Wilson, Edwin O.

E.O. (Edward Osborne) Wilson
Harvard University

Book: Consilience: The Unity of Knowledge  
YouTube (there are hundreds)

First email: Thu, Jul 21, 2016 at 8:14 AM


My dear Prof. Dr. E.O. Wilson:

In December 2011 a group of high school people went inside the tetrahedron, dividing by 2, and found the half-sized tetras in the four corners and an octahedron in the middle.  We went inside that octahedron, dividing by 2, found the half-sized octas in each of the six corners and eight tetras in each face, all sharing a common center point. We kept going within all 19 objects.  Within just a few steps we found our nematode friends. In another few steps the prochlorococc greeted us, “Set em up baby…”

In just 45 steps within we were zipping by the fermions and protons and just kept going!  In the next 67 steps, you wouldn’t believe what we saw! We were at the door of a singularity that Max Planck gave us and all those secret codes, but it took 100 years and Frank Wilczek to begin to interpret them (2001, Physics Today, Scaling Mt. Planck I-III).

Just over 112 notations.  What was that?

It didn’t take too long before we got the bright idea, “Let’s multiply by 2.” What an epiphany! In less than 90 steps we were out to the Age of the Universe and the Observable Universe. Looking at ourselves, we were lost within all this new information, so we decided to turn to the experts. Huh? We found Kees Boeke’s base-10 work from 1957 but he only had 40 quick jumps (Cosmic View) and missed so much of life!  We found Stephen Hawking but he was in tight with big bang theory. Where are our experts?

What? Huh?  Our knowledge of the universe is so incomplete, our sense of the universal is so limited, our understanding of the constants is so elementary, we are flying blind.

The Encyclopedia of Life truly needs a wonderfully integrative, expansive container so it doesn’t get walled in!  Of course, its website opens it to our world.  Let’s open it to the universe.  Yes, a wall-less container where ideas and creativity can explode old boundary conditions and creatively new parameter sets emerge.

Now we are amateurs, but we really feel that biology and the search for life must begin with that initial creation, the first moment, when there was a profound integration, and come through it all right to the 200th notation to our present day.  Let’s encapsulate the universe so we can truly address the “… transcendent qualities in the human consciousness, and sense of human need” (from your Ted Talk).

Are we crazy?  Of course, we are, but hopefully delightfully so! Thanks.

Most sincerely,

Bruce Camber



PS.  I grew up not far from the Peabody and all the glass flowers. My father was an HVAC machinist for the Mark I while my mother had been a nanny for Shady Hill characters.

In 2002, Wilczek reflects, “It therefore comes to seem that Planck’s magic mountain, born in fantasy and numerology, may well correspond to physical reality.” (PDF)

“Can’t you see, we are in a dialogue with the universe?” asks Charles Jencks.


Within the Quiet Expansion, what is mass and what is charge?

Next edits: November 2017

Notes: Under construction. This post is needed to support our comparison of the big bang theory to our Quiet Expansion model. One of those comparisons is for the general public. The other is for the academic-scientific community. To incorporate this question within those two working posts would make both altogether too long. This posting is also a sequel to these two open, working documents:
·   Dark Matter, Dark Energy, Cosmology and the Large-scale universe (2015)
·   Wrong: There is a possibility (December 2015)

The question
BangerQuestions about the nature of mass and charge have been addressed by the most highly-respected scientists over the centuries. Both mass and charge are manifestations of fundamental faces of reality.  Both have necessarily-related concepts.  Mass has density, weight, force and the mass-energy equivalence . And charge has electric charge (Coulombs, ampere, time and force) and color charge  (generating set of a group, symmetry groups, and Hamiltonian). All these concepts have been reviewed thousands-upon-thousands of times. However, to our knowledge, never have these concepts been reviewed within the framework of the first 65 or so notations of the Quiet Expansion model. Here, within each notation, we are using a most-simple mathematical formulation to ask the question, “What are these numbers saying about the nature of reality?”

A possible answer
It seems that the mathematics, particularly those ratios rendered within each doubling of the Planck base units, defines mass (weight, density, force, mass-energy equivalence) and charge (both electric and color) as a derivative of the other base units and all of the constants such as light, gravity, and the reduced Planck constant that define them.

To research what that means and to prepare to write this document, the very creative work of several  PhD research physicists came to our attention. It is all truly amazing work. These are scholars who are attempting to push through some of the well-known problems with the Standard Model. Some have posited exciting new theories and ideas. We could easily get lost in that sea of ideation. We can’t.  It is all very encouraging to feel their creativity, however, our model is based on simplicity — simple concepts and simple mathematics. So, we won’t stray too-too far from where we are as we attempt to impute meaning to our simple doublings of the five basic Planck units.

To establish a basic platform, we did return to the work of Prof. Dr. Frank Wilczek of MIT and his August 2012 work titled, The Origins of Mass (PDF), MIT Physics Annual, 2003, and the more recent  Origins of Mass,  ArXiv, Cornell University, August 2012.  We also recommend his 2004 lecture video,  The Origin of ^Most Mass and the Feebleness of Gravity. He addresses “regular mass” and readily acknowledges that mysteries remain within dark matter and dark energy. Over the past 20 years Wilczek has written many articles and books about the nature of mass and matter.

Notwithstanding, within the first 60 or so notations, mass, time, space, charge, and temperature take on a very different meaning. These five are so inextricably related, they can not be pulled apart and each truly exists in reality, but prior to the 65th notation can only be known by their ratios .These ratios are real, and a real definition of a very real reality. Each notation builds upon the prior notations. All notations continue their prior notation’s more fine doubling as well as what I’ll call their archetypal doubling; that is the doubling into the next notation. With each doubling our universe is increasingly networked and related. Within the gross doublings, these networks begin systematizing sets and groups, given the definitions within and between each notation, and begin to emerge as cells within the cells notation, as people within the “people” notations, as solar systems within the solar system notations, as galaxies within the galaxy notations, and so on.

Let’s work on some conclusions.
Is that clear?  Yes, I hear, “Clear as mud.”  Well, if it is a little clear, help us to make it more clear! This is just Day 2 for this document! We are in need of mentors! Help. So, we are asking for help from people around the world and throughout the scientific-academic communities. You could become the author or co-author of this page and/or any other page on these related sites.

Perhaps we are not doing any worse than the big bang theory according to Stephen Hawking and his cohort. They completely ignored Planck charge and then give rather bubbly notions as to how the universe went into its supercooling state.  At least our mathematics has a simple logic and rationale.  -Bruce

On Constructing the Universe From Scratch

UPDATED: SUNDAY, MARCH 20, 2016   Commentary/Reflections (new tab)

An Early Draft


“I have learned that many of the Greeks believe Pythagoras said all things are generated from number. The very assertion poses a difficulty: How can things which do not exist even be conceived to generate? But he did not say that all things come to be from number; rather, in accordance with number – on the grounds that order in the primary sense is in number and it is by participation in order that a first and a second and the rest sequentially are assigned to things which are counted.”
Theano, On Piety (as reported by Thesleff, Stobaeus, and Heeren)


Using the model of the universe generated through the Big Board – little universe Project where there are just over 201 base-2 notations from the singularity of the Planck base units (particularly from Planck Time) to the Age of the Universe, the question to be addressed is, “Which numbers come first and why?” Mathematical logic calls out the most simple-yet-powerful numbers that can be used to build and sustain a highly-integrated universe. Our other assumptions are here. Each of these key numbers and number groups are introduced; each will then become the focus of additional study, further analysis, and the basis for a more-in-depth report about each number. Our initial numbers are:
(1)   3.1415926535897932384626433+  or π or Pi
(2)  74.04804896930610411693134983% or the Kepler Conjecture
(3)  0, 1 where the numbers are: zero and one
(4)  7.356103172453456846229996699812° called the Pentastar gap
(5)  1:1.618033988749894848204 or the Phi ratio
(6)  4.6692016091029906718532 which is a ratio called the Feigenbaum constant
(7)   110 of Stephen Wolfram’s rules
(8)  6.6260709×10−34 J·s or Planck constant plus all related numbers
(9)  Groups of dimensionless constants, all known mathematical and physical constants
(10) 13.799±0.021 billion years, the Age of the Universe

Please note: Links inside the body of the article most often open a new tab or window within a Wikipedia page. For those occasional inks that  do not open new windows, please use the back-arrow key to return to the referring page. All links within the Endnotes will eventually go to source materials if posted on the web.

Page 1 of 10 https://bblu.org/2016/01/08/number/


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Most of us know the universe is infused with numbers. It seems nobody really knows how all these numbers are organized to make things and hold it all together.

In our work with high school students there is a constant demand that our numbers be intellectually accessible. Simplicity is required.  So, it is rather surprising that we ended up engaging the Planck Length (and the other Planck base units) very early in our study of the platonic solids. We also started to learn about base-2 notation and combinatorics. We had to do it. We had divided our little tetrahedron in half so many times, we knew we were in the range of that limit of a length, and we wanted to find a place to stop. Eventually, to get more accurate, we started with the Planck Length, used base-2 exponential notation, and multiplied our way out to the Observable Universe.1 It took just over 201 doublings.  What?  Huh?

That little fact is as unknown as it is incredible  (even as of January 2016 when this article was first posted).

In December 2011 we could find no references to the 201+ notations in books or on the web. We did find Kees Boeke’s 1957 work with base-10 notation. It was a step in the right direction, but it had no lower and upper boundary, no Planck numbers, and no geometry. It had just 40 steps amounting to adding zeroes.

We were looking for anything that could justify our “little” continuum. We didn’t know it at the time, and we later learned that we were looking for those deep relations and systems that give us homogeneity and isotropy, a cosmological constant, and an equation of state. Though we already had put everything, everywhere throughout all time in an ordered relation, we had no theoria, just the praxis of numbers. We tried to set a course to go in the direction of a theory that might bind it all together.

The first 60+ doublings constitute a range that scholars have been inclined to dismiss over the years as being too small;  some say, “…meaninglessly small.” Yet, being naive, it seemed to us that the very simple and very small should be embraced, so we started thinking about the character of the first ten (10) doublings. Trying to understand how to “Keep It Simply Simple,” we were pleasantly surprised to discover that there was so much work actively being pursued by many, many others throughout academia and within many different disciplines to develop the logic of the most simple and the most small.

Within the studies of combinatorics, cellular automaton, cubic close packing, bifurcation theory (with Mitchell Feigenbaum’s constants), the Langlands program, mereotopology and point-free geometry (A.N. Whitehead, Harvard, 1929), the 80-known binary operations, and scalar field theory, we found people working on theories and the construction of the simple. Yet, here the concepts were anything but simple.2

It is from within this struggle to understand how all these numbers relate, we began our rank ordering of all possible numbers. This exercise helps to focus our attention.

Planck Length and Planck Time. One might assume that we would put the five Planck base units among the most important numbers to construct the universe. As important as each is,  it appears at this time that none of them will be among the Top 5. Although very special, the Planck numbers are determined by even more basic and more important concepts and numbers. At the very least, all those numbers will come first.



page 3 of 10

First Principles. The work to find the Top Numbers was preceded by an end-of-year report after four years of studying and using the Big Board-little universe charts. That report titled, Top Ten Reasons to give up little worldviews for a much bigger and more inclusive UniverseView 3, was done with comedian David Letterman in mind. He often had a Top Ten on his show.

“#10” for us it is, “Continuity contains everything, everywhere, for all time, then goes beyond.” One of the key qualities to select our most important numbers is the condition of continuity and discontinuity starting with the simplest logic and simplest parts.

A Quick Review of the Top Ten Numbers in the Universe.

Because many scholars have addressed the question, we did a little survey.

Scholars and thought leaders. Our limited survey began with leading thinkers in the academic-scientific community and then thoughtful people from other disciplines:

Base-2 notation. Yes, our work with base-2 notation originated from within a high school. We have no published scholarly articles and there has been no critical review of our emerging model. Nevertheless, we forge ahead with our analysis of numbers and systems.



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Goals. Our singular goal is to try to construct our universe using mathematical logic. We begin with the magic of the sphere. Our #1 number is Pi (π).

#1 = π
Numerical constant, transcendental and irrational all rolled into one

For us Pi (π) seems to be a very good starting point. Non-ending or continuous, it is also  non-repeating which is discontinuous. This most simple construction in the universe requires just two vertices to make the sphere. How does it work? It appears to give form and structure to everything. Using dimensional analysis and scaling laws, this progression of the first 20 notations shows the depth of possibilities for constructions when multiplying by 8. Our open question: In what ways do the  Feigenbaum constants within (bifurcation theory) apply?4

B2 Vertices Scaling Vertices (units:zeroes) Bifurcation* Ratio*
0 0 0 N/A N/A
1 2 8 vertices 0.75 N/A
2 4 64 1.25 N/A
3 8 vertices 512 1.3680989 4.2337
4 16 4096 (thousand:3) 1.3940462 4.5515
5 32 32,768 1.3996312 4.6458
6 64 262,144 1.4008286 4.6639
7 138 2,097,152 (million:6) 1.4010853 4.6682
8 256 16,777,216 1.4011402 4.6689
9 512 134,217,728 1.401151982029 4.6689
10 1024 1,073,741,824 (billion:9) 1.40115450223 4.6689*
11 2048 8,589,934,592
12 4096 68,719,476,736  *This bifurcation and
13 8192 549,755,813,888  ratio columns come
14 16,384 4,398,046,511,104 (trillion:12)  from a Wikipedia article
15 32,768 35,184,372,088,832  about Feignebaum’s
16 65,536 281,474,976,710,656  constant.
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(18)

(discussion begins on the next page)
Page 5 of 10

Discussion.  Pi still holds many mysteries waiting to be unlocked.  Among all numbers, it is the most used, the most common, and the most simple but complex.  We assume, that along with the other mathematical constants, pi (π) is a bridge or gateway to infinity. We assume it is never-repeating and never-ending.  It is “diverse continuity.”  There are enough scaling vertices within ten doublings to construct virtually anything.  So, to analyze a possible logical flow, any and all tools that have something to do with pi (π) will be engaged. Spheres2Again, among these tools are combinatorics, cellular automaton, cubic close packing, bifurcation theory (with Mitchell Feigenbaum’s constants), the Langlands program, mereotopology and point-free geometry (A.N. Whitehead, Harvard, 1929), the 80-known binary operations, and scalar field theory.   Perhaps we may discover additional ways to see how  pi gives definition — mathematical and geometric structure — to our first 60-to-67 notations. What are the most-simple initial conditions?

More Questions. What can we learn from a sphere? … by adding one more sphere? When does a tetrahedral-octahedral couplet emerge? When do the tessellations emerge? At the third notation with a potential 512 scaling vertices, surely dodecahedral and icosahedral forms could emerge. Within the first ten notations with over one billion potential vertices, could our focus shift to dynamical systems within the ring of the symmetric functions?

#2 = Kepler’s Conjecture


Not a very popular topic, one might ask, “How could it possibly be your second choice?” Even among the many histories of Kepler’s voluminous work, his conjecture is not prominent. To solve a practical problem — stack the most cannon balls on the deck of a ship —  he calculated that the greatest percentage of the packing density to be about 74.04%. In 1998 Professor Thomas Hales (Carnegie Mellon) proved that conjecture to be true.  By stacking cannon balls, all the scholarship that surrounds cubic close packing (ccp) enters the equation.  The conjecture (and Hales 1998 proof) opens to a huge body of current academic work.5 There we found this animated illustration on the right within Wikipedia that demonstrates how the sphere becomes lines (lattice), triangles, and then a tetrahedron. With that second layer of green spheres emerges the tetrahedral-octahedral couplet.

Sphere to tetrahedron-octahedron couplet
Attribution: I, Jonathunder

This image file (right) is licensed under the Creative Commons Share-Alike 2.5 Generic license.

Revisions. As we find experts to guide us within those disciplines where pi has a fundamental role, undoubtedly sections of the article will be substantially re-written and expanded. Our goal has been to find the most logical path by which all of space and time becomes tiled and tessellated. Perhaps there is a new science of the  extremely small and  the interstitial that will begin to emerge. These just might be foundations of foundations, the hypostatic, the exquisitely small, the ideal.6  We plan to use all the research from Kepler to today, particularly the current ccp (hcp and fcp) research from within our universities, in hopes that we truly begin to understand the evolution of the most-simple structures.


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#3 = 0, 1

Circle to CoordinatesThe numbers, zero (0) and one (1) begin the mapping of pi to Cartesian coordinates. Beginning with a circle, each sphere is mapped to two-or-three dimensional Cartesian coordinates.  It is the beginning of translating pi to sequences and values. The first iterative mapping  is a line,  then a triangle,  then a tetrahedron, then an octahedron.  When we focus solely on this subject, with experts to guide us, perhaps we can engage the study of manifolds that are homeomorphic to the Euclidean space.6

#4 = Pentastar gap = 0

0.12838822… radians

7.356103172453456846229996699812179815034215504539741440855531 degrees

PentastarThe little known 7.356103 degree gap is our fourth most important number, the possible basis for diversity, creativity, openness, indeterminism, uniqueness and chaos.7 That Aristotle had it wrong gives the number some initial notoriety; however, it is easily observed with five regular tetrahedrons which would have eight vertices.  It appears to be transcendental, non-repeating, and never ending. Where the tetrahedron with four vertices and the octahedron with six have been been whole, ordered, rational, and perfect, tessellating and tiling the entire universe, the potential for the indeterminate which has the potential to become the chaotic resides somewhere deep within the system. We believe that place just may be right here.

Within this infinitesimal space may well be the potential for creativity, free will, the unpredictable, and the chaotic.  Here may well be the basis for broken symmetries. Of course, for many readers, this will be quite a stretch. That’s okay. For more, we’ll study chaotic maps and the classification of discontinuities.

#5 = phi = φ = The Golden Ratio

Phi-formula = φ = 1:1.618033988749894848204586

Of all the many articles and websites about the golden ratio and sacred geometry, our focus is on its emergence within pi and within the platonic solids.  Phi is a perfection.  It is a mathematical constant, a bridge to infinity. We are still looking to see if and how phi could unfold within the tetrahedral-octahedral simplex. Could that answer be within Petrie polygons? The magic of the golden ratio does unfold with the dodecahedron, the icosahedron, and the regular pentagon. Within this listing, phi has bounced back and forth with the Pentastar gap. Which manifests first? Is it manifest if it is inherent?

Starting with this article, we have begun an active study of Phi and its relations to pi and the Platonic solids.  Although there are many, many papers about phi, none are from our special perspective of 201+ notations.



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#6 = Feigenbaum constants

δ = 4.669 201 609 102 990 671 853 203 821 578

We are the first to admit that we are way beyond our comfort zone, yet to analyze and interpret the processes involved within each of the doublings, each an exponential notation, requires tools. This Feigenbaum constant gives us a limiting ratio from each bifurcation interval to the next…. between every period doubling, of a one-parameter map. We are not yet sure how to apply it, but that is part of our challenge.

It gives us a number. It tells us something about how the universe is ordered. And, given its pi connection, we need to grasp its full dimensions as profoundly as we can. We have a long way to go.

#7 = Rule 110 cellular automaton

Wolfram Rule 110There are 255 rules within the study of elementary cellular automaton.  Rule 110 was selected because it seems to define a boundary condition between stability and chaos.   All 255 rules will be studied in light of the first ten notations to see in what ways each could be applied. Any of these rules could break out and move up or down within this ranking. Steve Wolfram’s legacy work,  New Kind of Science (NKS) is online and here he lays the foundations for our continued studies of these most basic processes within our universe.8

#8 = Max Planck numbers

We have been working on our little model since December 2011. Over the years we have engaged a few of the world’s finest scientists and mathematicians to help us discern the deeper meaning of the Planck Base Units, including the Planck Constant. We have studied constants from which the Planck numbers were derived, i.e. the gravitational constant (G), the reduced Planck constant (ħ), the  speed of light in a vacuum (c)the  Coulomb constant, (4πε0)−1 (sometimes ke or k) and the Boltzmann constant (kB sometimes k). This engagement continues. We have made a very special study of the  Planck Base Units,  particularly how these numbers work using base-2 exponential notation and with the Platonic solids.  We had started with the Planck Length, then engaged Planck Time.  Finally in February 2015, we did the extension of Planck MassCharge, and, with a major adjustment to accommodate simple logic, Temperature.  We have a long, long way to go within this exploration.  Essentially we have just started.9

Notwithstanding, there is a substantial amount of work that has been done within the academic and scientific  communities with all the Planck numbers and those base numbers that were used to create the five Planck base units.  Perhaps chemistry professor, C. Alden Mead of the University of Minnesota began the process in 1959 when he first tried publishing a paper using the Planck units with serious scientific intent. Physics professor Frank Wilczek of MIT was the first to write popular articles about the Planck units in 2001 in Physics Today (312, 321, 328)From that year, the number of articles began to increase dramatically and experimental work that make use of these numbers has increased as a result.                                                                                       https://bblu.org/2016/01/08/number/#7


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 #9 = Mathematical & physical constants

Given we started with pi (π), it should not be surprising that we are naturally attracted to any real data that shows pi at work such as the Buckingham π theorem and the Schwarzschild radius.

We will also bring in Lord Martin Rees “Six Numbers” as well as the current work within the Langlands programs,  80 categories of binary operations, scalar field theory, and more (such as the third law of thermodynamics and zero degrees Kelvin).

In studying the functionality of these many numbers, especially those among the dimensionless constants, we believe this list will evolve and its ordering will change often. In searching the web for more information about about dimensionless constants, we came upon the curious work of Steve Waterman and an emeritus chemistry professor at McGill University in Montreal, Michael Anthony (Tony) Whitehead.  I showed their work to a former NIST specialist and now emeritus mathematics professor at Brown University, Philip Davis.  He said, “There are always people who wish to sum up or create the world using a few principles. But it turns out that the world is more complicated. At least that’s my opinion.   P.J.Davis”  Of course, he is right; Einstein did a good job with e=mc2.  Because claiming to find all the physical constants derived by using pi, the isoperimetric quotient, close cubic packing and number density is not trivial10, we’ll be taking a second look. Perhaps they are onto something!  We have brought their work out in the open to be re-examined and in so doing we will re-examine over 140 physical and mathematical constants. This work is also ongoing.

#10 = The Age of the Universe

13.799±0.021 billion years

This number is important because it creates a boundary condition that is generally recognized for its accuracy throughout the scientific and academic communities. Though it may seem like an impossibly large number of years, it becomes quite approachable using base-2 exponential notation.  Without it, there is no necessary order of the notations.

Although there are many different measurements of the age of the universe, for our discussions we will use 13.799±0.021 billion years. The highest estimate based on current research is around 13.82±0.021 years. Also, within this study there are some simple logic problems. In 2013, astrophysicists estimated the age of the oldest known star to be 14.46±0.8 billion years.

Notwithstanding, using base-2 exponential notation all these measurements come within the 201st notation. At the 143rd notation, time is just over one second. Within the next 57 doublings, we are out to the Age of the Universe. So, with the Planck Time as a starting point and the Age of the Universe (and our current time) as the upper boundary, we have a container within which to look for every possible kind of doubling, branching and bifurcation. We can study hierarchies of every kind, every set, group or system. Eventually we can engage holomorphic functions within our larger, ordered context, i.e. the seen-and-unseen universe.11                              https://bblu.org/2016/01/08/number/#8


 This article was started in December 2015.  It’s still in process. Your comments are invited.

Page 9 of 10                                                                                                                    EARLY DRAFT.

Endnotes about our open questions, plus a few references:

Our Initial exploration of the types of continuity and discontinuity: Continuous-discrete, continuous-quantized, continuous-discontinuous, continuous-derivative… there are many faces of the relations between (1) that which has a simple perfection defined in the most general terms as continuity yet may best understood as the basis of order and (2) that which is discrete, quantized, imperfect, chaotic, disordered or otherwise other than continuous.   These are the key relations that open the gateways between the finite and infinite.

Questions:  What is a continuum?  What is a discrete continuum?

2  We are simple, often naive, mathematicians. We have backed into a rather unique model of the universe. To proceed further we will need to understand much more deeply a diverse array of relatively new concepts to us; we are up for the challenge.  We have introduced just a few of  those many concepts that attempts to define the very-very small and/or the transformations between the determinant and the indeterminant. There will be more!

3  Of the Top Ten Reasons, the first three given are our first principles. We know it is an unusual view of life and our universe. The sixth reason advocates for a Quiet Expansion of our universe whereby all notations are as active right now as they were in the very earliest moments of the universe.  When space and time become derivative, our focus radically changes.  It opens a possible place for the Mind down within the small-scale universe.  Our current guess is between the 50th and 60th notations.  The archetypes of the constituents of our beingness are between notations 67 (fermions) to notation 101 (hair) to notation 116 (the size of a normal adult).  Then, we live and have our sensibility within notation 201, the current time, today, the Now.  So, this unusual view of the universe has each of us actively involved within all three sections of the universe: small scale, human scale, and large scale.  To say that it challenges the imagination is a bit of understatement.

4 Open Questions. There are many open questions throughout this document. It is in process and will surely be for the remainder of my life. All documents associated with this project may be updated at anytime. There should always be the initial date the document was made public and the most recent date it was significantly updated. Although the Feigenbaum constants are our seventh number selected (and there are more links and a little analysis there), we will attempt to find experts who can guide us in the best possible use of these two constants within our studies. Bifurcation, it seems, has an analogous construct to cellular division, to chemical-and-particle bonding, to cellular automaton (especially Rule 110,)  and to the 80 categories of binary operations.

5 Wikipedia, ccp, and genius. Jimmy Wales is the founder and CEO of Wikipedia. His goal is to make the world’s knowledge accessible to the world’s people. He has a noble vision within precarious times. In order to be published within Wikipedia, the material has to have its primary sources of information from peer-reviewed publications. As a result, Wikipedia is not where “breakthrough” ideas will first be presented. Blogging areas like WordPress are a more natural spot and Google quickly indexes all those blogging areas. It took only a day before they found this article. So with a little ingenuity one can quickly find many new references to new ideas and then go to Wikipedia to find the experts on that subject. Prior to this research, we had barely scratched the surface of ccp. We did not know about the Feigenbaum constants or Kepler’s conjecture. For sure, we had never seen the cannonball stacking illustration that helped us to visualize the process by which a sphere becomes a lattice, becomes a triangle, and then becomes a tetrahedron. We are quite confident that our first four numbers are the right selections possibly even within the right order. If you believe otherwise, of course, we would love to hear from you.



Page 10 of 10                                                                                                               IN PROCESS

6 A hypostatic science. Our small-scale universe, defined as the first 1/3 of the total notations, ranges from notation 1 to just over 67. It is established only through simple logic and simple mathematics. Because it cannot be measured with standard measuring tools or processes, validating its reality requires a different approach. Because it cannot be measured with standard measuring tools or processes, validating its reality requires a different approach. Our first indication that it may be a reality is found between notations 143 and 144 at exactly one second where the speed of light “can be made” to correspond with the experimental measurement of the distance light travels in a second. Currently it appears to be one notation off which could be as brief as just one Planck Time unit.

One of our next tasks is to carry that out to a maximum number of decimal places for Planck Time and Planck Length, and then to study the correspondence to a Planck second, a Planck hour, a Planck Day-Week-Month, a Planck Light Year, and finally to the Age of the Universe and the Observable Universe.

Our goal is to determine if this is the foundational domain for the human scale and large-scale universe. We are calling this study a hypostatic science because it is a study of the foundations of foundations.

7 From SUSY to Symmetry Breaking and Everything In Between. One of the great hopes of the Standard Model and many of the CERN physicists is that supersymmetries will be affirmed and multiverses will wait. Within the Big Board-little universe model, their wish comes true. Plus, they gain a reason for quantum indeterminacy and embark on a challenge to apply all their hard-earned data acquired to embrace the Standard Model to the most-simple, base-2 model.

Here are four of our references through which we learned about the heretofore unnamed pentastar gap.  The Lagarias-Zong article (#4) is where I learned about Aristotle’s mistake.
1. Frank, F. C.; Kasper, J. S. (1958), “Complex alloy structures regarded as sphere packings. I. Definitions and basic principles”, Acta Crystall. 11. and Frank, F. C.; Kasper, J. S. (1959), and “Complex alloy structures regarded as sphere packings. II. Analysis and classification of representative structures”, Acta Crystall. 12.
2.  “A model metal potential exhibiting polytetrahedral clusters” by Jonathan P. K. Doye, University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom, J. Chem. Phys. 119, 1136 (2003) Compete article, ArXiv.org as a PDF: http://arxiv.org/pdf/cond-mat/0301374‎
3. “Polyclusters” by the India Institute of Science in Bangalore, illustrations and explanations of crystal structure. PDF: http://met.iisc.ernet.in/~lord/webfiles/clusters/polyclusters.pdf
4. “Mysteries in Packing Regular Tetrahedra” Jeffrey C. Lagarias and Chuanming Zong. 

8 Cellular Automaton.  Although the discipline is intimately part of computer science, its logic and functions are entirely analogous to mathematical logic, functions, and binary operations. We have just started our studies here with great expectations that some of this work uniquely applies to the first ten notations.

9 The Planck Platform.  All the numbers associated with the generation of the Planck Constant and the five Planck base units, plus the Planck units unto themselves are grouped together until we can begin to discern reasons to separate any one number to a notation other than notation 1.

10 The Magic Numbers.  Mathematical constants, dimensionless constants and physical constants are studied in relation to the isoperimetric quotient, close-cubic packing, number density and to bifurcation theory and to the 80 categories of binary operations. We will working with the processes developed by geometer, Steve Waterman, and chemistry professor, Michael Anthony Whitehead and the generation of the 142 physical constants.

11 The first 67 notations. Given the work of CERN and our orbiting telescopes, we can see and define most everything within notations 67 to just over 201. The truly unseen-unseen universe, defined only by mathematics and simple logic, are: (1) the dimensionless constants, (2) that which we define as infinite, and (3) the first 60-to-67 notations. It is here we believe isotropy and homogeneity are defined and have their being. It is here we find the explanation for the most basic cosmological constant. It is here the Human Mind takes its place on this grid which claims to include “everything-everywhere-for-all-time.”


Please note: We are still working on this article. A running commentary is being developed within the LinkedIn blogging area for Bruce Camber. Besides editing the overall document, we’ll are still working on the end notes using some of these reference materials.

Just over 200 base-2 notations from the Planck scale render a highly-integrated model of the universe.

The Big Board–Little Universe Project USA

Last update: 8 August 2017

IntroductionBig Board-little universe
In December 2011 two teachers and about 80 high school students rather naïvely began to explore a geometric progression that first went down in size to the Planck Length then reversed to go back up all the way to the Observable Universe (most links open a tab or window and go to an in-depth Wikipedia page).

The first chart to be developed, pictured on the left, measures 60×11 inches. It is a view of the entire universe and has just over 200 base-2 exponential notations (dividing or multiplying by 2, over and over again). Thinking that this simple math was already part of academic work, they began asking friends and family, “What is right or wrong within our logic for this model?” A two-year search did not uncover any references to base-2 and the Planck Length.* In that time, asking around locally and then globally, many people were puzzled and asked, “Why haven’t we seen a base-2 scale of the universe before now?”

An Integrated Universe View

Dubbed Big Board – little universe, this project started as a curiosity; today, it is an on-going study to analyze and develop the logic and potential links from their simple mathematics to all the current mathematics that define the universe, all its parts, everything from everywhere, and from the beginning of time to this very moment in time. Their hope is that this simple logic has simple links to real realities. Their standing invitation is, Open To Everyone, to help. This chart follows the progressions from the smallest to the largest possible measurement of a length. Subsequent charts engage the other Planck base units. With more questions than answers, this group is trying to grasp the logic flows in light of current academic-scientific research. Progress is slow.

Yes, on December 19, 2011 the geometry classes in a New Orleans high school were introduced to the chart on the left (Planck Length to the Observable Universe). In December 2014 they began to track Planck Time to the Age of the Universe. When they added the other the Planck base units to each maximum value, it seemed to call out for a horizontally-scrolled chart to follow each line of data more easily. Natural inflation becomes self-evident. And, that opened the way to question the big bang theory, especially the first four epochs — the Planck Epoch, the Grand Unification Epoch, the Inflationary Epoch, and Electroweak Epoch. In their search for answers about this model, questions abound.

This first chart is very early work.
Click on it, then click on it again to enlarge it

What’s next?

They ask, “Where are the informed critics to tell us where we are going wrong?” One rather brilliant, young physicist told them that the concept for this project is idiosyncratic. They quickly learned how right he was. Nobel laureates and scholars of the highest caliber were asked, “What is wrong with our picture? Where is our fallacy of misplaced concreteness?” The group is slowly analyzing the logic and developing their thoughts as web postings with the hope that somebody will say, “That’s wrong” and be able to tell them in what ways they have failed logically and mathematically.

The first 36 of 200+ notations of the horizontally-scrolled chartIf not wrong, the extension of their basic logic could begin to yield rather far-reaching results. For example, the Big Bang theory could get a special addendum, the first 67 notations. That would make it simple, symmetric (entirely relational), predictive, and totally other. The entire universe could get an infrastructure of geometries whereby many issues in physics, chemistry and biology could be redressed. The finite-infinite relation is opened for new inquiries. In this model of the universe, time-and-space are derivative of two quantitative qualities of infinity: continuity-and-symmetry. As a result, these derivative relations begin to have an inherent qualitative or value structure. If so, ethics and the studies of the Mind (the discernment of qualities) just might, for the first time in history, become part of a scientific-mathematical continuum. A trifurcated definition of the individual may emerge whereby people are simultaneously within the small scale, human scale, and large scale universe. Embracing a different sense of the nature of space and time by which both are localized by notation is surely enough; yet there will always be more. There are many working postings that have been written since their first chart; all of it needs constant updating. Many can be found through the top navigation bar option, INDEX.

Notes, lesson plans and posts (and all new posts) are being consolidated and linked from this homepage. Now called, The Big Board – little universe Project, it is a Science-Technology-Engineering-Mathematics (STEM) application. Secondary schools from around the world are being invited to join the exploration. Daily work on the topic is being researched, developed, and communicated through a sister website, http://81018.com.

The earliest postings and blogs were done by Bruce Camber within a section of his website — SmallBusinessSchool.org. That site supports a television series, Small Business School, that he and his wife, Hattie Bryant, started. It aired for 50 seasons on most PBS-TV stations throughout the USA and on thousands around the world via the Voice of America-TV affiliates.

Articles and blogs have been posted on WordPress, LinkedIn, Blogger, and Facebook (often those links open in new windows). An April 2012 article, formatted for and displayed within Wikipedia for a few weeks, was deleted on May 2, 2012 as “original research” by highly-specialized Wikipedia editors. Only then did this little group of teachers and students finally begin to believe that base-2 notation had not already been applied to the Planck base units. And, as they have grown in their analyses, it has become increasingly clear that this area of simple math and simple logic is a relatively new exploration and that notations 1-to-67 may be a key to unlock a new understanding of the nature of physical reality.

The challenge is to study the logic flow within their many charts, all based on the Planck base units, both up and down and across, to build on the question, “Is this logic simple and consistent? What does it imply about the nature of the universe?”

So, even now, there is much more to come. At the end of the year, 2015, a Lettermanesque Top Ten was added. In January 2016 an article, Constructing the Universe from Scratch, emerged. In April 2016 the horizontally-scrolled chart provided a better sense of the flow and of phase transitions. Still a “rough draft” this project has a long way to go! Bruce Camber says, “You are most welcome to add your comments, questions, ideas and insights!


* Footnote: In 1957 Kees Boeke did a very limited base-10 progression of just 40 steps. It became quite popular. In July 2014, physicists, Gerard ‘t Hooft and Stefan Vandoren wrote a scholarly update using base-10. Notwithstanding, base-2 is 3.3333+ times more granular than base-10 plus it mimics cellular reproduction and other naturally bifurcating processes in mathematics, physics, chemistry, biology, topology, botany, architecture, cellular automaton and information theory; it has a geometry; it has the Planck base units, and, it has a simple logic and so much more.


If you would like to contribute content to this site, please contact Bruce Camber
at camber – (at) – bblu.org or click here for more contact information. Thank you.

We Are Family

Elitists of every kind are caught up in the fallacy of misplaced concreteness.  The  abstract thought they treat as real, is “I am more important than you and my insights about life are better than yours.”  They hold that their beliefs, attitudes, and sense of self  are a proper basis for making judgments about “really-real”  realities. In spirit and in fact, we are all more alike than different and we all don’t know what we doapronn’t know. Here is a simple example.

We are family whether we like it or not.  Mathematics provides a simple logic.

Back in 1992, I had a special apron made to give as a Christmas gift for everyone in my immediate family and some of the extended family. As you can see, this apron (as pictured on the right) proclaims, “We are family! Everybody …includes you and me.”

Below that heading was a progression of our gene pool as we go back each generation. With a 20-year average spread for each generation, it didn’t take long to see how richly diverse we necessarily would become within 1000 years. Even with all the inter-marriage within relatively small villages and towns, diversity is quickly introduced with the unknowns.

The final conclusion was simply, “You’ve got the whole world in your genes.”

Let us see.  Take a look at the picture on the right. Consider each of those four columns:

On far left are the years going back in time. It uses 30 years per generation. Many would argue that 20-year average might be more appropriate. It has only been in the last few generations that the average has climbed up over 20 years. In the USA in 2007, the average was 25.2 years (U.S. Census Bureau 2007, November 30, 2007).

The next column is the successive number of generations as we go back in time. Just imagine if everyone in your family throughout the last 400 years magically came alive and were present at your birth.  How many people would be there to greet you? Most people do not have a clue.

In the fourth column there is a discussion.  The challenge is to grasp the simple concept that you have the entire world in your genes… that everyone on earth is related.

The First Thousand Years

1st  = Your immediate family  = There is your Mom’s side & your Dad’s side.
2nd = Just 20 years ago  = Four grandparents – two more uniques
3rd = About 40 years ago  = Eight great-grandparents;  four more uniques
4th = 60± years ago  = 16 great-great grandparents; 8 more uniques
5th = 80± years ago  = 32 great, greats; 16 more possibilities
6th = 100±  = 64 Great-Greats; up to 32 more possibilities
7th  = 120±  = 128 Great-Greats
8th  = 140±  = 256 Great-Greats
9th  = 160±  = 512 Great-Greats
10th  = 180±  = 1024 Great-Greats
11th  = 200±  = 2048 Great-Greats
12th  = 220±  = 4096 Great-Greats
13th  = 240±  = 8192 Great-Greats
14th  = 260±  = 16,384 Great-Greats
15th  = 280±  = 32,768 Great-Greats
16th  = 300±  = 65,536 Great-Greats
17th  = 320±  = 131,072 Great-Greats
18th  = 340±  = 262,144 Great-Greats
19th  = 360±  = 524,288 Great-Greats
20th  = 400±  = 1,048,576 Great-Greats
400 + years ago. You can easily calculate the year. In just just 20 big generations we all have over 1±  million genetic strands and many, many unique family names.
21st  = 420±  =  2,097,152 Great-Greats
22nd  = 440±  = 4,194,304 Great-Greats
23rd  = 480±  = 8,388,608 Great-Greats
24th  = 500±  = 16,777,216 Great-Greats
25th  = 520±  = 33,554,432 Great-Greats
500 years ago – do a quick calculation of the date – what would you guess the world’s population is?  Estimates are right in the range 500 million people.
26th  = 540±  = 65,108,864 Great-Greats
27th  = 560±  = 130,217,728 Great-Greats
28th  = 580±  = 260,433,556 Great-Greats
29th  = 600±  = 520,867,112 Great-Greats
30th  = 620±  = 1,041,734,224 Great-Greats
31st  = 640±  = 2,083,568,448 Great-Greats
32nd  = 680±  =  4,167,136,496 Great-Greats
33rd  = 700±  = 8,334,272,992 Great-Greats

In relatively short order we have more genetics — 8,334,272,992 — than the total world’s population today.

That is over 8 billion genetic recombinations within 33 generations.  That is in as few as 700 years and perhaps as many as 1000 years.  What happens with another 1000 years by going back another 1000 years is staggering.

As we go back our genetic richness increases greatly, yet the world’s population decreases. Similar to the idea that there are only six degrees of separation, here we learn there is hardly a degree of separation.

No wonder there are so many people descendant from that little group on the Mayflower! About 1000 years ago we would all have over 15 billion women within our genetic pool. Given that there are so many overlapping genetic pools, it is a powerful thought that we are all in some manner related.

Of course, we recognize that not too long ago there was not today’s mobility and we were marrying not-so-distant cousins, yet with the introduction of one wandering troubadour, genetic diversity is guaranteed.