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# Free space, singularities, vacuums… all relative

by Bruce E. Camber, April 2018

In our model free space and singularities are a place for converging formulae.

Keys to this Quiet Expansion: Within the big bang theory (bbt) it is theorized that the four forces of nature — gravity, electromagnetism, the strong force, and the weak force — become a singularity. We are not convinced. We assume these four are encapsulated within all four Planck base units and the constants that define them, and some manifestation of this unification is carried throughout all 202 notations. Those Planck base units define length, time, mass, and charge; and, these are further defined by the speed of light (or special relativity), the gravitational constant (or general relativity), the reduced Planck constant (or ħ or quantum mechanics), the Coulomb constant (or ε0 or electric charge or electromagnetism), and the Boltzmann constant (or kB or of temperature).

This Planck scale is not beyond logic, numbers, and conceptual integrity. Rational, sentient homogeneity, isotropy and simple logic rule. Yet, within the Quiet Expansion (QE) model, we have applied that simple logic somewhat arbitrarily by placing Planck Temperature at the top of the scale, just beyond the 202nd notation and then dividing by 2, it goes down approaching Absolute Zero. We are ready to adjust this scale at any time when a more integrative logic prevails! Also, we are increasingly finding a simple relational logic between the four original Planck base units.

Within the QE model, the Planck Charge, a Coulombs value, is taken as given. Within the big bang theory (bbt), the Planck Charge is ignored. The bbt value is as large as possible. Their measurement is given in GeV units, one billion electron volts. Add 1016 zeroes and you have quite a charge.

To begin to understand all these numbers and their correlations, questions are asked, “Are these all non-repeating, never-ending numbers like Pi? Are all numbers that are non-repeating and never-ending somehow part of the infinite yet also the beginning of quantum mechanics?” The suggestion has been made that we carry out each of the Planck numbers at least 10 decimal places, and if need be, 100 decimal places, and possibly even 1000 decimal places, to see if patterns can be discerned. We recognize that relative to other units of measurement, such as the SI base quantities, the values of the Planck units are approximations mostly due to uncertainty in the value of the gravitational constant (G).

The QE model holds that things are simple before complex and everything is related to everything. Imputed, hypostatized and/or hypothesized are pointfree vertices and simple geometries as the deep infrastructure that gives rise to the work on combinatorics, cellular automaton, cubic close packing, bifurcation theory (and the Feigenbaum’s constants), Langlands program, mereotopology (point-free geometry), the 80-known binary operations, and scalar field theory. Here are people working on theories and constructions of the simple, yet their concepts are anything but simple.

The original document in its entirety is here…

# This project began on Monday, December 19, 2011.

###### CENTER FOR PERFECTION STUDIES: CONTINUITY•SYMMETRY•HARMONY  USA • JANUARY 2018 Homepages: Just Prior 1|2|3|4|5|6|7|8|9|10|11|12|13|14|15|16|17|18|19|20|Original

Before this project ever began, there were longstanding beliefs, presuppositions and first principles that shaped and colored every insight, concept and idea:

•  First, there was continuity and it created order.

•  Then, there was symmetry and it created relations.

•  And, there are moments of harmony that create perfect dynamics.

Big Board – little universe, December 2011: Starting with the Planck Length, multiplying by 2 over and over and over again, 202 times, brings us out to the Observable Universe.

.Not finding it anywhere on the web, we started developing our first chart.

.

This highly-integrated grid-matrix-system of the universe is on a 6×1 foot chart with 202 notations or doublings. Eventually a horizontally-scrolled chart from four Planck base units to the Age of the Universe emerged.

Quiet ExpansionApril 2014: After three years of reflections, it seemed that this grid should be looked at in light of the big bang theory. Hawking’s infinitely dense, infinitely hot start of the universe had always required extralogic and a meta-physics.

Easily contrasted is a Quiet Expansion, a natural inflation from the Planck units. It fills in the missing data for the first 300 million years;  100% predictive and prescriptive, this chart and model of the universe somewhat affirmed all the cosmological epochs as already defined.  Logic?

Question: Could the Universe Be Exponential? November 2017 Multiplying the Planck units by 2, and each result by 2, over and over again is like a base-2 exponential notation. Could this progression be seen in light of Euler’s equations?  Might this universe have a fundamental sense of order, not chaos. More than multiplying by 2 over and over and over again, more than a mathematical grid, we became painfully aware that we needed to define the place where the finite and infinite meet and greet. It seemed so clear, so self-evident, the question is now raised, “Why not?

.

Harmony.  Yes, harmony. The study of Euler’s equations began slowly in November 2017… the simplicity of 0, 1, and pi, and the complexity of  i , an expression for all imaginary numbers, started to come together to teach us.  Inside the radius of every circle and every sphere, we began to see string theory as a dynamic weaving throughout 64± notations, the earliest fabric of the universe. Nothing was static. It is as if this fabric is in part textured by the thoughts-feelings-actions within each spacetime notation. Though we are all within the 202nd notation, it seems that all notations are always available to us and there is total fluidity between them.  More

Symmetry.  Indeed, symmetry. Planck Length divided by Planck Time is equal to Light ( ). As that simple equation for light comes alive in every notation, absolute space and time are no longer so sure of themselves.  Sir Isaac stutters as Max Planck smiles. Like no other, here is a real potential to shake up the sciences and our commonsense logic. More

Continuity. Now a continuity like no continuity ever experienced, we begin to see the entire universe as a whole extending with all its dimensionality right through a transformation nexus to an infinite of ever-so-many-more dimensions, colors, shapes, sounds and senses.  How could it be so easy when we have made it all so hard?

***************

Notes:  Redefining the very nature of time:  Planck Time is so small that the first second of the universe doesn’t emerge until just after Notation 143. The first light year is within Notation 169. Our large-scale universe begins to emerge between notations 196 and 197. The current notation, 202, includes all of human history and most of the history of our little earth. The 202nd notation is 10.9816 billion years billion years (346,545,888,147,200,000 seconds) — of course, it is currently expanding, still very much “on the make.”

This article is a subset of a working index of key postings over the past six years; it marks the beginning of our official anniversary day celebration,  December 19.

The Current Horizontally-Scrolled Chart. In 2011, the project started with a very simple chart that followed the Planck Length. Today’s working chart came out in April 2016 and follows the Planck base units. Not being the brightest lightbulb in the family, it took me awhile to realize, “That’s Euler’s equation. Leonhard Euler was describing the universe! He didn’t know it, but he was.” [See Endnote 1]

We live in an Exponential Universe! That’s new information. Throughout all of our mathematics communities today, scholars have had a special affection for Euler’s equation. It is a pretty equation. It includes the most fundamental numbers of mathematics. But now, there is an even more compelling reason to love the equation. It describes the functional dynamics of our universe better than any other equation. [See Endnote 2]

## Big Board-little universe · Exponential Universe · Quiet Expansion

This project now goes by all three titles. The European Space Agency’s Planck space mission and our NASA’s Hubble space mission have released the most accurate and detailed maps of the oldest light in the universe. They’ve opened up the universe and we have all been flummoxed with its depth and breadth. Yet, right in the face of all that new knowledge, this project comes along and calls it “a little universe” because it is encapsulated in just 202 notations. [See Endnote 3]

“Just 202 notations!” Yes, but even more importantly, space and time begin to look like they are necessarily derivate and finite. Both drop their absolute status given to them by Isaac Newton in 1868 (Principia Mathematica). In this emerging model, all the notations are still active and imprinting our expanding universe. Everything is related to everything and every notation impacts all other notations. [See all the other endnotes]

Dialogue with the universe. World-famous landscape architect, Charles Jenks says, “We’re in dialogue with the universe!” It’s a nice sentiment, but most of the world’s people are hung up within some little worldview. We believe it is time to explore an integrated view of the universe. This is just one simple offering.

A dialogue with the universe has yet to begin in earnest. Let us all say, before we get completely out of control, “Let the dialogue begin!”

**************

Endnotes:

[1] Today, you can now get your own copy of that chart! It measures 6 inches by 16 feet! It is a great conversation starter. https://81018.com/chart

[2] Do we live in an exponential Universe? Is it time to change our orientation from worldviews to an integrated universe view. Worldviews are killing us. Yes, the purpose of this website and all these pages is to encourage your involvement with that idea.

[4] The Thrust of the Universe: What is it? / Visualizing the Universe (working notes)

[5] Measuring an Expanding Universe Using Planck Units (first draft)

[6]  First Principles and Key Equations as we explore the possibilities that our universe is exponential.

[7] Langlands IIIIIIIV

# On More Fully Recognizing The Infinite

###### ByBruce Camber, November 5, 2017

Précis: Whenever we look up into a clear night sky, often someone will say, “It goes on forever.” As children we learned to accept the infinitude of space and time. It is deeply ingrained within our thought structures. The problem is that this perception is not quite right.

History. Alchemist Isaac Newton was an experimenter and he made mistakes. He used trial and error. When he described space and time, he was off the mark. Though a genius, he was overly sure of himself and was often arrogant and condescending. Perhaps his penultimate contribution to our universe of knowledge is his sense of space-time and the infinite. These lasting imprints, however, were only partially right.

Isaac Newton, Lucasian Professor at Cambridge University (1669). Wikipedia says: “He was a devout but unorthodox Christian, who privately rejected the doctrine of the Trinity and who, unusually for a member of the Cambridge faculty of the day, refused to take holy orders in the Church of England.”

Infinity: Newton was confused about the nature of infinity. And, his confusion became our confusion; and, it has become the world’s confusion. Infinity to this day remains a problem for many in the academic community because it is too often interlaced with theological and religious language. The God wars between the arrogant among religious thinkers have caused many intellectuals to avoid religious language. A possible resolution to that conundrum is to use those terms that describe the universals and constants that originate in mathematics and science. Those terms should capture facets, a certain essence, that is part of both the finite and the infinite.

Three Faces of Infinity. Though most of these studies on this website are of the finite, the infinite has a substantial, abiding and fundamental role. The infinite describes a never-ending, never-repeating perfection or completeness or a wholeness that is not fundamentally part of the finite. Within these studies the infinite is defined as continuity, that which creates order, sequences, and the nature of time. The infinite is symmetry, that which creates the foundations of relations, of balance and of the nature of space. And, the infinite is defined as harmony, that which creates dynamics, and creates a space-time moment. The use of religious or theological language and concepts is left to each reader.
.
These three simple postulations about form-and-function assume a panoply of necessary-and-abiding transformations. When we look into the clear night sky, we “see” only as far as today’s transformations within this expanding universe.
.
Set within the 202 base-2 notations from the Planck base units to this current moment, the Now, it challenges us to see how the entire universe is bound together within what is initially a most-simple mathematical and geometrical system that profoundly redefines space-and-time and our relation to the universe. In 2011 the first name of the project was “Big Board – little universe.” Those 202 steps, all active, make for a rather intimate place.

We live in a highly-integrated exponential universe.
.
The continuity-symmetry-harmony concepts were first written down in 1972 to define the three faces of a perfected state in space-and-time. Each seemed to hold plausible answers to deeper questions about life and to such practical things as superconductors, quantum fluctuations, heartbeats, sleep, consciousness, reproduction… but the articulation of those facets of the transformations was too weak and generalized. There was no systemic application or coherence until it was discovered that our entire universe is contained within those 202 base-2 notations. So profoundly and deeply integrated, this chart gave us our first introduction to the first 67 notations that provide the footings to explain the homogeneity and isotropy of the universe. Here was the story of the Chessboard and Wheat all over again. There is so much space-and-time, every strain of mathematics will have its place within these first notations. There is enough room for consciousness, ethics, psychology and all other disciplines that have never had a place on a scientific grid.

This project opens new explorations. Certainly it re-awakens the finite-infinite relation, the nature of light, and the very nature of space-and-time. And, it thrusts enormous responsibility on each of us for our every thought, word and deed because it shows us how everything is related to everything and everything that we do impacts this little universe.

### ***

 Two additional pages to be added: (1) the small scale universe and (2) the large scale universe Small Scale Speculations Ideas Concepts and Parameters Boundaries and boundary conditions Trans- forma- tions Human Scale Numbers and Number Theory Large Scale 1 Planck Length ( ℓP ) Transition: Small-to-Human Scale 1. Display area: Every number/word hyperlinked – quick results display here 2. Options: Open full screen, new tab or window to the research of the experts 3. Also: Related videos-images and online collaborations with up to nine visitors 4. Key Links: Universe-View.org BigBoardLittleUniverse.org Transition: Human-to-Large Scale 205+ Observable Universe 2- 10 Forms1 Vertices:1024 77 Research ℓP:2.44×10-12m 78 X-ray Wavelength 95 Range: Visible Light 96 Bacteria Red Light 113 Hand-sizeH 16.78+cm 114 TextbookT 12.8+inches 131 Marathon 27+miles 132 54+ miles 87.99+km 204+ Observable Universe 11-20 Structure-Ousia V: 1+million 76 Gamma Wavelength 79 Huang Scale 94 Nanoparticles 100-10000+nm 97 Blood cellR 2.4+microns(µm) 112 Finger-size 3.3″(inches) 115 Things 67.134±cm 130 Race 21.998+km 133 Drive 108+miles 202-203+ Observable Universe 21-30 Substances V:1+ billion 75 Falstad Scale 80 Periodic Table 93 Gold LeafG 160.06±nm 98 Capillary 5.12+microns 111 Spoonful 4.19+cm 116 A child 52.86±in 129 Distances: 6.834+miles 134 Gravity-free 351.97+km 198-201 Superclusters 6.1-54+yottometers 31-40 Qualities V:1+ trillion 74 Research 1.52+x10-13m 81 HydrogenH 31±pm 92 Nanowires 80.03±nm 99 Cells 10.24±microns 110 MakeupM .82±inches 117 A bed 105.72±inches 128 Village 3.41±miles 135 Distance 437.41±miles 191-197 Virgo Supercluster3 41-50 Relations V:1+ quadrillion 73 Research: Tunneling4 82 HydrogenH 78+ pm 91 Little chipslc 40.01+nm 100 Sperm 20.48+microns 109 LipstickL 1.04+centimeters 118 Bedroom 5.37+meters 127 Walk 1.7+miles 136 Fly 874+miles 181-190 Galactic Group6 51-60 Systems The MindM 72 NucleusN 7.63+x10-14m 83 CarbonC 70±pm2 90 Viruses 20.007+nm 101 HAIR 40+microns 108 DiamondD 5.2+mmM 119 Home 35.24+feet 126 Downtown 1.37+km 137 Rivers 2815.81+km 171-180 Milky Way 61-65 Elementary Particles 71 GoldAU Nucleus 84 WATERW 3.12+x10-10m 89 Cell Wall 10+nm 102 Paper 81.95+microns 107 Ants 2.62+mm 120 Property 21.48+m 125 Superdome 687.45+m 138 USA-to-UK 3500+miles 161-170 SolarS Interstellar 65-67 Neutron Proton-Fermion 70 AluminumAl 1.90+x10-14m 85 DNAD 6.25+x10-10m 88 Insulin 5.00+x10-9m 103 EggE .16+millimeters 106 Sand 1.31+mm 121 Yacht 142+feet 124 Skyscraper 343.7+meter+ 139 EarthE 11,263+km 151-160 Solar SystemS 68 HeliumHe 4.77+x10-15 m 69 Electron 9.54+x10-15m 86 Buckyballs 1.25+nm 87 Ribosomes 2.50+nm 104 >.< Period .32+mm 105 Bacterium .65+mm 122 Sequoia 85+meters 123 Tall Building 171.86+m 140 GPS Satellite 22526+km 141-150 Earth Systems

###### Universe to Milky Way to our Solar System to Earth to 500 East 4th St. #484, Austin, TX 78701

https://81018.com/2017/11/04/infinitude/

# On More Fully Recognizing The Infinite

###### ByBruce Camber, first posted here on November 4, 2017 and updated over time

Précis: Whenever we look up into a clear night sky, often someone will say, “It goes on forever.” As children we learned to accept the infinitude of space and time. It is deeply ingrained within our thought structures. The problem is that this perception, in light of the base-2 exponentiation from the Planck units to the age and size of the universe, is probably not quite right.

History. Alchemist Isaac Newton was an experimenter and he made mistakes. He used trial and error. When he described space and time, I believe he was off the mark. Though a genius, he was overly sure of himself and was often arrogant and condescending. One of his many contribution to our universe of knowledge is his sense of space-time and the infinite. These lasting imprints, however, were only partially right.

Isaac Newton, Lucasian Professor at Cambridge University (1669). Wikipedia says: “He was a devout but unorthodox Christian, who privately rejected the doctrine of the Trinity and who, unusual for a member of the Cambridge faculty at that time, refused to take holy orders in the Church of England.” More (Wikipedia)…

Infinity: Newton was confused about the nature of infinity. And, his confusion became our confusion; and, it has become the world’s confusion. Infinity to this day remains a problem for many in the academic community because it is too often interlaced with theological and religious language. The God wars between the arrogant among religious thinkers have caused many intellectuals to avoid religious language. A possible resolution to that conundrum is to use those terms that describe the universals and constants that originate in mathematics and science. Those terms should capture facets, a certain essence, that is part of both the finite and the infinite.

Three Faces of Infinity. Though most of these studies on this website are of the finite, the infinite has a substantial, abiding and fundamental role. The infinite describes a never-ending, never-repeating perfection or completeness or a wholeness, given within the sphere and pi, that is not fundamentally part of the finite. Within these studies the infinite is defined as continuity, that which creates order, sequences, and the nature of time. The infinite is symmetry, that which creates the foundations of relations, of balance and of the nature of space. And, the infinite is defined as harmony, that which creates dynamics, and creates a space-time moment. The use of religious or theological language and concepts is left to each reader.
.
These three simple postulations about form-and-function assume a panoply of necessary-and-abiding transformations. When we look into the clear night sky, we “see” only as far as today’s transformations within this expanding universe.
.
Set within the 202 base-2 notations from the Planck base units to this current moment, the Now, it challenges us to see how the entire universe is bound together within what is initially a most-simple mathematical and geometrical system that profoundly redefines space-and-time and our relation to the universe. In 2011 the first name of the project was “Big Board – little universe.” Those 202 steps, all active, make for a rather intimate place.

Our conclusion: “We live in a highly-integrated, exponential universe.”
.
The continuity-symmetry-harmony concepts were first written down in 1970-72 to define the three faces of a perfected state in space-and-time. Each seemed to hold plausible answers to deeper questions about life and to such practical things as superconductors, quantum fluctuations, heartbeats, sleep, consciousness, reproduction… but the articulation of those facets of the transformations was too weak and generalized. There was no systemic application or coherence until it was discovered that our entire universe is contained within those 202 base-2 notations. So profoundly and deeply integrated, this chart gave us our first introduction to the first 67 notations that provide the footings to explain the homogeneity and isotropy of the universe. Here was the story of the Chessboard and Wheat all over again.  There is so much space-and-time, every strain of mathematics will have its place within these first notations. There is enough room for consciousness, ethics, psychology and all other disciplines that have never had a place on a scientific grid.

This project opens new explorations. Certainly it re-awakens the finite-infinite relation, the nature of light, and the very nature of space-and-time. And, it thrusts enormous responsibility on each of us for our every thought, word and deed because it shows us how everything is related to everything and everything that we do impacts this little universe.

+++

Isaac Newton did not have the advantage of Leonhard Euler‘s exponentiation. Base-2, the most simple, still lacks proper respect. Newton did not have Planck’s base units. He was Lucasian Professor #2 and gave us our commonsense worldview: Absolute space and time.
https://81018.com/uni/
https://81018.com/ math/
https://81018.com/lucasian/
https://81018.com/malaise/
https://81018.com/arrogance/

### ***

 Two additional pages to be added: (1) the small scale universe and (2) the large scale universe Small Scale Speculations Ideas Concepts and Parameters Boundaries and boundary conditions Trans- forma- tions Human Scale Numbers and Number Theory Large Scale 1 Planck Length ( ℓP ) Transition: Small-to-Human Scale 1. Display area: Every number/word hyperlinked – quick results display here 2. Options: Open full screen, new tab or window to the research of the experts 3. Also: Related videos-images and online collaborations with up to nine visitors 4. Key Links: Transition: Human-to-Large Scale 205+ Observable Universe 2- 10 Forms1 Vertices:1024 77 Research ℓP:2.44×10-12m 78 X-ray Wavelength 95 Range: Visible Light 96 Bacteria Red Light 113 Hand-sizeH 16.78+cm 114 TextbookT 12.8+inches 131 Marathon 27+miles 132 54+ miles 87.99+km 204+ Observable Universe 11-20 Structure-Ousia V: 1+million 76 Gamma Wavelength 79 Huang Scale 94 Nanoparticles 100-10000+nm 97 Blood cellR 2.4+microns(µm) 112 Finger-size 3.3″(inches) 115 Things 67.134±cm 130 Race 21.998+km 133 Drive 108+miles 202-203+ Observable Universe 21-30 Substances V:1+ billion 75 Falstad Scale 80 Periodic Table 93 Gold LeafG 160.06±nm 98 Capillary 5.12+microns 111 Spoonful 4.19+cm 116 A child 52.86±in 129 Distances: 6.834+miles 134 Gravity-free 351.97+km 198-201 Superclusters 6.1-54+yottometers 31-40 Qualities V:1+ trillion 74 Research 1.52+x10-13m 81 HydrogenH 31±pm 92 Nanowires 80.03±nm 99 Cells 10.24±microns 110 MakeupM .82±inches 117 A bed 105.72±inches 128 Village 3.41±miles 135 Distance 437.41±miles 191-197 Virgo Supercluster3 41-50 Relations V:1+ quadrillion 73 Research: Tunneling4 82 HydrogenH 78+ pm 91 Little chipslc 40.01+nm 100 Sperm 20.48+microns 109 LipstickL 1.04+centimeters 118 Bedroom 5.37+meters 127 Walk 1.7+miles 136 Fly 874+miles 181-190 Galactic Group6 51-60 Systems The MindM 72 NucleusN 7.63+x10-14m 83 CarbonC 70±pm2 90 Viruses 20.007+nm 101 HAIR 40+microns 108 DiamondD 5.2+mmM 119 Home 35.24+feet 126 Downtown 1.37+km 137 Rivers 2815.81+km 171-180 Milky Way 61-65 Elementary Particles 71 GoldAU Nucleus 84 WATERW 3.12+x10-10m 89 Cell Wall 10+nm 102 Paper 81.95+microns 107 Ants 2.62+mm 120 Property 21.48+m 125 Superdome 687.45+m 138 USA-to-UK 3500+miles 161-170 SolarS Interstellar 65-67 Neutron Proton-Fermion 70 AluminumAl 1.90+x10-14m 85 DNAD 6.25+x10-10m 88 Insulin 5.00+x10-9m 103 EggE .16+millimeters 106 Sand 1.31+mm 121 Yacht 142+feet 124 Skyscraper 343.7+meter+ 139 EarthE 11,263+km 151-160 Solar SystemS 68 HeliumHe 4.77+x10-15 m 69 Electron 9.54+x10-15m 86 Buckyballs 1.25+nm 87 Ribosomes 2.50+nm 104 >.< Period .32+mm 105 Bacterium .65+mm 122 Sequoia 85+meters 123 Tall Building 171.86+m 140 GPS Satellite 22526+km 141-150 Earth Systems

Finite-Infinite

# Dunning, Hayley

Hayley Dunning, Research Media Officer
Imperial College, London, Faculty of Natural Sciences
Article: http://phys.org/news/2016-07-big.html
WordPress: https://hayleydunning.wordpress.com/

`Most recent email: 9 June 2017`

Dear Hayley:

Well, obviously, my earlier note to you was not compelling!

A mathematically-integrated view of the universe in 202 notations
whereby everything is related to everything is not a theory of
everything. It is just a model of everything.

It is too simple for words.

We learned how to multiply by 2 in the second and
third grades and that is all we are doing.
The Planck base units are either wrong or right.
If they are wrong, where is the evidence?
There is plenty of evidence that they are right.

Ours is a model in the making:
https://81018.com/chart

Can we talk?

Thanks.
Most sincerely,
Bruce
*******************

Bruce Camber
http://81018.com

```First email: Thu, Oct 13, 2016 at 8:07 AM
Re: Article, "The Big Bang might have been just a Big Bounce"```

Dear Hayley:

Wonderful summary! “…physicists have long debated this idea as it means the universe began in a state of complete breakdown of physics as we know,” OR it began, not just simply, but very, very simply at the Planck scale (and as it does in so much of science), it just doubles.

Use base-2 notation from the base units and you get the universe as we know it in just over 200 doublings, notations, steps, groups, sets etc.

So simple, in 2011 a high school geometry class kinda-sorta backed into it!
http://bblu.org is the kids site (in the making).
http://81018.com is for everybody else.

I hope you will take a look and that we might hear from you.
Thanks.

Most sincerely,
Bruce
* * * *
Bruce Camber
New Orleans
http://bblu.org
http://81018.com

Reference: Perfect Quantum Cosmological Bounce, Steffen Gielen and Neil Turok, Phys. Rev. Lett. 117, 021301, 6 July 2016 ( https://arxiv.org/abs/1510.00699 ) Also: https://arxiv.org/find/all/1/all:+AND+Steffen+Gielen/0/1/0/all/0/1

# A Quiet Expansion of the Universe

##### ____________________________________________________________

Most recent update: February 2018

A working draft for the scientific – academic communities. Or a shorter version for the general public.

***********************************

Stephen Hawking rhetorically asked, “Where did the universe come from?” He continued, “The answer, as most people can tell you, is the big bang. Everything in existence, expanding exponentially in every direction, from an infinitely small, infinitely hot, infinitely dense point, creating a cosmos filled with energy and matter. But what does that really mean and where did it all begin?” Ref. [1] May 2016 PBS-TV series, Genius

Within this post, we focus on a very simple model and nascent theory that has only been explored by a relatively small group of high school people and others within our extended community. We ask, “Is it possible that the universe began with an infinitesimally small length and time, and a relatively small charge and mass? Yes, we use those numbers defined by Max Planck in 1899, the Planck base units, to begin. In this model the universe is most simple and the opposite of infinitely hot.  Also, this structure becomes part of the ongoing structure of the universe. It supports the claim of Neil Turok and his colleagues that this universe is in a state of perpetually starting.

Our simple journey started in December 2011. In 2012 we began asking more-pointed questions about the first 67 of 202 notations. In 2013 we began our rather informal studies of the big bang theory. In 2014 we began to question it. Today, we are hoping the experts can tell us why using the powers of 2, doublings from the Planck scale to the Age of the Universe is not a proper outline for a model and theory. Having learned how idiosyncratic it is, we have many questions. Might the mechanism for the doubling of a cell be a rather limited metaphor for the expansion of the universe? Could our universe be functionally based on the simplest mathematics, doubling both in size and in number up to this current notation and each step of the way? Is our universe, in fact, exponential (as in Euler’s equation), highly-ordered, and totally relational?

First principles. We postulate that the Planck scale is the unification of the four forces of nature with the unification of the Planck base units with those constants that define each unit, and that this unification, all defined as working ratios, is uniquely differentiated within each doubling throughout the entire 200+ steps from the first moment of creation to this moment, the current time and present day. It appears that all 202± steps are dynamic, actively participating in the current time and this definition of our universe. This postulation provides a working environment by which we hope to build a diversity of bridges from the Planck scale to all existing physical theories whereby each notation creates a very unique environment for predictive values.

We call this model the Quiet Expansion of the Universe, hereinafter, abbreviated QE.

We begin this study with the Planck Epoch, then attempt to justify reinterpreting the Grand Unification and Inflationary Epochs. The Electroweak Epoch begins the crossover which continues through the Quark Epoch and into the Hadron, Lepton and Electron Epochs. Thereafter, the QE will have so many bridges up from the Planck Epoch, it should become an expressway to the remaining epochs and all the useful definitions developed over the years within the big bang theory (hereinafter, abbreviated bbt).

The Planck base units. Further defined by the speed of light (or special relativity), the gravitational constant (or general relativity), the reduced Planck constant (or ħ or quantum mechanics), the Coulomb constant (or ε0 or electric charge or electromagnetism), and the Boltzmann constant (or kB or of temperature), all are bound within this Planck scale; and, herein it is proposed to be the foundations for a highly-ordered, totally-relational universe. The key to our model is multiplication by 2, starting with the Planck base units. A nexus of transformation between the finite and the infinite is defined by the crossing lines at “0” within the images on the right (just above Frank Wilczek).

We still have many questions. We have hopes and dreams. If the QE numbers can withstand the scrutiny of the academic and scientific communities, and we can begin to grasp the finite nature of space and time, and we can open a larger discussion about the nature of the finite-infinite relation, just maybe the bbt will recede and take a new role as an important chapter in academic as well as human history.

Our hope is that this posting will be able to stand the test of time; however, we full acknowledge that it is a “very rough first draft.”  Given the depth and breadth of the foundations upon which the big bang theory (bbt) currently rests, your comments while this posting is being refined, are most welcomed. If this embedded link does not open your email browser, my address is camber (at) 81018 (dot) com (or click on Contact (always within the navigation bar at the top).

Those pivotal Planck calculations were done between 1899 and 1905 by Max Planck. In December 2011 we were just beginning to learn about Planck and his calculations. We sought out experts and quickly found the work of Prof. Dr. Frank Wilczek (MIT).

Frank Wilczek. With very few exceptions, it was not until Wilczek began writing a series of articles in 2001, Scaling Mt. Planck, (Physics Today), did anybody think those Planck numbers amounted to anything more than numerology. It would take another ten years before we would come along, naively doing our thing with our geometries and simple doublings.

Though most academics are familiar with Kees Boeke’s 1957 work (Cosmic View) using base-10, we were not. Most all our academic contacts made quick reference to it, yet they were still surprised to see our chart from the Planck Length to the Observable Universe. Some asked, “Why haven’t we’ve seen this before now?” The others just thought it was more quantum mysticism  and numerology akin to Paul Dirac’s work with large numbers (link goes to a YouTube audio where Dirac explains it in his own words).

This simple work of multiplying the Planck units by 2, and then each result by 2, over and over and over again is a bit tedious. If you were to do it, in just over 200 steps you would emerge at the Age of the Universe and the Observable Universe. You can follow the progression in any one of several charts. A simple doubling is what cells do. Other processes like chemical bonding and bifurcation theory have analogous dynamics.

These 200+ doublings have at various points been called: (1) archetypes, (2) clusters, (3) containers, (4) domains, (5) groups, (6) layers, (7) notations, (8) ratios, (9) sets or (10) steps. We believe that each captures a face of the functionality within the notation. We recognize that these Planck base units can be computed in many different ways. Eventually, in order to refine results, the reduced Planck constant may be used. The various values of gravity (G) can be tested. Important at this time is consistency and equivalence of methodologies across all calculations within all 200+ notations. Our initial goal is to create a simple working model that outlines the general working parameters and boundary conditions to give us a platform. Now we begin looking at the key critical ratios throughout the model with a hope that we may discern natural groups and patterns that might help us to judge the veracity of the model itself.

The web page, Big Board-little universe, provides more background of our rather brief history.

## Big-bang Theory Drowns Out Discussions

To learn as much as possible as quickly as possible, we’ve used Wikipedia’s summaries. Wikipedia’s goal is to represent the best current thinking of the thought leaders within the relevant scientific communities. The scientists who are most often quoted have lived within this theory throughout their professional careers. It is part of their intellectual being. Notwithstanding, we believe most all of their work can be absorbed within the QE. Questions are primarily raised about the Planck Epoch, the Grand Unification Epoch, the Inflationary Epoch and the Electroweak Epochs. Taken together, the first three “epochs” represent less than a fraction of a fraction of a second within the QE model. And, with just a few tweaks, we believe some of this work and all the work within the subsequent epochs can be readily integrated.

The writers within the Wikipedia community overlap with those within these scientific communities. Wikipedia, constantly in the process of refining their writing, provides several summaries of the History of the Universe. All work based on observations and measurements has a place within the QE model. Our guess is that the interpretation of those observations and measurements will become richer and more informative when the QE parameters and boundary conditions are engaged.

In 1970 there were truly competing theories about the beginning of the universe. By 1990 the bbt had become dominant. In 2011 our little group of high school geometry people began to explore the interior structures of the tetrahedron and octahedron. Then we found within our tilings and tessellations, and then all the simple doublings from the Planck base units to the Age of the Universe and to the Observable Universe. That continuum appeared so simple, we first engaged it as an excellent STEM (Science-Technology-Engineering-Mathematics) tool. Yet, with further study and thought, it also seemed to challenge some of our basic commonsense assumptions about nature (the back story). As we studied our new little model, the bbt continued to solidify its dominance within the general culture at the same time we started to question it. We began to believe that the actual physics of the first moments of creation might be better defined by the simple mathematics of a quiet expansion, especially those first 67 notations. These 67 have never been recognized as such and certainly have not been discussed within academia. The great minds throughout the ages have been unaware of the 202 doublings, especially those first 67 steps. So mysterious are the 67, we began more actively to think about them and to make some postulations about their place and purpose.

This is our first posting about this quiet expansion. It is a result of our naive, informal, and often idiosyncratic studies of the Planck base units, simple doublings, and an inherent geometry assumed (hypothesized, hypostatized, and/or imputed) to be within every scale (doubling, layer, notation, step, etc) throughout the universe. We have moved slowly. Having backed into the Planck base units from our simple exercises in geometry class, we were not at all sure of ourselves. So, after observing our results for a couple of years, we began asking the question, “Could this be a more-simple, more-inclusive model of the universe than the big bang theory?” Because we only have the beginnings of an outline of a model, we continued our quest and continued to ask more questions:

## When? Where? How?

Who: The history of the Big Bang Theory (bbt) is highly documented. That doesn’t make it right because Its infinitely hot start is wrong. Notwithstanding, it became an intellectual cornerstone within experimental and theoretical physics, cosmology, and astrophysics.

What: To challenge the bbt appears foolhardy at best. Yet, there are many, many reasons to challenge it, but most of all because (1) it is overly complex and confusing, (2) it is not very good philosophy, and (3) it is very poor psychology.

Why: The first three key parts of the bbt, involving substantially less than a trillionth of a second, are based on hunches and a need to shoehorn data to support the model.

Wikipedia says, “Planck scale is beyond current physical theories; it has no predictive value. The Planck epoch is assumed (or theorized) to have been dominated by quantum effects of gravity.”

We say that the Planck scale is the starting point for the initial six notations (de facto defined by the bbt) and that these notations are shared by everything, everywhere in the universe. Painfully aware of the limitations of our vocabulary, these first notations are considered to be archetypal forms, structure and substance. Archetypal is used in the sense of the original pattern or model by which all things of the same type are representations, the prototype, or a perfect example. For more, see all of 67 encapsulating notations (opens in a new window or tab).

Both models have made key assumptions. We believe the QE model is internally more consistent, imaginative, and stimulating.

This “Singularity” Is a Meeting Place of Converging Formulae, perhaps also known as a Modulus-or-Nexus of Transformation

Keys to this Quiet Expansion: More than the big bang theory‘s four forces of nature — gravity, electromagnetism, the strong force, and the weak force — within this Planck scale we assume these four are encapsulated within all four Planck base units and the constants that define them, and some manifestation of this unification is carried throughout all 202 notations. And, as we have noted, the Planck base units are defined by length, time, mass, and charge; and, these are further defined by the speed of light (or special relativity), the gravitational constant (or general relativity), the reduced Planck constant (or ħ or quantum mechanics), the Coulomb constant (or ε0 or electric charge or electromagnetism), and the Boltzmann constant (or kB or of temperature).

The Planck scale is not beyond logic, numbers, and conceptual integrity. Homogeneity, isotropy and simple logic rule. Yet, within the Quiet Expansion (QE) model, we have applied that simple logic somewhat arbitrarily by placing Planck Temperature at the top of the scale, just beyond the 202nd notation and then dividing by 2, it goes down approaching Absolute Zero. We are ready to adjust it at any time when a more integrative logic prevails! Also, we are increasingly finding a simple relational logic between the four original Planck base units. Notwithstanding, this logic will be constantly revisited throughout our ever-so-slow development of QE model.

Within the QE model, the Planck Charge, a Coulombs value, is taken as given. Within the big bang theory (bbt), the Planck Charge is ignored. The bbt value is as large as possible. Their measurement is given in GeV units, one billion electron volts. Add 1016 zeroes and you have quite a charge.

To begin to understand all these numbers and their correlations, questions are asked, “Are these all non-repeating, never-ending numbers like Pi? Are all numbers that are non-repeating and never-ending somehow part of the infinite yet also the beginning of quantum mechanics?” The suggestion has been made that we carry out each of the Planck numbers at least 10 decimal places, and if need be, 100 decimal places, and possibly even 1000 decimal places, to see if patterns can be discerned. We recognize that relative to other units of measurement, such as the SI base quantities, the values of the Planck units are approximations mostly due to uncertainty in the value of the gravitational constant (G).

The QE model holds that things are simple before complex and everything is related to everything.

## Planck epoch

### Planck time:

#### <10−43 seconds

~~~~~~~~~~~~~~~~~~~~~~

## Epoch

<10−36 seconds~
1016 GeV

(gigaelectronvolts)

## Notations 0-6

Planck base units

≈4.4×10-27 (K)

## Notation 7 to 34

### ~~~~~~~~~~~~~~~~~~~~~~

4.02×10-9 Coulombs

## Notation 202+

#### Planck Temperature

Imputed, hypostatized and/or hypothesized are pointfree vertices and simple geometries as the deep infrastructure that gives rise to the work on combinatorics, cellular automaton, cubic close packing, bifurcation theory (and the Feigenbaum’s constants), Langlands program, mereotopology (point-free geometry), the 80-known binary operations, and scalar field theory. Here are people working on theories and constructions of the simple, yet their concepts are anything but simple.

The exacting nature of the correlations between the multiples of the Planck base units is just being explored for the first time. But, to say the least, within the QE everything everywhere is related through simple mathematics.

When: In the very beginning…

Wikipedia says that the Planck epoch requires speculative proposals, a “New Physics” such as “…the Hartle–Hawking initial state, string landscape, string gas cosmology, and the ekpyrotic universe.” Each is a conceptually-rich, dense jungle of ideas. Cutting through that entanglement is only for the highly-motivated and academically astute. Most of us will just go on to the grand unification epoch, in search of a logical system that builds consistently upon itself.

About the bbt model, Wikipedia simply says, “The three forces of the Standard Model are unified.” Of course, the QE goes much further, however, first consider a bbt problem. Electromagnetism, gravitation, weak nuclear interaction, and strong nuclear interaction are most often related to relations defined above the 65th notation.

Wikipedia says, “Cosmic inflation expands space by a factor of the order of 1026 over a time of the order of 10−33 to 10−32 seconds.[1] The universe is supercooled from about 1027 down to 1022 kelvins.[6] The Strong Nuclear Force becomes distinct from the Electroweak Force.” [1] (Our emphasis) First, consider that the Planck Temperature is 1.41683×1032 Kelvin. The bbt appears to skip the cooling from 1032 to 1027 Kelvin and it uses bubbly magic to address what causes the cooling to 1022 Kelvin. Also, consider the amount of expansion and the short duration assumed in their statement above. To create that much space in that short of an interval would require light to travel so far beyond its normal speed; it would constitute the penultimate anomaly (pardon us, Sean Carroll fans).

Also, because the bbt begins at the Planck Temperature, they truly need a supercooled concept. Within the Quiet Expansion model the temperatures from notations 1 through 102 are all superconducting, being well below the superconducting transition temperatures. Perhaps the very concept of temperature will become better understood as a result of our struggles to define a different model of the universe.

About this inflationary epoch, Wikipedia says, “The forces of the Standard Model have separated, but energies are too high for quarks to coalesce into hadrons, instead forming a quark-gluon plasma. These are the highest energies directly observable in experiment in the Large Hadron Collider.”

Within the QE, the quark-gluon plasma which requires 1012 Kelvin, is between notation 135 and 136, 9.6008×1011 Kelvin to 1.92016×1012 Kelvin respectively. Notation 136 is 4.6965×10-3 seconds from their space-time “singularity.” One second is between Notations 143 and 144. Also, the Kelvin scale is counter-intuitive in many ways. The temperature of the Sun is about 5,778 K. Within the QE, that is expressed between Notations 107 (3.5765×103 K ) and 108 (7153.178 K). The human temperature at 98.6 degrees Fahrenheit is 310.15 Kelvin which is between Notations 103 and 104 (447.073 K). Also, at Notation 103 the Planck Length is now .163902142 millimeters or 1.63902142×10-4 meters or about the size of a human egg.

1. How did it all begin? And, what does it mean? (January 2011)
2. Quiet Expansion of the Universe (June 2016)
3. A Chart: Our working, horizontally-scrolled chart is a most-simple, integrated model of the universe.
4. Notations 1-202: An analysis notation by notation has just begun!
5. Planck base units from 0 at the beginning to today: https://planckbaseunits.wordpress.com/

In Wikipedia, their category experts say, “The physics of the electroweak epoch is less speculative and much better understood than the physics of previous periods of the early universe. The existence of W and Z bosons has been demonstrated, and other predictions of electroweak theory have been experimentally verified.”

Finally the the bbt gives us something that isn’t incomplete or highly speculative. Yet, even with such assurance, the logic of the bbt is difficult to follow. Again, within the QE model the only duration that would allow for W and Z bosons is somewhere around notation 65. There is just not enough “conceptual” space and time for elementary particles and their effects.

Within QE progression, the first measurement with a visceral meaning is at Notation 31; the mass of the universe is 46.79 kilograms or about 103 pounds. By Notation 40 it is up to 2.39×104 kilograms (52,758.8 lbs or 27 tons. The universe is bulking up quickly and it is creating space and time as it goes. Though we have some ideas about this mass, it should become more clear as we begin experimenting with the calculations of the Planck base units. Beyond SI: We may also extend all the decimals out to at least ten places and begin to calculate more carefully each ratio within each notation to do in-depth ratio analyses of each progression.

Consider this unusual concept. Within every notation, the QE model aggregates base-8 pointfree vertices using scaling laws and dimensional analysis (recommended by Prof. Dr. Freeman Dyson). Base-2 and base-8 progressions are single line entries within the horizontally-scrolled chart.

There are 10,633,823,966,279,326,983,230,456,482,242,756,608 pointfree vertices at the 41st notation. These simple doublings could be aggregating structure as groups or sets. Defined by the Planck base units, in the range 41-to-60, we hypothesize that these domains are archetypal relations and systems: 549,755,813,888 base-2 pointfree vertices (Notation 41) and 5,070,602,400,912,917,605,986,812,821,504 (Notation 104).

The possibilities for mathematical constructions. Here ratios manifest as the real reality of the universe. The entitive nature of things (above the 67th notations) is derivative; the ratio is primarily real. In our world of subject-object thinking, the hyphen represents that ratio.

Here is the deep infrastructure of the universe where the simple mathematics of ratios between space, time, charge, mass and temperature create real realities within every notation. We postulate that these ratios are the “really real.” Within the continuum of charge here is the so-called dark energy within notations 185 to 200 and with the continuum of mass there is the dark matter. If this model is ever validated, perhaps it’ll be seen that both are deep energy and deep matter of the universe, the manifestations of really real mathematical ratios.

The bbt’s Quark Epoch generalizes 63 of the QE notations, from 41 to 104. These notations within the QE model are foundational so perhaps this comparison to Quark Epoch is a key. Consider the estimated requirement for temperature. The bbt epochs can not begin until the temperature is cool enough. Given that temperature requirement, within the QE model, the Quark Epoch would not begin until up-and-around Notation 136 where the temperature has finally risen to 1.9201×1012 Kelvin. If that is the right range, as suggested by proponents of the bbt, less than a second has transpired, the universe has a diameter of about 874 square miles and a mass of about 1.896×1032 kilograms.

Within the QE model from around Notations 65 to 69 is the transition from the small scale to the human scale. This “human scale” is the middle third of the 201 notations, i.e. 67-to-134. Even though two-thirds of the way through the 201 doublings, less than a second has transpired from the start.

In the Quark Epoch the bbt and QE begin to cross paths and overlap. Wikipedia says, “Quarks are bound into hadrons. Over the hadron epoch, the process of baryogenesis results in an elimination of anti-hadrons (baryon asymmetry).” As noted within Wikipedia, some of these perceptions come directly out of the laboratory, such as CERN in Geneva, where this phenomenon has been observed. So, other than the improbable placement within the time/temperature curve, all processes herein after become readily integrated within the QE model.

Let us take stock of where we are. Even though the Quark Epoch of the bbt seems to overlap and begin to become simpatico within the QE, there are fundamental logic and conceptual problems ahead.

A key question within the QE model is, “What is a notation?” All 200+ are also known as an archetype, cluster, doubling, group, layer, set, and/or step. Each word is perspectival. Each notation is dynamic, always in the process of being defined, right up to the current time within our current notation. Space and time are local per notation and all “past” is an imprint on the universe that literally defines it beingness right now, thus no time asymmetry.

What does that mean? Each notation has an active role right now in defining who we are and what this universe is here and now. Each notation has an active role in defining all other notations.

Today, right now, all of these notations are actively defining the now. We are imprinting on the universe right now. The past is not past; it is an imprint on the universe. There is only the Now, only right now, only today.

Each notation has an active role in defining who we are and what this universe is; and, each notation has an active role in defining all other notations. Today, right now, all of these notations actively define humanity or the human scale (67-to-134), must therefore be something like the archetypes of forms and functions (notations 1-to-67) that define our deeper beingness. The notations from 134-to-200 define our planetary and galactic systems and this is where most of the work of those physicists, cosmologists, and astrophysicists have worked.

In just a few more notations, between 142 and 143, the universe is at the one second mark. This measurement is most often used to determine the speed of light. Yet, as noted in earlier postings, within every notation, the Planck length divided by the multiple of the Planck Time renders an approximation of the speed of light. It is just commonsense when we see that the speed of light plays prominently in the definitions of Planck Length and Planck Time.

The question to be answered, “What is the meaning of temperature? …within the bbt? Within the QE model, we impute that it is the total temperature throughout the area defined by the notation (or cluster, container, domain, doubling, group, layer, or step). This measurement within the Hadron Epoch within the bbt is lower than it is within the QE. There is a natural correlation between all these numbers within the QE simply because they start with the same definitional characteristics (the Planck base units) and are the evolution of those numbers. The ratio of length to temperature renders 7.3322+ ratio. [Editor’s note: Please double-check this figure. Then check it again.] That result is currently being analyzed, space-to-temperature or kelvin per meters.

In 1972 George Ellis and Stephen Hawking began to explore the boundary conditions that define our universe between 10-13 centimeters (elementary particles) and 1028 cm, the assumed radius of the universe. They did not approach the Planck base units which would have expanded their range to 1.616199×10−35 meters (Planck Length) and then it would have tucked them in at about 5.1942×1025 meters according to current best guesses regarding the Age of the Universe.

Earlier it was observed that the big bang is not good philosophy and it is bad psychology. Philosophy is taken as a study of first principles and systems, the universals and constants that create the boundary conditions as well as the continuity equations that bind our universe together. Since 1972, especially with the very key question about the very nature of the first microseconds, the bbt has not progressed very far. Their Planck epoch is still mysterious. It is bad psychology for that very reason. It is so disjointed, so out of touch with anything human, it de facto encourages various forms of nihilism.

Theories should have elegance, beauty, coherence, and simplicity. Children should be able to begin to understand. And with the QE, children quickly begin to understand 2 times 2. We just have to carry it out a few more places for them.

Conclusions: What does it all mean?

What are the implications if the Quiet Expansion is true?

For us all:

1. The finite-infinite relation is the key and requires more study.
2. The universe is finite, quantized, and derivative. Space and time are also finite, quantized, and derivative.
3. The infinite is continuity, symmetry and harmony giving rise to order, relations and harmony.
4. There are, therefore, natural laws, ethics, and values.

For the big bang theory:

1. All the actual measurements and observational work that have gone into the big bang theory (bbt) are supported by the Quiet Expansion.
2. All the major theoretical constructs of the bbt including and after the Quark Epoch are supported by the Quiet Expansion. There are adjustments of the time scale in which things occur, yet these are minor.
3. The definitions of the Grand unification epoch, Inflationary epoch, and Electroweak epoch will be upgraded substantially.

For the Quiet Expansion (QE):

1. The continued expansion of the universe is fully supported within the Quiet Expansion.
2. There are just over 200 notations that define the universe.
3. These notations are all active, functional, and necessarily build on each other.
4. These notations will also be defined as: archetypes, clusters, containers, domains, doublings, groups, jumps (Boeke), layers, ratios, sets, or steps.
5. As an archetype, each notation serves specific purposes in defining the textures and substance of the universe determined by the ranges within the Planck base units.

The future, both short-term and long-term: Our “To Do” List.

1. Run the ratios: There is a meaningful ratio between each of the five Planck base units within each of the notations. Volunteers? Want to help?
2. Double-check the numbers. Just yesterday there was a question about the Coulombs doublings. The simple mathematics of every doubling has to be correct.
3. Study the progression of Planck Mass from 0 to 202. We will be trying to intuit the meaning of mass given by just the pointfree vertices throughout the twenty notations from 31 to 70. Formulate key critical questions? What are these ratios saying?

***

Disclaimer: Our charts and discussion are our first time to make a comparative analysis between the big bang theory and our Quiet Expansion. Silly errors are inevitable. We are neophytes, not scholars, within these fields, so please point out any of our failures with logic, math, and physics. We will be most grateful.

###### This ends the first story about two very different models of the universe. Of course, it is a story that is to be continued.

***********************************************************************************

## Footnotes and endnotes:

The first working title of this posting was “Can A Quiet Expansion Challenge the Big Bang?” which was deemed too confrontational. The more important question was, “How did it all begin and what does it mean?” That change was made on Friday morning, June 17, 2016.

Reference 1

Big bang theory: The world-renown Cambridge University physicist, Stephen Hawking, was the leading spokesperson for the big bang. He became a rock star among scientists because he was so successful as its primary advocate. Within his May 2016 PBS-TV series, Genius, he asks, “Where did the universe come from? The answer, as most people can tell you, is the big bang. Everything in existence, expanding exponentially in every direction, from an infinitely small, infinitely hot, infinitely dense point, creating a cosmos filled with energy and matter. But what does that really mean and where did it all begin?”

His confidence also exudes from his 1988, best-selling book, A Brief History of Time: From the Big Bang to Black Holes, and even from his foundational writing in 1973 (co-authored with Cambridge colleague, George F. R. Ellis) the highly-technical book, The Large Scale Structure of Space-Time.

(continued in right column)

(continued from left column)

Are space-and-time unbounded or bounded? If bounded, is our universe a container universe? Are the Planck base units and all the dimensionless constants part of the definitions of the boundaries between the finite and the infinite?

Within the current bbt analysis gravitational waves arise from within their inflationary period. The bbt thought leaders ascribe a much faster-than-light expansion just after the big bang. And, that begs the question: What are the preconditions of superluminal events and motion? There haven’t been any answers since 1902 when Jacobus Kapteyn made his initial observations, since the 1983 “superluminal workshop” at Jodrell Bank Observatory, and since the subsequent studies of microquasars, their accretion disks and such phenomenon as magnetorotational instability. It is all a very special language, logic and reality; the observational results are well-defined; yet, the most-penetrating conclusions are pending.

# How did the universe begin? And, what does it mean? Could a Quiet Expansion impact the Big Bang?

###### Initiated: June 2016 Most recent update: November 2017WORKING DRAFT for the GENERAL PUBLIC.For the scientific-academic community by Bruce Camber, USA*********************************************************

With all the chaos, disinformation and uncertainty in our little world, those old penultimate questions seem quite relevant, “How did this universe and our life begin? What does it mean?” Did it come into existence, as many scientists currently believe and world-renown physicist, Stephen Hawking, answers, “…expanding exponentially in every direction, from an infinitely small, infinitely hot, infinitely dense point, creating a cosmos filled with energy and matter“? Cf. Ref. [1]

There are other possibilities. Here we focus on a model that has only been explored by a small group of high school people and others within their extended community. Couldn’t the question also be asked, “Might it be possible that the universe began with an infinitesimal length, time, and temperature (and a rather small charge and mass), then expanded, doubling each step of the way?” Is our universe, in fact, highly ordered and totally relational?

Given the state of world affairs today, the quick answer would be “No.” Yet, if we were able to answer, “Yes,” perhaps there are things we could learn from the universe to solve some of our world’s most vexing problems.

With that goal in mind, let us begin by using the old journalistic framework for questioning:
“Who? What? Why? When? Where? And, how?”

Who: On one side you have the scholars of the Big Bang theory (hereinafter referred to as bbt) includes many Nobel laureates, and on the other side are a few high school math and science teachers and their students. The scholars’ bbt is highly documented. It is an intellectual cornerstone within experimental and theoretical physics, cosmology, astrophysics, and even ontology. The high school work has been primarily driven by this author and it has had virtually no peer review.
What: For us to challenge the bbt appears foolhardy at best. Yet, there are many, many reasons to challenge it, but most of all because (1) it is overly complex and confusing, (2) it is not very good philosophy, and it is very poor psychology, and (3) there are many excellent scholars and scientists who say, “It’s wrong!!”4) possibly, it’s actually wrong about its most-basic assumptions.
Why: The first three key parts of the bbt, involving substantially less than a trillionth of a second, are based on hunches and a need to shoehorn data to support the model. If we get a better model, we might be able to beget a better life.
When: Now, today. These models are more influential than we know.
Where: Everywhere. It seems that we are so intimately connected, a change in our model, changes everything immediately. Perhaps we can impact the various manifestations of insanity within our cultures.
How: Our working premise begins with what is known as a space-time singularity, the dynamic transformational nexus between the finite and infinite where there is a complete unification of all the basic forces of nature and the Planck base units (aka Planck scale). We postulate that this so-called unification is extended through dynamic working ratios throughout all 202 notations from the first moment of creation to the current time and present day. We further postulate that this working premise creates an environment to build a panoply of bridges from the Planck scale to all current well-established physical theories whereby each notation is a domain for unique predictive values.

We call our very simple model the Quiet Expansion (hereinafter we use the abbreviation, QE).

To explain such a position requires a detailed analysis and comparison between the big bang (and its many facets) and all the details created within each notation of the QE (a very large horizontally-scrolled file).

Not too many people question the big bang theory (bbt). Quite obviously, we do. Yet, it was only in September 2014 did we publicly raise questions about it. Given all the work that has gone into the big bang theory over so many years, only a fool would dare challenge it.

So, such is life; each of us must sometime play the fool.

This posting is a “working draft.” Given the depth and breadth of the foundations upon which the big bang theory (bbt) currently rests, your comments while this posting is being refined, are most welcomed. If this embedded link does not open your email browser, my address is camber (at) 81018 (dot) com or click on Contact.

The key to our model is multiplication by 2, starting with the Planck base units. It begins at the nexus of transformation between the finite and the infinite, defined by the crossing lines at “0” in the first image above on the right.

## Introducing Frank Wilczek who introduces Max Planck’s base units

When we began in December 2011, we knew nothing about those pivotal Planck calculations done in 1899 by Max Planck. We hardly knew his name. We asked everybody who seemed to know something about the Planck numbers, “Can we multiply each value by 2?” We sought out experts and quickly found the work of Prof. Dr. Frank Wilczek (at that time at MIT). With very few exceptions, it was not until Wilczek began writing a series of articles in 2001, Scaling Mt. Planck, (Physics Today), did anybody think those Planck numbers amounted to anything more than numerology.

Though it seemed that most everybody was familiar with Kees Boeke’s 1957 work (Cosmic View) using base-10, we were not. Most all our academic contacts made quick reference to it, yet were still surprised to see our base-2 chart from the Planck Length to the Observable Universe. A few suggested that to multiply by 2 was no better than multiplying by 10. Some thought it was a frivolous exercise. But because we had our geometries that went right down to that scale, we proceeded. Our work began in December 2011 by multiplying the Planck Length by 2, and then each result by 2, over and over and over again. It was straightforward, a bit tedious, but quite simple. When we discovered that there are only 202 doublings to get to the Age of the Universe and the Observable Universe, we couldn’t believe it. Though hard to believe, it’s true. That simple math, called “base-2 exponential notation,” is what cells do. It’s a bit like chemical bonding. Another way to envision these dynamics may well be bifurcation theory.

In December 2014 we included Planck Time within our chart. In February 2015 we included the other three Planck base units.

By the time one reaches the estimated Age of the Universe, this model has encapsulated every moment of time since the very beginning, all within 200+ “somethings” that have at various points been called: (1) clusters, (2) containers, (3) domains, (4) doublings, (5) groups, (6) layers, (7) notations, (8) ratios, (9) sets or (10) steps. The result is, by definition, an entirely-ordered universe. When we stopped looking at the numbers individually, we began to realize each was in an active relation (a ratio) with the others within each notation. Then, we began to see this multiplicity of ratios as living, dynamic relations struggling to be recognized. As long as we were consistent in using the same value structure to determine each number, these ratios became the penultimate determinants of a given reality within a given notation.

Within our web presence, Big Board-little universe, there is more background about our rather brief history.

# Big-bang Theory Drowns Out Discussions

To attempt to come up to speed, to learn more about it all as quickly as possible, we’ve been using Wikipedia’s summaries. Wikipedia’s goal is to represent the best current thinking of the thought leaders within the relevant scientific communities. These scientists have lived within this theory throughout their professional careers. It is part of their intellectual being. Notwithstanding, we believe most all of their work can be absorbed within the QE. Our primary questions are about the first four and most fundamental periods which they call “Epochs.” Taken together, these four epochs represent less than a fraction-of-a-fraction of a second within the QE model. With just little tweaks, we believe most all their work within the subsequent epochs can be readily integrated.

The writers within the Wikipedia community overlap with those within these scientific communities. Wikipedia, constantly in the process of refining their writing, provides several summaries of the History of the Universe. Work based on observations and measurements has a place within the QE and our guess is that the interpretation of those observations and measurements will become richer and more informative when the QE parameters and boundary conditions are engaged.

In 1970 there were competing theories about the beginning of the universe. By 1990 the bbt had become dominant. In 2011 our little group of high school geometry people began to explore the interior structures of the tetrahedron and octahedron and that is when we found within our tilings and tessellations, just over 201 base-2 exponential notations from the Planck base units to the Age of the Universe and to the Observable Universe. That continuum appeared so simple, we first engaged it as an excellent STEM (Science-Technology-Engineering-Mathematics) tool. Yet, with further study and thought, it also seemed to challenge some of our basic commonsense assumptions about nature (the back story). As we studied our new little model, the bbt continued to solidify its dominance within the general culture; nevertheless, we started to question it. We began to believe that the actual physics of the first moments of creation might be better defined by the simple mathematics of a quiet expansion, especially the first 67 notations. Those 67 have never been recognized as such and certainly have not been discussed within academia. The great minds throughout the ages have not been aware of the 201+ base-2 notations, especially those first 67 notations. So mysterious are the 67, we began more actively to think about them and to make some postulations about their place and purpose.

Our first posting about this Quiet Expansion was a result of our naive, informal, and often idiosyncratic studies of the Planck Base Units, base-2 exponential notation, and an inherent geometry assumed to be within every doubling throughout the universe. We have moved slowly. Having backed into the Planck base units from our simple exercises in a high school geometry class, we were not at all sure of ourselves. So, after observing our results for a couple of years, we began asking the question, “Could this be a more-simple, more-inclusive model of the universe than the big bang theory?” Because we only have the beginnings of an outline of a model, we have continued our quest and continue to ask more questions, primary among them, “If space and time are finite, then what is infinite?” Throughout recorded history, the infinite has been described as perfect. So, we began thinking about perfections in mathematics and science. As a result, our first answer to that question: (1) Continuity. Simple continuity creates every manifestation of order (equations). (2) Symmetry. Simple symmetries define simple relations. Complex symmetries define complex relations. (3) Dynamics. Perhaps the best description of a dynamic moment is captured by harmonic analysis. There appears to be layers of perfection based on the interactions of these three faces of perfection.

Here it seems, is the very basis for natural law, ethics, value and more.

The QE model holds that things are simple before complex; and “everything is related to everything.” Hypothesized are simple geometries, a deep infrastructure that gives rise to the work within these leading intellectual studies of our time: combinatorics, cellular automaton, cubic close packing, bifurcation theory (and the Feigenbaum’s constants), the Langlands program, mereotopology (point-free geometry), binary operations (80-known), and scalar field theory. Here are people working on theories and constructions of the simple, yet their concepts are anything but simple.

Consider this unusual-yet-very-important concept. Within every notation, the QE model aggregates what is called “base-8 pointfree vertices” using scaling laws and dimensional analysis. That insight came from a most prominent theoretical physicist, Prof. Dr. Freeman Dyson of the Institute for Advanced Studies in Princeton (Einstein’s old hangout). There are single line entries for both the base-2 (line 8) and base-8 (line 9) progressions within the horizontally-scrolled chart.

At the 41st notation there are 10,633,823,966,279,326,983,230,456,482,242,756,608 pointfree vertices. It takes just four vertices to make a tetrahedron. It takes six to make an octahedron. With a quintillion-quintillion vertices, a huge, possibly-quite complex, infrastructure necessarily evolves. Perhaps the base-2 simple doublings could be aggregating base-8 structures as groups or sets. Further defined by the Planck base units, in the range 41-to-60, we hypothesize that these are the domains for archetypal relations and systems.

There are 549,755,813,888 base-2 pointfree vertices at Notation 41 and 5,070,602,400,912,917,605,986,812,821,504 at Notation 104. That is more than enough groups and sets to create the diversity of atomic, chemical, and biological structures that define our universe and life.

Here it would appear is the deep infrastructure of the universe where the simple mathematics of ratios between space, time, charge, mass and temperature create real realities within every notation. The ratios are called, the really real. Within the continuum of charge here is the so-called dark energy within notations 185 to 200 and with the continuum of mass there is the dark matter. If we ever have a chance, we’ll rename both as the deep energy and deep matter of the universe, the manifestations of really real mathematical ratios.

Within the bbt there is what is called the Quark Epoch. It generalizes 63 of the QE notations, from 41 to 104. These notations within the QE model are so foundational, this comparison to Quark Epoch is a key. Within the bbt this Quark Epoch cannot begin until the temperature is cool enough. Given the bbt’s temperature requirement, within the QE model, the Quark Epoch would not begin until up-and-around Notation 136 where the temperature has finally risen to 1.9201×1012 Kelvin. If that is the right range, as suggested by proponents of the bbt, less than a second has transpired, the universe has a diameter of about 874 square miles and a mass of about 1.896×1032 kilograms. The Sun is estimated to be 1.989×1030 kilograms. Fascinating, isn’t it?

Our naïve-but-playful question, “How can the mass of the universe within just 874 square miles be larger than our sun?”

The simple logic of the QE model causes us to stop and ponder, What is mass? Is it weight in kilograms or is it a working ratio of energy and other dimensionless constants that are expressed as weight, density, and force. This major subject is addressed further and will be a key focus for a long time.

Within the QE model from around Notations 65 to 69 is the transition from the small scale to the human scale. This “human scale” is the middle third of the 201 notations, i.e. 67-to-134. Even though two-thirds of the way through the 201 doublings, less than a second has transpired from the start.

It is all quite fascinating. And it all demands a new logic about the universe, space and time.

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Let us take stock of where we are. Even though the Quark Epoch of the bbt seems to overlap and begin to become simpatico within the QE, there are fundamental logic and conceptual problems ahead.

A key question within the QE model is, “What is a notation?” All 200+ are also known as an archetype, cluster, doubling, group, layer, set, and/or step. Each word is perspectival. Each notation is dynamic, always in the process of being defined, right up to the current time within our current notation.

Space and time are local per notation and all “past” is an imprint on the universe that literally defines it beingness right now, thus there is no time asymmetry.

What does that mean? Each notation has an active role right now in defining who we are and what this universe is here and now. Each notation has an active role in defining all other notations.

Today, right now, all of these notations are actively defining the now. We are imprinting on the universe right now. The past is not past; it is an imprint on the universe. There is only the Now, only right now, only today.

Humanity or the human scale seems to be defined between notations 67-to-134, but the current notation is 200+. Therefore, these notations must be something like the archetypes of forms and functions (notations 1-to-67) that define our deeper beingness. The notations from 134-to-200 define our planetary and galactic systems and these are the notations where most of the work of the bbt physicists, cosmologists, and astrophysicists work.

In just a few more notations, between 142 and 143, the universe is at the one second mark. This measurement is most often used to determine the speed of light. Yet, as noted in earlier postings, within every notation, the multiple of the Planck length divided by the multiple of the Planck Time renders an approximation of the speed of light. Though commonsense when we see that the speed of light plays prominently in the definitions of Planck Length and Planck Time, it gives each notation a special substantiation.

The question to be answered, “What is the meaning of temperature? …within the bbt? Within the QE model, we impute that it is the total temperature throughout the area defined by the notation (or cluster, container, domain, doubling, group, layer, or step). This measurement within the Hadron Epoch within the bbt is lower than it is within the QE model. There is a natural correlation between all these numbers within the QE simply because they start with the same definitional characteristics (the Planck base units) and the evolution of those numbers using base-2 exponential notation. The ratio of length to temperature renders 7.3322+ ratio. That result is currently being analyzed, space-to-temperature or kelvin per meters.

In 1972 George Ellis and Stephen Hawking began to explore the boundary conditions that define our universe between 10-13 centimeters (elementary particles) and 1028 cm, the assumed radius of the universe. They did not approach the Planck base units which would have expanded their range to 1.616199×10−35 meters (Planck Length) and then it would have tucked them in at about 5.1942×1025 meters according to current best guesses regarding the Age of the Universe.

Earlier it was observed that the big bang is not good philosophy and it is bad psychology. Philosophy is taken as a study of first principles and systems, the universals and constants that create the boundary conditions as well as the continuity equations that bind our universe together. Since 1972, especially with the very key question about the very nature of the first microseconds, the bbt has not progressed very far. Their Planck epoch is still mysterious. It is bad psychology for that very reason. It is so disjointed, so out of touch with anything human, it de facto promotes a certain form of nihilism.

Theories should have elegance, beauty, coherence, and simplicity. Children should be able to begin to understand. And with the QE, children quickly begin to understand 2 times 2. We just have to carry it out a few more places for them.

What are the implications if the Quiet Expansion is true?
For us all:
1. The finite-infinite relation is the key and requires more study.
2. The universe is finite, quantized, and derivative. Space and time are also finite, quantized, and derivative.
3. The infinite is continuity, symmetry and harmony giving rise to order, relations and harmony.
4. There are, therefore, natural laws, ethics, and values.

For the big bang theory:
1. All the actual measurements and observational work that have gone into the big bang theory (bbt) are supported by the quiet expansion.
2. All the major theoretical constructs of the bbt including and after the Quark Epoch are supported by the quiet expansion. There are adjustments of the time scale in which things occur, yet these are minor.
3. The definitions of the Grand Unification Epoch, Inflationary Epoch, and Electroweak Epoch will be upgraded substantially.

For the Quiet Expansion (QE):
1. The continued expansion of the universe is fully supported within the quiet expansion.
2. There are just over 200 notations that define the universe.
3. These notations are all active, functional, and necessarily build on each other.
4. These notations will also be defined as:
• archetypes
• clusters
• containers
• domains
• doublings
• groups
• layers
• ratios
• sets
• steps

5. As an archetype, each notation serves specific purposes in defining the textures and substance of the universe.

The future, both short-term and long-term: Our “To Do” List.
1. Run the ratios: There is a meaningful ratio between each of the five Planck base units within each of the notations. Volunteers?
2. Double-check the numbers. Just yesterday there was a question about the Coulombs doublings. The simple mathematics of every doubling has to be correct.
3. Study the Mass” progression from 0 to 201 and intuit the meaning of mass given by just the pointfree vertices throughout the twenty notations from 50 to 70. Formulate key critical questions? What are the ratios saying?

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Disclaimer: Our charts and discussion are our first time to make a comparative analysis between the big bang theory and our Quiet Expansion. Silly errors are inevitable. We are neophytes, not scholars, within these fields, so please point out any of our failures with logic, math, and physics. We will be most grateful.

## Footnotes and endnotes:

The first working title of this posting was “Did A Quiet Expansion Precede the Big Bang?” which was deemed too confrontational. The more important questions were, “How did it all begin and what does it mean?” That change was made on Friday morning, June 17, 2016.

Cf. 1 Big bang theory: The world-renown Cambridge University physicist, Stephen Hawking, is the leading spokesperson for the big bang. He has become a rock star among scientists because he has been so successful as its primary advocate. Within his May 2016 PBS-TV series, Genius, he asks rhetorically, “Where did the universe come from? The answer, as most people can tell you, is the big bang. Everything in existence, expanding exponentially in every direction, from an infinitely small, infinitely hot, infinitely dense point, creating a cosmos filled with energy and matter. But what does that really mean and where did it all begin?” His confidence also exudes from his 1988, best-selling book, A Brief History of Time: From the Big Bang to Black Holes, and even from his foundational writing in 1973 (co-authored with Cambridge colleague, George F. R. Ellis) the highly-technical book, The Large Scale Structure of Space-Time.

Are space-and-time unbounded or bounded? If bounded, is our universe a container universe? Are the Planck base units and all the dimensionless constants part of the definitions of the boundaries between the finite and the infinite?

Within the current bbt analysis gravitational waves arise from within their inflationary period. The bbt thought leaders ascribe a much faster-than-light expansion just after the big bang. And, that begs the question: What are the preconditions of superluminal events and motion? There haven’t been any answers since 1902 when Jacobus Kapteyn made his initial observations, since the 1983 “superluminal workshop” at Jodrell Bank Observatory, and since the subsequent studies of microquasars, their accretion disks and such phenomenon as magnetorotational instability. It is all a very special language, logic and reality; the observational results are well-defined; yet, the most-penetrating conclusions are pending.

Prime factorization of 81018:
2 × 32 × 7 × 643
(2 × 3 × 3 × 7 × 643)

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

***

# Tiling and Tessellating the Universe: A Great Chain of Being

###### Initiated: December 1, 2014 Very minor update: Sunday, January 28, 2018

Tetrahedral-Octahedral-Tetrahedral (TOT) clusters and couplets tile and tessellate the universe1 (opens in new tab or window). In earlier writings, we have observed how the universe could be tiled in 202 exponential notations (or steps, layers, doublings, or domains).

The TOT Structure2 appears to be the “simplest, strongest, most perfect, interlocking three-dimensional tiling” within the Observable Universe. The TOT can be used to make ball-like structures, clusters, lines, domains or layers. Here we can find, perfectly-nesting within every possible layer, a great chain of being seemingly suggesting that everything is related to everything throughout the universe.

December 2011: The Start of Our Research Using Base-2 Exponential Notation, Planck Length, And Plato’s Geometries.3 We used very simple math and got simple results yet also found hidden complexities. After doing a fair amount of analysis of our initial results, we continue to make new observations, conjectures and speculations about the forms and the functions within this universe. From all our data and study, it seems logically to follow that this tiling is the first extension of geometry and number (the sequence of notations) in a ratio.

The most simple engaging the most simple: Here may be the beginning of value structure.4 If so, it necessarily resides deep within the fabric of the universe, the very being of being. Could these very first doublings be the essential tension of creation?

NOTE: The TOT as a tiling would be the largest-but simplest possible system that spatially connects everything in the universe. Yet, even with just octahedrons and tetrahedrons, it is also  exquisitely complex; we’ll see the beginnings of that complexity with the many variations of R2 tilings (two dimensional) within this initial R3 tiling (three dimensional).6 Thus, the TOT would also be expanding every moment of every day opening new lines instantaneously. One might say that the TOT line is the deepest infrastructure of form and function. Perhaps some might think it is a bit of a miracle that something so simple might give such order to our universe.

Notwithstanding, we acknowledge at the outset that our work is incomplete. By definition tilings are perfect and the TOT tiling is the most simple. In our application these tilings logically extend from the within the first doubling to the second doubling and throughout all 202 doublings necessarily connecting all the vertices within the universe.

In earlier articles we observed how rapidly the vertices expand7 Yet, that expansion may be much greater once we understand the mathematics of doublings suggested by Prof. Dr. Freeman Dyson,8 when he was Professor Emeritus, Mathematical Physics and Astrophysics of the Institute for Advanced Studies in Princeton, New Jersey.

We are still working on that understanding.

We are taking baby steps. It is relatively easy to get a bit confused as to how each vertex doubles. The first ten doublings will begin to tell that story.

And, of course, we are just guessing though basing our conclusions on simple logic.

THE MOST SIMPLE TILING. Using very simple math — multiplying by 2 — the first tetrahedron could be created in the second doubling (4 vertices). Then, an octahedron might be created in the third doubling. That would require six of the 8 vertices. The first group of a tetrahedral-octahedral-tetrahedral chain requires all eight. Today we are insisting on doubling the Planck Length with each notation and to discern the optimal configurations. By the fourth doubling, there could be 16 vertices or six tetrahedrons and three octahedrons. At the fifth doubling (32 vertices), we speculate that the TOT extends in all directions at the same time such that each doubling results in the doubling of the Planck Length respective to each exponential notation.

We Can Only Speculate. We can only intuit the form-functions of this tiling as it expands. And, yes, within the first 60 or so notations, it seems that it would extend equally in all directions. With no less than two million-trillion vertices (quintillion), using our simple math of multiplying by 2, we will see how that looks and begin to re-examine our logic. Again, this tiling is the most simple perfection. And although we assume the universe is isotropic and homogeneous, there is, nevertheless, a center of this TOT ball, Notations 1, 2 and 3.8

That center even when surrounded by no less than 60 layers of notations is still smaller than a fermion or proton. This model uniquely opens up a very small-scale universe which for so many historic reasons has been ignored, considered much too small to matter.

Nevertheless, it seems to follow logically that this TOT tiling is in fact the reason the universe is isotropic and homogeneous.9

Key Evocative Question from the History of Knowledge and Philosophy: Could this also be the Eidos, the Forms, about which Plato had been speculating? Could this be the domain for cellular automata that John von Neumann, Alan Turing, and others like Steve Wolfram have posited? Here we have an ordering system that touches everything and may well be shared by everything. Within it, there can be TOT lines that readily slide through larger TOTs. There could be any number of cascading and layering TOTs within TOTs.10

A SECOND GROUP OF TILINGS. Within the octahedron are four hexagonal plates, each at a 60 degree angle to another. Each of these plates creates an R2 tiling within the TOTs that is carried across and throughout the entire TOT structure.

These same four plates (R2 tilings) can also be seen as triangle. There are six plates of squares. One might assume that all these plates begin to extend from within the first ten notations from the Planck Length, and then, in theory, extend throughout our expanding universe.

Only by looking at our clear plastic models could we actually see these different R2 tilings.

We have just started this study and we are getting help from other school teachers.

We were challenged by Edkins work to see if we could find her plates within our octahedral-tetrahedral models and we were surprised to find most of her tilings within the model.

Within the Wikipedia article on Tessellation (link opens a new window), there is an image of the 3.4.6.4 semi-regular tessellation. We stopped to see if we could find it within our R3 TOT configuration. It took just a few minutes, yet we readily found it! One of our next pieces of work will be to highlight each of these plates within photographs of our largest possible aggregation of nesting tetrahedrons and octahedrons.

Here the square base of the octahedrons couple within the R3 plate to create the first manifestation of the cube or hexahedron. We will also begin looking at the very nature of set theory, category theory, exponential objects, topos theory, Lie theory, complexification and more.12

Obviously there are several R2 tilings within our R3 tiling. How do these interact? What kinds of relations are created and what is the functional nature of each? We do not know, but we will be exploring for answers.

A THIRD TILING BY THE EXPERTS. Turning to today’s scholars who work on such formulations as mathematical jigsaw puzzles, I found the work of an old acquaintance, John Conway. In 2011 with Professors Yang Jiao and Salvatore Torquato (all of Princeton University), they defined a new family of three-dimensional tilings using just the tetrahedrons and octahedrons.13

We are studying the Conway-Jiao-Tarquato (CJT) tiling. It is not simple. Notwithstanding, conceptually it provides a second R3 tiling of the universe, another way of looking at octahedrons and tetrahedrons. Here are professional geometers and we are still attempting to discern if and how their work fits into the 201+ base-2 notations. And, we are still not clear how the CJT work intersects with all of the R2 tilings, especially the four hexagonal plates within each octahedron.

AS ABOVE, SO BELOW

It takes on a new meaning within this domain of the very-very-very small. Fine structures and hyperfine structures? Finite and infinite? Delimited infinitesimals? There are many facets — analogies and metaphors — from the edge of research in physics, chemistry, biology and astrophysics that can be applied to these mathematical and geometric models.

From where do these expressions of order derive? “From the smallest scale universe…” seems like a truism.

Perhaps this entire domain of science-mathematics-and-philosophy should be known as hypostatic science (rather loosely interpreted as “that which stands under the foundations of the foundations”).

###

Notes & Work Areas:

Endnotes, Footnotes, and other References

2. Dr. Francis Collins. In 2006 I wrote to Dr. Francis Collins, once director of the National Genome Research Institute and now the National Institutes of Health. His publisher had sent me a review copy of his new book, The Language of God, and she and I spent several hours discussing it. The genome, the double helix and RNA/DNA have structure in common and it all looks a lot like a TOT line. Collins, a gracious and polite man, did not know what to say about the more basic construction.  More…

3. Tetrahedron-Octahedron-Tetrahedron: Also, on a somewhat personal note, although we call it a TOT line it is hardly a line by the common definitions in mathematics; it’s more like Boston’s MBTA Orange Line. Now here is a real diversion. Thinking about Charlie on the MTA in the Boston Transit (a small scale of the London Underground or NYC Transit), this line actually goes places and has wonderful dimensionality, yet in this song, it is a metaphorical black hole. Now, the MBTA Orange Line is relatively short. It goes from Oak Grove in Malden, Massachusetts to Forest Hills in Jamaica Plain, a part of Boston where I was born.

5. Where is the Good in Science, Business and Religion. Located in several places on the web, however, it was first published on September 2, 2014 within a LinkedIn blog area. The chart was first used in another blog, “Is There Order In The Universe” which was published on June 5, 2014.

6. The Concept of the Expanding Universe is part of the concept of the Cosmological Principle (metric expansion of space) that resides deep within the concept of the Observable Universe.

7. As of this writing, there does not appear to be any references anywhere within academia or on the web regarding the concept of counting the number of vertices over all 201+ notations. Using the simplest math, multiplying by 2 (base-2), there is a rapid expansion of vertices. Yet, it can also be argued that vertices could also expand using base-4, base-6, and base-8. That possible dynamic is very much part of our current discussions and analysis. It is all quite speculative and possibly just an overactive imagination.

9. If the Planck Length is a vertex from which all vertices originate, and all vertices of the Universe in some manner extend from it, the dynamics of the notations leading up to particle physics (aka Particle Zoo) become exquisitely important. Questions are abundant: How many vertices in the known universe? What is the count at each notation? Do these vertices extend beyond particle physics to the Observable Universe? In what ways are the structures of the elementary particles analogous? In what ways are the periodic table of elements analogous? What is the relation between particle physics and these first 60 or so notations? Obviously, we will be returning to each of these questions often.

11. The two small images in the right column are of a very simple four-layer tetrahedron. The Planck Length is the vertex in the center. The first doubling creates a dynamic line that can also be seen as a circle and sphere. The next doubling creates the first tetrahedron and the third doubling, and octahedron and another tetrahedron, the first octahedral-tetrahedral cluster also known as an octet. The fourth doubling may be sixteen vertices; it may be many more. When we are able to understand and engage the Freeman Dyson logic, the number of vertices may expand much more rapidly. Again considering the two images of a tetrahedron in the right column and its four layers, today we would believe that it amounts to three doublings of the Planck Length. When we begin to grasp a more firm logic for this early expansion, we will introducing an image with ten layers to see what can be discerned.

12. I went searching on the web for images of tetrahedrons and tessellations or tilings of hexagons. Among the thousands of possibilities were these very clean images from Jo Edkins for teachers. Jo is from the original Cambridge in England and loves geometry. She has encouraged us in our work and, of course, we thank her and her family’s wonderful creativity and generosity of spirit. http://gwydir.demon.co.uk/jo/tess/bighex.htm

http://gwydir.demon.co.uk/jo/tess/grids.htm#hexagon

13. Virtually every mathematical formula that appeared to be an abstraction without application may well now be found within this Universe Table, especially within the very small-scale universe. We will begin our analysis of set theory, category theory, exponential objects, topos theory, and Lie theory to show how this may well be so.

14. “New family of tilings of three-dimensional Euclidean space by tetrahedra and octahedral” Article URL: http://www.pnas.org/content/108/27/11009.full
Authors: John H. Conway, Yang Jiao, and Salvatore Torquato

Our example of a TOT line was introduced on the web in 2006. In July 2014, this configuration was issued a patent (USPTO) (new window). That model is affectionately known within our studies as a TOT Line.

This patent is for embedding a TOT line within a TOT line. There are two triangular chambers through the center; and for the construction industries, we are proposing four sizes to compete with rebar, 2x4s-to-2x12s, and possibly steel beams.

The Patent Number: US 8.769.907 B2, July 8, 2014 is fully disclosed at the WordPress website, http://octet12.wordpress.com/