Some of the more far-reaching implications of the Big Board-little universe model

Introduction.  The Big Board-little universe Project uses base-2 exponential notation from the singularity of the Planck base units going out to this present time, Right Now, to encapsulate everything, everywhere, throughout all time1. Though seemingly a bit of  an overstatement, the simple mathematics and logic appear to corroborate such a conclusion. The implications of this fledgling model seem rather far-reaching so five are presented for the discerning analysis and critical review of scholars and thinkers.

Some of the more far-reaching implications of the Big Board-little universe model:

  •  This model begs the question about the finite-infinite relation.  If space and time are derivative, finite, quantized and discrete, then what is infinite? Our working answer is continuity which creates order, symmetries which create relations, and harmonies (multiple symmetries working together) which create dynamics. These are the inherent qualities that define the infinite for science.2
  • There appears to be an ethical bias to the universe. Continuity-order, symmetry-relations, and harmony-dynamics also begin to define a valuation system whereby every notation at every moment has a perceived and dynamic value.3
  • Each notation defines an element of the current universe. Even though time is derivative, it still defines a duration within a single notation. Even though space is derivative, it still defines a length within which particular things have their beingness. In this model each notation has its own particular beingness. The entire universe actively appears to share this length (space) – time infrastructure within the small-scale universe.
  • The structure for homogeneity and isomorphism is defined within the small scale. It is also the bridge between the finite and infinite so renormalization works in quantum electrodynamics and universality works throughout physics on every scale.4
  • This model appears to trifurcate nature. These three seemingly natural domains of this model of the universe appear to be episodic:
    (1) The small scale from notation 1-to-67 could generally be described as ontology and each notation just might manifest again within the human scale and then again within the large scale.
    (2) Perhaps the human scale from notations 67 to 134 could be understood as the domain for epistemology. In some manner of speaking all 67 manifest in the notation for the current time.
    (3) The large scale from notation 134 to 201 is currently considered the domain for cosmology. It begins when the duration (or speed) is less than one second (see notations 142 to 143). Within notation 200 (possibly 201) is the current time.  Its duration is approximately 10.8 billion years.  The duration at notation 134 is within a thousandth of a second.

    Of course, each duration for each notation gets increasingly short as we approach the Planck Time. The duration at notation 67 is 10-to-the-negative-23 seconds (10-23).  Notation 67 is approximately the Planck Length multiple where fermions and protons appear.  There will be many adjustments of these numbers as others help to fine-tune the model.5

All people and things appear to be trifurcated.

One might hypothesize or hypostatize that from the small-scale universe we get our being. Systems are imputed between the 50th and 60th notation; and within systems, the human mind has also been imputed have notations within which to be.

From the human-scale we get our knowing.  Carl Jung called these archetypes.  A special vocabulary will emerge for this part of our self-definition.

Within the Now, this moment, today, there is an integration as a thing, an entity.  All human history, all civilization is within the 200th notation.  Just as an aside, if time travel were to become possible, it will be as an observer. Interactions would also require trifurcating, i.e. simultaneously entering the space and duration of the being and knowing of any given moment in time.

For more, consider these pages:

  1. The Big Board-little universe Project
  2. Top Ten Reasons Top Ten Reasons to give up those little worldviews for a much bigger and more inclusive UniverseView. These are the inherent qualities that define the infinite for science.
  3. Every moment has a perceived and dynamic value.
  4. An analysis of numbers
  5. A Simple View Of The Universe

Sheldon Glashow

On Fri, Oct 19, 2012 at 7:19 PM, Bruce Camber
Bruce Camber wrote:

Dear Prof. Dr. Glashow:

Just over 34 years ago I contacted you regarding a special project at MIT called, “An architecture for integrative systems.”  It was a display project in the main rotunda just off Massachusetts Avenue. It borrowed Erwin Schrodinger’s title from his much earlier work, “What is life?”  Seventy-seven leading, living scholars participated and you were one of them.

We are taking that old product and re-purposing it online within a very similar framework — Small Scale, Human Scale, Large Scale — however, we are using base-2 exponential notation from the Planck Length to the edges of the observable universe which gives us over 201 ordered steps in which to context information.  By assuming nested geometries at each doubling, it seems that we will have an inherent structure for analogous or metaphorical connection-making.

But before we go to far, I would like to re-engage you and ask for your advice:
1.   If the Planck Length is a dimensionful number representing a singularity or a point, can we multiply it by 2 and assume two points? ..multiply it again and assume 4, then 8, 16, 32 and on up to 1024 by the 10th doubling?
2.   Can we assume nested geometries throughout?
3.   We will use the same infrastructure as used by Wikipedia to build it out, so owner’s of information can readily edit and update content. Is there any particular recent work to which you would want us to take note?

Thank you.

Most sincerely,

Bruce Camber
Small Business School, a television series on PBS stations

PS.  A few simple web pages provide more background:
Our working model:

What Did We Ever Do Without Our Universe View?

1957: The Beginnings of a somewhat Integrated Universe View

In 1957 Kees Boeke’s book, Cosmic Vision, The Universe in 40 Jumps, was published; it was the first integrated view of the known universe. He could have but did not engage the Planck base units. He could have, but did not consider any geometric calculations. Yet, he did get the attention of prominent scientists including Nobel-laureate, Arthur Compton. Thereafter, the Eames film, the Phylis and Philip Morrison book, Powers of Ten, the IMAX (Smithsonian) movie (guide), and the Huang’s scale of the universe opened this conceptual door for anyone who chose to walk through it.  Anyone could begin to have an integrated view using base-10 notation of the entire universe. It was a fundamental paradigm shift; all the attention given to it has been justified.

Most of the world’s people live within what we might call, their OwnView.  Even though subjective and often quite naïve, the elitists and the solipsistic and narcissistic among us, lift up that view as the best view, the only view, and/or the right view.

If and when we start to grow up, spread our wings and begin to explore beyond our horizons, we develop an objective view of the world.  As we integrate more and more facets of our subjective and objective views, it begins to qualify as a WorldView (in the spirit of the old Weltanschauung).

In light of Boeke’s work, the next step for all of us is to bring whatever WorldView we have, and see how it fits and works within a view of the entire universe. Kees Boeke’s work is historically the very first UniverseView. Although Boeke only had 40 jumps and used base-10 exponential notation, it is still the first systematic view of the entire Universe.

2011:  A Second Universe View Emerges From Another High School

A high school geometry class just up river from the French Quarter of New Orleans developed what appears to be the second systematic UniverseView.  It is quite a bit more granular than Boeke’s work and it originated from the students’ work with simple embedded and nested geometries. Using base-2 exponential notation this  group emerged with about 202+ doublings, layers, notations, or steps from the Planck Length  to the Observable Universe.  Eventually beside each length, the calculations from the Planck Time out to the Age of the Universe were added.

This fully-integrated UniverseView first emerged in December 2011 and was officially dubbed, “Big Board – little universe.” One of the initial boards was over eight feet high and the second and third generations were around 60 inches high.  The entire universe, mathematically-and-geometrically related within 200 or so notations, seemed to bring the universe down to a manageable size!

Now, what do we do with it?

The first thought was that this UniverseView with its 200+ notations could be a good container for Science-Technology-Engineering-Mathematics (STEM) education.  It puts everything in the known universe within a simple ordering system.  Then, in January 2012, in the process of trying to find scholarly references to understand the foundations of their work, the students and their teachers discovered Kees Boeke.  In so many ways, it was a vindication — “Somebody had been here before us.”  Yet, even with all the fanfare around Boeke’s work, not too much was done to extract meaning from that model.

The base-2 model is quite different. It has simple geometries and a more granular mathematics.  The students and teachers thought this ordering system might help to answer those historic queries by Immanuel Kant about (1) who we are, (2) why we are, (3) where we are going, and (4)  the meaning and value of life.

Given this model has a starting point and an end point, the students and teachers opted to see the universe as finite.  Always encouraging students to go deeper in their understanding of mathematics, their teacher, Bruce Camber, commented To engage the Infinite it appears that we hold the objective and subjective in a creative balance and that balance is called geometry, calculus and algebra through which we can more fully discover relations.”

Boeke’s base-10 work has an important role in history.  It gave the human family a starting point to see an ordered universe.  The base-2 model takes the next step. Instead of just adding or subtracting zeroes, it adds 3.333 times more steps or doublings. It provides more data to explore the simplest continuities, relations and dynamics within and between each notation.  Base-2 is the heart and spirit of cellular division, chemical bonding, complexification (1 & 2), and bifurcation.

Perhaps it is here that the academic community might begin to create a truly relational, integrated and functional UniverseView. Surely it is here that we find the rough-and-tumble within science.

So, although base-2 UniverseView is the second UniverseView, it seems to hold some promise.  And though these are preliminary models,  just a crack in the doorway, what a sweet and simple opening it is.  Perhaps Kepler would be proud.

This high school group is now just starting to discover the work of  real-and-graciously-open scholars.  With the help of this larger academic community, our work just might  somehow capture the spirit of one of the world great physicists throughout history, John Wheeler, when he said, “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? How could we have been so stupid for so long?” 


What is space? What is time?

A working draft. On a long approach to a first draft.
Initiated:  Wednesday, 25 November 2015
Last Update:  Monday, 30 November 2015

Space and time: Using base-2 exponential notation starting at the Planck Length and Planck Time renders the most remarkable fact:  there are somewhere just over 200 base-2 exponential notations from the smallest to the largest possible measurements of a length and from the beginning of time to this present moment.

It is a simple mathematical and logical calculation. The results seem quite impossible and rather illogical, but on its most simple surface, results are results.

Discrete, quantized, finite and derivative.  Within this simple construct of the universe, space and time appear to be discrete, quantized, finite and derivative.  Each notation creates a simple range of a size within which appropriate things manifest and take their place in the universe. In this initial view of this model, the nature of each space is uniquely defined by the other four Planck base units.

Each notation works across the five Planck base units as well as up and down each individual column.  To locate where we are today within this chart, we always must go to the very largest measurement of time which we might call the Now, or the present moment, or perhaps, just “today.” If it is best measured by what we call, today, then the gauge that measures time may simply be sleep and time is always a profoundly subjective experience.

Of course, with our atomic clocks that statement flies in the face of our current realities.

Also, we have been examining the common elements of our daily experiences within  the 67th to the 134 notations. Although we live in the current moment,  some essential aspect of our being exists within the scales of the human domain.  Our essence comes from within this Planck Length column within very definitive notations, yet our living and experiencing is always within the largest measurement of time currently discerned to be in either notation 200 or 201. At this point there is a question. There’ll be much more discussion about how notations are “added” together. and the meaning of discrete, quantized and finite.

Epistemology and ethics. Also, as we move forward with our analysis, it seems that this model suggests that to the degree that we are whole, intelligent and good may be measured by how aware we are of all the notations that make up who we are within any given moment in time.

So, we have found that there are no more than 202 areas (spaces or lengths) in all of creation, then what is time?  It would seem that each “time notation” is the simple range of speeds by which transactions take place within one of those areas.  And, just like length, there are no more than 202 transactional ranges of speed within the entire universe.

Of course, this is a very rough draft, a work in progress, seeking meaning.

This summary was initiated on Wednesday, November 25, 2015.  We will come back to it frequently to see if its logic holds and then to see if the logic can be extended to specific applications within the sciences, particularly the history of the measurement and interpretation of cosmic microwave background radiation (CMB) and the continued expansion of the universe.  Thank you.


Related articles:

On evoking higher order thinking from our students

by Cathy Boucvalt, a teacher at the Curtis School in Physics, Chemistry and Biology.

The concept of bringing math and science together and helping evoke thinking outside of the box, sadly, we don’t have too often in the classroom.

Our students are programmed to memorize, regurgitate, and proceed on with “learning” more.  Have we stopped them from actually dwelling and expanding on ideas without fear of being “stupid”?

Common Core, LEAP, and other current educational parameters are encouraging  educators to “teach to the test” rather than inspiring the young minds of our world.  We judge someone by their ACT, SAT, Standardized Tests, GRE, LSAT, MCAT, etc..

Let us all evoke higher order thinking from our students.

The Big Board – little universe  (BB-lu) uses base units (familiar term in middle school and above) and brings them to “life” in an understandable perspective. The Big Board – little universe,  in a quantifiable way, allows people to look at the most simple beginnings (the Planck base units) and logically expand out from there.

Could there possibly be any other model that actually explains so much in such simple terms?  I suspect not.  About   Home

On Developing A Rationale For A Working Model Of the Universe Based On A Quiet Expansion

Please note:  Reviewed,  January 14, 2016 at 1:01 AM GMT.

Abstract: Key embryonic insights from within high school geometry classes back in December 2011 are postulated as a most simple, logical, hypostatic structure of the universe, a base-2 progression from the Planck Length  to the Observable Universe. In September 2014 the naive question was asked, “Could the universe be based on a quiet expansion not a Big Bang?”  When the numbers from Planck Time to the Age of the Universe were added in December 2014, this concept of a quiet expansion seemed less speculative. In February 2015 the remaining Planck base units were added to the chart.  By August 2015 extensive questions were raised primary among them, “Can this chart be integrated with the Lambda-CDM model (the parameterized cosmological model)?” The immediate task of this paper is to explore those questions in light of the numbers at each doubling to help to discern reasons why this simple model warrants the attention of the academic community.

Simple facts, figures, and logic in search of a theory.  The chart with  five columns for each of the base Planck units and 204 notations down, 1020 boxes, provides real data to examine the logic flows both across and up-and-down.  The goal of this article is to examine no less than 10 boxes. Looking across would be 50 boxes; adding two or three boxes up and down would total over 150 boxes.  Ten percent should be enough to learn if a simple logic actually flows through the numbers.  If it does… well, perhaps we have a new science in the making.

201+ Notations Begin With The Planck Length.  The simple mathematical progression that rendered the 201+ base-2 exponential notations was the result of following embedded geometries going smaller and smaller until in the range of the Planck Length. Going in the other direction, larger and larger, was achieved by multiplying by 2 until in the range of the Observable Universe. The total, just over 201 doublings, could not be found within the writings of the academic community. The base-10 work done back in the 1957 by Kees Boeke and his high school classes in Holland was abundantly indexed; there were no references to a base-2 progression from the Planck Length to the Observable Universe, especially as a result of following embedded geometries within the tetrahedron and the primary octahedron within that tetrahedron.

Planck Time to the Age of the Universe is applied.  There is general scientific concurrence regarding the estimates of the age of the universe. That figure provides a better framework for the doublings of Planck Time,  from the beginning of time to this moment, right now, our current time, which always defines the endpoint.  Planck Time and Planck Length track together in informative ways. For example, the notation that defines one second is between 142nd notation (.6011 seconds) and the 143rd (1.2023 seconds).  The doublings of the Planck Length are 180,212.316 kilometers at Notation 142 and 360,424.632 kilometers at Notation 143. As one might have expected, the speed of light is confirmed in between the two at 299,792,458 meters for one second.  At this point in time the other three Planck base units have become quite large, larger than any common number within human experience.

This Quiet Expansion begins at the first doubling. Quite literally, there is no room for sound until out to the 108th doubling (the beginning of sound waves) and on out to the 119th (the full spectrum of sound ranges from Notation 108 to Notation 119).  There is something quite helpful within a visceral sense of the number and parameter.  Examining groups of numbers associated with a common human experience is more than helpful; it provides the infrastructure of logic.  Yet, there is no point where simple logic flows across all five Planck units. Yet, as demonstrated, it is quite informative when even two such numbers correspond.

For example, one of the very smallest notations with an experiential human equation is Notation 93 where observable light begins to manifest. Notation 101 is within the range of the thickness of human hair. This, of course, is where a large group within Planck Length and Planck Time correspond. This is the human scale universe. And, within that group there is one place where length and temperature correspond.

Planck Length and Planck Temperature. First, it was a leap of faith to hold to our working premise, “Everything starts simply” and to place the extremely hot Planck Temperature at the top of the chart.  That put a very common number between Notation 103 and 104 where the temperature has cooled to 98.6 degrees Fahrenheit.  Here we find among many other common things, the human egg cell. At Notation 105 the temperature has risen to 894 Kelvin or a very hot 1149.53° Fahrenheit and at Notation 102 it has dropped to a very cool –58° Fahrenehit.

Planck Mass. The very smallest notation with a common figure is the 31st doubling (Notation 31) where we find 103 pounds (46.74 kilograms). For many people, it is a key weight threshold signifying our coming of age, quickly approaching being  an adult. Within this doubling the other four figures are so small, it causes one to ponder. So much seems to be happening with each of these doubling, that 103 pounds encourages some speculation. How about this? Perhaps the 103 pounds is the sum total weight of this notation! At the top end of this column are the outrageously large numbers that come very close to estimates by some of the more speculative within the scientific community, especially if each number in this column is the sum total weight of that notation.  In some peculiar ways, this just may be a measurable concept.

The Human Scale Universe. Within the human and large scale universe, there are many familiar things within the Planck Length notations, yet the other Planck figures remain largely remote.

Planck Time. Although we cannot meaningfully perceive much smaller than a tenth of a second (Notation 140), in 2010 machines at the Max Born Institute in Berlin measured down to 100 attoseconds (Notation 87).  Perhaps each notation with the Planck Time column describes a range in which relations are defined. Some elements of that statement may be measurable.

What Is Is? If looked to discern any special logic, one’s conclusion might be that each notation, with its vast array of vertices and multiples of the Planck base units, define the terms and conditions by which that notation-qua-notation is.  That is, these numbers define the “isness” of the notation.

So, let us look in depth at one second between Notation 143 and 144. The total mass ranges from 2.4268×1034 kilograms to 4.8537×1034 kg. It defines a range, “no greater than twice that amount, and not less than half that amount.” In a similar manner, the total energy has a range, 2.0913×1025 coulombs but not greater than twice this amount and no less than half that amount. The total of heat within the notation, a huge stretch of the imagination, is 2.4578×1014 K to 4.9156×1014 K. Though an unimaginable amount of heat to be spread out throughout this single Notation 142, it just may be a measurable concept.

Planck Charge.  Let’s look at which notations Planck Charge becomes a common number. For example, a lightning bolt is typically around 15 C, large bolts up to 350 C.  That is quite visceral, yet on the chart it is in the range of Notations 63 to 67, the run up to the transfer from the small-scale to the human scale universe.  If it represents the sum total charges within each notation, it certainly provides us with something to ponder.

These five Planck base units create very large continuity equations. Though imputed, remember that this schema is also based on the simplest geometries. Taking the entire chart and the weight of its simple logic, it suggests that the symmetries of these imputed geometries and these continuity functions are infinite, and that length (space), time, mass, charge and temperature are finite. These 201+ notations seem to define a finite universe and each notation defines a range in which particular subjects and objects are bounded by their Planck base units doubling, thereby each notation has a certain functional uniformity which provides a range within which particular groups or sets of things work.

Questions are asked, “Is this model the abiding, on-going, current structure of things as they are?  How?

201+ notations, divided by three, renders a small-scale, human scale, and large scale universe. The application of scaling laws and dimensional analysis to the first 60 notations resulted in learning about the power of base-8 expansion. By the 20th notation there are plenty of vertices with which to build structures; that is 1,152,921,504,606,846,976 or 1.152 quintillion vertices. By the 60th notation, add 36 more places (zeros). That is a robust infrastructure with 1152921504606846976000000000000000000000000000000000000 vertices (perhaps point-free vertices).

There is what would appear to be an infinite number of possible constructions. Add in the 131 better-known dimensionless constants and the fundamental physical constants, there should be enough variables to accommodate the Standard Model in physics as well as the science that has resulted from the standard model in cosmology. Please note that at the 60th notation, the size of the Planck Length doubling is not yet large enough to accommodate a fermion.  From the 1st doubling to at least the 60th doubling, all the “structure” may best be described as hypostatic, which means in this instance, the essence or underlying reality.

Humanity doesn’t physically appear within the Planck Time column until well into the 201st notation. There has been a dispersion of length (space) mass, charge and temperature throughout an ever-expanding universe.  Obviously there is a lot of science to learn between Notation 101 to Notation 202, and it will all be in relation to the deeper dynamics between Notation 1 and 101.

Reflections and Projections.  Our base-2 chart of the Planck Base Units was first published in February 2015. This is its first review. It is an introduction that requires many more years of work and analysis.  It frames a detective story whose final chapter could be written in many different ways.  To expand the grounds of the analysis will require going deeply inside the simple geometries within the first 60 notations to discern how these geometries extend undetected, but measurably present throughout the entire universe. The assumed universals — order and continuity,  multiple grids of relations with symmetries as well as asymmetries, and dynamics that seem to conjure up transformative instants of harmony, degrees of perfection and  the darkest forms of chaos within degrees of imperfection  —  will be studied in light of duality, finite and infinite sets, group theory,  and set theory.  That study will focus on the correlations with advanced combinatorics, matroids, amplituhedrons, and the Buckingham pi theorem.

All the questions raised within A Simple View of The Universe will now begin to be addressed.

Much more editing and perhaps a little more writing to come.

Working notes:  When this page is ready to be declared “a working first-draft,” I will post an index of related articles; and as a working first draft, this post will be the first in that list. -BEC

Editorial note:  Our world seems increasingly crazy. This model just might help to open new insights that might mitigate some forms of that craziness. So though still quite rough, it’s being brought into the light of the public rather early. Also, by working on it in public, perhaps others will have comments and suggestions to shape its potential.

This post is a continuation of a prior work, A Simple View of the Universe. There are more observations to make about the Planck Time progression and many more to make about the progressions of the other Planck base units.  So, to say the least, this document is very much in process and will be updated frequently throughout the day and throughout the month of September.

A More Simple View Of The Universe

Waterman“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?” by 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, 304–316), DOI: 10.1111/j.1749-6632.1986.tb12434.x

Is a simple mathematical and geometrical view of the Universe meaningful or useful?

Can we open a dialogue about the question?


Note: This article was initiated in July 2015 and it is now a Working Document. I fully acknowledge that the basic concept is idiosyncratic. There are profound challenges in many places, i.e. Planck Temperature and the order of dimensionless constants; and 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 other work; two earlier articles and two sequels:

Thank you. – BEC


In December 2011 we began our work on a very simple mathematical and geometric model of the universe; it was playfully dubbed, Big Board-little universe.

We had started using the following parameters — base-2 exponential notation, the Planck base units, and the Platonic solids — in ways that created heretofore unobserved boundary conditions.

Our Three Initial Conditions

1. A basic chart. There are just 201+ 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? The mathematical progressions within the charts are simple, but raise questions. One key question is addressed within the Endnotes (below).

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), 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 Standard Model (including confirmation of tetraquarks and pentaquarks) as well as the standard model in cosmology (Lamda 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.”


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 201+ notations. First, we assume that Planck’s base units are the singularity (the Void), yet, we now ask, “What happens when each is doubled? 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? There are many books and articles about these constants, however, our primary reference is the 2006 article by Tegmark, Aquirre, 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.

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. To observe this progression, we will eventually make a chart for our base units to the 65th notation.

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)
*Vertices or point-free vertices

With every one of the TARW 31 dimensionless constants, a guess will be made to see what happens to the number within each doubling. We will watch the simple logic of each doubling, especially between the 65th and the 70th doublings. When does that number punch out and become something that is reduced to practice? Or, in what notation does a dimensionless constant combine with anything that is manifest? When is there an apparent effect?

By the 20th notation, our vertex figure using dimensional analysis is up to an exabyte, the same number as 2-to-the-65th or 1.1529 quintillion vertices. We can see therefore that count continues out to 54 places (18 x 3) by the 60th notation. These numbers are so far beyond “large numbers” that it may seem meaningless. Certainly we all need to begin getting accustomed to very large and very small numbers! It seems that we could conclude that with so many vertices there is enough potential structure to contain every part of the Standard Model known to date.

Anything and everything seems possible.

6. Identity: Humanity at the center of this model of the universe. In December 2014, when we tracked the Planck Time next to the Planck Length, we found 201.264+ notations. Our very first chart in December of 2011 had 209 notations. We did not know where to stop. A NASA scientist helped us; he calculated 202.34 notations. Then a prominent French astrophysicist who did a calculation of 205 notations (See footnote 5).

From the 100th to 103rd notations we find sperm, hair, the thickness of today’s paper from a book or magazine, and the human egg, clearly a few of the basics that evolve to become humanity. And, of course, we recognize that there are many other objects within these four notations. Yet, within its simplicity, there was a quiet affirmation, “Perhaps we, the swarming sea of humanity, are not irrelevant. This model places us squarely in the middle of it all.”

7. The small-scale, human-scale, and large-scale Universe. In our chart of the Big Board – little universe there are 201.264+ notations. When divided by three, each scale would ideally have just over 67 notations. Following a longstanding convention within scholarship, we call these groups, the small-scale universe, the human-scale universe and the large-scale universe.

The small-scale universe ranges from the singularity of the Planck base units to notations 67 and 68. Within the 66th and 67th notations, protons, fermions and neutrons are indexed. Leptons, quarks may well be within the 64th and 65th domain. Some posit them at much smaller sizes. But, the measuring tape is mathematics and it is oblique mathematics to be sure. Common elements of the aluminum and helium atoms show up in the 68th notation.

This human-scale universe ranges from the 68th notation to the 135th notation. There have been times when we have been boldly speculative, perhaps just imaginative, thinking about the transition from the human scale to the large scale.

The large-scale universe ranges from the 135th notation to just over the 201st notation. Not just the domain for governments anymore, here the truly imaginative, speculative, and bold have gone where others would fear and tremble.

These three scales provide the second most-simple division of the universe and by studying the transitions between each, we will engage combinatorial mathematics, group theory and set theory in fundamentally new ways. The continuity conditions are redefined. Symmetry functions are expanded. And, there is a possibility of understanding something new about the harmony of the universe (see history of the Greats who used such terms, i.e. Pythagoras, Plato, Aristotle, Kepler, Newton and Leibniz).

We have begun to analyze other progressions or scales based on fourths, fifths sixths, and so on. In time, we may find something of interest.

8. Numbers and Operands (from Sequential Real Numbers, to Base-2 to Dimensional Analysis). We have observed how the simple mathematics of both base-2 exponential notation and dimensional analysis become unwieldy rather quickly by the 60th and 21st notations respectively. Virtually every day we say, “We need to go over this one more time. It seems that we are missing something.”

First, the notations (doublings or steps) are sequentially ordered, 1 to just over 201. What is that sequence? Is there any possibility that it could be related to the Fibonacci sequence? What is the very nature of addition?

Next, there is multiplication, division, and ratios. A former NIST scientist and mathematics professor at Brown, Philip Davis, cautioned that the circle and sphere are more simple than the tetrahedron. Of course, he is right. We are now learning more about cubic-close packing (ccp) and the world of pi. Within the first notation with its eight vertices, we now know that we have to understand ccp and anticipate that the entire small-scale universe is driven by ccp.

That will be an article in the near future.

At the top of this article is a quote from John Archibald Wheeler who was thinking about the standards for measurement within quantum mechanics. If Pi drives this small scale universe, we know Pi is an irrational number and transcendental number that never ends and never repeats. It gives each construction those qualities and those qualities reflect an essence of quantum mechanics; we know there is a lot to chase down here.

Also, one of the most simple ccp configurations will be the pentastar with seven vertices in the form of five tetrahedrons. There is a 7.38° (7° 21′) gap that we have called squishy geometry as well as quantum geometry; here are degrees of freedom that continue within the icosahedron (20 tetrahedral structure) and the pentagonal dodecahedron (60 tetrahedral structure). What is it all about? We are not sure, but we do know it is worth more study.

There are many notations as those Planck base units are being multiplied by 2, that raise questions. We say, “There are doctoral dissertations in there!” It is within our scope of work. Then it came time to ask, “What has over a quintillion units of something?” Today, we have answered, “Vertices or point-free vertices.” Are there any other possibilities?

What are the key operands? It seems that a vertex is a reasonable answer. It is a special kind of point defined by axioms, and these have no “…length, area, volume, or any other dimensional attributes.” Yet, within our logic these points give functional capabilities to continuity, symmetry and harmony. And, these points have within them the conditions for order, relations and dynamics.

We take the universe as a whole, just as it is given; however, we assume that it is all complete, integrated, where the historic is the current, the here and now.

Thank you.



  • At some notation, the geometries, logic, and all the somethings of the universe, must begin sharing a common space and time and as we approach the first doubling, everything shares it. We assume this shared space begins somewhere between the 60th and 67th notation. We call this domain, hypostatic, because it provides a working foundation for everything everywhere for all time. We have also referred to it as a substrate.
  • Of course, these observations, guesses, and working conclusions will be revisited often.
  • The model also works as a simple Science, Technology, Engineering, Mathematics (STEM) tool; it organizes data in a robust way and it opens many new doors for exploration. That seems to be a worthwhile use of our time.
  • Part of this project began in 1979 at MIT.


1. Four key charts and key question:

2. The Platonic Solids: The simple geometries still hold new insights

3. A Simple Logic: Continuity, symmetry and harmony

4. History within Logic, Mathematics, Philosophy, and Physics:

5. Starting Points:

6. Identity: Humanity at the center of this model of the universe.

7. Three Scales of the Universe: Small Medium and Large (more to come)

8. Numbers and Operands (more to come)


Pi equals 3.1415926535897932384626433832795028…


An arc of a circle with the same length as the radius of that circle corresponds to an angle of 1 radian.

A full circle corresponds to an angle of 2π radians.


  1. Pi is a constant.
  2. Pi is an irrational number.
  3. Pi is a transcendental number.
  4. Pi is a non-repeating number – no pattern has been identified using computer analysis within over twelve trillion places.
  5. Pi ( π ) is the exact ratio of the circumference of a circle to its diameter.   It is that simple.

Thank you, Wikipedia, for the graphics (above) that demonstrate this simple definition.  There are over 45 Wikipedia articles about pi.

So, what do you make of it?  What is going on?

Perhaps a few more questions and comments would help.

  1. What is it about a circle and sphere that pi is always-always- always true?
  2. How does a number become a constant, irrational and transcendental all at the same time?
  3. Let us compare pi to other unique numbers that have a special role among all numbers.  These are e, 0, 1, and I. They are all magical, but π stands out. So, let’s ask, “What are the shared qualities of these numbers?” Let’s study them to see if we can find any necessary relations.
  4. We have the ratio between a circle and a line. Perhaps this is the fundamental transformation between the finite and infinite? Are circles and spheres always implicating or imputing the infinite?

That is a big question and enough to ponder for awhile.

Notwithstanding, there are many more questions to ask.

Some speculations: Pi may be the key to unlock the small-scale universe within the big Board-little universe
1.   To get to the application of pi  within the Planck Units, we’ll need to emerge from the singularity of the Planck Units.  Is the radian a key to understanding this process?  First, a radius is extended from the singularity.  A radius extends into the preconditions for space and time, a now emergent small-scale universe. It makes that first arc equal to its own length.  It does it again and again and again and again and again (six radians) and then makes that last leap, 2 pi, to complete the circle. Is this a reasonable scenario? Why? Why not?

2. We need to run through dozens of scenarios, often, and slowly and carefully.  What scenarios are perfect and obvious?

3. We are at the singularity of the Planck Units.  We are establishing the foundations for the physical world.  If all things start simply, this must be the place to start.  It doesn’t get more simple and more mysterious. Nothing is a mistake, everything comes from a perfection to a space-time moment, so what could possibly happen?

What happens within the first six doublings?    (to be continued)

For further discussion:
1.  Is the Small-scale Universe the basis for the homogeneity and isotropy of space and time?
2.  Does everything in the universe share some part of the Small-Scale universe?
3.  How is Planck Temperature calculated?  Does it begin with the other Planck Units and expand from that figure at the first notation?

Note:  All of human history has occurred in the last doubling.  Yet, all doublings remain active and current and dynamic.  Continuity trumps time. Symmetries trump space.

What does sleep have to do with anything?  If all time is current, within the moment, we particularize by the day and uniquely within a given waking day.  Sleep seems to bring us into the infinite.  Dreams seem to be the helter-skelter bridge between the finite and infinite.  It seems that these naïve thoughts are worth exploring further.

This Shifting Paradigm Changes Our Perception Of Everything

Editor’s note:  This page was first posted within Small Business School, a television series that aired for over 50 seasons on PBS-TV stations (1994-2012).  It is the author’s business website, so many of the links go to that Small Business School website.    Eventually all links will be redirected to pages within The Big Board – little universe Project.


Background: Our study of the Planck Length to the Observable Universe began formally on December 19, 2011. Though we thought about the matrix from the Planck Time to the Age of the Universe, it took until December 8, 2014 to add it the Planck Length chart. Logically, but non-intuitively, the two tracked well together. Based on that work, we started looking at our own foundations for understanding first principles, universals and constants.

First, our television series began in 1994 based on first principles (linked from here). These were a direct reflection of our faith and our belief that faith and science must cohere or one of them is wrong.

Second, we used those first principles in all that we have done. That’s how one knows the first principles work. Yet, eventually, those first principles inform in new ways. It is not automatic. It takes time. But, there is always a next step. We can always improve on the initial conditions.

Third, we all need to extend our principles globally, then extend them throughout the universe. That drove our work on the Big Board-little universe back which started in December 2011.And oddly enough, we can now see how such principles just might become the core of a new small business revolution.

Here is a paradigm shift that just might change our perceptions of everything.

1. The Universe appears to be finite. That’s huge. It has measurable smallest units for space and time. It has measurable units for the largest dimensions of space and time, the Observable Universe and the Age of the Universe, respectively.More

2. The Universe has an ethical bias. Yes, hard to believe, but it seems to be true. If so, the theological among us have some very real work to do because theology will be informed by science and science will actually be informed by theology. And, those within radical Islam will learn that they still have much to learn from their Allah and our science!

3. The Universe is smaller and more ordered than we think.In 202+ steps, you go from the smallest measurement to the very largest.Initially it sounded ridiculous and it seemed inconceivable, yet over time, it sinks in.

4. The Universe is more connected than we think. In fact, everything is related to everything, all within 202+ steps! Seems impossible; it’s not.

5. The Universe gets structure from space-and-time, but not its essence. The structures go back to basic geometries that have become exquisitely complex (Also, see reference #4). One might conclude that the essence of that structure comes from the Infinite through our constants and universals which appear to be best engaged through the Planck Units.

Now, with all these references, we now say, “Let’s get focused; there are great things to do to get us all on track for a brilliant future.”


Center for Perfection StudiesThe Big Board–Little Universe Project 

What is finite? And, what is truly infinite?

“Finite or Infinite? Is That The Question?”    (link goes to Part II)

Some of our high school students think our scientific community makes the study of Science, Technology, Engineering and Mathematics (STEM) all too difficult to understand and overly complex by defying a certain commonsense logic. (Reference #1)

We have been studying simple math and simple geometries from the smallest possible measurement of a length to the largest (Reference #2). It appeared to some of the students, based on this work, that the universe is obviously finite. They have been told that intellectually and historically, it is an open question. For them, “Make a choice and see where it takes you.”

The students with strong faith statements said, “Only God is Infinite. All things within space and time are finite.” (Reference #3) When asked about all the universals-and-constants and space-and-time, the concurrence is that these are the access paths, interconnections and transformations between the Finite and the Infinite.

For the best of these students, asking the question, “What is the Infinite?” is like asking the question, “Who is God?” And, they have answers.

Of course, as a result of a little coaching, they say, “First, God is Perfect.” When asked, “What is perfection?” they echo their coach: “Perfection is order-continuity, relations-symmetry and dynamics-harmony, all rolled into one.” (Reference #4) That amounts to an understanding of the Infinite without importing all the related history and revelation from the various faith statements within our very short history throughout our little world. The Finite is another story. We turn to many people from Euclid to Einstein for inspiration to provide the academic and religious communities with our simple observations and assumptions.

Hardly postulates and axioms, our statements are a praxis in-search-of theoria:

If these statements are taken as a given, then what kind of universe and what kind of science do we have? Should we re-examine the use of infinity throughout the ages going back to the ancient Greeks? Should we reconsider the theory of indivisibles? And, perhaps we should even reconsider the very nature of the Big Bang and its theory.

Of course, that is our agenda (Reference #8),   our current focus for the immediate future.


1. One of two key general overview and working article,  Order in the Universe

2. One of the earliest reflections on all our efforts and work: Is it true that everything starts most simply?

3. Initially written in November 2012, just what is the nature of belief?

4. In light of those constants, universals and the finite-infinite relation, the nature of perfection seems to follow:

5. Examining basic structure in basic ways: Simple View of the Universe

6. Our first look at the progression of doublings.  This listing was written to accompany an article for Wikipedia: Written in March 2012 to support an article for Wikipedia

7. There are somewhere over 201 base-2 exponential notations (doublings, domains, layers or steps) within the Known Universe.

8. Another analysis of key points: There are 15 in this article.

Even between atheists and believers

Perhaps all it comes down to is an answer to the question, “Whose metaphor is more meaningful?” You will not find many atheists who deny science. They do not deny the constants and universals that are always in the back of the science textbooks.

There are three constants within the sciences that remain clear, in spite of quantum mechanics. The first is that there is order and continuity in the world. It is the basis of knowing. In every discipline there are multiple parameter sets where this is true. Beginning in mathematics, a rather pure form of thought, abstraction and representation, we then move into physics. It has multiple parameter sets as well. There is one for Newtonian mechanics, another for General Relativity and Special Relativity and yet another for quantum mechanics. Then chemistry and biology have their own parameter sets. All these parameters simply establish the boundary conditions of what is being measured within them.

Each has a formalized language. And, each has a metaphorical language that pushes into the edges of the unknown.

The sciences all embrace varying definitions of relations yet all of these definitions are understood by a symmetry function.

Specialized disciplines with each of the sciences hypothesize about the nature of the unknown, just beyond their limits of knowledge, and all these hypotheses are a study of the deepest dynamics of their discipline. The experience of insight, the “ah-ha” of the creative surge, is experienced as a concrescence of symmetries or harmony.

The atheists mostly object to the use of specialized language. They understand rules, mores, and societal law and order even though many are nihilistic, others narcissistic, and many both.

Yet, change will come. Some of these folks will begin to realize that time is not a fundamental frame of reference and that there are qualities of life that permeate everything in every way, and that these qualities empower order, relations, and dynamics, and that these three scientific functions with the faces of continuity, symmetry and harmony just might also be understood with very personal language. When and if they do, they are on their way to create a personal bridge to religion and some of the brave among them just may cross it.

Back to top