Redefine Our Universe With Three Conceptual Steps

What can we know about our universe? Is it necessarily mathematical and geometrical?

Re-examine Big Bang Enigmas



Does everything start simple before it becomes complex?

In order to begin to explore a natural, highly-integrated mathematical view of the universe, it seems that two of our major conceptual orientations need to be set aside: (1) absolute space and time from Isaac Newton (1643-1727) and (2) the infinitely-hot start of the universe, ostensibly big bang cosmology, as represented by Stephen Hawking (1942-2018).

Our alternative is a natural inflation defined from Planck’s base units to the age-and-size of the universe in 202 base-2 notations or doublings that are always active and are progressively building on each other. Our definitions for space and time are Max Planck’s formulas 1 from 1899 whereby both are quantized, discrete and finite.


Arguments about finite space and time and the finite-infinite relation are part of the earliest recordings of our history. And, those arguments continue today without abatement. Possible answers are still debated with strong opinions on the opposing sides.2

We backed into our understanding slowly by adopting three very different concepts and orientations and, if true, these three may begin to open a new door to explore our universe in ways heretofore undocumented.

The Infinitesimally Small: The Planck base units. We have found no other references to a cosmology whereby the universe is fundamentally defined by applying base-2 exponentiation or doublings to the Planck base units of time, length, mass and charge. These units become the standard units of measurement to define 202 base-2 notations that extend to the age and the size, and the mass and the charge of the universe.

To lift up or debunk these 202 notations is the goal of this project.

Our most naive application of that concept was when we started in December 2011 as a group of mathematics (geometry) teachers and students in a New Orleans high school. Though similar to the 1957 work of Kees Boeke using base-10 (“…to scale of the universe in 40 jumps“), our 2011 group started with a geometry. We divided-by-2 the edges of the tetrahedron and octahedron to discover what we initially thought was a Zeno-like progression. It isn’t. There are limits!

Physical limits. We had discovered those limitations that Max Planck defined in 1899, particularly what is now known as Planck Length and Planck Time. In just 45 divisions we were among the size of particles within the atom. In another 67, we were among the two smallest Planck numbers. Then, to be consistent, we started with the Planck units and simply multiplied-by-2 and in 112 steps we were back to the approximate size of our classroom objects. In another 90 steps we were at the approximate size and age of the universe. We discovered that it took just 202 base-2 doublings or notations 3 to encapsulate the universe. It defined a natural inflation. And, it appears that it could provide a base platform for a grand unified theory of mathematics.

That is enough, yet this nascent model also encouraged questions about the finite-infinite relation and the very nature of infinity.

Early thoughts about cosmology

The Very Large Scale. Our initial introduction to these numbers was just with the Planck Length. We assumed that the first 64+ notations were just prior to the big bang and were defined by the Planck Epoch and the Grand Unification Epoch. The problem quickly became clear that the size, mass, and charge within our nascent model could not support a “big bang.” And there was no reason to think these processes required “infinitely hot.” We obviously needed more data. In 2014 we added a Planck Time progression alongside Planck Length; and then in 2015, we charted Planck Mass and Planck Charge progressions. These numbers described a natural inflation of the universe and our analysis and comparison with the big bang epochs 4 defied the logic of big bang cosmology.

We were challenged, “How do we reconcile these two vastly different models?” We rather slowly realized that there was no reconciliation, so we began to review the logic of our mathematics. We wrote for the advice of those scholars who had made this area of study their life’s work.

At that time, nobody analyzed our work. Nobody engaged its logic. Of course, it is naive; so here, we bring our work forward as logically and consistently as we can and request help from our scholars and scientists to interpret the data. Because we have viewed Max Planck’s formulas in rather unique ways, it should be straightforward to tell us where and how we have strayed from pure logic and math.

Three concepts, three questions:

  1. Basic Construct: Does simple math-and-logic work consistently everywhere for all times?
    Science believes our universe is homogeneous and isotropic but can not tell you why that is so. Doesn’t this simple math and natural inflation based on the progressive geometries of the tetrahedron and octahedron provide a construct or framework for an initial answer? Does the simple multiplying and dividing-by-2 provide another answer? Though we concluded that these two progressions provided new insights to old questions, we did not want to conclude too-too much so we have always sought the feedback of experts.
    See footnotes 1 through 4.
  2. Basic Shape: What could possibly be the building block at the Planck scale?
    We decided that the most-simple, ubiquitous-but-mysterious building block is the sphere.5 Pi is deep in the heart of most of Planck equations and definitions of dimensionless constants. As a result, we hypothesized that the first notation, perhaps the first, second and third notations, results in an endless generation of spheres. This is the face of the four Planck base units, plus light and the other dimensionless constants involved in the definition of those Planck units. Perhaps not a crystalline clear picture of what is happening at this finite-infinite transformation, it is the best we can do today. Some have call these spheres, “Planck spheres.” That seems appropriate so we have adopted that nomenclature. It seems that these planckspheres do not come “out of nothing” but out of that which we do not define as finite. It could be part of a definition of a finite-infinite bridge. It may also be how the infinite is expressed within the finite without becoming finite.
  3. Basic Dynamics: What is the the most fundamental doubling mechanism?
    Cubic-close packing 6 is an inherent doubling function whereby geometric structures, particularly the tetrahedron and octahedron, emerge. The thrust 7 to inflate this doubling may well come from Planck Charge, light, and the never-ending, never-repeating numbers of pi and the dimensionless constants. It is instructive to follow any one of the numbers on our horizontally-scrolled chart where the logic flow can be analyzed. 8

Basic functions at the Planck scale

These rather different, simple concepts are possibly enough to start a dialogue. We backed into this model. We claim no genius or depth of knowledge regarding the issues involved. There are open questions that are raised, but at least these first three steps along this path have been presented and our standing request of our readers is to tell us where and how our logic fails and that invitation is open to everyone including you.

Our Challenge: Research baseline questions

  • Who has the best insights about the very nature of the Planck units? We are exploring the work of Paul Steinhardt (ArXiv), Ed Witten, Andrei Linde, Andreas Albrecht, and others.
  • What is the role of quantum physics in cosmology? …isotropy? …homogeneity? DAMTP
  • Does space-and-time give rise to quantum effects or is space-time a quantum effect?
  • Do the Planck units have a quantum origin or do they originate from light, the dimensionless constants, and each other?
  • Do the 202 base-2 doublings from Planck base units to the age and size of the universe constitute the infrastructure for a real cosmology?
  • How do quantum effects play a key role in controlling the rate-and-end of inflation?
  • What about all the successes of general relativity?
  • How do you explain the stages meticulously described by Einstein gravity (and in agreement with observations) when the universe is not inflating?”
Please note: The footnotes are still being worked-and-reworked.

Endnotes, Footnotes, References & Resources:

1 Max Planck’s formulas. Max Planck’s simple formula for light is part of his pre-definition of Planck Time. I don’t think anybody would dispute its basic logic, but its meaning is not straightforward. Has anybody truly answered the question, “What is light?” Of course, the first 93 doublings are below the visible spectrum (Notations 94 and 95). Notwithstanding, is there an inherent quality of light that presumably remains the same throughout all 202 notations? Certainly the electromagnetic spectrum provides a sense of the characteristics of light from gamma waves, to x-rays to ultraviolent on the infinitesimal side and then from infrared to microwave to radio waves within the human-scale and large-scale side of the spectrum. Yet, there is so much more going on here.

To date, our questions are also focused on the nature of the never-ending, never-repeating dimensionless constants. Do these define a bridge between the finite and infinite?

A key idea. Consider the nature of time. It seems that our Universe Clock, in light of this model, suggests that every second is active and continues to effect the content, the quality, and the substance of this universe. That time doesn’t stand still. It is always changing and it is always the the Now.

2 Strong opinions on opposing sides. We try to avoid religious and theological discussions per se by redefining the very nature of the infinite as continuity, symmetry, and harmony as evidenced with those words highlighted at the top of every homepage. Though several of our homepages extend this insight, perhaps it would be helpful if people could just lighten up a little.

3 The 202 doublings enclose a trifecta to define the universe: (1) encapsulate all the space and time of the universe, (2) define a natural inflation, and (3) provide a base platform for a grand unified theory of mathematics. The result is that space and time are finite, the universe is totally interconnected and integrated, and all mathematics is likewise. The reasons for the homogeneity and isotropy of the universe become self-evident. Our sense of time becomes the Now.

4 Big bang cosmology versus the Quiet Expansion: There are seventeen epochs defined by big bang cosmology. Each is superficially compared to the notations of our Quiet Expansion, also known as a natural inflation. Often just one of the faces of each big bang epoch is used to position the Quiet Expansion alongside it. Eventually all four faces will be used and perhaps the known failures of big bang cosmology can be addressed in new ways.

5 The Sphere: Within this infinitesimally small domain, the sphere becomes known as the Plancksphere and it is being extruded from the finite-infinite relation as a constant stream of spheres, providing no less than 64 doublings up into the domain of particle physics.

It would seem these spheres are the basis of string theory. Clumping and stacking, defining space and time and mass and charge, then come the geometries and infinitesimal form, structure, relations, and systems. This is emergence.

6 Doublings: We were in search of the gritty visualization that is not given within descriptive words like base-2 exponential notation, Euler’s perfect number, fractal division and/or bifurcation theory. We all need a visual reference whereby physical processes demonstrate the doubling phenomena that is the natural inflation of this universe. We found it in 2016 within a visualization of cannonball stacking by none other than Johannes Kepler.

Here is our first reference to it:

7 Thrust: I have always told myself, “You start small and build on it day by day and finally it progresses and you have something.” Nothing just explodes into beingness. Though an older article now, the focus on thrust will be continued throughout this study.

8 Logic: The numbers within our charts stretch our imaginations; there is no question about that. Yet, this stretching feels productive, like it might lead somewhere special. Our first article is here:

Our large-scale, notation by notation, effort has been opened up here:

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

Which concept is strongest? Which is weakest?


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