From the simplicity of pi to the complexities of E8


In Search Of Deeply-Informed Analyses

by Bruce Camber

Science around the globe today. Knowingly, most of our leading scholars 1 use old concepts with deep problems, i.e. space, time, and infinity.2 All three continue to be challenged.3 Our simple map of the universe, 202 base-2 notations or doublings 4 from the Planck units to the age and size of the universe, opens a different perspective. The first 64 notations are actual and symbolic, like the stories of the doublings of the wheat on the chessboard squares.5 It is an old provocative mathematical challenge, yet little understood.

Exponential notation is a most-basic function in mathematics, yet it also appears to us to be the most essential function in the operations of this universe. It puts the very small and the very large into perspective such that scale invariance lifts each up as co-equals, truly equally important.

Yet, one very fine Australian physicist told us that the small-scale range is too small to be meaningful. Although scholars have been reluctant to engage all 202 notations, this effort and website will persevere until the inherent logic of the sphere, sphere-stacking, and cubic-close packing of equal spheres has been debunked and the concept of continuity has been more deeply explored.

E8: Our challenge is to establish a mathematical bridge from well-established scientific measurements to all the base-2 numbers generated from Planck’s four base units. This homepage is an attempt to refine our focus so scholars can begin to discern possible mathematical relations within  these numbers. We’ve studied them and know we need help. We expect within Notation-0 the sphere* begins to manifest. An hypothesis: Before Notation 64, the complexities of E8 manifest. Another hypothesis: Between Notations 64 to 80 (see chart at the top), the Standard Model of Elementary Particles 6 emerges.

History. Yes, this work began in December 2011 in a high school geometry class.7 Its simple mathematics creates unique continuities from the infinitesimal Planck Time and Planck Length to the current age and size of the universe. That it takes just 202+ notations surprises most of us. That it logically encapsulates everything, everywhere for all time is a challenge. An early analysis of these numbers, six groups of prime numbers across the grid,8 is essentially logical, yet begs for a deep analysis of our chart; that is a notation-by-notation analysis.9 We did an initial comparison between our 202 notations and the big bang epochs.10 The key difference, just a fraction of a second, is the first three of the seventeen big bang epochs.11

Current research: Towards the Standard Model for Physics.

We have a long way to go before we will be confident enough to attempt to apply  these disciplines in a rigorous fashion, yet we are studying each and will slowly try to incorporate the best of that scholarship to examine the numbers of our chart more carefully.

Motivation is high. This model may resolve impasses in science today.

The primary assumptions for this website have been outlined in several online documents: 17 Three step-by-step analyses examine the simple logic as we understand it today. It is obvious the mathematics has got to jive with the mathematics currently available to us from the data that is the result of experiments and tests within our finest labs around the globe.

To that end, this chart from the 63rd to the 80th notation has been divided into six groups of numbers, each with the data from three notations.  We will study the numbers from the 80th notation, then go down to the 63rd.

Do any of these numbers show up in current research? In 2016 I was pleased to find one formula did. Dividing Planck Length by the Planck Time is very close to the laboratory measurement of the speed of light. As the Planck doublings approach one second between Notations 143 and 144, it is also very close to the lab’s speed of light. Just simple arithmetic logic confirms Planck’s calculations and the mathematical logic of doublings. It also confirms a variable speed of light,18  each uniquely defined within a notation. That alone prompts us to look deeper. There is so much to learn. We don’t have to be very imaginative! There is plenty of low-hanging fruit.

Just Eighteen Notations, 63-to-80, To Underpin The Standard Model

The 78th to 80th notations appear to be the beginning of the Periodic Table of Elements. It would be good to have a young scholar playing with all these numbers in these three columns to see if they might be reconciled with facts and figures that have already been established.

Although at the time of this writing, a time interval can not be measured until the 84th notation, we are close enough to run these numbers!

The 75th to 77th notations appear too small for atoms but not for particles and composite particles. Though difficult to get precise measurements of a length, there are many ratios to explore especially with mass, charge and time!

The 72nd to the 74th notations will require knowing as much as possible about particles and all their dynamics. We project that each notation will be qualified as an aspect of the infamous particle zoo. The Standard Model may well hold all the keys.

The 69th to 71st Notation are projected to hold three unique facets of particles. The length measurement, though apparently too small to be quite precise, may render very particular ratios that affirm data already in use in the Standard Model of Particle Physics.


The 66th to 68th notation is highlighted because it seems to be the boundary between the small-scale universe and the human scale. Mathematically the 67th notation is the beginning of those lengths that can be measured by the instruments of CERN and other accelerators.


The 63th to 65th notation. We will be asking our young scholars to look for numbers that are related to Lie group actions, exponential maps and differentiable manifolds. Our analysis of the 64th notation would benefit from a deeper ratio analysis to see if any of these numbers emerge.

The 1st to the 62nd notation. Somewhere within these notations, string theory emerges. We hypothesize that the mathematics of  E8 and the Sophus Lie group 19 will have become well established by the 63rd notation. If so and we begin to see those numbers from within the 202 notations from our charts (just above), this simple work will become a paradigmatic challenge. Our understanding of space-time, light, mass, charge and infinity will all begin to be increasingly refined. Yes, it will require some imagination, openness, and work.

Young scholars may well chart a path from the simple sphere to a simple Lie group in ways Langlands programs and string theory appreciate and then we will be well on our way to having gained access to various working theories of everything.


Open Questions, Simple Guesses, and Informal Discussions

  • The Sphere.  Is the simplest sphere the first manifestation of the physical? Can the universe be populated by what we call the plancksphere?  Is it the current expansion of the universe, the forward thrust of the earliest notations?  Just think how  infinitesimally smaller the plancksphere is when compared to a neutrino. If Notations 0, 1, 2 & 3 are the expansion of the universe right now, and each notation of these four notations is involved in some manner of speaking of blasting the universe with an endless stream of spheres, what a different model of the universe we have! All notations would be in some sense derivative and dependent. It is a struggle to understand Notation 202 with a  duration 10.9816 billion years! The sum total of all prior notations is also 10.9816 billion years! So, we are in the earliest part of Notation 202 and all of our common history is a very small part of 202. What is the current density of these spheres in order to support life? So this is the beginning of many more discussions within these pages about spheres: Connecting all things everywhere for all time.  See Notation 0, possibly 1, maybe 2 (but probably before 3).  “What is the most simple, ubiquitous thing?” It is a candidate for dark matter and dark energy. Please visit these pages referenced. More to come…
  • The Now. If all time is still active, each of the 202 notations, and each notation is currently encoding the universe, then what is time? How do we redefine it? Can time be redefined as that face of light and space that defines a continuity condition by its transaction rate or speed — the lower the notation, the higher the transaction rate (and all the notations are forever-and-now).  There is an exact point between Notation 143 and 144 that defines a second. Is that the iconic, archetypal second of all possible seconds? For more visit:
  • Space and light. The sphere readily generates triangles, tetrahedrons, and octahedrons. The interior dynamics of spheres are the interior dynamics of tetrahedrons and octahedrons. For more, see:  We’ll go back to Poincaré’s automorphic forms-and-functions and Lie groups.  More…
  • Matter-Charge and light. In this study, the Planck base units will be considered the four faces of light. When Einstein’s special formula ( e=mc2 ) exploded into the world’s consciousness on July 16, 1945 (Alamogordo Bombing Range within the Jornada del Muerto in New Mexico), how did we all interpret the event? Have we ever really redefined light to include space, time, charge and mass? More to come…
  • Consciousness. In 2014, in the process of trying to layout the 202 notations on an 8.5-by-11 inch piece of paper, two groups of the notations 1-to-67 and 141-to-202 were summarized in groups of ten notations. Between Notations 51-60 you will find, “Systems” and “The Mind.” Using a systems philosophy approach, it seemed a reasonable guess. It would be our first attempt to put consciousness on the grid! More to come…
  • Sleep and Light. What happens when sentient beings are not conscious? Simple answer is, we sleep. So, what is sleep? On the morning of April 17, 2019, I was feeling a bit lazy. I could not shake the sleep from my head. In that quiet time of semi-sleep, I realized, “It is not part of the discussion. You’ll have to add it. Now wake up.” And so, here I am writing and thinking about a subject that is getting a lot of scholarly attention and research, yet very few deep answers. If all time is Now, and all space is profoundly interconnected within a grid of 202 notations, our day is not defined by hours-minutes-and-seconds, but by periods between sleep. In the early days of computing, when machines were big and programmers were constantly working on getting everything to work together, there would be nightly compiles and recompiles. Perhaps a compile is a close analogy to sleep and a recompile is like a little nap. Everything we think, say and do are incorporated into the great whole.  More to come…
  • Quantum indeterminacy. There is a notation where the densities of the spheres allow for wiggle room whereby quantum physics begins to emerge. Perhaps it is when systems are projected between the 50th and 60th notationsMore to come…
  • Infinity. Although many scholars want to abandon the concept of infinity, we embrace it. We do not elect to enter the philosophical and theological debates around the word, so opt to define infinity in terms or continuity, symmetry and harmony. Those words are highlighted at the top of every homepage because the thrust of light, the never-ending, never-repeating dimensionless constants, and Planck Charge require an origin and it is definitely not finite. More to come…
  • Ethics of the universe. If everything everywhere is intimately connected, and if everything we think, say or do effects the actual quality of the universe, there emerges an ethics from within this scienceMore to come…

Thinking, working … want to help? We need all the help we can get!


Endnotes, Footnotes, References & Resources

Endnotes Navigation Update:  To return to the referencing sentence, click on that endnote number!

1 ScholarsThere are four key thrusts to communicate with scholars and leading thinkers:
(a) First, the focus was on those leading scholars who might enjoy seeing what high school students and teachers have been doing, people like Stephen Hawking, Alan Guth, Andrei Linde, and Andreas Albrecht among others. I wondered if they would think that we were clever, though obviously misguided, and might they take time to correct our errors of judgment! An appeal!
(b) Those with special knowledge, people like Frank Wilczek and Freeman Dyson, who could answer key questions and tell us what we were failing to understand within their work.
(c) The third group is relatively new. I am reaching out to the graduate students, postdocs, and young scholars who are working in these areas — they have webpages — and often have been published! Where the old scholars are reluctant to take time to be critical, I have been hoping that the young would be honest and tough.
(d) The fourth group is everybody else, but especially those people who have been bold leaders, thinkers, and movers-and-shakers.

The most comprehensive list is here:

2 Arkani-Hamed, Max Tegmark, Neil Turok: These three are calling for a more fundamental analysis of space, time, and infinity. Of course that group necessarily includes light (it’s another “Big Four”):

3 Persistent problems with space-time and infinity: Although there is an abundance of commentaries, in just ten pages back in 2006 Abhay Ashtekar ( Penn State – – PDF) provided a rather succinct overview.

Most people recognize that Nima Arkani-Hamed has bandwidth. But, since 2012 his message has not substantially changed. He says, “Space-time is doomed.”

I do not think Nima imbibed Max Planck’s 1899 work when Max unwittingly redefined both.  Perhaps that work just needs to be recognized. The implications are difficult; only a few embrace it.  Scholars like Carlos Rovelli (The Concept of Time, 2018) and Richard A. Muller do so within the confines of the big bang theory. Muller’s book  is called, Now: The Physics of Time.

4 The Chart of 202 notations:  In December 2011 this first iteration of our chart of 202 base-2 notations or doublings first emerged; it just followed the Planck Length. Planck Time was added in 2014 and Planck Charge and Planck Mass in 2015. The current horizontally-scrolled chart emerged in 2016. This webpage is small step along this path.

5 The doublings on the 64 chessboard squares:  There are many references to this story throughout the web.  Follow the numbers on the each of the 64 squares.

6 Standard Model for Particle Physics: Certainly it seems that the first 64 notations is ample space to develop the complexities of E8 from the sphere, and even to develop Langlands programs from the E8. We suspect that there is still plenty of real estate for consciousness and the earliest beginnings of the Standard Model.

The big bang hides these possibilities.

If this conjecture is true, we’ll  all need to begin to refine our goals.

7 December 2011, New Orleans: In a high school geometry class, we asked, “If we do a Zeno-like progression, how many steps within will it take to hit the Planck Wall??” The initial answer was “about 112.” To go out from our 2.5″ desktop tetrahedron, we were not quite sure where to stop! By getting the advice of experts, we added another 90 to 95 steps to capture the entire universe.  It took three years before Planck Time was added and just another year to add Planck Mass and Planck Charge. In April 2016 the current, horizontally-scrolled, chart was introduced.

8 Just Six Prime Numbers: There are 45 prime numbers between 1 and 202. We selected six that were somewhat evenly distributed starting with Notation 31. Our initial analysis of these the Planck multiples at these six primes, 31, 67, 101, 137, 167 & 199, stretched our imaginations, but each appears to be plausible outputs. With this analysis, we felt the big bang theory needed to be reconsidered.

9 Chart by Notation: There are 202 notations and each must be analyzed. We have to start somewhere, so we then picked up from the very beginning. This work could become a Unified Theory of Mathematics.

10 A Key Analysis: Astrophysicists and cosmologists are confident of all but the first three epochs, the Planck Epochthe Grand Unification Epoch, and the Inflationary epoch. We are rather sure of the mathematics of all  202 notations of our highly-integrated UniverseView. This is a key analysis because it shows that the UniverseView can logically accommodate most of the seventeen big bang epochs.

11 Three big bang epochs: Except for one, there is a consistent logic for formation of the big bang epochs. The Inflationary Epoch of the big bang theory does not compute.

12 Pi and emergence: The Sphere to E8:  If everything starts simple, questions are raised, “What is the most simple, ubiquitous dimensionless constant (that is also the most simple three-dimensional thing)?”  Hands down, the sphere wins. “What do we know about spheres and pi?” Answer: “Not much,” so we turn to scholars to learn. People like Steven Strogatz of Cornell teach us about the Fourier transform. Edward Frenkel gives us insights about the fabric of the Langlands programs.

We believed the concept of infinity was a key:  In our earlier studies of continuity, symmetry and harmony became the conceptual foundations of infinity; and, the concepts of emergence and thrust are used to move this effort forward from Notation 1 to 202.

13 Natural Inflation: We ask, “Is there a deep logic for natural Inflation?” We are trying to learn about natural inflation. We readily see that the chart of 202 notations creates a very different entry point to questions about Dark Energy-Dark Matter and isotropy and homogeneity, so we’ve begun to study the nature of thrust and then the work of people like Katherine Freese of University of Michigan, William Kinney of SUNY-Buffalo, Weinan E of Princeton, Masahito Yamazaki [1] of the University of Tokyo, and now many other scholars from around the world.

14 Multiscale Modeling: If each notation is a scale, and we believe it is, can there be a better example of multiscale modeling?  Probably not. With with this homepage, we begin our first real venture into applications of multiscale modeling or multiscale mathematics. To date, we have turned to the work of scholars like Pingwen Zhang of Peking University or Jack Xin, Editor-in-chief, SIAM journal, Multiscale Modeling & Simulation (and a Professor of Mathematics at the University of California at Irvine) and Weinan E, (Mathematics, Princeton), author of the book, Principles of Multiscale Modeling (PDF), and Björn Engquist (Mathematics, University of Texas-Austin), Multiscale Modeling and Simulation in Science and Simulation and visualization on the grid.

15 Bifurcation theory and period doubling: To understand doubling as “a mathematical study of qualitative changes in topological structure of a given family,we turn to scholars like Mitchell Feigenbaum, Gregory Chaitlin, and Stephen Wolfram.

16 Close-packing of equal spheres: We have barely scratched the surface of close-packing also known as cubic-close packing (ccp). Although encouraged by an expert, Tom Hales, it is a totally different application of the discipline’s historic concepts.

17 Three pages examine our assumptions & basic logic: This work is incremental. Our  assumptions must be reviewed often. There is much-too-much we don’t not know and there are now developments going on in every section of the globe. I often say, Let’s go over this one more time” then, at least review the conceptual frameworks within which we are working. It seems very important to do a periodic step-by-step analysis of our simple logic.

18 Variable Speed of Light:  We have only begun to learn about the deep nature of light.

19 Pi-to-E8The assumption is that to understand E8 requires understanding pi, the sphere, sphere stacking, and the interior dynamics of the sphere more profoundly.  There will be a deep analysis of Lie group actions, exponential maps and differentiable manifolds, Lie groupssimple Lie groups, Cartan–Killing classifications, differentiable manifolds, matrix exponentials, Euler integrations and the exceptional complexity.

References & Resources:  

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

About this page named, E8:
• Privately posted on April 2, 2019
• Publicly posted on April 7, 2019
• Most-active editing from April 2 to April 17, 2019