Could the first 64-notations-out-of-the-202 be our common ground?

by Bruce Camber

A First Draft

Introduction. One of my quiet goals in life has been to understand how concepts somehow transcend our diverse-and-sometimes-opposing points of view. Yet, nothing seems to work for groups of people who have been hating each other for centuries; peace-makers are hard-pressed to come up with a concept that heals such deep divisions.Tensions and divides are everywhere… and yes, these divides also exist within the sciences.

Over the years I have turned to a rather diverse group of scholars1 (going back into the 1960s) who have been wrestling with first principles and our understanding of the foundations of life and of our universe. Some of their concepts just might might help make a difference in the way we understand ourselves, our histories, our sciences and even our religions.

We started working on our base-2 chart of the universe in December 2011. It has become apparent to us that within this chart of 202 notations, there are many concepts that change our worldview and our views of space, time and infinity. We are aware of how idiosyncratic it is!

The first 64 notations out of 202 are most unusual. These may be common grounds of a most fundamental nature that might address age-old questions in physics and cosmology.

In 1899 Max Planck defined four fundamental natural units. He defined the numbers, but they were so unusual, he ostensibly ignored them. Only a few scholars1d picked up on his numbers over the next 100 years. In 2001 Frank Wilczek2 began to pull those Plank numbers free from numerology,3 and Planck’s base units began getting more consistent attention. Today, science tends to recognize the Planck units, i.e. their potential to become part of (1) an integrative theory about the nature of things, even a starting point for creation, and (2) the beginnings of complexity, a concept that helps us to understand the foundations of the sciences, mathematics, logic, and epistemology.

Geometries. Now, for a little perspective on our work, we were high school geometry people4 who in 2011 followed a very simple tetrahedral-octahedral complex5 back 45 steps (halving at each step) down among elementary particles and then another 67 steps to the Planck scale.Being rather naive about it all, we then decided to start with Planck’s base units and multiply by two (2). Sure enough, in 112 steps we were back in the classroom and in another 90 steps we were at the current expansion of the universe.6 We asked, “Did we just encapsulate everything, everywhere, for all time? …the entire universe in just 202 base-2 notations or doublings?

The Chart, A Map of the Universe. Although there are many blanks spaces, the chart seemed to be the beginning of a simple map7 of the universe using base-2 (doublings). We learned that the conceptual foundations of base-2 (exponential functions) were introduced to the world around 1740 by the Swiss mathematician, Leonhard Euler (there’s always so much to learn). Rather unwittingly, we took Euler’s base-2 to the 202nd power and have now begun to ask questions about its context in light of the nature of creation, space, and time.We had been unaware of the 1957 work by Kees Boeke in his private school, De Werkplaats, in Bilthoven, Holland. Boeke did his base-10 chart, Cosmic View: The Universe in 40 Jumps8 and over time it became sensationally popular.

Our chart is a bit different. First, we have our geometries. Second, we start with the Planck units. Third, we have a scale of the Planck’s units from the smallest units of space and time to the largest. Fourth, we have the current expansion of the universe within the 202nd notation. Fifth, our chart is 3.333+ times more granular than base-10. Sixth, this chart mimics life’s natural doublings. And seventh, our base-2 chart has a built-in, all natural inflation.9That is quite a lot, but then, it really began to challenge us:• Mathematical confirmation of the speed of light. We discovered between the 143rd and 144th notation, a simple mathematical confirmation of the speed of light,10 that validated both the distance and the time units.

That’s a key; it actually completes the simple logic of this chart. It has a mathematical, functional, and conceptual wholeness.

Dark energy and dark matter defined. Looking further, we observed the first 64 notations couldn’t be reached by CERN laboratories in Geneva, Switzerland or by all the experts at the Max Planck Institute in Garching Germany; they have held the record11 for the shortest unit of measured time. Those first 64 notations are too short and too small to ever be measured by physical tools. So, what is all that aggregating mass and energy? A simple, logical conclusion: it is the “impossible-to-define” dark energy and dark matter.12 As we bring it into the light of day, I believe we will discover it is also our long-sought-for common ground.

Retrospective. Granted, that’s rather radical for simple people using simple logic. Yet, once opened for inquiry, this virtually unexplored domain of just over 64 notations looks like it can also give us the footings to create a bridge13 between quantum mechanics and general relativity, and between the Langlands programs and string theory. These are not incompatible concepts but different faces of a common foundation just before those few transformations that precede the 67th notation where particles and waves are finally observed.

In 1999 NATO gathered our most elite astrophysicists and cosmologists14 living at that time. All were scholars of structure formation. At no time did they have a discussion about the Planck base units. Nobody was asking, “What could be the earliest manifestation of the Planck base units?” For us, twelve years later in 2011, it was the only question we wanted to try to answer.

Space-time defined by spheres.15

Looking around the scholarly world, it became obvious that we were unwittingly jumping on a bandwagon with Carlo Rovelli and Robert Muller who found space-and-time to be derivative, discrete and quantized. In our model, each notation builds on the prior notation(s). Each notation is part of the operational whole. Each is active and seemingly forever. Space and time are defined by pi (π), continuity, symmetry, and harmony. A simple circle, then a sphere, becomes a key nexus for transformations, all functions with qualities that describe (1) the infinite, (2) a finite-infinite bridge,15 and (3) the inherent quality and actual quantities that define the finite and our very first instant of time.


This is such a different perspective.16 In a very rudimentary way we’re coming full circle. As I explore the common grounds between pi (π), space, time, continuity, symmetry and harmony, there are both quantitative and qualitative shared expressions. Taking a rather speculative leap of faith, I believe these are also the foundations of ethics and aesthetics.16

Of course, altogether too simple for most, I know this will be bit difficult to sell but as a people and global community, what are our options? …continue going on the way we are?Quantitative science, qualitative living.17

Some time ago, in one of my many statements online, I said it would be wise for science to be critical of theology. Science can inform theology, yet theology can also inform the sciences. There can be mutual respect. So, I asked, “What might we learn from the core insights from within religious beliefs?” To create an example, I went back into my family’s traditions. Given the Abrahamic faiths have the attention of about 57% of the world’s population (that includes Jews, Christians and Muslims as well as the Druze, Bahá’í and Rastafarians), an example of such respect might be this very different interpretation of the Genesis story shared by all Abrahamic faiths. The antithesis of disagreements, nastiness, and even violence. In the face of hostility, there is symmetry and harmony as a foundational understanding18 of the very nature of our very beingness. Given all notations are always active, what we consider to be history is the active encoding of our universe.

That is, I would conclude everything you say, do or think; it all impacts the look and feel and quality of our little universe.You make a difference. And, that difference is greater than one could ever imagine.#It is refreshing to find people out on the web who are also shining their light in these seldom visited spaces and who are open and joyful in the process. If you, or anybody you know, has such a vision, please let us know! We would enjoy meeting you online. Thank you. -BEC

  • For more, go to these prior homepages:
  • A Simple Model – 12 points absorb the universe in 202 steps.
  • It’s been “top down” too long.  It’s time to build from the “bottom up”
  • Transformations – Cubic close packing, period doubling, Fourier transform

Common grounds — The first 64-notations

Every concept can be improved even if it seems complete unto itself

Questions, questions, and more questions


Endnotes and Footnotes: (currently the most heavily edited area of this work)

1. Scholars: In less cynical times, most of us believed that the truth always rises. And, some of us have had great faith that scholars engage that truth most readily:

1a. The most recent scholars to whom I have turned (and a few have disappointed)

1b. 77+ scholars in 1979. The project was called “An Architecture for Integrative Systems.”

1c. Influential, today, such work does make a difference.

1d. Aggregating articles and papers about Max Planck’s base units. To date, these are most substantial that I’ve found. If you can add any to it, I would be grateful. -BEC

2. Frank Wilczek: In his Physics Today article, “Scaling Mount Planck II: Base Camp,” Wilczek says: “The strong and weak couplings equalize — at roughly the Planck scale! Planck, of course, knew of neither the strong nor the weak interaction, nor of quantum field theory and running couplings. The reappearance of his scale in this entirely new context confirms his intuition about the fundamental character of the Planck scale” (fifth paragraph).

These are not coincidences. Numbers are numbers. Functions are functions. And, as well, our chart of numbers tells an important story of our time. Here is a highly-integrated mathematical scaling of the universe. Academic openness and integrity should subject this new conceptual frame of reference to a rigorous analysis.

3. 2004 Nobel Laureate and the Planck numbers: Wilczek’s three articles about the Planck base units in Physics Today stirred the pot; yet, when he received his Nobel Prize in 2004, all his writings took on a new vibrancy and importance. Wilczek became part of an elite group of celebrity physicists. His analysis of the Planck scale set these numbers apart in a most-special category even though there are other similar methods to generate fundamental numbers.

4-5. High school geometry people: Straying just a bit from the textbook, the teachers were fascinated with the way the octahedron and tetrahedron, two of Plato’s solids, were inextricably woven. Some of the students became equally fascinated.

6. Current Expansion, a chart: Starting with Planck Length in December 2011, Planck Time was added three years later, and Mass and Charge were added in February 2015. Today’s working chart emerged in April 2016. It was our first horizontally-scrolled chart whereby any one of the Planck numbers could be readily tracked. Notation 202 has a duration of 10.9816 billion years, and the current expansion defines the Now, this current moment of time which is shared everywhere throughout the entire universe.

7. Map of the Universe Using Base-2 (or doublings): Euler was a mathematician’s mathematician. He opened the way to infinitesimal calculus and a most-penetrating analysis of the infinite. We believe Euler will be instrumental in helping us interpret our charts. In 1988, 240 years after being published, one of Euler’s most seminal work, Introductio in analysin infinitorum (1748), was finally translated into English by John D. Blanton. Others quickly followed. We will be using an online translation by Ian Bruce. Of our 202 doublings, from the first notation to at least the 67th notation, could readily be considered infinitesimal. Our goal is to begin to understand the relation between the infinite and the infinitesimal, and we invite you on this journey with us.

8. Kees Boeke’s base 10 work. Here is a precedent for our work. In 1957 in a high school in Holland, headmaster Kees Boeke developed a wonderful teaching tool showing the relative sizes of things with his book, Cosmic View: The Universe in 40 Jumps. Within a short time, it had its champions and today it has become well-known through the world as an IMAX production and several online iterations. It appears that at no time did any scholar attempt to establish causal efficacy between successive notations.Using base-2, the challenge becomes apparent.

9. All Natural. With the work of Alan Guth (MIT) and so many others in the astrophysics community, the rapid expansion and continued inflation of the universe had become a major issue and stumbling block. Causal efficacy is stretched and strained. In the 1999 conference on structures, the most-elite inner circle of of cosmology threw up their hands and said, “Let’s come up with a better theory.”In our simple model a natural inflation is readily observed from the start. Several doubling mechanisms have been identified, however, the most-simple doubling, sphere stacking at the infinitesimal domains, could readily account for most all other doubling phenomenon.This explanation is sweet because it is so simple.

10.  Speed of light. The electromagnetic spectrum in some sense of the word extends from Notation 1 to 202. Let us start a deep search of the literature that explores this bandwidth beyond the first possible visible light (within the 94-and-95th notations). What is the initial very, very small charge? Does each new sphere bring and equal charge and do these aggregate with each doubling? Within the chart of numbers, it is assumed that there is an aggregation because at one second, between the 143rd and 144th notations there is a mathematical confirmation of the speed of light.

11. Measuring an interval of light. The Max Planck Institute in Garching Germany has held the record for measuring the shortest interval of time. They are down into the attoseconds (10-18 seconds). It is a long way to go to get to Planck Time at 5.39116(13)×10-44 seconds. Our understanding of the current range is limited. It goes from the somewhat familiar nanoseconds (a billionth of a second) to picoseconds, then to femtoseconds, and finally into attoseconds. Beyond the attosecond there are zeptoseconds and the yoctosecond 10−24, but SI units recognize nothing smaller. References:

12. Dark energy-matter. Just look at the chart and observe the line for coulombs and the line for mass. Each notation “fills up” so every notation has a percentage of dark energy and dark mass. This would be the most simple explanation for dark energy and dark matter. A science writer was complaining, “I’m the only one who doesn’t have a dark energy and dark matter theory.” So, I wrote to her and said she would be most welcome to adopt ours as her own. You would be welcomed to do the same! Our first analysis, October 18, 2018, is here.

13. Bridges to build. For over 100 years there has been an insurmountable divide between quantum mechanics and relativity theory. Some of the smartest people on earth have been unable to create that bridge. First, all the big bang talk obscured the primary playing field. They now have 64 notations within which to work. It might also help if these exquisitely smart people would create a bridge between the Langlands programs and string theory. All the factors involved with those two bridges will also be involved in building a bridge between the infinitesimal and the infinite (another look). All key bridges, none have been built because the experts and scholars have not had room to think or breath. Most have been unaware of those 64 doublings with 19 prime numbers with which to work. Our scholars’ imaginations have been hamstrung with particles and waves.

14. NATO and Structure Formation. At the Isaac Newton Institute for Mathematical Sciences, Cambridge University, the consensus among the world’s best scholars was that the big bang theory needed to be revised. The net-net. These scholars departed from this conference and many engaged in multiverse speculations, and speculations, and speculations. George Ellis, who authored a seminal work (PDF) with Stephen Hawking in 1974, has an excellent commentary, Physics on Edge (Inference: International Review of Science, VOL. 3, # 2, AUGUST 2017), on the fractured belief systems among scholars who study these issues. That seminal work, The Large Scale Structure of Space-Time, was highly influential, but failed to understand the infinitesimal structure of space-time.

15. Bridge Finite-Infinite-Divide: Not often discussed, a Google search in October 2019 with delimiter quotes rendered just 674 results, most referring to a May 24, 2016 article in Quanta Magazine. By using the word, bridge, as a noun, i.e. the “Finite-Infinite Bridge,” Google pulled up just six results of which three are from our work here.Key words to explore further: Carlo Rovelli Robert Muller derivative, discrete and quantized. pi (π) continuity, symmetry, and harmony circle sphere a key nexus for transformations

16. May the circle be unbroken: Not often within this kind of discussion are the subjects of ethics and aesthetics engaged, however, within our exploration of concepts that can bridge the finite and infinite, continuity, symmetry and harmony were applied to replace absolute space and time. Within those three concepts an understanding of both aesthetics and ethics emerge.

17.  Science & Theology: Too much “positional” time and energy is spent on this topic. Open questions should be clearly and carefully stated without all the positional gestures and maneuvers. We know there is incompleteness. We know that both sides of the equations have “stood their ground.” That is not enough. We need to do better. If we open up the dialogue of first principles in light of the first 64 notations, I predict that ground will be fertile. Not only will the Abrahamic faiths benefit, all religions including atheism, might discover common grounds. The creation story, the old Genesis story, can be opened up for all.

18. Universals: One of my earlier considerations of the emergence of constants and universals

Yes, work continues today, Saturday, October 26, 2019… thank you for your patience.One of the next articles for this site will use both expressions, Bridge Finite-Infinite-Divide, and Finite-Infinite Bridge in the title and subtitle. Comments? Please email me (BEC) or complete the form below.

Please send along your comments or questions.


References, research, and resources:

Set Theory, Zermelo-Fraenkel Set Theory, Future Summary, WilczekArts, Twelvefold way The zeta function Euler’s formula Unifying Lattice Models, Links and Quantum Geometric Langlands via Branes in String Theory, Meer Ashwinkumar, Meng-Chwan Tan, Quantum q-Langlands, Correspondence Mina Aganagic, Edward Frenkel, Andrei Okounkov 2007 – No time – Rovelli as seen in Discover magazine