Non-repeating, Never-ending Uniqueness


From order to chaos to order again, all built into this universe

Thomas Jefferson and the framers of the US Declaration of Independence captured a deep-seated truth about the very nature of the universe. They had intellectually and emotionally understood the importance of human freedom so they made a guarantee that all people should be free from bondage and enslavement. In that statement that had also intuited that such freedom is built-into the very design of the universe. The free will of the person runs deep.

Let’s see what we can learn about the design of the universe.

The most basic, simple object is the sphere. Deep within the sphere are the original non-repeating never-ending numbers. One might say, Pi“Here are the first openings, the initial pathways, between the finite and infinite.”

Here the perfect continuity of the infinite gives way to the Pi-unrolled-720.gifopenness, an inexplicable random-order, apparently never-ending, number generator of the most simple three-dimensional object in the universe. It is complex, but predictable. Built right into the most basic shape is
an open number, pi (π).  It seems to scream at us,
“Pay attention to the ratios. This number is irrational!
The ratio is the dynamic reality that captures the essence.”

Sphere to tetrahedron-octahedron couplet
Click on the spheres for more.

When the spheres are stacked and, as you can see demonstrated on the right, that stacking creates the forms for straight lines (lattices), triangles, tetrahedrons and octahedrons that perfectly enclose space. With just the tetrahedron and octahedron, you can tile the universe.

We started with the determinacy of the sphere, going within  to the indeterminacy within its inherent nature, and then going out, stacking multiple spheres, the result is a new  order of relations, spheres to the perfections within the tetrahedral-octahedral couplet.

Indeterminacy (non-repeating, apparently never-ending) is also built into other layers of the fabric of the universe.  There are constants and universals that define some of the most basic relations between things. Known as the fundamental physical constants such as the speed of light c, vacuum permittivity ε0, Planck constant h,  the gravitational constant G, the fine structure constant, αs, the coupling constant for the strong force and so many more are all pathways between the finite and infinite, from the perfect to the imperfect, from the unchangeable to the changing.

Yes, chaos is built into the universe in other very basic ways, yet it is time to stop and see what is going in in the world of science and research.  The big bang theory has been part of the culture since the 1920s.  It has been the dominant theory since 1975.  It allows an island of fundamental constants known as the Planck base units to rather meaninglessly drift in the ether.  Big Bang scholarship starts well beyond the Planck base units; and, until December 2011, there had been no path created between those numbers and our physical realities defined by the Standard Model.

The first path was just along the Planck Length. It was a precarious climb and very few chose to follow.  It wasn’t until a path up from the Planck Time was cut alongside the Planck Length did it seem like more than a fool’s dream.  When cuts were made for mass, charge, and temperature, it seemed a bit more ordered, but still quite idiosyncratic.

Today, there are plans to build super highways up from the Planck base units. Others are getting the vision that it just might be possible, a little like building a super highway over the Darién Gap, an impenetrable, deep rain forest between Panama and Columbia or the 51 miles across the Bering Strait (about 82 kilometres wide at its narrowest point) between Russia and the USA.

As unlikely and difficult as these things seem, it takes a vision to open the way.

In process…. More is on the way.  July 23, 2016

Thanks to Dee Hock and his friend, Alistair Fraser of New Zealand.

Does this quiet expansion challenge the big bang?

Although our naive answer seems the answer is “Yes,” surely more reflection is required. Here is where we are now (most recent postings first):

  1. How did it all begin? And, what does it mean? (June 2016)
  2. Quiet Expansion of the Universe (June 2016)
  3. Notations 1-204: A most-simple, integrated model of the universe. This project began in 2011. This page uses horizontal scrolling (a test started in April 2016) to provide a quick overview to all the numbers.
  4. Planck base units from 0 at the beginning to today:


Can you discern at least one unique formula within the 201+ notations? There are many to develop.

The challenge:  Come up with a formula based on the array of numbers within  the Big Board – little universe Project.  But, please be aware that all of the charts are now being fine tuned based on our recent work to develop a very large horizontal board with all five Planck base units in the progression from Planck Time to the Age of the Universe in just over 200 notations.

The horizontal board was initiated on April 10 and posted for insiders on April 25th. Those of you among my LinkedIn family are considered “insiders” (and you are most welcomed to join us).

We have been developing what we are increasingly thinking could become an alternative to the Big Bang theory. That’s a ridiculous statement to make, but now with well-over four years of looking at these numbers, it seems that our little model could have a place in the universe of academia. It may go through several versions, even transformations, but that struggle will be well worth the time and effort. There is real information within this “little” nascent model.

My special challenge to graduate students and post-docs. Take the five basic Planck units at one of the notations between 1 and 201 — and work out new formulas integrating any and all formulas used within the big bang theory. There is a place for every formula within at least one notation along this scale of the universe.

If nothing else, this project should get us thinking about number theory, the finite-infinite relation, the discrete-and-finite nature of space and time,  and the correspondence between the five Planck base units, space-time-mass-energy-temperature.

The very first  formula that I developed on May 1.  It is simple and it will be further developed. The next formula that we receive that is mathematically coherent will be given the designation: Formula #2.  Each subsequent formula will be numbered accordingly.  Each will become that student-or-professor’s formula and we will track the continued development and implications of each formula well-beyond this early-stage development and hopefully well-into an academic-development phase of The Big Board-little universe Project.

Thank you.   – Bruce 

PS.  Send your formula to me at camber (at)

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Could this fledgling outline of a model become the basis of a working model of the universe?

Initiated: April 16, 2016  Work-In-Progress: July  2016

Abstract: An alternative to the Big Bang theory originates from the studies of a high school geometry class of combinatorial geometries and base-2 exponential notation from the Planck base units, especially Planck Time, to the current time and Age of the Universe. Preliminary studies of five columns and 200+ notations begin to address key questions raised about the relation between the Standard Model of Particle Physics (SMPP) and the Standard Model of Cosmology (SMC). The simple doubling logic echoes bifurcation theory, imputes homogeneity and isotropy, and provides clues about the deeper workings of  renormalization and universality. The first 67 notations, a very different small-scale universe, provides the essential foundations for this model. At the 67th notation the  Planck Time doubling is still a very, very short duration: 1.59126 ×10−23 seconds. At the 134th notation it is just two-one thousandths of a second (from the first moment of creation) and the model already provides a deep infrastructure for life. Each of these notations might be considered an archetypal layer, the foundations for our Human Scale universe which must itself also be archetypal. It will take just another 67 more notations to bring us to this day.  From notation 134 to 201, traditionally referred to as the Large-Scale Universe, all of human life and our earth and solar systems evolved in that last notation, #201.  We hope to explain this model’s voracious appetite for information yet why its simplicity may give rise to the potential veracity as a model.

1. Key Questions

This article is built around five key questions to take us into the rows and columns of numbers within this model.

  • How can this model explain an integrated universe that includes everything, everywhere, and throughout all time?
  • Can such a simple model account for the complexity of the Standard Model of Particle Physics (SMPP)?
  • Could this model build bridges that create continuity from that small-scale universe to the large-scale universe in such a way to account for dark matter, dark energy, and inflation?
  • In what ways could the model account for quantum mechanics (SMPP) and gravitational forces within Condensed Matter Physics (CMP)?
  • Does this infrastructure give rise to homogeneity, isotropy, universality, and renormalization?

Let us take each question, one at a time.

2. How can this model possibly explain an integrated universe that includes everything, everywhere, and throughout all time?

There are now two charts that show the progression of tabulations from the Planck base units.  Our very  first in December 2011 only involved the Planck Length. In February 2015 all five of the Planck base units were tabulated together.  We now study up and down each of the five columns as well as across those columns.  We are also now studying the number of simple vertices and scaling vertices within the small-scale universe.  The simple logic evolves into complexity and a very different view of the universe.

The five Planck base units are time, length (space), mass, charge, and temperature. First, notice that Planck Temperature starts in the current notation and is halved with each successive notation down to the other Planck base units.At the Planck singularity, we assume 0º Kelvin.  On the first notation it jumps to 4.4084867×10-27 Kelvin.

You may notice that the first doubling of the Planck Length is repeated.  There are too few vertices for projective geometry, but there are enough for a pointfree vertex to establish a two-dimensional plane that on the next doubling becomes a three-dimensional sphere.

We impute that  infinity is a perfection and the most simple perfections  are order which is continuity, and relations which is symmetry.  Simple conceptual numbering such that the first sequence is necessarily related to the second and all subsequent sequences is continuity.  To build a universe, sequences interact with sequences forming relations that are best described as symmetries.

The computation of Planck Time…

3.  Could  a more simple model or theory account for the complexity of the SMPP model? Check the number of vertices by the 20th notation.  The September 2012 version of that chart begins with the simple doubling of the Planck Length to the Observable Universe.  The most instructive tabulations only happened after Freeman Dyson said, “Since space has three dimensions, the number of points goes up by a factor eight,* not two, when you double the scale.” As a result, on the horizontally-scrolled chart, there is a row labelled, the Scaling Vertices (×8).  Base-8 is not as fast as base-10, but it certainly is dramatic.  By the sixth notation base-2 has reached 16 pointfree vertices while base-8 is up to 32,768.

Much more to come….