A most simple-and-comprehensive map of our universe


We Can All Grasp This Map of Our Universe

by Bruce Camber  (a first draft that continues to be updated)
Not So Abstract. We started working on our base-2 chart of the universe back in December 2011 in a New Orleans high school. We then got the 6th grade science students involved. It seemed that most of the students understood that chart/map rather quickly. Yet, since that time this map, which we say is “…202 base-2 notations or doublings from the Planck base units to the current expansion” has challenged our worldviews, particularly our views of space, time and infinity. What we thought was a fascinating, new STEM tool became idiosyncratic and a bit revolutionary. The first 64 notations (out of the 202) were not accessible. Our hypothesis is that these virtually unexplored notations are common grounds of a most fundamental nature that seem to address age-old questions in physics and cosmology in new ways.

1899: Max Planck’s four fundamental natural units. Numbers, calculated using constants, were so unusual, Planck ostensibly ignored them. Only a few scholars1 picked up on his numbers over the next 100 years. In 2001 Frank Wilczek2 authored three articles for Physics Today that began to pull those Plank numbers free from numerology,3 and Planck’s base units began getting more consistent attention. Today, the sciences have begun to recognize the Planck units and their unique potential to become part of (1) an integrative theory about the nature of things, possibly 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 people 4 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.

Naively, we then started with Planck’s base units and multiplied by two. In 112 doublings we were back in the classroom and in just another 90 steps we were out to the current size and age of the universe and today’s 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 still many lines that have just the four numbers, the chart felt like the beginnings 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. Hardly known to us, we rather unwittingly 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 widely popular. Our chart is a bit different. First, we have our geometries starting with a sphere that generates tetrahedrons and octahedrons. Second, we start with the Planck units and its simple formula that the speed of light is equal to Planck Length divided by Planck Time. 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.9

That 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 validates those 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. We also observed the first 64 notations couldn’t be reached by CERN laboratories in Geneva, Switzerland or by the Max Planck Institute (MPI)11 in Garching Germany. MPI has held the record for the shortest unit of measured time. Those first 64 notations are much too short and much too small to ever be measured by physical tools. So, what is all that aggregating mass and energy? Our ever-so-simple, logical conclusion: it is the “impossible-to-define” dark energy and dark matter.12 As we try to bring it into the light of day, I believe we will discover it is also a 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 a very different perspective …and we’ve just begun our analyses!


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 even if just online. Thank you. –BEC



For more, go to these prior homepages:

  1. Been “top down” too long. It’s time to build from the “bottom up”
  2. A Simple Model – 12 points absorb the universe in 202 steps.
  3. Transformations – Cubic close packing, period doubling, Fourier transform


  1. Every concept can be improved even if it seems complete unto itself
  2. Questions, questions, and more questions.
  3. Bridge over troubled waters...


Endnotes and Footnotes:

   An introduction to this early work: The map is simple because it is just 202 notations, https://81018.com/home/    It is comprehensive because the current mapping done by the astrophysics and cosmology communities really doesn’t begin much before Notation 196 at about 171 million years. Notation 197 brings us to 343 million, Notation 198 to 686 million, Notation 199 to 1.3 billion, Notation 200 to 2.7 billion….

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. Aggregating articles and papers about Max Planck’s base units. Note: To date, these are most substantial that I’ve found. If you can add any to it, I would be grateful. –BEC
1b. The most recent scholars to whom I have turned (and a few have disappointed)
1c. 77+ scholars in 1979. The project was called “An Architecture for Integrative Systems.
1d. My early studies. Such work does make a difference.

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: Those three articles by Frank Wilczek about Planck’s 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 analyses of the Planck scale set those 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. https://81018.com/home/ https://81018.com/tot/

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. https://81018.com/chart/

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. This work originates from within a high school. We have no pretensions about our work. It is rough, raw, idiosyncratic and incomplete, always a work-in-progress.

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 throughout 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.” They had no essential geometries. They had no simple formulas. They had not defined space, time, mass, charge, or light.

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 an equal charge and do these aggregate with each doubling? Within the chart of numbers, it is assumed that indeed there is an aggregation because at one second, rather hidden in 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 the International System of Units (SI units) recognize nothing smaller.

References: https://81018.com/a84 https://81018.com/formulas/ https://81018.com/dark/

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: the 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. His seminal work with Hawking, 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:

Addendum: The heart of so many controversies

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.

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.

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

NextOne of the next articles for this site will open the discussion about Bridge Finite-Infinite-Divide or the Finite-Infinite Bridge. Comments? Please email me or send through this comments form.

References, research, and resources:

Initiated in private on Monday, October 14, 2019 (an update of an earlier version)
Publicly Posted: Monday, October 28, 2019
A first draft homepage: Monday, October 28, 2019
Most active editing: October 14 to November 5, 2019