Quantum Fluctuations

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An alternative to Big Bang Cosmology More work will be done on this page throughout 2020

An Exploration for Quantum Fluctuations Within Base-2 Exponentiation

Introduction.

Background. In December 2011, this project began by following embedded geometries, smaller and smaller, by dividing the edges of the tetrahedron by 2 and connecting the new vertices. In 45 steps following Zeno further and further within, we were in the domain of particle physics. In another 67 steps within we were in the domain of the Planck scale. In our naïveté we then multiplied our little tetrahedron by 2, and in 90 steps were were out to the age and size of the universe. Today, it is a mathematical and geometrical model based on the Planck units.

Gap

Why didn’t Max Planck and Albert Einstein do the simple math? Why did it take the extreme naïveté of high school people? It is anybody’s guess. It seems logical. It looks logical. But…obviously it dumbfounds the scholars within the academic community. Since 2011, we have asked hundreds of our best for advice. Very little has been given to us.

We know this much. Geometry and mathematics are real realities and Aristotle made a mistake when he thought one could tile the universe with just tetrahedrons. He missed a very simple and seminal gap.

Given the lack of understanding in this realm of physics, we postulate and hypothesize that this gap pictured above started the first fluctuation in the universe.

Sphere to tetrahedron-octahedron couplet
Face-centered cubic packing

Measurement: Our chart of base-2 exponentiation [1] starts with the Planck base units and goes to the Observable Universe and Age of the Universe. It has just 202 notations.  It is logical and simple, and a potential alternative to big bang cosmology.[2]

The first-possible physical measurements in our universe happen in labs like CERN (Geneva, Switzerland). Estimates of the ionic radius involved in their heavy ion collisions range from 30-to-300 picometers or approximately 3.9077×10-11 meters at the 81st notation to 3.12618×10-10 meters at the 84th notation.

Collider measurements are within the scale of the 67th notation (2.38509×10-15 meters), the 66th notation (1.19254×10-15 meters) yet some say down as small as 1.16459×10-18 meters at the 56th notation. These and the other numbers in the 200+ columns are real numbers, all multiples of the Planck base units.

Today these numbers are all just simple mathematics and imputed geometries and this system of numbers is not yet recognized by the academic-scientific community to be meaningful or significant.

Potential Significance: By themselves these numbers create a rich panoply of possibility. We believe it would be unimaginative not to try to do something with them, so we enter the domain of the mysterious quantum fluctuations. Unlike current theorists, their “out of nothing” is for us as many as 67 notations where distinctions between notation 2-to-66 are expected to be as great as those within the next 67 notations (67-134), and then again within the next 67 (134-201) that follow.

Pi And Never-ending, Non-repeating Numbers. The animated image (just above, on the left) challenges us in unusual ways. Looking for other possible parts of the puzzle, we accept the logic and necessity of a singularity, but conclude that it is a dynamic transformational nexus between the finite and infinite whereby there is a complete unification of all the basic forces of naturethe Planck base units (aka Planck scale),  the dimensionless constants,  and a very special class of circles and spheres.

That is our working hypothesis.  We further postulate that this working premise creates an environment to build a panoply of bridges from the Planck scale to all current physical theories whereby each notation is a domain for unique predictive values. The challenge will be to recognize the mechanisms that would confirm or deny these hypotheses and postulations.

Fact Gathering: The Tools of this Art. The first thing we did was look for the possible parts of the puzzle. Of course, there are the Planck base units. There are the 202 notations. There is the speed of light — Planck Length divided by Planck Time — within each and every notation. These are our starting points.

The universe appears to be logically divided into three scales. The small scale from notations 2-67, the human-scale from 67 to 134, and the large scale from 134 to just over 201.

The next big observation is that the progression of epochs defined by big bang cosmology is well-defined by the natural inflation  within base-2 exponentiation. Simple logic seems to suggest that each currently-defined big bang epoch can readily become a process within the base-2 model. And, significantly, there is no need for an actual big bang; natural inflation is quite enough.

Within our Top Ten Reasons to Put Big Bang Cosmology In Time Out, we now turn to a few of the many enigmatic questions[3]  within cosmology.  Perhaps within the base-2 model we can find answers or something new.

SPECULATIONS:

More Postulations. These first 67 notations could be the deep systems structure of the universe that give rise to richly-textured quantum fluctuations, cosmic microwave background radiation (CMBR), homogeneity and isotropy, dark energy and dark matter, magnetism, and gravity (defined by General Relativity). Big bang cosmology has no answers. Given that the base-2 model is simple, it may hold rather simple answers.  This article is our first to enter this configuration space starting at notations 0,1 with a point (vertex), then a line, a circle, a sphere, a tetrahedron, and then tetrahedrons and octahedrons. That animated image (top left) demonstrates a process that apparently has not been studied much beyond the problem of stacking cannonballs. (Insert footnote to Thomas Hales following up Thomas Harriot’s work)[4]

e8sophuslie

The Art:  Using dimensional analysis within the first 21 notations, there are over a quintillion base-8 vertices with which to experiment and build initial systems! Sophus Lie could make millions of his E8 structures. Within just the first ten notations, there are 134,217,728 scaling vertices. Possible analogues include the protein machines or nanomachines within the body. Other analogues could include genetic code machines.

So, let’s build some simple mechanisms, then work with the art (and magic) to bring all that richly-textured phenomena of the universe to life! Let’s see what we can do with the most artistic and unpredictable  of that group, quantum fluctuations.

Transformation Nexus. Once the singularity is multiplied by 2 (the form) or by 8 (the function), it is no longer the Planck singularity or Planck Epoch; it becomes the first possible transformation nexus between the finite and infinite.

Could it be that from this beginning, everything, everywhere, shares these eight vertices. “Ridiculous? Poppycock?

pentastar1

We ask that you hold those judgments in abeyance. To get into this model will require stretching, suspending judgment and imagining in rather new ways. With eight vertices the universe might organize those vertices as five tetrahedrons with a small space between the fifth and first tetrahedron. There is one extra vertex. It is elegant. It is imperfect. It creates degrees of freedom (7.356103 degree gap or 0.12838822 radians).

Couldn’t this be the birthplace, the earliest beginning of the quantum fluctuation?

Could this possibly be a key process that is extended throughout all 200+ notations? Of course, those who know molecular geometry readily recognize the figure.

In the next doubling there are 64 vertices.  Seven-plus-1 is established. The next 13 vertices extending from “The Seven” create a mathematically whole figure, an absolute figure of six tetrahedrons whereby there is potential action because the base is a perfect structure, a hexagonal plate.

Each cannonball is a vertex.  Or, is it an infinitesimal circle or sphere? Given that we are working with the five basic Planck units with real numbers that define each unit, the vertices are 134,217,728 scaling vertices.  a real manifestation within space-and-time.

The animated image (gif for “Graphics Interchange Format”) of the cannonball stack tells a powerful story.

The all-important quantum fluctuation seems like an art form on one hand and a fundamental energy source on the other.  Open this conceptual roadblock and we find a truly golden rainbow. Although each roadblock is a face of this small-scale universe, perhaps quantum fluctuations would best be known as the art of the universe!



active edit area:

Working Notes:

The most important fact about the new model is that each of the Epochs defined within Big Bang Cosmology are all logically replicated here.  All of our data is simple math and it is a fully predictive model of the universe without the bang!  Numbers

The world’s leading cosmological theory is challenged. Though our little model is  little-known today, that is about to change. Big bang cosmology is going to be placed on ice and assigned to timeout.

The Art, Mechanics & Systems

Let’s start at the very beginning: Notations 1-10

Please open the chart in a new window.

Each of the Planck base units, considered to be part of the so-called singularity, has a real number associated with it. Though the formulas for deriving the numbers of each Planck base are readily understood by many, watching how the numbers progress along their scale is new.

In the first ten notations, we assume the numbers represent vertices that will double and slowly become structure. Notice lines…

Perhaps John Wheeler’s “Quantum Foam” would better be understood as “Planckspheres.”

by Bruce Camber, 2018

Back in 1955…

Wheeler-JohnPrinceton:  Physicist  John Archibald Wheeler, wrote this unusual combination of words for the first time. Today, also known as spacetime foam, it has been suggested that this foam marks the beginnings of quantum mechanics and quantum fluctuations.  Also, the study of foam has evolved to spin foam theory and spin networks.  It is now a key topic within  loop quantum gravity (LQG).

Who Is John Wheeler and what is this foam?   This page is simply to aggregate as many articles as possible about quantum foam beginning with an introduction to John A. Wheeler and his work:
1. John Wheeler  (Wikipedia)
2. Wheeler, J. A. (January 1955). “Geons”. Physical Review. 97 (2): 511.
– – – Bibcode:1955PhRv…97..511W. doi:10.1103/PhysRev.97.511.
3. John Wheeler’s quantum foam  (Wikipedia)
4. John Wheeler, Geons, Black Holes, and Quantum Foam
5. YouTube with Wheeler: Quantum ideas, Quantum foam, Max Planck & Karl Popper
6. Quantum Foam,   (ArXiv), Y. Jack Ng, University of North Carolina, 
    •   Quantum Foam, Gravitational Thermodynamics, and the Dark Sector
7.  Planckspheres.  John Wheeler never used the term per se but it certainly overlaps.
8. Institute for Advanced Studies: https://www.ias.edu/idea-tags/john-wheeler
9. Roger Penrose, 1971

A different approach.  As you might imagine, within this website, the concepts of quantum foam and quantum fluctuations are treated rather differently. This will be our first attempt to describe both within the context of the 202 base-2 notations. Many updates are anticipated.

First, within our 202 notations, quantum mechanics does not begin in the first notations. Here, quantum fluctuations, which are assumed by most scholars to be responsible for the quantum foam, are associated with a very real geometric configuration. With just five tetrahedrons sharing a common edge (as shown), there is a pentastar1natural gap within that pentagonal structure which is then extended into the 20-tetrahedral complex or icosahedral complex which is then extended into the 60-tetrahedral Pentakis dodecahedral complex. It is hypothesized that the mathematics of the gap is the mathematics of Wheeler’s quantum foam which is the mathematics of quantum theory. At this time, it is not known within which notation the pentagonal structures first manifest.

Does the sphere become an incompressible foam?

At the Planck scale (A0) and its first doubling or notation (A1), circles and spheres are strictly mathematical. These physical manifestations are well below the possibilities of measurement until those doublings are in the range of today’s CERN scale. Yet, by our analysis of the 31st notation, there is a very real mass and charge. Nevertheless, at the A1, the circle and sphere are mathematically defined by dimensionless constants and this so-called foam is an absolute limit of space-time (Planck Length-Planck Time). In deference to Max Planck, we had dubbed the “foam” to be Planckspheres and then we began finding references in some of the more speculative within the literature to “Planck Spheres.”

See: “Mysteries in Packing Regular Tetrahedra
Jeffrey C. Lagarias and Chuanming Zong
http://ams.org/notices/201211/rtx121101540p.pdf

The Riddle of the Quantum Sphinx: In his Feb. 7, 2018 public lecture at Perimeter Institute, Robert Spekkens explains why he believes that many quantum mysteries are a result of a category mistake concerning the nature of quantum states.

Predictions in eternal inflation, Sergei Winitzki

“A Step Toward Pregeometry I: Ponzano-Regge Spin Networks and the Origin of Spacetime Structure in Four Dimensions” by Norman J. LaFave

https://en.wikipedia.org/wiki/Tetrahedron_packing

National Institute for Standards and Technology (NIST)

Geometries of spheres, triangles, tetrahedrons, fluctuations, imperfections and probabilities

Sphere to tetrahedron-actahedron couplet
Attribution: I, Jonathunder

Spheres, sphere stacking. Our studies of sphere dynamics (stacking), particularly the internal dynamics such as the Fourier transform, is still quite formative.  When we started we were most interested in Platonic forms, not the circle or sphere. The focus on spheres began to emerge when we discovered this sphere-stacking dynamic gif on the right. There is no known study of the possible dynamics of each sphere within the infinitesimal. The Fourier transform would be the beginning of such a study, yet the specific dynamics of adding one sphere at a time must be studied as well.  Three spheres create an internal triangle, four create the square, five the pentagonal, and six the hexagon.

pentastar1

Tetrahedrons. A geometry of fluctuations, imperfections and probabilities comes out of our studies of the pentastar (five tetrahedrons sharing a common centerpoint). There are several configurations of the pentastar to develop an icosahedron (twenty tetrahedrons) whereby a flexible five-tetrahedral cluster can be found with any group of five tetrahedrons.

terahedralclustersAmong the high school students, tetrahedral geometries are known as squishy geometry. Perhaps a better word for it is quantum geometry.

There are many excellent articles and studies that form the basis of our growing understanding of the tetrahedral clusters and the tetrahedral-octahedral clusters.

Introductions to the tetrahedron clusters:
•  Mysteries in Packing Regular Tetrahedra” by Jeffrey C. Lagarias and Chuanming Zong

Tot-line•  Cluster structure. Within our of the earliest articles, first published within Wikipedia in March 2012, explored the work of  Jonathan Doye who studied at Cambridge University and teaches at Oxford.

•  The tetrahedral-octahedral chain where an octahedron sits on two faces of the upper tetrahedron and two faces of the lower tetrahedron.  It forms a natural double helix and begs the question about its fundamentality as a more basic architecture that generates the helix.

•  The icosahedron (twenty tetrahedrons sharing a common centerpoint). It appears that these same geometries are also responsible for quantum fluctuations.

In the study of each notation we will look to see how each notation is necessarily derivative of the prior. And, we will continue to study the nature of these fluctuations.

___________________

First draft: Fluctuations (in process)

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Alternative to Big Bang Cosmology

Introduction to Quantum Fluctuations In Light Of Exponentiation

Overview: Our base-2 exponentiation chart[1] from the Planck base units to the Observable Universe and Age of the Universe has just over 200 notations.  It is  logical and simple,  and a potential alternative to big bang cosmology.[2]

The first-possible physical measurements in our universe happen in labs like CERN (Geneva, Switzerland). Estimates of the ionic radius involved in their heavy ion collisions range from 30-to-300 picometers or approximately 3.9077×10-11 meters at the 81st notation to  3.12618×10-10 meters at the 84th notation. It appears that the collider measurements are within the scale of the 67th notation (2.38509×10-15 meters), the 66th notation (1.19254×10-15 meters)  yet some say down as small as  1.16459×10-18 meters at the 56th notation. These and the other numbers in the 200+ columns are real numbers, all multiples of the Planck base units.  See more

Sphere to tetrahedron-octahedron couplet
Attribution: I, Jonathunder

Image file  licensed under Creative Commons Share-Alike 2.5 Generic.
Open for your comments:
Finite-Infinite relation
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Universe View: What is your expertise? There are many blanks; and all cells — over 2000 of them — will always be “under construction.”
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Still In Process: The first instance of the universe

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Cold-Start versus Infinitely-Hot Start
A Most-Simple Alternative to Lemaître-Hawking-Guth Cosmology

by Bruce E. Camber

ABSTRACT

…..

If a cold-start to the universe is assumed, and a basic structure is defined by the Planck base units, the forms and functions of science can be re-evaluated. (1).The.progenitor of the circle and sphere, pi (π), has a pivotal role as one of our earliest working equations. It is a.numerically-rich, universally-engaged, geometric, dimensionless constant; it is never-ending, never-repeating, invariant, transcendental and irrational. These qualities become among the most fundamental processes that define our universe. (2).Pi.comes out of the seminal concepts of continuity, symmetry and harmony, a simple perfection. (3).The.sphere comes alive. The “first manifestation of thingness” is the very first instance of space-and-time and mass-and-charge. These four faces of light set a rate of expansion. (4).Building on such concepts, Kepler and others give us sphere stacking and cubic-close packing of equal spheres. (5).Joseph.Fourier’s work on basic transformations (circa 1822) expands our understanding of pi and periodicity. (6) Our initial value formulation uses the 1899 logic of Max Planck’s natural base units of length, time, mass and charge; these four numbers, and all the dimensionless constants used to define them are fundamental. (7).To.create.order out of the large numbers of spheres within the infinitesimal, we apply Euler’s base-2 notation. From PlanckTime to this day, there are just 202 notations. (8).The.first.64 notations are below the thresholds of direct measurements. Within this model, these first 64 of the 202 are most foundational (all superconductingly cold). (9).This.is a new laboratory for explorations. (10).Here let us engage causal set theory, causal dynamical triangulation, string theory, Langlands programs and so many other logically constructed environments that are beyond reach of all current measuring devices. All are within the first 64 notations of this mathematical laboratory. -BEC

…….

1. INTRODUCTION

The infinitely-hot start of the big bang theory has key unanswered questions. In his 1927 reflections, Georges Lemaître advocated a cold-start, yet, by 1931 he had changed his mind and is now known for a rather-hot start. Max Planck’s 1899 calculation for Planck Temperature may have had something to do with that change, yet any explanation for this fundamental shift by Lemaître is yet to be discovered. [1] If Lemaître’s cold start had been adopted, I believe the fundamentality of pi would have been entertained in that process. The basic structure of the most-fundamental things tends to be spherical where the role of pi is pivotal. Herein, the hope of this article is to encourage a deeper analysis of the role of pi in the shaping of the first instant and the earliest universe.

2. CONTINUITY, SYMMETRY & HARMONY

Scale invariant, pi renders the qualities of continuity, symmetry, and harmony. First, there is the continuity of the never-ending and never-repeating numbers; there is also the continuity of all other dimensionless constants involved. Symmetry analysis begins within one of the five fundamental symmetry classes — dihedral, cyclic, tetrahedral, octahedral, and icosahedral. Each is a setting within which the dimensionless constants shape space-time, and mass-charge. Also, we assume Leibniz law of continuity and his transcendental law of homogeneity. The finite-infinite relation is a constant dynamic.

Harmonies of motion, symmetries extended through space-time, are described by Fourier transforms. It is a new order and value for all numbers; everything-everywhere-for-all-time has deep-seated, dimensionless, dynamic relations. Subjects and objects are derivative and the relations are primarily real. The first dynamic moment is the face of continuity-symmetry-harmony and it captures the very nature of space-time, and mass-charge.

Continuity, symmetry and harmony are conceptual words with exacting meanings within the infinitesimal scale. These words also are generalized observations that are applicable within 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.[2]

3. OUR UNIVERSE COMES ALIVE – THE PLANCK SPHERE*

Throughout our history, spheres have been the shape of fundamental forms. For several years I argued with mathematician, Phil Davis, on the faculty of Brown University. Phil held up the sphere; I held up the tetrahedron. Before he died in 2018, I capitulated. I had assumed that Max Planck’s four base units uniquely defined the very first instant and every instance thereafter and asked, “What would it look like?” Planck’s 1899 basic calculations render actual numbers, quantities that become the qualities of some manifestation. Herein I assume a primordial sphere.

We had learned how the tetrahedron is derivative of the sphere, and that spheres stack and discover each other. A simple graphic helped us to grasp that phenomenon (below).

PlanckTime has been said to be the time it takes light to travel one PlanckLength. Here it is assumed to be one PlanckSphere* per PlanckSecond (a unit of PlanckTime). Here the very nature of light renders Planck’s calculation of a natural unit of time which is 5.39116×10−44 seconds. A simple calculation gives us a rate of expansion of 539.116 tredecillion planckspheres per second.** Using base-2 to group those spheres, we find just 202 notations from PlanckTime to the current time. The more we engaged these numbers, the more every notation comes alive, fully interdependent with the others. The first 64 notations as such are relatively unknown and have hardly been explored. Those 64 notations are below the reaches of our measuring devices and most methodologies. For perspective, by Notation-136 the energy densities and temperatures are high enough for the Quark-Gluon Plasma (QGP) processes to begin. The first second of the universe emerges between Notations-143-and-144. Each notation is being defined by a Planck-base unit multiple, by prior notations, and then by each subsequent notation.

Thinking about Lemaître’s primeval atom, Wheeler’s geon, and Pati-and-Salam’s preon, with the introduction of the first 64 notations, these can no longer be considered “point interactions” with no known extension. By the 64th notation, concepts like the preon and geon will have deep, rich textures and many extensions.

To help make the shift from the infinitely-hot Big Bang theory to this Cold-Start UniverseView, consider this comparison, a simple chart. If so defined and understood, the PlanckSphere becomes the most essential, foundational unit that begins to quantize our universe. It prov\des immediate insights into the raison d’être and the very nature of homogeneity and isotropy, which taken as a whole is the aether, and measured as an effect, is dark matter and dark energy. [3]

* PlanckSphere: Not formally recognized, there are many references to word on the web (Also, see articles with ArXiv).
** If this model is anywhere close to correct, this expansion of our universe is, for most people, a very different image, second-by-second. Consider the simple calculations:
• 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 5,391,16: 2.35117694×1015
• Add the eight zeros from seconds and 37 zeroes from the planckspheres per second
• Estimated total number of planckspheres in the universe: 2.35117694×1060 planckspheres

4. SPHERE STACKING & CUBIC-CLOSE PACKING OF EQUAL SPHERES

To review, although orders-of-magnitude smaller than an atom or any known particle such as the neutrino, that very-first infinitesimal sphere, is always “never-ending, never-repeating, always the same and forever changing.” Along with the inherent qualities of all other dimensionless constants, the very nature of continuity is redefined. It is a new order and value for all numbers; everything-everywhere-for-all-time has many dynamic relations.

Here, subjects-and-objects are derivative and the relations become primarily real.

Sphere to tetrahedron-octahedron couplet

That first dynamic moment is the face of continuity; it captures the very nature of time, space, mass and charge, and the first thing that happens is the spheres necessarily stack and begin creating dynamic relations. The earliest stacking is best described by cubic-close packing of equal spheres. Structure builds on structure.

Symmetry brings balance and stability and knowingness to values of continuity. [4]

5. THE FOURIER TRANSFORMS OPEN THE DYNAMICS OF HARMONY

Harmony opens the richest dynamics of the universe and of life.

Another quality of the sphere dynamics is a range of harmonies, Fourier pairs, symmetries in motion, each creating a space-time moment defined by the Planck base units, dimensionless constants, and a rich variegation of numbers. There are many faces and forms of the Fourier Transform. To associate these with the infinitesimal universe will empower many new insights about the nature of things and the very nature of life. More to come

The three primary facets of pi and of life — continuity, symmetry, and harmony — are the definition of the essential structure of the sphere, which ultimately give rise to the very structures of our little universe, the deepest nature of both the finite and the infinite. I believe these three qualities define a perfection and a perfected state within space-time. Within the earliest notations there is a thrust of perfection. There is no room or time for imperfections. [5]

6. THE FOUR PLANCK BASE UNITS AND PI

That first instant, defined by Planck’s four base units, are all so small, the sphere is necessarily cold. From where would heat be generated? As each notation incorporates more units of Planck Charge – Planck Mass, there is a progression of forms, structures, substances, qualities, and systems. The initial guess is that systems begin to emerge around Notation-50 and one of the systems is the Mind. Here may be the first manifestation of what might be called, ontic fluctuations, well prior to physical measurements, yet mental events that are not perfect, but discontinuous, asymmetrical, and not harmonious. What will be known as quantum fluctuations become measurable within Notation-64 to Notation-67. Of course, quantum fluctuations are not measurable until the advent of measuring devices within Notation-202. Thus, there is a domain of perfection from Notation-1 to the notations when and where ontic fluctuations begin. And, some aspects of that perfection — continuity, symmetry, and harmony — are extended throughout the 202 base-2 notations that encapsulate everything, everywhere for all time.

This model is primarily about the infinitesimal universe. From the first instance with Notation-1 to Notation-144 includes the first second. The first year is within Notation-169, the first 1000 years is within Notation-179, the first million years is in Notation-189, and the first billion years is in Notation-199.

Today, Notation-1 to Notation-201 are fully symmetrical. Notation-202 contains the current time and will do so for another 7.9 billion years. Notation-202 is 10.89 billion years in duration. The sum total of all durations up to Notation-202 is also approximately 10.89 billion years. A simple calculation tells us that only a total of about 2.9 billion years of Notation-202 has been filed. There is what appears to be a flow of time experienced as time’s arrow. Within this model there is only one time, the Now. Our hypothesis is that the uniqueness of any moment-and-day is recompiled within the larger universe every time there is sleep. Of course, such a statement will be more deeply analyzed.[6]

7. BASE-2 NOTATION AND EULER’S EXPONENTIATION

To organize all this simple data — pi, spheres, continuity-symmetry-harmony, sphere stacking, cubic-close packing, the Fourier Transform, and an expansion rate of 539.116 tredecillion planckspheres per second — required a simple tool. Such a tool, introduced by Leonhard Euler in the 1700’s, is base-2 exponentiation. Those 539.116 tredecillion plancksphere (per seconds) could fill a circle slightly larger than the current low-earth, orbital paths, yet have a density of a neutron star that is orders of magnitude greater than the mass of the sun. If you can imagine that is happening every second, you have an image of a possible expansion of this universe.

The densities between Notation-2 and Notation 144 are unlike anything we can intuit. It would seem that such densities necessitate that the most simple symmetries emerge first. Nothing is by chance alone. No college course today imagines how symmetry groups flow within such densities and how cubic-close packing (ccp) occurs. We ask, “Do lines, tetrahedrons and octahedrons flow naturally within such density?” We are in search of scholars within the neutron-star disciplines who can help with these issues. [7]

8. THRESHOLDS OF MEASUREMENT

Although not formally named by NIST, CODATA, BIPM, ISO or any other international governing body for scientific naming and standards, some refer* to that very first spherical unit as a PlanckSphere (10−44). There are six infinitesimal ranges that are yet to be named: 10−27, 10−30, 10−33, 10−36, 10−39 and  10−42. The 10−42 group includes 10−44 where that unit of time is currently informally referred as the PlanckSecond.  Reference: https://81018.com/codata/

Here Notation-1 through to Notation-64 (9.945379×10-25seconds) have no common name for length or time by which each is known. A naming convention has not been convened since 1991.** That’s a statement. This part of the scientific identity de facto has been deemed to be unimportant, yet these may be the numbers necessary for deeper considerations of the proper definitions of dark matter and dark energy. Although dark matter and dark energy can be indirectly measured and we’ve known of their existence of over 100 years, our lack of names hinders discussion. We have reservoirs of infinitesimal data to couple with the growing reservoirs from large-scale CMB data. Names for these domains would help. So, as a result, we have become advocates that these high commissions name these six sets of numbers. [8]

* As of February 20, 2021, there are 1,420 online references to the “PlanckSphere.” Quotes are used to limit the search.
** Guide for the Use of the International System of Units (SI), Ambler Thompson and Barry N. Taylor, NIST Special Publication 811 2008 Edition, See Section 4.3, Decimal multiples and sub-multiples of SI units: SI prefixes, Table 5, p 7 PDF URL: https://physics.nist.gov/cuu/pdf/sp811.pdf

9. OUR “NEW” LABORATORY OPENED IN 2016

This lab will be more than an advocate for the clear recognition of this infinitesimal universe; it will be constantly refining our views of it. For example, we will continue to refine the work we did for the NASA SpaceApp innovation program to define a clock for the universe. We will continue to refine the horizontally-scrolled Chart of the Universes and our UniverseTable. But most importantly, we will continue to develop our understanding of the first 64 notations to bring dark energy and dark matter into the light. We will continue our understanding of how it all defines a new aether and renders a structure of homogeneity and isotropy. Yes, continuity-symmetry-harmony are three facets of any given moment and these lay the foundations for the expansion of the universe, the very nature of value, and the beginnings of economic theory. Some of our most important work will be interpreting this model as a value structure that inculcates aesthetics, ethics, morals, purpose and values.

Continuity is the beginning of value. Think of gold and silver coins and things made of these precious metals. 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. Each establishes standards for the best of what is. It is not unpredictable. It transcends time (as it creates time).

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.

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 and enriched. There is a sense of a deep harmony and joy. The values created are experienced and affirmed, and life is good. These are valuations that we yearn and strive for; and though seemingly illusive, they are everywhere, and always just a bit deeper within. Harmony opens the richest dynamics of life. [9]

10. STRINGs, LanGLands, causal set theory, causal dynamical triangulation

Empowered by concepts at the edges of our knowledge, here our students will engage causal dynamical triangulation, causal set theory, scalar field theory, loop quantum gravity, string theory, Langlands programs… the cutting edge of research of the very nature of our universe. We’ll also begin to grasp the very nature of value. Returning to these roots to go over it just one more time, we want to see what we have missed in order to give us a more-complete picture of the structure of our emergent universe. Our three most general concepts — continuity-symmetry-harmony — render space-time and mass-charge as the Janus face of each other. Here, too, we believe that we’ll begin to grasp how it is that electromagnetism and gravity have also been yoked. [10]

Our list of naive claims continues to grow and so this commentary will also grow.

SUMMARY

Does pi have a role within emergence, especially the first moments and seconds of the universe?

Max Planck’s base units were ostensibly ignored for over 100 years. Today, we recognize their reality but those numbers radically change with just these four working assumptions:

  1. The four Planck base units manifest as a basic building block, an infinitesimal sphere many orders of magnitude smaller than a neutrino. It is the first moment of spacetime.
  2. This sphere is also defined by pi and other dimensionless constant, then further defined by cubic-close packing of equal spheres and the Fourier Transform.
  3. Planck Time, 5.391 16(13)×10-44 seconds, defines a rate of expansion, one PlanckSphere per PlanckSecond renders 539.116 tredecillion units per second.
  4. Apply base-2 to that expansion; and, all those spheres and the universe are encapsulated within 202 notations. The first 64 are below the reaches of our measuring devices. Notation-1, the first moment in time, is that first sphere. The current time is within Notation-202. Those notations encapsulate everything, everywhere, for all time and our chart of those numbers provide a map to understand our universe.

We can begin to learn about a new aether, dark energy and dark matter, and the basis of homogeneity and isotropy which ultimately will help mitigate our inherent proclivity toward solipsism.

For Pi Day: https://81018.com/challenge/

CONCLUSION

The three primary facets of pi and of life — continuity, symmetry, and harmony — are the definition of the essential structure of the sphere, which ultimately give rise to the very structures of our little universe. It all starts superconductingly cold. Yes, and, these facets manifest the deepest nature of the finite and the infinite.

________

Footnotes   (To return, click on the number inside the brackets.)

[1] Lemaître, Georges, 1927
• Aguirre, Anthony N. (10 April 2000). “The Cosmic Background Radiation in a Cold Big Bang”, The Astrophysical Journal. 533 (1): 1–18. Bibcode:2000ApJ…533….1A. doi:10.1086/308660. ArXiv.
D. Layzer and R. Hively, Astrophys. J.179, 361 (1973).[30] Ya. B. Zel’Dovich, Adv. Astron. Astrophys.3, 241(1965)
• P.J.E. Peebles and R. B. Partridge, Finding The Radiation from the Big Bang, January 9, 2007

[2] Continuity, Symmetry & Harmony (at the top of most every homepage)
Dihedral, cyclic, tetrahedral, octahedral, and icosahedral
Law of continuity
Transcendental law of homogeneity

[3] “PlanckSphere” (or “Planck Sphere“): An unofficial word with a limited history — as of 23 February 2021, there were just 210 (or 1420) Wikipedia references. Until there is formal recognition of the word by some official international agency for naming conventions, we will attempt to update this footnote as often as possible. The concept of a most basic unit of the universe defined by something like Planck’s base units is essential. Planck’s base units have gained a level-and-status within the academic and scientific communities, many related words have followed. To date, there are no agreements about how these four Planck base units might manifest. Of the 1420 postings using the word, Planck Sphere, there is a wide range of implied definitions. We’ll continue our studies of the usage and update this footnote appropriately.

[4] Sphere stacking and packing: Cubic close-packing of equal spheres.
Johannes Kepler, Harmonices Mundi, Linz, 1619
Thomas Hales, A proof of the Kepler conjecture, Annals of Math. 162 (2005), no. 3, 1065–1185
Maryna Viazovska, The sphere packing problem in dimension 8, (PDF)
Jeffrey C. Lagarias and Chuanming Zong, Mysteries in Packing Regular Tetrahedra (PDF), AMS, Volume 59, Number 11, pp 1540-549 December 12, 2012
NOTE: Spheres, sphere stacking, and sphere packing have been profoundly studied. For our purposes, the two most important dynamics are (1) The dynamic image of spheres generating triangles, tetrahedrons, and then octahedrons and (2) dynamic images of the Fourier Transform. Both are derivative of pi.

[5] All things Fouriersymmetries in motion:
The role of symmetry in fundamental physics, David J. Gross, PNAS, December 10, 1996 93 (25) 14256-14259; https://doi.org/10.1073/pnas.93.25.14256
Fourier pairs: Grasping essential relations and dynamics

[6] Planck’s four base units:
Three new roads to the Planck scale, American Journal of Physics, 85, 865 (2017); https://doi.org/10.1119/1.4994804 https://aapt.scitation.org/doi/10.1119/1.4994804

[7] Base-2 exponentiation and Euler: This project got its start unwittingly doing a base-2 progression from a classroom tetrahedron inside the smaller octahedron within it, then into 112 successive steps back inside smaller and smaller octahedrons and tetrahedrons. We learned base-2 through geometry. It is how we learned about Euler and exponentiation. It was just a few months after that fateful day in class, December 19, 2011, when we began that I posted this article in Wikipedia. I was sure that our chart was already a STEM tool on the web somewhere, developed by different people, and that we only needed to find each other and pull our concepts together. It took four years to feel assured that we were outliers who had a very idiosyncratic view of cosmology.

[8] The Thresholds of Measurement: Since 2011 two measurement records for a unit of time have been broken by the Max-Planck-Institut für Quantenoptik in Garching, Germany. Prof. Dr. Ferenc Krausz group was able to measure an attosecond (10-18 seconds), then a femtosecond (10−15) and most recently a zeptosecond (10−21). It is still a long way to go to the Plancksecond 10−44). A hopeful glimmer on the horizon is the work of three doctoral candidates, Andrea Di Biagio (La Sapienza), Marios Christodoulou (Oxford), Pierre Martin-Dussaud (Aix-Marseille Univ, Université de Toulon) who are trying to formulate an experimental environment to determine time sequences as short as the shortest, the Planck second. They will also determine if time is ultimately discrete and digital.

https://81018.com/2012/03/31/notations/#Notations

[9] A Laboratory for the Infinitesimal: Three keys of the infinitesimal have not been explored:
The very first notation that is still generating one Plancksphere per Plancksecond
A domain of perfection from the first notation at least through Notation-50
A domain for the Mind and for Systems, perhaps from Notation-50 to Notation-60

[10] Out on the edges of our knowledge:
Causal dynamical triangulation: “…theorized by Renate Loll, Jan Ambjørn and Jerzy Jurkiewicz, and popularized by Fotini Markopoulou and Lee Smolin, is an approach to quantum gravity that like loop quantum gravity is background independent.”:
Causal set theory: Rafael Sorkin, David P. Rideout, David Malament, Graham Brightwell, Ruth Gregory… Space-time as a causal set
Scalar field theory: Pierre Ramond,
Loop Quantum Gravity: Abhay Ashtekar, Carlo Rovelli, Jorge Pullin and Jerzy Lewandowski, Francesca Vidotto, Israel Gelfand, Mark Naimark, and Irving Segal
String theory and superstring theory: Witten, Dean Rickles
Langlands programs: Emil Artin, Ngô Bảo Châu, Vladimir Drinfeld, Edward Frenkel [1], Stephen Gelbart, Robert Langlands [1], Laurent Lafforgue, Vincent Lafforgue, Gérard Laumon, Michael Rapoport, Andrew Wiles

Most Active Work Area: Footnotes are being worked and reworked. Endnotes, Reference-Resources, and Communications are all being added and updated. This page was supposed to be ready by yesterday; hopefully today we will fill-in most of the blanks. Thank you for your understanding. The next page being developed is regarding the 539 tredecillion plancksphere per second. It will be building upon an earlier page about expansion.

________

Endnotes

[1] Orders of Magnitude Smaller Than Any Known Particle. In the prior posting, the size of things using base-2 notation from the Planck base units was explored. Planck Length and Planck Time are so infinitesimal spheres, the first 64 notations are difficult to conceive. Also beyond imagination are the 539.116 tredecillion planckspheres by the first second between Notation 143 and Notation 144. The overall picture is reviewed in that prior posting, https://81018.com/challenge/#1f 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).

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. Lagrange points: All Lagrangians come home

[z] 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 already 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.

________

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?

Fine-Tuning, Complexity, and Life in the Multiverse, Mario Livio, Martin J. Rees, Jan. 2018 Two assumptions about the universe.
The emergent universe: inflationary cosmology with no singularity, George F R Ellis, Roy Maartens, IOP Publishing, Classical and Quantum Gravity, Volume 21, Number 1, November 2003
The Arrow of Time, David Layzer, Scientific American, December 1975.
Fourier Transform Pairs, A Listing, Peter Joseph Bevelacqua, 2010

More to come

________

Communications: Emails & Instant Messaging
Fine-Tuning, Complexity, and Life in the Multiverse, Mario Livio, Martin J. Rees

11:28 PM · Feb 24, 2021 @tara_taylor How about expanding our understanding of pi? Could it be involved in the very first instance of space-time? Could be involved with the defining of a PlanckSphere generated from the Planck base units? http://81018.com is where we struggle for answers. -Bruce

6:46 PM · Feb 21, 2021 @RepKinzinger We all need a different vision of who we are and why. All our little worldviews tend to trample anything in the way. Globalism is too small. We need an integrated view of the universe so we can get grounded in the basics: http://81018.com is my simple start.

6:34 PM · Feb 23, 2021 @Gary_D_Cohn Possibly our most basic problem is our worldviews are too small and solipsistic when we need to have an integrated view of the universe. http://81018.com started in 2011 by applying base-2 to the Planck units to encapsulate the universe in 202 steps!

2:50 PM · Feb 25, 2021 @TrenaWilkerson Math should be engaged, not according to our world, but to the universe. Apply base-2 to Planck’s base units and we have a simple, mathematically-integrated view of the universe: https://81018.com Just 202 notations to consider. See chart: https://81018.com/chart/ -BEC

3:59 PM · Feb 26, 2021 @FryRsquared Pi has to be more than the banality of so many Pi Day’s celebrations. Here’s a simple alternative: https://81018.com/challenge/ Puts Pi back at the beginning of it all. Here’s another: https://81018.com/instance/

4:01 PM March 1, 2021 An email sent to old contacts with whom I haven’t heard for awhile:
Quick questions. Have you ever thought:
1. Here we are 13.79 billion years of history and we barely know much about it, or think about it in order to context and understand our own time. Are we limited ourselves?
2. Here we are in a splendid universe but we rarely think about it, we rarely think beyond our home’s bounds (or the country’s bounds during the evening news)! Do we need to expand?
3. What if we had an integrated view of the universe, everything, everywhere for all time that entirely encapsulates it all within 202 base-2 notations? Don’t you think that would give us a new perspective and it just might help us break free of our naturally solipsistic views of things? Don’t you think a highly integrated view of the universe could open questions we usually do not entertain? Might it give new insights to all the old, open questions about life (and physics and cosmology)? Might it help us get beyond worldviews with inherently limited points of view? Interesting? Thanks.
Warmly,
Bruce

@KurdistanRegion@IKRPresidentand 2 othersA most important thing we can do is break free of our limited worldviews and adopt an integrated view of the universe. We’ll begin thinking about everything, everywhere for all time: https://81018.com is just a start, but start we must! The numbers: https://81018.com/chart/

________

Zzz’s
Afterthoughts. Pointedly equate pi with the first sphere, the first moment of space-time, and continuity-symmetry-and-harmony. When pi is brought back to the first moment of space and time, everything changes.

More to come…

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Key Dates for this document, Instance

  • This document was started on January 27, 2021.
  • First posted for collaborations: February 8, 2021
  • The URL: https://81018.com/instance/
  • The Prior Homepage: https://81018.com/challenge/
  • Headline: Cold-Start versus Infinitely-Hot Start
  • First Tagline: The first instance of the universe
  • Second tagline: A Simple Alternative to Lemaître-Hawking-Guth Cosmology
  • The last update of this page: February 26, 2021

A Challenge for Pi Day, March 14

Left Yellow Arrow
Right Yellow Arrow

CENTER FOR PERFECTION STUDIES: CONTINUITYSYMMETRYHARMONY GOALS_FEBRUARY.2021
PAGES:.ALTERNATIVE..| CHINESE |.DARK | MISTAKES | PHILOSOPHY | RELATIONS | TIMEUP

PRIOR POST | CLAIMS | ENDNOTES-FOOTNOTES | REFERENCES | EMAILS | TWEETS | Zzzzs

Power of Spheres, Circles and Pi (π)
Deepest Structures of the Universe Drive the Economics of Value
by Bruce Camber

Our Key Evocative Question: Could the key structures of pi (π) also be a key structure of our universe (as well as economic theory and valuation)?

Structure. Take as a given, a key structure of the universe is an infinitesimal sphere defined by the Planck units (orders of magnitude smaller any particle). What can we say about that sphere?
[1] It is defined by pi (π).
[2] It is defined by the Planck base units.
[3] It is defined by other dimensionless constants.
[4] This very-first infinitesimal sphere will exhibit a primary quality of pi — it is a never-ending, never-repeating number, always the same and forever changing.
[5] That quality redefines continuity. It creates order and numbers and it is the first moment of time and the very nature of time.

[6] Now, to better visualize this event, know that the rate at which these spheres are manifesting is very-very high. It is unbelievably high.
[7] This little image on the right of sphere stacking doesn’t at all capture the dynamics. It is, however, one of the earliest representations of sphere-stacking, 1611, by Johannes Kepler, of cannonballs on the deck of a ship.

Sphere to tetrahedron-octahedron couplet

[8] The second quality of this most-infinitesimal sphere is its symmetries which create relations which create space.
[9] There are college courses about the many types of symmetries.
[10] For our purposes we will focus on cubic-close packing (ccp) and the creation of lines, tetrahedrons and octahedrons.

[11] And, a third quality of this sphere is harmony which creates dynamics which creates a space-time moment defined by the Planck base units.
[12] This image takes pi and spheres and makes them dynamic, extending through time. It is called the Fourier Transform 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).

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.

PS. What about quantum fluctuations? This link opens all references on this site.

________

Footnotes & 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. If we take as a given that the Planck units define these infinitesimal spheres, 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 developed 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).

________

[2] The Planck base units, Part I. My hope is that grasp the essence much faster than the academic-scientific community did. With few exceptions them 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 is 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.

________

[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!

________

[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.

________

[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. It’s only a fool who 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.

________

[6] Unbelievably high. Six postings 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 to 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 you begin to become comfortable with those very large and very small numbers, you can begin to grasp 539 tredecillion spheres per second, the very raw calculation for an expansion of the universe per second. 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 many, many orders-of-magnitude 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.

________

[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.

________

[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 are 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.

________

[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.

________

[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.

________

[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.

________

[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.

________

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?

________

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

________

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 the one just before it, https://81018.com/essentials/

It is 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/

So, yes, there will be much more to come on this topic…

________

Key Dates for this document, Challlenge


Economic Theory, Value and the Structure of our Universe

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PAGES:.ALTERNATIVE..| CHINESE |.DARK | MISTAKES | PHILOSOPHY | RELATIONS | TIMEUP

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Power of Spheres, Circles and Pi (π)
Deepest Structures of the Universe Drive the Economics of Value
by Bruce Camber

Introduction. I did a cursory check and it seems that nobody is writing about how the structures of pi (π) are also the key structures of our universe, economic theory and valuations. I’ll try to keep this posting simple and short to encourage feedback. I will also try to tighten up the endnotes and footnotes. So please, let me know if it is still too abstract and convoluted.

Structures. Assume the key structure of the universe is an infinitesimal sphere that is much, much smaller than an atom or any known particle. [1] It is defined by pi (π), the Planck base units [2], and other dimensionless constants. [3] The very-first infinitesimal sphere exhibits a primary quality of pi; it is a never-ending, never-repeating number, always the same and forever changing. [4] That quality redefines continuity. It creates order and numbers and it is the first moment of time and the very nature of time. [5]

Now, to better visualize this event, know that the rate at which these spheres are manifesting is very-very high. It is unbelievably high. [6] This little image on the right of sphere stacking doesn’t at all capture the dynamics. It is, however, one of the earliest representations of sphere-stacking, 1611, by Johannes Kepler, of cannonballs on the deck of a ship. [7]

Sphere to tetrahedron-octahedron couplet

The second quality of this most-infinitesimal sphere is its symmetries which create relations which create space.[8] There are college courses about the many types of symmetries [9] involved; however, for our purposes we will focus on cubic-close packing (ccp) and the creation of lines, tetrahedrons and octahedrons. [10]

And, a third quality of this sphere is harmony which creates dynamics which creates a space-time moment defined by the Planck base units.[11] This image takes pi and spheres and makes them dynamic, extending through time. It is called the Fourier Transform [12] 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).

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.

PS. What about quantum fluctuations? This link opens all references on this site.

________

Footnotes & 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 developed 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).

________

[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.

________

[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!

________

[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.

________

[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. It’s only a fool who 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.

________

[6] Unbelievably high. Six postings 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.

________

[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.

________

[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.

________

[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.

________

[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.

________

[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.

________

[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.

________

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?

________

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

________

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 the one just before it, https://81018.com/essentials/

It is 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/

So, yes, there will be much more to come on this topic…

________

Key Dates for this document, Challlenge


A précis for this website, our world, and our universe

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Why is there so much trouble in our little world?
Ans: Our little worldviews need the universe.

by Bruce E. Camber

Nations are people; and, all people are in process. No one has all the answers. Surely, there are plenty of very smart people, but we are all still just people. Our leaders are just people, too. Like the rest of us, they have insecurities and gaps of knowledge. It is a recipe for problems!

Throughout our common history, we make many major assumptions. None of these assumptions should ever become sacrosanct. Working on our ideas and concepts never stops. Updating and improving is the essence of life! Notwithstanding, over the years our greatest scholars have made mistakes and sometimes, their students (our scholars) repeat those mistakes for too many years.

Significant Mistake by Aristotle
Ten Full Tetrahedrons Pictured

Perhaps the most egregious mistake by a great scholar is Aristotle’s claim that we can perfectly tile and tessellate the universe with tetrahedrons.1 One might respond, “So what, ho hum. Just a bit technical.” No, it’s a simple but key geometry; one face of the tetrahedrons perfectly covers a surface with no spaces. The flip side (noted by ten triangular peaks demarcated by the red dots within the image on right) cannot be perfectly filled with another layer of tetrahedrons. Therefore, Aristotle’s claim was wrong. It was a mistake and it was promoted for over 1800 years; and today, it is very rarely discussed.2

Today, it seems that we diss simple geometries and we do not grasp basic geometric structures.3


Continuity, Symmetry, and Harmony

Our most important failing: Please think about our oh-so-old, most-ubiquitous, most-studied pi. Mathematics and physics would be dead without it, yet you won’t find it within our concepts about the beginnings of this universe. Today, we tend to fool around with pi.4 If we took it more seriously, we would ask questions about spheres like Lemaître’s primeval atom,5 Wheeler’s geon,6 Pati & Salam’s preon,7 and those defined by the Planck base units.8 We would prioritize the study of the definition of continuity implied by those “never-ending, never-repeating” numbers. We would engage its manifold symmetries and the relations between lines and circles and spheres. We’d be going inside the sphere to study the types of harmony that manifest and the unique dynamics of each.9

These are failings in our time. These are also the failings of our great minds-and-scholars and our leaders; and these failings affect the way we see our universe, our world, each other, and ourselves. The key insight of this article is that we are deeply and profoundly related, connected, and interconnected. If that simple fact was embraced as a fact, we just might be more respectful of each other and be more creative as we engage each other just as we are.

We started working on our chart, a model of this universe on December 19, 2011 in New Orleans …in.a.high.school geometry class. There are 202 progressive doublings of the Planck base units to this day and size of our universe. That chart stretches credulity. It is so hard to believe, we’ve asked many great scholars for advice and criticism. We received modest encouragement, no endorsements, and no constructive criticism. Undeterred, we’ve continued on; and, each year the concepts simply become ever so much more rich and encouraging. We even set about critically reviewing “commonsense” worldviews like our understanding of space and time. We had the audacity to question Newton and to support his rival, Leibniz.10 Then, rather naively, we even challenged Stephen Hawking and his understanding of the first moment of space and time. Hawking had an infinitely-hot start. Ours is rather cool!11

A basic idea emerged; an infinitesimal sphere is always the first notation and a simple start.12 And, the universe is populated by infinitesimal spheres with a remarkable interiority.13 A whole new sense of space and time emerged. A whole new physics of interiority began to emerge. The universe was filled with these spheres, quite literally filling all space and time. These infinitesimal spheres are in everything, everywhere, throughout all time. Each is like a little recording device. Everything you say, do, think or feel, is encapsulated, noted, and footnoted!14

Everything matters. Historically, such a construction may naturally give rise to an understanding of the Akasha,15 a concept that is within the beliefs of Buddhists, Confucians, Hindus, Jains, Taoists, and other sects that lift up Wuji philosophies. Yes, within each belief system, there is a record for everything. In other traditions an analogy would be omniscience.

Our model may be simple, yet it is inclusive. It opens a “huge” domain, 64-to-67 doublings that are infinitesimal and can’t be reached by our measuring devices. So small it just might be the basis of a new science for systems theory and a beginning for complexity theory. It is a domain for string theory and has plenty of character to include Langlands programs and even the most oblique and abstract mathematics.16

Yes, everything starts simple. We all do; and to our simplicity we must humbly return if this world is not to collapse with the weight of people who are much too sure of their ideas and actions.


ENDNOTES-FOOTNOTES

Introduction. Not many people in this world have visited this website. This section is for those who are feeling a bit lost. Our concepts and language always need clarification. We hope that our first-time visitors will find it here.

[1] Aristotle’s Mistake: In 2015, my life changed because I came upon a reference to an article titled, Mysteries in Packing Regular Tetrahedra.” That article amazed me. It took over 1800 years to catch Aristotle’s mistake. Yet, along that way, Averroës (Abu al-WalidMohammad ibn Ahmad al Rushd (1126–1198), Leonardo of Pisa (Fibonacci) (c. 1228), Roger Bacon (c. 1214–1294), and Thomas Aquinas (c. 1225–1274) were among the greats of their time who reinforced his mistake. As a result, none of them would ever know about a most fundamental geometric gap. First, inferred by Johannes Müller von Königsberg (1436–1476), then documented in 1480 by Paul of Middelburg, a professor of astrology in Padua, the discussion was rebirthed by Dirk Struik (MIT) in 1926 while studying in Rome. Most recently, in December 2012, Jeffrey C. Lagarias and Chuanming Zong [also see, May 2020] brought it to life again. Yet, none of these people in their time contemplating that gap ever thought that it just might opened a path to quantum fluctuations, indeterminacy, and imperfection. Such a highly-speculative statement would appear to most physicists today to be uninformed. I do not believe that I would be overplaying my hand to say that this gap makes us all equally human. It is the beginnings of all our imperfections.

[2] Over 1800 Years to Catch a Simple Mistake: We all make mistakes, yet we are not Aristotle, Averroës, Bacon, or Aquinas. Some of our Nobel laureates might come close. Then there are others like Stephen Hawking and Roger Penrose. Nobody is exempt; we all make plenty of mistakes. Admitting our fallibility is the beginning of intellectual integrity, but unfortunately, the need of our cultures throughout time for stars and heroes just does not allow people to be people and the effect on people, culture and scholarship is not attractive.

Arrogance is never attractive.

[3] Basic Geometric Structures: We had an advantage over our scholars; we had boxes and boxes of perfectly clear, plastic tetrahedrons and octahedrons with which to create structures. Most scholars cannot tell you what is perfectly enclosed within a tetrahedron even when you divide the edges by two and connect the new vertices. They haven’t seen the octahedron in the middle. When they look at the octahedron they do not see “half-sized” octahedrons in each of the six corners and eight tetrahedrons, one in each face, with all fourteen objects sharing a common centerpoint. Nor do they see the four hexagonal plates within each octahedron and think about chemical structures. They have not seen how the five tetrahedrons create a most basic gap whereby one can actually make tetrahedrons do the jitterbug. It takes a high school geometry class and playful engagements.

How do these structures come to be? Our antenna were up when we began our studies of cubic-close packing of equal spheres. We thank Phil Davis; he had pushed our faces into the sphere, “…the most basic structure…” And given his expertise, the twinkle in his eye, and his abiding warmth and gracious spirit, we listened. And finally, here we found the work of Harriot, Kepler, Poincare, Gauss, Hales and so many others creating the bridge between spheres and our simple tetrahedron. Bottom line, we could only conclude that the most basic sphere is defined by the Planck base units!”

[4] The Very Nature of Pi: With all the fascination with pi, with the playfulness of Pi Day, with its status as history’s oldest, best-known, most-studied, and most-ubiquitous dimensionless constant, why haven’t we stopped long enough to acknowledge it for our culture, “Here is our deepest key to understanding of everything!” Here is the pathway to understanding continuity, symmetry, and harmony. Here is the transformation nexus between that which is finite and that which is infinite.

[5] Lemaître’s Primeval Atom or Sphere: A sphere is a sphere. How small can it get? How small is the Democritus atom? How small is Lemaître’s 1928 primeval atom? Did it get much bigger with his reintroduction with a very-hot beginning in 1931? Questions abound.

[6] Wheeler’s geon and quantum foam (1955): Perhaps John Archibald Wheeler, one of the great theoretical physicists of our time, had a deeper sense of the sphere when he introduced the geon and quantum foam. Reflecting on their work with him in 1952, Charles Misner, Kip Thorne, and Wojciech Zurek give Wheeler credit for naming Planck Time and Planck Length; they concur that Planck’s 1899 calculations define the most basic units of space and time. However, Wheeler and his biographers were all blinded by an imagined infinitely-hot start, and never asked the question, “What would our universe look like if we take the Planck base units as a description of the very first instant of space and time?” Instead their thinking dropped into an impossible singularity without much clarity. Over 350 dimensionless constants tell us that there is no singularity.

[7] Pati & Salam’s preon: Others made valiant attempts to fill in the blanks and voids when they found them. Jogesh Pati and Abdus Salam were among early attempts at a Grand Unified Theory (GUT). Like the others, it was all top-down and blinded by the big bang. The first 64 notations out of 202 that encapsulate the universe could not be seen.

[8] The Planck base units: In 2011 when we were constructing our very first Big Board-little universe, we asked ourselves, what is smaller than particle physics? What is on each line from Notation-0 to Notation-64? We asked, “Are these Planck units the next big thing?” It would take several years before fully engaging the concept that the Planck base units define an infinitesimal sphere. Then followed the concept that the expansion rate of the universe was one plancksphere per plancksecond, that time is derivative, and the continuity, symmetry, and harmony of the sphere-and-pi were extended to the foundations of the finite and the heart of the infinite.

[9] Harmony Manifesting Dynamics: First challenged to engage the Fourier Transform through a New Yorker article by Cornell University mathematics professor, Stephen Strogatz, it seemed that Jean-Baptiste Joseph Fourier opened the door to study any and all dynamical relations. Though scale independent, very little work had done to apply the Fourier Transform to the Planck scale. That begins to change here with our initial recognition of five transformations.

[10] Newton and Leibniz: The infamous debate was never completed; Leibniz died so Newton won by default. He shouldn’t have won. Yet, absolute space and time is so ingrained within our beings, most of us will have a bit of trouble breaking it down. His Philosophiae Naturalis Principia Mathematica of 1686 some say is the true beginning of the discipline of physics. Others say that it is possibly the greatest textbook of all of science. One would be judged a fool to take on such standing! Yet, when ones model coheres, we should never be intimidated by an arrogant, unpleasant person. It is entirely possible that he was still wrong about our most fundamental starting points, “What is space? And, what is time?

[11] The Infinitely-Hot Start of Stephen Hawking: As recently as 2016, Hawking was the host of the PBS-special television series titled, “Genius.” Everybody working with those scripts thought the big bang was the only true religion. With such a brief period of human history, perhaps as short as 400,000 years, we do not think it is wise to tout any particular belief systems unless it in some ways reflect the continuity, symmetry, and harmony within pi and the sphere. Here are universals that in some manner reflect the fundamentals of the finite, and the essential nature of the infinite.

[12] An Infinitesimal Sphere, the first notation: Back in 2017 Neil Turok and his colleagues famously proclaimed that the big bang theory was wrong. Most significantly, they added, There is a perpetual state of big bangs. Non-intuitive, the only model to date, where such an assertion makes sense is within 202 base-2 notations whereby every notation is still active and is responsible for the expansion of the universe.

[13] Remarkable Interiority of Infinitesimal Spheres: We have a huge task before us. The references within just the Wikipedia listings for the Fourier transform are voluminous. There is a lifetime of study. We cannot hope to begin to grasp it all. But, we will try! Our web searches began with “Planck scale” + “Fourier Transform” and returned over 50,000 results. We are starting to work through them all. A cursory analysis of a few pages is most encouraging.

[14] Everything, Everywhere, throughout All Time Encapsulated, Noted, and Footnoted: That summary statement just seemed to encapsulate the simple logic that had been guiding us. If Planck Time and the Planck Length represent the smallest possible units of each, is it logically possible for anything to exist outside of those domains. We revisit the question often and will continue on our summary document and our related claims.

[15] Omniscience: Religions jumped ahead of the sciences. To the best of my knowledge, there has not been a scientific-systems theory that would incorporate the concepts found within the belief of an Akasha. That the Buddhists, Confucians, Hindus, Jains, Taoists, and all other sects that lift up Wuji philosophies have somehow seen this from within their own journey will be explored further. The closest Western religions have come to the concept is omniscience.

[16] Simplicity and the Beginning of Complexity Theory. The 64 notations from the Planck base units to the CERN scale of particle physics represents a new domain for science. I have called it hypostatic because it cannot be directly measured with physical devices. Three young scholars have suggested a means to make possible indirect measurements. I believe their work could well open new methodologies for science that go back to 1884 when Lord Kelvin speculated about the nature of dark bodies within our galaxy. The measurement of dark energy and dark matter is a beginning.

We live in a complex universe that starts most simply. Within that simplicity are the key insights about how we can co-exist and more meaningfully engage our days.


REFERENCES & RESOURCES

Reminders to return to the work of these scholars and to think more deeply about their constructs of reality. THEIR ARTICLES HAVE BEEN PART OF THE CONSTRUCTION THIS ARTICLE.

The last six homepages have been keys to this page:
The Mind, the Self, the Brain and the Human Mystery (December 26, 2020)
The First Instant of the Universe – Pi Circle, Sphere (November 27)
The Expansion of the Universe (November 16)
Change the Metaphor – Rewrite the History (October 16)
Countdown: Minutes, Seconds, Nanoseconds… (October 16)
This World Can Become A Nicer Place (September 23)


EMAILS (1 of 10)

As an article begins to take shape, friends and scholars are engaged to provide initial feedback.

The images at the top of this article are of world leaders, left to right, starting with China’s
Xi Jinping
and going to Germany’s Angela Merkel. Each of those leaders will be sent an email that goes something like this:

“As one of the key leaders of our world today, you are pictured at the top of this page.

“The entire world is in search of peace-and-prosperity, respect-and-dignity, and love-and-integrity. Unfortunately our realities are quite different. It is obvious that our understanding of this world and our universe is incomplete. We need to adjust our understanding of some of the fundamentals through which life takes shape and things develop. I believe our biggest problems relate to our incomplete understanding of one of the most common, oldest, and best-known things in our life. That is pi with her circles and spheres. The three teach us about continuity and order, symmetry and relations, and harmony and her most important dynamics whereby lines, tetrahedrons and octahedrons, become space, time, the finite and infinite.

“More work is here: http://81018.com and https://81018.com/precis/


TWEETS (5 of 23)

Eventually to drive traffic to the site and create a little buzz, key words are used to find discussions on the web with people who might be interested.

6:13 PM · Jan 16, 202, Angela Merkel: Our problems require a new vision of who we are and why we are. We must address issues that go right back to how we understand space and time and this world and universe: https://81018.com/precis/ is a start. Have your best scientists, scholars, and thinkers focus on these issues.

6:18 PM · Jan 16, 2021, Angela Merkel #2: True, but we all believe things that are not true. Old ideas need to be re-examined. What is space? What is time? What is finite? What is infinite? How did it all begin? Some of the giants were only right in their time, not ours. See https://81018.com/precis for more.

10:06 AM · Jan 21, 2021 @davidburkus @mitchjoel @LauraHuangLA @thomaswedell None of us should ever stop growing. Babies are naturally solipsistic; they only have MyView. Most adults have limited WorldViews. Leaders need an integrated UniverseView. Today, Worldviews are too small. We all need the most-inclusive perspective possible. A start: http://81018.com

4:14 PM · Jan 21, 2021 @BillClinton @HillaryClinton @davidnour Did you know that in 1899 Max Planck calculated the smallest possible units of length and time. If you apply base-2 (doublings), there are just 202 notations that define the universe from the beginning of time until now. We all need to be working on an integrated UniverseView: http://81018.com

5:38 PM · Jan 21, 2021 @antonioguterres As SG of UN, lead the world in a new vision of who we are and why. Our little worldviews need to become highly-integrated, mathematical views of the universe. Space-time becomes derivative and finite. Relations become really real. A start: http://81018.com

11:06 AM · Jan 23, 2021 @RamonCruzDiaz Just sent an email; now to follow-up. We will not break free of our narcissism and consumerism until we break free of narrow worldviews. We all need to work on an integrated universe view. Here’s a start: http://81018.com …all simple math but a framework!


Zzzzs

The last word, often afterthoughts, about this article and what is happening in our little world.

We so kowtow to our leaders. There is a long, brutal, and largely-forgotten history behind it all. In so doing, we impart a little divinity to them. When we don’t, it may be demanded. The respect that comes with leadership sometimes is not earned, but required.

So, who within our world is the best leader? Who is the wisest? Who is the smartest? Who is the bravest? Who has the most integrity? Who has the most love? Who has the most generosity? We must begin to discern and compare such qualities so all our leaders compete to hold some part of those judgments.

Ten global leaders posted, enough to fit across the page in one row:

Xi Jinping: premier@mail.gov.cn Peng Liyuan (spouse), Xi Mingze (daughter) http://www.gov.cn/
Vladimir Putin: http://en.kremlin.ru/contacts
Kim Jong-un: https://www.korea-dpr.com/ https://www.korea-dpr.com/organization.html
Mr. Alejandro Cao de Benos korea@korea-dpr.com usa@korea-dpr.com http://www.rodong.rep.kp/en/
George Soros: https://www.opensocietyfoundations.org/
Pope Francis: https://twitter.com/Pontifex http://www.vatican.va/
Joe Biden: joe@joebiden.com http://joebidden.com @POTUS
Queen Elizabeth: https://twitter.com/RoyalFamily https://www.royal.uk/
Donald Trump: https://donaldjtrump.com/ (still a leader for many people around the world)
Benjamin Netanyahu: https://t.me/bnetanyahu https://twitter.com/netanyahu
https://www.netanyahu.org.il/
Angela Merkel
: https://www.bundesregierung.de/breg-en/chancellor

Who might undertake such a project?


Key Dates for this document, Precis

  • This document was started on January 13, 2021.
  • First posted for collaborations: January 14, 2021.
  • The URL for this document is https://81018.com/precis/
  • The Prior Homepage: https://81018.com/conscious
  • First Tagline: A little precis for this website and our universe
  • The last update of this page was on January 24, 2021.

Pi, Circles, Primordial Spheres at a Nexus of Transformations

Left Yellow Arrow
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CENTER FOR PERFECTION STUDIES: CONTINUITYSYMMETRYHARMONY GOALS.DECEMBER 2020
PAGES:.ALTERNATIVE.|.DARK.|.CONFERENCE | MISTAKES | PHILOSOPHY | RELATIONS | TIMEUP

PRIOR POST | CLAIMS | ENDNOTES-FOOTNOTES | REFERENCES | EMAILS | TWEETS | Zzzzs

The First Instant of the Universe

by Bruce E. Camber Related: WorldThe ThreeHistoryExpansionConsciousness

Background:1 In 1899 Max Planck began calculating what are now known as the Planck base units. In 2001 Frank Wilczek (MIT) wrote three related articles for Physics Today, all titled, Scaling Mt. Planck (I, II, III). Those articles opened a wider discussion about these units; and today, Planck Length and Planck Time are generally accepted as the smallest possible units of space and time. In 2011 our high school geometry class applied base-2 notation (doublings) to the Planck units. Our chart goes from the two smallest to the largest possible units of space and time (the most current approximate size-and-age of the universe). That scale has just 202 notations. Rather quickly it became apparent that this scale compared favorably with the “epoch scale” suggested by big bang cosmology. In our 2011 model there is a heretofore unexplored infinitesimal scale of at least 64 notations, so small that these are only accessed through math and logic. That scale opens many more foundational questions about the very nature of space and time.

Purpose: That infinitesimal scale represents a new parameterization of space, time, mass and charge; it is readily accessible through a very simple logic, base-2 notation, the Planck base units, and dimensionless constants. The infinitely-hot start of big bang cosmology is not necessary. Redefinitions of space, time, and infinity are queued. No singularities, this nexus of transformations is a keyhole to make direct correlations with the Langlands programs and string theory.

Methods: Functional optimization, logic and simplicity are the operational requirements, yet always within the framework of the 202 base-2 notations. Particularly, the primary focus of this article is on several natural groups of notations. The first twenty-five notations come before big bang hypotheses are possible. The first 64 notations of length and time are too small for our measuring devices. The first 143 notations out of the 202 capture the first second of the life of this universe. Here we have a very different experimental environment to test new concepts.

Key working results to date:
(1) Of the seventeen big bang epochs, this base-2 scale encapsulates fourteen of its major epochs and marginalizes the first three.
(2) Base-2 exponentiation becomes the foundation for a natural inflation which then becomes the foundations for homogeneity and isotropy.
(3) Dark matter and dark energy are defined by primordial spheres, the first emerging with Notation-1 and then 1044 spheres per second literally flowing through and creating all 201 dynamic and fully-symmetric notations. Currently those same spheres are creating Notation-202 at the same rate, 1044 spheres/second. Isn’t that 539 tredecillion planckspheres per second? For more, go here.
(4) The spheres constitute what was once considered the aether, a working concept used to interconnect all things, everywhere, for all time. As this model is in some way validated or re-textured, many more results will be considered.

Conclusion: These 202 notations, particularly the first 64, open a new model of the universe that is worthy of our time to explore.

I. INTRODUCTION

Calculations and Navigation: There are known problems with our calculations. We are constantly working on them and welcome your insights. Also, any link that pointed to pages outside of this website have been moved into our Footnotes-Endnotes section. Links pointing within the website open a new tab or window.

The Story: In 2011 we outlined a model of the universe with just 202 base-2 notations starting at the Planck Scale and evolving to the current time and age of the the universe. It became a STEM tool, then a science fair project. Though quite idiosyncratic and highly-speculative, it had enough simple logic to continue to pursue it. In 2016, we developed a horizontally-scrolled chart to analyze the flow of numbers more carefully, both their relations within any one notation and along the entire expansion from Notation-1-to-202. Special attention is given to the first 64 notations. Given that these had never been part of any model, each notation will continue to be analyzed with appeals for the help from among the leading, living scholars around the world.

II. THEORETICAL FRAMEWORK

A Different Orientation. Since 2011 the 202 base-2 notations have had a few names. The first was Big Board-little universe. For the purpose of this article this theoretical framework will be referred to as the 202 base-2 notations. It is a mathematically-integrated view of the Universe. Because all notations are always active, it requires much more thought about the derivative nature of space and time and the role of the finite-infinite relation.

Not an infinitely-hot beginning. Hawking’s big bang has only been partially successful. Partial is partial. Several key scholars say, “It’s wrong.” Among them is one of Hawking’s many co-authors, Neil Turok. We agree with Turok that the universe is perpetually starting. In our emerging model, Notation-1 is like all notations and it is always active and it resides deep within everything, everywhere, for all time. The 202 base-2 notations all start cold and have a natural inflation. Yet, the numbers actually compare well with most of the epochs of the Hawking’s infinitely-hot start. Ultimately this model absorbs the big bang. Yet, the question still remains, “How does that first notation of these 202 notations come to be?”

The first instant is the first sphere and the first moment of space and time. Dimensionless constants define the Planck base units. Among them, the oldest, best-known, and most-used concept is pi with its circles and spheres. So, let us examine pi, circles and the sphere in light of the 202 base-2 notations. This theoretical framework, subject of many preliminary analyses, has much more to reveal.

III. PI – CIRCLES – SPHERES

The first sphere is primordial, constant, ever-changing, always the same. Pi, a dimensionless constant, doesn’t end and doesn’t repeat. It doesn’t meet the definition of finite. If it is not finite, what is it? Can we take as a given, that it is the beginning of a definition of the infinite?

If we take it as a given that these words begin to define the infinite, how might those words-numbers-results be characterized? It has a random orderliness that is constantly defining a circle or a cycle that never ends, constantly changes, but it is always the same. Perhaps that is the best possible definition of continuity and order.

In earlier articles we concluded one plancksphere is rendered every plancksecond. That results in approximately 539 tredecillion planckspheres being generated every second, a baseline expansion of the universe (Planck Time: 5.39116(13)×10−44 seconds).

Sphere stacking is taken as a given; each sphere is creating its own space-time-density. Within each notation spheres stack uniquely. Looking at the numbers, perhaps that density is best examined around the one second mark. Notation-144 is 1.2023 seconds. The mass is about 4.8537×1034 kilograms. The anticipated diameter is 299,792.458 kilometers. That mass is well beyond the mass of the sun at 1.989×1030 kilograms (with its much larger diameter of about 865,690 kilometers).

Assuredly, we are asking questions about blackholes and we are reviewing the mathematics around the concept going right back to Einstein. Is there a better metaphor? Is it analogous with, and possibly profoundly related to, dark energy and dark matter? We are beginning to think so.

IV. A LITTLE HISTORY

Perspectives.2 In 1611 Johannes Kepler wrote ‘On the six-cornered snowflake‘ and part of it included reflections about stacking cannonballs on the deck of a ship. As recently as 2002, Thomas Hales proved Kepler’s Conjecture to be true. That sphere-stacking legacy opened the path to close packing of equal spheres. And, thanks to Cornell mathematician, Steven Strogatz, we are beginning to understand how Fourier’s Transform is also involved. In 1822 a French mathematician and physicist, Joseph Fourier, introduced functions that evolved from work with sine-cosine-tangent and the nature of periodicity. Here the interior of all spheres are interconnected. We speculate that such functions — harmonic functions — are profoundly inherent in everything-everywhere-for-all-time. A circle is stretched out as a cycle and these cycles readily binding all 202 notations from the Planck scale. Yes, highly speculative, we probably should affirm that these spheres are not empty but are defined by the Planck base units and an unknown number of dimensionless constants; and the smaller the spheres get, the more intense that activity appears. So, it is perhaps a bit ironic that our study of spheres continues to build upon Kepler’s work with cannonballs, and then within the atomic scale atomic-packing factors (APF), and now within the Planck base units.

At the Planck scale, long before big bang cosmology engages, our model has already created twenty-five highly-integrated and calibrated notations. In this emerging model, inflation begins immediately. Gravity and electromagnetism do as well. Within the sphere, it appears that there are internal dynamics that pull within and there are external dynamics that push out. My simple logic tells me that electromagnetism pushes out and gravity pulls in. Perhaps at the Planck scale, the Fourier dynamics may logically reveal that electromagnetism and gravity are the Janus face of each other. It is certainly not a new thought. Even more speculatively, the density numbers in the earliest part of each notations suggest either analogies to blackholes or perhaps the inverse definition of one (Notations 1-67). Being rather whimsically speculative, perhaps there are just the 135 (Notations 67-to-202) for the creation and 135 (Notations 202-to-67) for recycling… And yes, yes indeed, to be sure, that is whimsical speculation.

There are major discussions within the current dialogues of the physics community that focus on the open issues; however, until these discussions begin within the Planck scale within the 202- base-2 notations, it seems that those discussions will not be simple or basic enough.

Technicalities and today’s challenges. Although Max Planck was calculating infinitesimal space and time in 1899, it was too small to explore. The National Institute for Standards & Technology (NIST)3 of the USA works with most standards organizations. None have a formal name for units as small as 10−27, 10−30, 10−33, 10−36, 10−39, and 10−42 seconds. Within our model those numbers have purpose and meaning. The yoctosecond at 10−24 seconds is the smallest number with a name. As a result, we have formally requested CODATA,3 which is an agency of NIST, BIPM, and other international standards organizations, to name at least five, possibly six, groups of these pivotal numbers. In the grand scheme of things, each may be infinitesimal, but here each is a key foundation of the universe.

Grasping Density. Our four prior articles were an exercise to begin to become more familiar with basic questions about this scheme, then with basic concepts that define it, and then with our most-simple formula, one Plancksphere per Plancksecond, as an expansion rate of the universe. This article and the prior four articles will be updated as this infinitesimal scale is further opened up by today’s scholars as they begin to see relations well beyond our scope and capacities.

Planck Time is calculated to be 5.39116(13)×10−44 seconds. If “one plancksphere per plancksecond” is correct, and there are five-hundred, thirty-nine tredecillion planckspheres per second, it is a relatively easy calculation to determine the number of planckspheres for each notation.

Back in 2012 Freeman Dyson suggested to us that dimensional analysis should be applied to this expansion. Now, reflecting on his comments in light of this article, I would say to him, “That gives too much primacy to space and time. These spheres are creating space and time so it seems to me that the numbers of units would be a base-2 expansion, not base-8.”

For more, see the base-2 expansion (line 8) and the base-8 expansion on line 9 within the horizontally-scrolled chart. And because this is all so speculative, your insights and comments will always be most welcomed.

Base-2 expansion and the sphere count. By Notation-6, there would be only 16 planckspheres. To begin to visualize the dynamics, let us return to the five images (below) that are often used within this website. You’ll notice that in the first panel (left-to-right), the image displays eighteen spheres. By Notation-7 there would be 32 spheres. By Notation-12 there will be 1024 spheres. By Notation-25 there are 8,388,608 spheres. By Notation-64 there are 1.8446744×1019 spheres; and by Notation-144, there would be 5.57518×1042 spheres. There are many open questions. Can we reconcile the sphere count at 5.57518×1042 with the rate count of 5.39116(13)×10−44 seconds?

Sphere Dynamics: There are external dynamics between spheres as evidenced within the stacking within the first box below on the left. We are also examining projected internal dynamics that are generated through the many faces of the Fourier Transform. The next five graphical images (below) represent cyclical data that have been labeled Fourier-A to Fourier-E. Although the Fourier Transform is scale independent, it appears that little work has been done with it at the Planck scale. Understanding the possible applications of all five representations of cyclical functions is part of our work on this very special model of the universe. We are seeking experts who have deep working knowledge of the ways that Fourier-A to Fourier-E may open new pathways through each notation, especially those first 64 notations which hold possibilities of unimagined diversity and complexity.

Sphere to tetrahedron-octahedron couplet
Sphere Stacking-Packing
Fourier-A
File:Circle cos sin.gif
Fourier-B
Fourier-C
Fourier-D
Lagrangian point
Fourier-E

V. FINITE-INFINITE & THE TRANSFORMATION NEXUS

Throughout our ever-so-limited human history, there have been diverse speculations about the nature of infinity. However well-intentioned and earnest these have been, in this work, such speculations are set aside for a more mathematical approach.

Pi, circles and spheres continue to inform us. This work began back in 1972 when a simple perfection of the infinite was characterized as “continuity rendering order, symmetry rending relations, and harmony rendering dynamics.” Today, it is recognized that those simple perfections are all manifest within pi, circles and spheres. Although each is well understood, very limited work has been done to date at the Planck scale and then into a gateway or nexus of transformation between the finite and infinite. As we have seen from the chart of base-2 notations, these infinitesimal notations are so dense, there is no room for fluctuations. Those three simple perfections — continuity, symmetry, harmony — will keep things in line. Even within the first second of the universe, right on up to Notation-144, I can well imagine that everything is still “in line.” That’s just a guess.

From perfection to imperfection. When and where that first gap manifests is an open question. There is a “thrust for perfection” that conceivably could go on for a year (Notation-169), perhaps 1000 years (Notation-179). We don’t know, however, at some point five tetrahedrons will share a common edge, a simple fluctuation begins, systems engage and fluctuations become part of our universe. Our guess, perhaps just whimsical speculation, is that the first manifestation of some kind of fluctuation is where the homeostasis with the internal-and-external activities within the sphere become out-of-balance. Once established as a system within space-time, conceivably it moves back down into the earlier notations until the thrust for perfection doesn’t allow room for a fluctuation. At this point in our thinking, it seems that the domain of perfection would go from Notation-1 to about Notation-50 where we hypothesize the beginning of Systems and the archetypes for the Mind. Here we finally begin to see an infinite diversity of possibility within those five dynamics pictured above. Here, probabilities can be exploring the easiest possibilities.

With every new second within each notation, new layers of inter-connectivities emerge. Instead of just continuity, symmetry and harmony, the formulas are extended:
1. The infinite is continuity and it begets order, begets numbers which begets time.
2. The infinite is symmetry and it begets relations which beget geometries which beget space.
3. The infinite is harmony and it begets dynamics begets Systems begets space-time.

The Dynamics of the Infinitesimal:4 According to some scholars, some types of measurements can be inferred right down within Notation-50 in the range of 1.819679×10-20 meters. To date, we find no quark-related sizes that are smaller. Typically quarks are no smaller than 10-18 meters which ranges from Notation-56 to Notation 59. To find language to describe possible phenomena, we go back to Plato’s Forms, Aristotle’s Ousia, Langlands’ Automorphic forms, Witten’s strings, and so many other basic-basic structures that have no connection to the Standard Model for Particle Physics or the Lambda Cold Dark Matter model.

Scale Invariance and the Fourier Transform.5 Every image of a circle and a sphere needs to be considered and reconsidered for applications within the Planck scale. Because this model is logically scale invariant, all such images should apply within the finite-infinite transformation and within the Notations 1-to 201. Because Notation-202 is still in-process, directional and asymmetric, scaling within Notation-202 could be limited and/or adaptive. We hypothesize the primordial sphere as in Lemaître, opens sphere stacking and sphere packing. We uncovered that dynamic image online in 2014. It gave us a visualization of the transformation from spheres to interior functions, straight lines, and finally the Euclidean-Platonic geometries. So we are guessing. The functions of Fourier A to Fourier D may actually be fairly good representations of waves and standing wave patterns. Fourier E is even more speculative. It comes from celestial mechanics; and to the best of my knowledge, it has never been suggested to represent any activity on the human-scale, small-scale or infinitesimal-scale of our universe. The Lagrange point applied to the Planck scale just might open a pathway to automorphic forms and strings and it has some semblance to the visualization of the standard model of particle physics suggest by Chris Quigg in the October 22, 2020 issue of Quanta Magazine.5

There is so much more to discern. There are so many open issues… Foremost among them is the promise of even more uniqueness and diversity introduced by prime numbers. Also, this model starts with base-2. Others have argued that base-3, base-4, base-5 would do equally well. Now, I believe that is too quick a judgment. The prime number bases provide unique access to unique starting points; and within this model, all such starting points are held together within the base-2 structure. Mix into these considerations, all the other most-used dimensionless constants, this universe has a palette of possibilities far greater than the panoply of colors, sounds, smells, textures, and odors that we currently identify. Thank you.

###

Footnotes and Endnotes

Some of our concepts and language need clarification, especially if you are a first-time visitor. Any link that currently points to a page outside of this website is initially redirected here before going outside of this site. All links pointing to pages inside the website will open in a new tab or window. Also, these footnotes-and-endnotes are still being developed.

[1] Background. This introduction within this box (with its light-yellow background) is the most recent attempt to summarize work done since 2011. This box and its key links remain here especially for our first-time visitors.

[2] Perspectives. Old concepts have new meanings when looking at the universe as a highly-integrated, scale-invariant whole. As we return to 1611 to the work of Johannes Kepler, we begin to realize how very young our sciences are. Here Kepler is just beginning to formalize the concept of sphere stacking with the advent of the cannons and cannonballs just 150 years earlier. The irony of it being included within an article entitled, ‘On the six-cornered snowflake,’ should not be lost. As well, not until 2002 did Thomas Hales prove Kepler’s Conjecture to be true. We are all such simple and arrogant people. Thus, our next venue within these studies must be to be to understand the human mind and its rather natural capacity for deceit and self-importance.

[3] CODATA, An Agency of NIST, BIPM, and other SI-related Organizations: Because names are so important to shape the personality of a word or domain, we have appealed to CODATA to officially intervene. This body assigns official names to measurements. Even Wikipedia recognizes the importance of these agencies.

[4] The Dynamics of the Infinitesimal: The entire universe appears to share the first 64 notations. Individuation possibly begins to appear with Notation-50 to about Notation-54. Plato’s Forms, Aristotle’s Ousia, Langlands’ Automorphic forms, Witten’s strings. Other basic-basic structures that have no connection to the Standard Model for Particle Physics or the Lambda Cold Dark Matter model.

[5] Scale Invariance and the Fourier Transform. It all starts with a sphere and then sphere stacking which opens to sphere packing. Uncovered online in 2014, this image gave us the visualization of the transformation from spheres to interior functions, straight lines, and finally the Euclidean-Platonic geometries. All the descriptions and links go directly to Wikipedia.
Fourier A. “This wave pattern occurs often in nature, including wind waves, sound waves, and light waves. It is often said that the cosine function leads the sine function or the sine lags the cosine.”
Fourier B. “The sine is a trigonometric function of an angle. The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle, to the length of the longest side of the triangle (the hypotenuse).”
Fourier C. “A circularly polarized wave as a sum of two linearly polarized components 90° out of phase.” Also, see the Poincaré sphere.
Fourier D. “Animation showing four different polarization states and two orthogonal projections.” Also, see polarization states and circular polarization.
Fourier E. Most speculatively, because the Planck numbers appear to be scale invariant, let us see if that logic applies if we take a basic definition within celestial mechanics, the Lagrange point, and try to apply it to the Planck scale. Within 24-hours of speculatively hypothesizing that the Lagrange points describe activities within the infinitesimals of the Planck scale, a visualization came to my attention that has a semblance of it. An article by Natalie Wolchover in Quanta Magazine (October 22, 2020) introduces a visualization based on the work of FermiLab’s emeritus theoretical physicist, Chris Quigg. The Quanta team took it further. Their visualization helps enliven Quigg’s work and opens metaphorical and analogous thinking.

__________

References and Resources

While an article is being written, there will be many references opened, mostly to ArXiv and Physical Review articles. Some are included here. Most references are reminders to me to return to the work of these scholars and to think more deeply about their constructs of reality.

  1. China: Some Chinese scholars are very important consensus builders. For every 100 views of this website, close to 10% are from China and another 10% are from the United Kingdom. Typically within a given day, there will be visitors from as many as 15 different countries. To facilitate explorations by our Chinese friends, Baidu automatically translates the entire site. Here is a link to our current homepage in Mandarin: 这是当前主页 (translation can be slow).
  2. Tensor and pairing interactions within the QMC energy density functional, Martinez, Thomas, Guichon, Stone (April 2020)
  3. A Higher Dimensional Cosmological Model for the Search of Dark Energy Source, PS Singh, KP Singh, November 2020
  4. Quark-meson coupling model. What if the Mass-Length-Time [M0 L0 T1] of the quark is just too gross or large? You know that quarks are not directly measured per se but confirmed only by theoretical predictions. Best guesses puts them in the range of 1.81×−20 meters to 7.27×10-20 meters which puts them in our range of Notation-50 to Notation-52. Within this model the current speculation is that these notations are the edge of informational fluctuations, cellular automaton, and the beginning of Systems.
  5. Assume big bang cosmology is wrong, so our current worldviews are necessarily wobbly, incomplete, and too small. We need an integrated view of our universe that starts right at the very first instant and comes to this moment, the now, the current time and current expansion of our universe. Mathematically, in its most simple form, it requires 202 base-2 notations from the first instant to the current expansion today.

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Emails

Most emails are to scholars who know something about the issues involved. Their problem is like our problem; they, too, get set in their ways. They have their belief systems and they tend to stick to them. As politely as possible, these emails invite their help to look at our data in new ways.

Dec 2, 2020, 11:17 PM Ewan Palmer, a London-based reporter for @Newsweek.
Dear Ewan, It’s been awhile since you’ve been on Twitter. I just sent you this highlighted paragraph below. My current work is here: https://81018.com/instant/ Best wishes, Bruce
@EwanPalmer@joelockhart We are all so flawed. The primary flaw is our limited worldviews. On both sides of every equation! If we migrate to an integrated, mathematical view of the universe — https://81018.com/chart/ — it opens a new perspective and responsibility for integrity. See: https://81018.com/ethics/ Editor’s note: Joe Lockhart is a CNN political analyst.

Saturday, December 5, 1:02 PM, About Densities directed to Edward Kolb, Dean, professor, Kavli Institute for Cosmological Physics, Chicago, Illinois Key Question: “How about return to Lemaître’s primordial sphere? If such a sphere manifests, defined by the Planck base units, there would be about 539 tredecillion spheres per second. Too idiosyncratic to pursue?

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Tweets

Link to tweets that challenge people to stretch and to attempt to see the universe and not just the world that is in front of them.

9:51 AM · Dec 16, 2020 @justinbieber Be careful, Justin. Our little worldviews get in the way of having an integrated view of the entire universe – everything, everywhere, for all time. It’d inspire new lyrics and a gracious, loving heart. A start: http://81018.com I’d be glad to help explain.

12:57 PM · Dec 4, 2020 @erikvance Deep within is an intuitional network which sees the discontinuities such as a son with only his socks. You knew; you just thought it was too special to interrupt that flow. And it is! …especially in Mexico City… but not in Baltimore! https://81018.com/instant/ is a start (to define that intuitional network). Note: Erik is a staff editor at @NYTParenting and author of Suggestible You.

10:25 PM · Dec 3, 2020 @NRoberts_atHome The problem with religions, Christianity included, they are so intimidated by the sciences, they really haven’t had the guts to grasp infinity anew to be able to explain it to the intellectual, scholars and academics. For more: https://81018.com/infinity/

12:37 PM · Dec 4, 2020 @alwaleed_philan @Alwaleed_Talal http://www.kingdom.com.sa Until we’re freed of Newton’s absolute space and time, we have a handicap; our understanding of the universal and infinity is tied down. We need an integrated view of the universe: http://81018.com is a start!

4:39 PM · Nov 29, 2020· @loru22o and @NassimHaramein …our first 64 notations give us all the breathing room we need: https://81018.com/chart/ There’s much more here: https://81018.com -Bruce

10:38 AM · Nov 29, 2020 @atrupar@voxdotcom What if Newton was wrong in 1687 (when he published Principia)? What if space and time are derivative, not absolute? What if our worldviews are too small? What if an integrated-view of the universe is needed to right the wrongs? https://81018.com/chart is a start.

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Zzzzz

Afterthoughts. Within the perspectives of this website, time’s arrow is entirely limited to Notation-202. All other 201 notations are symmetric, space and time, like mass and energy, are derivative, yet profoundly related to each other and light. It is a radically idiosyncratic view of our universe that emphasizes at least 25 ways to engage the details of the universe.

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Key Dates for this file, instant

Stacked magnetic spheres (four, four, then one), Kandinsky spheres (background), is a dynamic.


The sphere prior to quantum fluctuations creates a domain of perfection within our physical universe.


APPENDICES
Names of Very-Large and Infinitesimal Numbers

NameNumberGroupSymbol
Largest-named to smallest-named
septillion1,000,000,000,000,000,000,000,000yottaY
sextillion1,000,000,000,000,000,000,000zettaZ
quintillion1,000,000,000,000,000,000exaE
quadrillion1,000,000,000,000,000petaP
  —Numbers-names from large to small —
quadrillionth0.000 000 000 000 001femtof
quintillionth0.000 000 000 000 000 001attoa
sextillionth0.000 000 000 000 000 000 001zeptoz
septillionth0.000 000 000 000 000 000 000 001yoctoy

NamePower of 10Decimal
Thousand1031,000
Million1061,000,000
Billion1091,000,000,000
Trillion10121,000,000,000,000
Quadrillion1015etc …
Quintillion1018 
Sextillion1021 
Septillion1024 
Octillion1027 
Nonillion1030 
Decillion1033 
Undecillion1036 
Duodecillion1039 
Tredecillion1042 
Quattuordecillion1045 
Quindecillion1048 
Sexdecillion1051 
Septemdecillion1054 
Octodecillion1057 
Novemdecillion1060 
Vigintillion106363 zeros

Working Towards a Mathematically-Integrated Model of the Universe

Left Yellow Arrow
Right Yellow Arrow

CENTER FOR PERFECTION STUDIES: CONTINUITYSYMMETRYHARMONY GOALS.NOVEMBER.2020
PAGES:.ALTERNATIVE.|. CONFERENCE .|DARK| EXPANSION|.MISTAKES | PHILOSOPHY | TIME | UP
____._________PRIOR POST | CLAIMS | ENDNOTES-FOOTNOTES | REFERENCES | EMAILS | TWEETS | Zzzzs

Change the Metaphor – Rewrite the History*

by Bruce E. Camber Related: WorldThe ThreeExpansionFirst InstantConsciousness

Underpinnings: Given the nature of insight and ideas, high school people with curious minds should be capable of asking difficult questions and proposing new concepts about the nature of space, time, blackholes… We hope that describes us and we don’t waste your time. This is our story. It begins in December 2011 in a high school geometry class. More story

We went inside a tetrahedron. You can, too. Divide the six edges by 2, connect the new vertices; there are smaller tetrahedrons in each of the four corners and an octahedron in the middle. Keep dividing all the edges by 2. In just 45 steps you will be among waves, particles, and quantum fluctuations. Keep dividing by 2; in 67 more steps you will be down within the Planck base units at the limits of space and time. Nothing gets any smaller. Tetrahedral image and octahedrons.

To get back where we began in the classroom, take Max’s Planck Length and multiply-by-2. In just 112 steps, you’ll be back in our classroom. Now, keep multiplying, but watch carefully! In just 90 steps that tetrahedron will be out on the edges of the universe and today’s expansion.

You will have spanned the universe from the smallest to the largest in 202 steps (notations or doublings)! It’s quite a bit more than a base-2 progression of numbers. It is a functional map and it hasn’t been formally studied within our academic and scholarly communities.

In 2011 we created our first, rather colorful base-2 chart of the universe. In 2016 we created a less colorful, but more-detailed, horizontally-scrolled chart. It was all quite challenging; very quickly it appeared to be an alternative to the infinitely-hot start that defined big bang cosmology. Here is our original 2011 Chart, our on-going Working Chart, and a Comparative Chart.

Three short years passed. Still naive, perhaps silly, maybe gutsy, we reflected once more about what we were seeing. More…

We now thought it was more than a STEM tool and more than simple math; those 202 base-2 notations from Planck Time to this day changed our metaphors and began to re-write our history. We tried writing up our STEM analysis for possible publication!

Planck Time (5.39124(60)×10−44 seconds) divided by Planck Length (1.61625(18)×10−35meters) is, of course, 299,792,422.8 meters per second. It is in the numbers, all natural units based on the fundamental constants of nature. We wondered, “What might those four Planck base units look like if the universe, like Lemaître first suggested in 1927, began close to zero degrees Kelvin?” We turned to experts at the National Institute for Science and Technology (NIST) for help.1

Our charts were helpful to us but they were considered idiosyncratic, even poppycock by some, because this unusual look at the universe had not yet been properly vetted within recognized scholarly publications.

By definition, the chart included everything, everywhere, for all time.2 So we asked, “What doesn’t it include?” …infinity? What else? …a path to infinity? Is there any causal efficacy between the finite and infinite? We decided we needed to learn about the many types-and-functions of dimensionless constants like pi. Of course, pi is the most studied, the oldest, the most-used,3 and the most underestimated of all the dimensionless constants. It is not finite. It goes on forever without repeating itself. So, we wondered, “Is pi a bridge between the finite and the infinite?”

Pi gives us a sense of perfection and value. Pi’s never-ending, never-repeating number is a perfection — perfect continuity. Her sphere gives us a perfect symmetry of relations and balance. And, with its many applications of the Fourier Transform, the sphere also gives us another fully dynamic perfection called harmony.

Throughout the first 64 notations, we are looking to see where and how the first imperfections manifest. We have guessed in prior postings that it would manifest as the gap created by five tetrahedrons sharing a common edge. The Gap.

Again, we turned to scholars around the world for insight. More

Our charts opened up at least 64 notations smaller than waves, particles and quantum fluctuations. It wasn’t in any textbooks. What’s down in there? What does it look like? If this was a grid for string theory, does it begin within the first notation? If it is a grid for Langlands programs, what is the bridge to string theory and particles-waves-fluctuations?

We asked a lot of questions; we had no answers. What is going on within that first notation? John Wheeler talked about quantum foam and geons. We tried consulting with Kenneth W. Ford,4 Wheeler’s co-author of Geons, Black Holes, and Quantum Foam: A Life in Physics. We asked, “Might our redefinition of quantum foam and geons work?” Along that path we uncovered many, many attempts to define something more basic than waves, particles and fluctuations.5 There was a logjam. Of all those attempts, might our model-presuppositions-assumptions help to break open this conceptual blockage?

We were becoming convinced by others. What is the simplest thing in the universe? The sphere. …the most perfect? The sphere. …the most ubiquitous? The sphere. Could a sphere be defined by the Planck base units and some combination of dimensionless constants? It was plausible.6

But as simple as this logic is, just like the simple logic for the unfolding of the 202 notations, it was quickly strained by a closer look at Planck Time.

One Plancksphere per Plancksecond: Calculating the rate of expansion of the universe. That will also amount to the addition of dark matter per second. We adopted the names, Plancksphere and Plancksecond from the internet. Plancksecond (10−44 seconds) is the very first unit of time defined by those Planck base units. The Plancksphere would be the smallest possible object that defines space and time. Though not quite in the spirit of naming by NIST, CODATA, ISO, BIPM1 and others of the yoctosecond (10−24), zeptosecond (10−21), and attosecond (10−18), it seemed appropriate. After all, it was Max Planck who opened up the infinitesimally small universe for us. There is a telltale gap from the yoctosecond (10−24) to the plancksecond (10−44). The academy, including all the scientists and scholars who are responsible for the scientific names of things, has not yet named anything smaller than the yoctosecond. One can imagine that our experts had concluded, “There is nothing to be discovered that is smaller.” So, there are five groups of numbers that await a formal name: 10−27, 10−30, 10−33, 10−36, 10−39, and 10−42 seconds. The 10−42 group includes 10−44 and, of course, there are many who have referred to it as the Plancksecond.

There is nothing easy about Planck Time. It strains credibility. The ultimate time calibrator, simple logic suggest that one plancksphere would be generated each plancksecond. Does that mean that 1044 planckspheres would be generated every second?!? A bit hard to imagine: 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000 planckspheres per second.

Spheres
As small as our plancksphere is, that is an unfathomable amount of planckspheres! Called a hundred tredecillion, in one second, it would be out in a line 299,792.458 kilometers long and it would fill all available space as it expands, so one can image that lines of spheres would always be equal to the amount of space within that notation. Ostensibly we would be following line 8 within the horizontally-scrolled chart. By that first second, the current chart allocates 1.3937×1042 base-2 vertices. Our math is off but not by too much. We continue working on it. To say the least, it would be a very dense 3-D structure of planckspheres that could be measured in cubic kilometers. We often remind ourselves that is so many factors smaller than neutrinos, these spheres are not in any way measurable by a physical device. That rate of the emergence, is the current expansion of the universe as well as the rate by which the dark matter of the universe increases.

That’s a bit bold so, of course, we know that we have an almost insurmountable amount of conceptual work to do!

Ideas and Concepts. Adopting a new concept is not easy, especially when we have to unlearn old concepts. Along that path we also have to begin to grasp why we didn’t learn other concepts as well as we should have. And then, these new concepts just take time, sometimes years to absorb. Take, for example, “Time is derivative, discrete, quantitative… hardly absolute.” Most of us have looked into the clear night sky and thought that it went on forever. Sir Isaac Newton whispers in our ears from his 1687 book, The Principia (Philosophiæ Naturalis Principia Mathematica). Within Newton’s days there was no science for particles, waves and quantum fluctuations. He didn’t have Max Planck’s infinitesimal numbers. And as sophisticated as our sciences and mathematics seem today, they are still so very young in the grand scheme of things.

Also, we still make a lot of mistakes. Personally, I am only now getting comfortable with our learning curve for time. It’s steep, but the learning curve for space and the instantiation of the first sphere is steeper.

Instantiation? What’s involved? The quick answer is the four Planck base units and at least pi among our dimensionless constants (and we suspect many others), all concresce to make the first sphere(s). Regarding dimensionless constants and our Lambda Cold Dark Matter model (ΛCDM) — remember John Baez has 26 dimensionless constants and Wilczek-Rees-Aguirre-Tegmark have 31. There are many to evaluate. NIST has identified over 350 and mathematician, Simon Plouffe, has 11.3 billion mathematical constants, all through his algorithmic programming.

We are entirely open to your insights, suggestions, and ideas. What other dimensionless constants might be involved with the production of that constant blast of 1044 spheres?

Though Max Planck’s numbers have been with us since 1899, it has only been since 2001 and 2002 that the scientific community actually began to think about them. It has only been since 2012 that we began to think of these numbers as the first moment of spacetime. It has only been since about 2015 that we’ve begun to think of that the first manifestation of the Planck base units as spheres. Of course, John Wheeler and others have been playing with the idea of primordial spheres since the 1950s, but, they had no container within which they could effectively build a system that would render particles, waves and quantum fluctuations. 

Those first 64 base-2 notations could well be an appropriate start.

If, and only if, pi-circles-spheres are the absolute shape of the first notations, and the container for our universe is continuity-symmetry-harmony, we have a very different model of the universe. It is a working model using cubic-close packing of equal spheres. The simple logic of our notations tells us that each one is always active and constantly building on all prior notations. That includes notations 1-to-201. Notation 202 is uniquely interacting because it includes the current time and current expansion of the universe. Of course, it feels directional.

Over 20 unique concepts now support this model.  It is time for each to be critically reviewed by scholars. Let’s review:

  1. What if the universe does start with the Planck base units, what might be the first “thing” created?
  2. What if the first thing created is a sphere defined by those Planck base units?
  3. What if there is an endless stream of spheres and the first functional activity is sphere stacking?
  4. What if sphere stacking opens cubic close packing of equal spheres and tetrahedrons and octahedrons are generated? Doesn’t the rest of Plato follow?
  5. What if the concept of infinity has been so tainted by philosophies, we miss its most simple definition — continuity creating order, symmetry creating relations, and harmony creating dynamics; and then we add, “Please keep all other definitions to yourself. They are not necessary here.”

In the meantime, we’ll try to grasp this model in light of the most challenging problems in mathematics today, such special projects as the Yang–Mills existence and mass gap. Thank you.

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Endnotes & Footnotes

* Any link that does not have a footnote is a page often referenced on this site:
https://81018.com/home/ is Our Story, one of our very first pages.
https://81018.com/tot/ goes to our special image of a tetrahedron.
https://81018.com/octahedron/ is one of the third key geometries in this universe.
https://81018.com/big-board/ is our first and most colorful base-2 chart.
https://81018.com/chart/ is our working horizontally-scrolled chart.
https://81018.com/2014/12/01/door/ begins within the power of metaphors.
https://81018.com/stem/ begins the bold charge into the top leadership.

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[1] Experts at NIST. One of our first encounters with NIST was through Prof. Dr. Philip J. Davis. At that time he was an emeritus professor of Applied Mathematics at Brown University and the former Chief of the Numerical Analysis Section at NIST. In 2012 Phil Davis was emphatic and entirely convincing about the sphere as the most basic structure.

Then came interactions with many others, starting with Peter J. Mohr.
• National Institute for Science & Technology (NIST)
• Planck Length (Also: See the definition of uncertainty)
• All things Planck related. 353 Dimensionless constants.
Values of Fundamental Physical Constants

Also, there are the following:.
CODATA, the Committee on Data of the International Science Council. It is part of the International Science Council (ISC).
ISO – International Organization for Standardization

[2] Everything, everywhere, for all time: Many scholars have spent a lifetime in search of a theory of everything (TOE). That is not our goal. We are on an exploration of the Planck base units and the logic of infinitesimal spheres as the first manifestation of space-and-time.

Can we follow the simple math and logic? Not a theory of everything (TOE), but it might be a structure to help understand how a TOE could come to be.

[3] Dimensionless constants: NIST has done an extensive amount of work on dimensionless constants. We will continue our efforts to get some of the NIST scholars to consider parts of the infinitesimal that is currently ignored, defined only by numbers, without nomenclature and formal standing within the ISO. We have approached Bonnie Carroll, the Secretary General of the CODATA group and associated with NIST.
• We will continue to follow related work by John Baez.
We’ll continue our study of the work of the Wilczek, Rees, Aguirre and Tegmark.

[4] Kenneth W. Ford, former director of the American Institute of Physics: From working with the leading theoretical physicists within Princeton’s Project Matterhorn to writing his textbook, Basic Physics (originally published in 1968 by Blaisdell; reissued in 2017 by World Scientific), Ford has soared with the best yet he has been deep in the weeds as well. His book with John Wheeler encourages us to explore the conceptual framework of the geon, blackholes, and quantum foam. We have also been encouraged by Ford’s empathy for ethics. Locate the Geon book near you.

[5] What could be more basic than waves, particles and fluctuations? How do we relate algebraic geometries (Grothendieck‘s scheme theory), Euclidean geometries, projective geometry, category theory, Mandelbrot set, Julia set, Möbius transformations, Kleinian group, S-matrix theory, unitarity equations, Hermitian analyticity, Golden ratio (Phi), the Fibonacci sequence, fluctuation theory, ratio analysis, pi, cubic-close packing of equal spheres, ring theory, and lattice generation? Out of that group we settled on pi and cubic close-packing of equal spheres at the Planck scale to begin.

[6] An Infinitesimal Sphere. How could the smallest, most-simple 3-D object be the structure by which the universe is held together, expands, and gives rise to all other shapes and energies? That is the question. And, we shall explore as many answers as we can possibly find.

One Plancksphere per Plancksecond should be equal to the current expansion of our universe. There are so many dynamics within the first few steps… notwithstanding, it is already an impossibly large number to grasp. We should also consider an even larger number by multiplying it by the total number of seconds since the start of the universe. That would give us an approximate total number of Planckspheres within the universe and it would constitute the physical foundations of the universe. It’s a rather novel concept and such a different vision of the old aether. We’ll need to revisit Michelson-Morley and Wilczek’s matrix or grid. Perhaps we should add it to our list of claims or novel concepts.

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References & Resources

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Emails

Thursday, November 3, 2020 at 5:55 PM: “If I were to write a summary statement about Kenneth Ford, it would begin: At 94 years old, Prof. Dr. Kenneth Ford has done enough. Among hundreds of papers and dozens of books that he has authored, he knows the open questions and the dead ends. With books like The World of Elementary Particles (1963), Basic Physics (1968, 2016), The Quantum World (2004) and 101 Quantum Questions (2012), Ford’s legacy is solid. He doesn’t need to continue to wrestle with all the open questions and tensions within science today.”

“The concepts being put forth within this website are just too much of a quantum leap. From primordial spheres to fluctuations and particles in 64 steps would have been an interesting concept to pursue. But eventually, it is all just too much!

“We extend our great thanks for all Kenneth W. Ford has done! -Bruce”

Tuesday, November 10, 2020 at 8:01 AM:
Dear Steklov Mathematical Institute (RAS):

  • Could the universe start with the Planck base units?
  • What might be the first “thing” created?
  • Could the first thing created be a sphere defined by those Planck base units?
  • Could there be an endless stream of spheres and the first functional activity be sphere stacking?
  • Does sphere stacking open cubic close packing of equal spheres and tetrahedrons and octahedrons are generated? Doesn’t the rest from Plato follow?
  • The concept of infinity has been so tainted by philosophies, we miss its most simple definitions coming from our observations of pi—continuity creating order, symmetry creating relations, and harmony creating dynamics. Perhaps we might consider adding, “Please keep all other definitions to yourself. They are not necessarily useful here.”
  • And so we finally ask, “Is there a glimmer of truth to the observations that give rise to our questions? If so, doesn’t that change our starting point and basic equations a bit?”

Might you have any advice for us? Thank you so much.
Warmly,
Bruce

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Tweets

A sample of a tweet that went out to many people: “We have all grown up within limited worldviews. We need to include the entire universe to calibrate and understand who we are and why.” A start on a highly-integrated view of the universe: http://81018.com

Here is the same tweet specifically focused for Dr. Jason Johnson who is a Professor within the School of Global Journalism and Communication at Morgantown State University in Baltimore: “Jason, cool it. You know better by now. We are all tied up in knots and so very limited in our perspectives and simple worldviews. Without a complete picture, we always get confused. An integrated view of the universe is better grounding: http://81018.com is only a start.”

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Afterthoughts

Zzzzzz: Back around 2014 we did a science fair project based on this base-2 model of the universe. I wrote up a little blog about becoming comfortable with very small and very large numbers. Exponentiation is a key.

Next: Desmos calculators

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The name of this page is History

An artist’s rendering of a blackhole from NASA

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