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. All are needed to start and grow this universe:

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 explosion 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. 202 notations (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. Small-medium-and-large scale universe. Our stumbling block is on how we see our universe. Langlands programs, string-and M-theory, SUSY, and a host of other small-scale studies define the first 67 notations. We know Notations 1-67. We simply are not looking at them in the best possible framework. 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. Within the most recent work using 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 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.

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. Though an explosive quantity at 539 tredecillion spheres per second (using Planck Time) to as high as 4609 tredecillion spheres per second (using Stoney Time), it 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). 6fWithin 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 the 2005 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 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 in 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 narcissism and eventually 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



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

[1] Mathematics. 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.

Within our time, Wigner and Tegmark carry on the historic tradition of Pythagoras and 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.

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.


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


[2] Notations. Just 202 base-2 notations to encapsulate today’s universe is an Art of the Impossible. Check the math. Savor Euler’s work. 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. Can you imagine our joy in discovering what we called the penultimate STEM tool? We wrote letters to the editors to begin getting some feedback.

We did some jiggering with the epochs of big bang cosmology as defined by Stephen Hawking and 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.


[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 is 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 spikes through all 202 notations.


[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 so many others it is no wonder that the Moonshine Shadow* (Umbral Moonshine Conjecture) is a part of this entourage.


[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.


[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 were barely recognized for over 100 years.
International Organization for Standardization is a key for quick dissemination to the world’s people.
Peter J. Mohr (AIP), David B. Newell (AIP), and Barry N. Taylor (AIP) of NIST: Three primary scholars.
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 we can work on together.


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


[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.


[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.


References & Resources

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

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.

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

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

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



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



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!


Keys to this document, agree

  • This page was started on Monday, May 9, 2022.
  • The last update was Saturday, May 21, 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


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

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