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. https://81018.com/bridge/

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. https://en.wikipedia.org/wiki/Lagrangian_mechanics


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