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

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

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

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

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

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

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

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

Sphere to tetrahedron-octahedron couplet

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

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

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

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

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

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

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

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

Continuity is the beginning of value.

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

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

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

Harmony opens the richest dynamics of life.

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

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

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


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


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


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


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


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


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

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

We’ll continue to check the math.


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


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


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


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


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


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


References & Resources

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


Communications: Emails & Instant Messaging

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

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

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

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

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

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


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


Key Dates for this document, Tredecillion

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

Petition to our leading scientific societies: “Please Investigate.”

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MATHCOUNTS mathletes, Massachusetts state competition. (PRNewsFoto/Raytheon Company)

If the big bang fades away, does pi (π) emerge?
You may sign this petition here.*

Pi (π) is the oldest, most-used, least-understood tool to engage the universe. Its never-ending, never-repeating numbers teach us about continuity. Its conversion of numbers to shape teaches us about symmetries. And, its conversion of spheres to tetrahedrons and octahedrons teaches us about basic harmonies that abide in everything, everywhere throughout all time.

Big bang cosmology is slowly being abandoned due to the results coming in from the James Webb Space Telescope (JWST) as well as other scientific research:

  • Too smooth for a big bang. The early images from the JWST confirm images from the Hubble spacecraft and earlier work from the Planck space observatory [European Space Agency (ESA), 2009 to 2013]. The Planck ESA mapped the anisotropies of the cosmic microwave background (CMB) and opened the questions about smoothness.
  • The big bang has no beginning. It cannot account for its earliest seconds. In contrast, pi (π) naturally starts at PlanckTime with an infinitesimal sphere to begin space-time. By applying base-2, doubling over and over again, there are 202 notations to this day and time. Continuity, symmetry and harmony within the finite and infinite helps us to to grasp meaning and value that the big bang cannot.
  • The big bang is on a slippery slope. Its story accommodates the news. It is not giving our students and scholars a firm foundation to build the new sciences required for our future.

This appeal is for the leading scientific organizations throughout our world to look critically at an alternative model and to evaluate its major points:

  1. Pi (π) redefines the very nature of the finite-infinite relation. Please go to this webpage for more: https://81018.com/continuity-symmetry-harmony/#Pi and https://81018.com/csh/ Is this conclusion worth exploring further?
  2. Pi (π) is how numbers become circles and spheres. Lines approximate circles at a point we can not discern. Assuming one infinitesimal sphere per unit of Planck’s base units, a simple calculation based on Planck Time, renders 539 tredecillion spheres/second, a cosmological constant, and these infinitesimal spheres most-densely pack the universe. Are these points worth exploring further?
  3. 1899: Max Planck’s base units (natural units) define the very first moment of space-time. By applying base-2, we emerged with a mathematical ordering system that can be easily followed. Planck Time, multiplied over and over again, results in well-over 13.81+ billion years within 202 notations. Applied to the PlanckLength, it approximates the size of the universe. Everything, everywhere, for all time is encapsulated. Are these points and our most-simple model worth exploring further?

Our world is beset with anxieties. Our models are not working effectively. There is too much hostility in the world. It is obvious to everyone that we need alternative models.

This appeal for a critical judgment is made to the following (this page is very much under construction in May-June 2023):

1. China: Chinese Academy of Sciences

2. USA: The American Academy of Arts and Sciences and American Association for the Advancement of the Sciences

3. Germany: The Max Planck Institutes and Helmholtz Associations

4. The Royal Society of the UK

5. The Japan Academy

6. The French Academy of Sciences

7. The Korean Academy of Science and Technology

8. National Academy of Sciences (USA)

9. Russian Academy of Sciences

10. Royal Swedish Academy of Arts and Science

11. And the Indonesian Academy of Sciences (AIPI), Indian Academy of Sciences, Academy of Science of South Africa (ASSAf), The Norwegian Academy of Science and Letters, and The Academia Brasileira de Ciências (Brazilian Academy of Sciences) and so many others throughout our world.

If you would like to help us carry this message to the organizations mentioned above, please sign our petition.

Thank you. -BEC

* Please note: This petition is hosted by Change.org and Change.org is supported, among many others, by Reid Hoffman, the founder of LinkedIN. Change is a reputable company; however, it takes money to support that infrastructure. Once you sign the petition, you’ll be asked to contribute. You do not have to make a contribution. If you do, it is a freewill offering. Thank you. –BEC

Ranking organizations:

  1. https://www.nature.com/nature-index/annual-tables/2022/institution/academic/all/global
  2. https://www.scimagoir.com/rankings.php


Endnotes & Footnotes
Footnotes will follow over the next few weeks.






References & Resources
As these references are studied, key references and resources will be added.within this website.



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


There will also be many instant messages to thought leaders about the key points.



You are always invited.


Keys to this page, petition

• This page will eventually become a homepage. It is now “under construction.”
• The last update was May 28, 2023
• This page was initiated on May 21, 2023.
• The URL for this file is https://81018.com/petition/
• The headline for this article: If the big bang fades away, does pi (π) emerge?
• First byline is: Petition to our leading scientific societies: “Please Investigate.



An open letter to Xi Jinping of today’s China Communist Party (CCP)

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Xi Jinping, Karl Marx, the Chinese Dream

If he were alive today, what would Karl Marx believe?
by Bruce E. Camber (first draft, May 2023)

Xi Jinping is the general secretary of the CCP. In China, the leaders always confer with Karl Marx before making strategic decisions. Of course, Karl Marx is long dead, so that conference has to be on a different plane, “in spirit, and in truth.”


Dear Xi Jinping:

Among all the experts of the world, you possibly know as much as anybody about the work and thoughts of Karl Marx. Yet given that he died in 1883, he was unable to engage two of the biggest scientific revolutions that followed him: Einstein’s relativity theory and the Planck-to-Bohr-to-Schrödinger quantum theory. Most know Marx as a philosopher, historian, sociologist, economist and political theorist; very few know that he was also very deeply involved and wrote about the foundations of mathematics.1 I believe his studies and writings about infinite series2 is a key to his willingness to explore new domains. I am still searching for his understanding of the place-and-importance of pi (π). I suspect it would directly impact our understanding of dialectical materialism. Today’s scientific community and her mathematicians engage pi (π) rather superficially. It is interesting to me, possibly as a symbolic gesture alone, Marx died on March 14 which is now considered “Pi Day” around the world. Stephen Hawking died on Pi Day. And, Albert Einstein was born on Pi Day.

Most of us learn the basic formula for pi (π); and, we think, “I’ve got it. Done that.” Yet, those scholars who have made careful studies of this most enigmatic equation, know that it holds many more secrets and surprises.

I assume you would consider Karl Marx to be a mentor and that you are his interpreter. I would like to ask you about three historic, intellectual failings (which are only discussed and studied among specialized scholars), “What would Marx say?” These are:

  1. Aristotle’s 1800 year geometry error.3 Quantum physics is yet to acknowledge this gap, the finite-infinite relation, a domain of perfection, and a dynamic container universe.
  2. Isaac Newton’s absolute time keeps tripping everyone. From Leibniz to Einstein, we’ve learned that time is not absolute but discrete, finite, relational, and necessarily related to space.
  3. Lemaitre, Hawking and Guth gave us the big bang theory and it is collapsing.

We quickly learn that our very best scholars all make key mistakes. Given the importance of these three concepts in our world, I believe each country should have a summit meeting of their best scholars to discuss those issues then appropriately advise their people:

  1. Pi redefines the very nature of the finite-infinite relation. Here there is some concurrence with Marx’s “ignore all religions” attitude. It redefines infinity as continuity-symmetry-harmony. For more: https://81018.com/continuity-symmetry-harmony/#Pi The second is: https://81018.com/csh/ Of course, pi (π) deserves much more of our attention.
  2. The magic of pi is how those numbers become circles. What in fact happens is those numbers approximate circles to a point we can not discern the straight lines at all. An example is this image: https://81018.com/simple/
  3. Planck’s base units (or natural units derived in 1899) are a level-set for the universe. They define the very first moment of space-time. By applying base-2, we create a mathematical ordering system that can be easily followed. Planck Time, multiplied over and over again, results in over 13.81 billion years within 202 notations. Applied to the PlanckLength, it approximates the size of the universe.

    Everything, everywhere, for all time is encapsulated. I believe Marx would have enjoyed learning about this inherent sense of order created by pi (π).

    The most surprising part of it is that PlanckTime also inculcates a cosmological constant that is the expansion of the universe. If one sphere is postulated for every unit of PlanckTime and PlanckLength, a rate of expansion can be calculated. It is 539 tredecillion spheres per second. It provides mathematical logic for the expansion of the universe.

Now all this data provides a very different picture of the universe. At the time of Karl Marx, many people were aware of the Milky Way galaxy, but most astronomers and cosmologists thought it was the scope of the entire universe.

If humanity is ever to get along and build on each other’s successes, we all need to break free of our little worldviews and begin to adopt a high-integrated, mathematical view of the universe.

I believe Karl Marx would have embraced it. Do you embrace it?

Thank you.

Most sincerely,


PS. With the greatest respect, I would like to ask you to consider signing a petition — https://81018.com/petition/ — to the leading intellectual societies in the world to do an analysis of this work and publicly comment on it. China holds the top positions. If you sign it, an analysis will surely follow. Thank you. -BEC


Endnotes & Footnotes
Footnotes will follow over the next few weeks.

[1] Marx, Karl (1983). Mathematical Manuscripts of Karl Marx. Translated by C. Aronson; M. Meo. London: New Park Publications. ISBN 978-0-86151-000-9. Retrieved from Wikipedia, May 29, 2023.

[2] The four treatises that open the concept of infinites: (a) On the Concept of the Derived Function, (b) On the DifferentialOn the History of Differential Calculus, and (c) Taylor’s Theorem, MacLaurin’s Theorem and (d) Lagrange’s Theory of Derived Functions

[3] Dirk J. Struik, Marx and Mathematics,Science & Society, Vol. 12, No. 1, A Centenary of Marxism, Guilford Press, pp. 181-196, Guilford Press, Winter, 1948

D. J. Struik, Het Probleem ‘De impletione loci’ (Dutch) (English: Translation by M Senechal), Nieuw Archief voor Wiskunde, Series 2, 15 (1926), no. 3, 121–137

Endnote: Dirk Struik rediscovered Aristotle’s 1800 year geometry error from the 1400s. Aristotle did not know there is a gap with five tetrahedrons. He thought tetrahedrons could tile-and-tesselate the universe perfectly. That mistake was recorded around 1450. Another 570+ years pass and Aristotle’s mistake was forgotten and never discussed. It is important because quantum theory is directly impacted. The finite-infinite relation is clarified. An actual domain of perfection is defined. And, the natural units defined in 1899 by Max Planck (and in 1874 by George Stoney) give us natural starting points for the universe; and, the current day, 13.81 billion years later, gives us a dynamic container.

[4] More to come…


References & Resources
As these references are studied, key references and resources will be added.within this website.

  1.  Variorum De Rebus Mathematicis Responsorum, Liber VIII, François Viète, (Tours, 1593) within The Analytic Art, François Viète, translated by T. Richard Witmer, Kent State Press, 1983, Dover, 2006 Also, see John Baez analysis.
  2. Development of an infinite series, Wikipedia (retrieved 2023)
  3. François Viète formula for pi (π)
  4. Continuum Mechanics Through the Twentieth – Maugin, Gerard A., Springer, 2013 See: 1.4.1 The University of Leningrad/St Petersburg, ppf 181


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

Wed, May 24, 12:05 PM, Abhay Ashtekar, Penn State
Tue, May 23, 6:03 PM, Donna Strickland, Waterloo, Ontario
Tue, May 23, 8:28 AM, Gérard Mourou, IZEST, Palaiseau, France


There will also be many instant messages to thought leaders about the key points.

9:49 AM · May 28, 2023 @the_xijinping I recently finished writing and editing an open letter that I would like to bring to your attention. It is about Karl Marx’s understanding of mathematics. That page will soon become a homepage. The URL is https://81018.com/marx/ Would you like to suggest any edits?

5:11 PM · May 23, 2023 @brattray @reidhoffman The big bang is fizzling. That opens the door for new models. We have one for the global scholars to evaluate. Would you please sign the petition to have the world’s leading intellectual organizations evaluate it? https://www.change.org/KnowYourUniverse



You are always invited.


Keys to this page, Marx

• This page will eventually become a homepage. It is now “under construction.”
• The last update was May 29, 2023
• This page was initiated on May 14, 2023.
• The URL for this file is https://81018.com/Marx/
• The headline for this article: If he were alive today, what would Karl Marx believe?
• First byline is: An open letter to Xi Jinping of today’s China Communist Party (CCP)



26 faces of time within 202 notations that encapsulate our universe

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You’re experiencing this moment, the Now.
Are you experiencing all 26 faces of time?

I answer, “Yes, you are.” by Bruce E. Camber a first draft (your comments welcomed)

1. The Now2028. Day16015. Picosecond – 104Informal, unofficial
2. Billion YR1999. Hour15516. Femtosecond – 9422. Mecosecond – 34
3. Million YR18910. Minute15017. Attosecond –8423. Duecosecond – 25
4. Thousand YR179 11. Second 14418. Zeptosecond 74 24. Trecosecond15
5. Year (YR)16912. Millisecond 13419. Yoctosecond6425. Tetrecosecond 5
6. Month16513. Microsecond – 12420. Rontosecond-54SI Certified (BIPM):
7. Week 16314. Nanosecond-11421. Quectosecond – 4426. PlanckTime 0

1017 1014 1010 107 106 104 1 10−3 10−6 10−9 10−12 10−15 10−18 10−21 10−24 10−27 10−30 10−34 10−36 10−39 10-42 10−44

Preface. This article starts with this moment in time — yes, right Now — and then works back to the very first unit of time, called PlanckTime. The question is, “Might you also be experiencing the other 25 faces at the same time?” I say, “Yes, necessarily so.” To that end, our focus today is on the continuity-symmetry-and-harmony of time. We postulate that at Notation-0, the Planck base units generate infinitesimal spheres as defined by pi (π) and within a finite-infinite relation. The imperfections (fluctuations) of this emergence of infinitesimal spheres are also a key part of this study.

This article will be a bit long and it will take awhile, possibly a few years of updates and recompiles, before it is finished. This first iteration has 26 pages of references each associated with each of the 26 faces of time. There are just 21 SI-certified numbers of time. Four of the pages do not even have an officially-recognized name from our international governing bodies (BIPM, CODATA, ISO and NIST).

This article is a sequel to the last homepage, Simple Model, and to our 2017 NASA study, the UniverseClock. That study was essentially based on determining the number of seconds that define our universe. Although it starts at PlanckTime (or the PlanckSecond), it immediately went to the first whole second which is within Notation-144 (the eleventh face of time within this study) and then to this very day and time.

The Now contains all 26 first faces and every possible unit of time.

  1. The Now: Within Notation-202, it is always today, this hour, this minute and this second. Although at any moment in time, humans do not compute must faster than a millisecond (even during sleep), if all time is now and all notations are eternally building on each other, simple logic tells us that we are experiencing the other 25 faces of time and each is contributing to our experience. If all of human history is within the Now and it starts at the PlanckSecond over 13.81 billion years ago, even that first PlanckSecond and today’s PlanckSeconds are contributing to each of our Now experiences. Also, if the experience of the “First Billion” years is shared by every living thing — our unique experiences are all within an infinitesimal slice (arguably only about 400,000± years) of Notation-202 (which is 10.98 billion years) — we all have substantially more in common than not. It is obvious to me that we’ve got to stop all the nonsense and bring on a deeper understanding of continuity-symmetry-and-harmony, the essence of time and both the finite-and-infinite.

    Just a few working notes about this page: I said to Hattie, “I bit off a bit more than I can chew with this homepage. I’ve never thought about the simultaneous experience of every possible face of time. There’s a certain logic to it, but it’s daunting.” This page takes what the Loop Quantum Gravity people say, “all time is now,” more seriously than most.

    Each face of time reminds us to be part of the universe in a different way. Each face gives us a different feel of our role in the universe. There are only eight of these faces that are even part of our daily vocabulary. There are four faces of time that are yet to be formally named; nobody really knows them. So, let me try to introduce you to all these faces of time. There are twelve you know. Eight you know well, but today you hopefully will see another part of those other 12 and learn a little about all 26! -BEC

  2. The First Billion Years: Every notation has a range. Notation-199 spans between Notation-198 and Notation 200. Not everything in the universe is a billion years or more. So, let us ask the question, is there an actual moment in space-time when things turns from 999 million years to one billion years? Of course, that moment in time will always be closer to one notation than the other. The actual number of seconds to make up a billion years is 43,318,236,018,400,000 seconds. The duration of this PlanckTime doubling is 1.3727 billion years. Notation 198 is 21,659,118,009,280,000 seconds and its duration is about 686.806 million years. That 4.331×1016 seconds is very-very close and within Notation 199.

    One billion years is hard to conceive. To put it into perspective, the earth has been calculated to be 4.54 billion years old (plus or minus about 50 million years). A billion years is known as an aeon; the next smaller group of time is a million years. So, a billion, a thousand-thousand-thousand, is a very long duration. One way to think about it is, “More galaxies!” Obviously, our solar system, older than earth, is estimated to be 4.6 billion years. The Milky Way, estimated to be 13.6 billion years in duration, was here before the Solar System.

    Blackholes or dark mater? Once the first 64 notations are acknowledged by academia and science, we can begin to straighten out the range of speculations around blackholes. The studies and debates about the dynamics of blackholes have been unwittingly hamstrung without a grasp of those notations. This page is part of my earnest struggle to begin to grasp its meaning.

    There are places in this universe that are turning a billion years old right now. What does it look like? How is it building on the prior notation, then all prior notations, and then with all the more current or “newer” notations? To attempt to enter such a space-time will hopefully evolve over time. Currently, all we can do is ask questions and think about it.

    Whereas the PlanckTime doublings are the consistent measurement across the entire grid, the top level labelling changes. From the PlanckTime to the first second at Notation-144, the labelling is in seconds. Then it changes according to the categorizations of our solar system and the naming conventions of humanity. Then it becomes consistently based on the year from Notation-169 to Notation 199.

  3. The First Million Years: Within Notation-189, we find the first million years. Notation 188 is 2.1151×1013 seconds while Notation-189 is at 4.2302×1013 seconds. There are 31,556,952,000,000 seconds in a million years (that’s 31.556955 trillion seconds) which is just a bit closer to Notation-189 than Notation-188. It is good to recognize these natural groupings, Notations 199, 189, 179, and 169 based on years. The next group of numbers — 165 for a month, 163 for a week, 160 for a day, 155 for an hour, and 150 for a minute — are all human perception based on our solar dynamics. Each is basic and defines who we are. Yet, those notations are “the firsts” for the universe. The next group will be based on seconds. From Notation 144, the first second, it goes by tens down to 34, and then Notations 25, 15, and 5. Please remember that this is a first pass at seeing the universe in terms of Planck Time and the “natural” time groupings that followed.

    In this model, all the notations are always active. There is always something turning a billion and a million years old. We use these firsts to remind us of the full dynamics of the universe at any one moment in time.

    We would not see the universe as it was in the very first million years. It would not be identical to how that domain looks today because it will have had incorporated 13,810 million years of relational changes (expansion or growth).

    Much more to come… We will be back!

  4. The First Thousand Years: Within Notation-179, Notation 178 is 20,655,744,561 seconds and Notation 179 is 41,311,489,123 seconds. Called a millennium, the first 1000 years is 31,556,952,000 seconds. The first thousand years falls just within notation-179.

    Our history is naturally cast within thousand years cycles. You could think back and ask, “What was happening in 1023?” But, that would be a history lesson. Is there an eidetic or archetypal, 1000 year point in the universe when it goes from being 999 years to 1000 years? What would that time-and-space look like? It raises more questions. The scholars looking at the data from the James Webb Space Telescope (JWST) actually believe the images they are seeing are the first look and feel of the universe 300,000 years after the universe had its very beginning moments. Is it? Or, is it as the universe looks today at about the 300,000 year time-and-space? That’s a very odd question and part of the puzzle.

    So, yes, our history is naturally cast within thousand years cycles. We study our history in blocks of 1000 years. At any point in time, we can imagine what it was like 1000 years ago. But, that’s not what we are asking. If indeed all time is now, the question is, “What are we looking at with redshift data? …with carbon-14 dating? Our oldest records of human-like species is over 2 million years old. In the time frames we are discussing, that’s just a very small sliver of Notation-202.

    We are just opening up this discussion about “all time is now.” Ultimately it is all based on that first infinitesimal sphere, the first manifestation of a thing at Notation-0. If these spheres are being generated at about 539 tredecillion spheres per second and they literally make the universe by filling it at extraordinary densities, we have a new definition of a blackhole and we have yet another issue to rethink. So, if the notational function is just a counting function, what is space-and-time? Questions, questions, questions… can we assume or hypothesize or hypostatize that two infinitesimal spheres are within Notation-1, four in Notation-2, eight in Notation-3, sixteen in Notation-4, and 32 in Notation-5? That count is kept on line 8 of our horizontally-scrolled chart and it would be shifted two notations to the left. Much more to come...

  5. The First Year: Within Notation-169, we find the first year. Notation-168 is 20,171,625.54 seconds and Notation 169 is 40,343,251.097 seconds. Using 365.2425 days per year and 86,400 seconds per day, there are 31,556,952 seconds in that first year. So, the first year falls within Notation-169.

    The first year is important for everything. Yet, at Notation-169, it is only the first year of the universe. I postulate that the first 169 notations begin with eidetic structure within the earlier notations and here they become archetypal. Plato’s eidos and Karl Jung’s archetypal will be redefined with the mathematics and physics of Langlands programs and operadic algebras in homotopy theory and string theory, LQG, SUSY, CST, SSM, and others. Every prime notation opens possibilities for new applications and configurations.

    Time and space are redefined within this model. Although all time is now, it is also part of the nature of the definitions of functions of spheres. To keep this page. relatively short, new developments will be entered into the page just for a notation, i.e. Notation-169 to attempt to keep this page from getting much too long. Those pages are in the early stages of development.

  6. The First Month: Within Notation-165, using 30.436875 days per month (based on a year of 365.2425 days divided by 12 months), there are 86,400 seconds per day and an average of 2,629,746 seconds per month. It is within Notation-165 that is 2,521,453.19 seconds.

    The first month and each of the eleven
    months that follow has a face. Business people know about Month-End Closings of their financial books. You can catch things before they get out of control. Yet, here we are just thinking of how the first month of the universe might manifest. The first weeks, have given our universe a sense of itself and its emerging rules and regulations or its continuity, symmetry and harmonic relations. Eidetic structure perhaps is now best described as archetypal. In an earlier study projected next to the epochs of the big bang theory, we would be entering their photon epoch which we would redeploy as the photon processes, an ongoing part of the unfolding universe.

  7. The First Week: Within Notation-163, also a prime number, we have one sense, the universe has another. This first week of the universe — just look at the numbers — is a very different place than we had ever imagined. Here is the first week, the very first week of the universe’s coming into existence. Could we locate such a place? Surely, within every family with a new baby, they know what a week is. Even now, there are plenty of discussions about what a week from conception is and the meaning and value of each week thereafter. There is a week of all the new growth of living things. Do all things that are just a week from there first moment of beingness, share a “same space” of any kind? Is there an eidetic structure for a week? Is there an archetypal structure for a week? How could that be? Is this cluster of seconds, any different from any other second of time?

    Each of the four-to-five weeks of a month has a face.

    We are just starting our explorations of eidetic forms and structure and archetypes.

  8. The First Day: For living things, each day defines a period between being asleep and being awake. For inanimate or inorganic things, is there any differentiation? Are all the minutes, hours, days, weeks, months, and years blended? The only things that differentiate that finely are those things with some kind of consciousness. Notation-160 is therefore a distinction between the organic and inorganic. Is the parsing of time within seven days a week significant or a function of being within a solar system?

    Do all things that are just a day from their first moment of beingness, share the “same space” of any kind? Is there an eidetic structure for a day? Is there an archetypal structure for a day?

    Of course, the very first day of the universe has a face
    . There is such a thing as “the first day of everything” but it is certainly not shared by everything. Is there any part of this universe that has a “first day” that is shared by everything?

  9. The First Hour: Yes, Notation-155 is another distinction between the organic and inorganic. Is the parsing of time by hour significant or just another function of being within a solar system?

    Do all things that are just an hour from their first moment of beingness, share a “same space” of any kind? Is there an eidetic structure for an hour? Is there an archetypal structure for a hour?

    The very first day of the universe, of course, has a face. There is such a thing as “the first hour of everything” but it is certainly not shared by everything, everywhere for all time. Is there any part of this universe that has a “first hour” that is shared by everything?

    That is face of the hour that we are in search to define uniquely

  10. The First Minute: Also, Notation 150 is a refinement and a distinction that probably is only appreciated by organic things. Might there be a possible parsing of time by the minute that makes a difference within the universe? Do all things that are just a minute from their first moment of beingness, share a “same space” of any kind? Is there an eidetic structure for a minute? Is there an archetypal structure for a minute? We know it if organic but only as a measurement of the spaces between a breath of air or conversion of energy to sustain life.

    The very first minute of the universe has a face of some kind. But, is there such a thing as “the first minute of everything” that is shared by everything, everywhere for all time? Is it eidetic and archetypal? What part of this universe has a “first minute” that is shared by everything?

    This is face of the minute that we are in search to define uniquely

  11. The First Second: Notation-144 (143 – .60116 seconds, 144 – 1.2023 seconds).

    There is definitely a face of the second: 539 tredecillion spheres per second
    . The logic of those 539 tredecillion spheres per second has been studied and argued in many places within this website. If there is one infinitesimal sphere per unit of PlanckTime and Planck Length, it is a calculation of a very different cosmological constant. The universe “as-it-is” is wall to wall with infinitesimal spheres. In these earliest faces of time, the densities and speed-of-transactions would require the greatest efficiencies. There would be no room or precedent for fluctuations. The universe would be perfect, exceedingly smooth, perhaps for millions, even billions of years. We’ll re-examine the densities and ask questions of the experts, both scholars and scientists who would know when the densities become low enough enough for the most simple five-tetrahedral structure to manifest. Then would come the five-octahedral, or ten or twenty tetrahedral complexes might manifest and become systemic. Some experts in the studies of neutron stars may be able to tell us.

  12. The First Millisecond: Within Notation- 134 (1.1741×10-3 s) 1000 milliseconds – one thousandth of second.

    For most people, a millisecond is meaningless. It obviously needs a huge and important face within our life. If you love the horses and races of any kind, you know the millisecond. It is the unit of the race. It is also the interface between humans and machines. It is also the edge of perception of living things. It is anticipated that it is the edge of consciousness, and the beginning of the finite-infinite relations. Perhaps it is the edge between “the perfect” and “imperfect” or between that which has fluctuations and indeterminacy and that which does not. The densities of the infinitesimal spheres is low enough that the five tetrahedral gap that Aristotle missed can now manifest. The suspicion is that they do not manifest eidetically or even archetypally. At some point the densities of the infinitesimal spheres will be low enough that five tetrahedral structure can manifest systemically. There is a domain when free will can overcome the thrust for continuity-symmetry-harmony.

  13. The First Microsecond Within Notation 124, (1.1466×10-6 s or 10−6) or a millionth of a second.

    A millionth of a second needs a face; it is beyond imagination so we have a lot of stretching to do.
    Those who work with lasers and computers certainly know about microseconds, nanoseconds. and picoseconds. We will defer to them and those involved in artificial intelligence and the nature of intelligence. All of our discussion are in light of continuity-symmetry-harmony of the earliest infinitesimal spheres. That is a heretofore unrecognized perfection within physical space-and-time. The universe has barely begun and it already has virtually unlimited possibilities for complexity.

  14. The First Nanosecond: (10−9) Notation-114 (one billionth of a second), 1.1197×10-9 seconds, Notation-115 is 2.2395×10-9 seconds, Notation-116 is 4.479×10-9 seconds, and Notation-117 is 8.958×10-9 seconds.

    That billionth of a second has many faces, yet its most prominent face is a computer chip.
    Artificial intelligence became mature with the nanosecond, one billionth of a second. It was young when just within the microsecond, a millionth of a second. At one time, we thought the human capacity for differentiation was the millisecond or one thousandth of a second. Today, we are postulating that humans also function within the nanosecond range all the way down into the quectosecond domain and even further into the next four domains that have only been provisionally named.

  15. The first Picosecond: 10−12 Notation-104 (1.0935×10-12 s) one trillionth of a second.

    A trillionth of a second has a huge face
    within our technologies today. We will exegete that statement over time because it is also the archetypal domain for so much of life, especially human life.

  16. The First Femtosecond: (10-15) or one quadrillionth of a second. Within Notation 94 1.0678×10-15s ( 2.1357×10-15s, 4.2715×10-15s, 8.543×10-15s).

    The Femtosecond has a face; it was first given life by Egyptian scholar, Ahmed Zewail, while a professor at Caltech, he was the first to calculate the transition states of chemical reactions using femtosecond spectroscopy. For that work he he was awarded the Nobel prize in 1999. Femtolaser surgery was the next big breakthrough and the rest is history. For those of us outside this domain, we need to know that femtosecond processing is part of who we are. We can’t feel it, but we know it. We call it intuition. It’s an “aha” moment. In 2018 Donna Strickland and Gerald Mourou received the Nobel Prize in Physics for methods of generating high-intensity, ultrashort femtosecond optical pulses.

  17. The First Attosecond: (10-18) Within Notation-84 (1.0428×10-18s)

    The Attosecond became part of this study through the Max Planck Institut für Quantenoptik
    in Garching, Germany. Its director, Prof. Dr. Ferenc Krausz and colleague,  Dr. Vladislav S. Yakovlev, were the first to locate the attosecond within Notation-84. They rather quickly moved on and defined the Zeptosecond as well.

    This is so much more to come because we postulate that this is the archetypal domain of periodic table and so much of the chemistry of life.

    When a word begins to be used within popular culture, you know its meaning is being appreciated, even if not fully understood. A case in point is the DC Comics superhero, Flash, where within one of their user groups the attosecond is discussed and there is even a screen rant about it all by Justin Epps (February 2023)!

  18. The first Zeptosecond, (10-21) Within Notation-74 (1.01841×10-21s).

    The Zeptosecond, a trillionth of a billionth of a second needs a bigger face. It is the active domain for so much research today and it is in the archetypal domain of so much of physics and the Standard Model for Particle Physics. Quantum computing and superconductivity… For more

  19. The First Yoctosecond (10-24) Within Notation-64 (64 – 9.945×10-25s, 65 – 1.989×10-24s, 66 – 3.978×10-24s, 67 -7.95630×10-24s).

    An Yoctosecond needs a face
    . Beyond imagination, a trillionth of a trillionth of a second, there are a few scientists who are engaging it seriously. Although the domain of very specialized teams within physics and mathematics, we look at it in the scope of all 202 notations. Our analysis places the Yoctosecond on the cusp between particle physics and quantum physics. We might want to refer to it as beginning of an archetypal domain of transformations. Although we’ll be working to define what that means, in September 2021, Yuri Shvyd’ko and Peter Schindelmann reported, On yoctosecond science, and stirred the pot of imagination.

  20. The first Rontosecond (10−27) (Notation-54) (9.71228×10-28s, 1.942456×10-27s, 3.8849×10-27s).

    The Rontosecond needs a face.
    Within Wikipedia, this fraction of a second has been added to their listings but it has only been described as 300 rs: The mean lifetime of W and Z bosons. That designation will be meaningful to a small population of scientists. Within this website, we’ll try to give it many more flavors, colors, dimensions, and textures. Within this space, it is for systems theory, all the possible archetypes for systems. It’ll be a most fascinating area to develop. We may use some of the ongoing work of Ervin Laszlo and the historical work of Wittgenstein.

  21. The first Quectosecond (10−30) (Notation-44) (9.4846×10-31s, 45 – 1.8969×10-30s. There is no description of the quectosecond within Wikipedia. It is, for now, just listed.

    BIPM: At their meeting from 15-18 November 2022 in Paris, the General Conference on Weights and Measures (CGPM) of the International Commission of Weights and Measures (BIPM) adopted Resolution 3 making it a globally accepted name for the range 10−30 to 10−32 of the infinitesimal scale of time.

    Relations. Now, the Quectosecond also needs a face. We began thinking about it when we developed our desktop chart of the universe: https://81018.com/table-2/ In the first column and tenth columns the notations are in groups of ten. Looking at the first column, it begins with Notation-1 for the Planck Length. Today we would have that define Notation-0 as the instantiation of the first moment of space-time. Notation-1 would begin when the second and third spheres manifest. The sphere count is kept on the eighth line of data on the horizontally-scrolled chart. It is earlier work and all that data should be shifted to the left by two cells. Notwithstanding, by 10-30 seconds, we are in the range of what we defined to be “Relations.” Here within this domain we would turn to mathematicians of Langlands programs and operadic algebras in homotopy theory and to the physicists in string theories, LQG, SUSY, CST, SSM, and others.

  22. (10−33) Informally known as a Mecosecond It is Notation-34 (9.262×10-34 seconds, 35 – 1.85×10-33 seconds).

    The Mecosecond needs a formal name as well as a face
    . Over the years I had asked folks at CODATA, ISO, BIPM, and NIST to consider it, but there were no acknowledgements per se. So we will use the conventions currently in use by Wikipedia. At least there is a little consensus! In 2013 when we first developed our “desktop” version of the Big Board-little universe chart, we called this the domain for mathematics and geometries of qualities. Here would be the archetypes for textures, flavors, colors, and dimensions. This range is defined by 10−33, 10−34, and 10−35 on the horizontal chart. Once these mathematicians adopt the 202 base-2 notations and the continuity-symmetry-harmony necessarily built within it all, and once they can imagine the perfections of those first 50 or more notations, their mathematical formulations will have a place on the grid and can be integrated within what may be called a newly-revised Standard Model for the Universe. It’s a bit presumptuous, but we know that things are never quite right within the first editions! Much more to come thanks to Martin Bojowald and his colleagues!

  23. (10−36) Informally known as a Duecosecond. It is Notation-25 (24 – 9.045269×10-37s, 25 – 1.809×10-36s.

    The Duecosecond also needs a formal name as well as a face
    . This part of the scale, from 10−36 to 10−39 within the horizontally-scaled chart, includes notations 20-to-30. Within our “desktop” version of the chart, it is the domain for the archetypal formulation of substances. Again, we believe the mathematics and the geometries have been worked out within these studies: Langlands programs and operadic algebras in homotopy theory, string theories, LQG, SUSY, CST, SSM, CDT, field theories, and all the hypothetical particles.

  24. (10−39) Informally known as a Trecosecond. It is Notation-15 (14 – 8.832712×10-40s, 15 – 1.766542×10-39 s).

    The Trecosecond needs a formal name as well as a face
    . This part of the scale, from 10−39 to 10−41 brings us into Notations 10-to 20 which within our “desktop” version of the chart, is for structures. Aristotle called it ousia. Again, we believe the mathematics and the geometries have been worked out within these studies: Langlands programs and operadic algebras in homotopy theory, string theories, LQG, SUSY, CST, SSM, CDT, field theories, and all the hypothetical particles.

  25. (10−42) Informally known as a Tetrecosecond. It is Notation-5 (1.72517×10−42 s).

    The Tetracosecond needs a formal name as well as a face
    . We have adopted Plato’s formulation and call it forms. It is the domain of 10−42 to 10−44 to the PlanckSecond. Again, we believe the mathematics and the geometries have been worked out within these studies: Langlands programs and operadic algebras in homotopy theory, string theories, LQG, SUSY, CST, SSM, CDT, field theories, and all the hypothetical particles.

  26. PlanckTime. It has also been referred to as the PlanckSecond: 5.391 16(13)×10-44 Notation-0, (10-44), the first moment in Time. For more, for now, go to this explanation of this expansion.

These are the 26 faces of time. They are sketched out today. It is the beginning of a new study. Welcome aboard. -BEC


Under consideration:

  1.  Variorum De Rebus Mathematicis Responsorum, Liber VIII, François Viète, (Tours, 1593) within The Analytic Art, François Viète, translated by T. Richard Witmer, Kent State Press, 1983, Dover, 2006 Also, see John Baez analysis.
  2. Development of an infinite series, Wikipedia (retrieved 2023)
  3. François Viète formula for pi (π)
  4. Zeptosecond Birth Time Delay in Molecular Photoionization, Science (2020). DOI: 10.1126/science.abb9318 , https://science.sciencemag.org/content/370/6514/339


References & Resources
As these references are studied, key references and resources will be added.

  1. Physical Implications of a Fundamental Period of Time, Garrett Wendel, Luis Martínez, and Martin Bojowald, Department of Physics, The Pennsylvania State University, 104 Davey Lab, University Park, Pennsylvania 16802, 2020
  2. Absence of Singularity in Loop Quantum Cosmology, 2001. ArXiv -177.

BIPM: International Bureau of Weights and Measures
CGPM: Conférence Générale des Poids et Mesures
Resolution 3 of the 27th CGPM (2022) 15-18 November 2022
CODATA: Committee on Data of the International Science Council (ISC)
ISO: International Standards Organization.
NIST: National Institute for Science & Technology (USA)

There will always be more to come.


There will be emails to many of our scholars about these points.

Wed, May 24, 12:05 PM, Abhay Ashtekar, Penn State
Tue, May 23, 6:03 PM, Donna Strickland, Waterloo, Ontario
Tue, May 23, 8:28 AM, Gérard Mourou, IZEST, Palaiseau, France
Mon, May 22, 4:48 PM, Carlo Rovelli, Marseille, France
Sat, May 20, 8:04 AM, Céline Fellag Ariouet, BIPM, Paris
Wed, May 17, 6:41 PM, Martin Bojowald, Penn State
Wed, May 3, 12:48 PM, Jogesh Pati, Maryland
Tue, May 2, 10:01 PM, Adrian Ocneanu, Harvard, Penn State
Mon, May 1, 11:14 AM, Hsuan-Yi Liao, Taiwan – operads


There will also be many instant messages to thought leaders about these points.

9:49 AM · May 28, 2023 @the_xijinping I recently finished writing and editing an open letter that I would like to bring to your attention. It is about Karl Marx’s understanding of mathematics. That page will soon become a homepage. The URL is https://81018.com/marx/ Would you like to suggest any edits?

5:11 PM · May 23, 2023 @brattray @reidhoffman The big bang is fizzling. That opens the door for new models. We have one for the global scholars to evaluate. Would you please sign the petition to have the world’s leading intellectual organizations evaluate it? https://www.change.org/KnowYourUniverse

4:21 PM · May 17, 2023 @TheNormanLear @NYUEmpathy What will bring us all closer together is to drop our little worldviews and adopt a highly-integrated mathematical view of the universe. Its inclusivity teaches us about continuity-symmetry-harmony. Here’s a start: https://81018.com Why not?

8:23 AM · May 9, 2023 @JeffreyGoldberg The myth of “a comprehensive understanding of things” can readily be understood within the failings of our limited worldviews. Only when we have it all in context with the universe will we begin to understand. https://81018.com is my sandbox.
[Please note: Jeffrey is the Editor-in-chief of The Atlantic.]



You are always invited.

Keys to this page, the-firsts

• This page became the homepage on May 22, 2023. It is still very much “under construction.”
• The last update was May 27, 2023.
• This page was initiated on May 4, 2023.
• The URL for this file is https://81018.com/the-firsts/
• The first headline for this article: If you start at this moment and call it the Now,
could you be experiencing all 26 faces of time?

• Teaser: 26 faces of time within 202 notations that encapsulate our universe.

Log of significant updates (with related pages):


For more, go to https://81018.com Also: https://81018.com/presuppositions/


Most-simple model of the universe starts with the most-simple concepts

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Right Yellow Arrow


A Most-Simple Start
and Different Model of the Universe

by Bruce E. Camber (your comments are most welcomed)

John Archibald Wheeler’s 1986 vision of “so simple, so beautiful

We are beginning to see the reality of physicist John Archibald Wheeler’s increasingly well-known statement, “Behind it all is surely an idea so simple, so beautiful, that when we grasp it — in a decade, a century, or a millennium — we will all say to each other, how could it have been otherwise?[5]

Our on-going narrative — under construction since 2011
(all links open pages within this website)

This “most-simple” start uses most-simple concepts. The first is that the universe is logically and mathematically parsed within 202 base-2 notations using Planck’s natural units. Through the stacking-and-packing of infinitesimal spheres that are defined by those Planck numbers, this emergent universe naturally includes everything, everywhere, for all time.

Math is math. Logic is logic. An expanding universe, it readily goes from that very first-moment in time to this very moment, within what many scholars and scientists call the Now. In 2013 we also thought, “It’ll be a great STEM tool.”

The second big concept is that the most-simple physical object is the sphere and the most-simple qualities of pi — continuity-symmetry-and-harmony — are defined by a sphere. That is a very different orientation to the infinite than Kurt Gödel and David Hilbert gave us. That it renders an expansion of 539 tredecillion infinitesimal spheres per second is a very different perception of a cosmological constant. And, here the earliest universe, up to and through the first year, starts infinitesimally small but at the highest-possible speed, uniformity, and packing density. That’s Notation-0 to Notation-169.

The third big concept has very little precedence. Nobody is talking about “a domain of perfection.” Yet the speed of emergence and those packing densities do not allow for the gaps of quantum fluctuations to emerge. Of course, there will be many who will object to reducing all fluctuations to the geometries of a gap. Based on a bit of guessing, today that domain could readily extend to about Notation-50 yet could, on occasion, extend much higher. Of course, the mathematics of imperfections whereby all quantum fluctuations are reduced to the geometries of a gap also has little precedence. Notwithstanding, it seems that the logic of gap geometries remains to be studied within academia.

And, the fourth big concept to consider is the finite-infinite relation which has been reduced to those three commingled concepts being generated by pi, continuity-symmetry-harmony.

There are over 30 presuppositions that we’ve made to come to these four simple concepts.

Four concepts: Right or wrong? Who shall we ask?

So we are on a search to learn why these concepts are on the right path or the wrong path. Here is a sample of recent questions of leading scholars around the world:

  1. Do you know any scholar who is making it his or her mission to study the geometric gaps starting with the five-tetrahedral gap that Aristotle missed? Lagarias and Zong were awarded the 2015 AMS Conant prize for their studies of the tetrahedral gap. Unfortunately they focused on packing densities and not on that gap’s effects throughout the scales of physics (original).
  2. There are many who are studying beyond the standard model and many who start at the Planck base unitsDo you know of any scholar who is looking at a base-2 expansion of those Planck units? 
  3. There are just 202 notations from the smallest possible measurement of space-time to the largest. The infinitesimal notations, 1-64, represent an area for composites that I suspect are already defined by mathematicians within operadic theory and within these nine groups. Might we hypothesize that its all on the grid?
  4. Do you know of any scholar who would not object if we were to say that infinitesimal composites start at or near the Planck base units?

Where and what are our missteps?

In December 2011 we were so sure that we were onto something a little different, we created that first chart: https://81018.com/big-board/ The project went by two names: Big Board-little universe and Quiet Expansion.
In January 2012, we began writing about it and posted it within free webpages so we could ask for critical reviews. https://bigboardlittleuniverse.wordpress.com/2013/02/23/beginning/ https://81018.com/early-story/
By 2013 we were asking for help from the very finest scientists: Frank Wilczek, Freeman Dyson, Stephen Hawking, Alan Guth and so many others. Nobody corrected us. And, every time we were ignored, it would embolden us to find scholars who could help us; “Somebody will know why we are wrong.”
By 2016, we wrote it up as sensibly as we could and every journal ignored us. Not even the American Academy of Arts & Sciences would take time to reply. That is when we got the domain, https://81018.com, to consolidate everything that we had written and to begin to dig down as deeply as needed to find the foundations and grounds for truth.


I know there will be push back, especially where we explore how values and ethics6 come from within the finite-infinite definitions of continuity-symmetry-and-harmony. It seems natural, but I guess it is too simple for many.

Today, we look more closely at the issues being popularly addressed on the web within places like ArXiv, Physical Review, and so many others. We are learning about new concepts and new studies every day. It is great fun and eventually we will understand why we are on the wrong path, or perhaps, why we are on a good path that will open new doors to see new vistas. Thank you.



Endnotes & Footnotes
There may not be many because all these points already have pages within this website.

[1] How could it have been otherwise? Two key links: The first moment of time is Planck Time. It is Notation-0 and it is always the start of the universe. How can it be otherwise? If we were to apply base-2 to Planck Time there are just 202 base-2 notations to the current time. Within academia, it is often referred to as the Now

Those 202 base-2 notations necessarily encapsulate everything, everywhere, for all time. It is not that hard to grasp. Our sixth-grade AP class and high school students mostly got it.

Unfortunately the big bang theory gets in the way. During his lifetime, nobody wanted to be hard on Stephen Hawking. He was suffering enough. Plus, the world has always been desperate for heroes and true leaders, yet we haven’t been taught how to think about these people. We tend to put them on a pedestal and celebrate their celebrity status. Instead, we all need to be taught that people and information are dynamic and we all have failings. We were so excited about our simple model we even to wrote to Hawking. Questioning people and ideas was what we were taught to do even though they are on a pedestal and seem untouchable.

Now, our first use of this Wheeler quote was in a 2015 document: https://81018.com/simple/ It will now be re-worked a little.

[2] Exponential growth. A simple logic and dimensional analysis inspired the conclusion that there is one infinitesimal sphere per unit of the Planck base units. It’s an assumption or hypothesis. The result is exponential growth which renders 539 tredecillion spheres per second most-quickly, most-densely, and most-efficiently. It amounts to a heretofore undeclared cosmological constant.

[3] Perfections and Imperfections.There will be a fair amount of push back from the classic physics community. I am not sure why there hasn’t been a more pointed study of Aristotle’s mistake and Newton’s absolute time. The simple formula for pi renders geometries-and-notations with perfect continuity-symmetry-harmony. The geometries of the gap are such a natural foundation for quantum fluctuations, how has it been missed?

[4] Finite-Infinite. The working relation between the finite and the infinite can be simplified by grasping a deeper understanding of the oldest, most-used equation in history, pi (π). We all need to learn to be more gracious.

A more simple definition of infinity is overdue.

[5] John Wheeler, his 1986 article, and the quote. John Archibald Wheeler had an enormous, global reputation. His focus was to define the most fundamental relations. By 1986 the particle zoo was overflowing. He knew that we were all missing something simple. So if you click on that quote, “Behind it all is surely an idea so simple, so beautiful, that when we grasp it — in a decade, a century, or a millennium, — we will all say to each other, how could it have been otherwise? the link opens to the full article. If he were alive today, I would be asking for his advice, “Is this simple enough? Or, is it too simple?”

[6] Ethics and values from the sphere. Given the failings and aggressions of the leadership in the USA, China, Russia, Iran, North Korea and so many others throughout our little world, it behooves the academic world to come up with a better model of the universe and the meaning and value of life. This model proposed from the most-simple concepts also has a value proposition, possibly an ethical bias: https://81018.com/values/

There will always be more to come.


References & Resources
As this topic is studied, key references and resources will be added.

These related pages on this website are recommended:
1. What are our starting points? Why? What is the first unit of time?
__• https://81018.com/continuity-symmetry-harmony/
2. Why isn’t there a sense of order among the hypothetical particles?
__• https://81018.com/universe-numbers/
__• https://81018.com/infinitesimal-composites
3. Kurt Gödel‘s mathematical universe.
4. Eugene WignerThe unreasonable effectiveness of mathematics in the natural sciences, 1960
5. Max TegmarkOur Mathematical Universe: My Quest for the Ultimate Nature of Reality, Knopf, 2014
__ Also see: ArXiv (PDF) 2007
6. Redefine space, time and infinity, 81018, 2020

Within our time, Wigner and Tegmark carried 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.


There will be emails to many of our scholars about these points.

Wed, May 3, 12:48 PM, Jogesh Pati, Maryland
Tue, May 2, 10:01 PM, Adrian Ocneanu, Harvard, Penn State
Mon, May 1, 11:14 AM, Hsuan-Yi Liao, Taiwan – operads
Sat, Apr 29, 5:46 PM, Maxim Kontsevich, IHES, France
Thu, Apr 27, 4:59 PM, Connor Malin, Notre Dame
Tue, Apr 25, 8:08 PM, Alberto Cattaneo, Zurich – GAP
Mon, Apr 24, 10:33 PM, Christof Wetterich, Heidelberg
Mon, Apr 24, 11:46 AM, Tim R. Morris, Southhampton (UK) – trace anomaly
Sat, Apr 22, 5:54 PM, Alexandre V. Borovik, Manchester
Fri, Apr 21, 4:33 PM, Kirsten Wickelgren, Duke, GAP
Fri, Apr 21, 9:10 AM, Dorina Mitrea, Baylor Univ


There will also be many instant messages to thought leaders about these points.

8:23 AM · May 9, 2023 @JeffreyGoldberg The myth of “a comprehensive understanding of things” can readily be understood within the failings of our limited worldviews. Only when we have it all in context with the universe will we begin to understand. https://81018.com is my sandbox.
[Please note: Jeffrey is the Editor-in-chief of The Atlantic.]

5:44 PM · May 3, 2023 @the_xijinping Marxism “…was created in order to change the destiny of human history. …a collectivized world is just there, over [the horizon]. Whoever rejects that world will be rejected by the world.” – Xi Jinping Sounds like you! Can we talk about it? https://81018.com

1:39 PM · May 3, 2023 @TempletonPrize and @AnoushehAnsari Redefine space-time. It’s the only path to a real paradigm shift. The attached image is here: https://81018.com/2020/01/26/ansari/… Please explore the past four homepages: https://81018.com (click on the left back arrow at the top of each homepage).

9:32 PM · May 2, 2023 @AnoushehAnsari We won’t get far until we grasp the essence of space and time. And we won’t grasp that essence until its in context within a highly-integrated, mathematical view of the universe. Our start on it all is here: https://81018.com/ and https://81018.com/most-simple

9:53 PM · May 2, 2023 @xprize @PeterDiamandis @raykurzweil Real progress begins by redefining space-time. Try continuity-symmetry-harmony, the three facets of pi (π) — https://81018.com/pointing/ https://81018.com/csh/ — and a finite-infinite relation. Simple models follow: https://81018.com/most-simple/



You are always invited.


Keys to this page, most-simple

• This page became a homepage on May 3, 2023. It is still “under construction.”
• The last little updates were on May 18, 2023.
• This page was initiated on April 30, 2023.
• The URL for this file is https://81018.com/most-simple/
• The first headline for this article: Universe starts with the most-simple concepts
• Second headline for this article: A Most-Simple Start and Beautiful Model of the Universe
•The teaser* is: Most-simple model of the universe starts with the most-simple concepts

*Or, wicket, kicker or eyebrow.


For more, go to https://81018.com Also: https://81018.com/presuppositions/

On learning about pulsars from Andrew Cameron

Andrew Cameron, Swinburne University

Homepage(s): Google Scholar, IMPRS, IN, Twitter
Sample article: Discovery of Millisecond Pulsars in the Globular Cluster Omega Centauri, The Astrophysical Journal Letters, Volume 888, Number 2, DOI 10.3847/2041-8213/ab621a

First email: 22 April 2023 

Dear Prof. Dr. Andrew Cameron:

If we start at the Planck base units, tabula rasa, what might manifest and be best described by those four units:Planck Length, Planck Time, Planck Mass and Planck Charge?

Might we assume an infinitesimal sphere?

Well below the thresholds of measurement, those spheres would be voluminous. If being generated at a rate of one sphere per unit of Planck Length and Planck Time, there would be 539 tredecillion per second. Even though infinitesimal, these spheres could readily be generating other structures; cubic-close packing of equal spheres demonstrates it. 

As a dimensional point or vertex, it could be important to knot theory, string theory and Langlands programs. Those first 64 notations would be hard to initially accept, but….

Also, quantum fluctuations are real. Geometry is real. The gap that Aristotle missed has yet to be studied. The latest attempt by Lagarias and Zong got stuck in the study of packing densities. What happens in basic physics because of these gaps? https://81018.com/geometries/ is my rudimentary study. 

Also, the finite-infinite discussions are opened; that thrust has to come from somewhere. My preliminary analysis: https://81018.com/csh/. It redefines the infinite. I don’t think Tegmark and all those before him, Gödel, Hilbert, etc. will object.

Now you have written the rest of the story out to those pulsars.

May I hear from you?

Thank you.



[Editor’s Note: Not too long ago, Lemaître (1928) suggested a primeval atom. Atoms may be small, but this entity would be like an atom compared to our solar system. The word, primeval, doesn’t capture that disparity, plus we now know too much about the particle zoo.]

On discovering the work of Peter W. Graham…

Peter W. Graham,

Focus: Physics beyond the Standard Model
(s): ArXiv (73), inspire, Publications, Research, Publications, Stanford

First email: 22 April 2023 @ 4:26 PM

Dear Prof. Dr. Peter Graham:

Might we approach an axion definition by assuming it is an infinitesimal sphere on the order of the Planck base units? If our only preconditions are those postulated by the Peccei–Quinn 1977 theory to resolve the strong CP problem in quantum chromodynamics, what can we intuit or know? If those infinitesimal spheres are defined by the Planck base units — length, time, mass and charge — it is well below the thresholds of measurement. Notwithstanding, those axions would be voluminous.  If being generated at a rate of one axion per unit of Planck Length and Planck Time, there would be 539 tredecillion per second. Even though infinitesimal, these spheres could readily be generating other structures using the concepts of cubic-close packing of equal spheres. As a dimensional point or vertex, it could be important to knot theory, string theory and Langlands programs.

Just guessing. We primarily work within secondary education.




On discovering the work of Christopher Weaver

Christopher Weaver, Illinois Center for Advanced Studies of the Universe, Urbana-Champaign, Illinois

Website, Routledge: Fundamental Causation, ArXiv

First email: 22 April 2023, Earth Day @ 3:42 PM

Dear Prof. Dr. Christopher Gregory Weaver:

On this Earth Day perhaps we need to consider the role of pi (π), and other key dimensionless constants, the Planck base units, and a bit of base-2 exponentiation (just to keep track of things).

That first second using the Planck units and base-2 is within Notation-143. Things are already way too complex. Even the first nanosecond, between Notations 114-to-117, is still too complex. Even the first femtosecond (one millionth of a billionth of a second or 10-15), out between Notation 94-to-97, is complex. At the edge of our measuring capabilities, the yoctosecond (10-24) between Notations 65-to-67, too much has happened.  It begs the question, “Are there any scholars looking at those first 64 notations from Planck Time?”

If the first spheres manifest within Notations 1-to-10, what are the dynamics? If spheres are being created at a rate of 539 tredecillion spheres per second (assuming one sphere per unit of Planck Time-Length-Mass-Charge),  what are the possible geometries? What forms? Does cubic-close packing of equal spheres help? It doesn’t take much and densities and speeds are such that only the perfect is possible. No quantum indeterminacy, we’ll have to study that finite-infinite relation to discuss causal efficacy.

I’ve gone on and on, too much for an introductory note. Please forgive me. Most of my ruminations are here: https://81018.com Besides the links embedded above, you may appreciate these:
Background story: https://81018.com/home/
Earliest analysis: https://81018.com/stem/
Most recent ;analysis: https://81018.com/continuity-symmetry-harmony/

Thank you for all your writing and for looking deeply into causality.

Warm regards,



Drop-down menus from the top navigation bar

Top Navigation Bar (pictured below) is on every page of this website.

HOME. The drop down menu from HOME shows the dates and titles for over 150 more homepages. You can scroll down that list all the way back to the first homepage in July 2016.

PI (π). On the right side of that Top Navigation Bar is PI (π) with its six options in the drop-down window. These are six of the most important links within the website: THE FIRST FORMULA, THE SECOND FORMULA, THE THIRD FORMULA, THE FOURTH FORMULA, APPLICATIONS, and THE UNIVERSE-IN-A-GRID.

ABOUT is an informal collection of pages that seem to catch the spirit of this enterprise. These will change very slowly over time.

CHARTS: Of course, the charts have been a constant reminder to answer the question, “What do these numbers represent? How do we interpret them?” The scholarly community has all but ignored them. I believe they are sure that these numbers are all too simple.

CONTACT. The most important link is ALPHABETICAL LISTING. I use this option frequently each day when I want quick access to a scholar’s work. The options below it are still rough and need work.

INDEX is an historic relic of a lists of pages by subject matter. It needs a “do-over” to make it more easy to find a subject. I will use the SEARCH function up in the far right corner before scrolling through the INDEX!

Thank you.


Hypothetical particles? Or, dynamic composites of infinitesimal spheres?

Left Yellow Arrow
Right Yellow Arrow

Pages: Agreements | Hypostasis | Mistakes | Pi (π) | Questions | Sphere | STEM | Up

Every “hypothetical” begs the question,
“What is fundamental?”

by Bruce E. Camber (First draft)

Overview: Obvious to some who work to discern the nature of hypothetical particles, we need a more basic paradigm; particles with all their hypothetical particles are not the most-basic organizing structures of our universe. So, if not, what defines our most-basic relations?

Proposal: Go down to the Planck base units, start with the most-simple, three-dimensional, geometric object, a sphere, and ask, “How could it start so simply?” Be imaginative. Be bold. Then, come back with a proposal.

Our postulations: https://81018.com/continuity-symmetry-harmony/ Called..The First Formula, it is on the drop-down menu from Pi (π) at the top of every page within this website. It opens the magic of pi (π). There is still so much that we do not understand about pi (π), let’s try to go to a deeper level of engagement. Surely, we should never give up trying. [1]

So, what is the essence of a sphere?

Can it open key questions in mathematics, physics, and philosophy?

That question triggered the next two formulas, cubic-close packing (ccp) and a natural inflation of 539 tredecillion spheres per second. Watch how our basic geometries emerge and how there is an explosion of spheres. To begin to analyze those spheres and attempt to grasp some order, we applied base-2 notation. It outlines the universe in 202 notations. Two key scales emerge — https://81018.com/scales-2/ — which give structure to all formulas. Applications come next; and with them, all the hypothetical particles and the Standard Models follow.

Aether (or grid). In 2011 when we created our first chart, it was mostly “just numbers.” Then we began to realize, “All of those 202 base-2 notations are always active. They build on each other.” Then it began to simmer… “What could be more simple? Just 202 steps to outline the universe and it necessarily includes everything, everywhere, for all time within a grid of infinitesimal spheres.” It seemed like John Wheeler’s claim was coming into view: “Behind it all is surely an idea so simple, so beautiful, that when we grasp it — in a decade, a century, or a millennium — we will all say to each other, how could it have been otherwise?”[2]

A fifth formula is being studied and developed to capture quantum fluctuations within specific geometries and mathematics (equations). One group of scholars, GAP (Geometry And Physics),[3] is being approached to see if any of their associates are studying the physical gaps created by simple geometries. In 2016 we were introduced to gaps: https://81018.com/number/#Gap Then in June 2020, there was this analysis: https://81018.com/biased/#Aristotle And, in May 2022, we uncovered a heretofore unacknowledged octahedral gap: https://81018.com/geometries/

Why not? I have asked hundreds of scholars and will continue asking,”Why not?” of many, many more. We have ignored the basics and the foundations of our foundations altogether too long. Continuity-symmetry-harmony define nine perspectival studies of our foundations. Each of these studies involve many, many scholars and each group defines part of the deeper dynamics of our grid. This grid, a logical and mathematical outline of the universe within 202 notations, has not yet been recognized. The first notations (0-to-64) hold the foundations of our foundations. It is hypothesized to be the domain of infinitesimal composites, already mathematically studied within work on algebraic operads and applied within these nine studies.

Simple Chart: That base-2 chart is the most-inclusive, most-complete, most-simple numbers to outline our Universe. There is a place for Kees Boeke’s rudimentary base-10 chart, but it comes later. There is a necessary relation between Planck Length and Planck Time, and then with Planck Mass and Planck Charge. The work of mathematicians, Milnor and Smale, will also include attractors and repellers (gravitation and electromagnetism) within this mix of infinitesimal dynamics. [4]

This grid of infinitesimal spheres is making and necessarily-expanding our universe. It has a lot to teach us. It is time to take a look and work with those earliest notations, the most simple part, before it all becomes exceedingly complex.

Thank you. –BEC


Endnotes & Footnotes
There may not be many because all these points already have pages within this website.

[1] Never give up trying. This footnote will document current articles and papers that are attempting to understand the very nature of pi (π). To that end, the work of a Baylor University mathematics professor, Dorina Mitrea, is recommended. Further, the concept of a trace anomaly when scale invariance is broken requires study. It begs the question about dimensionless constants, “When are such constants no longer dimensionless?”

[2] John A. Wheeler, How Come the Quantum? Annals of the New York Academy of Sciences, 480 (“New Techniques and Ideas in Quantum Measurement Theory”), pp. 304-316 (1986),doi: 10.1111/j.1749-6632.1986.tb12434.x

[3] GAP Group: Here GAP means Geometry And Physics. Some say, Geometry-Algebra-Physics. They meet annually and have been since 2003. The list of speakers and their work will be surveyed to see if any are engaging pi (π) in new ways.

[4] Infinitesimal Dynamics and Attractors-Repellers: Concepts are related to the concept of dynamic modality and they regard the long-term behaviour of a dynamical system. (Review: https://81018.com/parameters/#9a)


References & Resources
As these references are studied, key references and resources will be added within this website.

It gradually reveals itself to us as we try to understand the very fabric of mathematics. Even now there are many unanswered questions and open problems which are both intriguing and incredibly difficult. It never stops amazing us.” — Dorina Mitrea, Ph.D., Baylor

Another dynamic of the sphere. “Attractors are trajectories of the system state variable that emerge in the long-term, with relative independence with respect to the exact values of the initial conditions. These long-term trajectories can be either a point in the state space (a static asymptotic behaviour), named fixed-point, a cyclic pattern (named limit cycle), or even a chaotic trajectory. “

  • See Milnor and Smale: “Repellers correspond, qualitatively speaking, to the opposite behaviour of attractors: given a fixed-point or a cyclic trajectory of a dynamic system, they are called repeller-type trajectories if small perturbations can make the system evolve to trajectories that are far from the original one.” From IGI-Global on April 11, 2023

Our basics: four hypotheses, based on conjectures and facts that are not currently recognized:

The first 64 notations accommodate the mathematics of the following studies: (1) Langlands programs, (2) string theory (including M-Theory, F-theory, type II and offshoots), (3) supersymmetry (SUSY), (4) loop quantum gravity (LQG), (5) causal dynamical triangulation (CDT), (6) causal set theory (CST), (7) field theories, (8) spectral standard model (SSM), and (9) all the hypothetical particles.


There will be emails to many of our scholars about these twelve points.

Mon, May 1, 11:14 AM, Hsuan-Yi Liao, Taiwan
Sat, Apr 29, 5:46 PM, Maxim Kontsevich, IHES, France
Thu, Apr 27, 4:59 PM, Connor Malin, Notre Dame
Tue, Apr 25, 8:08 PM, Alberto Cattaneo, Zurich
Mon, Apr 24, 10:33 PM, Christof Wetterich, Heidelberg
Mon, Apr 24, 11:46 AM, Tim R. Morris, Southhampton (UK)
Sat, Apr 22, 5:54 PM, Alexandre V. Borovik, Manchester
Fri, Apr 21, 4:33 PM, Kirsten Wickelgren, Duke
Fri, Apr 21, 9:10 AM, Dorina Mitrea, Baylor University
Thur, Apr 20, 12:03 PM, Earth Day USA 1970- April 22, 2023
Wed, Apr 19, 2023, 11:10 AM, Reminiscing about technology: An Open Email to old friends
Wed, Apr 12, 2023, 3:39 PM, Mathieu Stiénon, Penn State
Wed, Apr 12, 2023, 3:14 PM, Adrian Ocneanu, Harvard, Penn State


There will also be many instant messages to thought leaders about these twelve points.

@BlackRock Migrate from a simple worldview to an integrated view of the Universe. https://81018.com It’s a start.

Follow the numbers: https://81018.com/chart/

The model is based on universals: continuity-symmetry-harmony.

@JamesClayton5 (BBC Tech Reporter) Authentication, integrity, and honesty require creating continuity, symmetry, and harmony. https://81018.com/csh/ is the backdrop for a highly-integrated, mathematical view of the universe that liberates and integrates everything, everywhere for all time!

 @MarsGlobal If we are going to create a better world, we need a better model of who we are and why. That takes breaking out of our limited worldviews and embracing the universe with continuity-symmetry-harmony: https://81018.com/csh/ Look at: https://81018.com for more.

10:41 PM · Apr 15, 2023 @LidianeJones We’re all have too many loose-ends and need a better grounding. A mathematically-integrated view of the universe is a start: https://81018.com/chart/ and seeing the universe filled with infinitesimal spheres — https://81018.com/continuity-symmetry-harmony/ — could help. Glad to explain.


You are always invited.


Keys to this page, universe-numbers

• This page became a homepage on April 20, 2023.
• The last update was Monday, May 1, 2023.
• This page was initiated on April 4, 2023.
• The URL for this file is https://81018.com/universe-numbers
• The headline for this article: Hypothetical particles beg the question, “What is fundamental?”
• Teaser* is: Life is too short. We need to re-engage our basics, the foundations.
__#2: Hypothetical particles? ….a dynamic composite of infinitesimal spheres?


*Or, wicket, kicker or eyebrow.