# A Simple View Of The Universe “Behind  it  all  is  surely  an  idea  so simple,  so  beautiful,  that
when  we  grasp  it  — in a decade, a century, or a millennium —
we will all say to each other, how could it have been otherwise?”
– John Archibald Wheeler, 1911-2008, physicist

How Come the Quantum? from New Techniques and Ideas in Quantum Measurement Theory,
Annals of the New York Academy of Sciences, Vol. 480, Dec. 1986 (p.304–316), DOI:10.1111/j.1749-6632.1986.tb12434.x

## Is this simple mathematical-geometrical view of the Universe meaningful? Can we open a dialogue about the question?

##### by Bruce Camber, August 8, 2015  Updated: January 2018

Introduction:  I recognized the basic concept for our base-2 chart of  the universe is idiosyncratic. There are profound challenges, i.e. Planck Temperature and the order of dimensionless constants. There are more questions than answers. Although I do not want to waste your time, the reason for working in public is to get your insights, suggestions and comments. Links, footnotes, and endnotes are rough. This article builds upon earlier work (See the Index). Thank you. – BEC

In December 2011 we began our work on this very simple mathematical and geometric model of the universe; it was playfully dubbed, Big Board-little universe. We had started using the following parameters — the Planck base units, doublings of the Planck base units (an application of base-2 exponential notation), and the Platonic solids — in ways that created heretofore unobserved boundary conditions.

Our Three Initial Conditions: We started with a simple mathematical chart extending the Planck base units to the Observable Universe. We were studying basic geometries and nesting geometries.  Of course, given our simplicity, we used very simple logic.

1. A basic chart. There are just 202 base-2 exponential notations from the base Planck units of Length and Time to the Observable Universe and Age of the Universe respectively. In our chart these two base Planck units tracked together in informative ways and raised many questions. Here the operative function was multiplication by 2 while the two base Planck units were the known properties being multiplied. Notations took on a diversity of names depending on the functional qualities we were observing. A notation could be a cluster, domain, doubling, group, layer, set and/or step. The known universe was defined from about the 65th notation to the 201st-to-202nd doublings. A largely-undefined, very small-scale part of the universe was given a simple geometric and mathematical structure from the 1st to 65th doubling.

Is it significant?

2. Geometries. We imputed a pervasive, simple geometry throughout the universe. This project started within our high school geometry classes by going inside the simple tetrahedron by dividing the edges by 2 and by connecting those six new vertices. We could see four half-sized tetrahedrons in each corner and an octahedron perfectly in the middle. We then went inside the octahedron; there we found six half-sized octahedrons in each corner and a tetrahedron within each face. Our geometry classes were exploring the question, “How far within could we go by continuously dividing by 2 each tetrahedral-octahedral layer?” Then we asked, “How far out can we go by continuously doubling what we had?” With just these two Platonic solids, we could tile and tessellate each layer and between layers or doublings throughout the entire model. We learned about the limits in both directions and we have begun learning about this progression called base-2 exponential notation.

Our initial structures were all three-dimensional. When we found many two-dimensional plates across all the notations, coherence throughout the universe seemed possible.

The cross-notational plates were quickly recognized within nature. The one with just hexagons was an easy analogue of graphene. Within manifold geometries, the analogue would be to fullerenes.

Although there is no evidence that these analogical constructions exist within every layer, we imputed, hypostatized, or hypothesized that in some manner of speaking, such analogues do exist, especially within the first 60 doublings. We could then ask the question, “Given this ubiquitous, four-dimensional web (continuum, matrix, grid, aether), why does the universe work in the manner that it does?” In looking for answers, we have begun to see a means to attract, relate, bind, break or repel constructions within each, and between each, of the 201+ layers.

3. Logic. Our current chart redefines the continuity function to start with the infinitesimally small measurements, the base Planck units, and go out to their largest possible measurements using the Observable Universe and the Age of the Universe as the primary outer limits. Though imputed, this continuity function became our first principle for order in the universe yet it took a period of contemplation of the Big Board-little universe charts and images to begin to see the universe as a natural container for space and time.

As a container with a definitive beginning and current limits, the weight of logic seems to favor the conclusion that the universe is finite. That quickly raises questions about the infinite, such as, “If it is not defined by space and time, how is it defined?”

Within the tilings and tessellations of our pervasive-but-simple geometries and with our base-2 expansion from the base Planck units, we began finding an extraordinary diversity of possible symmetries and potential relations. We asked, “Could symmetry-making and symmetry-breaking through time be the basis for all dynamics? Could the illusive harmony be a perfection of those symmetries within a moment in time?” Unto itself, this logic seemed to become its own system of value and for valuations.” Perhaps the very nature of space and time is derivative; and order, relations, and dynamics and their three functional qualities — continuity, symmetry and harmony — somehow constitute the infinite and are infinite.”

This simple logic became an important building block to postulate our first principles. Our charts had become a model of the known and a largely-unknown, infinitesimally-small universe.

### Who? What? Why? When? Where? How?

4. History. This highly-integrated view of the universe must now be tested within the history of logic, mathematics, philosophy and physics. If this embryonic model is to have a place within the work of scholars, it must be critically analyzed. And, we know it has a long way to go before it earns such a place within scholarship. It must address very basic related questions about duality, finite and infinite sets, group theory, set theory, then advanced mathematical concepts that seem to be necessarily related like advanced combinatorics, matroids, amplituhedrons, and the Buckingham pi theorem. Like breadcrumbs, these topics will be followed up in the near future.

We are still within a very young and naive stage in our development and there are many very-very basic questions to explore:

• Who are the players — the scientists and mathematicians — who are experts within this small-scale domain?
• What are the “somethings” that are doubling within each notation?
• Why have these first 65-or-so notations been declared irrelevant by academics? Why haven’t the philosophers and brain-mind scholars explored the possibility that this continuum is the domain of the mind and values?
• When does simple logic and simplicity itself override experimental data?
• Where are the indicators that there is a domain that gives rise to gluons, hadrons, and the rest of the particle zoo?
• How do the doublings of space and time work to become the container within which those “somethings” begin to expand? Could those somethings best be defined by causal set theory, pi, the dimensionless constants, symmetry making, and perfected states?
• Does the Michaelson-Morley experiment provide insights from their historic quest to define the aether?
• Does this small-scale domain have anything to do with the continuum (Cyclic Conformal Cosmology) that was proposed by Roger Penrose of Oxford?
• Is it the matrix or grid that Frank Wilczek (MIT) delineates? Why? How?
• Could this small-scale universe be all of the above?
• Thinking about CERN and their current research from quarks to gluons, how does this small-scale universe work in such a manner to give rise to the impeccable successes of the Gauge Theory and Standard Model (including confirmation of tetraquarks and pentaquarks) as well as the standard model in cosmology (Lambda CDM)?
• Might this small-scale domain be the basis for homogeneity and isotropy in the universe? How do dimensional analysis and dimensional homogeneity apply?
• Might this domain be the basis of fundamental interactions giving rise to dark matter and dark energy?

These are some of the subjects (or objects) that occupy our attention and focus our time. “Let’s go over the details just one more time to attempt to learn how this model provides new footings and foundations that could give rise to some of our current perceptions and accepted models and theories.”

### Calculations-Measurements-Observations

5. Starting point or domain or … The key question is, “What is being measured by the doubling of each Planck base unit?” Something is being doubled within each notation of those five columns and 202 notations. Although the Planck base units are at a point some call a singularity and others, the Void, we now ask, “What happens when each is doubled? It is hardly a singularity or Void. What is manifest that doubles?” …only natural units? These are always based solely on universal dimensionless physical constants. But, all of them? Some of them? If so, which come into play and when do they come into play and why do they come into play?

Frank Wilczek. There are many books and articles about these constants, however, our primary reference is the 2006 article by Tegmark, Aguirre, Rees, Wilczek (TARW), “Dimensionless constants, cosmology and other dark matters” where they identify 31 dimensionless physical constants (PDF). The Planck Length (space) and Planck Time are two of their 31.

Once we have begun to understand the TARW conceptual frame of reference, we will attempt to take on the other 104 dimensionless constants defined within Wikipedia and the 300+ defined by the National Institute for Standards & Technology (NIST).

Our short-term work is to begin to understand the published works of an expert with each of these constants. Perhaps we will begin to see how our two base units create a nondimensionalized plenum and vinculum so an “archetype” of mass(kg) and electric charge (q) begin to manifest and we begin to discern how the parameterizing functions of the Planck constant (h) including the speed of light in vacuum (c), the gravitational constant (G), the electric constant (ε0) and the elementary charge (e) as each comes into play. We assume somewhere along our progression of doublings, the fine-structure constant (α) will present itself as will all the other dimensionless constants.

What is manifest? First, we have the actual calculations by Max Planck for length, time, mass and electric charge. Questions abound. “How do these manifest? Though infinitesimal, is there a manifestation of something?”

Our first assumption is that the “somethings” could be either simple vertices or what are known as point-free vertices. Part of our on-going study, we are told by Freeman Dyson that we should be using dimensional analysis and scaling laws to count the vertices within base-2 exponential notation; thus, we should be multiplying the number of vertices by 8 with each doubling. If so, there could be eight vertices within the first or second doubling.

With the second doubling we have the simple calculations — multiplying by 2 — of base Planck units of length, time, mass and electric charge. Then we have the scaling number or 64 vertices.

The first twenty doublings open our analysis. The first eight vertices constitute the first chapter of the story. Theoretically or conceptually, here is the first abiding step to construct and sustain our little universe. Here we will start our analysis with the tools of causal set theory, cubic close packing, Pi, the dimensionless constants, and a perfected state with continuity, symmetry, and an infinitesimally short moment of harmony.

Then the story becomes increasingly complex with each doubling.

 Notations: Doubling: Scaling Vertices* (units)(zeroes): 0 0 0 1 2 8 2 4 64 3 8 512 4 16 4096 (thousand) (3) 5 32 32,768 6 64 262,144 7 138 2,097,152 (million) (6) 8 256 16,777,216 9 512 134,217,728 10 1024 1,073,741,824 (billion) (9) 11 2048 8,589,934,592 12 4096 68,719,476,736 13 8192 549,755,813,888 14 16,384 4,398,046,511,104 (trillion) (12) 15 32,768 35,184,372,088,832 16 65,536 281,474,976,710,656 17 131,072 2,251,799,813,685,248 (quadrillion) (15) 18 262,144 18,014,398,509,481,984 19 524,288 144,115,188,075,855,872 20 1,048,576 1,152,921,504,606,846,976 (quintillion) (18)