On Constructing the Universe From Scratch

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

An Early Draft

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“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)

Abstract

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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Introduction.

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.

https://bblu.org/2016/01/08/number/#2

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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.

https://bblu.org/2016/01/08/number/#3

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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
3.1415926535897932384626433+
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)
https://bblu.org/2016/01/08/number/#4
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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

74.0480489693061041169313498345

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.

                                                                                       https://bblu.org/2016/01/08/number/#6

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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

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 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.

https://bblu.org/2016/01/08/number/#9

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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.”

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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.

What shall we call the Pentastar 7.38 degree gap?

Pentastar

  • Eight vertices can be ordered to make five regular tetrahedrons.
  • These five regular tetrahedrons using a common center edge will create one 7.38º (degree) gap which is, to date, unnamed.

OldChryslerLogo119

  • Five irregular tetrahedrons were used to make the Chrysler logo; introduced in 1962,  it was named the Pentastar.
  • For the purposes of this article our object is called a Pentastar and the focus is on the 7.38º  gap.

There is a dynamic between the Pentastar and pi.  There is also a dynamic with cubic close packing, bifurcation theory and cellular automaton.

The purpose of this short article is to introduce the Pentastar 7.38º  gap, to invite initial comments, and to invite experts to study those relations and dynamics with pi.  Is it here that we find the foundations for quantum theory, identity, chaos, indeterminacy, and the self?

It is one of the most simple constructions in the universe, and it must in very special ways interact with the non-repeating, never-ending numbers of pi and the other nine fundamental numbers and number groups that are discussed in the article about the importance of numbers, On Constructing The Universe From Scratch.

References:

  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) The compete article is also available at ArXiv.org as a PDF: http://arxiv.org/pdf/cond-mat/0301374‎
  3. “Polyclusters” by the India Institute of Science in Bangalore has many helpful 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, a focused look at the history.
  5. http://www.hyperflight.com/pentagon-construct.htm

Steve Waterman & Michael Anthony Whitehead

Our effort to discern the Top Numbers of Key Importance  within our little universe for The Big Board-little universe Project  began with this work by Steve Waterman and Prof. Michael Anthony (Tony) Whitehead (Chemistry, McGill University, Montreal).

Steve and Tony got together to publish an article, Self-Consistent Field Approach To The Physical Constants: All Physical Constants Are A Function Of Pi (Π) Though poorly received by the academic community, the article will be studied to attempt to understand their rather unique sense of numbers.

The generalized claim is that all the physical constants are derived from four math constants.  They did the work to explain this statement with 142 such constants.  Over time, every calculation and conclusion will be reviewed. Currently, our study look at their four math constants:

  1. Pi (Links go to Wikipedia when within the body of the subject)
  2. The isoperimetric quotient of a sphere
  3. Sphere packing  (CCP and NCCP)
  4. Number density

On its face, these four math constants do not seem to have enough substance to define all the better known physical constants. Yet, the Waterman-Whitehead team may have the kernel of an idea that truly opens the way to define the first 67 notations in ways that inform isotropy, homogeneity, the nature of infinity, the nature of the finite,  and the function of math constants to create the bridges to infinity and the physical constant to build bridges to physicality or space and time

Top Ten Reasons to give up those little worldviews
for a much bigger and more inclusive UniverseView

  T  h  e   B  i  g   B  o  a  r  d   –   l  i  t  t  l  e    u  n  i  v  e  r  s  e    P r o j e c t

GreyLine

“Number 10.” The Infinite is known through continuity, number and order.  The Finite is defined by space and time.

The first principle of the Big Board-little universe is that God the Creator creates and sustains everything, everywhere, for all time, which gives our universe continuity, the necessary condition for order.

Explanation: We uncovered two of the largest continuity equations. First, we started at the smallest possible measurements of a unit of length and time. We  used base-2 exponential notation, multiplying by 2 over and over again. Using this simple math and logic, two of the most fundamental continuity equations are created within just over 201 notations or doublings from the Planck Length and Planck Time out to the Observable Universe and the Age of the Universe respectively (click here to review the chart in another tab or window). It is all very approachable and it goes right to the heart of the commonsense logic instantiated by Sir Isaac Newton’s infinite sense of space and time. Within The Big Board-little universe Project, space and time are discrete, quantized, derivative-yet-dynamic. Each has a beginning and an end. And, that changes everything.

More... And even more...

 

Please note: Links within each paragraph go to Wikipedia pages and most often open a new tab or window. Links from “More” at the end of each item, go to some of our earlier discussion within the project.

 

“Number 9!”  The Love Equation is a real equation and it is best understood  through symmetries.

Also a first principle of the Big Board-little universe, there are deep and abiding geometries that bind everything, everywhere, for all time, within those 201+ notations.  Symmetries structure everything, both the seen and the unseen.

Explanation: Help to uncover the deepest and most-compelling symmetries throughout the universe by working with just our first continuity equation, from Planck Length to the Observable Universe. In the first notation we doubled the Planck Length. Still so small, it is meaningless. Yet, when we follow scaling laws and dimensional analysis and assume the Planck Length is a vertex, we multiply by 8 so the numbers of vertices increase, 1, 8, 64, 512, 4096… Complexification occurs rather quickly. By the 20th notation, there are over a quintillion vertices with which to work. There are at least 40 doublings (or notations or groups or sets) before there is an expression of physicality within measurable space and time. A point-free geometry (Whitehead) is assumed (hypothesized, hypostatized, imputed and/or instantiated) to give structure and definition to those first 60+ notations. The only evidence of such structure is given within the homogenity and isotropy throughout our little universe (and within the supersymmetries of particle physics). Thereafter, manifestations of symmetry are actually seen throughout the universe.

More...   Even more...  And, even more...

 

“Number 8.” Harmony creates a fleeting moment of perfection that inspires us and guides us.

Harmony is also a first principle of the Big Board-little universe. All those symmetries that bind everything, now begin their movements across all time within those 201+ notations. On occasion, there are moments of perfection.

Explanation: Empower symmetries to interact with other symmetries within each notation and across notations. The old concepts related to the harmony of the spheres take on new meaning. By adding the continuity equations defined by Planck Time, symmetries have more than a form; they have a function that moves within a notation and throughout the notations, creating a momentary perfection or perfected state within space-time. Also, we begin to understand the very natural antithesis, chaos and indeterminacy, especially by looking at the most basic structures with the first 60 or so notations…

More... More to come... (pages about harmony being developed)

 

“Number 7.” We can re-engage all the mystery in  Science-Technology-Engineering-Mathematics (STEM).

Every aspect of education is touched and opened up. Our goal is to use the Big Board-little universe as a STEM resource, first within 10 high schools, then a pilot of 100, then 1000 schools…

Explanation: Help to introduce this new order of things whereby space and time are derivative of continuities and symmetries. Empower deeper insights into Science, Technology, Engineering and Mathematics within the Big Board-little universe construct. One of the initial aims of our Kickstarter program is to engage no less than 100 high schools to use the Big Board- little universe model to encourage STEM research. We can see and feel a burst of creativity that begins to address the old questions and opens up a huge boat of new questions.

More to come... (STEM work for schools is being tightened up now)

 

“Number 6.” Calm your soul within a Quiet Expansion of the universe.

Could the Big Bang theory be deflated by the Big Board-little universe’s Quiet Expansion (QE)? Could a QE become a source of order and inspiration within education… for the general public?

Explanation: We will build upon an article that was written in September 2014; we were thinking about the Big Bang theory while working with the chart of just the Planck Length. It seems that one could easily impute those first 60 doublings became the foundation of pervasive, unseen structural geometries that finally give rise to the physicality of particle physics. It seemed that the first 67 notations could have been a rather quiet expansion of creation.

More...

#5. You are the center of it all.

Humanity and so many facets of our human population has been marginalized by science, religious beliefs and arrogance. Within this emerging model of the universe, people are key.

Explanation: Within the 201+ notations at 100 is the human sperm cell and at 103 is the human egg. In the middle of the Planck Length doublings is the vibrancy that gives us modestly intelligent life. A molecule of water, the source of continuity within life, is just 280 picometers, within the 80th notation, has a special symmetry with so many other chemical and biological processes within the next 20 notations.  If you are the center of it all, we say, “Sit up and be sure to drink a lot of water.”

More... (new tab or window; a tour of the Planck Length chart)

#4. Your Mind is actually on the grid after all.

The brain-mind debate is centuries old. The mind has had no place to be… no place to rest. Unwelcomed and questioned, here we hypostatize its place on the grid between notations 50 and 60.

Explanation: Nothing can be measured that fits into the first 60 notations or doublings of the Planck Length, so by engaging systems philosophy, we begin to construct an ideal (the same challenge that faced Lawrence Krauss with his book, A Universe from Nothing) starting with Plato’s forms. The doublings quickly become complexity. From Forms, to Structures, to Substances, to Relations, and finally to Systems, this is an idealized structure where the Mind seems to naturally reside within Systems.

More to come... (a page about the Mind is being specially developed) 

 

#3. You have choices: Small, Medium or Large.

We have obviously thrived in the Human-Scale Universe, yet we live and have our being within the 201st notation where we find the current time. Obviously there are huge intellectual challenges ahead!

Explanation: The three major divisions of the Universe — the Small Scale, the Human Scale, and the Large Scale — each has about 67 notations. As we study the chart of the five Planck base units, we can see ourselves in many places throughout it all at the same time. We hypostatize new functionality for wormholes for the mind and begin to grasp the very nature of a blackhole. To that end we now return to Hawkings’s 1975 paper, Particle Creation by Black Holes.

More...  (goes to a page of the Planck Length chart)

 

#2. You can get your act together.

We have been constrained by worldviews that ignore the larger universe and our role within it. We have been constrained by a science that has difficulty penetrating those notations below the 67th.

Explanation: An Integrated Universe View changes everything. Continuity takes its place at the centerfold. The symmetries within it capture our eye and imagination. There appears to be goodness in the universe and the place of asymmetries, indeterminacy, questions and openness, and the very nature of the self begins to thrive as a creative nexus! If only my Mom were still alive, she might just understand what motivated her to say so often to me, “You’re cruisin’ for a bruisin’.”

More... 

 

#1. Religion & Science can get together again.

Our worldviews can no longer ignore the constants and universals that define and give structure to the universe and our role within it.

Explanation: Our very-young and often naïve UniverseView is a call to all religions of every flavor. We all need a touch of humility to engage the openness of those constants and universals so we can see how each is used within the sciences and how these create bridges with the metaphors and analogies within religious history. My father was an Episcopalian turned Unitarian Universalist. As we were growing up, he would often say, “You can’t legislate morality.” He was right. It is much deeper than legislation and rules. Religion is part of the very fabric of ethics, universals, and constants. Their metaphors can be richer and more robustly textured. The Universe is so simple, so marvelous, so intricate, and extraordinarily complex all at the same time, we all should celebrate every hour of every waking moment.

More...   And more...

Top Ten Reasons

“Number 10.” Continuity contains everything, everywhere, for all time, then goes beyond.

The first principle of The Big Board-little universe Project is that the infinite is defined by continuity, number, order, symmetry, and relations and that the finite is defined by space and time.  Here the entire universe gets blanketed with simple equations.

Explanation: Help to drag the largest continuity equation out of the closet. It starts at the smallest possible measurements of a unit of length and time. That is the Planck Length and Planck Time; and, it goes out to the Observable Universe and the Age of the Universe respectively. It is all just simple math and logic. These two continuity equations, created by multiplying by 2 (base-2 exponential notation) have just over 201 notations or doublings. It is all very approachable and it goes right to the heart of our commonsense logic, the legacy of  Sir Isaac Newton’s infinite sense of space and time. Within The Big Board-little universe Project, space and time are discrete, quantized, derivative-yet-dynamic; each has a beginning and an end. And, that changes everything.

More... And even more...
Please note: Links within each paragraph go to Wikipedia pages and most often open a new tab or window. Links from “More” at the end of each item, go to some of our earlier discussions within the project.

 

“Number 9!” Symmetries structure everything, both the seen and the unseen.

Also a first principle of the Big Board-little universe, there are deep and abiding geometries that bind everything, everywhere, for all time, within those 201+ notations.

Explanation: Help to uncover the deepest and most-compelling symmetries throughout the universe by working with just our first continuity equation, from the Planck Length to the Observable Universe. In the first notation we doubled the Planck Length. Still so small, it is thought by most to be meaningless. Yet, when we follow scaling laws and dimensional analysis and assume the Planck Length is a vertex, we multiply by 8 so the numbers of vertices increase, 1, 8, 64, 512, 4096… Complexification occurs rather quickly. By the 20th notation, there are over a quintillion vertices with which to work. There are at least 40 doublings (or notations or groups or sets) before there is an expression of physicality within measurable space and time. A point-free geometry (Whitehead) is assumed (hypothesized, hypostatized and/or instantiated) to give structure and definition to those first 60+ notations. The only evidence of such structure is given within the homogenity and isotropy throughout our little universe (and within the supersymmetries of particle physics). Thereafter, manifestations of symmetry are actually seen throughout the universe.

More...   Even more...  And, even more...

 

“Number 8.” Harmony creates a fleeting moment of perfection that inspires us and guides us.

Harmony is also a first principle of the Big Board-little universe. All those symmetries that bind everything, now begin their movements across all time (within just over 201 notations) from the first moment to the current time.

Explanation: Empower symmetries to interact with other symmetries within each notation and across notations. The old concepts related to the harmony of the spheres take on new meaning. By adding the continuity equations defined by Planck Time, symmetries have more than a form; they have a function that moves within a notation and throughout the notations, creating a momentary perfection or perfected state within space-time. Also, we begin to understand the very natural antithesis, chaos and indeterminacy, especially by looking at the most basic structures with the first 60 or so notations…

More... More to come... (pages about harmony being developed)

 

“Number 7.” You can re-engage all those mysteries in Science-Technology-Engineering-Mathematics (STEM) and start to understand it all.

Every aspect of education is touched. Our goal is to use the Big Board-little universe as a STEM resource, first within 10 high schools, then a pilot of 100, then 1000 schools…

Explanation: Everything everywhere starts simply. This new order of things where space and time are derivative of continuities and symmetries (and occasional harmonies) will empower deeper insights into fabric and applications of STEM. One of the initial aims of our attempted Kickstarter program was to engage no less than 100 high schools to use the Big Board-little universe model to re-ignite a love for science and mathematics and all their derivatives. We can see and feel a burst of creativity that begins to address the old questions and opens up a huge boat of new questions.

More to come... (STEM work for schools is being tightened up now)

 

“Number 6.” Calm your soul within a Quiet Expansion of the universe.

Could the Big Bang theory be deflated by the Big Board-little universe’s Quiet Expansion (QE)? Could a QE become a source of order and inspiration within education… for the general public?

Explanation: We will build upon an article that was written in September 2014; we were thinking about the Big Bang theory while working with the chart of just the Planck Length. It seems that one could easily impute those first 60 doublings to be the foundation of pervasive, unseen structural geometries that finally give rise to the physicality of particle physics. It seemed that the first 67 notations would have been a rather quiet expansion of creation.

More...

#5. You are the center of it all.

Humanity and so many facets of our human population has been marginalized by science, religious beliefs and arrogance. Within this emerging model of the universe, people are key.

Explanation: Within the 201+ notations at 100 is the human sperm cell and at 103 is the human egg. In the middle of the Planck Length doublings is the vibrancy that gives us modestly intelligent life. A molecule of water, the source of continuity within life, is just 280 picometers, within the 80th notation, has a special symmetry with so many other chemical and biological processes within the next 20 notations. If you are the center of it all, we say, “Sit up, and be sure to drink a lot of water.”

More... (new tab or window; a tour of the Planck Length chart)

#4. Your Mind is actually on the grid after all.

The brain-mind debate is centuries old. The mind has had no place to be… no place to rest. Unwelcomed and questioned, here we hypostatize its place on the grid between notations 50 and 60.

Explanation: Nothing can be measured by an instrument that fits into the first 60 notations or doublings of the Planck Length, so by engaging systems philosophy, we begin to construct an ideal (the same challenge that faced Lawrence Krauss with his book, A Universe from Nothing) starting with Plato’s forms. The doublings quickly become complexity. From Forms, to Structures, to Substances, to Relations, and finally to Systems, this is an idealized structure where the Mind seems to naturally reside within Systems.

More to come... (a page about the Mind is being specially developed) 

 

#3. You are in three places at the same time.

We have obviously been defined in the Human-Scale Universe, yet we live and have our being within the 201st notation where we find the current time. And, just perhaps, our minds exist within a Systems construct of the universe between notation 50 and 60.

Obviously there are huge intellectual challenges ahead!

Explanation: Each of the three major divisions of the Universe — the Small Scale, the Human Scale, and the Large Scale —  has about 67 notations. As we study the chart of the five Planck base units, we can see ourselves in at least three places at the same time. We now need to determine how all three scales work coterminously to create personal identity. As a result, we hypostatize new functionalities for wormholes for the mind and the archetypal definition of human throughout the Human Scale Universe.  Hopefully, along the way we may even begin to grasp the very nature of a blackhole. To that end we now return to Hawkings’s 1975 paper, Particle Creation by Black Holes.

More...  (goes to a page of the Planck Length chart)

 

#2. You can get your act together.

We have been constrained by worldviews that ignore the larger universe and our role within it. We have been constrained by a science that has difficulty penetrating those notations below the 67th.

Explanation: An Integrated Universe View changes everything. Simplicity is the starting point. Continuity takes its place at the centerfold.  Symmetries within it capture our eye and imagination. There appears to be goodness in the universe and the place of asymmetries, indeterminacy, questions and openness, and the very nature of the self begins to thrive as a creative nexus! If only my Mom were still alive, she might just understand what motivated her to say so often to me, “You’re cruisin’ for a bruisin’.”

More... 

 

#1. Religion & Science can get together again.

Our worldviews can no longer ignore the constants and universals that define and give structure to the universe and our role within it.

Explanation: Our very-young and often naïve UniverseView is a call to all religions of every flavor. We all need a touch of humility to engage the openness of those constants and universals so we can see how each is used within the sciences and how these create bridges with the metaphors and analogies within religious history. My father was an Episcopalian turned Unitarian Universalist. As we were growing up, he would often say, “You can’t legislate morality.” He was right. It is much deeper than legislation and rules. Religion is part of the very fabric of ethics, universals, and constants. Their metaphors can be richer and more robustly textured. The Universe is so simple, so marvelous, so intricate, and extraordinarily complex all at the same time, we all should celebrate every hour of every waking moment.

More...    And more...

You are invited to be involved.

Introduction

BruceCamber130Hi, my name is Bruce Camber and I would like to take you on a quick tour of our entire universe.

You will see everything, everywhere, throughout all time, in just 202 steps, notations, layers or domains. It is all so very simple, we’ve asked, “How could something this simple be ignored for so long?”

We thought there must be something wrong with our simple logic. Just by dividing an object in half, over and over and over again, we found the smallest possible unit of measurement of a length (the Planck Length) in just over 112 steps.

We multiplied this object by 2. Just 90 times and we were out to the largest measurement of a length (the Observable Universe). That’s a total of just over 202 steps from the smallest to the largest possible measurements in the universe.

We started this exploration back in December 2011.  When we couldn’t find it on the web, I began sending out emails to my smartest friends, “What’s wrong with this picture?”

We quickly learned of Kees Boeke’s 1957 work in a Dutch high school where they toured the Universe in just 40 quick jumps.  They had no geometry. They didn’t use those smallest and largest measurements as their container and they were multiplying by 10, just adding  zeroes.

We started with a geometry. We were multiplying and dividing by 2. Now that’s how cells divide. Our process is more natural, more lifelike, and most importantly, we get to see a much more granular universe.

Plus, those largest and smallest measurements are some of the most important numbers in science today.  They are called the Planck Base Units; they were formulated between  1899 and 1905 by Max Planck, a Nobel laureate in 1918, one of Einstein’s mentors, and the father of quantum theory.

Today, we have two primary charts.  This original from 2011 is based on the Planck Length.  It has been updated many times. And, now there is a comparative chart using all five  Planck Base Units.

Our project is to collect all our thoughts and writings from the past four years, consolidate and refine them for prime time for all the university scholars to come in to either take it apart or to attempt to incorporate it into the fabric of academic research today.

At the very least, the great physicist, Freeman Dyson, agreed with me that it would make an excellent STEM tool for our high school students to learn Science- Technology-Engineering-Mathematics.

If it challenges the Big Bang theory, so be it.  Let’s be intellectually honest and explore the most simple logic and most simple model of our universe. Called, The Big Board-little universe Project, we welcome you to join us.

Tetrahedral-Octahedral chains

https://bblu.org/2015/12/11/tot/  https://bblu.org/2012/12/11/tot/

Of course we just may be wrong.

A working draft
First posted:  December 8, 2015
Most recent update: Sunday, 25 September 2016 (Yes, still in process, still being updated!)

Please note:  All links open a new tab or window.

It was inevitable. Our little Big Board-little universe model is getting rammed by the big bang theory and its illusive black holes.

In September 2014 I tested an idea: “Did a Quiet Expansion Precede the Big Bang?” There seemed to be some credible scientific questioning by respected scientists about the cosmology of the big bang theory. Also, given that academia had never wrestled with base-2 exponential notation from Planck Length and Planck Time to the Edge of the Universe and the Age of the Universe (respectively), we thought there was a possibility that the big bang cosmology was a bit upside-down. Yet, our simple challenge from our simple perspective was still quite young and admittedly naïve; we knew we would not, and could not, be a serious challenge to one of the most formidable theories in science. But then on November 26, 2015, an article in AAAS Science magazine (DOI: 10.1126/science.aad1182) raised fascinating questions within black hole physics; it has become entirely obvious to go forward with the Big Board – little universe model, we must engage the entire history of big bang cosmology and ultimately every related facet within its astrophysics. It is such a daunting task, one would be inclined to give up quickly. But, logic is logic; simplicity is simplicity. We’ll take it one slow step at a time.

Nevertheless, we just may be wrong. Let me review our work a little more.

Using our very simple logic, simple mathematics (power of two) and the Planck base units, we developed our first charts with somewhere just over 202 notations. Our emphasis had been on just the Planck Length. Rather sweetly, that first chart had placed humanity in the center of the 202+ notations. In December 2014, we plotted Planck Time side-by-side with the Planck Length and followed it out to 13.78 to 13.81 billion years. Now our charts logically included everything, everywhere, throughout all time. Yet, our known universe and the entire history of humanity were all within notation 202 (possibly including a bit of 201). Human life and history are barely a speck within those 13.78+ billion years of this universe. Though the Planck Time chart offered many new insights and raised some hard questions, in February 2015, with the addition of the other three Planck base units, mass – charge – temperature, even more difficult questions were raised.

The placement of Planck Temperature was such a key question. Does it begin simply or does it begin with a bang, a full bore, the hottest of the hot?  And, if it starts with the other Planck numbers, does it continue to double from there?  The universe is getting warmer, but not quite that warm!  And, of course, the opposite makes no logical sense; the universe is not getting cooler. So, we wonder, “Maybe our progression is a straw man. Maybe it should be ignored.”

As we studied the progression of the others, we asked “Is there any inherent logic anywhere?” [A later analysis seems to suggest there is.]

The first number that provides us with a commonsense experience is Planck Mass. At the 31st notation we see that the total mass of the universe is now up to 103 pounds or 46.702 kilograms.  With the other units so small, there does appear to be a certain simple logic to it all. At the 67th notation, with the first instances of physicality, the weight of the universe is now over 3.21196×1012 kg (or 7.08115968×1012 pounds). Yes, and there is a certain logic to that, too.

The temperature scale is the key. We know there is order in the universe. Yet, the Planck Temperature makes it a special challenge. Some scientists claim if we were to start it with the other Planck base units, it is already hotter than the sum total of the universe. So, we reversed-order its progression. While the other Planck base units are doubling from the bottom up, the Planck Temperature started at notation 202 and is divided-by-2 from the top down.  It just so happens between notations 104 and 103, very much within the primary human scale, the temperature is 310K which is 98.33°F or 36.85° C.

The logic within the time column suggests that the history of discussions about a variable speed of light could be reviewed in light of this model of the universe.  Though most of the figures within the column can not be tested, there may be logical constructs that could suggest something about the overall cogency of the model.

That AAAS Science magazine article, placed within the context of the list of unsolved problems in physics and mathematics, posses a challenge to us, yet certainly no more than those larger lists of unsolved problems.

We’ll stop here for awhile to see what holds water.

Thank you.  -Bruce Camber

Dark Matter, Cosmology and the Large-Scale Universe

First draft. In process. Your feedback is key.  Last update: January 19, 2016

Yes, today is Thursday, November 26, 2015. Paris is healing. Al-Raqqah is burning. And, without question, we all need a new model of who we are and why we are. There is simply too much darkness within this world and within our views of the universe.

Many people are aware that we have been on a speculative journey 1 that began in 2011 in a high school. Our journey is based on an idiosyncratic way of looking at our universe.2 Everything, everywhere, throughout all time is contained within just over 201 base-2 exponential notations from the Planck Base Units out to their largest possible measurements, always “this given moment”  or the Now.  Although our charts are simple, logical, and comprehensive,  and all the numbers show us an exquisitely interconnected universe, they challenge some of our commonsense worldviews.

It is not easy to change one’s conceptual frame of reference. Oftentimes I feel a little slow because it becomes so difficult to put one-and-one and two-and-two together. But, we are motivated to break through the bottleneck of questions that have remained unanswered over our lifetime and throughout the centuries. We are pushed to ask, “What are we missing?” Taunting myself, I say, “Go over this one more time; you really are missing something here.”

Dark Matter and Dark Energy are in that camp for me. Yet, recently a faint light has come on. A new book by physicist, Lisa Randall, had become a subject of a discussion over lunch.  The subjects of cosmology have always been way out there for me. Since childhood, especially on the occasion of a dark, clear Maine night, I have had a visceral reaction to it all. Spooked, jammed and suffocated by the vastness of the seemingly infinite universe, truly impossible to take it in, I learned to avoid cosmology and astronomy.

Dark Matter 3, 4 (links that go to Wikipedia open new tabs or windows).  I had begun thinking that Dark Matter was a misnomer. Within the Big Board – little universe model, it is not dark per se, especially if part of the first 60 notations where there is an absence of light. Within our isotropic and homogeneous universe, space-time-charge-mass-and-temperature have a tightly-woven fabric, tiled and tessellated defined by base-2 exponential notation and the Planck Base Units.

Though associated with analyses of structures on the order of galactic scale, Dark Matter may best be seen within the context of all 201+ base-2 notations, yet especially the first 60 or so notations.

Everything, everywhere, throughout all time.  That is the simple mathematical model we call the Big Board-little universe.  We can see that space and time are contained.  We can see a very simple beginning  and we see-experience-feel the current time.  We have our seeing-experiencing-feeling moments within the current time which is within the 201st notation.  We have the physical definition of parts, for now I call these our physical archetypes  between the 67th and 116th notations within the Human-Scale Universe.  Our most essential being, the archetypes of our archetypes, are within the small-scale universe. Everything-everywhere-throughout-time has some kind of presence with the small-scale, human-scale, and large-scale universe. 

There will be many challenges ahead to texture, define and defend such statements especially given that Dark Matter now constitutes only as much as 26% of the universe.5   Out of our naïveté, it just may be that our simple model, this Big Board – little universe,  gives Dark Matter a space and time, mass and charge, and a reason for being, and for being where it is.Gold & Diamonds

I believe our little chart is like a gold and diamond mine because the key figures of the universe are all there just waiting to be examined.  These figures have been given a cursory review.  It is now time for the professionals to go in and take a hard look.  I believe we can find configurations within those first 60 notations that can give rise to the observations and research throughout the entire history of cosmology and astronomy.

Most speculative:  The small-scale universe is the human-scale universe is the large-scale-universe. It is discrete, quantized and derivative of continuities and symmetries and even an overarching harmony of the universe. Within this speculative journey we are defined by every notation. Our particularity and humanity come out within the 101 to 116th of the Planck Length but we are fully at the 201+ notation within “the moment” or “the now.”

A special challenge will be to  come up with a better name than Dark Matter.  Although the inherent continuity equation for those 201+ notations has classic characteristics generally used to describe God, here we will rely strictly on the simple logic and mathematics, the Planck Base Units, and basic geometries to create the parameters for our naming convention.

Dark Energy. Though this conceptual frame of reference is related to the expansion of the universe, and dark energy weighs in at 68.3% of the total energy in today’s observable universe, we would postulate that it, too, is related through the Planck Base Units and the systemic expansions within the first 60 steps of the Big Board – little universe model. Light (a light second) does not appear until the 143 notation; that requires another 80 or so steps or notations or doublings from those first 60.

Projections. It has been almost four years since we began the discussions about our charts of the Big Board – little universe.  It was only three years ago that we were encouraged to continue our study of the Planck Base Units by Prof. Dr. Frank Wilczek6,7 of MIT (a world-renown physicist and champion of Planck’s work). In December 2014 Planck Time was added to the chart.  Then, in February 2015 the other Planck base units were included.

Obviously, for me, concepts need time to incubate.

First, as uneven as we are, I hope we are getting closer to justifying to the academic communities to come in to take a look at the inherent structures of the first 60 notations. To begin examining how those first 60 notations came to be and why they have been ignored, we have begun to focus on all the research and all the data from cubic-close packing (ccp), face-centered cubic (fcc), hexagonal close-packed (hcp), root system (A3) and Lie theory. It seems that all these applications and functions apply to the first 60 notations. And, inside those first 60 steps come all the dimensionless constants and soon thereafter, all the physical constants, and soon thereafter, the fermions and every expression of physicality.

That’s a rough outline within which our research of the first 60 notations will proceed. Now, where’s Lisa Randall 8 this morning and what has she been saying about dinosaurs?

Thank you.

***

Endnotes:
1  Speculative journey, dubbed the Big Board – little universe, began in December 2011 in our high school geometry classes.
2  Idiosyncratic way of looking at our universe is actually based on simplicity itself. In December 2014, Planck Time was added alongside the Planck Length. That was filled with pleasant surprises. Then in February 2015, the Planck Mass, Planck Charge, and Planck Temperature were added.
3,4,5  Dark Matter is the subject of many scholarly articles.  The Wikipedia entries, however, are straightforward, easy reading:
https://en.wikipedia.org/wiki/Dark_matter
https://en.wikipedia.org/wiki/Lambda-CDM_model
https://en.wikipedia.org/wiki/Planck_%28spacecraft%29#2015_data_release
6,7  Prof. Dr. Frank WilczekThroughout December 2011 and then throughout the following year, I asked literally hundreds of people, “Can you responsibly multiply the Planck Length by 2?” In December 2012, we got a response, an answer from Prof. Dr. Frank Wilczek,  “One can certainly divide (or multiply) by two repeatedly, and generate different numbers or scales, just as one can with powers of ten.”
https://bblu.org/2012/09/03/analysis/#Wilczek
https://bblu.org/2015/07/24/simple/#CMO
8 Many years ago, back when we were doing our weekly television productions, I called and talked with Lisa Randall about doing a PBS-special about her book, Warped Passages. She had been inundated with such proposals. Subsequently, in 2012, I sent a note to ask about the cogency of our base-2 model. We had been told by an astute-but-young theoretical physicist (who asked to remain anonymous) that our work was idiosyncratic, but he wasn’t quite ready to say that it was not even wrong. We’ve asked some of the finest scientists from around the world and the brave among them in some way said, “Carry on (…but please don’t quote me).”

Lisa’s new book, Dark Matter and the Dinosaurs: The Astounding Interconnectedness of the Universe, reaches the same general conclusion as we do about the connectedness of the universe, yet I am rather confident that she would distance herself from our work and the reasons for our conclusion!

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A few of the articles that have been written over the years.  These are all being updated and consolidated here.

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.

 

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