On Looking In The Dark


Dark Matter & Dark Energy — Not Dark

Navigation: All links go to the Endnotes, Footnotes, References & Resources. To return, click on the reference number.

Abstract. Overwhelming evidence for dark matter and dark energy has had scientists and scholars trying to define its nature as early as 1922 with the work of astronomer, Jacobus Kapteyn of Holland. Today, increasingly refined measurements and models of the Cosmic Microwave Background Radiation (CMBR) have greatly expanded the hypotheses and speculations. It appears that at no time have any of our scholars been aware of the 202 base-2 notations that provide a very simple mathematical outline of our entire universe from the Planck scale, especially Planck Time to the Age-of-the-Universe-right-now. None have been aware that no less than 64 of the first notations (or doublings, or clusters or groups) are well below the thresholds by which particles are currently defined and measured. Proposed is a mathematical physics that progressively works within each of the first 64 doublings, building successively upon each other, and in so doing, encapsulating the so-called dark matter and dark energy. This project necessarily requires a redefinition of light, space, time, and infinity.

History. Jacobus Kapteyn was a contemporary of Max Planck, yet there is no record that either he or Max Planck believed that Planck Time defined the very first moment of the physical universe whereby the four Planck base units emerge 1 as an infinitesimal sphere (perhaps best called a planksphere).2 Though the four base units were defined between 1899 and 1905, even Max Planck ignored his numbers. It wasn’t until Frank Wilczek (MIT, Nobel 2004) wrote a series of three articles, Scaling Mount Planck, I, II, and III (Physics Today, 2001) did the scientific community begin to take note. Yet, apparently old concepts never die. Einstein’s new insights about time were hard to grasp, so Sir Isaac Newton’s absolute space and time readily retained its status as our commonsense worldview. Also, by the time Wilczek’s article came out, big bang cosmology had been the dominate theory for about 20 years. Our work with the Planck units didn’t begin until 2011. It took over four years to gain the footings to propose a quiet expansion3 from the Planck base units. On June 1, 2016, that first article was posted on the web based on the data from our horizontally-scrolled chart.4

The most-constant, most-intense stream of infinitesimal spheres, plankspheres, since the first moment of time until this current moment is the expansion of the universe right now. Within this model, everything is literally connected to everything.

Facts and figures. Doubling, bifurcation, and base-2 exponential notation are well-studied concepts. Yet, in 2011 it appeared that applying base-2 to the Planck base units had not been done. The first chart of numbers facilitated the analyses for that very first article. Those first 64 notations5  with actual numbers in each notation raised questions about the essential relations between the four base units: Planck Length/Planck Time, and Planck Mass/Planck Charge.

These Planck base units require further study. Planck Length is an infinitesimal 1.616229(38)×10-35 meters. Planck Time is 5.39116(13)×10-44 seconds. Planck Mass is 2.176.470(51)×10-8 kilograms. And, Planck Charge is 1.875545.956(41)×10-18 coulombs. If we were to look for common numbers within the first 64 notations, the 31st doubling6 is where the Planck Mass becomes 103 pounds (46.79 kilograms). Yet, the universe is still quite young at 1.157794×10-34 seconds and still rather infinitesimal in size being 3.470762×10-26 meters. Not until the 67th notation does that length become a more familiar measurement, 2.38509×10-15 meters. Within the 31st, Planck Charge is 4.0278116×10-9 coulombs. Though small, the charge of one electron is about 1.602(98)×10−19 coulombs. By the 64th notation, the Planck Charge is still a rather modest, 34.598 coulombs. A typical thundercloud ranges from 15 to 350 coulombs.

By the 64th notation7, time at 9.945379×10-25 seconds is still well below the thresholds of measurement. It will not be until the 84th notation that an actual measurement of a unit of time unit is achieved. Within attoseconds (1×10-18 seconds), that measurement was done by a team led by Prof. Dr. Ferenc Krausz, Ludwig-Maximilians-Universität, Max-Planck-Institut für Quantenoptik, Garching, Germany.

Sphere to tetrahedron-octahedron couplet
Spheres, triangles, tetrahedrons and octahedrons tile and tessellate the universe

By the 64th notation, the universe itself is still infinitesimally small at 2.981362×10-16 meters, yet it is  4.01495×1011 kilograms  (just over 400 billion kilograms or 400 million tonnes, of course, defies all logic). Its transaction speed measured as seconds is 9.945379×10-25 (substantially below current thresholds of measurement). This instant or moment will be compared and analyzed through the lenses of a neutron star where a teaspoon of such material would be about 5.5×1012 kilograms or 5000 million tonnes. Although counter-intuitive, the first spheres at the first notation have a mass, a length and a charge. They have a look and feel; it seems that the image on the right might capture that dynamic.

This just may be the heart of dark matter and dark energy.

A better image may emerge.8  This one also serves us today as an image of dark matter and dark energy which began as one plancksphere within the first notation and has become ubiquitous planckspheres, tiling and tessellating the universe.

If it is assumed that the first notation creates one sphere, by the 64th notation there are no less than 4.611686×1018  spheres. Yet, there could be as many as 6.2771017×1057  if we use the logic by Freeman Dyson of Institute for Advanced Studies. He shared with us his insights about scaling vertices. And at this scale, each sphere might be considered a vertex.  Also, if the transformations within the first five notations are actually represented by the image above, those tetrahedral-octahedral couplets tile and tessellate the universe in such a way that isotropy and homogeneity throughout the universe have a structure and entanglement is not so entangled after all.9

PlanckTimeLight, Infinity, Space- Time. Such a chart of the universe, starting at a definitive point in time about 13.8 billion years ago, suggests that we should review our understanding of light, infinity, and space-time.

The simple part of Max Planck’s formula for Planck Time caught our attention. Of course, tP= lP ÷ c  can readily be rewritten as  c = lP ÷ tP.

Is light and Max telling us something new?

That analysis was coupled with the ongoing analysis of the chart and the work of people like Neil Turok and Job Feldbrugge10 of the Perimeter Institute of Waterloo, Ontario and people like Carlo Rovelli11 of Loop Quantum Gravity (LQG) fame and Katherine Freese12 of the University of Michigan (an expert on natural inflation and CMBR). Taken together, it seemed as though nothing was ever in the past. All the notations had a necessary and ongoing relation. That seemed to square with observing that Max Planck’s simple equation for light was meaningful within each notation (see line 10)13 of the chart. Space and time seemed finite, quantized, and derivative.

Light and the dimensionless constants that helped to define each of the Planck base units seemed to be part of a finite-infinite transformation. And, here infinity is best understood in light of the never-ending, never-repeating pi-like continuities, symmetries and harmonies.

All quite vague, but pointed, we know we have a lot of work to do, but also we think a lot of the work has already been done by the scholars who are still untethered, like the string theorists14 and not part of a grid. We believe most of their work, and the work of people like Edward Witten15 and Robert Langlands16, can be readily applied to these first 64 notations.

Is it possible? Is it possible that dark matter and dark energy are simply below our thresholds of measurement? When asked the question of our sixth grade Advanced Placement science class, “Well, boys and girls, what do you think? Is it possible that all that dark matter and dark energy is out of reach of our physical instruments but in reach of our mental instruments (pointing at the brain)?” The resounding response was “Yes,” but what do we know? -BEC

Endnotes, footnote, references & resources

1 Four Base Units: Emergence. There are two homepages that dwell on emergence and growth. An extended chart was started so each of the 202 notations could be examined, each unto itself.  Max Planck could have proposed doing a base-2 application using the Planck base units to Jacobus Kapteyn in 1922; he could have assumed that Planck Time was the first possible moment of space-time. He didn’t, but we are today. So, we ask, “Why not? What is wrong with this picture?”

2 The Plancksphere: The Ever-Ubiquitous Infinitesimal Sphere. It is one of the oldest concepts in mathematics; perhaps its time has come to take center stage again. Here the ubiquitous presence of PI (π) becomes even more ubiquitous. These infinitesimal spheres, dubbed Planckspheres for now, are the deep state of space-time-mass-and-energy and the transformation nexus between the finite and infinite. Don’t like the infinite? Get over it. Religious people are rather tedious. Yet, atheism is a religion, too. Let’s define the infinite more deeply than it has been done to date.

3 A Quiet Expansion. This comparison of the epochs of big bang cosmology to the processes of a quiet expansion began with this article. It was rough and verbose and it remains that way today! It has been updated often and that process will continue.

4 The horizontally-scrolled chart: This chart of 202 columns changed everything. Being horizontally-scrolled made following the numbers easy. Though the not easily supported by the webpage software, it became an important step in the development of our concepts. We began to understand natural inflation and could readily watch each base unit inflate. Nevertheless, our first simple analyses raised more questions than it generated answers.

5 The very first 64 notations: Those first 64 notations are very special. It became obvious that each notation now needed its own analysis. This would force us to continue our efforts to construct a natural progression of numbers and mathematics that evolve from that most simple sphere. Within the first chart from December 2011, at the 46th notation, there is an entry, Pati Preons. In 1974 with Abdus Salam and Jogesh Pati proposed a preon model, essentially two families of spin-½ fermions: leptons and quarks. Even more-recent preon models account for spin-1 bosons and preons sticks. Each of the preon models postulates a set of fewer fundamental particles than those of the Standard Model. That’s good. Our model reduces their numbers even further.

6 The 31st Doubling: The 101 Pound Universe. Thankfully the studies of neutron stars give us an analogy by which to evaluate the mass/energy correspondence as well as the mass/length correspondence. It is all work that will be done within this website.

7 The 64th notation: Remember the story about the wheat on the 64 squares of the chessboard?  That’s the story of these 64 doublings.  The space between the CERN scale and the Planck scale has been underestimated and it has always been taken as a whole. That is a mistake. We all need to begin to recognize that there are at least 64 unrecognized notations smaller than the CERN-scale. There are 64 layers of mathematical complexity to begin to grasp.

8 The Nature of Emergence:  The nature of emergence is a key. The first definition of space-time is a key. The finite-infinite relation is a key.  These three keys are each addressed within the first notation. We can get a handle on these issues.

Sphere to tetrahedron-octahedron coupletThis dynamic image was first introduced within this website on January 4, 2016 in an article about numbers, “Constructing the Universe from Scratch.” It has now become the center point within this analysis. In that initial article, the question was asked, “Which numbers come first and why? Which numbers are the most important to know and understand?”

The image was also used within the following articles:
Fabric of the Universe (November 2017, just below point #4)
Consider how symmetries within the first 67 notations actually create space (Sept. 2017)
Symmetry: Circles-to-Spheres-to-Triangles-to-Tetrahedrons-to-Octahedrons (Sept. 2017)
Possibilities for New Explorations (October 2018)
Sphere-stacking, we believe it is a fundamental dynamic of the universe (March 2019)

9 Entanglement: Jean-Pierre Vigier. In 1980 at the Institut Henri Poincare, J.P. Vigier in a private conversation proposed that there was a background “something” throughout the universe such that when spin or position changed in one place, the twin particle was immediately affected. He used the image of falling dominoes, yet qualified that image such that there was no spacing so the effect was immediate anywhere in the universe. -BEC

10 Turok & Feldbrugge: “The big bang theory is wrong.” Neil Turok says that the universe behaves as if it is always starting from scratch. That is a clue. What model of the universe could “always be starting.” Of course, this quiet expansion, where every notation is always active and always building off the prior, begins with the base units and the first notation or doubling. The analysis now shifts from the horizontally-scrolled chart to each notation, until all 202 are well defined.

11 Loop Quantum Gravity (LQG) has roots in Abhay Ashtekar’s mathematical work in 1984 at Pennsylvania State University. In 2018 Carlo Rovelli appears to be LQG’s leading theorist. It seems from the naive perspective of a quiet expansion, that spin states, like temperature, are derivative. Yet, importantly, the LQG people recognize the derivative nature of time. Sir Isaac Newton is put on hold.

12 Natural Inflation and Cosmic Microwave Background Radiation (CMBR). Doing a search of just the words, “natural inflation’, out of the top ten references returned today (October 17, 2018), the first (1993), the second (2014), the fourth (2004), and the tenth are the work of Katherine Freese of the University of Michigan. Yet, her work (with her collaborators) is set within the Standard Model of cosmology. An article submitted on 11 December 2017 is an examination of the “perturbative inflaton decay to SM fermions.” My hypothesis is that all this work will define an aspect of the natural inflation from the Planck base units somewhere within the first 67 notations. None of the work currently done within the confines of the Standard Model will be lost. It will all find a place within a notation of the quiet expansion. My hope is that a scholar of their stature will break the lock that big bang cosmology has had on our creativity.

13 The simple equation for light. Line 10 within the horizontally-scrolled chart is still quite rough, but when pondered just a bit, the scaling of both the Planck Length and Planck Time will require three-to-four doublings to shift within a base-10 cycle. There will be a natural variable that will expand and contract along all 202 notations. That is evidenced even within this rough draft of line 10. I believe that “Line 10” of the horizontal chart has much more to reveal to us. -BEC

14 Grounding String Theory. I can hear an old friend, Patricio Anibal Letelier Sotomayor, (1943-2011), react almost like he did in 1974. He was the first person I knew who believed in string theory and worked hard to ground it to the rest of physics. He would say to me with a smile, “No way. It has nothing to do with infinity.” But now, after more than 40 years within academic turbulence, he might be more inclined to say today, “…let’s take a look.”

15 Edward Witten, IAS.  Letters to a leading thinker of an intellectual enterprise adrift in the universe.  I stopped my formal academic work in 1980. A lot has happened in these intervening years. In 1980, after eight years of going in circles around the Einstein-Podolsy-Rosen thought formula of 1935, and Bell’s inequality equations, it was time to make a living. Today, to attempt to fill in the holes, I read and then write to those scholars who I have adopted as my de facto online teachers.  Of course, probably to his chagrin, the highly-esteemed Prof. Dr. Edward Witten of the Institute for Advanced Studies (IAS) based in Princeton, New Jersey,  is among them.

16 The Langlands Program. Also, at the institute is Robert Langlands.  His programs command global attention, yet for many, his programs are untethered as well.

More notes from the Editor: The first attempt to analyze the Planck units across the 202 notations was Measuring An Expanding Universe Using Planck Units.
The five key assumptions of this website: https://81018.com/opening/

Key documents that were homepages:

October 12: What would you do with this model of the universe?
October 1: The first 64 notations out of the 202
September 28: An Open letter about nature of light
September 20: “Gravity, Oh Gravity… Why Such Gravity?”
September 19: On Validating The Efficacy of our Model.
September 17: Open Letter (email) – Many similar notes are sent to scholars everyday.
September 14: Your critical review is encouraged.
September 12: Questions – Frequently Asked Questions.
September 5: Commonsense – It is not common and it is not a sense.
August 31: Reviews – You are invited to review an alternative to Big Bang Cosmology.
August 26: Problems – We all must become problem solvers.
August 5: On embracing the functions of our Universe
August 2: This Simple Scale of the Universe
July 23: Big Bang Theories Unnecessary In Light Of A Natural Inflation
July 12: An addendum to the Standard Models and for all algorithms
July 8: Compilations of concepts that could give rise to the 202 doublings
July 4: Revolutions: Foundational Concepts & First Principles

June 21: Planckspheres, dimensionless constants, doublings
May 18: Alternative to the Big Bang theory

April 30: Emergence & Growth from the first moment in time
April 21: More about emergence, growth, and imagination
April 18: Einstein’s Postulates

Join us. Challenge us. Help us. We need all the help we can get!

An excellent resource to translate any of our pages by its URL:

If you liked this page and website, please do not hesitate to follow us on Twitter or Linkedin.