# Cubic-close packing of equal spheres (ccp)

The Dynamics of Infinitesimal Equal Spheres

a little working document by Bruce Camber, May 2021

Introduction to a finite-infinite working machine. Scientific theories of the beginning of the universe largely ignore the concept of infinity and the qualities of infinity. It has been tainted by centuries of religion, mysticism, and romanticism. Within this website, the qualities of infinity are inferred from the qualities of pi and other dimensionless constants. Given pi’s primacy among all dimensionless constants, we can logically infer that the inner dynamics of the infinite are the very dynamics of pi and the dynamic relation between the finite and infinite.

For this website defining infinity in any other way would ultimately be a contrivance. In problem-solving language it’s called a forced-fit. So, as stated in the first four support documents, continuity-symmetry-harmony, the very definition of pi (π).is necessarily the beginning of a definition of the infinite.

The first infinitesimal spheres establish space-time, mass-energy, they necessarily stack, and now they become functional. The first dynamic, interior to all spheres is continuity-symmetry-harmony that itself creates a mechanism called cubic-close packing of equal spheres. Throughout this website, you will see the dynamic image on the right. Sphere stacking and packing becomes triangulations, tetrahedralizations, and octahedralizations. The preliminary forms of Euclidean geometry emerge with Notation-2 and build throughout all 202 notations. In this model of the universe, all notations are always active.

Other pages to review: https://81018.com/ccp/

The page before it is https://81018.com/starts-4.
And, the page after it is https://81018.com/starts-6.
The primary resource page is https://81018.com/starts/.

Also, see the pentastar, pentagon, tetrahedron, octahedron, and more spheres.

# Pi points well beyond circles and spheres.

by Bruce E. Camber

History: The first Pi Day celebration was in 1988 (San Francisco science museum, Exploratorium). By 2009 it was recognized as a national holiday (USA). And, by November 2019 Pi Day was adopted by the United Nations, particularly UNESCO, as the International Day of Mathematics.

What had been a focus on pie-eating and reciting some part of the 100-trillion known digits of pi (π) is increasingly becoming a celebration of the power of mathematics in our lives. However, we shouldn’t lose focus of our studies of the very nature of pi (π) especially her perfections that reveal a deeper essence and purpose of this ubiquitous equation.

Pi (π) is the continuity, symmetry, and harmony from which all circles and spheres evolve. That statement opens at least ten key points to explore:

• Three perfect functions. These are currently not taken together as a whole and with their functional dependencies: Continuity is the never-ending, never-repeating numbers of pi. Symmetry is a deeper nature within those numbers that become relations which become circles and spheres. And, harmony is an even deeper dynamic nature of the sphere, first explored in 1820 by Joseph Fourier. He revealed a most simple harmony can be found within every sphere.
• Taken as a whole, continuity-symmetry-harmony are finite and infinite. Some may want to say that it is an expression of both the finite and infinite. Our summaries of documents regarding infinity
• Our scholars continue to build on Fourier’s insights. Visit with Poincaré, Gauss, Planck, Einstein, Smale, Milnor and others who have uncovered even more exacting relations with pi. Yet, at its core, continuity defines time; symmetry defines space, and harmony defines the dynamics of space-time.
• Perfected states within space-time. The Planck base units defined by Max Planck in 1899 use dimensionless constants which render natural units and a vision and definition of the smallest possible units of space and time. Simple logic says that the smallest are also the first, the most-simple starting points. At the bottom of the graphic on your right there is Planck Time and Planck Length where the first infinitesimal-and-perfect spheres emerge. Could one sphere per unit of Planck Time and Planck Length define a rate of expansion?
• If so, 539 tredecillion spheres per second are generated. To grasp some order, apply base-2 notation. The result is 202 notations (or doublings) to explore that encapsulate the known universe. These are the numbers that keep the score for something. What?
• Those numbers are timestamped with sphere-stacking.
• Then the numbers are geometrized with cubic-close packing of equal spheres. In the first notations, there is an absence of gaps. The basic geometries all fit perfectly. By following Aristotle’s mistake with tetrahedrons, we learn about basic geometric gaps. Associated with quantum fluctuations, it is hypothesized that these do not manifest until at least Notation-50.
• Langlands programs and string theory are further defined.
• Then the known equations that define our foundations begin to emerge. By the 202nd notation, we have our universe, everything, everywhere for all time, all intimately connected by infinitesimal spheres.
• All 202 notations are always active. Many scientists say “all time is now.” Each notation adds definition. As we go down the scale, there is increased particularity and coherence. The only possible singularity is at the very beginning, and even then, it is a convergence of equations. Exacting definitions of the infinitesimally small evolve, first through sets, then groups, and then obviously working systems that involve all 202 notations.
• Logically there is a domain with no gaps. Perfectly fitting geometries exist prior to the emergence of quantum fluctuations.[2] Notations 0-to-50 have been proposed.
• Values. Those perfectly-fitting geometries may possibly account for the first 50 notations where the continuity-symmetry-harmony of the spheres creates no gaps and this could be the basis for values.

If this were to become a new platform, UNESCO could change the world through mathematics by having us all truly begin to explore the positions and functions of infinitesimal spheres, especially the generation and labelling of every sphere after the first. Perhaps we will begin to fill in the gaps between the Planck Scale and the Electroweak Scale as well as between the Lambda Cold Dark Matter model (or the Standard Model for Cosmology) and the Standard Model for Particle Physics. Yet, it all begs the question, “What is the role of light within each notation? Is it what holds it all together (as in e=mc2)? Is it the deepest part of continuity- symmetry-harmony? Is it the beginning of values, ethics, and even love-versus-hate?

None of those questions are beyond our imaginations and our capabilities. Thank you.

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Endnotes & Footnotes
All these points already have pages within this website.

[1] Pointing beyond circles and spheres. Between the finite-infinite transformation and between the faces of continuity-symmetry-harmony (CSH) are equations. Many equations converge within the numbers that make up the Planck base units. Although there are alternatives to the Planck numbers (Stoney, Ralston, and ISO numbers), Planck’s have become a standard. Eventually we will probably be using new ISO base units, yet I’ll suggest the results will be very similar. The convergence of equations is the point. It is the necessary convergence of the finite-infinite. It also appears to be the beginning of values and even our sense of ethics.

Bringing the infinite into the equation is difficult for many. Within this website, you will find this declaration:

All other definitions of the infinite are put on hold. Most are personal definitions that come from personal experiences and family history. That is one’s own business, not ours. If those beliefs help you through life, that is great. Our goal here is to engage those principles and functions that give rise to mathematics, physics, and eventually all the other sciences.

from Continuity-Symmetry-Harmony (CSH), 1972

CSH is the infinite and the finite. Its first expression as the finite is the Planck base units. The first expression of those units is an infinitesimal sphere. This is an unprecedented definition of the finite-infinite relation. Doing a simple calculation with Planck Time, assuming one sphere per unit of Planck Time, renders 539 tredecillion spheres per second. That may well be considered a new definition of the cosmological constant. To begin to grasp that natural expansion, we apply base-2 notation and the first second, manifests within Notation-143. The first year manifests within Notation-169. The first 1000 years manifest within Notation-179. The first million years manifest within Notation-189 and the first billion years within Notation-199.

These 202 base-2 notations functionally outline the universe have been studied within and throughout this website. For more: https://81018.com/inflaton/#202

Fourier transform. Every formula that involves pi (starting with the Fourier transform) needs to be re-reviewed in light of CSH and the 202 base-2 notations. Pi is everywhere.

[2] Geometries of indeterminacy. There is a look and feel of quantum fluctuations; the mysteries appear to be within all the geometries. Perhaps scholars were first foiled by Aristotle (384-321 BC). Five tetrahedrons create a gap that he missed; and for 1800 years that mistake was repeated by scholars. It is worth pondering. Aristotle was so great it took 1800 years to countermand his mistake. And, it is still untouchable. That correction was eventually forgotten until in 1926, a little-known MIT mathematician, Dirk Struik, rekindled the scholarship. Struik’s work did not receive much attention until in 2012 when two scholars, Jeffrey Lagarias and Chaunming Zong, lifted it up again. Yet, these two mathematicians were more interested in packing densities. There is no exploration of the meaning of the gap. Subsequently, in May 2022, a five octrahedral-gap was first introduced to the world from within this website and questions were asked of many scholars, “What are these gaps all about?”

Our charts, interpretations and prognostications. Simple logic, simple math, and simple geometries render our charts, interpretations and prognostications. It all awaits critical review, so until then, there will be more to come.

Review and summary of at least ten new ways to look at pi:

1. A celebration of Continuity-Symmetry-Harmony
2. Pi as the primary clue about the Finite-infinite relation
3. Planck’s base units defining the most infinitesimal spheres
4. No less than seven new perspectives: FourierPoincaréGaussEinsteinSmaleMilnor and many others
5. 539 tredecillion infinitesimal spheres per second
6. Sphere-stacking
7. Cubic-close packing of equal spheres
8. Infinitesimal spheres populating the universe and making everything, everywhere, for all time
9. Responsible for the first fluctuation and the geometries of quantum fluctuations
10. 202 notations always active
11. Continuity-symmetry-harmony become a foundation for values.
12. Filling in the gaps between Planck Scale and the Electroweak Scale and between Lambda Cold Dark Matter model (or the Standard Model for Cosmology) and the Standard Model for Particle Physics

Please note for March 2023: Work continues, yet a new homepage has been started. The sections below, also used in prior homepages, may also be reworked.

Thank you. -BEC

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References & Resources
As references are studied, these references and other resources will be updated.

Pi (π): Dimensional analysis, scale invariance, functional dependencies
Symmetry in QFT and Gravity (video), Hirosi Ooguri (homepage) and Nathan Seiber), 2022
Mathematically, equations building on natural functional dependencies:
….–  Using math in physics: 5. Functional dependence (PDF), E. F. Redish, Univ. Maryland, 2022
•  Quantum Energy Inequalities along stationary worldlines,
Christopher J. FewsterJacob Thompson, 4 Jan 2023
•  ESA Group (PDF): The universe at 380,000 years
https://www.esa.int/Our_Activities/Space_Science/Planck/Planck_reveals_an_almost_perfect_Universe,2009
•  Pure Natural Inflation, Yasunori Nomura, Taizan Watari, and Masahito Yamazaki,
Berkeley Center for Theoretical Physics, Department of Physics, 2017
The Friedmann–Lemaître–Robertson–Walker (FLRW) Metric
•  A pedagogical explanation for the non-renormalizability of gravity, (PDF), Assaf Shomer, 2008.
Path integrals and Gaussian fixed point. See Assaf Shomer’s on page 7:
“The derivation of the path integral formula in quantum mechanics of a massive particle involves chopping up the quantum evolution into very short time intervals and inserting complete sets of states between them.”
•  Doplicher S, Fredenhagen K, Roberts JE (1995) The quantum structure of spacetime at the Planck scale and quantum fields. Communications in Mathematical Physics 172(1):187–220
•  Scale invariance and conformal symmetries

Of the 202 notations, the first 64 notations open a new map to make the deeper connections. There’ll be a place for the some of the big bang numbers but not until after the first few seconds (Notation-143 and higher).

Thrust in our universe. In September 2017, I wrote about the thrust in our universe. So now, over five years later, it is time to revisit that article and update it as much as possible. The major update would involve our understanding more about the three facets of pi and how each is a Janus-face for the finite and the infinite. How are the functions of continuity-symmetry-harmony abiding?

Major studies. I have written to Robert Langlands, Ed Frenkel, and others within Langlands programs. They have not yet acknowledged the 202 mathematical notations. Why not? It’s just math and logic. There is no philosophy. There are no agendas. It is what it is, simple math.

I have also written to people within string theory. None have acknowledged the 202 notations.

I believe people are naturally incrementalists. It is more comfortable. The Planck units were ostensibly ignored until 2001 and by that time Hawking-Guth-and-family had a hold on the theory about the start of the universe. With Hawking’s death, that hold has become somewhat more relaxed. With results from the James Webb Space Telescope (JWST), it’s time to open up the discussions. It will include conformal-quantum-and-scalar field theories (CFT, QFT). Although John Wheeler’s sense of simplicity is a good idea, for most of the octogenarians and nonagenarians, this base-2 model of 202 notations is just too simple. It is too obvious. Yet, maybe not. Prior to Frank Wilczek’s three articles about the Planck scale, Planck’s numbers were aloofly small much like Paul Dirac’s were aloofly big.

#

In 1980 in Paris at the Institut Henri Poincaré, Jean-Pierre Vigier and I made a six-month study of the EPR paradox in light of the work of Alain Aspect in d’Orsay. Instead of infinitesimal spheres, Vigier had suggested that we use the metaphor of dominos falling. That type of action-at-a-distance is not instantaneous. Infinitesimal spheres within the packing densities suggested by the Planck-or-Stoney-or-ISO numbers would be instantaneous. Also, in this period, an equal amount of time was spent with Olivier Costa de Beauregard.

Do the mathematics and physics of the finite begin here?

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Emails
There will be emails to many of our scholars about the key points.

14 March 2023 Audrey Azoulay, UNESCO, Paris*
3 March 2023: David F. Robinson, Kings College (London)
2 March 2023: Steven Strogatz, Cornell
2 March 2023: Kevin Dykema, National Council of Teachers of Mathematics
2 March 2023, Pi Day Puzzle to many of those already contacted
1 March 2023, Edward F. Redish, Univ. of Maryland
25 February 2023, Anna Ijjas, NYU
25 February 2023, Katherine Freese, University of Texas, Austin

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Many instant messages to thought leaders.

3:49 PM · Mar 9, 2023 @TheAtlantic @marinakoren You won’t believe this history of the universe. https://81018.com/chart/ It’s too simple. Base-2 notation from the Planck scale: https://81018.com/stem/ Pi day celebrations shed some light, too. https://81018.com/pointing/

7:46 AM · Mar 9, 2023 @TonomusNEOM Three levels of cognition: continuity, symmetry, harmony work together within pi and define the finite-infinite relation: https://81018.com opens that door. “Let’s pi… work together.”

9:22 AM · Mar 4, 2023 @DrOsamaSiddique @Harvard_Law @UniofOxford @IGLP_HarvardLaw Natural law can be found within the fundamentals of pi (π): https://81018.com/pointing/ The relation becomes the primary real. Editor’s note, also see: https://81018.com/values/ https://81018.com/oxford/ https://81018.com/harvard/

4:00 PM · Mar 2, 2023 @RushHolt Pi Day is coming up on March 14. I think we’ve underestimated the importance and place of pi (π): https://81018.com/

1. Is it possible that the first instance of the universe is defined by Planck’s base units?
2. Is it possible that the first manifestation of those base units is an infinitesimal sphere?
3. Might the characteristics of pi describe those spheres?
4. Might the Fourier Transform impart either electromagnetism or gravitation to each sphere?
5. Is it possible that one sphere manifests per unit of length and time?
6. Doesn’t that compute to 539 tredecillion spheres per second using Planck units and 4605 tredecillion per second using Stoney Time?
7. Is it possible that the densities within the earliest notations are on the order of a blackhole or neutron star?
8. To create some sense of order with the generation of infinitesimal spheres, may we use base-2 notation?
9. Using base-2 notation, are there 202 base-2 notations from Planck Time to the current time?
10. Is it significant that at one second the Planck Length multiple is a very close approximation of the distance light travels?
11. Is it significant that quantum fluctuations are measured within Notation-67? Notation-72 appears to be the limit of our abilities to measure a duration of time.
12. Would these notations, 1-64, provide 64 possible redefinitions of a point-particle? (And, I would add a vertex.)

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[*] Putin’s Heart and Mind: All people who instigate violence against another have not learned the basics about life. Arrogance and crudeness block paths for light and understanding. UNESCO is about shining light wherever there is a problem in the world. They need to illuminate Vladimir Putin’s heart and mind. They can reach him. He is ill and facing death; he just may be receptive to their words about education,

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• This page became a working homepage at 8 AM on March 2, 2023.
• The last update was March 20, 2023.
• This page was initiated on February 24, 2023 at 7 AM.
• The URL for this file: https://81018.com/pointing/
• The eventual headline: A Global Celebration of Mathematics
. . .Sub-header and link: Our Call to Expand Our Understanding of Pi (π) for Pi Day 2023
• First byline: 14 March 2023: Pi Day points us beyond circles and spheres.

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# Stacking spheres

by Bruce E. Camber A Working Draft, May 8, 2021

Much has been said about cubic-close packing of equal spheres within this website. Before it can begin to work its magic, the spheres must stack. The key concept is that they immediately stack, the density is such that all possible space is used. Compression and compactification are extreme.

Key pages are here: https://81018.com/stacking/ https://81018.com/ccp/

This site has only begun to discuss compression, compactification, and density. One of the first explorations was in August 2017: https://81018.com/planck_universe/#31 Entitled Measuring An Expanding Universe Using Planck Units. At Notation-31, the units of time and length are extremely infinitesimal, yet the mass calculation is 103 pounds. At Notation-64, the mass (which we know using Planck’s numbers is not quite right), is 3.211×1012 kilograms. That is in the density range of Neutron stars and nuclear pasta. We need the advice of scholars, experts within these fields to advise us. Although we’ve engaged a few such scholars and will continue to do so, much more needs to be done. So, if you happen to be among this very select group, could you take a few minutes to look at the flow of numbers and densities along all 202 notations, the density levels begin to drop slowly from 1-to-202 yet within Notation-202 we observe the extreme densities of Neutron stars at the end of a star’s lifetime. Is there a way to know from which notation information is being observed? It is an open question.

The most extreme are within the first 64 notations. The density slowly decreases until at Notation-202. The base-2 mathematics brings it right in the range of what is measured uniformly through the universe today. The compression of the first spheres is on the order of blackholes. We will begin a more intentional study of blackholes because this my first realization that we have a “black hole domain” within this model. Here, however, one might imagine that each primordial sphere is pulling the next out of the pi “birthing channel.” So, although coming out at a blistering pace, the logic for movement-and-placement may well be predetermined. As well, it seems that the definitions within each prime number notation may well be predetermined within those small-scale notations.

Stacking. We have said that the thrust of the first group of notations is to create forms. The next group will be to create structures. And further following the logic of simple-to-complex progressions, perhaps the next group would be substances, then qualities, relations, and systems. Here we project the mathematics of Langlands programs, the many faces of string theory and M-theory, Loop Quantum Gravity, causal dynamical triangulation, causal set theory, scalar field theory, perhaps Spectral Standard Model… all work currently within one or more of the faces of these 64 notations. Here, engaged at the cutting edge of research of the very nature of our universe, these disciplines are given the necessary space to develop and interact. It starts with sphere stacking.

Currently our biggest struggles to go forward is to deem the logic of each notation, both the forms and functions within a notation and the very nature of the transitions themselves. Any thoughts or advice? Please. Your help will be most appreciated.

Starting with each notation within the Small-Scale Universe, Notations-0 to Notation-67. A special focus must be on the prime number notations:
2, 3, 5, 7: Forms. Might base-3 be for triangulations and triangular plates?
11, 13, 17, 19: Structures
23, 29: Substances Might Notation-23 be related to genetic materials?
31, 37: Qualities
41, 43, 47: Relations
53, 59: Systems
61, 67: Standard Model of Particle Physics?

Later we will be dealing with The Human-scale Universe: Notations 67; 71, 73, 79; 83, 89; 97; 101, 103, 107, 109; 113; 127, and 131, 137, and 139.

Even later, we will begin dealing with The Large-scale Universe: 137, 139; 149; 151, 157; 163, 167; 173, 179; 181; and finally 191, 197, and 199.

This prior page is https://81018.com/starts-3/
The next page is https://81018.com/starts-5/

The source page is https://81018.com/starts/

# Primordial spheres defined by something like Planck’s base units…

a little working document by Bruce Camber, May 2021

These primordial, most-infinitesimal spheres emerge without a trace. Each is exponentially smaller than a neutrino and trillions of neutrinos pass through us every day. Yet, in an a most-understated manner — one sphere per unit of primordial time — it computes to an extraordinarily large number of spheres per second and as we shall see in section 7 of this analysis, that we might assume it is the approximate rate of expansion of our universe.

In 2012 for professional advice I turned to Philip Davis, a Brown University applied mathematician. He was one of the first scholars asked to help interpret our first chart. It had used just Planck Length and base-2 to encapsulate the universe. Phil had been the Chief of the Numerical Analysis Section of National Bureau of Standards (NBS) which in the 1980s became our National Institute of Standards & Technology (NIST). He had grown up in Lawrence, Massachusetts. the same place as Leonard Bernstein and the 1912 Bread and Roses Strike, one of the more important labor actions in American history. We had argued about the most simple possible three-dimensional object. He claimed the sphere. I claimed the tetrahedron. I granted him the two vertices of the sphere against the four vertices of the tetrahedron, but, “How do you build anything with just spheres?”

Phil pushed me beyond my study of Frank-Kasper phases to consider cubic-close packing of equal spheres. A Wikipedia illustration by Jonathunder was most convincing. On Tuesday, May 8, 2012, I gave in: “The sphere is more basic than the tetrahedron; it creates tetrahedrons!” By 2014, I was making my own prognostications about pi.

Scale invariant, pi takes it place within the infinitesimal. Whether we use Stoney’s numbers, Planck’s base units, or new calculations by mathematicians like John Ralston, these infinitesimal spheres will be the smallest possible and the most-densely packed (on the levels of a blackhole or neutron star), and still have all the Fourier dynamics of any sphere.

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This document is starts-3.
The prior document in this series is: https://81018.com/starts-2/.
The next document in this series is: https://81018.com/starts-4//.
The source document is: https://81018.com/starts/

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# Expansion of the Universe: 539 tredecillion spheres/second?!?

Tredecillions of spheres per second
One primordial sphere per primordial unit of time
PlanckTime: 5.391 ×10-44 seconds StoneyTime: 4.6054×10-45 seconds
by Bruce E. Camber (the first draft)

If and only if we take the Planck units as a given, and if we assume one primordial sphere per Planck unit of time, then sequential, primordial spheres are generated faster than anything else in the physical universe. These spheres are also more dense than anything else in the physical universe.

This emergence at the Planck Scale is also defined by the Planck Length. Well below the thresholds for measurement, ostensibly they define a very different kind of blackhole. Here things are building and growing in number constantly.

Yes, it would seem that this is an excellent candidate for dark energy-dark matter.

How spheres begin to stack has everything to do with the mass-charge-density relations whereby as spheres stack, each sphere “discovers” others. Although the concept of sphere-stacking began with the 1611 Johannes Kepler discussions with Thomas Harriot, never have so many spheres been envisioned to emerge seemingly ex nihilo or from the infinite. We say these spheres emerge from the continuities, symmetries, and harmonies existent within the finite-infinite relation.

The finite-infinite relation is shrouded with history, religions, philosophies, mysticism, magic and more. In our constructions, the connection is through pi and then the other dimensionless constants. It is pi that opens access to the perfections of continuity, symmetry, and harmony.

Pi appears to be the first formula defined by continuity-symmetry-harmony that truly tells us something about the finite-infinite relation. The first qualities of that first sphere are the never-ending, always changing, always-the-same numbers, that define pi and manifest as continuity which creates order which is experienced as time.

The second quality of this most-infinitesimal sphere is its symmetries which create relations which are experienced as space.

There are college courses about the many types of symmetries involved.

For our purposes we focus on the most basic, cubic-close packing (ccp) of equal spheres and the creation of lines, tetrahedrons and octahedrons.

And, a third quality of this sphere is harmony which creates dynamics which creates a space-time moment defined by the Planck base units. This image takes pi and spheres and makes them dynamic, extending through time. It is called the Fourier Transform [3] and we are now researching possible faces of it and the harmonic functions uniquely created.

Within these three images, space-time and mass-charge become the Janus face of each other. Here, too, we should begin to see how electromagnetism and gravity have been yoked (through the spin states [direction and type] of the Fourier Transforms as also understood by Steve Smale and John Willard Milnor within their work on attractors and repellers).

Continuity, symmetry and harmony are conceptual words with exacting meanings within the infinitesimal scale. These words also are generalized observations that are applicable on the largest-possible scale. Yes, these words have applications from the most finite to the infinite and in so doing, create a de facto value structure for things.

Continuity, symmetry, and harmony are extended throughout the 202 base-2 notations that encapsulate everything, everywhere for all time. Yes, these three facets of any given moment lay the foundations for the expansion of the universe, the very nature of value, and the beginnings of economic theory.

Continuity, Symmetry, Harmony. Think of gold and silver coins. Think of fine homes, fine cars, fine clothes, and fine food. The first quality and value of each is that these things are the instantiation of continuity. Continuity establishes standards for the best of what is. It is not unpredictable. It transcends time (as it creates time).

Continuity is the beginning of value.

Now think of the people involved with the making, selling, and maintaining of all these fine things. Here are symmetries of many relations over time. All circles and spheres, here are affirmations, texturing, and imparting continuity. Every relation establishes, sustains and increases the inherent values.

Symmetry brings balance and stability and knowingness to value (continuity).

Now think about how those fine things bring joy, pleasure, and moments of perfection. As all the finer things are used or consumed, life is enlivened. There is a sense of a deep harmony and joy. The values created are experienced and confirmed and life is good. These are valuations that we yearn and strive for and though seemingly illusive, they are everywhere, just a bit deeper within.

Harmony opens the richest dynamics of life.

Conclusions: The three primary facets of life — continuity, symmetry, and harmony — coming from deep within pi, are the definition of the essential structure of the sphere, which ultimately give rise to very structures of our little universe. These facets manifest the deep nature of the finite and the infinite.

*Relatively slow, the shortest measurable duration is currently a sextillionth of a second which runs from Notations-74 (1.01841×10-21 seconds) to Notations-77 (8.1472×10-21 seconds).

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Endnotes
[1] An atom or any known particle. To grasp how small these spheres are, we apply base-2 notation to the Planck base units. The Planck units define these infinitesimal spheres. By applying base-2, we can account for all the spheres within natural groups. Most of it is quite straightforward, yet rather remarkable. It takes no less than 64 to 67 doublings before reaching the size of a neutrino and other elementary particles. The periodic table of elements ranges from about Notation-70 to Notation-80. Life comes alive between Notation-90 to Notation-103. The size of the earth and its environment come to manifest around Notation-144 where the Planck Time doubling has just passed one second. The size of our solar system manifests at about a light year within Notation-169. According to big bang cosmology, large structure formation requires 150 million years to begin. One million years manifests within Notation-189. One billion years manifests within Notation-199. Our current time is within Notation-202. To review these numbers, please see our horizontally-scrolled chart that we started to develop in 2016. It is still being developed! Notwithstanding, one can see that our infinitesimal sphere within Notation-1 is orders of magnitude smaller than a neutrino (and trillions upon trillions of neutrinos pass through us every day).

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[2] The Planck base units, Part I. These Planck base units become solid gold (after 69 notations). My hope is that you’ll grasp their essence much faster than the academic-scientific community did. With few exceptions it took over 100 years to begin to understand Max Planck’s 1899 work. Here were units of time and space defined by four universal physical constants such that it was inconceivable that a smaller or shorter unit of time could exist. It is well worth the time to engage the Wikipedia accounts. My writing about these units has been on the job learning which will continue for my lifetime. There is that much more to learn.

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[3] Other dimensionless constants. If these constants are dimensionless, where do they exist? Do these numbers exist only within themselves? There is so much to learn about dimensionless constants. Coming in two flavors, physical dimensionless constants and mathematical dimensionless constants, our all important Pi (π) is purely mathematical. Scholars work to define which constants are necessary for the Standard Model of Particle Physics (a)(b). Perhaps 31 is as good an answer as any in 2012. However, I believe we all have a huge amount of work to do to reconcile not just the 31 constants, but also the 300+ constants defined by NIST and the all those defined by Simon Plouffe (over a billion). This work is just getting started!

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[4] Always the same and forever changing. The pure number and dimensionless constant, Pi (π), deserves its own day. Making pies and demonstrations are fun, yet this day should become a day that we all return to our foundations. It is here we can begin to grasp a bit of the perfection that is ours. How can something always be the same and be forever changing? That is the Great Enigma! We are all participating within it all the time. Life is a profound mystery that can actually be banal! It is everywhere within everything through all time.

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[5] The very nature of time. For many years now, our leading scholars and scientists have been telling us that time is an illusion. We laughed at them. “Hardly true. Just take a look at my arrow of time. I look terrible, I’m 50 years beyond my prime. Only a fool makes such statements.” And then, I joined them. But my take on it is quite different. “I have 201 notations that are complete and symmetric; and, the current notation– that is Notation-202 — is directional. It is not an illusion; here time is directional, but only until you sleep. During sleep, all your uniqueness is recompiled into the universe. It is like throughout your waking hours, you are out mining gold — perfections of continuity, symmetry and harmony. And while you sleep, you make either a positive impact or a negative impact on the universe. It is a a rather novel, rough concept, but it is all that I have so far. Time provides part of the labeling of everything you do, think, believe, and process. I believe that is its most basic purpose. You uniquely label everything you do, think, believe, and process. Nothing is exempt.

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[6] Unbelievably high. These prior studies of the emergence of structures, [1] [2] [3] [4] [5] [6] [7], and this overview make for a lot of reading, however, if we are going to join the crowd debunking the infinitely-hot big bang, we’ve got some work to do. Breaking free from a worldview that starts infinitely hot (big bang) where time and space go on forever (Newton’s absolutes) is not easy. Learning very large numbers to describe things that are infinitesimally small is not easy. Yet, once a person begins to be comfortable with those very large and very small numbers, one begins to grasp 539 tredecillion spheres per second, the expansion of the universe! That rate of expansion would be about the size contained within the current orbit of the International Space Station around the earth. This expansion would be quiet because these spheres are so much smaller than sound waves. It’d be deafeningly silent. Plus, this expansion begins superconductingly cold, not infinitely-hot. Yet, within just one second, the mass — 4.85×1034 kilograms — would be considered like a neutron star and the temperature would rise to support the quark-gluon plasma. The dark energy and dark matter experts should take a look. We may have a candidate here.

Consider a few simple calculations base on Planck Time, 5.39116(60)×10−44 second:
• 539,116,000,000,000,000,000,000,000,000,000,000,000,000,000 planckspheres/second
.. Read: 539.116 tredecillion or 539116000000000000000000000000000000000000000
• 436,117,076,900,000,000 seconds (approximately 13.82 billion years)
.. Read: 436 quadrillion, 117 trillion, 76 billion, 900 million seconds or 436117076900000000
• 4,361,170,769 times 5,391,247: 2.90655442×1013
• Add the eight zeros from seconds and 37 zeroes from the planckspheres per second
• Estimated total number of planckspheres in the universe: 2.90655442×1058 planckspheres

We’ll continue to check the math.

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[7] Cannonballs on the deck of a ship. The best-known person to engage cubic-close packing of equal sphere is Johannes Kepler. We need to know his work and that of Thomas Harriot and a dozen other on the way to Thomas Hales in our day. Much more fundamental than the CCP that China proclaims, this ccp (1) (2) is a deep, fundamental process that evolves out of sphere stacking. It doesn’t get any more basic! And, with 539 tredecillion spheres expanding our universe every second, it is an image that our very finest cinematographic minds have not yet imagined.

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[8] Creating relations which create space. The relation, a ratio also known as a formula, with continuity (time) is what is fundamentally real. Everything else is derivative. Creating relations with balance or love is the purest form. Those whose hearts bleeding the most for others, those who want everything for everybody, feel this fact even if they can not elucidate a concept around it. The problem is creating value to give to others takes away the possibility of that person creating their own unique value. I’ll come back to this footnote often; it needs to become a major discussion.

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[9] Types of symmetries. Every symmetry is a key. We are just scratching the surface. Some geometers have been at it for decades; they know remarkable things about pi and symmetry. Yet when I ask them about the interiority of the octahedron and they can not tell me about those four hexagonal plates within, I know too much that is fundamental has been missed. We all need to be celebrating every honey bee in the world. Somehow they are in harmony with those hexagonal plates and everything that comes out of them has a deep hexagonality. We all need to know and experience every natural symmetry.

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[10] Lines, tetrahedrons and octahedrons. Our earliest work was with points, lines, tetrahedrons and octahedrons. Even though we knew the sphere was important, we didn’t know what to do with it. It seemed rather removed from our basic building blocks. Then, cubic close packing of equal spheres showed up in a search. There is lattice generation. It changed everything. Yet, it still takes awhile to absorb; and to this day, there is still a lot to absorb and a lot more to learn.

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[11] The Planck base units, Part II. We are all in search of an essential universe. Religious people of our world are often more stridently in search of what is essential. And, many are sure that they have what is most essential. Yet, until we understand more about the parts-whole relations, our talk is barely textured. We paint with such broad brushes, we often miss fine details that add to the majesty, the miracle, and the mystery of belief. All the dimensionless constants, both mathematical and physical, are the fine and extra-fine paint brushes. Until we know them, we don’t naturally use them. We can’t use them effectively. We may well use them unwittingly, but there is an art form, a perfection, within each of them. Here transformations may open new dynamics that have not even been imagined except for the most loving of our science fiction writers. Perhaps a new generation of artists-scholar-scientists can open ways to these dynamics and lead the way.

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[12] The Fourier Transform. There are no less than six dynamics that naturally come with spheres. All can be applied to the Planck scale and to each notation thereafter.
Cubic-close packing of equal spheres: Though lifted up within this website first (2016), this image naturally builds on the next five dynamic images.
Sine-Cosine-Waves: We’ll all learn about the wave’s fundamental relationship to the circle.
Focus on Sine: We’re all going to learn a little trigonometry and calculus, too.
An all-natural polarization: An open metaphor and analogical construction (mimetic).
Lagrange points: All Lagrangians come home.

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References & Resources

A More Simple Model: Six top postings, a summary overview
Worldviews to UniverseView
: Engage a Planck-scale Defined Universe.
The three
: Continuity-Symmetry-Harmony will take time to incubate.
History
: Change the Metaphor – Rewrite the History.
Expansion
: One plancksphere/plancksecond, a natural-but-unorthodox expansion
First Instant
: Remember Pi, a primordial, constant, ever-changing, always the same
Consciousness
: Who am I? Who are you?

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Communications: Emails & Instant Messaging

3:37 PM · Jan 30, 2021 @franlebowitz We all need a lift… outta the blues. We need a new view on life. Worldviews are too small. How about the universe? Here’s one for you: http://81018.com It’s real and it has pi, and spheres, and logic, and real moments of perfection. What’s not to love?

3:59 PM · Jan 31, 2021 @PNASNews Perhaps there’ll be a convergence here. We are starting at what we think is the first instant where Planck’s base units encounter pi and give us our first mathematical sphere: https://81018.com/challenge/ But at 539 tredecillion spheres per second, how are we going to sort things out?

4:43 PM · Jan 31, 2021· @walkingthedot You might enjoy this take on the first instant of the universe defined first by pi and the Planck base units. Gives the start of a full-blown view of the universe instead of little worldviews.
PDF: https://brucecamber.files.wordpress.com/2021/01/challenge.pdf
or https://81018.com/challenge/

5:39 PM · Jan 31, 2021 @mthomps I’ll start working on a koan for the first instance of the universe with pi and Max Planck’s base units (Nobel, 1918, mentor of Einstein, began quantum theory). Basic, basics. Webpage: https://81018.com/challenge/ If you get there first, please let me know!

6:01 PM – Jan. 31, 2021 @SarahZielinskiWhy not start a different take on pi? What would be the most basic-basic use of pi? Could we start the universe? What if we were to use the Planck base units and add pi? I thought about it a bit: https://81018.com/challenge/ Perhaps it could add to the Pi Day discussions. Thanks. -Bruce Please Note: This little message was sent from within Sarah’s website from her comment page. She had written an article for Pi Day, March 14, 2011. Although the many links, i.e. the first to Pi’s history might best go to Wikipedia’s listing. There is also the book, the movie, a song, and a uniquely-focused, specialized website (with many more options).

1:14 PM · Feb 3, 2021· @ScienceWriters @SarahZielinski @sciencedirect @APSphysics @JAMA_current Pi Day is coming up. Here’s a different take on pi: “Pi is necessary for the start the universe!” Max Planck’s 1899 base units require pi (and the Fourier Transform) to get it all moving: https://81018.com/challenge/ Let’s go deeper with all the Pi Day discussions. Thanks. -Bruce

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Zzz’s
Afterthoughts. Like so many pages on this website, this is the first time we have so pointedly equated pi with the first sphere, the first moment of space-time, and continuity-symmetry-and-harmony. A sequel posting will be developed by merging this document with an earlier one titled, The First Instance of Our Universe. It also reflects the many other pages including: https://81018.com/instant/ https://81018.com/expansion/ https://81018.com/conscious/ https://81018.com/essentials/ https://81018.com/almost/ https://81018.com/particle/

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• This document was started on February 21, 2021.
• First posted for collaborations: February 25, 2021 (Password protected)
• The URL for this document is https://81018.com/tredecillion/
• First posted as a homepage: January 2, 2022
• Prior homepage: https://81018.com/almost/
• A related homepage: https://81018.com/instance/
• First Tagline: Expansion of the Universe
• Second Tagline: One PlanckSphere per PlanckTime
• The last update of this page was on January 5, 2022.

# Cubic Close Packing (ccp)

###### by Bruce Camber, April 2019, last update, May 5, 2021

Cubic-close packing (ccp) had its start back in 1587 with the work of Thomas Harriot. Johannes Kepler continued that work in 1611. Calculations were made to attempt to stack cannonballs on the deck of a ship most effectively. It became a more sophisticated study in the 20th century when it was applied to discern atomic-packing factors.

Our application brings ccp down into the Planck scale.

Defined by dimensionless constants, the sphere is projected to be the most simple structure and the first structure within space-time.

Before John Ralston called into question the veracity of Planck’s calculation for the Planck constant, we actually concurred with those people who have call it a plancksphere. Within the studies of ccp, particularly focusing on the functions within sphere-stacking, it is hypothesized to be the basis for all forms, structures, substances, qualities, relations, and systems (functions) and it is best understood within the very first notations of the first 64-notations out of the 202 that encapsulate our universe.

The deep dynamics of the sphere, ostensibly all the lines within this illustration (dynamic gif, above right) are being analyzed. Here begins the tetrahedral-octahedral tiling and tessellating of the universe. Here is where Aristotle failed. From one sphere to another and another, then within the internal dynamics of these spheres, triangles, tetrahedrons, octahedrons; and then plates of triangles, squares, and hexagonals begin interlocking all things for all time and all spaces.

Another image of the tetrahedron naturally filling space to create the octahedron came out of our high school geometry class many years before December 2011 when we went deep inside and down into the Planck scale.

Here are the first 67 notations. It is a huge domain of the infinitesimal. There are so many doublings, here we obviously find the essence of dark matter and dark energy. Here, too, is the basis of isotropy and homogeneity.

These additional images and references implicate the sphere as our first order of space-time business:

John Archibald Wheeler, a most distinguished Princeton physicist (1938-1975) and University of Texas-Austin (1976-1986), was seeking to define a fundamental unit within space-time. He conceived of a quantum foam (1955). It wasn’t small enough. Although the Planck numbers have a pre-history going back to 1881 with Irish physicist, George Johnstone Stoney, both Stoney’s and Max Planck’s 1899 work were largely ignored and remained in the background. In 1982 John Barrow introduced both the Planck numbers and the Stoney numbers but that paper did not ignite deeper studies.

When Frank Wilczek wrote the Climbing Mt. Planck I, Climbing Mt. Planck II, and in 2002 Climbing Mt. Planck III for Physics Today, interest in the Planck numbers began to spike.

For us, it all started here: https://81018.com/number/#Kepler

This image was discovered within Wikipedia when I was looking to discern the most fundamental number, and the meaning of that number as it is related to any given shape. Cubic-close packing, both face-centered cubic (fcc) and hexagonal close-packed (hcp), has a rich history beginning in-and-around the 1570s starting with the problem of stacking cannonballs on the deck of a ship. The display of the transformation from stacking to tetrahedrons and octahedron was the most compelling.

This document was started on April 6, 2019 and was updated June 5, 2020.

# The first formula changes the way we see every formula.

Pi (π) opens our universe & infinity
through the concrescence of continuity, symmetry and harmony.

by Bruce E. Camber

Background: No other mathematical symbol is recognized with its very own celebration and holiday. In 1988 the Exploratorium, a San Francisco museum, celebrated “Pi Day” and set a precedent for eating pies and pizza decorated with pi’s symbol and endless numbers. An historic moment in 2009, the day, March 14, was recognized as a national holiday in the USA. In November 2019 Pi Day was adopted by the United Nations (UNESCO) as the International Day of Mathematics.* As the day becomes a general celebration of the extraordinary power of mathematics in our lives, more detailed studies of pi|(π) take a backseat. This posting is a simple precaution… Pi (π) is more than we think. Within the ratio of the circumference of a circle to its diameter is the keyway to the universe and infinity..BEC

Key words: Pi (π), Pi Day, International Day of Mathematics, continuity-symmetry-harmony, sphere-stacking, cubic-close packing of equal spheres, 539 tredecillion spheres per second, 202 base-2 notations from the Planck scale, quantum fluctuations, and everything-everywhere-for-all-time

We should not lose focus of our studies of the very nature of pi (π) especially her perfections that reveal a deeper essence of this ubiquitous equation.

Pi(π) is the concrescence of continuity, symmetry, and harmony from which all circles and spheres evolve. That opens key points to explore further:

Perfect functions of the circle and sphere: Continuity is the never-ending, never-repeating numbers of pi. Symmetry is a seemingly magical, deeper nature within those numbers that become relations which become perfect circles and spheres. And, harmony is an even deeper dynamic nature of the sphere. First explored in 1820 by Joseph Fourier, his work reveals a basic harmony of every sphere.

Taken as a whole, continuity-symmetry-harmony are both finite-infinite, a.perfection and a transformation nexus.1 Our ongoing studies of the finite-infinite relation are here.

Our scholars continue to build on Fourier’s insights. Visit with Poincaré, Gauss, Planck, Einstein, Smale, Milnor and others who have uncovered even more exacting relations with pi. Continuity defines time; symmetry defines space, and harmony defines the dynamics of space-time.

Perfected states within space-time. The Planck base units were defined by Max Planck in 1899 using dimensionless constants which render natural units and a vision and definition of the smallest possible units of space and time. Logic tells us that the smallest are also the first, the most-simple starting points. At the bottom of the graphic on your right there is Planck Time and Planck Length where the first infinitesimal-and-perfect spheres emerge. An expansion rate, one sphere per unit of Planck Time and Planck Length, is hypothesized.

If so, 539 tredecillion spheres per second are generated. Base-2 notation is applied to investigate basic relations. The result is 202 notations (or doublings) to explore that encapsulate the universe.

Cubic-close packing of equal spheres further geometrizes each number. In the first notations, there is an absence of gaps. The time interval requires efficiencies; and, densities render perfectly-fitting geometries.

By studying Aristotle’s mistake with tetrahedrons, we learn about basic geometric gaps. Associated with quantum fluctuations, it is hypothesized that these do not manifest until at least Notation-50.

Then the known equations that define our foundations begin to emerge. By the 202nd notation, the universe as we know it — everything, everywhere for all time — is encapsulated and all intimately connected by infinitesimal spheres that are many orders of magnitude smaller than the elusive neutrino (of which about 100 trillion pass through our bodies every second according to the IceCube Neutrino Observatory, the University of Wisconsin–Madison and the National Science Foundation (2017).

All 202 notations are always active. Some scholar-scientists say “all time is now.” Each notation adds definition. As we go down the scale, there is increased particularity and coherence. The only possible singularity is at the very beginning, and even then, it is a convergence of equations. Exacting definitions of the infinitesimally small evolve, first through sets, then groups, and then obviously working systems that involve all 202 notations.

Logically there is a domain with no gaps. Perfectly-fitting geometries are hypothesized to come prior to the possible emergence of quantum fluctuations.[2]

Values. These perfectly-fitting geometries might account for the first 50 notations where the continuity-symmetry-harmony of the spheres (and the extreme densities and absolute efficiencies) create no gaps and this becomes the basis for value.

If this were to become a new platform for mathematics, the world would change because mathematics would be pushing us to explore the meaning of those values as expressions of continuity, symmetry and harmony.

The positions and functions of infinitesimal spheres, especially the generation and labelling of every sphere after the first, would be the beginning of a new paradigm for the sciences. We would begin to recognize the tools to fill in the gaps between the Planck Scale and the Electroweak Scale (and between the Lambda Cold Dark Matter model or the Standard Model for Cosmology and the Standard Model for Particle Physics). Yet, it all begs the question, “What is the role of light within each notation? Is it what holds it all together (as in e=mc2)? Is it the deepest part of continuity- symmetry-harmony? Is it the beginning of values and ethics?

None of those questions are beyond our imaginations and our capabilities to answer. Thank you.

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Endnotes & Footnotes
All these points already have pages within this website.

[*] Einstein’s birthday and the day of Hawking’s death. Many historians mention that the day, March 14, has unusual symbolic meaning. Two of the most influential people of our time seem to be pointing at pi (π) as if saying, “Pi (π) is a key.”

[1] Pointing beyond circles and spheres. Between the finite-infinite transformation and between the faces of continuity-symmetry-harmony (CSH) are equations. Many equations converge within the numbers that make up the Planck base units. Although there are alternatives to the Planck numbers (Stoney, Ralston, and ISO numbers), Planck’s have become a standard. Eventually we will likely be using new ISO base units, yet the results will be very similar. The convergence of equations is the point. It is the necessary convergence of the finite-infinite. It also appears to be the beginning of values and even our sense of ethics.

Bringing the infinite into the equation is difficult for many. Within this website, you will find this declaration:

All other definitions of the infinite are put on hold. Most are personal definitions that come from personal experiences and family history. That is one’s own business, not ours. If those beliefs help you through life, that is great. Our goal here is to engage those principles and functions that give rise to mathematics, physics, and eventually all the other sciences.

from Continuity-Symmetry-Harmony, (CSH), 2022. Originated in 1972

CSH is the infinite and the finite. Its first expression as the finite is the Planck base units. The first expression of those units is an infinitesimal sphere. This is an unprecedented definition of the finite-infinite relation. Doing a simple calculation with Planck Time, assuming one sphere per unit of Planck Time, renders 539 tredecillion spheres per second. That may well be considered a new definition of the cosmological constant. To begin to grasp that natural expansion, apply base-2 notation and the first second, manifests within Notation-143. The first year manifests within Notation-169. The first 1000 years manifest are within Notation-179. The first million years manifest within Notation-189 and the first billion years within Notation-199. All notations are always active.

These 202 base-2 notations functionally outline the universe; having been studied within and throughout this website, there’s more: https://81018.com/inflaton/#202

Fourier transform. Every formula that involves pi (starting with the Fourier transform) needs to be re-reviewed in light of CSH and the 202 base-2 notations. Pi is everywhere.

[2] Geometries of indeterminacy. There is a look and feel of quantum fluctuations; the mysteries appear to be within all the geometries. Perhaps scholars were first foiled by Aristotle (384-321 BC). Five tetrahedrons create a gap that he missed; and for 1800 years that mistake was repeated by scholars. It is worth pondering. Aristotle was so great it took 1800 years to countermand his mistake. And, it is still untouchable. That correction was eventually forgotten until in 1926, a little-known MIT mathematician, Dirk Struik, rekindled the scholarship. Struik’s work did not receive much attention until in 2012 when two scholars, Jeffrey Lagarias and Chaunming Zong, lifted it up again. Yet, these two mathematicians were more interested in packing densities. There has been no exploration of the meaning of the gap. Subsequently, in May 2022, a five octahedral-gap was introduced to the world from within this website and questions were asked of many scholars, “What are these gaps all about?”

Our charts, interpretations and prognostications. Simple logic, simple math, and simple geometries render our charts, interpretations and prognostications. It all awaits critical review, so until then, there will be more to come.

Review and summary of at least ten new ways to look at pi:

1. A closer-look at Continuity-Symmetry-Harmony
2. Pi, the primary clue about the Finite-infinite relation
3. Planck’s base units defining the most infinitesimal spheres
4. No less than seven new perspectives: Fourier, PoincaréGaussEinsteinSmaleMilnor and many others
5. 539 tredecillion infinitesimal spheres per second
6. Sphere-stacking
7. Cubic-close packing of equal spheres
8. Infinitesimal spheres populating the universe and making everything-everywhere-for-all-time
9. Responsible for the first fluctuation and the geometries of quantum fluctuations
10. 202 notations always active
11. Continuity-symmetry-harmony become a foundation for values.
12. Filling in the gaps between Planck Scale and the Electroweak Scale and between Lambda Cold Dark Matter model (or the Standard Model for Cosmology) and the Standard Model for Particle Physics

This homepage follows

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References & Resources
As references are studied, these references and other resources will be updated.

Pi (π): Dimensional analysis, scale invariance, functional dependencies
Symmetry in QFT and Gravity (video), Hirosi Ooguri (homepage) and Nathan Seiber), 2022
Mathematically, equations building on natural functional dependencies:
….–  Using math in physics: 5. Functional dependence (PDF), E. F. Redish, Univ. Maryland, 2022
•  ESA Group (PDF): The universe at 380,000 years
https://www.esa.int/Our_Activities/Space_Science/Planck/Planck_reveals_an_almost_perfect_Universe,2009
•  Pure Natural Inflation, Yasunori Nomura, Taizan Watari, and Masahito Yamazaki,
Berkeley Center for Theoretical Physics, Department of Physics, 2017
The Friedmann–Lemaître–Robertson–Walker (FLRW) Metric
•  Scale invariance, conformal symmetries, and asymptotic freedom.

Of the 202 notations, the first 64 notations are a novel map to examine. There’ll be a place for the some of the big bang numbers but not until after the first few seconds (Notation-143 and higher).

Thrust in our universe. In September 2017, I wrote about the thrust in our universe. So now, over five years later, it is time to revisit that article and update it as much as possible. The major update would involve our understanding more about the three facets of pi and how each is a Janus-face for the finite and the infinite. How are the functions of continuity-symmetry-harmony abiding?

Major studies. I have written to Robert Langlands, Ed Frenkel, and others within Langlands programs. They have not yet acknowledged the 202 mathematical notations. Why not? It’s just math and logic. There is no philosophy. There are no agendas. It is what it is, simple math.

I have also written to people within string theory. None have acknowledged the 202 notations.

I believe people are naturally incrementalists. It is more comfortable. The Planck units were ostensibly ignored until 2001 and by that time Hawking-Guth-and-family had a hold on the theory about the start of the universe. With Hawking’s death, that hold has become somewhat more relaxed. With results from the James Webb Space Telescope (JWST), it’s time to open up the discussions. It will include conformal-quantum-and-scalar field theories (CFT, QFT). Although John Wheeler’s sense of simplicity is a good idea, for most of the octogenarians and nonagenarians, this base-2 model of 202 notations is just too simple. It is too obvious. Yet, maybe not. Prior to Frank Wilczek’s three articles about the Planck scale, Planck’s numbers were aloofly small much like Paul Dirac’s were aloofly big.

#

In 1980 in Paris at the Institut Henri Poincaré, Jean-Pierre Vigier and I made a six-month study of the EPR paradox in light of the work of Alain Aspect in d’Orsay. Instead of infinitesimal spheres, Vigier had suggested that we use the metaphor of dominos falling. That type of action-at-a-distance is not instantaneous. Infinitesimal spheres within the packing densities suggested by the Planck-or-Stoney-or-ISO numbers would be instantaneous. Also, in this period, an equal amount of time was spent with Olivier Costa de Beauregard.

Do the mathematics and physics of the finite begin here?

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Emails
There will be emails to many of our scholars about the key points.

3 April 2023: Dudley Herschbach, Harvard
3 April 2023: Cora Dvorkin, Harvard
31 March 2023: Arieh Ben-Naim, Jerusalem, Israel
29 March 2023: C.S. Unnikrishnan, DIAT (Pune)
26 March 2023: Christoph Sorger, IMU, University of Nantes
25 March 2023: Michael Spannowsky, Durham
25 March 2023: James Warren, NIST, DC
21 March 2023: CIMPA’s educators throughout the world
14 March 2023 Audrey Azoulay, UNESCO, Paris*
3 March 2023: David F. Robinson, Kings College (London)
2 March 2023: Steven Strogatz, Cornell
2 March 2023: Kevin Dykema, National Council of Teachers of Mathematics
2 March 2023, Pi Day Puzzle to many of those already contacted
1 March 2023, Edward F. Redish, Univ. of Maryland
25 February 2023, Anna Ijjas, NYU
25 February 2023, Katherine Freese, University of Texas, Austin

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Many instant messages to thought leaders.

3:49 PM · Mar 9, 2023 @TheAtlantic @marinakoren You won’t believe this history of the universe. https://81018.com/chart/ It’s too simple. Base-2 notation from the Planck scale: https://81018.com/stem/ Pi day celebrations shed some light, too. https://81018.com/continuity-symmetry-harmony/

7:46 AM · Mar 9, 2023 @TonomusNEOM Three levels of cognition: continuity, symmetry, harmony work together within pi and define the finite-infinite relation: https://81018.com opens that door. “Let’s pi… work together.”

9:22 AM · Mar 4, 2023 @DrOsamaSiddique @Harvard_Law @UniofOxford @IGLP_HarvardLaw Natural law can be found within the fundamentals of pi (π): https://81018.com/continuity-symmetry-harmony/ The relation becomes the primary real. Editor’s note, also see: https://81018.com/values/ https://81018.com/oxford/ https://81018.com/harvard/

4:00 PM · Mar 2, 2023 @RushHolt Pi Day is coming up on March 14. I think we’ve underestimated the importance and place of pi (π): https://81018.com/

1. Is it possible that the first instance of the universe is defined by Planck’s base units?
2. Is it possible that the first manifestation of those base units is an infinitesimal sphere?
3. Might the characteristics of pi describe those spheres?
4. Might the Fourier Transform impart either electromagnetism or gravitation to each sphere?
5. Is it possible that one sphere manifests per unit of length and time?
6. Doesn’t that compute to 539 tredecillion spheres per second using Planck units and 4605 tredecillion per second using Stoney Time?
7. Is it possible that the densities within the earliest notations are on the order of a blackhole or neutron star?
8. To create some sense of order with the generation of infinitesimal spheres, may we use base-2 notation?
9. Using base-2 notation, are there 202 base-2 notations from Planck Time to the current time?
10. Is it significant that at one second the Planck Length multiple is a very close approximation of the distance light travels?
11. Is it significant that quantum fluctuations are measured within Notation-67? Notation-72 appears to be the limit of our abilities to measure a duration of time.
12. Would these notations, 1-64, provide 64 possible redefinitions of a point-particle? (And, I would add a vertex.)

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Editor’s Note: Putin’s Heart and Mind.All people who instigate violence against another have not learned the basics about life. Arrogance and crudeness block paths for light and understanding. UNESCO is about shining light wherever there is a problem in the world. They need to illuminate Vladimir Putin’s heart and mind. They can reach him. He is ill and facing death; he just may be receptive to their words about education,

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• This page became a working homepage at 8 AM on March 2, 2023.
• The last update was March 21, 2023.
• This page was initiated on February 24, 2023 at 7 AM.
• The URL for this file: https://81018.com/continuity-symmetry-harmony/
• A headline: A Global Celebration of Mathematics
. . Sub-header and link: Our Call to Expand Our Understanding of Pi (π) for Pi Day 2023
• First byline: Pi Day points us beyond circles and spheres.

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# Step 1: A less-than-500 words press release

History: The first Pi Day celebration in 1988 at the San Francisco science museum Exploratorium was initiated by their resident scientist, Larry Shaw. They ate a lot of pie and had fun with mathematical trivia. Notwithstanding, by 2009, Pi Day was recognized as a national holiday (USA). By November 2019, UNESCO adopted Pi Day as the International Day of Mathematics.

For immediate release: Center for Perfection Studies, Austin, Texas. Contact: Bruce E. Camber (214) 801-8521

Pi Day celebrations often begin with pie-eating contests and evolve into a recitation of some part of 100-trillion known digits of pi, yet the perfections of pi (π) reveal its deeper essence and purpose.

Pi is the continuity, symmetry, and harmony from which circles and spheres evolve. That opens at least ten key points to explore pi more rigorously.

#1 Take those three perfect functions as a whole. Continuity is the never-ending, never-repeating numbers of pi. Symmetry is the deeper nature within those numbers that become relations which become circles and spheres. And, harmony is an even deeper dynamic of the sphere, first opened in 1820 by Joseph Fourier,  that is a simple harmony that defines every sphere.

#3 Our scholars continue to build on Fourier’s insightsMany others have uncovered even more exacting relations with pi. At its core, continuity renders time; symmetry renders space, and harmony renders the dynamics of space-time.

#4 Perfected states within space-time. The Planck base units defined by Max Planck in 1899 use dimensionless constants which become natural units and definitions of the smallest possible units of space and time. The smallest are logically the first, the starting points of our universe.Planck Time and Planck Length are where the first infinitesimal-and-perfect sphere emerge. Using Planck’s numbers, one sphere per unit of Planck Time and Planck Length redefines emergence.

#5 At that rate, 539 tredecillion spheres per second are generated. To grasp some order, we apply base-2 notation. The result is 202 notations (or doublings) to explore that encapsulate the known universe. There are numbers to keep the score.

#6 Those numbers are timestamped with sphere-stacking.

#7 Then the numbers are geometrized with cubic-close packing of equal spheres. In the first notations, there is an absence of gaps. The basic geometries all fit perfectly. It is hypothesized that quantum fluctuations can not manifest until at least Notation-50.

#8 Langlands programs and string theory are further defined with pi.

#9Then the known equations that define our foundations emerge. By the 202nd notation, we have our universe, everything, everywhere for all time, all intimately connected by infinitesimal spheres.

#10 All 202 notations are always active and “all time is now.” Each notation adds definition. As we go down the scale, there is increased particularity and coherence. There is no singularity. In the very beginning, within the convergence of equations, there are exacting definitions.

#11 Logically there is a domain with no gaps. Perfectly fitting geometries exists prior to the emergence of quantum fluctuations.

#12 Values. Perfectly-fitting geometries account for earliest notations where there are no gaps; it becomes the basis for value.

With this platform, Pi Day becomes a study of infinitesimal spheres to define the Planck to Electroweak Scale and our Standard Models (Particle Physics and Cosmology).

It is not beyond our imaginations and capabilities.

# For immediate release:

Introduction: A working draft of the press release — https://81018.com/pointing/ — was first written for academics then it was toned down to become a general press release and its purpose was greatly expanded. A goal is to have several versions of that article, each weighted for particular audiences. The next audience to reach are the online-broadcast-printed news outlets so they run a press release a few days after March 14. That version will be emerge here, then a new release of 500 words will be done. The goal is to stir people to talk about entirely new dimensions of pi.

A new version for academics with the benefit of feedback will be done.

This press release may be run anywhere in the world on any publication, news broadcast, or website. It may also be re-written to eliminate footnotes.

For immediate release:
Center for Perfection Studies, Austin, Texas. Contact: Bruce E. Camber

Background: Bruce Camber, the Managing Director of the Center for Perfection Studies in Austin, Texas, has been critical of most Pi Day celebrations. He has advocated that Pi Day be addressed by further considering the three functions that define it: continuity, symmetry, and harmony. “A core part of science is to define its functional dependencies; yet dimensional analysis starting at the Planck base units and extending through to electroweak scale has been virtually ignored. It’s an Achilles Heel for science and humanity.”

In 2016 the Center Perfection Studies did the first mathematical map of the universe that starts with the Planck base units and goes to the current time. It is a base-2 map with 202 notations. In 1957 Kees Boeke did a base-10 map of much of the universe that captured the widespread attention (credits within films, Cosmic Zoom, National Film Board of Canada, 1968; Powers of Ten, Charles and Ray Eames, 1968; and Cosmic Voyage, IMAX  and Smithsonian National Air & Space Museum, 1996).

“The difference between base2 and base-10 is that our base-2 map encourages scholars to look for the functional dependencies,” Camber went on, “There is causal efficacy between notations. Dimensional analysis is a key.”

History: In 1988 Larry Shaw of the San Francisco science museum, Exploratorium, started the first known Pi Day celebration. By 2009 Pi Day was recognized as a national holiday in the USA. In November 2019 UNESCO adopted Pi Day as the International Day of Mathematics. The challenge each year is to do something significant on that day and progress beyond pie-eating contests and the recitation of some part of the 100-trillion known digits of pi (calculated using Google Cloud in 2022 by Emma Haruka Iwao).

The Center for Perfection Studies believes that Pi Day could be a rapprochement to explore the first principles of pi and to better define the very nature of pi. That it has real potential to define common foundations that could bring people together. heretofore has not been explored. The Center is seeking to partner with UNESCO (emails to Audrey Azoulay, Director-General, and David Atchoarena, Director, UNESCO Institute for Lifelong Learning, Hamburg, Germany) to make Pi Day a true International Day of Mathematics.  The center’s most simple math — multiplying by 2 — encapsulates the universe within just 202 notations (https://81018.com/chart/).

In the center’s study, pi (π) is defined by continuity, symmetry, and harmony. Circles and spheres are derivative. There are no less than ten key points that they ask people to consider:

• Three perfect functions have not taken together as a functional whole. Continuity is the never-ending, never-repeating numbers of pi. Symmetry is the deeper nature within those numbers that become relations which become circles and spheres. And, harmony is an even deeper dynamic nature of the sphere that was first opened in 1820 by Joseph Fourier. A most simple harmony is found within every sphere. p;
• Taken as a whole, continuity-symmetry-harmony are both finite and infinite.
• Our scholars continue to build on Fourier’s insights. Visit with Poincaré, Gauss, Planck, Einstein, Smale, Milnor and many others who uncovered even more exacting relations with pi. Yet, at its core, continuity defines time; symmetry defines space, and harmony defines the dynamics of space-time.
• Perfected states within space-time. The Planck base units defined by Max Planck in 1899 use dimensionless constants which render natural units and a vision and definition of the smallest possible units of space and time. Simple logic holds the smallest are also the first, the starting points of our universe.At the bottom of the graphic on your right there is Planck Time and Planck Length where the first infinitesimal-and-perfect spheres emerge. Using Planck’s numbers, one sphere per unit of Planck Time and Planck Length is logically defined. There are just 202 doublings to explore to encapsulate the known universe. These numbers keep the score.
• At that rate, 539 tredecillion spheres per second are generated.
• Those numbers are timestamped with sphere-stacking.
• Then the numbers are geometrize with cubic-close packing of equal spheres. In the first notations, there is an absence of gaps. The basic geometries all fit perfectly. It is hypothesized that quantum fluctuations cannot manifest until at least Notation-50.
• Langlands programs and string theory are further defined with pi.
• Then the known equations that define our foundations emerge. By the 202nd notation, we have our universe, everything, everywhere for all time, all intimately connected by infinitesimal spheres.
• All 202 notations are always active. Many scientists say “all time is now.” Each notation adds definition. As we go down the scale, there is increased particularity and coherence. The only possible singularity is in the very beginning, and even then, it is a convergence of equations. Exacting definitions of the infinitesimally small, first start within groups, and then obviously become part of a working system that involves all 202 notations.
• Logically there is a domain with no gaps. Perfectly fitting geometries exists prior to the emergence of quantum fluctuations.[2]
• Values. Those perfectly-fitting geometries may possibly account for the first 50 notations where the continuity-symmetry-harmony of the spheres creates no gaps and becomes the basis for value.

Camber concludes, “With all this as a platform, Pi Day could be turned in to an extraordinary International Day of Mathematics. It could become an exploration of the positions and functions of infinitesimal spheres, particularly the generation and labelling of every sphere after the very first. And, it just might begin to fill in the gaps between the Planck Scale and the Electroweak Scale as well as between the Lambda Cold Dark Matter model (or the Standard Model for Cosmology) and the Standard Model for Particle Physics.”

“It is not beyond our imaginations and our capabilities. Thank you.”

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Endnotes & Footnotes & Graphics
These points already have pages within this website.

[1] Pointing beyond circles and spheres. Between the finite-infinite transformation and between the faces of continuity-symmetry-harmony (CSH) are equations. Many equations converge within the numbers that make up the Planck base units. Although there are alternatives to the Planck numbers (StoneyRalston, and ISO numbers), they’ll use the same dynamics (and equations). Eventually we will probably be using new ISO base units, yet I expect the results will be very similar. That convergence of equations is the point. It is the necessary convergence of the finite-infinite. It’s also the beginning of value.

Bringing the infinite into the equation is difficult for many. Within this website, you will find this declaration:

All other definitions of the infinite are put on hold. Most are personal definitions that come from personal experiences and family history. That is one’s own business, not ours. If those beliefs help you through life, that is great. Our goal here is to engage those principles and functions that give rise to mathematics, physics, and eventually all the other sciences.from Continuity-Symmetry-Harmony (CSH), 1972

CSH is the infinite and the finite. Its first expression as the finite is the Planck base units. The first expression of those units is an infinitesimal sphere. This is an unprecedented definition of the finite-infinite relation. Doing a simple calculation with Planck Time, assuming one sphere per unit of Planck Time, renders 539 tredecillion spheres per second. That could be considered a new definition of the cosmological constant. To begin to grasp that natural expansion, we apply base-2 notation and the first second, manifests within Notation-143. The first year manifests within Notation-169. The first 1000 years manifest within Notation-179. The first million years manifest within Notation-189 and the first billion years within Notation-199.

The only place where these 202 base-2 notations that functionally outline the universe have been studied is within and throughout this website. For more: https://81018.com/inflaton/#202

Fourier transform. Every formula that involves pi (starting with the Fourier transform) needs to be re-reviewed in light of CSH and the 202 base-2 notations. Pi is everywhere.

[2] Geometries of indeterminacy. There is a look and feel of quantum fluctuations; the mysteries are all within the geometries. It appears that scholars were first foiled by Aristotle (384-321 BC). Five tetrahedrons create a gap that he missed; and for 1800 years his mistake was repeated by scholars. That is worth pondering. Aristotle was so great it took 1800 years to countermand his mistake. And, it is still untouchable. That correction was eventually forgotten until in 1926, a little-known MIT mathematician, Dirk Struik, rekindled that scholarship. Struik’s work did not receive much attention until in 2012 when two scholars, Jeffrey Lagarias and Chaunming Zong, lifted it up again. Yet, these two mathematicians were more interested in packing densities. There is no exploration of the meaning of the gap. Subsequently, in May 2022, a five octrahedral-gap was first introduced to the world from within this website and questions were asked of many scholars, “What are these gaps all about?”

Our charts, interpretations and prognostications. Simple logic, simple math, and simple geometries render our charts, interpretations and prognostications. It all awaits critical review, so until then, there will be more to come.

A Review-Summary of least ten new ways to look at Pi Day in this universe:

1. A celebration of Continuity-Symmetry-Harmony
2. Pi is the primary clue about the Finite-infinite relation
3. No less than seven new perspectives: FourierPoincaréGaussMilnor and many others
4. Planck’s base units begin to define those infinitesimal spheres.
5. 539 tredecillion infinitesimal spheres per second
6. Sphere-stacking
7. Cubic-close packing of equal spheres
8. Infinitesimal spheres make everything, everywhere, for all time yet start with Langlands programs and string theory.
9. All the known equations that define our foundations emerge.
10. 202 notations encapsulate our universe, all defined by pi.
11. A domain with no gaps, then comes the first fluctuation and the geometries of quantum fluctuations
12. A foundation for values
13. Filling in the gaps between Planck Scale and the Electroweak Scale and between Lambda Cold Dark Matter model (or the Standard Model for Cosmology) and the Standard Model for Particle Physics
• Audrey Azoulay, Director-General, UNESCO (speeches, 2023) (in Iraq) “Mathematics, with its many technical applications, now underpins all areas of our lives. Together with algorithms, mathematics plays a key role in artificial intelligence and technological disruptions – and, as we address global issues such as the COVID-19 pandemic and climate change, we are reminded of the importance of mathematics in responding to the challenges of our time.”
• Hiraku Nakajima, Secretary General of the International Mathematical Union, Hausvogteiplatz 11A, D-10117 Berlin, Germany
• Andreas Matt, Managing Director of IMAGINARY and of the IDM
• Christiane Rousseau, Chair of the IDM Governing Board
• Djamel Eddine Cheriet, Vice-President of the Algerian Mathematical Society,
• National Institute for Mathematical Sciences, Korea
• European Mathematical Society
• Helge Holden, former secretary-general of the International Mathematical Union

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# Big bang or big board? (This version has no endnotes and footnotes.)

Abstract. Our STEM tool is becoming a working model. It has a simple logic, geometry and algebra based on spheres, tetrahedrons, octahedrons and doublings. It begins with natural units; it is driven by pi (π). And, its 202 predictive, base-2 notations readily absorb big bang cosmology. This mathematically-integrated view of the Universe addresses key issues that big bang cosmology cannot. Five examples follow.

I. Smoothness. The James Webb Space Telescope images have raised anxieties that the early universe is too smooth for our working understanding of the dynamics of big bang cosmology. The transition from smooth to lumpy is not a problem within the 202 base-2 notations. In this model geometric gaps do not become systemic until later in the unfolding of the universe. The earliest notations begin perfectly smooth because it starts with the most simple geometries that tile and tessellate this universe perfectly.

II. The first minute, the first second, and the first zeptosecond. The first minute of the universe is within Notations 149-150. The first second is between Notation 143-and-144. Zeptoseconds (1×10-21) are between Notations 65-and-67. Eminent scholars, Sean Carroll of John Hopkins and James Peebles of Princeton (Nobel laureate, 2019, and a pioneer of cosmic microwave background radiation research) acknowledge the importance of articulating the first minute of the universe. In June 2020 over twenty scholars focused on the emergence. Their publication was “The First Three Seconds: A Review of Possible Expansion Histories of the Early Universe” (arXiv:2006.16182 [astro-ph.co]); they were unable to define the first minutes. The zeptosecond is on the cusp of quantum fluctuations. The first notations begin with the natural units that were defined by Max Planck in 1899 and George Johnstone Stoney in 1874. It is a natural grid. As each notation builds on the prior notations, geometries, numbers and relations necessarily refine the nature of time. Those first 64 notations have been unwittingly defined by hundreds of scholars within Langlands programs, string theory, and like disciplines … all while big bang cosmology hides any access to those first notations.

III. Quantum fluctuations and quantum physics. The study of a geometry of quantum fluctuations over the years is most limited. A most-simple place to start is to recognize the tetrahedral gap that Aristotle did not see. That gap is real. Plus, there are others that are ignored. Add to it our octahedral gap and then the icosahedral gaps. Here are possibilities for fluctuations. Big bang cosmology has no simple geometry and certainly no geometry for chaos and indeterminacy. Our mathematically-integrated view of the Universe begins with the inherent geometries of doublings that perfectly tile and tessellate and it has a geometry for fluctuations that is inherently indeterminant. One of our primary studies is to grasp the varieties of gaps and the probabilities for each manifestation within a given notation.

IV. A natural inflation and dark energy and dark matter. Dark matter and dark energy are below all possible thresholds of direct measurement. The indirect effects have been well-regarded since the work of Lord Kelvin (1884), Jacobus Kapteyn (1922), Jan Oort (1932) and Fritz Zwicky (1933). The mystery prevails. Big bang cosmology blocks the view of both the geometries of perfection and of imperfection. Initially there are no gaps as spacetime is dynamically created. Within this mathematically-integrated view of the Universe, a natural inflation starts with the most simple infinitesimal sphere, sphere stacking, and cubic-close packing of equal spheres. Tetrahedrons and octahedrons are generated and naturally tile and tessellate the early universe.

If taken as a given that one infinitesimal sphere is generated per unit of length and time, the rate would range from 539-to-4609 tredecillion spheres per second. Of course, that range is established by Planck Time and Stoney Time.

V. Finite-infinite, quantitative-qualitative. Big bang cosmology has no finite-infinite relation and makes no distinction between the quantitative and the qualitative. It does not posit the smallest physical unit of spacetime. It makes no statements about pi (π), nor recognizes the essential faces of pi (π): continuity (ordering), symmetry (relating) and harmony (making dynamic). Naturally, the ubiquitous dimensionless constant that generates the natural units for Planck and Stoney is pi (π). We hypothesize that these three faces of pi (π) define the qualitative and the infinite. Within big bang cosmology the Planck Epoch and a singularity are the baseline whereas within our mathematically-integrated view of the Universe, it is the simple perfections of the infinitesimal sphere and the simple perfections and imperfections-or-gaps within tetrahedrons and octahedrons.

Thank you. -BEC

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