New ideas that become key concepts usually start as a simple idea.

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On creating a place to study the 202 base-2 notations
Those 202 base-2 notations need to be more deeply and widely researched.
by Bruce E. Camber (a first draft)

Abstract. Conceptually, 202 base-2 notations mathematically and geometrically encapsulate the universe. There is no other mathematical model that actively defines our universe quite so simply. Since December 2011, we’ve been studying the mathematical and geometric potentials within this model. Although we started innocently and naively, we learned that we were doing “original research.” We didn’t know it, but we were blazing a new path. Though exciting, it was also confusing. It was idiosyncratic and we were just high school teachers using simple geometries (.https://81018.com/home/ ). We turned to scholars for help through letters, emails, instant messages, and an occasional visit. We actually had hoped that one of these scholars within academia (.https://81018.com/alphabetical/ ) would say, “Been there, done that, and here’s why it is wrong,” but, nobody has so we persevere.

After ten years of study and many emails1 we have concluded that there is something right about these charts of the universe that we’ve created over the years. Our goal now is to evaluate the differences between the facts and our guesses.2

The Planck Scale.
The 202 base-2 notations create a dynamic grid. The first 64 of the 202 notations start at the Planck scale and go up to just below the scale for quantum fluctuations and particles-and-waves where the Standard Model begins. There are legions of scholars within specialized studies with well-defined domains of consistent information but they’re not on that grid. The list includes Langlands programs, string and M-theory, SUSY, and hypothetical particles.3

Further, many specialized mathematical studies are also off the grid; there has been no coherent, integrative model to help them. See: https://81018.com/questions-questions/#Scholars

Base-2 from the Planck base units to particle physics is a basic container within which to begin to figure out how to integrate these studies. Those first 64 notations are necessarily hypostatic, the mathematical foundations of the foundations. It is a challenge that begs people to hold back judgments of the unknown and to make thoughtful time to entertain the potential of a domain defined by no less than 64 base-2 notations, all well-below direct measurements. New conjectures have to go substantially beyond our current work. As stated in earlier posts, I believe it would be good to generate at least three articles for ArXiv about the 202 notations and that we should ask multiple authors with long ArXiv histories to help craft each properly.

The net-net.
The 202 notations are given a chance to become an intellectual reality within some part of our scholarly community. After all, that container is already a mathematical and logical reality. Once the 202 notations are recognized, we believe essential paradigms.https://81018.com/paradigm/ — will begin to shift.

Our chart of numbers — https:81018.com/chart/ — is more right than wrong.

STEM: The 202 notations simplify one’s view of the universe by interconnecting everything, everywhere for all time. It is a penultimate teaching tool that inspires creative thinking within a well-defined container with a multiplicity of possibilities.

Our working document — https://81018.com/stem/ — I believe is more right than wrong.

Fluctuations. If the two most simple gaps, currently referred to as a five-tetrahedral gap or a five-octahedral gap, can be definitively related to structures and functions within quantum theory, it will deepen our grasp of the very nature of quantum fluctuations and will have an impact on quantum computing. I believe quantum fluctuations are a product of the geometries of the gap. If so, that’s a revolution. It’ll be like sand thrown under our wheels to keep them from spinning. If we are able to stop some wheels from spinning, new directions will open.

Geometries may well be just as important as the numbers — https://81018.com/geometries/

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Anticipation.
Here we believe there will be new functions and structures with which to work. We will be researching space-time beginning at the Planck scale. We will be engaging infinitesimal, primordial spheres. We’ll learn the nature of the first “particles” — https://81018.com/particle/ — and so much more.

Open the Standard Model. A long-term goal is to define places on the 202 notational grid for major studies including Langlands programs, string and M-theory, SUSY, hypothetical particles, causal set theory (CST), causal dynamical triangulation (CDT), scalar field theory (SFT),  spectral standard model (II, III)  and loop quantum gravity (LQG). The Standard Model is re-opened for geometries and any and all studies looking for a place on the grid. Our conjecture is that every study will be included.

Short Term. We have five short-term goals:
(1) Explore Notation-0 and Notation-1 as another plausible start of the universe whereby people engage an encapsulated universe defined by all 202 active base-2 notations.
(2) Further engage those scholars currently doing thought experiments within the domain from the smallest Planck scale up to particle-wave duality to explore their questions and answers about the Planck base units. There are many such scholars-researchers.
(3) Answer the key question, “How might these units become the start of the universe?
(4) Focus on the infinitesimal, primordial sphere as the first manifestation of space-time.
(5) Further research sphere stacking, especially cubic-close packing of equal spheres and the dynamics with the Fourier transform and the role of attractors and repellers (Smale & Milnor).

All five may result in new, highly-strategic insights about the nature of things.

The 202 Notations are understood to be a very plausible reality. To date we have relied on the work of many scholars for insight. A few of these scholars share some of our insights: Stephon Alexander of Providence (Rhode Island, Brown University), Espen Garner Haug of Norway, Tim Palmer of Oxford, and Xijia Wang of China. The work of scholars who research the first instants of the universe, especially the work regarding the Planck base units, are key.

Scholars in the USA who work between particle-wave boundary of quantum fluctuations and the Planck scale include some of our most rigorous scholars. I would also include work by people like Monika Schleier-Smith and her lab at Stanford. They recognize the boundaries of entanglement by attempting to correlate quantum systems to phases of matter found in nature. That work may be specifically correlated within actual notations out of our 202 base-2 notations. 

Other work could add most-valuable parameters. At Santa Barbara’s Kavli Institute there is a range of research being done between the Planck scale and particles-waves. Key research by Isabel Garcia-Garcia and David Gross (with his long legacy with the Solvay lectures) may well open new paths. And, we will continue to explore for possible correlations with those first 64 notations.

The people of the Simons Foundation have frequent insights about foundations of science. Their writers within Quanta Magazine are constantly on the edge of research. Their own work within the Flatiron Institute, SUNY-Stony Brook Simons Center for Geometry and Physics, and their Qubit collaborations all hold new keys.

Of all the dimensionless constants, pi is most senior and most ubiquitous. It is the core of continuity, symmetry, and harmony which redefines the finite-infinite and the quantitative-qualitative. We can better understand spin, bonding, and attractorsrepellers.

There will be a thrust to communicate results to the world’s people. Growing relations with NIST and the ISO network, and with key science communicators around the world will facilitate.

All the scholars whose work is being analyzed will be the first to begin to communicate this model to others. These are all people who have the greatest motivation to understand a very idiosyncratic view of the universe. They will also all be the initial group of interpreters of that view of the universe. A very large second group of people will be all the professors and their extended groups of support people, the professional science writers, and the undergraduates, graduates, and postdocs (who will be adjusting current research). And, the third group will be the general population. To drop our limited worldviews will not be easy for most people. To engage an integrated universe view, however, will be liberating. To see the universe in 202 notations will be fun. All information will become approachable and ordered. Our experience in our high school classes and a sixth grade class showed us a relatively-fast adoption curve.

The original team will be immediately expanded with those scholars in the USA whose published ArXiv articles have been used within our work and with whom we have been in communication over the years. -BEC

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Endnotes & Footnotes

[1] Emails. Very early in our quest, we realized that email was no longer respected like it had been. It seemed that email from an “unknown” was either ignored or blocked. These were not “email blasts.” I had genuine questions based on that person’s scholarly work. Yet, admittedly I sent so many, it was easy to get confused. So, I began gathering up those references by the scholar, particularly those that intrigued me, and placed them on a page with my notes below. It was to be a memory aid. Slowly my “/alphabetical/” page emerged. Now, it is more than a memory jog for me. Every tweet and every email, is about key issues for these times. We can no longer be cavalier about our constructs. What you believe really makes a difference within our world and this universe. -BEC

[2] Facts & Guesses. The 202 base-2 notations are not a guess. It’s simple math and geometry. It has a logic structure that defines at least 64 notations that science heretofore has not considered. It is a simple, but extraordinarily challenging concept.

Pi is not a guess. It is the oldest, most-widely used, mathematical equation, yet the very essence of pi is summarily ignored as if Richard Feynman’s 1964 summation was the final word (See the Krulwich NPR 63-second summary) whereby you do an experiment and it is right or wrong. Although not an experiment, it is not wrong.

The sphere is not a guess, it is the most simple object in geometry. Scale invariance is not a guess; we see it everywhere. Although not an experiment, it is not wrong.

Yet, space, time and infinity are all a guess and we just love to argue and guess about the nature of each. What were once our presuppositions have now become a checklist; so, of course, there is more to come. Think about the qualities of infinity, spheres, and pi, as well as particles and hypothetical particles. Many specialized mathematical studies will soon have a place to interconnect to everything everywhere.

[3] Hypothetical particles. Wikipedia, List of particles, Retrieved 7 June 2022)

There’ll be more to come…. Simons Foundation, Flatiron Institute, SUNY-Stony Brook Simons Center for Geometry and Physics, Qubit collaborations, Solvay lectures

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References & Resources

What every physicist should know about string theory, Ed Witten, Physics Today, 68, 11, 38 (2015) https://doi.org/10.1063/PT.3.2980

•  Wikipedia, List of fictional elements, materials, isotopes and subatomic particles, 2022

• Quantum fluctuating geometries and the information paradox (PDF), Rodolfo Gambini, Rodrigo Eyheralde, Miguel Campiglia, Jorge Pullin, 2017

•  John Willard Milnor (1985). “On the concept of attractor”. Communications in Mathematical Physics99 (2): 177–195. doi:10.1007/BF01212280S2CID 120688149.

•  John Willard Milnor is one of the five mathematicians to have won the Fields Medal, the Wolf Prize, and the Abel Prize (the others being SerreThompsonDeligne, and Margulis.)

•  Bell’s Theorem, Non-Computability and Conformal Cyclic Cosmology: A Top-Down Approach to Quantum Gravity, T.N. Palmer, arXiv:2108.10902, August 2021

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Emails

• Dharam Vir Ahluwalia, Center for the Studies of the Glass Bead Game, June 7, 2022
• Johannes Buchner, June 5, 2022
• David J. Gross, Kavli Institute, University of California at Santa Barbara, June 5, 2022
• Espen Gaarder HaugNorwegian University of Life Sciences (NMBU), May 24, 2022
• Paola Zizzi, University of Padua, June 5, 2022 @ 4:24 PM
• National Science Foundation, Washington, DC, May 31, 2022
• Monika Schleier-Smith, Stanford University, May 30, 2022
• Matthew J. Strassler, June 6, 2022

There are many more to add….

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IM

More messages to follow in July 2022

10:08 PM · Jun 11, 2022 @Pontifex You say, “Abba. Father.” To give those comments deeper credibility, we need to steer people beyond limited worldviews and to a highly-integrated view of the universe. The simplest is base-2 from Planck units till today: http://81018.com for more.

8:08 AM · Jun 9, 2022 @7homaslin @nattyover Congrats. You all have been doing sensational work for ten years. Natalie has been excellent, but many others are as well. I’ve written a letter to you here — https://81018.com/quanta/#Lin The top of that page is my tribute to the magazine and to Simons people.

2:57 PM · Jun 8, 2022 @CSRDay An email and a tweet in one day! Please forgive my exuberance, but I had backed into our page about your work herehttps://81018.com/charles-day/ — and just had to write a year to the day since the last time! We are making a little progress.

3:00 PM · Jun 6, 2022, @MattStrassler Can you help us unfold this base-2 chart of the universe: https://81018.com/chart/ The current homepage is always my latest struggle with it all: https://81018.com/

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Participate

The world is increasingly nihilistic. Many parts of it are dystopian. We all need to do something. We are preparing special pages so virtually anyone can become a teacher of an integrated view of the universe whereby we all begin to understand as profoundly as possible that what we do each and every moment effects the quality of life within this universe.

This is a key document. Click on the “Back Arrow” or “Left Arrow” at the top of this page to go back to three or four other key documents. If you agree and you will begin to teach others about this integrated view of the universe, we will list you within our soon to-be-added “Teachers” page. Thank you.

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Keys to this page, idea

• This page became the homepage on Saturday, June 11, 2022
• The last update was Sunday, June 30, 2022.
• The URL for this file is https://81018.com/idea/
• The headline for this article: On creating a place to study the 202 base-2 notations
• First byline is: New ideas that become key concepts usually start as a simple idea.

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Also see:
https://81018.com/agree/
https://81018.com/geometries/
https://81018.com/common-ground/
https://81018.com/64-notations/
https://81018.com/open-envelope/

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Questions for our National Science Foundation

Questions. Can we discern another plausible start of the universe? Who among those currently exploring the domain from the Planck scale to particle-wave duality might be open to earnestly engage the Planck base units? Is it a symbolic place to start? Could these units describe the start of the universe? Could an infinitesimal, primordial sphere be the first manifestation of space-time? Does base-2 notation best encapsulate the simple stacking of equal spheres? Is cubic-close packing of equal sphere the initial dynamic?

To date we have turned to many scholars yet now have a small coterie of international people, Xijia Wang of China, Stephon Alexander of Providence (Rhode Island, Brown University), Espen Garner Haug of Norway, Tim Palmer of Oxford. People like Natalia Berloff of Cambridge (and Moscow) could be involved. But now the focus turns to scholars in the USA. Among them are:

  1. The Monika Schleier-Smith lab at Stanford where they explore entanglement through the formulation of correlations in quantum systems that dictate the phases of matter found in nature.
  2. Isabel Garcia-Garcia at Santa Barbara’s Kavli (naturally includes the work of David Gross and the Solvay lectures).
  3. Edward Frenkel, Berkeley, and Robert Langlands and Ed Witten of IAS.
  4. Communicators: Plus, there are groups like Simons Foundation with Quanta Magazine and their Qubit collaborations. When there is consensus among the scholars that the 202 base-2 notations are meaningful and that the first 64 notations could be the foundations for all things within space-time, there will be a thrust to communicate it to the world’s people. Another large group is the ISO network. In the USA NIST leads the charge. Footnote: Phil Davis was a lead mathematician within NIST and one of our early advisors.

There are many others whose work may scale with ours. These include:

  1. The leading proponent of constructor theory, Chiara Marletto of the University of Oxford, where she asks, “Can the second law be tightened up into more than just a statement of likelihoods?
  2. Very-small scale research by a diversity of groups around the world which include the old guard, The Langlands programs, string and M-theory, and SUSY. There are so many others. People like Paola Zizzi (Italy) are continuing the qubit work of John Wheeler. Anabel Quan-Haase (Canada) brings hyperconnectivity to a new level. Frédérique Godin with her U7 Alliance and Mila Quebec are opening up the AI ecosystems.

Potential practical applications within the domain of quantum computing with leading theorists within the following research groups: 

  1. Hidefumi Hiraishi, University of Tokyo, Kashiwa, Chiba, Japan
  2. Jeannette (Jamie) M. Garcia, IBM Quantum Computing & Network (e) (c)
  3. Valerii M. Vinokur et al, Arrow of time and its reversal on the IBM quantum computer (ETH-PDF), Nature, 2019, https://doi.org/10.3929/ethz-b-000332774
  4. Currently researching work at the MIT Lincoln Laboratory, Thomas Lord Foundation, Competence Center Energy and Mobility, Swiss Electrics.

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Classics as assets within these studies:

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This project unwittingly started in December 2011 within a high-school geometry class. The first base-2 chart from the start of the universe to this very day was quickly adopted as a STEM tool. Because that tool appeared to be an alternative to the infinitely-hot big bang theory, we pulled its study back from students until we were more sure that we were not missing some simple logic and that we were not misleading the students. Once there is some concurrence among our leading scholars that this model should be studied for its possibilities, STEM exercises can be readily developed and disseminated. Also, virtual reality tools can be developed to piggyback off of Google Earth so at any point when people arrow down it becomes possible to go smaller and if they arrow up, to go larger out into the universe.

As valuable as the heuristic tools may be, the radical shift will be to see the entire universe as a relational whole. All notations will become active. All time will become the Now and our sleep will be functionally and necessarily enmeshed within this model. A science, mathematics, and geometry of the gaps will formally open and begin to impact our understanding of sciences, ourselves, and our behavior. There will be a clear alternative to our solipsism and limited worldviews. Continuity, symmetry and harmony, as a functional description of infinity, will begin to open up possibilities of studying perfected states within space-time.

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All these links just below go to key pages within this website.

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Unprecedented. Not a middle or third way.
It’s a totally-integrated way to study the universe
.
by Bruce E. Camber (first draft)

On grappling with life’s purpose and structure1

More than a middle way or a third way2

A good way.3

Plus, we’ve just started, so there will always be more. Thank you. -BEC

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Endnotes & Footnotes

Some of these links may go to other websites.

1a. Our universe: MathematicalGeometricalExponential.
Background: Pythagoras, Plato, and Galileo are among the historic greats to say, “It’s a mathematical universe.” We take it further. From the very first instant of the universe to this very moment, it is all mathematical (even quantum indeterminacy). Equations rule. Our simple base-2 chart encapsulates everything, everywhere, for all time. This is an exponential-geometrical universe. Only the small sliver we call the current time is linear. It’s not an illusion, but we have to sleep on it.
1b. 202 base-2 notations, a dynamic grid of the universe. Most academics, scholars and scientists do not know there are 202 base-2 notations from the base units (by Planck or Stoney) to this very moment in time. These pages appear to be the first public discussion (on the internet since 2012).
1c. An infinitesimal, primordial sphere. Most academics, scholars and scientists have not yet embraced such a sphere at the Planck scale. Many have embraced Lemaître’s primordial atom, yet it is a very different concept. This sphere is conjectured because among the dimensionless constants hypothesized for the start of the universe [Baez, 2011; Wilczek-Aguirre-Rees-Tegmark, 2005], pi (π) dominates. On further analysis of pi (π), we conjectured that order (numbers), symmetry (space), and harmony (dynamics) are instantiated from the infinite to the finite, from the qualitative-to-the-quantitative. With such a conjecture it was natural to follow that one primordial sphere emerges per each unit of Planck time.
1d. Spheres and pi (π). Spheres and pi hold the mysteries of the Fourier transform, plus the attractors and repellers of John Milnor and Steve Smale. So many studies have opened up to us, we find learning to be an adventure and fun, but such a challenge. Many of our primary teachers have died within these short ten years. Many have become weak. The new challenge now is to find young scholars who are open to such a radically different model of our universe.
1e. Notations always active; all time is now. When this model started to come alive and all the notations began to contribute to the current time, our grasp of the very nature of time was profoundly challenged. Keeping so many new ideas working together becomes problematic and new integrative ideas seem illusive.

We know that we’ve only scratched the surface; it would be nice to have some friends with whom we could bounce around new ideas and concepts.

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2. Not a middle or third way. Moving beyond political parties of every stripe and flavor (and their power plays), our world is ensnared by people who want to be in charge. Today they elbow their way to the top of a political party and then elbow their way to the top of their country’s leadership, and then the country elbows its way to the top of global leadership. It is never leadership. It is always about power and mostly centralization. The accent is on the wrong syllable. We all need to recognize the very deep relational structure of the universe that binds everything, everywhere for all time.

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3. Ethics and values. It seems there are no others suggesting that our ethics are built into the structure of pi. It also seems there are no others suggesting that the primary qualities of pi — continuity, symmetry, and harmony — taken together, become de facto values and the transformation nexus between the finite and infinite. This shall continue to be the major discussion within this website.

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References & Resources

Please Note: References and resources used to shape this posting are not yet footnotes; concepts are still being formulated. Thank you.

Ronald J. Adler, Six easy roads to the Planck scale (PDF), ArXiv, 2010 AAPT, 2010)

Philip Ball, Physicists Rewrite the Fundamental Law That Leads to Disorder, Quanta Magazine, May 23, 2022

Doug Bonderud, 5 Odd Theories of the Universe That Might Just Be True, Now, Northrop Grumman, April 2022

Marios ChristodoulouAndrea Di BiagioMarkus Aspelmeyer, Časlav Brukner, Carlo Rovelli, Richard Howl, Locally mediated entanglement through gravity from first principles, Feb. 2022

Valerio Faraoni (e), Three new roads to the Planck scale (PDF), American Journal of Physics 85, 865 (2017); https://doi.org/10.1119/1.4994804

Universe’s Constants Now Known with Sufficient Certainty to Completely Redefine the International System of Units, NIST, 2016. See: CODATA Recommended Values of the Fundamental Physical Constants: 2014, See: Current their list of sixteen fundamental constants.

Valerii M. Vinokur et al, Arrow of time and its reversal on the IBM quantum computer (ETH-PDF), Nature, 2019, https://doi.org/10.3929/ethz-b-000332774

• Garth Warner, Harmonic Analysis on Semi-simple Lie Groups I, Springer-Verlag, ISBN 0-387-05468-5, 1972

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Emails (More emails will be added over the next couple of weeks.)

Dharam Vir Ahluwalia, Center for the Studies of the Glass Bead Game, June 7, 2022
David J. Gross, Kavli Institute, University of California at Santa Barbara, June 5, 2022
Paola Zizzi, University of Padua, June 5, 2022 @ 4:24 PM
National Science Foundation, Washington, DC, May 31, 2022
Monika Schleier-Smith, Stanford University, May 30, 2022
Espen Gaarder Haug, Norwegian University of Life Sciences (NMBU), May 24, 2022

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IM

Please Note: Some communications, particularly instant messages and tweets, because none of this work is done in a vacuum; our world is in turmoil. We need new models of who we are and why.

8:08 AM · Jun 9, 2022 @7homaslin @nattyover Congrats. You all have been doing sensational work for ten years. Natalie has been excellent, but many others are as well. I’ve written a letter to you here — https://81018.com/quanta/#Lin The top of that page is my tribute to the magazine and to Simons people.

7:55 PM · May 29, 2022 @linakhanFTC Every decision should be made in light of our history and in light of the universe. Our little worldviews are too often laced with personal bias. We need to graduate to a fully-integrated, mathematical view of the universe; our start is here: https://81018.com/. Lina Khan is Chair of the Federal Trade Commission.

10:54 AM · May 26, 2022 @WatsonInstitute If we were to all recognize that we all share the first 64 notations (out of 202 base-2 notations from the start of the universe till now): https://81018.com/chart/ and we each qualitative effect the whole: https://81018.com/ethics/ just maybe we’d begin to change.

10:44 AM · May 26, 2022 @DalaiLama More than live together, we need to see how we are all deeply, profoundly, and totally interconnected and come from the same active stuff, the first 64 notations of the 202 base-2 notations that define everything, everywhere for all time: https://81018.com/chart/ Also see: https://81018.com/agree/

4:25 PM · May 17, 2022 @POTUS Please don’t give up on any part of the USA or any person. Our biggest problems result from incoherent scientific theories. We are breaking free of little worldviews and moving toward an integrated view of the universehttps://81018.com — is just a start!

1:43 PM · May 12, 2022 Xi Jinping The question is “more centralization” or “decentralization.” Centralization requires obedience, monitoring, and control. Decentralization requires education and a most compelling offering that empowers people’s creativity for self-control: https://81018.com

May 12, 2022 @WHO @UNDESA @UNECOSOC The question is “more centralization” or “decentralization.” Centralization requires obedience, monitoring, and control. Decentralization requires education and a most compelling offering that empowers people’s creativity for self-control: https://81018.com

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Participate

The world is increasingly nihilistic. Many parts of it have become dystopian.

We are all needed to do something. We are preparing these pages so we all become teachers of an integrated view of the universe whereby we all begin to profoundly understand that what we do each and every moment effects the quality of life within this universe.

This is a key document. Click on the “Back Arrow” or “Left Arrow” at the top of this page to go back. Click again. With this page, these three pages describe a very different point of view and purpose. If you agree and you will begin to teach others about this integrated view of the universe, we will list you within our soon to-be-added “Teachers” page. Thank you.

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Keys to this document, way
• This page became a homepage on Monday, May 30, 2022.
• The last update was Thursday, June 9, 2022.
• The URL for this file is https://81018.com/way/
• The headline for this article: Here is a new way, not a middle or third way… It is a totally-integrated way, a place to study the universe.
• First byline is: This page links to key pages throughout this website.

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Following the work of Barry N. Taylor, NIST, USA

See: http://physics.nist.gov https://www.nist.gov/people/barry-n-taylor

National Institute of Standards and Technology (NIST):  Barry N. Taylor of NIST’s Data Center joins David B. Newell and Peter J. Mohr of NIST’s Physical Measurement Laboratory’s Atomic Physics Division to write the “2014 CODATA recommended values.” These standards are generally recognized worldwide for use in all fields of science and technology. The values became available on 25 June 2015 and replaced the 2010 CODATA set. They are based on all of the data available through 31 December 2014.

Second email: 12 May 2022 at 3:30 PM

Dear Dr. Barry Taylor:

Six years ago, I sent a note to you about our work. It was a plea for help to interpret our data. We thought, “Math is math and geometry is geometry and logic is logic, so what are we doing wrong?”

Our most recent homepage makes reference to you and your team and I thought you’d want to know: https://81018.com/agree/ is the long term URL.

If I could do it all over again, I would have requested a meeting with you all back in 2012, just weeks after we began our journey into this infinitesimal universe. It has been a long ten years of challenges and discoveries. Thank you.

Warmly.

Bruce

First email: Jan 14, 2016, 5:42 PM

Dear Dr. Barry Taylor:

We are now working extensively with the NIST values for dimensionless constants.  We found some very interesting work where the values for the physical constants are generated using pi, close cubic packing, number density, and the isoperimetric quotient. 

Now that may sound like we might know what we are talking about! 

We are just simple high school folks who have spent the last four years pondering constants and universals because we backed into it all from a very simple exercise while studying the platonic solids.  We divided in half all the edges of a simple tetrahedron, connected the new vertices and found four half-sized tetrahedrons in each corner and an octahedron in the middle. We then divided the octahedron; and unlike Zeno, we knew we could stop at the Planck Length. To make things consistent we started with the Planck base units and multiplied by 2 until we were at the Observable Universe and the Age of the Universe. 

There were just 202 notations to cataloged everything, everywhere for all time.  We thought it was remarkable until we couldn’t find a professional version of our very rough model on the web or in textbooks. We discovered Kees Boeke base-10 work, but it had no lower and upper boundary, it didn’t expand like in bifurcation theory, it had no geometry, and it didn’t have the Planck base units to define it all. Our first 67 notations became a truly small-scale universe.  Although infinitesimally small and discounted by academia, we found many ways to impute meaning.

Freeman Dyson of the Institute for Advanced Studies and Frank Wilczek of MIT have encouraged us.  Perhaps it is better for the naive to make idiots of themselves. Yet, four years later we are still at it and the closest anybody has come to being harsh was to tell us that our work is idiosyncratic. We certainly knew that much.

Your thoughts would be profoundly appreciated.  Thank you.

Most sincerely,
Bruce
***********************
Bruce Camber
New Orleans

Let’s agree about the base units of our universe.

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Eight Initial Conditions
by Bruce E. Camber REVIEW: Mathematical speculations
(Navigation: Also use the yellow arrows just above)

Eight concepts follow. I believe all are needed to understand how this universe started:

1. We live in a mathematical universe. In 1960 Nobel laureate Eugene Wigner (Princeton) wrote an oft-quoted article, The unreasonable effectiveness of mathematics in the natural sciences. In 2014, Max Tegmark (MIT) took Wigner further within his book, Our Mathematical Universe: My Quest for the Ultimate Nature of Reality. These two scholars did not discuss:
a. The never-ending, never-repeating numbers of pi (π),
b. The fundamentality of an infinitesimal, primordial sphere, and,
c. The essence and the place of the Planck Length and Planck Time.

So you may not agree because here, in this model, the universe first begins within pi (π), spheres, and the Planck base units. Many, many orders of magnitude smaller than quantum fluctuations and particles, this model is also well within the 325,000 years before the first particles and atoms evolve and well prior to the cosmic microwave background radiation (CMBR). Yes, here, the universe begins and extends within our ever-present pi (π), an extraordinarily-fast-but-orderly incursion of infinitesimal-primordial spheres, and Planck’s base units of length and time.

These numbers and geometries relate everything, everywhere throughout all time. Though some of our most powerful tools within our mathematical arsenal, we know that our simple results do not sit well within current cosmological theory.

To open space for such results, we start where we began in 2011 within high school geometries.

2. Base-2 notation (clusters, doublings, functions, groups, jumps, layers, keys, ratios, sets, steps…). The universe is naturally defined by 202 base-2 notations. Mathematics is mathematics and geometry is geometry. Euler’s most-basic equation encapsulates the universe quite-simply and most-relationally. Our first page on the web describes how we were chasing basic geometries and discovered that it was a base-2 application. Of course, many more pages followed. It became our very own, most-comprehensive STEM tool. We wrote it up as a letter to the editors and as a plea for help from our many leading scholars and thinkers. Though idiosyncratic, it had logic, geometries and base-2 notations. We knew something very fundamental was happening when it absorbed big bang cosmology. So, although entirely idiosyncratic, we decided to persevere.

3. Pi (π) is the oldest, most-used, best-known equation within our mathematical arsenal. Unfortunately, pi (π) is taken for granted and ignored, yet it quantitatively and qualitatively defines our universe. The quantitative is the finite and the qualitative is the infinite. Pi’s qualities of continuity, symmetry and harmony create a natural bridge between the finite and infinite. Continuity gives us order, numbers and time. Symmetry gives us relations and space. And, harmony gives us the dynamics of space-time.

Perfected states of these qualities are part of the earliest notations.

4. The first Notation, then the Small-medium-and-large scale universe. Our stumbling block is the way we see our universe. Some might say we do not know our small scale universe, those notations smaller than particles and quantum fluctuations. But, we do know Notations 1-67. We are not looking at them in the best possible framework. Langlands programs, string-and M-theory, SUSY, and a host of other small-scale studies define the first 67 notations. Notations 67-134 have been the subject of our sciences and philosophies for millennium. The essence of the human scale is defined yet it remains nascent until well into Notation-202 when there is the necessary infrastructure and support for its current unfolding. With the most recent work using the measurements from cosmic microwave background radiation (CMB or CMBR), Notations 178-202, we have been inundated with new data. Our large-scale universe is on fire with new concepts and ideas. It will all become most meaningful when all that data is seen in light of the first 67 notations and woven throughout Notations 67-to-134. We should note that Notation-134 is within a millisecond of the universe’s beginning. A year is within Notation-169. 325,000 years is between Notations 177-and-178 (and the emergence of particles and waves).

Obviously, this model is foundationally about the earliest universe.

5. Infinitesimal, primordial spheres. The geometry of the straight line is held by the centerpoints of spheres which activate the centerpoints of octahedrons to form the first triangle that becomes a tetrahedron with an octahedron locked within it. From basic logic we find the first three shapes of our universe and the first dynamic, cubic-close packing of equal spheres. Seemingly an “explosive” quantity of spheres –539 tredecillion spheres per second using Planck Time to as high as 4609 tredecillion spheres per second using Stoney Time — is a quiet expansion of infinitesimal-primordial spheres.

The universe begins.

6. Dimensionless and Fundamental Physical Constants. Long before George Johnstone Stoney and Max Planck worked to discern natural units, scholars have tried to discern the most basic units that define us throughout time. In the 1800s that effort became an international collaboration and by 1992, it became a global standard, ISO-31, defined by the International Organization for Standardization (ISO). Within that framework, in 2016, Peter J. Mohr, David B. Newell, and Barry N. Taylor published “CODATA Recommended Values of the Fundamental Physical Constants” in the Journal of Physical and Chemical Reference Data.

Their constants define the bridge between the finite and infinite.

Discussions about the necessary dimensionless constants needed to construct the universe are helpful. There is the 2011 work of John Baez, How Many Fundamental Constants Are There? In 2005 the work of Frank Wilczek, Anthony Aguirre, Martin Rees, and Max Tegmark emerged; they thought 31 dimensionless constants would be required to start the universe.

Within our simple model, in effect, a rather different dynamic emerges whereby the dimensionless constants that are part of the Planck base units and infinitesimal-primordial spheres dynamics become penultimate. These equations all bridge the finite and infinite. These become the geometries of the earliest universe. And somewhere in that process — I speculate between Notations 50-to-67 — five tetrahedrons or five octahedrons bond, and eventually those so-called pentastars and pentagons begin to move and we have a new kind of motion that appears independent and free of the earlier structures and we call this motion, quantum fluctuations. There are four most-basic geometric manifestations for these fluctuations.

7. All time is now. In this model all notations are necessarily active right now. Each builds on the other. It resonates with the concepts within loop quantum gravity with Carlo Rovelli. It is a key issue in physics and philosophy. Within this model time’s arrow only appears within Notation-202 and that directional may well be mitigated by sleep cycles. As with the work of Neil Turok, this universe is forever just starting within Notation-0 and Notation-1 and every notation shares in common those first 64-to-67 notations. That it is possible to begin to address this key issue of time symmetry is a bellwether.

8. The finite-infinite relation: Continuity, Symmetry, and Harmony. That these three qualities of infinity nurture and shape the finite is another key issue. Too many of our finest scholars have limited infinity over the years. By doing so, they ostensibly remove the qualitative from our models of reality. Within that attitude there is a panoply of bad behaviors that start with solipsism, become a narcissism and then a form of nihilism which too often devolves to become dystopian. We can do better.

Thank you.

Here are eight concepts, ideas generated over ten years of looking at those 202 notations. It was called idiosyncratic by one scholar and we agreed. It is entirely idiosyncratic, yet it is based on the most simple logic, geometry and mathematics that we have.

Let’s figure this out together. Again, I thank you. -BEC

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Endnotes / Footnotes

Please Note: Footnotes and endnotes are dynamic. Based on the feedback from our visitors like you, these could be updated at any time. Thank you. -BEC

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[1] Mathematical universe.

Eugene Wigner, The unreasonable effectiveness of mathematics in the natural sciences, 1960
Max Tegmark, Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, Knopf, 2014
Also see: ArXiv (PDF) 2007
Redefine space, time and infinity, 81018, 2020

Within our time, Wigner and Tegmark carry on the historic tradition of Pythagoras and many of the greats of history. Within our studies, we provide actual numbers, all an extension of Planck units and basic geometries, that outline our universe from the very first instant of creation to this very day and time.

For millennium, scholars have proclaimed the place and importance of mathematics. In January 2016, I posted my initial analysis of numbers. Pi (π) is still my #1.

It is unique and requires a very different view of the universe.

Nobel Laureate James Peebles said back in 2019 that there is no theory for the start. He had not seen our chart of numbers; it is our simple start on defining the very first instants of this universe using Planck Time, pi (π) and her infinitesimal-primordial spheres. If we assume one sphere per unit of Planck Time, there is an explosion of spheres that goes on even today. That process is a most-intimate binding of everything, everywhere throughout all time.

Crazy? Of course. But then, this all started in a high school.

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[2] Notations. Just 202 base-2 notations to encapsulate the universe is an Art of the Impossible. Check the math. Savor Euler’s equation. We were confused and dumbfounded in 2011 when we first did the math. It was too easy and too comprehensive. For high school people, it was fun but overwhelming. We asked, “What could this mean?” and turned to our scholars for answers.

I suggest doing a study of “Notations. Within these pages, click on the image of the magnifying glass on the top right on every page within this website. Enter the word, Notations, then do a key word search on Notations. We’re slowly making it a study.

STEM. You can only imagine our joy in discovering what we called the penultimate STEM tool. We wrote letters to the editors to begin to get some feedback.

Working with the epochs of big bang cosmology as defined by Stephen Hawking, we were surprised to find just a picosecond’s difference with our model. We thought ours was more integrative, predictive, and comprehensive. And, we began to think that Hawking was wrong about the nature and place of infinity.

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[3] Pi (π). “Let’s go over this one more time. We are missing something.” Even kids become arrogant; we learn to be big shots early. We say, “I understand,” when we have barely scratched the surface.

At one time I thought that it was overly simplistic to try to make a case that infinitesimal-primordial spheres at the Planck Length were the primary building blocks of the universe, then I began looking into that simple sphere and found complexity. Cubic-close packing of equal spheres looks like a simple stacking exercise until the center points of each sphere connect. The Fourier transform comes alive. Then, drilling within further, attractor and repeller spheres come active. There continues to be so much to learn.

A key facet of these earliest notations, i.e. all those prior to quantum fluctuations, is the perfections of the sphere and basic geometries. There should be many notations where it is too small and too dense for imperfections. We speculate that that domain of perfection dominates at least the first 50 notations and possibly can momentarily spike through all 202 notations.

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[4] Small-medium-and-large scale universe. The scholarly community works within Notation-202. Their current work in cosmology brings them back to about Notation-178. In photonics and optics, the work is down within Notation-74. In particle physics, the work is within Notation-67, perhaps Notations 66-and-65. The mysteries seem to be from Notations 1-65, yet there are many disciplines where fast arrays of mathematics define most, if not all, notations. Langlands programs, string and M-theory, and SUSY are the oldest three disciplines. Then comes a host of other small-scale studies, that include causal dynamical triangulation (CDT), causal set theory (CST), scalar field theory, loop quantum gravity (LQG), spectral standard model, and Moonshine Shadow* (Umbral Moonshine Conjecture).

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[5] Infinitesimal-primordial Spheres. The simple keys to start this universe have been discussed on virtually every page of this website. Yet to reduce it down to cubic-close packing of equal spheres and the Planck base units is just too simple. That there would be an explosive quantity of infinitesimal-primordial spheres is simply beyond comprehension unless one engages an active, total finite-infinite relation based on the continuity, symmetry, and harmony inherent within each infinitesimal-primordial sphere.

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[6] Constants. Scholarship moves slowly to develop a consensus. It skips over people all the time.
George Johnstone Stoney appears to be the first to try to define natural units. He’s an unknown.
Max Planck’s natural units are better known, but barely recognized for over 100 years.
International Organization for Standardization, quick dissemination to the world’s people.
Peter J. Mohr (AIP), David B. Newell (AIP), Barry N. Taylor (AIP): Three primary scholars of NIST.
Constants define the bridge between the finite and infinite: Here I jump off into the deep end. I am in search of any scholarly work that makes a similar claim. The headwinds are strong with the work of David Hilbert, Kurt Gödel, Max Tegmark and the people working on renormalization. They create various firewalls around the infinite.
John Baez, How Many Fundamental Constants Are There? John was early to these questions yet he quickly engages the most difficult parts of the subject so complexity comes quickly. Instead of spheres, he engages the octonion!
Frank Wilczek, Anthony Aguirre, Martin Rees, and Max Tegmark. Four of the leading scholars of our time, this work was first published in 2005 yet it struggles to gain real traction but it does open many basic questions. It came to my attention in February 2018 and I was smitten by it!
Pentastars. Aristotle’s 1800-year old mistake has become a 2400-year old mistake. Scholarship has not engaged the 7.3561031724+ degree gap. The most recent “rediscovery” of the gap was by Lagarias & Zong in 2012.
At least four most-basic geometric manifestations. Geometric constants are as important as all other constants! I think this could be a project where we all work on it together.

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Peter J. Mohr (AIP), David B. Newell (AIP), and Barry N. Taylor (AIP), “CODATA Recommended Values of the Fundamental Physical Constants” in the Journal of Physical and Chemical Reference Data (45, 043102) https://doi.org/10.1063/1.4954402

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[7] Time. Non-intuitive, we feel the flow of time each evening when we go to sleep and every morning when we look into the mirror. Those who suggest that all time is Now seem to engage in specious thinking at best. My first exposure to such a conclusion was in 2016 when reviewing the work of those who attended a conference, Cosmology in Time at Perimeter Institute for Theoretical Physics in Waterloo (Canada). Also, at that time, Richard Muller of Berkeley had released his book, Now: The Physics of Time and Carlo Rovelli was rethinking the very nature of time through Loop Quantum Gravity (LQG). It was the beginning of a popular upsurge and interest in time symmetry, yet it has not gained deep traction among scholars. Something is missing.

The universe is symmetric, except Notation-202 appears and feels asymmetric because the perspective is from within a local solar system and not that of the universe. Over the years we have made a few highly-speculative guesses about how sleep is the time that our unique time and experience is recompiled into the universe of experience. Of course, much more will be done with that speculation.

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[8] Continuity-Symmetry-Harmony. The qualitative exists in our minds. It is real, yet it requires a judgment that involves continuity, symmetry, and harmony. These three qualities of pi permeate the universe at its finest, smallest, deepest level. Ignoring that continuity, symmetry, and harmony is possible because quantum physics readily masks its presence so we can develop our own solipsistic universe which for us becomes our really real. As a result, there is a raft of bad behaviors that start as a form of solipsism, morphs into a narcissism which opens the way to nihilism that devolves into dystopian thinking and behaviors.

To reverse direction within this world, we need to return to the inherent values that are “baked” into our universe. Thank you. -BEC

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References & Resources

Please Note: References and resources used to shape this posting are not yet footnotes; concepts are still being formulated. Thank you.

Ronald J. Adler, Six easy roads to the Planck scale (PDF), ArXiv, 2010 AAPT, 2010)

Philip Ball, Physicists Rewrite the Fundamental Law That Leads to Disorder, Quanta Magazine, May 23, 2022

Doug Bonderud, 5 Odd Theories of the Universe That Might Just Be True, Now, Northrop Grumman, April 2022

Valerio Faraoni (e), Three new roads to the Planck scale (PDF), American Journal of Physics 85, 865 (2017); https://doi.org/10.1119/1.4994804

Universe’s Constants Now Known with Sufficient Certainty to Completely Redefine the International System of Units, NIST, 2016. See: CODATA Recommended Values of the Fundamental Physical Constants: 2014, See: Current their list of sixteen fundamental constants.

Valerii M. Vinokur et al, Arrow of time and its reversal on the IBM quantum computer (ETH-PDF), Nature, 2019, https://doi.org/10.3929/ethz-b-000332774

• Garth Warner, Harmonic Analysis on Semi-simple Lie Groups I, Springer-Verlag, ISBN 0-387-05468-5, 1972

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Emails

Please Note: Just a few of the emails I have sent out regarding this posting. The first emails are to those who have been referenced in the article.

11 May 2022 at 11:16 AM, Frank Wilczek (MIT), upon receiving the 2022 Templeton Prize
11 May 2022 at 6 PM, James B. Hartle (UCSB)
12 May 2022 at 2:51 PM, Max Tegmark (MIT) on the homepage today
• 12 May 2022, 4:00 PM, Barry Taylor (NIST)
• 12 May 2022, at 8:15 PM, Jisuke Kubo

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IM

Please Note: Some of my other communications to people, particularly instant messages and tweets. None of this work is done in a vacuum. Our world is in turmoil. It needs new models of who we are and why.

7:16 PM · May 10, 2022 @K_JeanPierre The most important thing we can do as a people is to get us all talking about the first principles of our sciences. There we’ll discover continuity, symmetry and harmony. All three must work together. Here’s a start: https://81018.com/

1:43 PM · May 12, 2022 Xi Jinping 习近平 @xijinpingc The question is “more centralization” or “decentralization.” Centralization requires obedience, monitoring, and control. Decentralization requires education and a most compelling offering that empowers people’s creativity for self-control: https://81018.com

May 12, 2022 @WHO @UNDESA @UNECOSOC The question is “more centralization” or “decentralization.” Centralization requires obedience, monitoring, and control. Decentralization requires education and a most compelling offering that empowers people’s creativity for self-control: https://81018.com

4:25 PM · May 17, 2022 @POTUS Please don’t give up on any part of the USA or any person. Our biggest problems result from incoherent scientific theories. We are breaking free of little worldviews and moving toward an integrated view of the universehttps://81018.com — is just a start!

10:44 AM · May 26, 2022 @DalaiLama More than live together, we need to see how we are all deeply, profoundly, and totally interconnected and come from the same active stuff, the first 64 notations of the 202 base-2 notations that define everything, everywhere for all time: https://81018.com/chart/ Also see: https://81018.com/agree/

10:54 AM · May 26, 2022 @WatsonInstitute If we were to all recognize that we all share the first 64 notations (out of 202 base-2 notations from the start of the universe till now): https://81018.com/chart/ and we each qualitative effect the whole: https://81018.com/ethics/ just maybe we’d begin to change.

7:55 PM · May 29, 2022 @linakhanFTC Every decision should be made in light of our history and in light of the universe. Our little worldviews are too often laced with personal bias. We need to graduate to a fully-integrated, mathematical view of the universe; our start is here: https://81018.com/. Lina Khan is Chair of the Federal Trade Commission.

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Keys to this document, agree

  • This page was started on Monday, May 9, 2022.
  • The last update was Sunday, May 29, 2022.
  • This page became the homepage on Thursday, May 12, 2022.
  • The URL for this file is https://81018.com/agree/
  • First headline is: Initial Conditions: Eight basic concepts
  • Second headline: Eight Initial Conditions
  • First byline is: Agreements between us about fundamental units is critically important.
  • Second byline: Agreements between all of us about fundamental units is a key.
  • Third byline: Let’s agree about the base units of our universe.
  • Memorial Day in the USA, a time to remember. Life was simple but we made it complex. So, we fight. Many die. We all can do better…

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Navigation: The links in each section go to the endnotes and footnotes just below. Please read through the entire article — it is relatively short — and then go back through it again. If you have been here in the past, you may already know where each link goes. Click on just those links that raise a question. Within the Endnotes/Footnotes, those links will take you to pages outside this website. Thank you. -BEC

A potential geometry for quantum fluctuations starts with Aristotle.

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Gaps, Fluctuations and Perfected States
by Bruce E. Camber (a working first draft)

Abstract: Most people are unaware that Aristotle made a mistake that was not caught for about 1800 years.* That mistake has also been largely ignored by academia. It had to be re-discovered at least twice yet then only within limited scholarly circles. If this gap, created by five tetrahedrons (and any gap with pentagonal structures), is not better understood, we limit our knowledge and understanding of the universe and ourselves. These fundamental gaps in geometry deserve more attention. Imagine if the gaps can be ordered based upon their adoption within other configurations and formulas. Imagine if the gaps have a possible role within quantum fluctuations. Also, the role of a geometry without gaps shall be more closely examined. It might be considered a domain of perfection (out of our 202 base-2 notations) that have (1).higher densities, (2).shorter time sequences, and (3).no-gap, simple geometries.

Introduction. Aristotle thought the universe could be tiled and tessellated with tetrahedrons. It cannot. Within his context, it requires both the tetrahedron and octahedron to fill a three-dimensional space perfectly (without gaps).

Aristotle’s mistake is quickly discerned with just five tetrahedrons, all sharing a common edge, two center points, and at least one face with another tetrahedron. There will be a 7.356103172453456+ degree gap between the first and fifth tetrahedron. For this study, it is called a five-tetrahedral gap. Within our work, that analysis began in 2016.1

There is also a five-octahedral gap created by five octahedrons sharing a center point (three octahedrons share two faces and two octahedrons share just one face). It’s a real gap and our analysis of it began in May 2022.

Gap Geometry-Physics-and-Chemistry.2 Also, there are the icosahedral gaps when an icosahedron is constructed with twenty tetrahedrons. In our high school classes it was called imperfect geometry, squishy geometry, and sometimes, quantum geometry. With four 7.35610+ degree gaps, one could easily squish or otherwise compress our classroom models. If evenly distributed over the twenty tetrahedrons, there is at least a 1.47+ degree gap between each tetrahedron.

The Pentakis dodecahedronal gaps are also considered.

These rarely-discussed gaps have been a key part of our analysis of numbers, geometries, chaos theory, fractals, and quantum fluctuations. It is also possible that these gaps are part of the dynamics of creativity, openness, indeterminism, uniqueness and human will.

These gaps are not arbitrary. Each is considered to be a very different kind of standard and each will be logically defined (“measured”) and categorized. Stretching, we include the mass gap of the Yang-Mills theory. The nature of mass and a very wide variety of hypothetical particles is open. Within the context of the first 64 notations out of the 202 that encapsulate everything-everywhere-for-all-time, more basic networks of more basic relations may be defined.

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Visualizations: Geometric software systems and geometric construction kits.3
We are just now starting to learn about the most popular interactive geometry software (IGS) and their dynamic geometry environments (DGEs) that are created. Wikipedia has a working summary of over twenty competitive programs. We are learning that this object on the right with its gap is quite possibly a first!

Our initial step will be to ask each IGS to create a five-tetrahedral object and a five-octahedral object. The icosahedron (twenty tetrahedrons pictured) has almost 30 degrees of gaps to include! Because these systems use two flavors of programming — continuity or determinism — we will ask for a sample from each.

We will do the same for geometric construction kits. There are over twenty popular sets. It is currently anticipated that none of these sets will display a gap.

We will report the results if any other system, hardware of software, can re-create a gap.

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Out of 202 base-2 notations: The most-infinitesimal scale — the 64 notations from the Planck scale to the scale for particle physics — can only be defined by logic and functions that are scale invariant, particularly key dimensionless constants.4 There are more than enough variables to speculate and postulate about the gap’s emergence within spacetime. The first notations are by definition the most dense with the shortest time sequences, and the most-simple geometries. With Planck’s base units, if we postulate one infinitesimal sphere per infinitesimal unit of time — that’s 539 tredecillion spheres per second — the dynamics of sphere stacking and cubic-close packing of equal spheres open and the most-basic tetrahedral-octahedral configurations emerge. It is a subject of extended studies by scholars like F. C. Frank and J. S. Kasper5 (circa 1957) and more recently by scholars like John Conway, Salvatore Torquato, and Jonathan Doye.6

The first column (pictured) from our 2014 desktop version of the original chart opened our first discussion about Langlands programs. Our question, “Can Langlands programs work within 202 base-2 notations that are defined by continuity-symmetry-harmony? Can it accommodate these gaps?”

These questions are asked of string-and-M theory, SUSY, CDT, CST, LQG, SSM, SFT and hypothetical particles. I believe all of this work can be located on this grid of 64 notations. And, in their midst will also be quantum fluctuations and the gaps.7

A place for those 202 base-2 notations to be studied.8 Since December.2011, we’ve known that the 202 notations mathematically and geometrically encapsulate the universe. Although starting naively and simply,.the discovery process was exciting albeit confusing. Our roots were from within a high school geometry class and we had, and continue to have, a step learning curve. This model is idiosyncratic. It flies in the face of current theory. Our letters, emails, and instant messages to scholars around the world have asked for help. We were prepared to hear someone say, “Been there, done that, and here’s why it is wrong.” Nobody did. So now, after ten years of study, we conclude there is something right about these charts and our goal has become to find out what that is.

The first base-2 chart of the 202 notations was published in December 2011. We had a simple container within which to put everything. On most the lines we had something to study. Yet, most of the first 64 notations were blank. By 2013 we were increasingly focused on the range from the Planck base units to particle physics.

If Langlands, Witten, S.J. Gates or any of our leading scholars make a claim on a notation or group of notations, the paradigm will shift. It is a challenge that begs people to hold back judgments of the unknown and to take thoughtful time to entertain the potentials of this domain defined by no less than 64 base-2 notations.

New speculations about these 64 notations have to go substantially beyond current work. To do that, three articles for ArXiv are being developed. Each will have multiple authors with long histories of pre-publishing through ArXiv. Outlines of these articles are given within many articles already online here, particularly STEM, this page, and New Ideas-New Concepts. So, yes, these new articles will extend and perhaps change the conclusions within previously-posted articles on this website. Thank you.

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Endnotes & Footnotes __

When an article is initially constructed, links often go outside this website. Most-often, within a couple of weeks of its first draft, those links become a footnote or an endnote.

* Mysteries in Packing Regular Tetrahedra, Jeffrey Lagarias, Chaunming Zong, (PDF), AMS, 2012
A domain of perfection or https://81018.com/perfection/

[1] 7.356103172453456+ degree gap between the fifth and first tetrahedron: It has no formally-recognized name within the scientific community. We once called it a pentastar gap, but now more accurately and generally, the five-tetrahedral gap. We have also begun calling the other “simple” gap, the five-octahedral gap. Our casual introduction to this gap was in 2011. We began writing about it in 2016. That five-octahedral gap was first discerned in May 2022. These structural gaps are really real. And, they are part of the physics of the infinitesimal. Our challenge is to begin to figure out what difference these gaps make.

[2] Gap Geometries, Gap Physics and Gap Chemistry. The icosahedron, one of the basic five Platonic structures, can be created with twenty tetrahedrons. Of course, each set of five tetrahedrons has a total gap of 7.35610+ degrees. We are asking about the necessary mechanisms for attractors and repellers and for dimensionless constants to manifest. What might that circuitry be? Is it vertex-to-vertex, along the edges or from face-to-face (or plate-to-plate), or holistic? Our hope within our studies of Langlands programs, string-and-M theory, SUSY, and other related disciplines, is that we will find new insights to these questions. Our simple start is to look for connections to tetrahedrons-and-octahedrons and to base-2. We are also asking questions about infinity defined here as continuity-symmetry-harmony.

Our goal is to further define the first ten notations. Our hope is to affirm the most likely paths to the five-tetrahedral structure, then to the twenty-tetrahedrons as an icosahedron, and then to twelve sets of five tetrahedrons known as the Pentakis dodecahedron. By the way, that calculation of squishiness, a distribution of the four gaps, each 7.35610+ degrees, render 29.4244 degrees now spread over 20 tetrahedrons or approximately 1.47+ degrees per tetrahedron. In reality, it looks considerably looser.

From the geometric gaps to actual physical gaps such as the mass gap, to chemical gaps such as synaptic functions, there is an anharmonicity that is being explored. The synaptic function is re-engaged; systems are systems and analogies open new insights. There is a kind of dissonance with these gaps; however, here it can be constructive and productive. As a work in progress, the Wikipedia’s analysis of anharmonicity is instructive. If continuity, symmetry, harmony are the perfections of the sphere, the imperfections of the gap (discontinuity, asymmetry, and dissonance or anharmonicity) are not necessarily negative qualities.

Certainly human creativity requires room to breathe.

An unsolved mystery is the Yang–Mills existence and mass gap. One might readily conclude that is unsolved because it has not been considered within the grid of 202 notations, particularly with the grid of the first 64 notations, and most especially within the grid of the first ten notations where the paths, shapes, and textures of mass are initially developed.

[3] Visualizations. In our high school we tried using Mathematica, but it was too advanced for most, including me. We did use the Zometool; however, it was disconcerting not to be able to see the gaps. Our clear-plastic tetrahedrons and octahedrons were a better representation of the real realities. Math manipulatives, both as physical objects and computer-generated graphical models, are important teaching tools. So, with this article we have made an earnest commitment to explore both interactive geometry software (IGS) and a diversity of geometric construction kits. Wikipedia has a working summaries of these dynamic geometry environments (DGEs) whereby the features and results for continuity and determinism can be tested.

[4] Key Dimensionless Constants. In 2011 when we started, John Baez had identified 26 constants necessary for our study of the Standard Model of Particle Physics. As we researched further we found the 2006 work of Wilczek, Tegmark, Rees, and Aguirre where they had identified 31 constants in search of a theory of everything (TOE). Wikipedia identified 104 dimensionless constants. The National Institute for Standards & Technology (NIST) had identified over 300 (PDF – 2008, SI Report). Most interestingly, a Canadian (Quebec) geometer, Simon Plouffe, has identified, through algorithmic programming, 215 million mathematical constants (as of August 2017) which includes pi, Euler’s number (I am still chasing claims about more11.3 billion, computer-generated, mathematical constants). The Standard Model for Particle Physics (Wikipedia) is well known. Its weaknesses are, too. The first 64 notations open a huge infrastructure whereby the model can become a continuum from the Planck scale to the standard cosmological model.

[5] Frederick Charles Frank and John Simon Kasper. Frank, F. C.; Kasper, J. S. (1958-03-10). “Complex alloy structures regarded as sphere packings. I. Definitions and basic principles”Acta CrystallographicaInternational Union of Crystallography (IUCr). 11 (3): 184–190. doi:10.1107/s0365110x58000487ISSN 0365-110X. Also see: Frank–Kasper phases retrieved from Wikipedia on June 24, 2022.

[6] Jonathan P.K. Doye. Jonathan P. K. Doye, A model metal potential exhibiting polytetrahedral clusters, https://doi.org/10.48550/arXiv.cond-mat/0301374, 2003

Also, see my personal correspondence, Jonathan Doye.

[7] Quantum fluctuations. Our study of quantum fluctuations is still young and naive. For the many scholars within Langlands programsstring-and-M theory, SUSY, CDT, CST, LQG, SSM, and SFT, and those working with hundreds of hypothetical particles, a base-2 container for their work could be insultingly simple. Also, for all those who have held onto historic definitions of infinity, it may be difficult to redefine infinity quite so simply as continuity-symmetry-harmony (and to have time become the Now). For all those who have held onto Hawking’s concept of the big bang, it may be quite difficult to let it go. It’s ok. These kinds of transitions are difficult for everyone.

[8] Place where the 202 base-2 notations are studied. There is nothing easy about exponential notation. It’s non-intuitive within our current framework for thinking about spacetime. Those 202 notations that encapsulate the universe seem altogether too simplistic. With over four centuries of a Newtonian worldview, it is will not be easy. Yet, base-2 notation from the Planck scale to current time is upon us. It is time to make it a serious study.

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References & Resources

Okuma, R., Kofu, M., Asai, S. et al. Dimensional reduction by geometrical frustration in a cubic antiferromagnet composed of tetrahedral clustersNature Communications, 12, 4382 (2021). https://doi.org/10.1038/s41467-021-24636-1, , (e)

• Quantum fluctuating geometries and the information paradox (PDF), Rodolfo Gambini, Rodrigo Eyheralde, Miguel Campiglia, Jorge Pullin, 2017

• What every physicist should know about string theory, Ed Witten, Physics Today, 68, 11, 38 (2015)https://doi.org/10.1063/PT.3.2980

•  John Willard Milnor (1985). “On the concept of attractor”. Communications in Mathematical Physics99 (2): 177–195. doi:10.1007/BF01212280S2CID 120688149.

•  John Willard Milnor is one of the five mathematicians to have won the Fields Medal, the Wolf Prize, and the Abel Prize (the others being SerreThompsonDeligne, and Margulis.)

•  Bell’s Theorem, Non-Computability and Conformal Cyclic Cosmology: A Top-Down Approach to Quantum Gravity, T.N. Palmer, arXiv:2108.10902, August 2021

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Emails

• Dharam Vir Ahluwalia, Center for the Studies of the Glass Bead Game, June 7, 2022
Johannes Buchner, June 5, 2022
• David J. Gross, Kavli Institute, University of California at Santa Barbara, June 5, 2022
• Espen Gaarder HaugNorwegian University of Life Sciences (NMBU), May 24, 202
• National Science Foundation, Washington, DC, May 31, 2022
• Monika Schleier-Smith, Stanford University, May 30, 2022
Matthew J. Strassler, June 6, 2022
• Paola Zizzi, University of Padua, June 5, 2022 @ 4:24 PM

Many geometers, chemists, and physicists know that five tetrahedrons sharing a common edge create a gap: https://81018.com/gap/ Most do not know that five octahedrons create the same gap; and that stacked, this gap is a beautiful thing to see: https://81018.com/15-2/

My study of that gap is here: https://81018.com/geometries/

We have unsuccessfully searched for studies that explore the very nature of that gap.
We’ve asked many scholars, “Might that gap be associated with quantum fluctuations?
Could there be a geometry for quantum fluctuations?”

Might you have any insights that could help us grasp these realities more profoundly? Thank you.

Caltech (IQIM): Jason Alicea (June 29, 2022) and a few others
University of Maryland (Joint Quantum Institute): Maissam Barkeshli and a few others

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IM

8:08 AM · Jun 9, 2022 @7homaslin @nattyover Congrats. You all have been doing sensational work for ten years. Natalie has been excellent, but many others are as well. I’ve written a letter to you here — https://81018.com/quanta/#Lin The top of that page is my tribute to the magazine and to Simons people.

3:00 PM · Jun 6, 2022, @MattStrassler Can you help us unfold this base-2 chart of the universe: https://81018.com/chart/ The current homepage is always my latest struggle with it all: https://81018.com/. PS. Note that at the Center for the Fundamental Laws of Nature, we have begun following the work of Andrew Strominger, Cumrun Vafa and you. Perhaps you all can help Lisa Randall and Howard Georgi.

9:25 PM · Jun 4, 2022 @DM_Rubenstein Our worldviews are too small; we need the universe and the only way to begin to get it is with mathematics that start with the Planck base units. There are 202 base-2 notations from Planck Time to this day. http://81018.com opens a start to a highly-integrated view of the universe.

7:05 PM · Jun 4, 2022. @theo__oneill How about a paradigm shift so we don’t get caught up in our own little worldviews (solipsism at best)? How about entertaining a base-2 parsing of the universe? There are just 202 notations: https://81018.com is a start. Your comments would be wonderful.

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Participate

The world is increasingly nihilistic. Many places have become dystopian. We all need to do something.

We are preparing pages so we all become teachers of an integrated view of the universe whereby we all begin to profoundly understand that what we do each and every moment effects the quality of life within this universe.

This is a key document. Click on the “Back Arrow” (or “Left Arrow”) at the top of this page to go back to another key document. If you agree and you will begin to teach others about this integrated view of the universe, we will list you within our soon to-be-added “Teachers” page. Thank you.

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Keys

• This page became the homepage on June 14, 2022.
• This page was initiated on Friday, May 6, 2022 at 7:34 PM, National Space Day.
• The last update was Saturday, July 8, 2022.
• The URL for this file is https://81018.com/geometries/
• Related URLs include: https://81018.com/idea/ https://81018.com/editors/
• The headline for this article: From Perfected States to Gaps & Fluctuations
• First byline is: The Geometries of Quantum Fluctuations: Re-visiting Aristotle and Others.
• The current byline is: A possible geometry of quantum fluctuations starting with Aristotle.

Future work:
3.3 inches (8.39 cm): 1.2980×1033 units (Notation 112) Read: “1.298 decillion touchpoints”
6.6 inches (16.7835 cm): 2.60×1033 units (Notation 113)
13.22 inches (33.56 cm): 5.1922×1033 units (Notation 114)
26.43 inches (67.1343 cm): 1.03845×1034 units (Notation 115) Read: “10.38 decillion touchpoints”
52.75591 inches(1.34 meters) 2.08×1034 units (Notation 116)
105.72 inches (2.68 meters or 8.8 feet): 4.15×1034 units (Notation 117)

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On following the work of Magdalena Skipper…

Magdalena Skipper (PhD), Editor in Chief, Nature
Chief Editorial Advisor, Nature portfolio including Nature Communications

Articles: Day in the life of the editor in chief of Nature, 31 October 2019
ArXiv: Legends of Nature and Editors-in-chief (PDF), Zhiwen Hu, Chuhan Wu, Zhongliang Yang, Yongfeng Huang, Thu, 24 Oct 2019 15:11:39 UTC
Homepage: Nature Communications, Springer Nature
LinkedIn
Twitter
Wikipedia
YouTube: Magdalena Skipper, Editor in Chief, Nature Research Journal

Most recent and second email: 20 April 2022, at 10:10 PM

Dear Dr. Magdalena Skipper,

This is my third time to communicate with you. About a year ago I responded to your tweet (below) about equity and gender bias. And a bit earlier, May 31, 2021, I had sent an email about our work that came out of a New Orleans high school geometry class on December 13, 2011. It was our penultimate STEM project; it was logical and simple, but… iIt was much more. If it prevails, it is a very different view of space, time and infinity.

I think there is a general reluctance to be critical of a high school STEM project. Besides, it takes time and energy, especially if the work falls outside the general thrusts within academia, and ours does! So, our progress has been slow. There has not been a lot of feedback… mostly one-word statements like “idiosyncratic.”

To remind me what questions I’ve asked of a scholar in the past, I create a reference page to critical work and to my notes, emails and tweets to them. My page about your work is now “in process.” The URL for it is: https://81018.com/skipper/ 

In 2018 I had written to your Elizabeth Gibney. Long before that, I sent a “Letter to the Editors” asking for help. We genuinely wondered where and how our base-2 logic was failing us. We were told our article was rejected (yet it wasn’t an article — it was a letter to the editors).

Since that time many more questions have come up.

“Why are people overlooking one of the most basic relations in mathematics and science?” — pi (π). We decided that it was a “been there-done that” response.

I often stop my students and ask, “What are we missing? Can we go back over this one more time?” They groan but are often surprised to learn so much more the second, third and fourth time around. Weeks later we might do a fifth and sixth time around. I did that with John Conway as we were looking at the octahedron, and even the surreal man himself was surprised to learn something new.

Our general website is: https://81018.com/

My challenge is to figure out in what ways our 12 steps to start the universe fail the simple tests of logic. Of course, eventually we will reduce those 12 to axioms, postulates and theorems. That is our next step, yet logic is logic and at the current level of generality, I think people can engage, guess, and question.

Yes? No? Thank you.

Warm regards,

Bruce

Tweet: June 26, 2021

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.”

Here is her tweet. I responded with 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!

First email: Monday, May 31, 2021, 5:55 PM

Dear Magdalena Skipper:

I thought the big bang theory was about the first instant. It’s not. The scholars can get within a billionth of a second with some glimmers of a trillionth of a second. There is no model or theory that brings us closer. James Peebles said it in his 2019 acceptance speech in Sweden (Nobel physics from Princeton). I didn’t believe it, but then Dan Hooper (Chicago-Kavli-Fermilab) just confirmed it this morning.

Our problem is essentially the hotly debated finite-infinite relation. If we all could lighten up a bit on both sides of that equation and just do a little logic and science, we just might get somewhere: https://81018.com/envision/

There is nothing easy about it: https://81018.com/alphabetical/ is a partial list of the big brains and thought leaders who I’ve hoped would answer my questions.

My needling of Peebles is here: https://81018.com/peebles/ while my overviews are here: https://81018.com/2021/03/23/peebles/ and here: https://81018.com/starts/

I thought you would find it of some interest. Surely I wish you well with your enterprise.

Warmly,

Bruce

PS. Our model developed in a high school geometry class in 2011 resulted in these numbers in 2016: https://81018.com/chart/ where a trillionth of a billionth of a second (10-21 seconds), a zeptosecond, ranges between Notation 65-to-67. PlanckTime or StoneyTime or Primordial Time (Lemaitre) is at Notation-0 and the first instant is Notation-1. -BEC

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On discovering the work of Rashmi Shivni

Of course, the best place to learn about Rashmi’s work is her website: http://www.rashmishivni.com/ It is difficult to find anybody to look into work that is not part of the standard fare. On my first introduction to her work, I thought, “She might want to try to figure out this puzzle. It is not a trivial pursuit.”

Articles, Homepage, Twitter, YouTube

Second email: 26 April 2022 @ 3:08 PM

Dear Rashmi:

With all my communications now, I log them on the website so I can quickly have a memory jog and links to those people whose work has been studied during the development of a new homepage and other key pages. My reference page to your work is here:
https://81018.com/shivni/ and the page being developed is here:
https://81018.com/gravity/ I thought you would want to know.
Best wishes,
Bruce

First email, 20 April 2022 @ 11:38 AM

Hi Rashmi –

Our STEM story is a mystery and monster. How can math work some time but not all the time? All the big and important folks — AAAS, Scientific American, Nature — ignore us because our work started in a high school geometry class where we went inside a tetrahedron. Sounds pretty tame, but we discovered there are four smaller tetrahedrons in each corner and an octahedron in the middle. We went inside the octahedron and discovered the smaller octahedrons in each of the six corners and the eight tetrahedrons, one in each face.

Well, that could easily be an infinite progression. 

So we started dividing by 2 even further. In just 45 steps going deeper and deeper within, we were inside particle physics; and in 67 more steps, we were in Max Planck’s scale. Just 112 steps from that original tetrahedron (linked above) to their very smallest possible tetrahedron very near the Planck scale.

That all seems quite logical. No fancy theories. No crazy ideas.Just simple geometry. But now it gets crazy.

We multiplied our objects by 2 (instead of dividing by 2) and in 90 additional steps, Planck Time was out to well over 13.81 billion years; and the Planck Length was well beyond the size of the universe! Check the numbers: https://81018.com/chart/

Yes, this all happened in a high school geometry class in 2011.

We first talked about it among teachers but rather quickly discovered it didn’t work with current cosmological theories. So, we pulled back and started asking our leading scholars questions. 

They are a little reluctant to criticize but that is exactly what  we need. If we are missing something, it is an enormously important piece of logic. If they are missing something (and even they admit that they are perplexed at all their complexities), well then, let’s work on this together! Yet, that’s not happening as of today.

Of course, I would be delighted to hear from you and get your preliminary reading on our little conundrum!  Thanks.

Warmly,

Bruce

PS. Your path is so inclusive of so many basic, core disciplines, I thought you’d love this enigmatic problem. It opens STEM wide and far.  -BEC

Twelve Open Questions * About Our Universe

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Answering “Yes” starts a paradigm shift
by Bruce E. Camber (a working draft)

In 2019 Nobel Laureate James Peebles, Princeton, said that we do not have a theory about the first moments of the universe. He says that we do not know how this universe got its start. So, let’s be asking a few questions:

  1. Is it possible that the very first moment of the universe1 (much-much smaller than a trillionth-of-a- trillionth of a second) manifests as base units like those defined by Max Planck or George Stoney?
  2. Is it possible that the first manifestation2 of those base units is an infinitesimal sphere?
  3. Do the characteristics of pi describe those spheres? (Yes, they do.3)
  4. Does the Fourier Transform impart either electromagnetism or gravitation to each sphere?4
  5. Is it possible that one sphere manifests per unit of length and time?
  6. Does that compute to 539 tredecillion spheres per second using Planck units and 4605 tredecillion units per second using Stoney time? Within that range just may be a variable cosmological constant.
  7. Is it possible that the densities within the earliest notations are on the order of a blackhole?
  8. With this generation of infinitesimal spheres, would base-2 notation create a sense of order?
  9. In using base-2 notation, are there 202 base-2 notations from Planck Time to the current time? I believe that simple math is correct.
  10. Are the calculations for Notations 143-and-144 significant? These notations may help to affirm the viability of the model. For example, the simple calculation for time for Notation-143 is .60116 seconds and for Notation-144 it is 1.2023 seconds. At one second the Planck Length multiple is a very close approximation of the distance light travels in that second.
  11. Is it significant that quantum fluctuations are measured within Notation-67? It appears to be the limit of our abilities to measure an actual physical length. Notation-72 appears to be the limit of our abilities to measure a duration of time. A variable domain of perfection is postulated within notations 1-64.
  12. Are notations 1-64 redefinitions of a point, point-particle and a vertex?

Your help is requested. If you can answer “Yes” to any question here, please let us know. If you answer “No” and can tell us why, that response will make a difference (embedded link: https://81018.com/comment/ ) Thanks. -BEC

Those embedded links above (that are not footnotes) open new pages:

  1. Planck’s base units: https://81018.com/planck-base-unit/
  2. Infinitesimal sphere: https://81018.com/sphere/
  3. Characteristics of pi: https://81018.com/challenge/
    Continuity-symmetry-harmony: https://81018.com/almost/#CSH
    Fourier Transform: https://81018.com/fourier/
  4. Fourier Transform: https://81018.com/gravity/
  5. One sphere per unit of length and time: https://81018.com/expansion/#4b
  6. 539 tredecillion spheres: https://81018.com/tredecillion/#Top
  7. Blackhole: https://81018.com/blackhole/
  8. Base-2 notation: https://81018.com/virtual/#2f
  9. 202 Base-2 notations: https://81018.com/chart/ 
  10. Planck Length multiples at Notation-143: https://81018.com/a143/
  11. Quantum fluctuations: https://81018.com/fluctuations/
    Duration of time: https://81018.com/particle/
  12. Point-particle and vertex: https://81018.com/point-particles/

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Endnotes & Footnotes

* More 12 points: (1) Twelve key concepts (formulas), (2) A twelve-step program (to move beyond big bang addictions), (3) The 2018 Overview (12 points), and, for now, (4) A 12-question survey about the start of the universe. There will be more!

1The first moment of the universe. One might say, “This is the very start of the universe when space, time, matter and energy are first created.” Yet, there are many in our little world who still affirm Sir Isaac Newton’s absolute space and time; those people might say space and time is forever. That issue has been debated for centuries, the most famous from 1715 to 1716, well-documented within “The Leibniz-Clarke Correspondence” and other papers. It seems, however, that there is a growing consensus that there is an actual starting point for space and time. Even in the Hawking model of the big bang, their postulated start was the beginning of time. -BEC

2The first manifestation. Given that Planck Length and Planck Time are considered the smallest possible units of both, in the base-2 progression, the first measurable length is within Notation-67 and the first measurable unit of time is within Notation-72, the question is, “What is manifest within each notation prior to a possible measurement?” A friend tells me, “Many people believe that spacetime could emerge from pre-geometric concepts.” I ask somewhat rhetorically, “True. So, what is this pre-geometry?” And I answer, “It is the most simple geometries. Don’t make it any more esoteric than it needs to be. Go back to pi. Go back to the dimensionless constants. This domain is hypostatic; it is the foundations of the foundations. Keep it as simple as possible. The simplest thing we know is an infinitesimal sphere. Just two vertices.”

3Of course they do! So many scholars like to make up new words to describe their abstract concepts. Occasionally, some of these concepts get lifted up into the public’s discourse, but it is rare. I believe it is far better to use the words and concepts that are currently available to us. As we go over them just one more time, new insights emerge. I remember the great geometer John Conway asking me, “Why are you so hung up on the octahedron and its tetrahedrons?” My answer, “…because we are missing something. That octahedron has much more to teach us!” He laughed, but knew it was true. We all should know the most simple internal geometries of the octahedron and hardly anybody does. We should all know how the octahedron and tetrahedron emerge from sphere stacking and packing. Hardly anybody does. And, it all starts with most simple-but-utterly-complex pi (π) with its inherent dimensionless constants and continuity-symmetry-harmony.

4From Each Sphere. This point will ruffle many feathers. It is a stretch. With electromagnetism and gravity dominating the public discussion for so long, it will be an idiosyncratic leap for sure. I encourage a closer examination of the three commonly-accepted faces of the Fourier Transform. The images on that page come from Wikipedia people. If those faces of the Fourier Transform are the basis for spin, and then the basis for pulling within and pushing out, the paradigm will begin to shift!

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References & Resources

•  Instantons and FourManifoldsDaniel SFreedKaren KUhlenbeck; Mathematical Sciences Research Institute, Springer-Verlag, 1984

•  Bell’s Theorem, Non-Computability and Conformal Cyclic Cosmology: A Top-Down Approach to Quantum Gravity, T.N. Palmer, arXiv:2108.10902, August 2021

Every hypothetical particle holds clues. Every formula within Langlands program and string -and-M theory hold clues. They all have to work together and be part of a continuum.

Like the endnotes and footnotes, the references and resources are already within those webpages linked from each question. Notwithstanding, any question coming from our visitors may become a reference or a resource.

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Emails

April 21, 2022, Silvia Milana, Nature, London
April 20, 2022, Karen Uhlenbeck, IAS
April 20, 2022, Magdalena Skipper
, Editor-in-chief, Nature
April 19, 2022, James Peebles, Princeton
April 15, 2022, Renate Loll, Radboud, Netherlands
April 14, 2022, Jamie Farnes, Oxford
April 13, 2022, Robert Langlands, IAS
Apr 12, 2022, 4:54 PM, David Kaiser, MIT
Apr 12, 2022 @ 10:53 AM, Ulrike Tillmann, Cambridge (Oxford): Redefine the point and vertex.

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IM

, 2022: @R_Trotta We have a sense of infinity; for most people, it is rather overwhelming. The concept of the universe is, too. Yet, if we engage a mathematically-integrated view, the universe is not so imposing, and infinity is more approachable. Start here: https://81018.com/

@3_takeaways. An integrated view of the universe, especially with pi (π) refocusing the finite-infinite relation, solipsism and narcissism may be replaced by the three basic facets of pi — continuity, symmetry, and harmony. We’ve been duped long enough! https://81018.com/duped/

@blviray @maano The most diverse, equitable mathematics will happen when we have a mathematics for the beginning of the universe, the very beginning or first moment, i.e. Peebles — https://81018.com/peebles/ Everybody will fall in love with math! https://81018.com/question/

@ArnoKeppens @petertallack @sciencefactory Y’all should enjoy a dozen questions about the beginning of the universe. James Peebles (Princeton, Nobel Physics 2019) says we have no theory of the beginning moments. Maybe not …until now. See: https://81018.com/question/

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Participate

Worldviews may be comprehensive; but until they include the universe, I believe they are all too small. Our universe view started in 2011. At that time, Kees Boeke’s base-10 was the only one out there. That work was from 1957; and although it has had champions, there has been no thrust by any one group or person to enrich it. Our base-2 view of the universe apparently was a first to be used in a classroom (December 19, 2011) and on then on the web early in 2012. That base-2 model has been championed most every day since that time. Until someone shows us that there is a better, more comprehensive view, we will continue our efforts.

Developing a consensus. This highly-integrated view of the universe is comprehensive. It includes everything, everywhere from all time. It empowers ethical thinking. It begins to demarcate the interface between the finite and infinite. It gives us a foundation to call people to question if they do stupid or sick things.

We invite you critically review this base-2 model of the universe with its 202 notations. Thank you. -BEC

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Keys dates for this file, Question

• The URL for this page is https://81018.com/question/
• Initiated: 15 April 2022 (based on an email to Jamie Farnes and Renate Loll)
• It became a homepage on 15 April 2022.
• Last update: Wednesday, 8 June 2022
• Prior Homepagehttps://81018.com/checklist/

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Searching for the start of our infinitesimal universe

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Mathematical Speculations About the First Moment
by Bruce E. Camber Also see: Essentials and Question.

Introduction. Using simple mathematics (doublings), basic geometries, logic, and commonsense, we found 202 base-2 notations from Planck Time to this day. Within that scale, there is a domain of the infinitesimal. It appears that the smallest, first “things” of the universe are her base units, Planck Length and Planck Time. Virtually ignored for over 100 years after their formulation in 1899, these two Planck units have become de facto ISO standards that define two of the core concepts within our sciences. The largest “things” within this infinitesimal scale — particle physics and quantum fluctuations — are well-studied. Both are measurable and a key part of the corpus of today’s science. If we are ever to build consensus within the sciences, we’ve got to look at our core concepts and agree, “These are core concepts” and “this” is what each means. When we agree, we can begin to build access paths to all of our current applied sciences.

The Tetrahedron and Octahedron. Our path to these two concepts was a bit unusual. We were studying the tetrahedron in high school and we decided to explore its interior structure by dividing each edge by 2 and by connecting those new vertices. We found four smaller tetrahedrons, one in each corner, and an octahedron in the middle. We went further within all five objects.

Within that octahedron we found smaller octahedrons, one in each of its six corners, and tetrahedrons, one in each of its eight faces. We could see how we could tile and tessellate all space using both the tetrahedron and octahedron. We could also see that we could go further within each object, so we did. By our 45th time dividing by 2, we were observing lengths used within particle physics and within the measurement of quantum fluctuations. We continued to go deeper inside. Another 67 times dividing by 2, we were using numbers on the order of the Planck Length. We then used the Planck Length as our edge, and multiplied it by 2. In 112 doublings we were back in the range of our original tetrahedron. We continued. Within another 90 doublings the numbers approximated the size of the universe. At that time we learned there are 202 base-2 notations from the smallest to the largest possible measurements (a story).

STEM. We thought it was the penultimate STEM tool and began sharing it with other math teachers. Nobody had seen a base-2 chart and many pointed to similarities with Kees Boeke’s 1957 base-10 chart. Eventually we began to accept the thought that this base-2 chart just might be an original. We knew it was idiosyncratic; it was not part of any cosmological model.

Although the best scholars within the sciences have wrestled with many hypotheses about the infinitesimal scale, most of the scale can not be measured directly. The best possible approach for now is through logic and math (which, of course, includes geometry). Among the more powerful tools within this domain are natural units and the first documented work to develop natural units was by George Johnstone Stoney in 1874 in Dublin, Ireland. In 1899 Max Planck did his first calculations. In our time in 2022, the units by Planck are better known than those by Stoney.

Here are natural numbers that describe “something” within the earliest universe. Over time, we have come to believe this “something” is the starting point of this universe.

The Key Question: What does that starting point of the universe look like? Although we had natural units, we used two Platonic solids, the tetrahedron and octahedron, to tile and tessellate the universe. We had not asked if there was a particular form those Planck or Stoney natural units might take.

Circles and spheres. These are the most simple constructions — two vertices — yet not until we actually saw how tetrahedrons and octahedrons emerge from spheres were we ready to concede the role of “the starting point” to a primordial, infinitesimal sphere. The dynamic image of cubic-close packing of equal spheres found in Wikipedia opened that door. Images of the Fourier Transform pushed unexpected new frameworks for thought about spheres.

In reality, spheres are always in motion; only our images are static.

The Nature of a Sphere. To begin to know the sphere, one must know pi (π) and getting to know pi is not trivial. It may well be the oldest, best-known, most-used mathematical equation; I believe we have barely scratched its surface. A key subject within all of mathematics, and although discussed within this website, only within the first few months of 2022 have the more penetrating aspects started to become apparent.

Continuity, symmetry, and harmony. I first developed that working progression from simplicity to complexity in 1971 to describe “a perfected state within space-time.” Pi wasn’t an issue. The development of a moment of new insight was. Yet, as a result of these studies of spheres, I see that perfection is perfection and the progression from continuity to symmetry to harmony is also described by the three most basic facets of the sphere. Of course, within one’s mind’s eye, the sphere is always perfect. Those three qualities, continuity-symmetry-harmony, are deep and abiding studies within academia, however, the study of harmonic functions is its youngest, and the Fourier Transform is its science.

Wild-and-crazy Speculations. There are no less than five Wikipedia dynamic images that are being studied and speculations are being made. For example, the Fourier Transform imparts electromagnetic or gravitational qualities within each infinitesimal, primordial sphere [1]. Further, there are 539-to-4605 tredecillion spheres per second (one primordial sphere per primordial unit of time). Although such speculations are not yet recognized within the academic community, we’ve continued. Each sphere has a natural functionality of continuity-symmetry-harmony as given within pi (π) and her Fourier transform.[2] Here a finite-infinite boundary (or bridge) is defined.[3] Here each sphere manifests with its own flavors and functions which begins as an attractor or repeller.[4] As our universe expands very rapidly, those first 64 notations continue to provide unique foundations for Langlands programs, string-and-M theory, hypothetical particles, SUSY, and so much more.

Of course, these points are all idiosyncratic, unconventional, and a necessary paradigm shift. In this model gravity and electromagnetism begin to be created in the first notations. Each results from a Fourier Transform and these transforms are scale invariant.

I believe it could be the beginning of a new science and I think a good name for it is one that has been around for millennium, hypostatics, which can be loosely translated as “That which stands under” or “the foundations of the foundations.” If we start at the very beginning, within the very first moment, we can watch the universe construct itself with all the working mathematics that has already been developed. Every type of sphere could tells us something about our earliest structures. Every process will have a place. These 64 to 67 notations hold the penultimate puzzle pieces. Just maybe, this may could become an introduction to the start of a new science of the infinitesimal universe. Thank you. -BEC

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Endnotes/Footnotes

[1] Each infinitesimal, primordial sphere. Somebody has to postulate it! Also, perhaps the initial conditions of “sphereness” are best described as an attractor sphere (even more fundamental than a hypothetical particle) or repeller (or repellor) sphere. Why not? It was in this discovery of the attractor scholarship that I also discovered two of its primary thinkers, Steve Smale of the University of California, Berkeley, and John Milnor of Stony Brook, Institute for Mathematical Sciences. Immediately I began to think these scholars might be able to shed light on my questions in recent emails to David Kaiser of MIT and Karen Uhlenbeck of IAS.

While engaging the work of John Milnor to define an attractor, I began thinking about the models of the Fourier Transform and those actions, although considered scale invariant, most scholars seem to hesitate to move that invariance into the infinitesimal scales. There is no hesitation here because within our base-2 chart of the universe, the infinitesimal scale of quantum fluctuations within Notation-67 quickly drops below all thresholds of direct measurements. The inclination today is to assume that Notation-1 is the manifestation of the first infinitesimal sphere and Milnor’s work describes part of the processes within that sphere.

[2] The Fourier transform. Scale invariant, these infinitesimal spheres adopt what amounts to attractor- and-repeller functionalities and these functionalities, building upon each other, manifest differently within each notation. The possibilities for complexity and uniqueness are staggering and most bewilderingly. Much more to come

[3] The finite-infinite boundary (or bridge). Pi is under-appreciated and little understood. The absolute mystery of pi is that it defines both the finite and the infinite, all within three concepts-not-3000 volumes. The inexplicable never-ending, never-repeating, always-changing, always-the-same qualities are beyond comprehension yet here can be summarized in a word, continuity, and its function is to create order. A simple formula that renders the most complex qualities is enigmatic enough, pi-and-its-spheres define space uniquely and perfectly and that is called symmetry and it is the first working relation. The majesty of that perfection is barely grasped and is profoundly unappreciated. The third quality has only been engaged for a short time in human history, perhaps a bit by Kepler, Gauss, Euler, Fourier, and Poincaré, yet new applications seem to emerge daily. Here are the dynamics of a moment, particularly the deepest, most intimate dynamics of motion that bring everything alive, is best summarized as harmony. Everything qualitative is infinite and everything quantitative is finite. A bridge of dimensionless constants connect the two. We have so much to learn and even more to begin to understand and truly appreciate. More… Even more…

[4] Spherical functionalities: From attractors and repellers, to electromagnetism and gravity. The functionalities of spheres is a young science within one of our oldest studies. Yes, the most-basic functionality of pi (π) is within the first 67 notations of the 202 that currently encapsulate the universe. Of the 67, the first ten notations are the foundations of a new science. It is well beneath the domain of quantum fluctuations as well as any direct measurement. These are the foundations under the known foundations; we’ve referred to this domain as hypostatic, for “that which stands under,” and here we take that to be continuity, symmetry, and harmony. Here are the essences, the first principles, and the starting point for every possible application and understanding of spherical functionalities.

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References & Resources

Auslander, J., Bhatia, N.P., Seibert, P., Attractors in dynamical systems (PDF), NASA-CR-59858. 1964.
• Mohsen KhodadiKourosh Nozari Fazlollah HajkarimOn the viability of Planck scale cosmology with quartessenceEur. Phys. J. C 78, 716 (2018). https://doi.org/10.1140/epjc/s10052-018-6191-4
• John Willard Milnor (1985). “On the concept of attractor”. Communications in Mathematical Physics99 (2): 177–195. doi:10.1007/BF01212280 (excellent bibliography). Wikipedia
• Gideon Rosen, “Abstract Objects”, The Stanford Encyclopedia of Philosophy (Spring 2012 Edition), Edward N. Zalta (ed.)(Also, see Zalta, Edward, Principia Metaphysica, online PDF manuscript, 2022)
• Steve SmaleThe Emergence of Function, ArXiv, 2016
• Steve Smale, The mathematics of time Springer-Verlag, New York-Berlin, 1980. ISBN 0-387-90519-7
• David Tong, Classical Dynamics (PDF), University of Cambridge Press, Part II Mathematical Tripos, 2004, 2015
• Within this website: Transformations (2019)

Cubic-close packing of equal spheres: Though lifted up within this website in 2016, this image naturally builds on the next five dynamic images.
• Fourier-A: Sine-Cosine-Waves: We’ll all learn about the wave’s fundamental relationship to the circle.
Fourier-B: Focus on Sine: We’re all going to learn a little trigonometry and calculus, too.
• Possible Fourier-C-D: An all-natural polarization: An open metaphor and analogical construction.
Possible Fourier-F: Lagrange points: Lagrangians come home.

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Emails

30 April 2022: Willy Fischler
30 April 2022: Richard Streit Hamilton
25 April 2022: Indika Rajapakse
24 April 2022: John Milnor
23 April 2022: Steve Smale
21 April 2022, Silvia Milana, Nature, London
20 April 2022 @ 11:38 AM Rashmi Shivni

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IM

2:07 PM · May 5, 2022 @BillGates, @sundarpichai (Apple CEO) The best cosmologists-physicists, people like Princeton’s James Peebles, Nobel Laureate 2019, say we do not have a theory for the first microseconds of the universe. Perhaps your most brilliant people can work on it: https://81018.com might be helpful place to start.

2:17 PM · May 1, 2022 @FinitePhysicist Can the finite be quantitative and the infinite be qualitative? Does pi (π) (and how it never ends) tell us about continuity, a perfect sphere about symmetry, and its harmonic functions about dynamics? https://81018.com/

2:06 PM · May 1, 2022 @Pontifex Teach us to grasp the infinite. Rediscover pi (π) and how it never ends (continuity) and its symmetry is perfect, and its harmonic functions pervasive. There’s the infinite, all qualitative, and the finite is quantitative: https://81018.com You can do it. We can!

1:15 PM · Apr 26, 2022 @CERNCourier On July 10, 2021 your tweet was about the next generation of detector designs. What about the Planck scale? It is so far beyond detectors, a new approach is needed. The first 64 notations of 202 base-2 that contain the universe need study: https://81018.com/chart/

8:05 AM · Apr 21, 2022 @TheDailyShow We all do circular arguments. We’re locked up within little worldviews when a view of the entire universe is needed. How presumptuous it is to think the universe is us when our solar system is part of the Milky Way and… Here’s the universe: https://81018.com/chart/

4:08 PM · Apr 9, 2022. @anabelquanhaase We’re caught by three historic errors, one by Aristotle: https://81018.com/duped/ another by Newton, and also by Hawking as understood by his co-author Neil Turok: https://81018.com/bbtheory/ We’re confused because our grasp of the foundations is wrong. Also, see: https://81018.com/quan-haase/

Looking back…

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Keys to this document, hypostatics

  • This page was started on Tuesday, April 5, 2022.
  • The last update was Monday, May 9, 2022.
  • This page became a homepage on Saturday, April 30, 2022.
  • The URL for this file is https://81018.com/hypostatics/
  • The first headline is: Highly-integrated mathematical study possibly named, hypostatics
  • The second headline is: Mathematical Speculations About the Very Beginning
  • The third headline: Mathematical Speculations About the First Moment
  • The first byline is: Introducing the start of a new science of the infinitesimal universe
  • The second byline is: Searching for the start of the infinitesimal universe

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