet projected
Last edit of substance: December 6, 2019

Possible Paradigm Shift For Time, Space, Mass And Charge


On Asking Nobel Laureates Key Questions*

Yonath278 Ada E. Yonath
Steven WeinbergSteven Weinberg
Barack ObamaBarack Obama
Kip ThorneKip Thorne
Donna StricklandDonna Strickland
G't HooftGerardus ‘t Hooft

by Bruce Camber, working draft, initiated in August 2019
Related: Base-2, Dark, Lemaître, QuestionsStructure, Subjects-Objects, Time, Transformation

Background. In 1969 I worked for a group that developed new priorities for the USA. One of my jobs was to do the initial research and compile data, including one-on-one interviews with scholars from around the world.1 These were people who had expert knowledge and key insights about a pivotal subject for our time. That experience served me well.

When my attention turned to creativity, invention, scientific anomalies, and paradigm shifts, the 1935 Einstein-Podolsky-Rosen thought formula 2 became my most obstinate-and-key challenge. Something wasn’t right.  It became an on-going challenge to determine what was missing. For the next ten years I called on some of the best who might have new key insights. By 1980, it became entirely obvious, I was going in circles. It was time to earn a living. I backed off knowing eventually somebody would breakthrough.3

In 2011, thirty-one years later, something finally hit me; I was helping a high school teacher in our extended family with his geometry classes. That early story is now well-told; a very-simple mathematical model of the universe emerged.4  It had just 202 base-2 notations (successive doublings) of the Planck base units whereby the first notation is the first moment of time. The 202nd notation holds this day (the Now). That 202nd notation also holds all of human history as well as the current expansion of the universe. Fresh from an experience of working with over 100 school kids who seemed to grasp it all, I began asking questions of everyone else.

Potential breakthrough. I’d ask, “Did we back into a new paradigm?  Is it _right or wrong?” 5

Nobody had an answer. A few made one or two-word comments. So, what does one do? Ask the smartest among us? …Nobel laureates? Surely they are among our best; so why not? Of course, these laureates are all extremely busy and in high demand. And, to be fair, we also know that they don’t have all the answers. Just look at our world’s problems. Look at how very nasty we can be with each other. Obviously, there is something we haven’t quite grasped. And, my suspicion is that even the smartest among us haven’t a clue how to answer our most vexing questions. Yes, I’m still asking the same questions that I asked in 1979 for a “first principles” project at MIT.

Yet, what if this rather radical re-engagement of our starting points opens a new door? Could it become a major paradigm shift? We know that every one of the concepts that give meaning and value to our life can still be improved even if a concept seems complete unto itself. Our world is filled with silos of information that do not readily communicate with other silos of information.

Our basic premise — a very different starting point — shows how everything is related to everything. There is connective tissue. There is an aether. There is a a grid or matrix. So, we will ask questions until our simple little starting point is either more fully understood or discredited. To date, it seems that those 64 doublings from the Planck Scale to the CERN-scale, if examined, just might give us access to new answers.

Three levels of engagement became increasingly clear: (1) cubic close packing of equal spheres and sphere stacking from the Planck scale, (2) period doubling bifurcation at the Planck scale and (3) the Fourier transform at the Planck scale.6

Let’s critically evaluate it. To that end, I have sent notes, emails, and tweets to many Nobel laureates, six of whom are pictured above (each picture is linked to a discussion that then goes to recent letters to them). At no time has any one of them said, “Yes, let’s look into this further.” That could change.

The Future. We will not rest until we know how it is that we are wrong.  Our simple paradigm of reality is based on the following concepts:

  • Continuity (order). All time is now.7 There is no past or future. There are 202 notations that encapsulate our universe, and every notation is active, different, and encodes every thought, word and deed of every person and every change of every thing. Notations 1-201 are fully symmetric and 202 becomes symmetric, possibly individually through sleeping.
  • Symmetry (relations). The primary real.8 Space and time are derivative, albeit fundamental relations. Mass and charge are also derivative, albeit fundamental relations. Each of the 202 base-2 notations have different parameters that defines it, yet base-2 (doublings) are held in common by all notations. And, it logically seems all notations are active in the current definition of who we are and why we are.
  • Dynamics (harmony). Networks.9 There is a plenum, an aether, grid or matrix of planckspheres. It fills the universe within those 202 notations and this is the basis of homogeneity-and-isotropy, dark matter-and-dark energy and moments of perfection also known as harmony.  Notations 1 to 64 are the basis of the continued expansion of the universe.

Leading-edge thinking. Of the eleven Nobel Laureates pictured on this page, questions have already been raised with eight. Those letters to each are linked from the discussion about each below. More questions will be pursued. Any answer will be deeply appreciated and analyzed. Additional questions will be raised. Questions with those laureates listed just below will also be raised.  Others will be asked, especially those who carry on the traditions of laureates who have died. 

Either our simple construct is true or it is not.
And, either way, we will learn a lot about mathematical logic.


Much more research to come

  • The Nobel Prize in Physics 2016: David J. Thouless, F. Duncan M. Haldane and J. Michael Kosterlitz “for theoretical discoveries of topological phase transitions and topological phases of matter”
  • The Nobel Prize in Physics 2015: Takaaki Kajita and Arthur B. McDonald “for the discovery of neutrino oscillations, which shows that neutrinos have mass”
  • The Nobel Prize in Physics 2008:  Yoichiro Nambu “for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics”
  • The Nobel Prize in Physics 2004:  David J. Gross, H. David Politzer and Frank Wilczek “for the discovery of asymptotic freedom in the theory of the strong interaction”
  • The Nobel Prize in Physics 2003: Alexei A. Abrikosov, Vitaly L. Ginzburg and Anthony J. Leggett “for pioneering contributions to the theory of superconductors and superfluids”
  • The Nobel Prize in Physics 2001: Eric A. Cornell, Wolfgang Ketterle and Carl E. Wieman “for the achievement of Bose-Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the condensates” 

The study of critical insights of scholars is a key…

Marie CurieMarie Curie
MourouGérard Mourou
Frank WilczekFrank Wilczek
Barry BarishBarry Barish
Rainer WeissRainer Weiss
FreeseKatherine Freese

Endnotes, Footnotes, References and Resources

A basic premise of this website: Every concept can be improved even if it seems complete.
* Six Nobel laureates. Pictured at the top of this page (with another five just above this section endnotes, footnotes, etc.) have all been asked key questions about our simple, mathematical  (base-2) model of our universe. Letters to each are linked below. Plus, there are many others among our listings of people who have also been contacted about this work.

Ada E. Yonath (Email) is included because she never gave up. Who can claim 25,000 trials over ten years? Not many people. Most of us would have given up. But, Ada had an insight, a hunch, an inner driving motivation. She may have gotten discouraged, but she would not be deterred. So, who better to ask about the very nature of life? There is a huge discussion within biology — genomics, RNA/DNA, protein, bioinformatics, back to the simple archaea family.  How-when-where does it begin? How is it sustained? How would you answer our questions to her? In our base-2 model, life as we know it today doesn’t begin until the 202nd notation. Only 2.83 to 3 billion years of this notation has unfolded. Also, the earth is just 4.543 billion years old, the sun 4.6 billion and the Solar System 4.51 billion! That all began in the 201st notation!

Steven Weinberg  (Email & Letters) was awarded his share of a Nobel prize in 1979. Even before that time, he did not suffer fools gladly. This special assurance of knowing what is right and who is wrong often bristles people, but I rather enjoy such folks. I continue to nudge this ever-so-famous emeritus professor and his group of scholars working on basic theory through a grant from the National Science Foundation, Department of Energy. As expansive and detailed as their knowledge is, I think they have a limited view of the possibilities between the Planck scale and fundamental particles. In our model dark matter and dark energy emerge within those first 64 notations, well-below the thresholds of actual measurement! Just because these theorists have never considered that there could be “the first 64 notations,” it is easily written off as poppycock!

Barack Obama (Letter and emails) was awarded the Nobel Peace Prize. It was controversial at the time and  continues to be so. Notwithstanding, our former president is included here because with the Prime Minister of Israel, Benjamin “Bibi” Netanyahu, and the Ayatollah Seyyed Ali Khamanei of Iran, they were all introduced to our work, particularly where it invokes continuity, symmetry and harmony, the quantitative/qualitative faces of this project. This value dimension is a key part of the project. This note was to invite them to challenge the incompleteness of religious hermeneutics and the our understanding of the finite-infinite relation. Although this work now falls to all thoughtful world leaders, I believe it should be a component of every Nobel Peace Prize, i.e. an intellectual contribution to our understanding of, and need for, an ever-improving quality of life for everyone.

In his Nobel speech, Obama said, “To say that force may sometimes be necessary is not a call to cynicism – it is a recognition of history; the imperfections of man and the limits of reasonWe do not have to live in an idealized world to still reach for those ideals that will make it a better place… Let us reach for the world that ought to be – that spark of the divine that still stirs within each of our souls.” My comment: I think we can go deeper.

Kip Thorne (Letters) has allowed his knowledge to be challenged by everyday people. He has had a primary role with the development — writing, production, and follow-up — of the 2014 movie, InterstellarOur hope is that with his unique sense of openness, he will eventually tell us where, how, and why our model could work within the world of physics and even general science.

Donna Strickland (Email) was awarded her share of the Nobel Prize in 2018 within key areas of laser technologies. Who better to ask the question, “What is light?”  Much more than visible light, the rest of the electromagnetic spectrum doesn’t look like light. Can we understand light in new ways from the four Planck base units? We think so.

Gerardus ‘t Hooft (Email) in 2011 with his Dutch colleague, Stefan Vandoren, wrote the heart of their book, “Time in Powers of Ten: Natural Phenomena and Their Timescales.” Translated into English by Saskia Eisberg-t’Hooft and republished in 2014, it was a natural sequel to the 1957 work of another Dutch educator, Kees Boeke with his book, “Cosmic View: The Universe in 40 Jumps.” ‘t Hooft became a Nobel Laureate in 1999. Though our work has not been embraced by our Dutch friends, it also has never been challenged.

Frank Wilczek (Emails, meetings) was the first Nobel laureate to teach us about Max Planck and the nature of the Planck scale. His articles and books are everywhere within this website and our offices. He has not yet shut us down and at times, he has encouraged us.

Rainer Weiss (Email) is a new Nobel Laureate and his LIGO experiments are being heavily analyzed and discussed. He has spent a lifetime focused on the subject. For us to ask him to consider a completely different set of starting principles was a bit presumptuous. But, one never knows. A seed may have been planted.

Katherine Freese (Email) is not a Nobel laureate but there is good reason to think that she could become one. In 1999 principal thought-leaders among cosmologists and theoretical physicists were called in to make sense of inflation. They haven’t. Here we find the work of somebody who has. She further opened her study of natural inflation (appears to have begun in 1991).  She seems like the kind of person who might consider asking what natural inflation would look like if it were to begin at the Planck scale. If she and her associates were to find a natural, exponential inflation that redefines time, she would be in line for a Nobel prize and I would be most pleased.


1 New priorities for the USA. Cold-calling is an essential part of business growth and it seems also to be true about intellectual growth. To grow we have to risk a little. Science advances incrementally and most often it is slow and even arduous. Paradigm shifts are very rare. Yet that “cold calling” modus operandi prevailed and served me wellA little more history


2 The 1935 Einstein-Podolsky-Rosen. Commonly referred to as the EPR paradox, my first encounter in 1970 was through David Bohm when a friend introduced me to his work with Aharonov from 1957. As one thing always leads to another, soon we were studying his other 1957 article about “Paradox of Einstein, Rosen, and Podolsky.” There were 77 scholars whose insights I especially sought out.  


3 Something new will come. That’s the creative process. Sometimes you just have toback off until something hits you.” We had gone over the details incessantly. We asked the question, “What are we missing?”  We didn’t know. We had continuity-symmetry-and-harmony, but also Bell’s inequalities, quantum fluctuations and action-at-a-distance. It was enigmatic!


4 A mathematical model of the universe. Long before we had that simple model, I had questions for everyone.  A mathematical physicist, Patricio Letelier, told me in and around 1976, that strings were the smallest constituents of matter. We were all working on our PhDs at Boston University and even at that time I was thinking that string theory had something to do with a finite-infinite bridge. Though renormalization was helpful in getting specific mathematical equations to work, it did not mitigate or truncate the concept of infinity, especially if we redefine infinity as continuity (order), symmetry (relations) and harmony (dynamics). In 2011 we quickly discovered that our 202 base-2 notations were not part of current academic thinking. Base-10 (Kees Boeke’s 1957 work and the ‘t HooftVandoren 2014 work) was, yet it was also functionally aloof and not granular enough. We began to tell the unfolding of our 2011 story, “Isn’t this remarkable? What’s happening within those first 64 notations?” We had questions for everyone, but at least, we had a STEM tool


5 …a new paradigm? …not even wrong? It took seven years (2011-2018), but the light is shining a little more brightly. Then, in July 2019 the homepage article (herein to be known as “the transformation homepage“) just seemed to open it all up. There was a concrescence of concepts. At no time had those concepts been applied to the Planck scale. As it was happening, it just seemed right. So, our rather radical re-engagement of these starting points is either right or wrong I’ll give it until August 31 — “Let’s go over that just one more time” — and we’ll begin submitting that article to professional publications. When they reject it, we will plead for some explanations. Maybe we can get some conceptual clarity.

My 1979 MIT project is finally back in business!


6 Three faces or forms of the transformation. From among all the concepts examined over the years, three unlikely, principal concepts emerged for our transformation homepage
1. Cubic close packing of equal spheres (and sphere stacking) from the Planck scale
2. Period doubling bifurcation at the Planck scale
3. The Fourier transform at the Planck scale

Literally, taken together, I will guess that all three will touch most every academic discipline.  I cannot see how it could be otherwise.


7 Three infinite functions of the transformation. Of the principal concepts within that Transformation homepage, our paradigm for infinity will be applied.  The first is continuity (order) whereby all time is now


8 Symmetry (relations). A primary real. Instead of running away from the concept, we embrace infinity. With only a superficial analysis of pi, people like David Hilbert are challenged. When we begin to explore space and time as derivative, what becomes fundamental is clear — the relations. Mass and charge are also derivative, albeit fundamental relations. These 202 base-2 notations each have different parameters that define it, yet base-2 (doublings) are held in common by all notations. And, it logically seems all parameters are active in the current definition of who we are and why we are.


9 Dynamics (harmony). Networks. There is a plenum, an aether, grid or matrix of planckspheres. It fills the universe within those 202 notations and this is the basis of homogeneity-and-isotropy, dark matter-and-dark energy and moments of perfection also known as harmony. Within every second of our universe, there are 143 notations that pulsate, like a heart beat, expanding the universe.


More editing to come.

References & Resources

Reference/Resource #1. David Bohm in his book, Causality & Chance in Modern Physics, 1957, pages 163-164, said: “Thus, in the last century only mechanical, chemical, thermal, electrical, luminous, and gravitational energy were known. Now, we know of nuclear energy, which constitutes a much larger reservoir. But the infinite substructure of matter very probably contains energies that are as far beyond nuclear energies as nuclear energies are beyond chemical energies. Indeed, there is already some evidence in favour of this idea. Thus, if one computes the “zero point” energy due to quantum-mechanical fluctuations on even one cubic centimetre of space, one comes out with something of the order of 1038 ergs, which is equal to that which would be liberated by fission of about 1010 tons of uranium.”

Reference/Resource #2. A seminal work, Discussion of Experimental Proof for the Paradox of Einstein, Rosen, and Podolsky, D. Bohm and Y. Aharonov, Technion, Haifa, Israel Phys. Rev. 108, 1070 – Published 15 November 1957 (Received May 10, 1957 [PDF]

Reference/Resource #3. On of the most seminal works in physics, On the Einstein, Podolsky and Rosen Paradox [PDF], J.S. Bell, Physics Vol. 1, No. 3, pp. 195—200, 1964


Challenge us, coach us. We need all the help we can get.  I’d be pleased to hear from you. -BEC

On using base-2 from the Planck base units versus big bang theories

Yellow Arrow
HOMEPAGES: Assumptions|Dark|Emerge|Infinity|Intro|Max|Review|Scholars|WEINBERG|ORIGINAL
36 of 202 base-2 exponential notations from the first moment of time to the current age of the universe.

BY BRUCE E. CAMBER FEBRUARY 2019 Just Prior: Unified Theory?|Ask Scholars?|ASSUMPTIONS?|INFINITY?|MORE

A Fraction Of A Second Difference

Comparison. The key difference between the big bang theories and our base-2 Quiet Expansion is about one picosecond  (just 10-12 seconds or one trillionth of a second).  The following chart was buried in a larger June 2016 document. It has been extracted so we can focus on the differences between the models and then begin to explore the connections with the two Standard Models.

Who? What? Why?
When? Where? How?

Who: The history of big bang cosmology (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. Perhaps our horizontally-scrolled chart of all 202 encapsulating notations (opens in a new window or tab) can help.

Both models have made key assumptions. We believe our base-2 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 a 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. Simple logic and simple math rule. Homogeneity and isotropy are the results. 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. That 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.

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~


>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
Note: Seeking expert help.



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: 41,919.31 years

201: 10 billion years

184: 5.4×1026 Kelvin

201: 7.0×1031 (K)

Notation 187

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

Approach Planck Temperature

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 kelvin.[6] The Strong Nuclear Force becomes distinct from the Electroweak Force.” [1] (Our emphasis) First, consider that the Planck Temperature is 1.41683×1032 Kelvin. The bbt appears to skip the cooling from 1032 to 1027 Kelvin and it uses bubbly magic to 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 (Pardon us, Sean Carroll fans).

Also, because the bbt begins at the Planck Temperature, they truly need a supercooled concept. Of course, within the Quiet Expansion model, temperatures begin near absolute zero and Notations-1 through-102 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.”

QGP.  Within the QE, the quark-gluon plasma which requires 1012 Kelvin, is between notation 135 and 136, 9.6008×1011 Kelvin to 1.92016×1012 Kelvin respectively. Notation 136 is 4.6965×10-3 seconds from their space-time “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 (3.5765×103 K ) and 108 (7153.178 K). The human temperature at 98.6 degrees Fahrenheit is 310.15 Kelvin which is between Notations 103 and 104 (447.073 K). Also, at Notation 103 the Planck Length is now .163902142 millimeters or 1.63902142×10-4 meters or about the size of a human egg.

  1. How did it all begin? And, what does it mean? (January 2011)
  2. Quiet Expansion of the Universe (June 2016)
  3. A Chart: Our working, horizontally-scrolled chart is a most-simple, integrated model of the universe.
  4. Notations 1-202: An analysis notation by notation has just begun!
  5. Planck base units from 0 at the beginning to today: