# Redefining points, point particles, and vertices

A word of caution. This website’s construct of the universe is different. With this page, it is gets more so. In December 2011 when we began this trek, the first 64 notations were a mystery to us. We wondered, “How do we understand something that is below the thresholds of measurement even though each notation has very specific values for length, time, mass and charge?” Long-long ago I remember not liking the definitions for points and vertices in our geometry textbooks. That goes back to 1961 in my high school geometry days; I felt those definitions were too limited and often circular.[1] Now, 61 years later, insights have opened to redefine both as well as many other terms used within this range known as the infinitesimal, our Notation-1 to Notation-64 out of a total of 202 notations. -BEC

Point particles also redefined. That definition has been very much in process.[2] It is hardly settled science. So, within these web pages a point particle is an infinitesimal, primordial sphere that emerges within Notation-1 and continues to emerge to this day and moment. It is only known logically and mathematically and are called hypostatic particles.[3] Around Notation-64, we are able to detect and measure aspects of quantum fluctuations. It is hypothesized that these spheres represent at least 64 different vertices, all functioning like those represented by points within classic geometry. These vertices first have all the functionalities of an infinitesimal sphere, and then those functionalities that are already well-defined within Langlands programs and string and M-theories. Other working theories that define some aspect of the infinitesimal will eventually be included.

When better understood, some of these vertices may also begin to look like known characteristics of hypothetical particles.

In the first instance, these infinitesimal spheres through the Fourier Transform are either gravitationally or electromagnetically active (attractorsrepellers) and then each builds from there.

So, yes, within this redefinitions of points, point particles and vertices, we’ve hypothesized that each becomes part of the functionality of everything finite, everything within the 202 base-2 notations from the Planck Time to the Age of the Universe Right Now. Again, there are no less than 64 doublings from the Planck scale to quantum fluctuations, so an entire science of the functionality of points/point particles/vertices at each notation may begin to be identified, especially within those studies that have not found a means to connect to the grid.

Within our 2013 Universe Table chart, we hypothesized that from Notation-1 to Notations-10 are forms and the mathematics of Langlands programs. Vertices look like automorphic forms. Hypothesized from Notation-11 to Notation-20 are structures and the mathematics of string theory and M-theory and the vertices look like the mathematics of strings.

Hypothesized from Notation-21 to Notation-30 are archetypal substances well prior to the Periodic Table of Elements which is well prior to the Standard Model for Particle Physics. Hypothesized from Notation-31 to Notation-40 are archetypal qualities. The closest we’ve come to a chart of qualities is here. Hypothesized from Notation 41 to Notation-50 are archetypal relations. And, hypothesized from Notation 51 to Notation-60 are archetypal systems.

More to come…

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[1] Laurie E. Bass, Randall I. Charles, Art Johnson, and Dan Kennedy, Geometry, Prentice Hall Mathematics, 2004, page 11: “Point: You can think of a point as a location. A point has no size. It is represented by a small dot and is named by a capital letter. A geometric figure is a set of points. Space is defined as the set of all points.” page 11

“Vertex: A vertex is a point where three or more edges intersect.” page 512.

Endnote: This definition of a vertex is unsatisfactory. When just fourteen-and-fifteen years old, I asked questions, “How do those point cohere? Who ties the knot or anchors or glues them together? What is going on between the two or more lines? Is there any energy along the line or within the enclosed space?” There were no answers at that time and there are still no answers today.

[2] Point Particle, Wikipedia, retrieved on April 22, 20: “Its defining feature is that it lacks spatial extension; being dimensionless, it does not take up space.”[Reference]

Endnote: In our redefinition of a point particle, each has unique spatial extension. Though generated by dimensionless numbers, each has specific quantities of length, time, mass and energy, yet all these quantities are below the thresholds of any possible direct measurement. Within this website, these are called hypostatic particles. The [Reference] just above for within Wikipedia goes to F. E. Udwadia, R. E. Kalaba (2007), Analytical Dynamics: A New Approach. Cambridge University Press. ISBN 978-0-521-04833-0

[3] Hypostatic particles. Hypostatic jammed packings of frictionless nonspherical particles, Kyle VanderWerf, Weiwei Jin, Mark D. Shattuck, and Corey S. O’Hern, Physical Review E 97, 012909, 2018

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References & Resources

Historic or traditional point particle defined:
1. Point Particle Model (PPM) and Superstring theory
2. Wikipedia. Because the first 64 notations are not recognized, Findzus E. Udwadia (USC) and Robert E. Kalaba (authors of Analytical Dynamics: A New Approach, (2007) said that the defining feature of the point particle is the lack spatial extension. Being dimensionless, they assumed that it does not take up space. They needed the 202 base-2 notations and to have recognized the 64 notations well prior to particle physics and beyond the thresholds of measurement.
3. Learning Constrained Dynamics with Gauss’ Principle adhering Gaussian Processes

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Email Social media, the press, television and the political class often miss the universal face of truth and justice which these emails attempt to convey. -BEC

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IM

@deseretmagazine and @DNewsOpinion Our problem will always be incomplete worldviews that compete for mindshare when every worldview is too small. We need a highly-integrated view of the universe to context concepts and ideas. Here’s a start: https://81018.com/

We need an inherent ethics: https://81018.com/ethics/

12:38 PM · Apr 12, 2022 @QuantaMagazine Thanks, QM. Deep within pi (π) is continuity which yields to symmetries which yield to harmonies and all things qualitative and infinite. Bring in the Planck or Stoney scale for the start of time, and in 202 notations (doublings) you have the universe!

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Keys

The last update was Sunday, April 17, 2022.

involves lying, cheating and deception.

# On following the work of Steven H. Strogatz…

Articles: Why Pi Matters
BooksThe Joy of x (Mariner, 2013), Infinite Powers (Houghton-Mifflin, 2019)
ArXiv
Homepage(s): Cornell, CV -2019 Joy of Why Podcast (2022 article), Google Scholar, Twitter, Wikipedia

References within pages on this website:
List of scholars, Strogatz on the Fourier Transform, Nexus of Transformation (August 2, 2019), Pi is fundamental to everything, Cubic Close Packing (ccp), Pi Day is 3.14… March 14, Deeper Matters

`Most recent email: 2 March 2023`

My idiosyncratic views, in part opened up by your 2015 article on the Fourier, are getting stranger and stranger: https://81018.com/pointing/

It eventually opened many new ways to engage a very old group: FourierPoincaréGaussPlanck, Einstein, Smale, Milnor, and others. So, I’ll be looking for your most current Pi Day contribution. The subheading of mine is: Pi Day’s puzzles point beyond circles and spheres. The heading is What do we know?

Again, I thank you for all that you do!  -Bruce

`Eighth email: Friday, August 12, 2022, 1:23 PM`

Without question you are one of the favorite intellects of the country and I would dare say of the world. You surely are for me. I am eternally grateful for eating some of the most delicious pi ever from your bakery.

Now, your David Tong interview was brilliant. To take the next step, I recommend eating more of your pi.

Two new references: https://81018.com/fourier/  Your joy: https://81018.com/2015/12/19/strogatz/

Of course, I know you get altogether too much email and you have your cadre of followers, students, pre-docs, and post-docs, and, and, and. Please, I don’t expect a reply.

-Bruce

`Seventh email: 21 March 2022 at 1:17 PM`

I went looking for your Pi Day article and found your Joy of Why podcast with Quanta magazine. Fantastic. I’ll try to remember to give it a tease on our homepage the day before you go live!

I still think you should have a Zoom conference for the masses on Pi Day. Remember how last month I had said in my note to Brigid Danziger of MathGiraffe.com, “He (YOU) should have one huge Pi Day Zoom class for us all. Each hour could go from easy to more difficult.”  I would think Quanta would do it in a heartbeat.

BTW, I now maintain two pages about Steven Strogatz: https://81018.com/strogatz/ and https://81018.com/2015/12/19/strogatz/ (the original).

Again, congratulations on your latest rendition of the podcasts with Quanta.

Best wishes always,

Bruce

PS. Our base-2 container may well encapsulate all your work but it changes nothing about the work per se. It just opens a larger interpretation because time’s asymmetry is only within the current notation (202) and sleep is a natural compiler for one’s own internal symmetry…. yes, I’ll work on it!  -BEC

`Sixth email: February 13, 2022 at 2:27 PM`

Dear Prof. Dr. Steven Strogatz:

I look forward to your 3.14 article to inspire us all to think more integratively. I think people like Brigid Danziger of MathGiraffe.com are sensational, too. She’s doing for middle-and-high school teachers what you do for undergraduates, graduates, post-docs, professors and the public (people like me).

I recently said this to her: “Geometry is dynamic. We do not learn enough about pi, spheres, and symmetries. The current pi celebrations are often silly and it all needs to be ratcheted up each March 14.”

“A student’s first engagement should be with Steven Stogatz of Cornell: https://81018.com/strogatz/ His Pi Day articles are mostly within the New York Times and the New Yorker. His books are sensational. He should have one huge Pi Day Zoom class for us all. Each hour it could go from easy to more difficult. His work on the Fourier transform and pi is transformative — https://81018.com/fourier/ — and empowering.”

“He brings images like this on cubic-close packing alive: https://81018.com/ccp/

I thought you might enjoy seeing what I’ve been saying about you (obviously a groupie)!

Best wishes,

Bruce

`Fifth email: Friday, 12 March 2021`

You might appreciate the audacity: https://81018.com/challenge/

Are you published this year regarding pi?

Thanks. -Bruce

`Fourth email: Friday, 5 April 2019`

Of three related articles, today’s has a reference to your work and a link

These are the three related articles:
https://81018.com/e8/ (April 5, 2019 https://81018.com/e8/#SHS )
https://81018.com/maybe/ (Wednesday, April 3, 2019)
https://81018.com/standard_model/ (Tuesday, April 2, 2019)

At some point in time, the evidence will become
compelling enough, our scholarly community may begin to address it;
and at that time, perhaps Wheeler’s comments will become true:
“Behind it all is surely an idea so simple, so beautiful, that
when we grasp it — in a decade, a century, or a millennium —
we will all say to each other, how could it have been otherwise?”

Thanks.

Best wishes always,
Bruce,
See: https://www.nytimes.com/2019/03/14/science/pi-math-geometry-infinity.html

`Third email: Friday, March 1, 2019`

RE: Why Pi Matters, The New Yorker, March 13, 2015

Dear Prof. Dr. Steven Strogatz:

Out of your article, seemingly written with just a little impatience for the contrivance or forced-fit, Pi-to-Pi Day, you so brilliantly empowered learning about the Fourier series and for that I am most grateful.

On our bulletin board is a clip out of that article (attached). Beside it are three related dynamic images from our researching the generation of the sine and cosine waves.

Thanks again for all your work and inspiration.

-Bruce

PS. Posted on the bulletin board: Excerpt from Why Pi Matters, and three dynamic images. We have to go full circle, inside and out, to begin to understand the dynamics of strings.

`Second email: Friday, December 18, 2015`

Dear Prof. Dr. Steven Strogatz:

Congratulations on all you do.* Just wonderful.

My late-in-life exploratory was a result of helping a nephew with his high school geometry classes. We were charting the Planck base units to their natural limits using base-2. It’s been fascinating. http://81018.com
https://81018.com/chart

Most sincerely,
Bruce
**************
Bruce Camber
http://81018.com

*Of course, your book, The Joy of x (linked above), is everybody’s favorite.

`First email: December 1, 2014`

Dear Prof. Dr. Steven Strogatz-

Though an infinitesimal length, just double it and each result 202 times and we are out to the approximate size of the universe.”

I like your spirit and the way you write about math and life.

Now, it seems impossible, but applying base-2 exponential notation to the Planck base units, there are 101 notations to the width of a typical hair (103 to the human egg), and then another 101 or so to the approximate size of the Observable Universe. Kees Boeke did something like it in 1957 using base-10 in what he thought were 40 jumps (his book, Cosmic ViewWikipedia).

There’s something going on here. And, given you are an open person with all the cards on the table, face up, it would be great to hear your thoughts:  https://81018.com/order/

If there is any merit here, might we talk a little about it? Thanks.

Most sincerely,
Bruce

# Our rather simple overview about the start of the universe

CONTINUITYSYMMETRYHARMONY
Pages: Blackhole | C.| .Empower  | Hope.|. Mistakes.|. PI (π) |.Redefine |.Singularity | Sphere.TOE.|.Up
|

Abstract
An unusual STEM tool from a 2011 high school geometry class is based on simple geometries and mathematics. This study began when students and teachers divided the edges of a tetrahedron in half and connected the new vertices. A little like Zeno’s paradox of dividing by 2, going within, there are 112 steps to get to the Planck Length. Going out, there are just 90 steps (doublings) to the Age and approximate size of the Universe today. That chart of just 202 base-2 notations maps the universe from the first moment until this day. Logically and by definition, this map or model starts with something that is archetypal and primordial at the very first moment of time and then goes out to encapsulate everything, everywhere, for all time. So comprehensive, it has taken years of thought and analysis to identify key components of the model and those key components are now introduced for further analysis. What started as a simple exploration that created a STEM tool is now an avenue for lifelong learning.

Key words: STEM, STEM education, physics education, base-2 notation, Platonic solids, close cubic packing of equal spheres, sphere dynamics, pi, finite-infinite, topology, combinatorics

Introduction

Plato’s five solids, the first concepts to define space, are often covered within a single session of our Geometry 101 studies.[1] By asking several key questions, that one session became a STEM tool for lifelong learning. The first key question was, “How far within the tetrahedron can one go by dividing its edges by 2 and connecting those new vertices?” The class had constructed a model of the tetrahedron with three layers of measurements. The first layer is the simple tetrahedron.

The first division yields four tetrahedrons, one in each corner, and an octahedron in the middle. Dividing the edges of the octahedron in half, there are smaller octahedrons in the six corners and eight tetrahedrons, one in each face. We continued building many different configurations. See close-up image.

On paper, the class made forty-five (45) additional calculations and the edge of the tetrahedron was now within the CERN-scale of particle physics. In sixty-seven (67) additional calculations, the edge of the tetrahedron was within the Planck scale. The results of dividing or multiplying by 2, we learned, is called base-2 notation. [2]

At some notations we identified an application for a natural doubling. We have come to believe that for most notations there will be a discernible application, a dynamic for doubling that goes beyond our simple mathematics from stacking. The prime number notations deserve special study.

The class then used the ISO calculation for the Planck Length for the first measurement of a length. In 112 doublings that progression returned the students to the classroom. They continued to double that multiple of the Planck Length. Within just 90 additional doublings, the length was out to the estimated size of the universe. When Planck Time was added, that 202nd notation had also encapsulated the estimated age of the universe at 13.81 billion years.

The two other Planck base units for mass and charge were added. The logic of that expansion opened many new questions about continuity equations, symmetry relations, and sphere dynamics. As these studies continue, anticipated are also harmonic functions that dynamically link each abutting notation and Notation-0 to Notation-202. There is a causal efficacy. Its inherent order predefines each emerging number. Its inherent relations create geometries, and its inherent dynamics define a relational nexus between those numbers and all possible geometries.

Clear plastic models of those Platonic geometries provided visualizations. Among our building blocks the tetrahedron, the octahedron, and the icosahedron [3] were primary. The emerging numbers of the Planck base units quickly filled out the first chart: https://81018.com/big-board/.

It took a few years to believe that our first chart was an original [4]. Then more numbers from other Planck base units quickly filled out additional charts. Our first “desktop version” was obviously an original [5].

Our current working chart emerged in 2016. It was our first horizontal chart, 34 pages wide. It helped us to follow the numbers more readily. The most-original version of that chart, an upgrade on our tenth anniversary, December 19, 2021, includes a start with the infinitely-hot Planck Temperature. If an infinitesimally-short blast of light, we hypothesize that cooling follows the inverse square law so that the quark-gluon plasma appropriately manifests. [6]

Follow-up: Chart – https://81018.com/chart/ First principles – https://81018.com/ultimatum/
Tagline: We started our first chart in 2011 and quickly turned to scholars for help.

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2. Research Methods.

2a. Multiplication and division by 2. This model of the universe is a map with 202 layers that start with the Planck base units. The four basic continuity equations, starting at the Planck scale, go out to this current time. In so doing, mathematics encapsulates the universe from the first moment of time to the current moment of time, the Now.

2b. Embedded geometries. This project had begun by dividing the edges of a tetrahedron in half. To begin to grasp the origins of the Platonic solids starting with the tetrahedron and octahedron, we began our studies of cubic-close packing of equal spheres [7] (there’s so much more to learn).

To understand sphere dynamics, we need to more deeply understand pi, harmonic functions, infinitesimals, and the finite-infinite relation.

2c. Sphere dynamics. Key evocative questions opened even more searches well beyond our studies of geometry. The chart progressed from the study of emergence to structure formation (including Langlands programs and string theory), then to particles and their hypothetical particles, and onto chemistry, biology, systems theory, and cosmology. The foremost criterion within this research is the simple logic of continuity-symmetry-harmony [8]

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3. Results

Base-2 exponential notation opens a diversity of bifurcation and fractal studies. Sphere stacking and cubic-close packing of equal spheres open pathways to deeper tetrahedral and octahedral studies, including an analysis of the tetrahedral gap created by five tetrahedrons sharing a common edge. It is now hypothesized that the gap is the first instantiation of quantum physics and it is now hypothesized that quantum dynamics could manifest before Notation-64, however, today’s laboratory-based fluctuations are first measured at lengths and durations orders of magnitude larger than those within Notation-64.

The focus on Planck Time opened questions about a cosmological constant defined as “one Planck sphere per unit of PlanckTime and Planck Length.” Using Planck’s numbers, it computes to 539 tredecillion spheres per second. [9] Using George Johnstone Stoney’s 1874 base units, it would be as high as 4605 tredecillion spheres per second. [10]

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4. Analysis.

In 2011 when we emerged with the 202 steps, we slowly learned that it was a base-2 progression. We had followed embedded geometries to get down into the Planck scale. It seemed a bit of simple logic to turn around and use the Planck Length (and in 2013 add Planck Time). There was a profound relation between the two. We knew there was a profound relation with Planck Mass and Planck Charge; Einstein had done that work. Now it seemed the right time to figure out how the four all related. The resulting numbers as the four base units expand together the same 13.81 billion years later stretched our understanding of things and strained our logic, yet there is a compelling coherence and our on-going analysis. [11]

We didn’t know what we didn’t know. When one highly-respected scholar told us our work was idiosyncratic, we tried finding anything similar to our emerging chart.

We discovered the 1957 work of Kees Boeke, a base-10 map of the universe. It became apparent that his work, Cosmic View: The Universe in 40 Jumps, challenged people for the first time in history to see the universe holistically-and-mathematically from the first moment to the current time. Books were written about it. An IMAX movie was made. Yet, at no time was casual efficacy ascribed to these 40 jumps, as Boeke called them. Nature has not revealed any causal efficacies whereby a transition is naturally made by multiplying or dividing by 10.

In 2011 when we emerged with the 202 steps, it seemed to be the best-possible, high school STEM tool. It defined the outside boundaries. The parameters were dynamic. It logically included everything, everywhere for all time. Although puzzled by the first 64 notations, it seemed like the penultimate Science-Technology-Engineering-Math (STEM) tool. [13]

After four years searching for other base-2 studies within articles, books, and the worldwide web, we decided the thrust of this work was original and it was time to consolidate our many pages on many sites around the web into one website. We obtained the address —- http://81018.com — whereby “8” was for our understanding of infinity. “1” was for the finite, unity and singularity and “0” was for transformation. It became our on-going work area. Although entirely idiosyncratic and not readily embraced by the scholarly or scientific community, this study had an inherent logic and it was a simple map of the universe that even our 6th grade students understood.

The sphere or tetrahedron. If something manifests per each unit of PlanckTime and Planck Length, it would have to be simple. At that time I was in discussions with Brown University applied mathematics professor, Phil Davis. He had been a mathematician for the National Institute for Standards and Technology (and for its precursor organizations). Phil proposed the sphere. I had proposed the tetrahedron. Once introduced to cubic-close packing of equal spheres and by seeing just how tetrahedrons and octahedrons were generated, in May 2012, I finally agreed with Prof. Dr. Davis. For me, it was an essential moment in time. [14]

In 2015 Steve Strogatz of Cornell reintroduced me to the Fourier transform through his article in The New Yorker. It was for Pi Day 2015. Pi’s importance had never been so heightened. [15]

The place and importance of the sphere was established, so the question was asked, “How do spheres come to be?” Looking at the never-ending, never-repeating, always changing but-always-the-same, numbers resulting from an enigmatic-but-simple formula for a circle and sphere, it becomes obvious that this continuity equation is not of the physical world. It is not finite. Though it is all numbers, it is not just quantitative, but qualitative, too. So, if it is not fully finite, is it infinite? If it is not infinite, is it a facet of infinity or a bridge between the finite and infinite?

Looking further at the sphere, its symmetries are ever apparent. Although a facet of every sphere, symmetry per se is not just a geometric facet; it is qualitative facet. It’s not just quantitative. Is it finite or infinite? Although it may be both, it seems fundamentally more infinite than finite. That third facet of the sphere, its harmonic functions, are measurable, however, the very nature of harmony is not finite. It is always dynamic and appears more infinite than finite.

We will discuss and argue about these three facets of infinity. Each given within the simple sphere, it becomes obvious that we all need to re-engage the finite-infinite relation.

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5. Discussion.

In 2011 the first chart, a 60″ by 11″ board that started with the Planck Length and went to the Observable Universe, was readily shared with other secondary school math teachers. It seemed like the perfect little STEM tool because it touched the primary academic disciplines. It had a simple logic. Yes, even our sixth-grade science classes understood it! But, Scientific American ignored this project and our questions. Wikipedia rejected our summary as “original research.” The AAAS and their Science magazine, as well as Nature magazine, all rejected us without comment. A diversity of scholars were reluctant to comment. So, assuming an egregious mistake within our logic and math, the question continues to be asked, “What are we doing wrong?” Our simple plea for help: “A small group of high school students and a few of their teachers has been trying to figure out what to do with an all-encompassing-but-simple mathematical and geometrical model. Findings to date are presented with the hope that the academic-scientific community can tell us how best to proceed with our very simple charts.”

We had dubbed our little project, Big Board-little universe.

In the earliest days of this exploration, it was not clear where to stop. Each notation had three of four numbers, so experts, NASA’s Joe Kolecki, and the director of the Paris Observatory, Jean-Pierre Luminet, helped us with our calculations.

In 2014 we finally added Planck Time to the chart. Stefan Vandoren and Gerald t’Hooft were our inspiration. They had done a base-10 progression and published a book, Time in Powers of Ten.

The Planck Time numbers tracked well with the Planck Length. Also, the Age of the Universe, 13.81 to 14.1 billion years, was no longer a mysterious number and it gave us a place to stop “multiplying by 2.”

We then discovered that the ratio of of the Planck Length to Planck Time within each of the 202 notations was always within .1% of the speed of light. We quickly asked, “What does that mean?” and knew it would be an open question for a while.

Finally in 2015, we then added the other two Planck base units to the chart, Planck Mass and Planck Charge.

There were so many things to discover, our heads began spinning. It all continues to be a challenge. Each notation is filled with data to analyze. Although each chart is a highly efficient way to organize vast amounts of information, these charts raise rather fascinating questions.

At first we wondered why we couldn’t find some vestiges of these charts within our textbooks or someplace on the World Wide Web. Then, when Wikipedia rejected our article as “original research,” we asked, “Isn’t all this information somewhere within the academic world?” Stepping back from our charts, we asked, ”Isn’t each column of the chart a very basic continuity equation from a Planck base unit to its largest possible measurement? Isn’t continuity the bedrock of order? Shouldn’t this be the first principle within our work?”

The small numbers were impossibly small and the large numbers were impossibly large, yet the 202 notations were relatively manageable. There was always one nagging question: “Is there a problem with our logic and math?” It was exponential notation that helped us get comfortable with both extremes and it helped make these numbers more manageable. When we learned a little about Leonhard Euler’s equation, we decided that we lived in an exponential universe! It has taken time. It has been a steep learning curve; we now have feelings or intuitions about the very nature of a number!

We also realized that our universe was perpetually starting. Every notation was always active. The 202nd notation was the only one that was not perfectly symmetrical. It was in process; there’s an arrow of time within it. So, what does sleep and the mind have to do with it? Is it like a computer program in need of recompiling?

What more could these numbers tell us about the universe and ourselves? The geometries started simple, but became exceedingly complex. We asked, “What is geometry? How is space necessarily defined? Does it require all the Planck base units? Does it require the extended Planck units?”

The human family seems to dominate the middle of this chart, yet the time epoch for humanity’s existence is entirely within a very small slice within Notation-202. What is the correlation, the working relation, between the current time and the other notations? If all notations are concurrent, active and forever, what does it say about the nature of space and time? When the chart is divided into thirds, the small-scale universe is extremely small. It goes from the Planck Length to about the size of the quark.

This particular view of the small-scale universe is virtually unknown yet it has a substantial amount of data waiting to be properly analyzed. We reached out to many of the finest scholars for their inputs. Everybody seemed puzzled.

The human scale and large scale did not seem to challenge our simple logic until the “time line” was observed, particularly the figures at one second. What does it mean that the Planck Length multiple is the distance light travels in a second? Well over two-thirds of all the notations are within that first second and within an area defined by the earth to the moon. What does that tell us?

Nobody seemed to know what to do with these charts. So, to get some scrutiny, online articles, blogs and emails, were written. Feedback has been limited. How can that change?

We did get some very helpful suggestions. In 2013 Prof. Dr. Freeman Dyson recommended that we use dimensional analysis and scaling laws to determine the number of possible vertices starting at the Planck base units. We did. The numbers became extremely large rather quickly; nevertheless, because these first 64+ notations were not on anybody’s charts of known things within space and time, we concluded that these vertices must be shared by the entire universe and have something to do with homogeneity, isotropy, the very nature of symmetry and the symmetry of nature, and the cosmological constant.

It was easy to ask ourselves, “Are we crazy or what?”

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6. Conclusions

These numbers, geometries, equations, and charts appear to be a reasonable STEM tool. Elementary students have followed these numbers and appreciated seeing the universe all inter-related on a single page. A holistic view of the universe replaced smaller worldviews. Yet, these numbers, geometries and equations hold much greater potential to address historic problems between the silos of information that divide the sciences. At the same time, it will be helpful to have a larger community to critically engage the intuitions, conjectures, and rather-wild speculations that this map-and-model seems to stimulate. We need to learn if-when-and-how our simple logic and simple math have failed us. We are now trying to understand how continuity-order and symmetry-relations, then harmony-dynamics, are truly bedrock principles of Science, Technology, Engineering, and Mathematics.

By December 2012 a few of our best students, recently-graduated seniors, now students at Tulane and Loyola just down the street, dropped back by their favorite high school. They told us that their professors had never seen a base-2 progression like ours. The students were confused and so were we. It did not take too long to realize that this work was indeed out of the mainstream. Our little mathematical and geometric model even seemed a bit seditious. It raised too many questions. Within a year, we became cautious. Within another year, even more cautious, and within three years, we stopped teaching our students about this model.  At that time this project became a cause, “We’ve got to figure out what’s going on here.” So, we continue working at it.

The future?

We see a day when every student is challenged to grasp the foundations of STEM so every one of them can become a STEM teacher. Everyone is empowered to expand the horizons of family, friends, and colleagues to be inclusive, creative, and open to the greatest possible diversities in life.

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Afterword
Let’s build a discussion group. It’s time to find a professional publication about STEM and submit an article. We found a few publications:

Thank you very much. –BEC

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Click on the bracketed number to return to the body of the footnote or endnote.
[1] Laurie E. Bass, Randall Charles, Dan Kennedy, Geometry, Pearson Prentice Hall, 2004, page 517
[2] Conway, John H., and Guy, Richard K.,  The Book of Numbers, Springer, 1996
[3] R. Buckminster Fuller, Synergetics I & II (PDF), Macmillan Co., 1979
[4] An original base-2 chart of the universe. Using Planck Length, this chart was first used in high school geometry classes, Monday, December 19, 2011.
[5] Universe Table: An original, the Universe Table was introduced on the web in December 2013.
[6] Planck Temperature: The original 2016, horizontally-scrolled, base-2 chart of the universe (using Planck Time, Planck Length, Planck Mass and Planck Charge) was updated so Planck Temperature, as calculated by Max Planck, began at Notation-0. It was first on the web on Sunday, December 19, 2021.
[7] Conway, John HortonSloane, Neil J. A., Sphere packings, lattices, and groups (PDF), Springer, Section 6.3. ISBN 9780387985855, 1999, ResearchGate PDF
Endnote: Cubic-close packing of equal spheres. Wikipedia: accessed March 4, 2022. Also, see the many references to cubic-close packing of equal spheres within this website and to the structure of elements in the periodic table.
[8] Continuity-symmetry-harmony: An original formulation for the primary facets of infinity.
[9] 539 tredecillion spheres per second. An original interpretation based on Max Planck’s calculation of Planck Time at 5.391 16(13) × 10−44 seconds whereby one infinitesimal sphere manifests per Plancksecond. That sphere is sometimes referred to as a Plancksphere. That assumption renders 539 tredecillion spheres per second.
[10] 4605 tredecillion spheres per second. An original interpretation based on the work of George Johnston Stoney in 1874, the earliest known calculation of the smallest-possible units of time.
[11] The basic logic of the expansion. This original model is subject to constant analysis and revision. There is an abundance of original insights and information that has come out of it and will continue to come out of it. This study of the logic of the expansion is an early analysis that was first presented here in August 2017: https://81018.com/planck_universe/
[12] Human logic imposed on nature. Edward Zalta, Mechanizing Principia Logico-Metaphysica in Functional Type Theory, Nov. 2017
[14] Essential Moment in Time. An original concept, as applied within the 202 base-2 notations whereby there is concurrence and transformation across notations for an individual, family, community, nation, or all people residing on earth.
[15] Steven Strogatz, Why Pi Matters, The New Yorker, March 13, 2015

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References & Resources

• Aharonov, Yakir and Petersen, Aage, Definability and measurability in Quantum Theory, Ted Bastin, ed., Quantum Physics and Beyond, Cambridge University Press, 1971 https://doi.org/10.1038/069194a0

Bell, E. T. , Finite or Infinite?, Philosophy of Science, The University of Chicago, PressVol. 1, No. 1, 1934, pp. 30-49 (20 pages)

• O’Sullivan, Simon, “A Diagram of the Finite-Infinite Relation: Towards a Bergsonian Production of Subjectivity.” Bergson and the Art of Immanence: Painting, Photography, Film, Performance, edited by John Mullarkey and Charlotte de Mille, Edinburgh University Press, 2013, pp. 165–186, https://www.simonosullivan.net/articles/bergsonian-production-of-subjectivity.pdf

Wang, Xijia, Cosmic Continuum Theory: A New Idea on Hilbert’s Sixth Problem, Journal of Modern Physics, Vol.9 No.6, 2018, DOI: 10.4236/jmp.2018.96074

Also see: Some Calculations and Thoughts Regarding Measurement by Joe Kolecki, NASA scientist, retired:  https://81018.com/kolecki/ and Jean-Pierre Luminet.
• The original 2012 Wikipedia article: https://81018.com/2012/05/05/wikipedia/
Euler, Poincare, Fourier, Gauss, Karl Schwarzschild and Arthur Holly Compton
The Planck Temperature – Absolute Hot: What is the hottest temperature possible (YouTube)

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Disclosures: There are no competing interests regarding this data or the use of this data. All data and charts originated with the authors and there have been no rights granted regarding any of this data or the resulting charts.

Data access: This project began with equations, numbers, charts and geometries. All the data is available online within the website: https://81018.com/
The working chart is here: https://81018.com/chart/
The first chart is here: https://81018.com/big-board/

Ethics: No human subjects or animals or insects or other living things have been used in these studies. The studies are based solely on logic, mathematics, equations, and geometries. Of interest, however, is that these studies have emerged with its own unique definition of ethics: https://81018.com/ethics/

Funding: This work has received no funding from any sources. It has been an intellectual exercise whereby the authors were glad to do their work without any payments whatsoever.

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Emails

Many pages within this site start out as an email. The following email was sent to several key scholars around the world and it is now emerging as a page here.

General: We all need to see this world in a very different way:
1. There is a necessary and dynamic finite-infinite relation. Just look at pi. This oldest, most-used equation in the world, defines spheres and circles yet it is not entirely finite. There are three key dynamic facets of infinity within every sphere and circle: continuity-symmetry-harmony and that’s a paradigm shift.
2. The Planck scale is assumed to be the first manifestation of space-time. It begs the question, “What does it look like?” Necessarily the answer is an infinitesimal sphere.
3. One infinitesimal sphere per Planck Length and Planck Time. The universe starts and grows. Cubic-close packing of equal spheres provides a mechanism for generating the Platonic solids, Riemannian geometries, Langlands programs, strings, SUSY, and quantum fluctuations.
4. Apply base-2 to the expansion. We emerge with 202 notations that encapsulate the universe from the very beginning of time to this point in time.

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IM

8:14 PM · Mar 7, 2022 @elonmusk We all need to be working together: https://81018.com It is a simple model of the universe. It could make us a little wiser. Even Putin. -Bruce

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Key dates for this document, stem

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# Structure of spacetime at the Planck Scale: An infinitesimal sphere

The First Particle Is Not A Particle Per Se.
It’s pure geometry and mathematics.
by Bruce E. Camber

Abstract (as a series of hypotheses from a high school thought experiment)
The first particle has all the structural and dynamic elements of a most simple sphere. It is defined by the four Planck base units of time, length, mass and charge. It is an infinitesimal, archetypal, primordial sphere that defines the first moment of space-time. The Planck scale is also defined by dimensionless constants so here we propose several mechanisms to begin to bridge the Planck scale with the electroweak scale. Our model using base-2 and the Planck base units originated in 2011 and it begs for more analysis. For example, if Planck Time also defines a rate of expansion by taking as a given that there is one “Planck particle” per unit of Planck Time and Planck Length, it’s a different model of our universe. Seemingly logical, please suspend your harshest judgments in order to explore whatever mechanisms we can imagine in light of the Standard Model for Cosmology (ΛCDM or Lambda cold dark matter) and the Standard Model for Particle Physics with all their successes and problems. [*].BEC

Key words: Structure of spacetime at the Planck Scale, Planck particle, physics at the Planck scale, shell particle, plancksphere, infinitesimal sphere, archetypal sphere, sphere dynamics

Introduction
There are many concepts about the nature of the first particle. This article postulates that it is defined by the most basic structural and dynamic values of a most-simple sphere and that is further defined by the four Planck base units of time, length, mass, and charge. Of course, it is many orders of magnitude smaller than a fermion (neutrino) and is too small to show up on any measuring device. It would be considered categorically as we do dark matter and dark energy.

Naming: Planck Particle or Planck Sphere or infinitesimal sphere.
Some will want to call it a Planck Particle. That term has been used by others where there seems to be a consensus that this hypothetical particle is a tiny black hole whose Compton wavelength is equal to its Schwarzschild radius.[1]

For our current considerations, the 1916 calculations by Karl Schwarzschild for Einstein’s field equations “…for the gravitational field outside a non-rotating, spherically symmetric body with mass” is placed on a bit of a hold to determine how it fits in with our emerging model. Although quickly celebrated, Schwarzschild’s original work within our postulated model evokes Alfred Whitehead’s (Process and Reality, 1929) concept, a fallacy of misplaced concreteness. The concept of “a tiny black hole” is too quickly used as a primary definition upon which to draw too many conclusions about the role and place of its exacting numbers. It should also be noted that Compton’s wavelength is also placed on hold and John Wheeler’s concept of a blackhole did not emerge until 1952, and effective use, not until the 1960s.

All these definitions have a place and role. Compton’s wavelengths should play a more exacting role as the studies of each hypothetical particle becomes a key piece of this larger puzzle. Where the current physics community sees a black hole, we see a space-time particle with a vast array of variables. Within their linear view of space-time, there is no conceptual space within which to breathe, imagine and postulate anything up to the electroweak scale. Within our base-2 exponential view, there are no less than 64 doublings to consider.

Any postulation about the first instant, the first sphere, and the first moment of space-time ought to be part of the most-complete picture. Yet, to my scant knowledge, most of these postulations have not been defined within the first 64 of 202 base-2 doublings of those four Planck units. That grid of 202 doublings starts at the “first particle” and first moment of space-time and goes to the current expansion of the universe and current time right now. Our chart follows the numbers.

The term, Planck Sphere, has been used by several scholars; the work of Victor J. Stenger [2] stands out. In his book, The Comprehensible Cosmos: From where do the laws of physics from?, he says, “The energy density within that sphere, for this brief moment, will be on the order of (1038)/(10-33)3 = 10121 electron volts/cm3 which we call the Planck density. This density would be equivalent of a cosmological constant.” And later he says, “…a Planck sphere is akin to a black hole whose entropy is maximal for an object of the same radius.” It appears that the general consensus of the academic community is with Stenger, a Planck sphere is akin to a black hole. [3]

Thus, naming the first particle is not straightforward. For now, the simple term, the first particle, will be used along with “infinitesimal sphere.” The hadron was the last confirmed particle in 2012. Again, this first particle is highly speculative and many orders of magnitude smaller than any hadron. Nevertheless, someday this first particle may be considered for the Wikipedia topic, Timeline of Particle discoveries? [4]

Parameters as mechanisms
Our definition of a sphere starts with continuity-symmetry-harmony defined within pi.). The very nature of those dynamics establishes the basis for homogeneity and isotopy. Also, stated in prior articles, there is a natural inflation. Quantum mechanics and its indeterminacy only begin to emerge within geometries of indeterminacy. [5] Although not a topic that attracts much attention, the emergence of very specific geometries through which quantum fluctuations could become a major component of emergence studies.[6] The implications of those geometries have not been fully considered and, even less so, that prior to those notations where indeterminacies (quantum fluctuations) actually manifest, states of perfection can be logically inferred. Highly speculative, our goal is to use our most simple formulations within logic to engage those parameters (principles) and mechanisms (functions) that give rise to mathematics and physics (and eventually all the other sciences).

Within this model, as developed in several prior articles, the infinite is profoundly within the finite. It is not finite, but actively and constantly imparts qualities to the finite. So, yes, those scholars who follow David Hilbert are asked to stay open. Pi’s three primary facets of the infinite are real realities of every circle and sphere. These qualities condition the finite.

Extending the discussions about Theano on Pythagoras, that statement above has become the byword of this website. To carry it a step further, a priority is given to defend this statement, “Everything-everywhere-for all time is also necessarily an expression of exponentiation, Euler’s number, e, and the Buckingham pi theorem.” The challenge to unpack such postulations is further complexified by the dimensionless constants of the Planck base units and the distinct types of harmonic functions necessarily part of every sphere. We postulate that this first particle is the archetypal form and function of all particles, strings, and automorphic forms.

Shell Particle
The first particle is anything but simple. It is the encapsulation of many facets of the infinite (continuity-symmetry-harmony) and the bridge between the finite-and-infinite. It is projected to be a shell for hypothetical particles as well as all known particles. Within the first 64 base-2 notations, the configurations within that shell are virtually infinite. With a very-small measure of confidence, I project that Langland programs, strings and M-theory, and SUSY can all be readily worked into the dynamics of those 64 progressions.

Expansion
From earlier discussions about Infinitesimal spheres stacking and packing
, and given one particle per Planck unit of time and length, the rate of expansion using Planck Time computes to over 539 tredecillion particles per second. Dimensional analysis and our much earlier interactions with Freeman Dyson may cause us to adjust that statement. This rather different cosmological constant, 539 tredecillion particles per second, unfolds our base-2 chart of just 202 notations. Between Notations 143-144, Planck Time is one second and Planck Length computes to be 299,792,422.79 meters. That calculation, Planck Length divided by Planck Time, is within .001% of the NIST/ISO value for the speed of light set in 2019. The extrapolations for each of the 202 notations are within a range of .001% to .1% of the speed of light. Analyses of those figures are ongoing. Analyses to discern other well-known values throughout the chart are also ongoing.

Quantum openness
With these studies, quantum mechanics is considered an artifice of geometry that only manifests with a five-tetrahedral structure (and as of May 2023, five-octahedral structures as well) sharing an edge that creates a 7.356103+ degree gap. This natural gap is also within every expression of dodecahedral and icosahedral structures; here spatial dynamics are currently generally classified as quantum fluctuations. Such fluctuations are not an inherent part of the first particle and possibly other classes of particles (See Wikipedia).

The 202 Notational Grid
To add to the many variables already cited, in many earlier articles, it has been stated that all notations are always active. Every notation within the first 64-to-67 notations are profoundly active and dynamically changing. Such a concept redefines space-time and it redefines “the Now.”

That first particle has no less than four variables of the Planck units, the three primary variables of the the three facets of pi (π), the dimensionless constants within the Planck base units, and the many expressions of harmonic functions generated within every sphere. Cubic-close packing of equal spheres further complexifies as it generates new forms and functions within the tetrahedral-octahedral structures. With every prime number notation even more possibilities unfold. Then every prime number base progression adds another possibility. Where does it stop? It’s anybody’s guess! And, yes, there have been a lot of facts and guesses since the days of Einstein and Planck.

Our challenge now is to examine our emerging model in light of the bleeding edges of physics. We all know the answers; we simply have not properly defined the playing field and its most basic forms and functions. That is the purpose and goal of these studies: Langlands programs, String theory and M–theory, SUSY (including work Beyond the Standard Model), Causal sets and causal set theory, Loop Quantum Gravity, Scalar Field Theory, Spectral Standard Model and Causal Dynamical Triangulation. [7]

Within our simple model, the universe is just beginning and already it has the potential for far more complexity than within existing models as currently understood. It doesn’t discount any prior work; our work is to context it so these studies open even more potentials for diversity than so far imagined.

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Footnotes & Endnotes

* Our models and our scholars. It seems that the search is for three master keys: (1) a Finite-Infinite key, (2) the “Integrative Systems that Structure the Universe” key, and (3) the “Redefinitions of Space-Time (Mass-Charge)” master key. There are many prior homepages that touch on these three topics and there are many ways to access those pages. One of my favorite ways is to click on the left arrow at the top of each page. That will take you back, homepage by homepage, to the beginning of this website in August 2016. Work on these concepts, particularly the base-2 progressions, started in a high school in 2011. Here are my presuppositions that fall outside the mainstream: https://81018.com/presuppositions/ The definitions of a perfected state, particularly the continuity-symmetry-harmony expressions began back around 1971.

[1] Schwarzschild radius. Michel M. Deza; Elena Deza. Encyclopedia of Distances. Springer; 1 June 2009. ISBN 978-3-642-00233-5, p. 433. (PDF) Also: See Wikipedia: Karl Schwarzschild and The Planck Particle today: http://www.scientificlib.com/en/Physics/LX/PlanckParticle.html

[2] Victor J. Stenger, The Comprehensible Cosmos: From where do the laws of physics from? (2006), Prometheus Books, pp. 134, 295, and 298. Also see: A Scenario for a Natural Origin of Our Universe, (PDF), arXiv:0710.3137 [gr-qc]

[3] Victor J. Stenger, Defending The Fallacy of Fine-Tuning (PDF), p. 7, 2012, arXiv:1202.4359

[4] Particle discovery. Wikipedia’s Timeline of Particle discoveries, retrieved January 10, 2022

[5] Geometries of indeterminacy. Wikipedia, Quantum indeterminacy, retrieved January 10, 2022 Also, see my earlier work, Determinant becomes undecidable, uncomputable and unpredictable.

[6] Indeterminacy. Mysteries in Packing Regular Tetrahedra (PDF), Jeffrey C. Lagarias, Chuanming Zong, 2012

[7] Logic and Puzzles. Wikipedia topics: (1) Langlands programs, (2).String theory and Mtheory, and (3) SUSY (including work Beyond the Standard Model), (4).Causal sets and causal set theory, (5) Loop Quantum Gravity, (6) Scalar Field Theory, (7).Spectral Standard Model and (8) Causal Dynamical Triangulation.

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Editor’s notes: Perhaps it is not evident, but I try to write as if I had a group of high school students and other teachers all collaborating with me, reading every word. Perhaps eventually we’ll get out of the weeds and closer to first principles and the first particle. To that end, the most dynamic part of this page follows. These are the evolving references, emails, and instant messages, yet be forewarned, sometimes these people are quite deep in the weeds! -BEC

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________Prior / Next

Go to back to prior references from within this website. Also, review these earlier documents:
1. This work began in 1971 within the study of the 1935 EPR paradox.
2. It was part of a conference at MIT in 1979 in search of first principles.
3. There are many pages that consider the first instants of the universe.
4. There are also these presuppositions and assumptions.
5. Equally speculative is the concept that these foundations give rise to our ethics and values.
6. My struggle page. It’s among the current pages being updated, yet quite incomplete.

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Emails

1. Christoph Schiller: A classically-trained physicist at Universität Stuttgart (Germany) and received his Ph.D. in physics at the Université Libre de Bruxelles (Belgium), and a most-creative spirit and talent for writing about technical concepts for the average person. I believe his six volumes on the foundations of physics can help fill in some of the gaps in my education.
2. Pierluigi Poggiolini: One of the world’s leading research scientists, a specialist within optics, light, and nonlinearity, his work challenges us to figure out a way to test our concepts.
3. Elena Deza: Author of Dictionary of Distances (with Michel Deza, Elsevier, 2006), Encyclopedia of Distances (with Michel Deza, Springer, 2009; 4th ed., 2016) and others, she is a professor of mathematics at Moscow State Pedagogical University.
4. Chiara Marletto: A Research Fellow within the University of Oxford’s Physics Department of University of Oxford, she is an active member of Wolfson’s Quantum Cluster and of the New Frontiers Quantum Hub. Her work on constructor-theoretic concepts caught our attention.
5. Karl Schwarzschild: A Letter to A Legend (first draft)
6. : Her team brought to life The Routledge Handbook of Emergence (2019). With Robin Findlay Hendry and Tom Lancaster, that book is filled with different types of analysis of emergence. Searching for some corroborative work, the concept of an actual geometry for indeterminacy was not found. The concept is still quite naive and young.
7. Karen Crowther: Author of Appearing Out of Nowhere: The Emergence of Spacetime in Quantum Gravity(PDF), 2015, she is a professor of the foundations of physics at University of Oslo.
8. Moataz H. Eman: Author of Covariant Physics: From Classical Mechanics to General Relativity and Beyond, Oxford University Press
9. Molly Ball: Time Magazine, National Political Correspondent.
10. Arthur Holly Compton: A letter to a legend, Nobel laureate, 1927, whose work opened the way to quantum indeterminacy.

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IM

@EtheHerring @Exconsul @DurhamIAS @Routledge_Phil The Routledge Handbook of Emergence opens key concepts. How did it all begin? What is the most basic building block? Here is a very different model — https://81018.com – a mathematically integrated universe.

Sent to many others: If there is ever going to be a little harmony in this world, we’ll need to break out of our little worldviews for an integrated view of the universe. Here’s a simple start: https://81018.com

Here’s a variation on that theme:

@TIME @mollyesque (Molly Ball, Time Magazine) We’re all tied up within narrow worldviews. Thanks Isaac Newton! We need a mathematically-integrated view of the universe. We started in December 2011 in a New Orleans high school — https://81018.com/home/ It works. And it places today in proper context. It’s simple; not easy!

@TheEconomist The world is not enough. We are discombobulated people because we live within narrow worldviews; a highly integrated view of the universe is needed to understand each other and even basic ethics. http://81018.com and https://81018.com/ethics/

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Invitations and Collaborations

With whom do we collaborate? Of the hundreds of people who visit this site every month, who among them might want to extend a right hand and say, “Let’s work together.” Our only thrust is that the foundations of this universe and life itself be seen in light of infinity and the continuity-symmetry-harmony that the infinite engenders. Please, talk to us. Thank you. -Bruce

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+ About the two dates at the top of the home page Close to 6 AM (TZ-19 or USA CST) each day, the days listed at the top of this page get advanced by one digit. It should be a relatively easy program to write, yet I rationalize that I do it manually just to remind me of our granular (sun-to-earth) sense of time. TZ-19 is time zone #19 assuming that the International Date Line is #1 and Greenwich Mean Time falls within Time Zone #13 (TZ-13). Notwithstanding, we all learning that the only time is Now.

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# Beyond Limited Worldviews

Abstract. Most everything starts simple. Our base-2 outline of the universe starts with the first instant of space-and-time (for now, we’re using Planck’s base units, taken-as-given, and assumed to manifest as a primordial sphere). Calculated with dimensionless constants, Planck’s units also define a rate of expansion. The role of pi, the finite-infinite relation, basic geometries, and quantum fluctuations are explored. Issues within big bang thinking are also explored within this alternative model. -BEC

Introduction: Eight key points constitute the foundations of this emergent model of the universe: (1).Key Numbers, (2).Key Geometries, (3).The Heart of Dynamics, (4).Finite-infinite and all their dimensionless constants, (5).Perfections, (6).Imperfections, (7).Mind-values-consciousness, and (8).Everything, everywhere, for all time. A discussion about each point follows.

1. Numbers are used to grasp continuities, order, and time.

Numbers define: Assumed are primordial numbers like those calculated by Max Planck (1899) and by George Stoney (1874). Scholars like John Ralston (University of Kansas, 2021) advocate for new calculations based on current knowledge, yet Planck’s results create a conceptual basis for working parameters and boundaries. The numbers can always be tweaked. Taken as a given, his numbers give us a place to start. Though in part metaphorical, we have a starting point of the universe. With the calculation of the age of the universe, we also have an endpoint; one might call it “Today” or perhaps “Right now” or even the “current point.”

Also, between the smallest number and largest number is every possible second and every infinitesimal part of every second. It is all encapsulated, accounted, and grouped; and, simple boundaries and largest-possible scale are established. [1]

2. Geometries are used to grasp symmetries, relations, and space.

Shapes define the look-and-feel of the first instant. Lemaître intuited a primordial atom. Within our emerging theory, it is an infinitesimal primordial sphere defined by dimensionless constants starting with pi (π). Pi reaches beyond the finite and provides our first look at the nature of the infinite. Pi, a key dynamic ratio, is never-ending and never-repeating, always the same and always changing. Everybody knows pi but none of us know it very well.

Geometries at work. In 2011 in our high school geometry classes, we chased tetrahedrons and octahedrons, going within, smaller and smaller. From our classroom model to the Planck length there were just 112 base-2 steps by dividing the edges by 2 and connected the new vertices until we were about as small as Planck’s length.

Then, when we multiplied Planck Length by 2, there were 112 steps to the classroom and just 90 more steps to the edges of the universe. Our working chart of 202 notations began to emerge in 2014. We then engaged the far-reaching Langlands programs. We studied a bit of string theory and M-theory. But, when we finally learned about cubic-close packing (of equal spheres), we began thinking that we just might be onto a different model of the universe. Ours had simple numbers, well-explored and generally-understood concepts, and potentially every possible geometry from the first instant, i.e. the very start of the universe.[2a]

Within the heart of our geometries. Planck’s infinitesimal numbers pushed us into a very different logic. Here dimensionless constants dominate. And among all the constants, pi dominates. Then we identified three facets of pi, continuity, symmetry, and harmony. How could such a dimensionless constant be finite? Is “never-ending and never-repeating” finite?

Intuiting the essence of pi. Quickly we ran into the closed-or-open universe debates. So, we postulate that the universe is finite and infinity is totally other. We postulate that infinity is the source for pi and the other dimensionless constants such that pi reaches between the finite and the infinite. Then, we postulate that pi’s first finite manifestation is a primordial sphere — the first sphere and first thing in the universe.

Imputing boundaries and boundary conditions. Base-2 is a most simple means to sort all the seconds and parts of a second that define our universe. Symbolically and analogically, we’ve used Planck’s numbers from his 1899 calculations to create our working chart of the universe. And yes, the result is the 202 notations to encapsulate the universe — all time, all space, everything, everywhere. Like a DNA sequence, numbers define and shapes define. [2b]

3. And, dynamics are used to grasp continuities-symmetry in motion.

We assume all notations are always active. Each builds on the prior; therefore, only the current notation has time asymmetry. That key issue is being addressed in several ways, albeit it’s one of our youngest issues among many open issues within this emerging theory. [3a]

The number of notations, of course, is not the key. The concept of a grid from the first moment to this day is. Again, using Planck Time, we go from the first moment to the first second (Notation-143) to the first light year (Notation-169), and then to 370,000 years (Notation-187) for recombination, to 300 million years (Notation-196) for large-scale structure formation, to the first billion years within Notation-198 to this very time right now (Notation-202). And, yes, these numbers outline aether theories which would include lattice Higgs theories!

The stacking and packing of spheres is a key activity and a natural inflation. By following the progression of Planck Charge and Planck Mass, we find that there is more than enough heat for the Quark-Gluon Plasma (QGP) between Notations 134-and-135. Using Euler’s base-2 exponential notation, from a cold start (very close to absolute zero), the QGP begins within the first second.[3b]

Natural Inflation: One primordial sphere per primordial unit of length. The thrust for an expanding universe starts with one primordial sphere per unit of primordial time. If the expansion is then calculated for just the first second, using Planck’s base units, PlanckTime generates 539-tredecillion spheres per second. StoneyTime generates 4605-tredecillion spheres per second. Those numbers are necessarily woven together with Planck Mass, Planck Charge, and the speed of light.

4. We assume a necessary, always-active, finite-infinite relation.

Finite-infinite. Many scholars say that infinity is messing up science. Perhaps their concept of infinity is incomplete. Perhaps they do not think about the origins of dimensionless constants. Now, we have a very large number of infinitesimal primordial spheres per second coming from somewhere. If we say “infinity” most scholars will have a problem. Yet, if we say that pi is the concrescence of continuity, symmetry and harmony, and that looks like a sphere, there will be fewer problems. If we say that the qualities of continuity, symmetry and harmony define the infinite, I believe we should stop and contemplate that.

Think. Reflect. Be gracious… because that is exactly what is being asked of every scholar-scientist-student.

Infinitesimals. Creating a transitional logic, infinitesimals challenge us to begin to grasp the dynamics between the finite and infinite. If on one hand we open the definition of the infinite and on the other we radically limit its scope, we might begin to understand how infinitesimals relate to strange things like blackholes, singularities, multiverses, and all our hypothetical particles proposed over the years.

Science is the continuity and symmetry that start within the sphere. And, science is also the harmony that is found deep within the sphere’s Fourier Transform. Continuity has simple values: order… memory. Symmetry has more complex values: relations… balance. And harmony has the most complex values: continuities-and-symmetries in motion. It is life, consciousness, and perhaps all our other values, even hope and love.

Those values, continuity-symmetry-harmony, define pi. Taken all together, they also define the infinite.[4]

Categorically, infinity is continuity, symmetry and harmony, nothing more and nothing less. All metaphorical, confessional, or personal language is left to the individual. We can respect each other’s privacy and personal beliefs; we are hoping that you can respect ours as we search for the most simple truth; and for us, that opening line of this paragraph seems to be it for now.

5. We assume domains of perfection...

In the face of quantum fluctuations. In light of the 202 notations, the focus is first between Notation-64 and Notation-67, a range within which current research detects fluctuations. It begs the question about what is happening between Notations 1-and-64. If cubic-close packing is generating basic geometries within densities that are on the order of neutron stars (based on Planck’s numbers), one can imagine that only the most efficient combinations of points, lines and geometries manifest. There is a thrust of simple perfections; yet, there are also many more factors to analyze that could interrupt a flow of the geometries of a simple perfection. [5]

6. We assume domains of imperfection (quantum fluctuations).

One possible indeterminacy that could give rise to quantum fluctuations is the gap created by five tetrahedrons sharing a common edge. If systems begin to manifest around Notation-50, there could be many notations where indeterminacy prevails but is too infinitesimal to be measured..[6]

7. There’s a place on this grid for the Mind-consciousness-values.

Further considering the continuity, symmetry and harmony within pi. Throughout our brief history as a civilization, the wise among us have said something like, “Truth sets you free.” Surely the best of science has empowered us. The best of science has liberated the human mind. Yet, freedom is a rather value-laden word and I would argue that at its core, science begins with the continuity that we first find within the sphere.

Pi, spheres, infinitesimals and notations are well-known parameters within science yet at no time have those parameters been applied to the first instance of the universe. The progression, Notation 1-to-64, have not been formally engaged. Within one of our early charts, we made groups of ten notations and postulated Forms (like Langlands programs and automorphic forms) develop in the first ten notations, 2-11. Archetypal Structures develop in the next ten, from Notations 11-20. Archetypal Substances developed in the next ten, Notations 21-30. Here within these thirty notations might be the hypothetical particles that mirror the particles within the Lambda Cold Dark Matter (ΛCDM) model and the Standard Model for Particle Physics. From Notations 31-40, Archetypal Qualities, were given a place along the grid. And from Notations 41 to 50, Archetypal Relations, were postulated. From those five groups, Archetypal Systems were then postulated (Notations 51-60). Here within these notations was the beginning of systems theory, the Mind, consciousness and values. It is all physical. Yet, the physical systems measured by our most sensitive devices like the Large Hadron Collider can only measure effects from around Notation-65 and larger.

So, within those 65 notations, perhaps even more boldly, we will continue to consider further how these infinitesimal spheres manifest the Fourier transforms and all other integral transforms. These dynamics are so rich, surely here are the very keys for electromagnetism and gravity and the yoke that ties them together. [7]

8. Everything-everywhere always affects everything-everywhere.

Our history is so short, so minuscule, and we’re on a step learning curve. And, describing this infinitesimal universe has been problematic. Now, we are not scholars, certainly not a cosmologist nor astrophysicist. We are high school people, but that has not stopped us from discovering Tim N. Palmer of Oxford and his work with Invariant Set Theory, or Simon White of the The International Max Planck Research School on Astrophysics in Munich who is developing a Cold Dark Matter paradigm.

We have asked for advice from many people — “What are we doing wrong?” We have so many more questions. [8]

Where pi has continuity from the first moment of time to the current time, phi (φ) has a very different ordering principle that appears to be limited within each notation. There may be other kinds of fluctuations where these two ordering principles seat together. It is ideation that is currently being explored.

Many brilliant scholars have been working on these problems from quite a different perspective. None have acknowledged the simple outline created by the 202 base-2 notations. To say the least, our first 64 notations are enigmatic. Although infinitesimal, Notations-65-to-67 are on the edge of our measuring capabilities of our finest instruments (i.e. the LHC, CERN, Geneva).

Notwithstanding, we can apply logic and intuit the dynamics of Notations 1-to-64. Here is the basis for a natural inflation and homogeneity and isotropy. Here is dark energy and dark matter. Yet, here, too, is a domain of perfection prior to quantum fluctuations. And, yes, our universe looks and acts like its exponential.

We recognize how idiosyncratic such statements are. For many our work would naturally be characterized as crackpottery. Yet, this is just our beginning. If we take the base units as defined by Planck or Stoney, densities are in the range of neutron stars and blackholes. It is a very different picture of our expanding universe. Yet, the enigmatic and idiosyncratic may be necessary to open new paradigms of who we are and why.

Thank you. -BEC

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Endnotes

Concepts and ideas. On my path, I have met a few of our finest living scholars. All struggle. It’s never easy even though a few make it look easy. Many of us do not have the finesse of others and our work is written off too quickly. There are so many ways to interpret a data set like the chart of 202 notations. When the data doesn’t cohere or leaves questions unanswered, theories provide temporary work-arounds. Our theory has been known by many names. Big Board-little universe captured the sense that space and time are disintermediated and the two need to be redefined. Quiet Expansion was our simple way to distance ourselves from the Big Bang. Yet, the most descriptive was “the Mathematically-Integrated View of the Universe.” This model, to my knowledge, is the only one that outlines the universe with mathematics — both numbers and geometries — with causal efficacy from the first instance to this very moment. It is based on unique assumptions and presuppositions. Once all 30 of our presuppositions have, in some manner, been engaged, we believe there could be a profound intellectual awakening and possibly a resurgence of ethics. -BEC

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Footnotes

[1] Boundaries & Parameters. First we have a start time 13.81 billion years ago. Then we have our current time. Just like DNA, every moment has its special numbers that identify it within the universe. Every instant using base-2 is part of key continuity equations. Like Emma Iwao’s 31 trillion digits of pi (31,415,926,535,897) that are never-ending and never-repeating (always changing and always the same), here is the heart of our horizontally-scrolled chart of the universe. Of course, the first continuity equation is Planck Time to the current time. Planck Length to the size of the universe is next. Then, Planck Mass to the total mass of the universe and Planck Charge to the total charge in the universe follows. It is a bit too much to grasp and its veracity is questioned and explored throughout this website.

Keep questioning everything. We get bored and dull if we don’t. For many years (and within some quarters, even today) if you questioned the big bang, you’d be laughed out of the room. Part of our problem is our arrogance that cuts off intellectual discussion. For example, many scholars are sure that science is value neutral. That’s just a bit of silliness. Its deepest definitions exude value and values. Eventually we’ll realize that we have adopted old constructs that impede our thinking and our sciences. Here are three:
Hawking’s infinitely-hot big bang start holds us back. It blocks a cold start.
Newton’s cosmology of absolute space and time suffocates us. It blocks the current point.
Aristotle’s failures with geometry truncate creativity. It blocks our grasp of indeterminacy and creativity.

[2a] Geometries have been making a comeback. Topology, shape theory, representation theory, category theory, Langlands programs, string theory (M-theory) and supersymmetries (SUSY) are all mathematical formulations that have a place on our grid. Base-2 is the simplest grid. Mathematical realities are precursors of physical realities. These and many other disciplines need the first 64 notations out of the 202 that outline the universe and redefine space-time and infinity. A simple function like cubic-close packing of equal spheres can take its place as a most-simple, key function of our universe. Why not?

[2b] Continuity is numbers. And, numbers define a face of continuity. Inculcating the spirit of Pythagoras, we first turn to Theano, On Piety (as reported by Thesleff, Stobaeus, and Heeren), “…he did not say that all things come to be from number; rather, in accordance with number – on the grounds that order in the primary sense is in number and it is by participation in order that a first and a second and the rest sequentially are assigned to things which are counted.”

Big bang cosmology lacks continuity. First, it’s too hot. Problematically, it tries to cool things off too quickly. Then, it runs out of energy. And, it fishtails with inflationary excuses.

It is, however, very difficult to imagine that one primordial sphere is generated for every unit of an infinitesimal primordial length. That’s a tall order, but it is logically coherent. The net-net is the generation of a phantasmagorical number of infinitesimal primordial spheres per second. Every second something on the order of the area defined by the path of the International Space Station is created (seemingly out of nothing). Within a year, an area about the size of our solar system is created.

An infinitesimal sphere defined by dimensionless constants has a metaphorical equivalent in every level of science and within each notation. The universe would appear to be constantly testing, changing, and evolving to be more efficient or “more integrated”. It is not difficult to imagine. Stephon Alexander’s group, The Autodidactic Universe, is working on it.

So, again, our essential challenge is to re-engage our understanding of the nature of infinity and to give it some breathing room without all the poetry and mythopoetics.

Our model sometimes called the Quiet Expansion, is a mathematical — both numerical and geometrical– model of the universe and it is entirely predictive.

[3a] Scholars like Neil Turok make similar claims. I thought for sure that Neil Turok and his colleagues, Feldbrugge and Lehners, would quickly embrace our model. They did not. One of their claims is that the universe acts like it is constantly starting. Within big bang cosmology, such a claim is counter-intuitive. Within a cold-start model, it at least has a chance to work. They reached their conclusions from a totally different path. Our first note to them was back in 2016, but they have had nothing to say to us. I think if they could point to something that was wrong, one of them would have said as much. At times scholars can be a rather close-knit group.

In his book, A Different Universe (page 120-121), Robert Laughlin, a Nobel laureate, cautions us about the aether. It is a tainted concept. Notwithstanding, an aether at the Planck scale is not your father-or mother’s aether.

[3b] Scale Invariant Sphere Dynamics. From the infinitesimal sphere to the movement of galaxies, pi and phi (circles and Fibonacci sequences), are fundamental dynamics within everything. Pi crosses notations; phi builds within a given notation. This model not only uses numbers and geometries, it uses pi, phi, prime numbers, values, and more where big bang cosmology is based on singularities that do not account for dimensionless constants like pi. The mathematics of materialism generally disregards other systems of engagement. How is it that pi is scale invariant? What are the deep dynamics of spheres? We are trying to learn… we are in the earliest stages of our studies of the Fourier transforms and integral transforms. Of course, we’d welcome any and all help to understand these disciplines as well as Steven Strogatz.

[4] Scientific truth. The influence of Tegmark, Arkani-Hamed, and Turok on our thinking is substantial. Until we are able to grasp a better definition of space, time and infinity, all scientific truth is relative or incomplete. It is clear that the concepts of continuity-symmetry-harmony have an “extra” scientific truth. Being first derived from dimensionless constants that are not finite, these qualities beg the questions about the very nature of infinity. It may well be true that we have built up the concept over the centuries. Perhaps all that it is are these three basic concepts. Why not?

[5] Perfection. The concept of perfection was increasing minimized as quantum theory developed. All the greats of physics were involved. Starting with Max Planck, Albert Einstein, Niels BohrErwin SchrödingerWerner Heisenberg, and Max Born, concepts like the uncertainty principle, indeterminacy, and quantum entanglement were increasingly mathematically formulated and began dominating scientific thought. Only in 2001 did Planck’s base units receive the kind of scrutiny that would cause them to be lifted up and examined. It wasn’t until December 2011 that we did our little geometric progression back to his base units. It wasn’t until 2015 did we begin examining the numbers assuming that the first instance was an infinitesimal sphere and that pi defined three facets of perfection within the sphere. And because those spheres are the footings and foundations of each base-2 notation, the concept of perfection and a place for perfection was re-introduced within a very limited framework.

[6] Imperfection. In 2011 in those high school geometry classes, we made models of the five-tetrahedral star, the icosahedron and the Pentakis dodecahedron; we called it squishy geometry. The pieces do not perfectly fit together. There are natural gaps. Aristotle made a mistake that was reinforced by academic thinking for over 1800 years. Even after the mistake was discovered in the 15th century, it had to be rediscover in 1926 and then again in 2010 and still there has been no general debate about the significance of five-tetrahedral star and its gap. Here is one profound imperfection built into the very geometries of the universe and it is largely ignored. Here is one critical gap and a place for quantum physics. There are possibly several other equally important places that will be discussed in future homepages. This is a topic of ongoing analysis.

[7] Transformations. Within the panoply of “big bang” cosmologies, the Fourier transform is ignored. Pi and the simplest geometries are as well. If we are to create a working theory, it seems that it should start simple and begin building as best we can using simple concepts. In our model of the universe, the most basic tools of mathematics and science are, by design, all used progressively, building off of one another. In this model there is a place for Langlands programs. There is a place for point-free geometries. There is a more fundamental place for binary functions, scalar field theory and Lagrangian field theory. It is all a bit much for high school people, yet our intuitions help to guide us.

[8] Out on the edge. The eight scholars pictured — Stephon Alexander (Brown Univ.), Mansoora Shamim (CERN), Nima Arkani-Hamed (Institute for Advanced Study-IAS), Sabine Hossenfelder (Frankfort IAS), Ard Louis (Oxford), Emma Haruka Iwao (Google), Thanu Padmanabhan (Inter-University Centre for Astronomy and Astrophysics), and Claudia de Rham (Imperial College London) — each represent a facet of what might be called bleeding-edge research. Earlier Sylvester Gates had been pictured. A result of our engagement with their work is the linked resource page with our notes and emails. Some scholars, people like Renate Loll and Lee Smolin (Causal Dynamical Triangulation or CDT) have never responded to our emails, so progress with CDT has been slow.

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References

• Stephon Alexander: The Autodidactic Universe (PDF), 2021: The universe learns its own laws by exploring a landscape of possible laws (a class of matrix models) and constantly evolves. Stephon Alexander has his six co-authors. Their work has parallels with the elemental principles of our model: 1) each notation builds on the prior, 2) all notations are always active, 3) there is a dynamic, never-ending relation between the finite and infinite, 3) the facets of pi help us to understand a perfection within the finite which is the perfection of the infinite which is continuity-symmetry-harmony, and 4) continuity-symmetry-harmony are facets of the infinite creating, the order, relations and dynamics within the most infinitesimal spheres.
• Ard A. Louis: Generalization bounds for deep learning, Guillermo Valle-Pérez, Ard A. Louis, arXiv:2012.04115v2, December 2020 With some caution, it seems that our theory complies with the requirements for a theory for deep learning, i.e. such a theory would readily scale with data complexity. In our theory we eventually scale to include everything everywhere for all time. We’ve become a de facto school to capture the differences between the architectures within the first 64 notations. It is entirely computable on the surface and we are confident it will accommodate the differences between any and all optimization algorithms. We had been familiar with prior work by Ard Louis and from this December 2020 ArXiv article we will now turn to others within the deep learning space.
• Thanu Padmanabhan: Planck length: Lost + found, Thanu Padmanabhan, Elsevier, Science Direct, Physics Letters B, Volume 809, 10 October 2020. Thanu Padmanabhan has been focused on the Planck scale as long as anybody living today. It is a domain of the mind. It cannot be reached by anything other than logic and mathematics. One might think that at such an infinitesimal scale, there is an absolute convergence of time, space, matter and energy. It all becomes a singularity. It is a viewpoint now echoed throughout the scholarly world. For me, it begs the question, “What are Planck’s four base unit calculations? Shall we ignore them?” I don’t think so. Padmanabhan tells us that a “relativistic point particle is a zero dimensional object.” I am not so confident. Even though these calculations look like a “point” particle, all the dynamics of the dimensionless constants that define those units are theoretically scale invariant; those characteristics or qualities do not go away. The classically-schooled scholars still think in terms of the qualities of particles and waves when those calculations are quite obviously much smaller than any wave or particle measurement. We can only know that these physical things exist mathematically. As high school people we found that there are no less than 64 base-2 steps to get into the most infinitesimal Planck scale state. It would seem that each step defines a very unique reality. More to come regarding his comments about the (Feynman) propagator and his 1988 examination of the conceptual framework for blackholes.
• Claudia de Rham: Although much of Claudia de Rham’s work is co-authored with others and they use specialized language within very unique conceptual settings, her videos and interviews tend to be more general and generally more self-aware and critical of their collective progress. She is her own best critic and has a delightful sense of humor, so as we go forward, we’ll try to weave a path between her public expressions and her very challenging research. So, yes, there’s more to come.
• Nima Arkani-Hamed. He may forever be known by his lecture in Cornell on October 6, 2010 and for his statement, “Spacetime is domed.” It provoked lots of discussion. I say that a key to a transformative concept of spacetime is to establish its boundaries, then its boundary conditions. We have a symbolic or metaphorical start with Planck’s units. If we accept as a given that the calculations for the age of the universe are close enough, we have a range. If we apply a mathematical construct, Euler’s base-2, we have a process. It is simple and builds on prior work: period doubling bifurcation, Feigenbaum’s constant, PoincaréThe 202 notations become functional. The first second comes out within Notation-143. The first light year is within Notation-169. The first billion years emerges toward the end of Notation-198. Every notation builds of the priors. All time is active. All space-and-time share that emergence and thus spacetime is being redefined. There’s an alternative.
• Emma Haruka Iwao: The Endless Number. It took a single-minded dedication for Emma Haruka Iwao to singlehandedly introduce the world to the largest possible number in all of creation. From her early childhood she has had a fascination with pi. She may not be Archimedes, yet her work runs circles around him. She has pulled pi out of the finite. And, we proclaim that it is the bridge between the finite and infinite. We further claim that the facets of pi — continuity-symmetry-harmony — are the very definition of the infinite. That’s it. Stop there. We do not need the millions of books about infinity and the infinite. Pi gives us the infinite in a nutshell and Emma Iwao pushes our nose right into it. Here is where we should begin our theories about the start of the universe!

You’ll find squarks and gluinos in the pages of the Standard Model of Particle Physics but both remain illusive. Why? Could it be that all the mathematics that define these hypothesized particles are just “too infinitesimal” for the Large Hadron Collider? Dr. Mansoora Shamim just might be able to tell us so. She may be the one who opens a path to Notation-64.

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Communications: Emails

1. Short emails to those mentioned within the article: Includes Simon White, Tim.Palmer, Renate Loll, and Lee Smolin. We started with Stephon Alexander, Mansoora Shamim, Nima Arkani-Hamed (also on a recent homepage), Sabine.Hossenfelder, Ard Louis, Emma Iwao (recently on this homepage), Sylvester Gates, Thanu Padmanabhan and Claudia de Rham.

2. Email to Robert Laughlin: “Deep inside the tetrahedron (and its octahedron within), this dynamic GIF (Graphics Interchange Format) showed us how both were derived from spheres (cubic-close packing or sphere-stacking in action). When we started to follow pi back to its source, continuity-symmetry-harmony were deep within. Acknowledging a symbolic starting point (defined by some analogue to the Planck Length and Planck time), space and time became derivative, finite, and quantized. When Newton’s absolutes are tamped down, a dynamic finite-infinite relation opens up. Here, pi, as the key dimensionless constant, is quantitative in practice while her infinite expression is qualitative. We had a start of the universe with a single, infinitesimal sphere, Lemaitre’s 1927 long-sought-for primeval atom.

3. Email to scholarly collaborators with the scholars mentioned above: Guillermo Valle Perez (June 22).

Opening the Pandora’s box at the core of black holes, Raúl Carballo-Rubio (Corresponding author), Francesco Di Filippo, Stefano Liberati, Matt Visser, 2019

4. Google+: Get free of little worldviews. Get the entire universe. Get access to a simple logic. Pi holds clues that opens it all up. Pi is continuity, symmetry and harmony. Continuity-symmetry-harmony is a bridge between the finite and infinite. Learn more here.

5. WordPress: This work and website is to break the impasse created by infinitely-hot big bang theories (versus a cold start — https://81018.com/start/) and by misleading concepts of space and time (https://81018.com/duped/#Newton) and by a failure of Aristotle in basic geometry, a mistake that was repeated for over 1800 years (https://81018.com/duped/#Aristotle). As a result of this effort, we anticipate there could be a profound intellectual awakening and possibly a resurgence of ethics. -Bruce

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Communications: Instant Messages

A complete left turn, I just sent Reed Hasting (co-CEO of Netflix) a note to congratulate him for his past ten years of hard-fought successes. Yet here, I recommend that he incorporate an integrated view of the universe in all that he does.

Magdalena Skipper writes, “Confronting gender bias in Nature’s journalism – at Nature, we know we need to continue to work hard to eliminate gender & other biases.” To which I sent the following Tweet.

@Magda_Skipper No surprise. So going forward, empowering all people is the name of the game. To do it, we’ll all need to break through our limited worldviews so we totally engage the universe, everything, everywhere for all time: http://81018.com No surprise indeed!

Simon Ainslie, NEOM “The thrust for perfection is built into the very fabric of the universe. Continuity-symmetry-harmony, the essence of the circle and sphere, are infinite qualities that are the foundations of the finite, the first moment. To open a way to a sustainable future, build on these three universals defined by the oldest equation in our common history, pi. http://81018.com is a small start on a model of the universe that uses such logic, mathematics, and physics. Until we break through our limited worldviews, our ethics and values will also be limited. Thank you. -Bruce

@rweingarten Of course, “honest history” is perspectival. Our problem is our little worldviews all have differing vanishing points. Only a highly integrated view of the universe has the long history and greatest perspective: http://81018.com is just a start. Note: Randi Weingarten is the president of American Federation of Teachers and in a recent speech she said that she wants her teachers to engage accurate history. In light of the universe, the record of human activity beginning in the 4th millennium BC is all current events. And, very little of it is a pretty picture, but it does tell us who we are to date. Have we changed? Have we grown? How much better can we become? Many, many people are trying hard to keep us growing, learning, and doing good. In this model of the universe, that thrust is built into the universe. See more.

@philipbull Beyond ΛCDM: Problems, solutions, and the road ahead, Physics of the Dark Universe. Thinking about your collective work here: https://81018.com/cdm/ Under References, there is a link to your site. The primary page regarding it all is here: https://81018.com/empower/

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A few final words

In 1980 in Paris at the Institut Henri Poincaré, one day I would be in discussions with Jean-Pierre Vigier and the next day with Olivier Costa de Beauregard. We focused on the EPR Paradox and Bell’s inequality equations. By the time I returned to Boston University later that year, I thought, “Nobody has an answer. You could spend your life spinning in circles.” I collected my books at BU and continued walking. I went back to a business that I had started ten years earlier. Little did I know that by helping out in a high school geometry class (December 2011), all these issues would be reopened. It would take me at least five years to get reoriented to learn what today’s scholars were saying. They’ve made some progress. Many new concepts have been introduced. But unanswered is the question, “How does it all cohere?” Solutions to key issues were still outstanding. I do not have that much more time in my life so I have asked quite a few scholars, “What’s wrong with this picture?” Those 202 base-2 notations, “Is it a framework, an outline within which to work, or not?” I believe it is. -BEC

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There are many ways to be involved:

1. Tweet or email the link to this page to those who you believe would be interested.
2. Complete a survey. There are two surveys, both using simple Yes / No / Maybe answers.

We would celebrate if you could take time to answer the questions of either survey! Copy the questions to an email and send them in with your answers and comments!

• This document: Started on Thursday, June 10, 2021 @ 7 AM
• First posted for collaborations: June 10, 2021 at 2 PM
• It also became a homepage: June 14, 2021 at about 6 PM
• The URL: https://81018.com/empower/
• The Prior Homepage: https://81018.com/re-envision/
• First Headline: Defining a new model of the universe
• Second headline: Grow Beyond Those Limited Worldviews
. . . . . . . . . . . . . . .Adopt an Integrated View of the Universe
• First Tagline: Empowering scholars, scientists, and students of every kind
• Second Tagline: Eight Steps: Scholars, scientists, and many students are helping us.*
• Third tagline: Towards An Integrated Understanding of our Universe
• Another tagline: Let’s go deep and be all-inclusive in our understanding of this Universe.
• Another tagline: Opening boundaries and parameters to context more of our Universe
• Another tagline: We are beginning to grasp numbers & systems that define our Universe.
• Possibly the next homepage: https://81018.com/tredecillion Password: Tredecillion
• The most recent update of this page: Wednesday, July 14, 2021

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# Grasp the numbers and systems that define our Universe

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..Blackhole. | c |.hope.| .PI (π).|. redefined.singularity.| SPHERE.|..TOE |.UP |.VR
|.references |. EMAILS.| IM | PARTICIPATE.| Zzzzs

Abstract. Things start simple. Our base-2 outline of the universe starts with the first instance of space-and-time. For now, Max Planck’s base units are taken-as-given and assumed to manifest as a primordial sphere, defined in part by key dimensionless constants which are all used to calculate Max’s historic results. These units also define a rate of expansion (assuming one primordial sphere per Planck unit of time). The role of pi, a dynamic bridging of the finite-infinite, as well as basic geometries and quantum fluctuations are explored. Issues within big bang theories are also explored.

I invite you to explore an alternative model for the emergence of our universe. -BEC

Introduction: Eight key points constitute the foundations of this emergent model of the universe: (1).Key Numbers, (2).Key Geometries, (3).The Heart of Dynamics, (4).Finite-infinite and all our dimensionless constants, (5).Perfections, (6).Imperfections, (7).Mind-values-consciousness, and (8).Everything, everywhere, for all time. A discussion about each point follows.

1. With numbers we grasp continuities, order, and time.

Numbers define: Assumed are primordial numbers like those calculated by Max Planck (1899) and by George Stoney (1874). Today’s scholars like John Ralston (University of Kansas) advocate for new calculations based on current knowledge, yet Planck’s base units, taken as given, open a conceptual model for the initial conditions, parameters, and boundaries of our universe. Planck’s numbers will be tweaked. His calculations are based on dimensionless constants. Natural units have a special status and give us a metaphorical-yet-clear start of the universe. If the current calculations for the age of the universe are also taken as given, we have a duration and an endpoint we might call, “today’s expansion,” the Now, and even “the current point.”

Between the smallest number and largest number is every possible second and every possible part (infinitesimals) of every second. It is all encapsulated, numbered, and accounted; and, simple boundaries and the largest-possible scale are established. [1]

2. With geometries we grasp symmetries, relations, and space.

Shapes define the look-and-feel of the first instant. Lemaître intuited a primordial atom. Within our emerging theory, it is an infinitesimal primordial sphere defined by dimensionless constants starting with pi (π). Pi reaches beyond the finite and provides our first look at the nature of the infinite. Pi, a key dynamic ratio, is never-ending and never-repeating, always the same and always changing. Everybody knows pi yet it seems that very few know it well.

Geometries work. In 2011 in our high school geometry classes, we chased tetrahedrons and octahedrons, going within, smaller and smaller. From our classroom model to the Planck length there were just 112 base-2 steps by dividing the edges by 2 and connecting the new vertices until we were about the size of the Planck’s length.

Of course, when we multiplied the Planck Length by 2, there were 112 steps back up into the classroom and just 90 more steps to the edges of the universe. We were more than flummoxed; it was all too simple.

By 2014 our current working chart of 202 notations began taking shape. We engaged the far-reaching Langlands programs. We studied a bit of string theory and its M-theory. When we finally learned about cubic-close packing (of equal spheres), we began thinking that we just might be onto a different model of the universe. Ours had simple numbers, well-explored and generally-understood concepts, and potentially every possible geometry from the first instant, i.e..the very start of the universe. [2a]

Within the heart of our geometries. Planck’s infinitesimal numbers push us into a very different logic. Here dimensionless constants dominate. And, among all the constants, pi dominates. And, there we identified three facets of pi, continuity, symmetry, and harmony. How could such a dimensionless constant be finite? Is “never-ending and never-repeating” finite?

Intuiting the essence of pi. Quickly we ran into the closed-or-open universe debates. So, we postulate that the universe is finite and infinity is totally other. We postulate that infinity is the source for pi and the other dimensionless constants such that pi reaches between the finite and the infinite. Then, we postulate that pi’s first finite manifestation is a primordial sphere — the first sphere and first thing in the universe.

Imputing boundaries and boundary conditions. Base-2 is a most simple means to sort all the seconds and parts of a second that define our universe. Symbolically and analogically, we’ve used Planck’s numbers from his 1899 calculations to create our working chart of the universe. And yes, the result is the 202 notations to encapsulate the universe — all time, all space, everything, everywhere. Perhaps a little like a DNA sequence, here numbers and shape define it all. [2b]

3. And, within dynamics we grasp continuities-symmetries in motion.

We assume all notations are always active. Each builds on the prior; therefore, only the current notation, 202, has time asymmetry. That key issue is being addressed in several ways, albeit it’s one of our youngest issues among many open issues within this emerging theory. [3a]

The number of notations, of course, is not the key. The concept of a grid from the first moment to this day is. Again, using Planck Time, we go from the first moment to the first second. Out of 202 notations, the first second is within Notation-143. The first light year is within Notation-169. Then, we go 370,000 years (Notation-187) for recombination, to 300 million years (Notation-196) for large-scale structure formation, to the first billion years within Notation-198 to this very time right now (Notation-202). And, yes, these numbers outline aether theories (and that would even include lattice Higgs theories).

The stacking and packing of spheres is a key activity and a natural inflation. By following the progression of Planck Charge and Planck Mass, we find that there is enough temperature for the Quark-Gluon Plasma (QGP) between Notations 135-and-136. Using Euler’s base-2 exponential notation, from a cold start (very close to absolute zero), the QGP begins within the first second of the start of the universe.[3b]

Natural Inflation: One primordial sphere per primordial unit of length. The thrust for an expanding universe starts with one primordial sphere per unit of primordial time. If the expansion is then calculated for just the first second, using Planck’s base units, PlanckTime generates 539-tredecillion spheres per second. Those numbers are necessarily woven together with Planck Mass, Planck Charge, and the speed of light. If we were to use StoneyTime, it would generate 4605-tredecillion spheres per second.[3c]

4. We assume a necessary, always-active, finite-infinite relation.

Finite-infinite. Many scholars say that infinity is messing up science. Perhaps their concept of infinity is incomplete. Perhaps they do not think about the origins of dimensionless constants. Now, we have a very large number of infinitesimal primordial spheres per second coming from somewhere. If we say “infinity” most scholars will have a problem. Yet, if we say that pi is the concrescence of continuity, symmetry and harmony, and that looks like a sphere, there may be fewer problems. If we say that the qualities of continuity, symmetry and harmony define the infinite, perhaps we should stop and contemplate that.

Think. Reflect. Be gracious… because that is exactly what is being asked of every scholar-scientist-student.

Infinitesimals. Creating a transitional logic, infinitesimals challenge us to begin to grasp the dynamics between the finite and infinite. If on one hand we open the definition of the infinite and on the other we radically limit its scope, we might begin to understand how infinitesimals relate to strange things like blackholes, singularities, multiverses, and all our hypothetical particles proposed over the years.

Science is the continuity and symmetry that start within the sphere. And, science is also the harmony that is found deep within the sphere’s Fourier Transform. Continuity has simple values: order… memory. Symmetry has more complex values: relations… balance. And harmony has the most complex values: continuities-and-symmetries in motion. It is life, consciousness, and perhaps all our other values, even hope and love.

Continuity-symmetry-harmony define pi. They also characterize the infinite. [4]

Infinity is continuity, symmetry and harmony, nothing more and nothing less. Categorically, that’s it for now.

5. We assume domains of perfection...

Facing quantum fluctuations. In light of the 202 notations, the focus is first between Notation-64 and Notation-67, a range within which current research detects fluctuations. It begs the question about what is happening between Notations 1-and-64. If cubic-close packing is generating basic geometries within densities that are on the order of neutron stars (based on Planck’s numbers), one can imagine that only the most efficient combinations of points, lines and geometries manifest. There is a thrust of simple perfections; yet, there are also many more factors to analyze that could interrupt a flow of the geometries of a simple perfection. [5]

6. We all know there are domains of imperfection.

Indeterminacy and quantum fluctuations are inherent in our universe. Yet, many people are unaware of the gap created by five tetrahedrons sharing a common edge and how within the infinitesimal scale it opens the way to fluctuations. If systems begin to manifest around Notation-50, there could be many notations where indeterminacy prevails but is too infinitesimal to be measured..[6]

7. A place on this grid for the consciousness-values-and-The Mind

Further considering the continuity, symmetry and harmony within pi. Throughout our brief history as a civilization, the wise among us have said something like, “Truth sets you free.” Surely the best of science has empowered us. The best of science has liberated the human mind. Yet, freedom is a value-laden word. What is continuity? What is symmetry? What is harmony? Are all three necessarily what defines both the first sphere and the concept of freedom?

Pi, spheres, infinitesimals and notations are well-known parameters within science yet apparently at no time have these three been applied to the first instance of the universe. Also, the progression, Notations 1-to-64, has not been formally engaged within academia. Within one of our early charts, we made groups of ten notations and postulated (guessed, imagined, hypostatized) the following:
1. Forms (like Langlands programs/automorphic forms) develop in the first ten notations, 2-11.
2. Archetypal Structures develop in the next ten, from Notations 11-20.
3. Archetypal Substances develop in the next ten, Notations 21-30.

Here within these thirty notations might be the hypothetical particles that mirror the particles within the Lambda Cold Dark Matter (ΛCDM) model and the Standard Model for Particle Physics.

4. From Notations 31-40, Archetypal Qualities are given a place along the grid.
5. And from Notations 41-to-50, Archetypal Relations are postulated.
6. From those five groups, Archetypal Systems are then postulated (Notations 51-60). Here within these notations was the beginning of systems theory, the Mind, consciousness and values. It is all physical. Yet, the physical systems measured by our most sensitive devices like the Large Hadron Collider can only measure effects from around Notation-65 and larger.

The first 64 notations. We will continue to explore how these infinitesimal spheres manifest the Fourier transforms and all other integral transforms. These dynamics are so rich, surely here are the very keys for electromagnetism-and-gravity and the yoke that ties them together. [7]

8. Everything-everywhere always affects everything else-everywhere.

Our history is so short, so minuscule, and we’re on a step learning curve. And, describing this infinitesimal universe has been problematic. Now, we are not scholars, certainly not a cosmologist nor astrophysicist. We are high school people, but that has not stopped us from discovering Tim N. Palmer of Oxford and his work with Invariant Set Theory, or Simon White of the International Max Planck Research School on Astrophysics in Munich who is developing a Cold Dark Matter paradigm, or Alain Connes (and company) regarding their Spectral Standard Model.

We’ve asked for advice from many people — “What are we doing wrong?” “Is this a theory of everything? How can it have only a picosecond difference with the big bang theory? We have so many more questions. [8]

Where pi has continuity from the first moment of time to the current time, phi (φ) has a very different ordering principle that appears to be limited by notation. There may be other kinds of fluctuations where these two ordering principles seat together. It is ideation that is currently being explored.

Many brilliant scholars have been working on these problems from quite a different perspective. None have acknowledged the simple outline created by the 202 base-2 notations. To say the least, our first 64 notations are enigmatic. Although infinitesimal, Notations-65-to-67 are on the edge of our measuring capabilities of our finest instruments (i.e. the LHC, CERN, Geneva).

Notwithstanding, we can apply logic and intuit the dynamics of Notations 1-to-64. Here is the basis for a natural inflation and homogeneity and isotropy. Here is dark energy and dark matter. Yet, here, too, is a domain of perfection prior to quantum fluctuations. And, yes, our universe looks-and-acts like its exponential.

We recognize how idiosyncratic such statements are. For many our work would naturally be characterized as crackpottery. Yet, this is just our beginning. If we take the base units as defined by Planck or Stoney, densities are in the range of neutron stars and blackholes. It is a very different picture of our expanding universe. Yet, the enigmatic and idiosyncratic may be necessary to open new paradigms of who we are and why.

Thank you. -BEC

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Endnotes

Concepts and ideas. On my path, I have met a few of our finest living scholars. All struggle. It’s never easy even though a few make it look easy. Many of us do not have the finesse of others and our work is written off too quickly. There are so many ways to interpret a data set like the chart of 202 notations. When the data doesn’t cohere or leaves questions unanswered, theories provide temporary work-arounds. Our theory has been known by many names. Big Board-little universe captured the sense that space and time are disintermediated and the two need to be redefined. Quiet Expansion was our simple way to distance ourselves from the Big Bang. Yet, our most descriptive was the “Mathematically-Integrated View of the Universe.” This model, to my knowledge, is the only one that outlines the universe with mathematics — both numbers and geometries — with causal efficacy from the first instance to this very moment. There are thirty presuppositions. If, in some manner, these are engaged, we believe there could be a profound intellectual awakening and possibly a resurgence of ethics. -BEC

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Footnotes

[1] Numbers, Boundaries & Parameters. First, we have a start time around 13.8 billion years ago. Then we have our current time. Just like DNA, every moment has its own unique identify within the universe. Every instant using base-2 notation is part of key continuity equations. Like the 31 trillion digits of pi (31,415,926,535,897) (See the work of Emma Iwao) that are never-ending and never-repeating (always changing and always the same), here is the heart of our horizontally-scrolled chart of the universe. Of course, the first continuity equation is Planck Time to the current time. Planck Length to the size of the universe is next. Then, Planck Mass to the total mass of the universe and Planck Charge to the total charge in the universe follows. A bit much, the veracity of such a concept is questioned and explored throughout this website.

Keep questioning everything. We get bored and dull if we don’t. For many years (and within some quarters, even today) if you questioned the big bang, you’d be laughed out of the room. Part of our problem is our arrogance that cuts off intellectual discussion. For example, many scholars are sure that science is value neutral. That’s just a bit of silliness. Its deepest definitions exude value and values. Eventually we’ll realize that we have adopted old constructs that impede our thinking and our sciences. Here are what may be considered the biggest three:
Hawking’s infinitely-hot big-bang start holds us back. It blocks a cold start.
Newton’s cosmology of absolute time and space suffocates us. It blocks the current point.
Aristotle’s failures with geometry truncate creativity, blocks our grasp of indeterminacy and creativity, and diminishes geometry in general. This story is one of the deep failures of scholarship.

Current work: Fine Structure Constant and Pi. Scholars have been challenged and mystified by these two physical constants. They should be. Inherent in both are starting points for the universe. I am now working through the scholarship of Jeff Yee, author of The Relationship of the Fine Structure Constant and Pi (June 2019) and of Giuseppe Dattoli, the author of The fine structure constant and numerical alchemy, 2010. Yee has clearly stated, “…the fine structure constant is derived from a geometric ratio of surface areas, as a result of vibrations in a lattice with a body-centered cubic arrangement.” Then later, “The fine structure constant can be derived in terms of pi due to a ratio of geometric shapes, possibly the result of the motion of something that fills empty space.” He’s on it!

Written within my mind’s eye, “We should not underestimate the place, position, and power of pi!” We still have many open questions within number theory.

[2a] Geometries have been making a comeback. Topology, shape theory, representation theory, category theory, Langlands programs, string theory (M-theory) and supersymmetries (SUSY) are all mathematical formulations that have a place on our grid. Base-2 is the simplest grid. Mathematical realities are precursors of physical realities. These (and many other) disciplines need the first 64 notations out of the 202 that outline the universe and redefine space-time and infinity. A simple function like cubic-close packing of equal spheres can take its place as a most-simple, key function of our universe. Why not?

[2b] Continuity is numbers. And, numbers define a face of continuity. Inculcating the spirit of Pythagoras, we first turn to Theano, On Piety (as reported by Thesleff, Stobaeus, and Heeren), “…he did not say that all things come to be from number; rather, in accordance with number – on the grounds that order in the primary sense is in number and it is by participation in order that a first and a second and the rest sequentially are assigned to things which are counted.”

Big bang cosmology lacks continuity. First, it’s too hot. Problematically, it tries to cool things down too quickly. Then, it runs out of energy. And, it fishtails with inflationary excuses.

An infinitesimal sphere defined by dimensionless constants has a metaphorical equivalent in every level of science and within each notation. The universe would appear to be constantly testing, changing, and evolving to be more efficient or “more integrated.” It is not difficult to imagine. Stephon Alexander’s group, The Autodidactic Universe, is working on it.

It is, however, very difficult to imagine that one primordial sphere is generated for every unit of an infinitesimal primordial length. That’s a tall order, but it is logically coherent. The net-net is the generation of a phantasmagorical number of infinitesimal primordial spheres per second. Every second something on the order of the area defined by the path of the International Space Station is manifest (seemingly out of nothing). Within a year, an area about the size of our solar system is created.

So, again, our essential challenge is to re-engage our understanding of the nature of infinity and to give it some breathing room without all the poetry and mythopoetics.

Our model sometimes called the Quiet Expansion, is a mathematical — both numerical and geometrical– model of the universe and it is entirely predictive. Just silliness? Please let us know: 12-question survey for this article.

[3a] Scholars like Neil Turok make similar claims. I thought for sure that Neil Turok and his colleagues, Feldbrugge and Lehners, would quickly embrace our model. They did not. One of their claims is that the universe acts like it is constantly starting. Within big bang cosmology, such a claim is counter-intuitive. Within a cold-start model, it at least has a chance to work. They reached their conclusions from a totally different path. Our first note to them was back in 2016, but they have had nothing to say to us. I think if they could point to something that was wrong, one of them would have said as much. Also, it is natural that close-knit groups evolve with specialized language and concepts which those outside their group do not fully understand.

In his book, A Different Universe (page 120-121), Robert Laughlin, a Nobel laureate, cautions us about the aether. It is a tainted concept. Notwithstanding, an aether at the Planck scale is not your father-or-mother’s aether.

New Physics Beyond the Standard Model (Wikipedia). Stymied for so long, Beyond the Standard Model has its own acronym now, BSM. It has become its own special category of study. And, it should be. We’ve all got to push the edges of our understanding of things. These studies are all too important to be left in the hands a few elite scholars. Among those who cannot yet imagine a new physics based on infinitesimal spheres that are defined by the Planck scale, an excellent read is John Ellis‘ May 2021 ArXiv article from the Andromeda Proceedings (BSM-2021 Conference, Zewail City, Egypt), SMEFT Constraints on New Physics Beyond the Standard Model (PDF). The Center for Fundamental Physics (CFP). In collaboration with the Faculty of Engineering and Natural Sciences at Sabancı University, this online international conference was titled, “Beyond Standard Model: From Theory to Experiment (BSM-2021)” and it ran from March 29-April 2, 2021. It seems to me that a conceptual stumbling block goes back to the general acceptance of the concept that the infinite is nowhere found within the finite (Hilbert). Of course, we start with pi. Is it finite or infinite? We observe the continuity of its never-ending, always the same, forever-changing numbers. …finite or infinite? We observe its perfect symmetry. Is it finite or infinite? Now, how about the sphere’s inherent Fourier transforms? Are those harmonic functions finite or infinite? Both? A dynamic bridge between the two?

[3b] Scale Invariant Sphere Dynamics. From the infinitesimal sphere to the movement of galaxies, pi and phi (circles and Fibonacci sequences), are fundamental dynamics within everything. Pi crosses notations; phi builds within a given notation. This model not only uses numbers and geometries, it uses pi, phi, prime numbers, values, and more where big bang cosmology is based on singularities that do not account for dimensionless constants like pi. The mathematics of materialism generally disregards other systems of engagement. How is it that pi is scale invariant? What are the deep dynamics of spheres? We are trying to learn… we are in the earliest stages of our studies of the Fourier transforms and integral transforms. Of course, we’d welcome any-and-all help to understand these disciplines as well as Steven Strogatz.

[3c] Expanding Universe. This model of the universe has a very natural inflation. It is naive on the surface — one primordial sphere per primordial unit of length and time — the result is bewildering. How can we begin to imagine what 539-tredecillion spheres per second means? If necessarily woven together with Planck Mass, Planck Charge, and the speed of light, it is a radically different model of who we are and why. That finite-infinite relation becomes penultimate.

[4] Scientific truth. The influence of Tegmark, Arkani-Hamed, and Turok on our thinking is substantial. Until we are able to grasp a better definition of space, time and infinity, all scientific truth is relative or incomplete. Continuity-symmetry-harmony have an “extra” scientific truth. Derived from dimensionless constants that are not finite, these qualities beg the questions about the very nature of infinity. Over the centuries, scholars and religionists have built up the concept of infinity. Perhaps all that we can definitively know are the three basic concepts. Why not?

[5] Perfection. The concept of perfection was increasingly minimized as quantum theory developed. All the greats of physics were involved. Starting with Max Planck, Albert Einstein, Niels BohrErwin SchrödingerWerner Heisenberg, and Max Born, concepts like the uncertainty principle, indeterminacy, and quantum entanglement were increasingly mathematically formulated and began dominating scientific thought. In 2001 Frank Wilczek scrutinized Planck’s base units and caused them to be lifted up and re-examined. It wasn’t until December 2011 that we did our little geometric progression backing into Planck’s base units. Not until 2015 did we begin examining the numbers assuming that the first instance was an infinitesimal sphere and that pi defined three facets of perfection within the sphere. And because those spheres are the footings and foundations of each base-2 notation, the concept of perfection and a place for perfection has been re-introduced within a very different framework:
Foundations Within Foundations: https://81018.com/foundations/
Perfections of Pi: https://81018.com/perfection/

The Start: https://81018.com/starts-8/
Center for Perfection Studies: https://81018.com/center/

[6] Imperfection. In 2011 in those high school geometry classes, we made models of the five-tetrahedral star, the icosahedron and the Pentakis dodecahedron; we called it squishy geometry. The pieces do not perfectly fit together. There are natural gaps. Aristotle made a mistake that was reinforced by academic thinking for over 1800 years. Even after the mistake was discovered in the 15th century, it had to be rediscovered in 1926 and then again in 2010; and still, there has been no general debate about the significance of five-tetrahedral star and its gap. Here is one profound imperfection built into the very geometries of the universe and it is largely ignored. Here is one critical gap and a place for quantum physics. There are possibly several other equally important places that will be discussed in future homepages. This is a topic of ongoing analysis.

[7] Transformations. Within the panoply of “big bang” cosmologies, the Fourier transform is ignored. Pi and the simplest geometries are as well. If we are to create a working theory, it seems that it should start simple and begin building as best we can using simple concepts. In our model of the universe, the most basic tools of mathematics and science are, by design, all used progressively, building off of one another. In this model there is a place for Langlands programs. There is a place for point-free geometries. There is a more fundamental place for binary functions, scalar field theory and Lagrangian field theory. It is all a bit much for high school people, yet our intuitions help to guide us.

[8] Out on the edge. We have asked questions of the eight scholars pictured — Stephon Alexander (Brown Univ.), Mansoora Shamim (CERN), Nima Arkani-Hamed (Institute for Advanced Study-IAS), Sabine Hossenfelder (Frankfort IAS), Ard Louis (Oxford), Emma Haruka Iwao (Google), Thanu Padmanabhan (Inter-University Centre for Astronomy and Astrophysics), and Claudia de Rham (Imperial College London) — each represents a facet of what might be called bleeding-edge research. Earlier Sylvester Gates had been pictured. A result of our engagement with their work is the linked resource page with our notes and emails. Some scholars, people like Renate Loll and Lee Smolin (Causal Dynamical Triangulation or CDT), have never responded to our emails, so progress with CDT has been slow.

These eight scholars have inspired us. This website is an open dialogue with leading scholars, scientists, and students who think about things like space, time and infinity. These eight scholars are well-known to the people who frequent this website. Each has a reference page to their work, especially as it applies to introducing a new model for the start and growth of our universe. With all the brilliance within academia over the years, it is inexplicable that our base-2 model originated within a high school geometry class. In 2011 we were just following the path down inside a tetrahedron and octahedron to the Planck base units. It was that simple. Today, we will document those efforts by scholars who are beginning to use analogous constructs._

references

• Stephon Alexander: The Autodidactic Universe (PDF), 2021: The universe learns its own laws by exploring a landscape of possible laws (a class of matrix models) and constantly evolves. Stephon Alexander has his six co-authors. Their work has a few parallels with the elemental principles of our model: 1) each notation builds on the prior, 2) all notations are always active, 3) there is a dynamic, never-ending relation between the finite and infinite, 4) the facets of pi help us to understand a perfection within the finite which is the perfection of the infinite which is continuity-symmetry-harmony, and 5) continuity-symmetry-harmony are facets of the infinite creating, the order, relations and dynamics within the most infinitesimal spheres.
• Ard A. Louis: Generalization bounds for deep learning, Guillermo Valle-Pérez, Ard A. Louis, arXiv:2012.04115v2, December 2020 With some caution, it seems that our theory complies with the requirements for a theory for deep learning, i.e. such a theory would readily scale with data complexity. In our theory we eventually scale to include everything everywhere for all time. We’ve become a de facto school to capture the differences between the architectures within the first 64 notations. It is entirely computable on the surface and we are confident it will accommodate the differences between any and all optimization algorithms. We had been familiar with prior work by Ard Louis and from his December 2020 ArXiv article (linked above); we will now turn to others within the deep learning space.
• Thanu Padmanabhan: Planck length: Lost + found, Thanu Padmanabhan, Elsevier, Science Direct, Physics Letters B, Volume 809, 10 October 2020. Thanu Padmanabhan has been focused on the Planck scale as long as anybody living today. It is a domain of the mind. It cannot be reached by anything other than logic and mathematics. One might think that at such an infinitesimal scale, there is an absolute convergence of time, space, matter and energy. It all becomes a singularity. It is a viewpoint now echoed throughout the scholarly world. For me, it begs the question, “What are Planck’s four base unit calculations? Shall we ignore them?” I don’t think so. Padmanabhan tells us that a “relativistic point particle is a zero dimensional object.” I am not so confident. Even though these calculations look like a “point” particle, all the dynamics of the dimensionless constants that define those units are theoretically scale invariant; those characteristics or qualities do not go away. The classically-schooled scholars still think in terms of the qualities of particles and waves when those calculations are quite obviously much smaller than any wave or particle measurement. We can only know that these physical things exist mathematically. As high school people we found that there are no less than 64 base-2 steps to get into the most infinitesimal Planck scale state. It would seem that each step defines a very unique reality. There’ll be more to come regarding his comments about the (Feynman) propagator and his 1988 examination of the conceptual framework for blackholes.
• Claudia de Rham: Although much of Claudia de Rham’s work is co-authored with others and they use specialized language within the very unique conceptual settings of astrophysics, her videos and interviews tend to be more general and generally more self-aware and critical of their collective progress. She is her own best critic and has a delightful sense of humor, so as we go forward, we’ll try to weave a path between her public expressions and her very challenging research. So, yes, here there’s more to come as well.
• Nima Arkani-Hamed. He may forever be known by his lecture in Cornell on October 6, 2010 and for his statement, “Spacetime is domed.” It provoked lots of discussion. I say that a key to a transformative concept of spacetime is to establish its boundaries, then its boundary conditions. We have a symbolic or metaphorical start with Planck’s units. If we accept as a given that the calculations for the age of the universe are close enough, we have a range. If we apply a mathematical construct, Euler’s base-2, we have a process. It is simple and builds on prior work: period doubling bifurcation, Feigenbaum’s constant, PoincaréThe 202 notations become functional. The first second comes out within Notation-143. The first light year is within Notation-169. The first billion years emerges toward the end of Notation-198. Every notation builds of the priors. All time is active. All space-and-time share that emergence and thus spacetime is being redefined. There’s an alternative.
• Emma Haruka Iwao: The Endless Number. It took the single-minded dedication of Emma Haruka Iwao to singlehandedly introduce the world to the largest possible number in all of creation. From her early childhood she has had a fascination with pi. She may not be Archimedes, yet her work runs circles around him. She has pulled pi out of the finite. And, we proclaim that it is the bridge between the finite and infinite. We further claim that the facets of pi — continuity-symmetry-harmony — are the very definition of the infinite. That’s it. Stop there. Science does not need the millions of books about infinity and the infinite. Pi gives us the infinite in a nutshell and Emma Iwao pushes our nose right into it. Here is where we should begin our theories about the start of the universe!

You’ll find squarks and gluinos in the pages of the Standard Model of Particle Physics but both remain illusive. Why? Could it be that all the mathematics that define these hypothesized particles are just “too infinitesimal” for the Large Hadron Collider? Dr. Mansoora Shamim just might be able to tell us so. She may be the one who opens a path to, and down smaller through, Notation-64. Please do a word search of this website on her first name, Mansoora.

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More references:

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Communications: Emails

1. Short emails to those mentioned within the article: Simon White, Tim.Palmer, Renate Loll, and Lee Smolin. We started with Stephon Alexander, Mansoora Shamim, Nima Arkani-Hamed (also on a recent homepage), Sabine.Hossenfelder, Ard Louis, Emma Iwao (recently on another homepage), Sylvester Gates, Thanu Padmanabhan and Claudia de Rham.

2. Email to Robert Laughlin: “It may be a very different universe.” Deep inside the tetrahedron (and its octahedron within), this dynamic GIF showed us how both were derived from spheres (cubic-close packing and sphere-stacking). When we started to follow pi back to its source, continuity-symmetry-harmony were deep within. Acknowledging a symbolic starting point (defined by some analogue to the Planck Length and Planck time), space and time became derivative, finite, and quantized. When Newton’s absolutes are tamped down, a dynamic finite-infinite relation opens up. Here, pi, as the key dimensionless constant, is quantitative in practice while her infinite expression is qualitative. We had a start of the universe with a single, infinitesimal sphere, Lemaitre’s 1927 long-sought-for primeval atom.

3. Emails while hammering on the homepage: Inspirations come from many places. First, there are all the many collaborators and co-authors mentioned within our scholars’ published works, plus there are journalists and world leaders who cause us to write. For example, Guillermo Valle Perez is a co-author with Ard Louis. Then, I receive an email soliciting money for the Obama Library. A special listing of a range of people will evolve as each are sent emails about how our work is related to their work.

4. Google: “Break free of little worldviews.” Get the entire universe. Get access to a simple logic. Pi holds clues that opens it all up. Pi is continuity, symmetry and harmony. Continuity-symmetry-harmony is a bridge between the finite and infinite. Learn more here.

5. WordPress: The purpose of this work and website is to break the impasse created by infinitely-hot big bang theories (versus a cold start — https://81018.com/start/) and by misleading concepts of space and time (https://81018.com/biased/#Newton) and by a failure of Aristotle in basic geometry, a mistake that was repeated for over 1800 years (https://81018.com/biased/#Aristotle). As a result of this effort, wouldn’t it good to have an intellectual awakening around integrative thinking, a resurgence of ethics, and a hypersensitivity about the nature of our walk in this universe. To that end, many.emails are sent to key academic thinkers and leaders throughout the world. -Bruce

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Communications: Instant Messages

A complete left turn, I sent Reed Hasting (co-CEO of Netflix) a note to congratulate him for his past ten years of hard-fought successes. Yet here, I recommend that he incorporate an integrated view of the universe in all that he does.

Magdalena Skipper writes, “Confronting gender bias in Nature’s journalism – at Nature, we know we need to continue to work hard to eliminate gender & other biases.” To which I sent the following Tweet.

@Magda_Skipper No surprise. So going forward, empowering all people is the name of the game. To do it, we’ll all need to break through our limited worldviews so we totally engage the universe, everything, everywhere for all time: http://81018.com No surprise indeed!

Simon Ainslie, NEOM “The thrust for perfection is built into the very fabric of the universe. Continuity-symmetry-harmony, the essence of the circle and sphere, are infinite qualities that are the foundations of the finite, the first moment. To open a way to a sustainable future, build on these three universals defined by the oldest equation in our common history, pi. http://81018.com is a small start on a model of the universe that uses such logic, mathematics, and physics. Until we break through our limited worldviews, our ethics and values will also be limited. Thank you. -Bruce ( A message through Linked IN)

@rweingarten Of course, “honest history” is perspectival. Our problem is our little worldviews all have differing vanishing points. Only a highly integrated view of the universe has the long history and greatest perspective: http://81018.com is just a start. Note: Randi Weingarten is the president of American Federation of Teachers and in a recent speech she said that she wants her teachers to engage accurate history. In light of the universe, the record of human activity beginning in the 4th millennium BC is all current events. And, very little of it is a pretty picture, but it does tell us who we are to date. Have we changed? Have we grown? How much better can we become? Many, many people are trying hard to keep us growing, learning, and doing good. In this model of the universe, that thrust is built into the universe. See more.

@philipbull Beyond ΛCDM: Problems, solutions, and the road ahead, Physics of the Dark Universe. Thinking about your collective work here: https://81018.com/cdm/ Under References, there is a link to your site. The primary page regarding it all is here: https://81018.com/empower/

Then there are all the short spontaneous ones like these: @brianmclaren You need an integrated view of the universe… part epiphany, a little MEGO, but a bit of fun: https://81018.com Or, like this: @lsarsour@CoriBush@AOC Yes, yes, yes, but we need a new context for this atonement. Our little worldviews are clashing all the time. A step out of that foray is an integrated view of the universe — just 202 simple base-2 notations. Our start on it: http://81018.com It is easy and calming, too!

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In 1980 in Paris at the Institut Henri Poincaré, one day I would be in discussions with Jean-Pierre Vigier and the next day with Olivier Costa de Beauregard. They were polar opposites. We focused on the 1935 EPR Paradox and Bell’s inequality equations. By the time I returned to Boston University later that year, I thought, “Nobody has an answer. You could spend your life spinning in circles.” I collected my books at BU and continued walking. I went back to a business that I had started ten years earlier. Little did I know that by helping out in a high school geometry class (December 2011), all these issues would be reopened. It would take me at least five years to get reoriented to learn what today’s scholars were saying. They’ve made some progress. Many new concepts have been introduced. But unanswered is the question, “How does it all cohere?” Solutions to key issues are still outstanding. I do not have that much more time in my life so I have asked quite a few scholars, “What’s wrong with this picture?” referring to our 202 base-2 notations, “Is it a framework, an outline within which to work, or not?” I believe it is. –BEC

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There are many ways to be involved:

1. Tweet or email the link to this page to those who you believe would be interested.
2. Complete a survey. There are two surveys, both using simple Yes / No / Maybe answers.

We would celebrate if you could take time to answer the questions of either survey! Copy the questions to an email and send them in with your answers and comments!

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• This document: Started on Thursday, June 10, 2021 @ 7 AM
• First posted for collaborations: June 10, 2021 at 2 PM
• It also became a homepage: June 14, 2021 at about 6 PM
• The URL: https://81018.com/empower/
• The Prior Homepage: https://81018.com/re-envision/
• First Headline: Defining a new model of the universe
• Second headline: Grow Beyond Those Limited Worldviews, Adopt an Integrated View of the Universe
• Third headline: An Integrated View of the Universe Enlivens Any and All Worldviews
• First Tagline: Empowering scholars, scientists, and students of every kind
• Second Tagline: Eight Steps: Scholars, scientists, and many students are helping us.*
• Third tagline: Towards An Integrated Understanding of our Universe
• Another tagline: Let’s go deep and be all-inclusive in our understanding of this Universe.
• Another tagline: Opening boundaries and parameters to context more of our Universe
• Today’s tagline: Attempting to grasp the numbers and systems that define our Universe
• Possibly the next homepage: https://81018.com/tredecillion Password: Tredecillion
• The most recent update of this page: Monday, March 13, 2021.
August 30, 2021, added Ellis reference.

###

# From left to right, we can all be better and do better.

Nations are people; and, all people are in process. No one has all the answers. Surely, there are plenty of very smart people, but they 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.

Aristotle. 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 truly 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 the universe compressed into a very small sphere that gave rise to an infinitely-hot start. On one hand, ours is rather cool start and on the other, it is just a flash of light. 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

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. Maybe. Maybe not, so please allow me to speculate that It is the beginnings of all our imperfections, an imperfection geometry and quantum fluctuations.

[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.

[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 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 brief 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 universals become the fundamentals of the finite and reflect the essential nature of the infinite. If it all starts infinitely hot — the Planck Temperature– and it cooled so quickly, we must engage the concept of light.

[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.

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 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, 2021, 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!

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:

Who might be the wisest, smartest, bravest, most-loving, most-generous and the one with the greatest integrity? Who will lead us?

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 February 26, 2022.

# 3. 2. 1. 0: Minutes, Seconds, Nanoseconds, Picoseconds… Plancksecond!

###### CENTER FOR PERFECTION STUDIES:CONTINUITY•SYMMETRY•HARMONYGOALS.October.2020PAGES: ARISTOTLE|DARK|FORMULAS|HAWKING|KEYS|NEWTON |RELATIONS|Transform|UPPrior Post|Claims|Endnotes-Footnotes|References|Emails|Tweets|Zzzz

A Most-Basic Building Block of the Universe:
One Plancksphere per Plancksecond *

###### by Bruce E. CamberRelated:World – History – Expansion – First Instant – Consciousness

In 1899 Max Planck calculated numbers for Planck Length & Planck Time.1 Max Planck knew he was onto something significant, but he couldn’t quite make it work. One can imagine that he had hoped that the young Einstein could help. Surely Einstein opened new doors to explore, but his were different. And, we have learned over the years that all big ideas and concepts incubate slowly.

Within Max Planck’s equations, space-and-time are necessarily yoked. One is always a face of the other and a primary characteristic of light. As such, both are also yoked to mass-and-charge. Planck and Einstein redefined the very nature of space-and-time, and mass-and-energy. In so doing, they unwittingly redefined the finite and infinite.

A goal of this article will be to examine how this could be so. We start with one of the world’s oldest, best-known, and most-used mathematical constructs, pi, along with her circles and spheres. Most of us have not explored how in some manner of speaking these three are derived from continuity-symmetry-harmony. Another intention of this posting is to see how pi-circles-and-spheres generate space, time, and geometries.

__________

Max Planck ignored his own calculations.2 Perhaps he didn’t know what to do with them. It took out-of-the-box thinkers, a bold scholar like C. Alden Mead, to open that door. In 1959 he wrote about the place of the Planck scale. Leading first-principles scholars like John Barrow (1982) and Thanu Padmanabhan (1985) also began wrestling with the Planck units. Frank Wilczek finally broke open the Planck scale to the world in 2001 with a series of articles in Physics Today.

More recently scholars around the world have wrestled with the meaning and value of the Planck Scale. Most top-level posts within this website attempt to be deeper exploration of  those issues.

Too small to measure, Planck Length and Planck Time redefine the infinitesimal. It appears nothing is meaningfully smaller, shorter or faster.

When the Planck base units are re-envisioned to create a base-2 chart from the smallest to the largest measurements of space and time, it becomes increasingly evident (1) neither space-nor-time are absolute, (2) time-and-space are Janus-faced, correlated with the Janus-face of mass and energy, and (3) all the notations are, even today, generating one Plancksphere per Plancksecond.

There are around 64 notations (doublings) before waves, particles, and fluctuations. Sixty-four successive doublings of the Planck Length and Planck Time are enough space and time to do a lot of mathematics-and-geometry, but key leaders within the academic-intellectual community think it’s too small for much of anything.

The First Three Minutes.3 In this 1976 book Steven Weinberg begins his study of the universe at about 1/100 of a second after the big bang. That is Notation-138 within our horizontally-scrolled chart. There are 202 base-2 notations or doublings from Planck Time, the very first infinitesimal moment of the universe, to this very day. And, yes, there are just 202 simple doublings.

We all know that life is about doublings. Every living thing doubles in some special way. Yet, Weinberg could not explore from Notation-1 to Notation-137. Though the Planck units have been around since 1899, that progression of Planck doublings did not come out until 2011. To date, we know of no other model of the universe that starts and builds  on the Planck base units initially manifest as an infinitesimal sphere.

The First Three Seconds: A Review of Possible Expansion Histories of the Early Universe, (June 2020). Twenty-seven leading scholars from around the world collaborated on a composite article about the first three seconds. The very first second is between Notation-143 and 144. They, too, assumed an infinitely-hot start of the universe so their first three seconds are shrouded in mystery. They didn’t explore the concept of a cold-start model which was first proposed in 1927 by Lemaître when he began to share his earliest thoughts about the beginnings of this universe, so they, too, missed a lot of possible action between Planck Time and that first second.

__________

Planck-Time Transformations
________________5.391 16(13)×10-44 seconds________________

New ideas take time to incubate.4 Max Planck first wrote about Albert Einstein’s new ideas back in 1905. Years later, after Planck died in 1947, Einstein wrote to Planck’s widow about his special memories with Max yet acknowledged how general relativity and quantum theory would, for now, have to stand awkwardly together. These two seemingly irreconcilable pillars of modern physics have continued to stymie the world so much so that the world’s people, especially her leading scholars, have been quite unsure of space and time.

We inherited our commonsense worldview from Isaac Newton.5 So with all due respect and for a very long time, we’ve believed that time and space are absolute.

It seems most people still do. To stray from that bit of so-called commonsense is not easy. If space and time are not absolute, then what is? What holds it all together?

What’s in the heart of every Planck Time transformation? The Planck scale is a different scale but it may not be as strange as so many scholars seem to think today. As a result of our studies of this model since December 2011… though still fuzzy, some clarity is becoming apparent.

__________

Pi’s Continuity-Symmetry-Harmony

A Possible Domain of Perfection.6 Learning a bit more about pi, going over it one more time — even attempting to go inside it — finally my old 1972 definition of a moment of perfection seemed relevant. Inherent within the many definitions of pi is continuity, symmetry and harmony. There is the continuity of the never-ending, never-repeating numbers, the perfect symmetry of the circles and spheres, and special internal and external dynamics, harmonics, introduced to us through the Fourier transform.

Continuity-symmetry-and-harmony are such key concepts, there are links to those three facets of reality at the top of every homepage or top posting within this site.

Where do these concepts reside? Or, could the three be the container for everything, everywhere, for all time? Here the answer is a cautious “Yes.”

__________

Finite & Infinite

Simple logic tells us that the very first spheres are still being pushed forward.7 By going over those progressions of the doublings, over and over again, it slowly became apparent that each notation is always active. Each builds on the prior notations. Time is a face of light, the Janus face of space. So, along with the oldest-most-popular mathematical construct, pi, all of the dimensionless constants became our focus.

If these special equations and relations do not reside within the finite, might we assume that they are somehow aspects of the infinite? Can the infinite be brought into the finite without becoming finite? What connects the finite and infinite? Quite puzzling, it behooves us to ask, “In what ways might David Hilbert have been wrong about his conclusion regarding the finite-infinite relation?”

Simple logic seems to tell us there is an ever-so-active, rather intimate bridge between the finite and infinite. By definition, the finite is the quantitative. Perhaps we should be thinking about the infinite as the qualitative. So, we now propose (and have begun exploring the idea) that this bridge is defined by all the dimensionless constants and the infinite is the qualitative face of reality and beingness.

We’ve all been taught that the infinite is some abstract superlative that is not part of our immediate reality. Here, quite the opposite, it appears that the infinite is not only an intimate part of our experience, it is the experience of the experience that can not be defined by space and time. It is defined by ratios and relations. And, the infinite is experienced as some expression of continuity, symmetry and harmony. That’s a perfection and it appears to extend into the finite.

Yet, recognizing the transitioning from spheres to tetrahedrons and octahedrons, somewhere along that progression of notational doublings, the most simple tetrahedral gap, just five tetrahedrons sharing a common edge, would be among the many combinations that would be tested. My suspicion is such a gap doesn’t become part of fabric of the universe until as late as the first three seconds up within Notation-143, Notation-144 and Notation-145 and then over time, that structure begins working its way back to earlier notations between 48 and 64.

It is a new topic opened for discussions and analyses. Again, in this model, we shall give the infinite everything qualitative. We’ll give the finite everything that is quantitative. And within this model of the universe, quite obviously the quantitative and qualitative co-exist quite well together.

Yet, those age-old questions about good and evil are implied.8 Might we say that all qualities that do not reflect continuity, symmetry and harmony (but do reflect discontinuity, asymmetry, and disharmony) are perspectival and are actively impressed within the very fabric of this dynamic universe? The implications are so far-reaching. More…

__________

Nanosecond to Plancksecond (Planck Time)

A long, long way from the Nanosecond to the Plancksecond.9 Our mathematically-defined chart of the universe captures the nanosecond within Notation-114 at 1.1197×10-9 seconds. Notation-115 is 2.2395×10-9 seconds, Notation-116 is 4.479×10-9 seconds, and Notation-117 is 8.958×10-9 seconds.

That encompasses the first four groups of nanoseconds of the universe. The related length scale is in the domain in which most of life takes place. Here time is dynamic right back to the first instant.  Each notation defines the look and feel of the universe within that notation.

Wouldn’t you think that our entire universe shares this moment in time? If it is true for the first 116 notations, it may well be true for the next 86 notations.

A nanosecond is equal to 1000 Picoseconds. The Picosecond (10-12) is followed by the Femtosecond (10-15), the Attosecond (10-18) and the Zeptosecond (10-21 which is within Notations-74-to-77).

The accuracy of time determination. The greatest accuracy achieved to date, the zeptosecond, was achieved in 2016 by a collaboration of three groups: Max Planck Institute of Quantum Optics (MPQ) in Garching, Technical University of Munich (TUM) and Ludwig Maximilian University (LMU) of Munich. They captured the timescale of photoionization. They were the first to make such a short determination of a unit of time. That followed their earlier work to establish the attosecond under the MPQ leadership of Ferenc Krausz and Vladislav Yakovlev.

The measurement of the Zeptoscond, just one sextillionth of a second — that’s a trillionth of a billionth of a second — is work led by a laser physicist, Martin Schultze. It is truly a measurement by devices, not just a mathematical calculation, and Schultze steps us back into Notation-74 to Notation-77 within our horizontally-scrolled chart.

On to Planck Time. As fast as it is, that zeptoscond is still rather slow when compared to 10−44 seconds given within Planck Time. Next will be the Yoctosecond (10−24), just one septillionth of a second (10−24). Within our chart, the Yoctosecond ranges from Notations 65-to-67.

No Names. The actual words for the next six categories (or groups) down to the Planck scale do not yet exist. Hardly trivial, until each group has a name, they have a limited identity and study of them is more difficult.

The last International System of Units (SI) categories to be added were in 1991. It may well be time to call them back together again. They need to name those next six new groups: 10−27, 10−30, 10−33, 10−36, 10−39, and 10−42 seconds. Planck Time at 5.391 16(13)×10-44 seconds is within the 10−42 seconds’ expansion. It could be named a Plancksecond or PlanckSecond. To date, that combination of words has only been used casually to refer to an extremely short period of time.

__________

Stretching Credulity Even Further

The four base units in lockstep.10 There is literally no room for error within the first groups of notations. It would seem that even with the abundance of scaling vertices, 8.5 billion within Notation-12, and 5.902958×1020 vertices at Notation-24, the thrust of precision would keep everything perfectly aligned. Yet, we know by Notation-64 with its 6.2771017×1057 scaling vertices, quantum fluctuations are emerging. That’s well-established fact.

Consciousness is also a fact.11 We assume it is within the earliest sixty notations. Back in and around 2016, our guess for consciousness was that a primitive consciousness might emerge as early as Notation-48 and that domain could be considered a place for the introduction of a type of fluctuation. We are now researching to see if there may be a better nomenclature already established to distinguish the emergence of various kinds of fluctuations. At Notation-48 there are 2.2300745×1043 scaling vertices. It may well be the area in which we begin our search for the first manifestations of a gap integral to creating a system for the five most primitive perceptions.

Review. These Planck spheres manifest the most complete sense of continuity, symmetry and harmony possible. Sphere stacking would be generating “pure” tetrahedrons and octahedrons. Yet, within each doubling, new dynamics are introduced.

Prime numbers. 12 Rather casually proposed in a few sentences and brief paragraphs in earlier postings is the role of the prime numbers. There are 45 prime notations within the 202 notations that currently encapsulate the universe. There are just nineteen primes within the first 67 notations. The postulation is that each prime supports a new mathematical system that initiates even more diversity and complexity. As within computer programming, there is an order of operations based on the logic of mathematical expression. Each expression gives us clues about our universe and their ordering and we need to pay attention to all of them.

The Hubble Constant.13 Reviewing the work of Wendy L. Freedman, Professor of Astronomy and Astrophysics at the University of Chicago, I learned about their standing enigma — the two values for the Hubble Constant. The editors at PSW Science ask, Is There a Crisis in Cosmology? A New Debate Over the Value of H0. For a November 6, 2020 Zoom webinar with Prof. Dr. Wendy Freedman, PSW Science comments, “If the tension is real, it may signal a new physics beyond the standard model.”

Astronomers make observations and have an observational framework. We have a strictly mathematical framework.

1. Can the two work together? Can their observational data work with this simple mathematics?
2. Can the observational data work if the concept of time is derivative and finite?
3. Can the observational data tolerate infinity defined as continuity, symmetry, and harmony?
4. Would the Hubble Constant work with 201 fully-symmetric notations in one manner and with an asymmetric Notation-202 in another manner? That is, might the Hubble measurements that are within Notation-202 be different from any measurement that is within Notations-0-to-201?

Of course, our suspicion is, “Yes, of course,” observation and mathematics most often concur.

We know how idiosyncratic this model of the universe is. We also know how simple and logical it is. We also know there are over twenty assumptions, all departures from the academic norms, that have been made since 2011. With this posting, we’ll add another: Time measurement varies between the 202nd notation and all other notations. Notation-202 feels directional and seems linear; it is asymmetric. Notations 1-201 are all symmetric and each notation has been “filled” with infinitesimal spheres that are defined by the Planck base units.

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Open-or-Closed?

Fundamental key question, “Is the universe open or closed?”14 In 2017 a most-helpful work by Joseph Silk, Challenges in Cosmology from the Big Bang to Dark Energy, Dark Matter and Galaxy Formation (2016) had come to my attention. In a quick note of thanks and an introduction, I asked for help, “Where did we go wrong?” More recently, I discovered a provocative article that he had written with two others, Planck evidence for a closed Universe and a possible crisis for cosmology (Nov. 2019). With this work I awkwardly engaged his question, “Is the universe an open or closed system?” I was confused; and an email to Joseph Silk, Alessandro Melchiorri, and Eleonora di Valentino (November 2019) certainly reflects that confusion; and rather predictably, that confusion continues to this day.

It seems the answer to their question is “perspectival, yet fundamentally open.” The five dynamics of pi push our faculties to imagine what these small-scale dynamics look like within the largest-possible scale, i.e., the size and age of the universe at this moment in time.

Emergence, Inflation, Acceleration.15 The other dynamic in all these equations is within light. In one of her earliest articles by Eleonora Di Valentino, with her co-authors Alessandro Melchiorri, Valentina Salvatelli, and Alessandra Silvestri, wrote Parametrised modiﬁed gravity and the CMB Bispectrum (ArXiv 2012). They conclude, “Cosmic acceleration is one of the major challenges faced by modern cosmology and understanding the very nature of what is sourcing, it is the main focus of up-coming and future cosmological experiments.”

What has happened in the intervening eight years?

Those comments reflect the blinding problems created by big bang cosmology that seem far more approachable within our mathematically-integrated view of the universe. In our simple model, there is a natural inflation, a thrust of the universe, that can all be seen within the numbers of our chart of the universe and these generally approximate the majority of big bang epochs.

Conclusions

Continuity, symmetry and harmony are three facets of reality that define both the finite-and-the-infinite, as well as light, space-and-time and pi-circles-and-spheres.

Old mysteries become evidence as new mysteries are uncovered. Thank you. –BEC

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https://en.wikipedia.org/wiki/Orders_of_magnitude_(time)

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# Endnotes and Footnotes

*  One plancksphere per plancksecond, and if Planck Time is equal to 5.391 16(13)×10-44 seconds:

That number would be the top end. It 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. -BEC

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[1] The Speed of Light and the Nature of Light in a Very Different Light: 202 Notations.
Light defines (1) each notation, (2) space-time, and (3) mass-energy. Yet, in this model of the universe, each is defined even more fundamentally by continuity, symmetry, and harmony. The speed of light is defined within each notation as well. When we first started exploring the numbers for these Planck Length doublings, we had no idea that we would find a simple correlation between Planck Length and Planck Time. Then, we started thinking about Planck’s formulas, particularly the more simple expression for Planck Time:

Our first reflections began in 2012. By 2014 we began to grasp how well all the numbers worked together. Those formulas worked! We looked for articles by experts but could find no references. Yet, right there on the page, simple mathematics was validating the relation. We began to realize that light is a much broader category than photons, just as photons are a much broader category than visible light.

The results of that simple act of division — Planck Length divided by Planck Time is equal to the speed of light — was nowhere to be found so we began writing it up. Planck’s formula in light of the 202 notations, the instantiation of the sphere as the first expression of space-time, mass-energy, and the building of geometries (cubic close packing), and 64 to 67 notations to quantum fluctuations, particles, and waves, extends the deeper definitions of light as an aether, matrix and grid.

Planck’s calculations render the speed of light more accurately than the 2019 SI number or ISO number (299,792,458 m⋅s). More

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[2a] C. Alden Mead (UMinn) In 1959 he began his struggle to publish his work about the Planck Length. Though finally published in 1964, the article, Possible Connection Between Gravitation and Fundamental Length Phys. Rev. 135, B849 (10 August 1964), was ignored by the scholarly community. Planck Length commanded no respect as a fundamental unit of length.

[2b] John Barrow (1982): With an extraordinary depth and range of scholarship, and a sensitivity to young students, my first letter to John Barrow in 2013 was an earnest request for help, “What do we do with these numbers?” He never commented about my naive attempt to shoehorn everything-everywhere-for all time into 202 notations. Barrow died on September 26, 2020.

[2c] Thanu Padmanabhan: His 1985 article — Physical significance of planck length (PDF) — captured my attention. His nonperturbative approach produced a quantum cosmological model free from singularities and the horizon problem. I was very surprised and gratified to see that his article was published so early in his career. He was just 28 years old (born March 10, 1957). Yet, with guidance from India’s renown astrophysicist, Jayant Vishnu Narlikar, he has been a most prodigious scholar.

[2d] Frank Wilczek (2001) became a Nobel Laureate in 2004, yet he continued his wide-eye, open and enthusiastic approach to the unknowns within life. He was one of the first of those within his caliber who encouraged our explorations. His three articles about Planck units truly opened the door for the rest of us.

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[3] From Three Minutes down to Three Seconds. It seems that most within the general population and many of our best scholars hold the positions spelled out in 1976 within the book, The First Three Minutes, by Steven Weinberg. A Nobel laureate and one of our most cited scholars, Weinberg still missed over two-thirds of the most fundamental structures of the universe.

In June 2020, twenty-seven leading scholars from around the world argued most convincingly about the early structures of the universe. A tribute to Weinberg, their article was titled, The First Three Seconds: A Review of Possible Expansion Histories of the Early Universe, (June 2020). Forty-four years after Weinberg’s popular work, they acknowledge the abundance of mystery within the first three seconds. More

Those are the magical three seconds that open up to an entirely new and profoundly simple universe.

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[4] Yes, New Ideas Do Take Time To Incubate, Sometimes Centuries. Those “seemingly irreconcilable pillars” have been screaming at us for over one hundred years, “It’s incomplete. You’re missing key parts.” So instead of going in circles with the same parameters trying to do a different thing, break the circle so it becomes a spiral and find those missing parameters! Our simple guess is the first 67 notations.

Brandon Brown wrote the book, Planck: Driven by Vision, Broken by War, OUP, 2015. He is Prof. Dr. Brandon Brown on the University of San Francisco campus and he has become a foremost Max Planck scholar with his comments and analysis from his 2015 book published by Oxford University Press. The Planck-Einstein relation was one of the most formative personal relations in history and one of the reasons their silos stand today is because physics has not fully embraced mathematics and mathematics hasn’t fully embraced physics. Arrogance and turf wars keep them apart. The first 64-to-67 notations are grounds for reconciliation; and with it, I predict will come the birth of entirely new science.

Though it appears that Planck was unable to break out of Newton’s commonsense worldview, Einstein made some progress. Yet, he was wrapped up in his own vision. With the help of Max Planck Institutes and people like Brandon Brown, an actual dialogue between Planck and Einstein about the Planck base numbers may yet be uncovered. To date, there is no record of it. If the two of them really focused on those Planck numbers, they just might have discovered those 64-to-67 notations prior to particles, waves, and fluctuations.

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[5] “Commonsense is not so common.” It took the intellect of Sir Isaac Newton to define perhaps the most widely-held “commonsense” worldview which today makes very little sense at all. That is, of course, Newton’s claim that space and time are absolute. To this day, it is still pushed forward by respectable scientists and philosophers among us. For me it stands as one of history’s most egregious intellectual mistakes that has created walls and silos within our current picture of the universe. The expression has been credited to several — Voltaire (1764), poet and political writer, Nicholas Amhurst (1726), and a Roman poet, Decimus Iunius Iuvenalis (aka Juvenal, Book III of Satires, circa AD 181). It has become so true, today it’s a truism!

We have missed something most fundamental.

Tensions are real and there are many reasons why these tensions are signals for what people have in so many different ways characterized as a “new physics beyond the standard model.” That expression has been repeated so often, it now has its own acronym, BSM.

More to come: breaking though commonsense and the BSM

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[6] Perfection and possible degrees of perfection. We have all experienced a moment that was profoundly moving. Possibly it felt transcendent. Some might call it a moment of perfection. In 1971, confronted with such, I attempted to describe them in the most general mathematical and scientific terms that caught the spirit of such an experience — continuity-symmetry-harmony. I quickly learned that all experiences are within space and time and Newton’s container universe was the generally-accepted, commonsense description of such. It wasn’t enough for me, so I took on those conditional expressions — continuity-symmetry-harmony — to evaluate all new information about the structures of reality. So within quantum physics, I gravitated toward quantum chaos theory and the EPR paradox and what has become known as quantum entanglement.

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[7] The very first spheres are still being pushed forward. Hard to believe, of course, but so much about this sphere generation is hard to believe. There is no name for 1044 spheres. One could say, “Somewhere just under a trillion-trillion-trillion-trillion.” It doesn’t compute easily. Then, if we are to imagine that amount per second, it becomes rather unfathomable. Nevertheless, very large and very small numbers are the next steps for all of us to begin to grasp the boundaries of this universe. More

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[8] Qualitative, values, ethics, morals, aesthetics. Continuity, symmetry and harmony became the basis to make valuations: What is good? What is better? And, what is the best? These valuations are perspectival. They slide around plancksecond-by-plancksecond, second-by-second, day-by-day, and year-to-year. So even though seemingly arbitrary, there are aggregations of value which also become a basis for judgement and evaluations such that a quantitative value may be assigned to an experience, an artform, or performance, and especially to things. More

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[9] Scale of Infinitesimal Measurements: From Nanosecond to Plancksecond. The six groups of numbers between the Yoctosecond and the Planck Time need formal names that everybody within the global scientific community recognizes.

The group responsible for such standards is CODATA, the Committee on Data of the International Science Council (ISC). They are charged to improve the availability and usability of data within all areas of research. Having a name for these infinitesimal measurements is the first step in having the reality of these dimensions become adopted science. I have asked many of the members of their Executive Committee to take up that cause. More

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[10] Four Planck base units in a base-2 notational lockstep: At this point, we can only use our intuition and logic to construct the very nature of simplicity and perfection. Langlands programs and string theory may help yet those disciplines will have to incorporate, then evolve out of the functions of pi, circles, and sphere. They’ll have to find places into which they can pick up and integrate all their earlier work, accommodating the four Planck units working together. In this model, each of these initial 64-to-67 notations represent unique opportunities, relations, and functions. More

As we continue this analysis, it will be coming increasingly important that the six groups of scales of the universe with no names, be named officially-and-formally by the ISO and CODATA and all their consultative entities like NISTBIPM, and standards groups within 141 other countries. Prior to quantum fluctuations, there are these clusters of measurements that have no name: 10−27, 10−30, 10−33, 10−36, 10−39, and 10−42 seconds. As we observed earlier, Planck Time at 5.391 16(13)×10-44 seconds is within the 10−42. More

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[11] Consciousness: We know where the brain is located, but we do not know how where the mind is located nor are we profoundly sure how the brain/mind relation works. The first experts to whom I turned for insights about these issues was John Eccles. His report with Karl Popper is The Self and Its Brain (Springer, 1977). It set the stage for me. The next was Roger Penrose, author of The Emperor’s New Mind (Oxford, 1989) and Shadows of the Mind (Oxford, 1994). Their genius is clear and their concepts robust, yet neither Eccles nor Penrose were able to define a grid within which the mind and brain were in concert.

Enter Computational Neuroscience. While an undergraduate in-and-around 1957, Stephen Grossberg posited nonlinear differential equations for neural networks. One could say that it was a stroke of genius as well as a deep-seated intuition. Grossberg was among the first to begin to define computational neuroscience. Yet, the scientific community has been limited without a simple grid that includes everything, everywhere, for all time, including consciousness. The first grid by Kees Boeke used base-10; and though digital, it encouraged analogical thinking with no causal efficacy. Here within a base-2 grid, causality is driving the exploration.

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[12] Prime numbers: Prime numbers have a key role within encryption technologies today, but one might still ask, “Is that all there is? Could primes be playing a more fundamental and pivotal role within the structure of things?” We think so. To that end, as an exploration, we would assign the first 19 primes — 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, and 67 — to absorb the expansion of structures and functions within Mathematical Systems Theory  (Also, see the text of that title by Diederich Hinrichsen and Anthony J. Pritchard, Vol. 48, 2005).  Prime elements and irreducible elements, prime ideas, group theory There will be more to come.

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[13] Two values for the Hubble constant: In lectures and papers, Wendy Freedman is an expert and leading scholar regarding all things related to the Hubble Constant. She says, “Our value of the Hubble constant, Ho = 69.8, with statistical and systematic uncertainties of 0.8 and 1.7 km/sec/Mpc, respectively, falls midway between the value obtained from the Planck Cosmic Microwave Background analysis, and that obtained using Cepheids.” Freedman has not seen our base-2 scale from the Planck Time, assumed to be the first moment of time, to our current time. Nor has she seen the comparative analysis with the big bang epochs. She is also unaware of the difference between Notation-202 and the first 201 notations. Using the simple logic of this simple model of the universe, the age of the area in the universe being measured will render one result for all images within 2.82+ billion years and another Hubble Constant for all images within areas older than 2.82+ billion years (perhaps as high as 3.2 billion). More to come

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[14] Open or closed: Joseph Silk is highly-regarded within the Astrophysics and Cosmology community. His overview gave me a chance to go over the basics just one more time, and ask myself, “What am I missing? Why is our idiosyncratic theory so wrong and the big bang theory so right?”

So, I empathize with those people who started within this industry back in the 1970s. Now fifty years later, those people (like me who are now over 70 years old) remember when there was a certain respect for Sir Fred Hoyle’s steady-state theory as an alternative, competitive theory to the big bang. Since that time investments in the big bang theory skyrocketed and reached an all-time high under the leadership of Stephen Hawking. With its many unresolved problems exacerbated by time and with the Planck base units finally becoming recognized, the value of big bang cosmology is falling. Those who have invested heavily in it cannot be absurd to themselves. Yet, we all know that which is more-true-than-false prevails.

Of course, these kinds of transitions are not easy.

I was glad to discover that second article by Joseph Silk with his two younger colleagues. There is an honesty to their question and we need to explore these kinds of questions. For me, it helped to shape the finite-infinite analysis, especially our focus on dimensionless constants: finite, infinite or in that hyphen between the two. This time, however, it shaped that quantitative-qualitative analysis; and so far, it feels good and seems to work.

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[15] Inflation, expansion: A young, Italian astrophysicist, Eleonora diValentino, was part of the “Closed or Open?” discussion with Joseph Silk (just above). In 2014 she was asking key question about  cosmic acceleration, particularly “…the very nature of what is sourcing it…” She appears to be the next generation of the Wendy-Freedman-types who are in search of fundamental truth; these are  people who expect that their quest will never ever finish. As an academic exercise, we are going to focus on a joint article,  Parametrised modiﬁed gravity and the CMB Bispectrum (ArXiv 2012) where Eleonora Di Valentino and her co-authors Alessandro Melchiorri, Valentina Salvatelli, and Alessandra Silvestri arrived at that conclusion. The study now is to answer the question, “How can you believe in big bang cosmology when you have done this analysis and made these conclusions?”  So, yes, there is more to come

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# References & Resources

1. Planck scale: A special page of references and resources will be dedicated to exploring the work of people like Serge Timashev of the Karpov Institute of Physical Chemistry (Moscow) with his ArXiv article, The Planck numbers and the essence of gravitation: phenomenology (2017),  and Ronald J. Adler of Hansen Experimental Physics Laboratory (Gravity Probe B Mission) of Stanford University with his ArXiv article, Six easy roads to the Planck scale (2010).
2. Wendy Freedman, Professor of Astronomy & Astrophysics, Univ. Chicago, November 2020: Is There a Crisis in Cosmology? A New Debate Over the Value of HAlso see: Measuring and Understanding the Universe, https://arxiv.org/abs/astro-ph/0308418&nbsp;
3. HubblesiteGalaxies Used To Calibrate The Hubble Constant
4. April 11, 2019, Marclay’s Clock: 24-hour installation highlights a modern obsession with time, Jean-Michel Johnston, University of Oxford Also in Nexus NewFeed
5. In 1925, the great mathematician, David Hilbert wrote, “We have already seen that the infinite is nowhere to be found in reality, no matter what experiences, observations, and knowledge are appealed to.” Even today, many scholars would agree, but perhaps Hilbert and those scholars are mistaken.
6. Research: “Primordial adiabatic and Gaussian perturbations
7. Is a time symmetric interpretation of quantum theory possible without retrocausality? Matthew S. Leifer and Matthew F. Pusey
8. Not all mathematical advances relating to π were aimed at increasing the accuracy of approximations. When Euler solved the Basel problem in 1735, finding the exact value of the sum of the reciprocal squares, he established a connection between π and the prime numbers that later contributed to the development and study of the Riemann zeta function.  Fore more:
Complex numbers and Euler’s identity
Number Theory and RZF
9. October 24, 2020 at 12:22 pm · Reply to “Infinity Is Not The Problem” Does the qualitative reside within the finite? Could the perfection of the sphere be an example? Is pi an example? I’ve been playing with it within an examination of the Planck scale: https://81018.com/the-three/ &nbsp; Might all the dimensionless constants be the bridge between the finite and infinite
10. Experimental result cannot be explained by the Standard Model (SM): Non-zero masses for the neutrinos (elementary particles traveling close to light speed, electrically neutral, and weakly interacting). The SM assumes that they are massless. Therefore, particle physics explores a new physics beyond the SM.
11. The Standard Model is not a complete description of Nature: it does not account for dark matter, dark energy, gravity, or neutrino masses and mixings. There are also remain many features of the Standard Model itself which are not understood, and which may find their answers in speculative ideas beyond the Standard Model such as supersymmetry, large extra dimensions, and/or extended Higgs sectors.
12. Conspiracy of BSM physics and cosmology, Maxim Yu. Khlopov. Nov 2019: The only experimentally proven evidence for new physics is the effect of neutrino oscillations, but the physical nature of neutrino mass is still unknown. “… the conspiracy of Beyond the Standard model (BSM) Cosmology [1] is puzzling taking into account the plethora of nontrivial cosmological consequences of BSM particle models. “
13. Yakov (YaB) Zeldovich: ”…though the probability for existence of these phenomena seems low, the expectation value of their discovery can be hardly overestimated” (ArXiv, Conspiracy of BSM physics and cosmology, Maxim Yu. Khlopov, Nov. 2019
14. The Crisis in the Foundations of Mathematics, José Ferreirós, Universidad de Sevilla 2008, 2011 https://personal.us.es/josef/pcmCrisis.pdf
15. Proyecto Hephacos, 2014:
16. Is The Universe Finite? PBS, sponsored by Brilliant, 2019

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Emails (just a few)

1. Marios Christodoulou, Andrea Di Biagio, Pierre Martin-Dussaud, An experiment to test the discreteness of time

2. Wendy Freedman, Kavli Institute for Cosmological Physics, Astronomy & Astrophysics University of Chicago

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Tweets (just a few)

@Pontifex What you are saying is actually backed up by a mathematical-and-scientific model of the universe. There are just 202 base-2 notations from the Planck units to the current-time-and-size of the universe: https://81018.com/chart/ Also: http://81018.com

@lori_deschene You’ve got good spirit, a good heart… now we have to break free of our little worldviews and get a highly-integrated, mathematical view of the universe (all within 202 base-2 notations). http://81018.com Everything we say and do affects the universe.

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Zzzzs (afterthoughts)

What works survives. Every possible geometric combination that works provides form, function, structure, and then substance, relations, and networks of relations. What works best, survives. The universe, the penultimate opportunist, is creating something big that requires solid foundations. Perhaps somewhere around Notation-50, our universe begins to experiment with those five tetrahedrons with its built-in gap. Out of an abundance of shapes and configurations, the five tetrahedral structure is surrounded by perfectly manifesting forms and structures. Within a moment, that gap comes alive. Perhaps as early as Notation-50, the gap becomes a structural system, and then becomes a systemic fluctuation. Just a guess, the first expression of these systemic fluctuations just might be considered a primitive consciousness. By Notation-67, when it can be measured and “observed”, it will be defined as a quantum fluctuation.

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# Wikipedia, March 2012

## Base 2 exponential notation: Proposed, produced, and then rejected by Wikipedia as “Original Research.”

Please note: We started this project in December 2011 and it now continues as a “work in progress.”  This project is a result of substituting for a nephew’s high school geometry classes. At one time the words on the right of some sections below, “[edit the original]” went to the article within Wikipedia. Today, they go to an invitation to join the editing team! At some time in the “not too distant future, it just might be re-posted on Wikipedia and then, this page could be edited by all others. My hope in pulling all those pieces and history together is to open the discussion to a wider audience so if parts of it are wrong or could be improved, you can do it or advise me so I can update this article below and the one on Wikipedia.

## Contents

Base-2 exponential notation is based on the power of two. It should not be confused with a base-2 number system – the foundation of most computers and computing. Exponential notation is used within computer programming, however, its use in other applications to order data and information has wide implications within education. Here the form and function of space and time — measurement — operates in the range between the Planck length and the edges of the observable universe.

Base 10 scientific notation is widely studied and used to depict the universe in colorful ways. [1] [2] [3] [4] [5] Base-2 scientific notation is more granular and relational. It is an ordering system that de facto can be used within any academic discipline. A didactic example is given within the substantial work that has been done in mathematics, particularly geometry.

Base-2 scientific notation in geometry uses a nested hierarchy of objects, particularly space filling polyhedron and other basic structures that create polyhedral clusters and apply combinatorial geometries.

## The process

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The simplest of the platonic solids, the tetrahedron, is also a simple starting point. Take as a given that the initial measurement of each edge is just one meter.  Starting at the human scale, that object is both divided and multiplied  by 2. If one starts at the Planck length, it would always be multiplied by 2.  If one were to start at the edges of the observable universe, the result would always be divided by 2.

## The limits of base-2 scientific notation

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There are limits. Going within, the limit of the smallest division is the Planck length. It is reached in 115 notations by dividing by 2. Going out through multiplication, the limit is to the edges of the observable universe. It is reached in 91 notations multiplying by 2. The result is similar to the orders of magnitude using base-10 scientific notation.

## Diversity

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With each successive division and multiplication, base-2 scientific notation within geometry readily expands to include the other four basic platonic solids, then the Archimedean and Catalan solids, and other regular polyhedron. Cambridge University maintains a database of some of the clusters and cluster structures.

Base-2 scientific notation in geometry involves every form and application of geometry and geometric structures. Arthur Loeb (Space Structures, Their Harmony and Counterpoint [1]) analyzes Dirichelt Domains (Voronoi diagram) in such a way that space-filling polyhedra can be distorted (non-symmetrical) without changing the essential nature of the relations within structure (Chapters 16 & 17).

There is no necessary and conceptual limitation of the diversity of embedded or nested objects [2].

## Geometers

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Geometers throughout time — people such as Pythagoras, Euclid, Euler, Gauss, Buckminster Fuller, Robert Williams, Károly Bezdek, John Horton Conway, and thousands of others have contributed to this knowledge of geometric diversity. These manifestations of structure are well-documented within many notations (see Buckyballs and Carbon Nanotubes, using electron microscopy). The Frank-Kasper phases[3] including the Weaire-Phelan polyhedral structure have even contributed to architectural design within the human scale, i.e. Beijing National Aquatics Centre.

## Constants & Universals

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There are constants, inheritance (in the legal sense as well as that used within object-oriented programming) and extensibility between notations. Each notation has its own rule sets[4]. Taken as a whole, from the smallest to the largest, this polyhedral cluster has been described as dodecahedral by astrophysicist Jean-Pierre Luminet at the Observatoire de Paris in France.

Polyhedral combinatorics is a subgroup of base-2 scientific notation in geometry.

## 202 notations

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In 90 steps of multiplying, one reaches the edges of the observable universe, the largest possible representational geometric number. In 112 steps of dividing, one enters the area of Planck’s constant, the smallest possible representational geometric number. In 202 notations every scientific discipline is necessarily related between notations. Every act of dividing and multiplying involves the formulations and relations of nested objects, embedded objects and space filling. All structures are necessarily related. Every aspect of the academic inquiry from the smallest scale, to the human scale, to the large scale is defined within one of these 206 notations. Both calotte model of space filling and the pleisohedron of space filling are used and continuity, symmetry, and harmony are taken as given to define order, relations, and dynamics respectively.

Geometries within base-2 scientific notations have been applied to virtually every academic discipline from game theory, computer programming, metallurgy, psychology, econometric theory, linguistics [5] and, of course, cosmological modeling.

1. ^ Loeb, Arthur (1976). Space Structures – Their harmony and counterpoint. Reading, Massachusetts: Addison-Wesley. pp. 169. ISBN 0-201-04651-2.
2. ^ Thomson, D’Arcy (1971). On Growth and Form. London: Cambridge University Press. pp. 119ff. ISBN 0 521 09390.
3. ^ Frank, F. C.; Kasper, J. S. (1958). “Complex alloy structures regarded as sphere packings. I. Definitions and basic principles”. Acta Crystall. 11. Frank, F. C.; Kasper, J. S. (1959). “Complex alloy structures regarded as sphere packings. II. Analysis and classification of representative structures”. Acta Crystall. 12
4. ^ Smith, Warren D. (2003). “Pythagorean triples, rational angles, and space-filling simplices”. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.124.6579&rep=rep1&type=pdf .
5. ^

# [17] Fuzzy Universe

###### [13] PlanckspheresOne second: 299,792± km[14] Automorphic forms[15] BASE-2 AND PRIME NUMBERS[16] Aristotle’s Mistake[17] Fuzzy Universe[18] Scholars
 Background: FQXi called for papers. It encouraged people to focus on the raw power of logic and mathematics to anticipate the structure of real realities. If there is logical and mathematical cohesion, there is probably a real physical reality that it describes. Matching them up and learning where and how such a unit of cohesion fits within the larger frameworks is the challenge. More... [17] Our Fuzzy Universe.  The work of John Wheeler and Richard Feynman are central to this work. With the help of Gödel, Einstein, Planck, Poincaré, Gauss, Euler, and Leibniz, a new path will be found.  The age-old questions about fluctuations and dark energy and dark matter will be answered.