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…