There are many references throughout this website to the octahedron. The first two images below are result of cubic-close packing of equal spheres (ccp). All  links go to pages go to earlier studies.

Our initial study of the octahedron began with our study of the tetrahedron.  It was such a surprise to find the octahedron making up the center of every tetrahedron.  And, it was extremely satisfying to find all fourteen objects sharing a common center  point and to see that all of these centerpoints were also center of four hexagonal plates. Following our simple logic, when we observe graphene as a single atom thickness, it is always so much more. It is the manifestation of a plate from a period-doubling bifurcation.

1. Dynamic unfolding of tetrahedrons and octahedrons from sphere-stacking

2. Tetrahedral-octahedral couplet -: evolves out of cubic-close packing of equal spheres (ccp)

3. Our first model of the tetrahedron (above) and our first model of the interiority of the octahedron (right) from 1997. To make these models required developing molds to manufacture thousands of perfect octahedrons and tetrahedrons. These models were all part of our teaching Platonic geometries in high school.

4. Four bands of hexagonal plates around a centerpoint represented by yellow, red, white, and blue tape.

It was not until we had our larger model of a tetrahedron with two generations of embedded objects did we begin to see the plates of triangles, squares and hexagons.

moleculeWe are not sure how many doublings from the first octahedron would we then have fracturing of these plates. Our guess is somewhere between the 67th notation (or doubling) and 87th depending on the element being made.

Here, for example, is the hexagonal plate defining a single cell.

This article was begun on May 3, 2018. It is still a rough draft. It has its origins at MIT in 1979.

Note:  Richard Fitzpatrick (2006-03-29)  http://farside.ph.utexas.edu/teaching/329/lectures/node54.html

Symmetry: Circles-to-Spheres-to-Triangles-to-Tetrahedrons-to-Octahedrons


Sphere to tetrahedron-octahedron couplet From a conjecture about cannonball stacking:
In 1611 Johannes Kepler opened the door on a foundational relation in mathematics by addressing a difficult practical question about stacking cannonballs on the deck of a ship. The result, represented by this dynamic image on the left, shows the transition from circles to spheres to lines (lattice) to triangles to tetrahedrons to octahedrons. Here we begin to tile and tessellate the entire universe and encapsulate everything, everywhere throughout all time within 202 notations. Here symmetries go from simple to complex and appear set for action. Though the cannonball stacking problem appears inconsequential today, Thomas Hales introduced a series of proofs that have also open new dimensions within mathematics that includes his background work on the fundamental lemma, automorphic forms, unitary groups, and the stabilization of the Grothendieck–Lefschetz formula.
A key page of the Symmetry discussion
Screen Shot 2017-09-08 at 9.09.16 AM A Door on CCP (or FCC) and HCP is also opened by the Kepler conjecture.
Cubic Close Packing also known as face-centered cubic (fcc) and hexagonal close-packed opens key discussions about the honeycomb conjecture, atomic packing factors (APFs), discrete translation operations, and crystal structure. All these faces of mathematics will be explored in an attempt to applied them within the base-2 structure of the first 67 notations.  Our Symmetry discussion
Screen Shot 2017-09-08 at 8.40.45 AM Feigenbaum constant: The doublings of the circles, then the spheres
are assumed to be a direct analogy to the emergence of these symbolic cannonballs. We’ll assume that the first circle emerges from the perfection of pi and the thrust of the universe, and we guess that the outlines of a sphere emerge with the next doubling. If so, then this dynamic image (top left box) can be replicated within six steps. 2-4-8-16-32-64. For the black and then the green, there are nine initial circles, then another nine to become spheres. That is 36 construction vertices. Possible?  Symmetry discussion…
CCP-FCC-HCP Honeycomb conjecture with Thomas Hales: A bold, creative mathematician, Hale’s work opens key doors to the foundations of the universe. Although still concerned with Kepler’s technical problem, this structure may have profound applicability to the deepest “real world” questions about the nature of space and time. So, we will pursue this line of inquiry as it is related to the “first generation” of the infrastructure of the universe.
Go to the symmetry page…
Octo70 Hexagonals in octahedron: This image of an octahedron has six half-size octahedrons, one in each of the four corners and on the top and bottom. It has eight tetrahedrons in each of the eight faces. These objects evolve around a counterpoint that is also the center of four hexagonal plates shown here as red, white, blue and green.  In the discussions of the the honeycomb, there appears to be no acknowledgement that these hexagonal plates are part of the tetrahedral-octahedral structure and that it emerges, as demonstrated within the dynamic image, from circles and spheres. It is easy to imagine these basic shapes replicating and morphing to create the Periodic Table of Elements.
Symmetry page…
Olympicene2 2010 Olympicene molecule: An organic carbon-based molecule was synthesized with five rings (four benzene rings) to honor the 2012 London Olympics. What makes this especially significant is that in 2012 IBM researchers in Zurich captured this image using non-contact atomic force microscopySymmetry page…

There are many other pages that  use this stacking image: [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], and [12].

Tetrahedrons & Octahedrons

Can you envision the 29 tetrahedrons and 11 octahedrons within this very large tetrahedron?
Sphere to tetrahedron-octahedron couplet
Transition from spheres to

Emergence from spheres and doubling functions:
1. A Study of Numbers: https://81018.com/number/#Kepler
2. Growth: https://81018.com/growth/
3. Emergence: https://81018.com/emergence/
4. Fabric: https://81018.com/fabric/
5. Symmetry:  https://81018.com/symmetry/
6. Circles-spheres: https://81018.com/circles-spheres/
7. Stacking: https://81018.com/stacking/
8. Spheres: https://81018.com/sphere/
9. Start: https://81018.com/start/

The text within the picture reads as follows:

Three levels of simple complexity:

1. Observe the tetrahedron in the bottom left corner.

2. Notice that it is enclosed in a larger tetrahedron. Right beside it is
an octahedron, plus there is a tetrahedron in each of the other three corners. Every tetrahedron encloses four half-sized tetrahedrons and an octahedron.

3. Notice that our larger tetrahedron is enclosed by an even larger tetrahedron. This pattern repeats itself getting smaller and getting larger. Part of the complexity can be seen by observing the center octahedron. Notice the red, black and blue hexagonal plates. A white plate has been obscured. Each shares the common centerpoint.

4. Notice the octahedron in the middle whereby that center triangle is one of its eight faces. There are four faces that are the center faces of each side of the tetrahedron and there are four interior faces. The octahedron has a half-sized octahedron in each of its eight corners and a tetrahedron in each of these eight faces.

For more, please follow this page on the website:

Freedman, Wendy L.

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

Articles: Cosmology at a crossroads, Nature, May 2017 (PDF)
ArXiv (152): The Hubble Constant with Barry F. Madore, August 2010
_______Mathematical Underpinnings of the Multi-Wavelength Structure of TRGB, August 2020
Books: Measuring and Modeling the Universe: V2, Carnegie Observatories (2004)
Gruber Foundation
Homepage (KICP)
NASA Hubble (July 16, 2019)
YouTube: Misel Family Lecture Series (2017)

First email:  17 October 2020 (started on October 8)

Dear Prof. Dr. Wendy Freedman:

You and your people have been teaching me so many things these past few weeks, I had to write and say, “Thank you.” I have even quoted one of your key summaries, “The Hubble constant is the cosmological parameter that sets the absolute scale, size and age of the universe; it is one of the most direct ways we have of quantifying how the universe evolves.”

Out of high school. High school teachers can be entirely naive and I am no exception. Yet, I love geometry and mathematics enough to explore what I don’t know even if it opens idiosyncratic questions: [1] Can geometries build from the Planck base units? Is it the first moment of time?
[2] Might the first manifestation defining space-time and matter-energy be the sphere?
[3] Could cubic-close packing of equal spheres be a primordial functional activity?

In 2011, our geometry classes were having some fun with embedded geometries. We went inside the tetrahedron, doing a Zeno-like walk, going deeper and deeper inside a tetrahedron and then the octahedron within it. In just 45 steps, dividing each of the edges by 2 and connecting the new vertices, we were quickly down within our CERN-scale of particle physics. In another 67 steps we were within the Planck-scale. To go back out, we used the Planck Length, multiplying by 2, and in the 112 steps we were back in the classroom. We decided to keep going and in just 90 additional steps were were approximately out to the size of the universe. In just 202 base-2 exponential notations we had mathematically encapsulated the universe. We thought it was amazing. Euler came alive. The universe became accessible. Everything, everywhere for all time was within a continuum.

A little overview: https://81018.com/home/
Just three layers of tetrahedrons-octahedrons: https://81018.com/tot/
Our perfect little STEM tool: https://81018.com/stem/
Our horizontally-scrolled chart: https://81018.com/chart/

Of course, we quickly discovered Kees Boeke base-10 work and all the related books, films, and websites. We still liked our chart better; the Planck numbers are so very basic, base-2 is so Euler, so biological — could it be related to period-doubling bifurcation, emergence, cubic close packing of equal spheres, homogeneity and isotropy, natural inflation?

We got so far ahead of ourselves.

Back in 2014 we mapped in Planck time, then the other Planck base units. The earliest notations jumped out at us with questions, so we created a horizontally-scrolled chart to follow the numbers more easily: https://81018.com/chart/

Then, last week, I discovered your most prodigious work. You have an observational framework. We have a strictly mathematical framework.
[1] Can they work together?
[2] Can your work tolerate time if it is derivative and finite?
[3] Can your work tolerate infinity defined as continuity, symmetry, and harmony?
[[4] Can the Hubble Constant tolerate 201 fully-symmetric notations and an asymmetric Notation-202 (which includes the edge of the current expansion)?

Notation-202 is defined by 10.9816 billion years (346,545,888,147,200,000 seconds). The 201st notation is 5.4908+ billion years. All prior notations added together also amounts to 5.4908+ billion years. Taking 10.9816 billion years from 13.81 billion years is 2.8284 billion years. Perhaps a notation becomes symmetrical when “filled” with planckspheres. It immediately begins to create the next notation and the dynamics of that notation. There are what seems to be an unlimited number of variables to consider.

I hope our questions are not useless and that this inquiry is not a waste of your time. If it is, I apologize for all my naïvetés.

Thank you.

Most sincerely,

Tong, David

David Tong
Department of Mathematics and Theoretical Physics (DAMPT)
Cambridge University, Wilberforce Road
Cambridge, England

ArXiv (99)A Matrix Model for WZW (2016), DBI in the Sky (2004)
Google Scholar
Video:  YouTube Quantum Fields: The Real Building Blocks of the Universe, The Royal Institution, 15 Feb  2017

Most recent email: September 30, 2020

Dear Prof. Dr. David Tong:

Just over three years ago I sent a  little note after listening to your 2017 Royal Institution Faraday Lecture. Today, I pulled from my shelf a periodical, Fields Within Fields…Within Fields, that back in 1970 in NYC, Julius Stuhlman gave me. He was the founder of the World Institute Council and the Publisher of a Fields Within Fields… Within FieldsDr. Ervin Laszlo was part of his entourage of writers.

There were people who would cheer and support your work even before you were born!

Of course, we’ve had the benefit of Frank Wilczek’s work to exegete the 1899 insights and calculations of Max Planck, along with Max’s 1905 publication of The Theory Of Heat Radiation, and the 1914 English translation with Morton Masius.

My questions are few:
1. Can we take the Planck units as a starting point for the universe?
2. In the spirit of John Wheeler and his quantum foam, is there any possibility that it could instantiate as an infinitesimal sphere?
3. If so, might that sphere inculcate all the dynamics of cubic close packing of equal spheres

I will include an updated copy of my earlier note. As I continue my studies of your work, I will build on those references to your work and to my notes here: https://81018.com/2020/09/29/tong/

Again, I thank you for your most formidable work, truly an inspiration.

Most sincerely,


First email: June 30, 2017, 9:13 PM

Dear Prof. Dr. David Tong:

What a lovely thing to do on Friday evening — I listened to your Faraday lecture* about magnetic fields. Excellent. It has taken awhile to appreciate the deep mysteries of our electromagnetic fields. Perhaps Planck’s 1899 insights that opened the way to his Planck base units of Time, Length, Mass and Charge might open some interesting, even deeper explanations.

It has taken awhile for Planck’s work to be appreciated. Even Planck ignored his base units. Frank Wilczek seemed to open the door and turned on the lights in 2001 with his Physics Today three-part article, Scaling Mt. Planck. It took the naivete of a high school geometry class to drill down inside the tetrahedron and octahedron the 45 steps to the CERN-scale and 67-additional steps to the Planck scale. Multiplying by 2 was easy. In just 90 steps we were in the range of the Observable Universe and the Age of the Universe! The infinitesimal scale went from Planck’s numbers to the 67th doubling. The human scale went from Notation-67 to Notation-134. And, the large-scale went from from Notation-135 to 202.

That’s all there is: 202 doublings, notations, steps, layers, groups, clusters sets… from the Planck Time to the current Age of the Universe, right now, this second.

Perhaps science visualizes the waves, fluids, bundles and fields a little too quark-like. Perhaps if we were to start at the Planck units and follow that simple multiplication by 2, each doubling being the power of 2, we are given 67 new layers to explore! Wouldn’t that be novel? …even fun? The CERN-scale is just so gross.

What might we do with all that math? If we start simple, and we also start with a few scaling vertices, perhaps we can build all the mathematics and geometries and spin that we need… Fields Within Fields Within Fields.

Here’s all our sweet, little math:
Horizontally scrolled: https://81018.com/chart/
Vertically-scrolled: https://81018.com/chart4/

Novel. Fanciful. But, is it useful?

To date, it is a simple STEM tool with many open questions. Obviously it is not a big bang but a quiet expansion and rather natural inflation that is  entirely predictive as it defines the cosmological epochs. Thanks.

Most sincerely,

* Quantum Fields: The Real Building Blocks of the Universe, The Royal Institution (London)

The world wide web obviously connects the world. Another 81 levels, each an ever-finer grid, interconnect literally everything, everywhere for all time.

Prior Post|Claims|Endnotes-Footnotes|References|Emails|Tweets|Zzzzs

This Universe Is Planck-Scale Refined
What You Think Actually Makes A Difference

In 2011 our high school geometry class backed into a radically different model of the universe. We used base-2 notation to go from Planck Time to this day, the Now, all in just 202 doublings. We’ve been nine years working to grasp what it means. We’ve been searching for concepts that could support a highly-integrated, mathematical model of the universe.

A summary of our “progress” (or lack of it) year by year and to date:
Our first-ever chart of the universe is 202 base-2 notations, a mathematical grid…
______By definition, this matrix includes everything, everywhere, for all time.
2012: 64 notations are smaller than particles. We explore dimensionless physical constants.
2013: All without that bang. Circles-spheres to straight lines, triangles, tetrahedrons and more…
2014: Planck Time to this very second, a Zeno-like progression of  tetrahedrons-octahedrons
2015: Mathematical chart of all five Planck units. Newton is challenged. Janus-faced space-time.
2016: Horizontally-scrolled chart. Infinitely-hot challenged with just a picosecond’s difference.
2017: Natural thrust. Natural inflation. It is 100% predictive and logical, but redefines time.
2018: Dark matter and dark energy, Homogeneity & isotropy. All notations are always active.
2019: Pi’s never-ending, never-repeating defines the infinite. There are domains for perfection.

2020: Pi defines ContinuitySymmetryHarmony, and these three define pi (circles and spheres). Here the relations become primarily real, not subjects and objects. These three are also the heart of the first principles of logic, mathematics, and science. Always highlighted at the top of each homepage, these three concepts also define the value chain, even a moment of perfection. The three define a face of the finite, the quantitative, and a face of the infinite, the qualitative. We’re closer to understanding something very different about the finite and the infinite.1

Results. Within our base-2, mathematical model of the universe these three most basic facets of reality define everything, everywhere for all time. Continuity-Symmetry-Harmony has no size restriction. From the Planck scale to the universe scale, cubic-close packing of equal spheres (ccp) is our first application for constructions. Kepler used it in 1611 to stack cannonballs on ships; today it’s for GPS and satellite communications, heart arrhythmia and atomic packing factors.2

On the other side of our equations, we hold onto too many mistaken concepts. Of three most-basic, historic errors, one was promoted by Aristotle, another by Newton, and the third by Hawking. These three have seriously limited our imaginations and clouded our vision. Although introduced within an earlier homepage, these big three need constant study:
Aristotle misled us about a key geometry that stymied science and our creativity for over 1800 years. He missed a basic gap that opens the way to quantum fluctuations.
Newton was sure that absolute space and time were the most fundamental facets of reality. The world.unwittingly followed; and his concepts became our commonsense. He rejected a more relational view and truncated the thinking of the world’s people and her emergent sciences.
Stephen Hawking, the symbolic leader of big bang cosmology, gave no ground to any competitive theory all while his big bang encouraged solipsism and gave us an excuse for our narcissism and nihilism, especially for the dystopians among us.

Result. Those three errors have placed an integrated view of our universe just beyond our reach. The three have also made us all feel rather inconsequential and our little world increasingly insensitive, abrasive and abusive. Everyone everywhere is on edge. Especially when we consider the processes of getting and holding onto power, even within a democratic state, from the left to the right, it has become altogether very nasty business.

Change is possible. There are much more inclusive perspectives of who we are. We can see ourselves within an intimate relation with the universe, within this world and with each other. What you think, say and do affects the quality of life throughout the universe.

For us, the most simple start to a basic change of our understanding has been this base-2 chart. Envision the Planck Scale, the smallest scale, necessarily the beginning of the universe, and it goes to the largest scale, the size of the universe as it is today, right now. In 2011 high school geometry classes backed into this model of just 202 steps. It has taken all this time to begin to understand it and to recognize its place and importance for our life together.

We have not been shy to invite people to study it and help us to understand it.


Twitter: A tweet went out to leaders of the Left and the Right within the USA:
@georgesoros @OpenSociety @Thomas1774Paine @maddow @Heritage @realDonaldTrump

“How can we all be so far off?”
Answer: Our worldviews are too limited. We’re missing the universe.

The universe can anchor us. It’ll give each of us perspective. See: http://81018.com https://81018.com/chart It’s just a start.


We are moved to ask:
• What if the universe starts with the Planck base units, what might be the first “thing” created?
• What if the first thing created is a sphere defined by those Planck base units?
• What if there is an endless stream of spheres and the first functional activity is sphere stacking?
• What if sphere stacking opens cubic close packing of equal spheres and tetrahedrons and octahedrons are generated? Does Plato follow?
• What if the concept of infinity has been so tainted by philosophies, we miss its most simple definition — continuity creating order, symmetry creating relations, and harmony creating dynamics; and then we’d add, “Any personal and confessional definitions are not necessary here.”

And so we finally ask, “Is there a glimmer of truth to our simple what if questions? If so, does that glimmer change our approach to our most basic equations?”

Emails. There have also been many emails that review our struggles to understand something so simple. I write, “I hope you can help us grasp the scope of our model of the universe; it came out of a high school back in December 2011. Here are a few of our key documents:
Our history, https://81018.com/home/
Our first chart, https://81018.com/big-board/
Our current chart, https://81018.com/chart/
Our STEM perspective, https://81018.com/stem/
Our current homepage, https://81018.com (this page for now)

We had to stop using this model in our high school curriculum; we didn’t want to taint the students going to college with a model that had not yet been vetted. Of course, this model has a special logic, it’s simple, it has a natural inflation, and most importantly, it readily supports homogeneity and isotropy. Yet, it still needs to be vetted by scholars.

It still needs much deeper explorations, so we welcome your thoughts.

Here, space, time, finite and infinite are all actively redefined. Leading scholars from around the world have been earnestly calling for it since the turn of this century-and-millennium.

This view of the universe starts cold. It models Lemaître’s earlier 1927 theory. It starts with the Planck base units whereby the universe is fundamentally exponential. And, it is a model that has not yet been evaluated by the scholarly and scientific communities.

It’s time. Thumbs up or thumbs down? Can you help?


Endnotes and Footnotes

[1] The Finite-Infinite Relation. One of the most divisive issues throughout all the cultures of our world, we grasp three facets of pi: continuity-symmetry-harmony. From one perspective, these three are the best description of the qualitative and the infinite. From another perspective these three are the best description of the quantitative and the finite.

We say, “Continuity begets order begets numbers which beget time.”
Then,Symmetry begets relations which beget geometries which beget space.”
And then, Harmony begets dynamics which begets systems which begets space-time.”

That is a summary for logic, math and science. All other declarations about the infinite are considered personal statements, nothing more.


[2] GPS and satellite communications to heart arrhythmia to atomic packing. In 2015 Cornell mathematics professor, Steven Strogatz, opened up our understanding of pi. Obviously, something profound is going on inside every sphere. A strong spherical magnet is a better analogy than a soccer ball filled with air. Simple Pi became “Most-dynamic Pi.” Its manifestations of the Fourier transform appear to work within everything, even something as personal as arrhythmia and as fundamental as atomic packing factors.

The Dynamics of Pi. These five dynamic images open the door to begin to grasp the internal and external activity of pi and the nature of the very dynamics of all that is. Each image opens a page of explanations.

Sphere to tetrahedron-octahedron couplet File:Circle cos sin.gif

 Poincaré,   Poincaré polarization B, Poincare sphere Please note: Our speculative projection is that these five dynamics also describe the expansion of the universe. It is not closed, but it looks closed. It’s not flat, but could be described as flat.


References & Resources 



We have problems understanding each other and our universe. Arrogance slows us all down. We all can do better. This page URL is:  https://81018.com/world/ The past ten homepages are also very closely related. Use the Left Yellow Arrow at the top to scroll back or choose from the listings on this page.

Reference links: There are ten scholars cited just above under References and Resources. Each will be linked to their own page on this site. Also, see David Tong of the Cambridge DAMTP and Hermann Nicolai of Max-Planck-Institut für Gravitationsphysik



22 September 2020: I just sent a tweet to a rather insensitive soul who has 2.8 million followers on Twitter today. I had never heard of him and I don’t recommend his vulgar work to anybody. His crudeness debases the human family. This is what I said to @DaBabyDaBaby: “Someday you’ll die like the rest of us; and, what will people say? What’s your legacy? Did you help us see the world in a new way? How about the universe? When you see yourself as part of the universe maybe you’ll start to understand.” http://81018.com

“Everything you do and say makes a difference.”

24 September 2020: Jenna @JennaBExplorer  @zoplaplace: What do we know? If space-and-time are derivative and quantized at the Planck scale and base-2 and cubic close packing of equal spheres are the most basic dynamic, we are all like your “dead” and “stupid” comments because we’ve blissfully ignored the rest of the universe.

28 September 2020: Magdalena Skipper, Editor-in-chief, Nature, @Magdalena Skipper:  I just started following you… surprised to see just 15.1K who do. “Nature” (an historic, highly-influential, scientific magazine) is so very important. In Jan. 2013 Geoff Brumfiel wrote “Shrunken Proton…” of 2010 research. It needs a sequel! “Point particles” are not small; the Planck scale has so much more to teach us: https://81018.com

28 September 2020: @gbrumfiel @Magda_Skipper Jan. 2013 your “Shrunken Proton…” (2010 research) needs a sequel! “Point particles” are not small. If the Planck scale is the start, there are 67 base-2 notations to your proton: https://81018.com



This section is for my Afterthoughts. As a start, the purpose of this section is to open the website up for deeper study. Click on the top yellow arrow on the left, and flip through each home page right through this summer (and all the way back into 2016). Each top level posting or homepage is an attempt to show if the universe starts cold. Within our little mathematical model, in less than a minute, it is hot enough to pick up on the big bang theory’s so-called epochs. In effect, the big bang is only wrong about its understanding of about a picosecond! Just look at this comparison and how the numbers quickly fall in line with each other.


Key Dates for this document, World

This article was initiated on Tuesday, September 22, 2020
World became a homepage on Thursday, September 24, 2020.
Last update: Saturday, October 17, 2020
The Prior Homepage: https://81018.com/continuity/
The URL for this page: https://81018.com/world/
The initial tagline: Changing the course of our history from war and enslaving people to…
• This World Can Become A Nicer Place
• The reason we all have so many problems among nations and as a people:
• We Do Not Yet Grasp The Deeper Interconnections Within Our Universe.  
The universe is everything, everywhere, for all time. And, what you think, say, or do affects it all.

A Note from the Editor: This image floats around the web and has been used in many instances to describe quarks and/or “the smallest things within the physical universe.” To check on it, I used Google’s image search. In our model of 202 notations, this image might be applicable in the range from Notation 55 to Notation 65. Also, in 2018 it was this top level post. – BEC

The PDF for this document is World-October-2020.


Countdown: Minutes, Seconds, Nanoseconds, Picoseconds… Plancksecond!

Prior Post|Claims|Endnotes-Footnotes|References|Emails|Tweets|Zzzzs

Another Foundation for Our Little Universe
One Plancksphere per Plancksecond *

All generated through continuity-symmetry-harmony

by Bruce E. Camber

In 1899 Max Planck calculated the actual numbers for Planck Length & Planck Time. Take those values as given, then divide Planck Length by Planck Time. The result is 299,792,437.99 meters/second. That is 21 meters/second less than the 2019 SI number or ISO number (299,792,458 m⋅s) for the speed of light in a vacuum.1

Light is never naturally in a vacuum. Calculated for each of our 202 base-2 notations (line 10) that encapsulate our universe from the Planck Time to the current time, that speed is a variable, yet the difference per second amounts to little more than rounding errors.

Max Planck knew he was onto something significant, but he couldn’t more fully grasp it. One can imagine that he had hoped that the young Einstein could help. Surely Einstein opened new doors to explore, but big ideas and concepts incubate slowly. To date, it appears that neither Planck nor Einstein ever made that simple calculation: “Planck Length divided by Planck Time is equal to the speed of light.” It appears that nobody did until sometime around 2014.

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

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


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

The four formulas for the Planck base-units

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

When the Planck base units are re-envisioned to create a base-2 chart from the smallest to the largest measurements of space and time, it becomes evident (1) neither space-or-time are absolute, (2) time-and-space are Janus-faced, correlated with the Janus-face of mass and energy, and (3) all the notations are, even today, generating one Plancksphere per Plancksecond.

There are around 65 notations (doublings) before waves, particles, and fluctuations. Sixty-five successive doublings of the Planck Length and Planck Time are enough space and time to do a lot of mathematics-and-geometry, but key leaders within the academic-intellectual community think it’s too small for much of anything.

Older, Slower Studies 3

The First Three Minutes.3 In this 1976 book Steven Weinberg3 begins his study of the universe at about 1/100 of a second after the big bang. That is Notation-138 within our horizontally-scrolled chart of 202 notations from Planck Time (the first infinitesimal moment) to this very day. And, yes, there are just 202 simple doublings.

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

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


Planck-Time Transformations
5.391 16(13)×10-44 seconds

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

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

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

Planck Time. Yes, it is a rather different scale but, it may not be as strange as most scholars seem to think today. As a result of our studies of this model since December 2011… though still fuzzy, some clarity is becoming apparent.


Pi’s Continuity-Symmetry-Harmony

Learning a bit more about pi, going over it one more time — even attempting to go inside it — finally my old 1972 definition of a moment of perfection seemed relevant.6 Part of the definition of pi is continuity, symmetry and harmony. There is the continuity of the numbers, the perfect symmetry of the circles and spheres, and special internal and external dynamics introduced to us through the Fourier transform.

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

Where do these concepts reside? Could these three be the container for everything, everywhere, for all time?


Finite & Infinite

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

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

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

We’ve all been taught that the infinite is some abstract superlative that is not part of our immediate reality. Here, quite the opposite, it appears that the infinite is not just an intimate part of our experience, it is the experience of the experience that can not be defined by space and time. It is defined by ratios and relations. And, the infinite is experienced as some expression of continuity, symmetry and harmony. That’s a perfection and it appeared to extend into the finite. Yet, recognizing the transitioning from spheres to tetrahedrons and octahedrons, somewhere along that progression of notational doublings, the most simple tetrahedral gap would be opportunistically tested. My suspicion is that gap became part of fabric of the universe possibly as late as the first three seconds up within Notation-143, Notation-144 and Notation-145 and then it began working its way back to earlier notations, 48 to 64.

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

The age-old questions about good and evil: Might we say that all qualities that do not reflect continuity, symmetry and harmony (but do reflect discontinuity, asymmetry, and disharmony) are perspectival and are actively impressed within the very fabric of this dynamic universe?


From The Nanosecond to the Plancksecond (Planck Time)
(10-9 seconds, the nanosecond is just one billionth of a second)

The Nanoseconds. Within our mathematically-defined chart of the universe, Notation-114 is 1.1197×10-9 seconds, Notation-115 is 2.2395×10-9 seconds, Notation-116 is 4.479×10-9 seconds, and Notation-117 is 8.958×10-9 seconds.

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

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

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

The accuracy of time determination. The greatest accuracy achieved to date, the zeptosecond, was done in 2016 by a collaboration of three groups: Max Planck Institute of Quantum Optics (MPQ) in Garching, Technical University of Munich (TUM) and Ludwig Maximilian University (LMU) of Munich. Here the timescale of photoionization was captured. It is history’s first to make such an extraordinarily short determination of a unit of time. This follows their earlier work to establish the attosecond under the MPQ leadership of Ferenc Krausz and Vladislav Yakovlev.

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

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

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

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


Stretching Credulity Even Further

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

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

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

Prime numbers. Proposed in sentences and brief paragraphs in earlier postings is the role of the prime numbers. There are 45 prime notations within the 202 notations that currently encapsulate the universe. There are just nineteen primes within the first 67 notations. The postulation is that each prime supports a new mathematical system that initiates even more diversity and complexity. Every logical mathematical expression gives us clues about our universe and we need to pay attention to all of them.

The Hubble Constant. I have been reviewing the work of one of our leading astrophysicists, Wendy L. Freedman. She is a Professor of Astronomy and Astrophysics at the University of Chicago and I just learned of a longstanding enigma that has led to two values for the Hubble Constant. The editors at PSW Science ask, Is There a Crisis in Cosmology? A New Debate Over the Value of H0. For a November 6, 2020 Zoom webinar with Prof. Dr. Wendy Freedman, they comment, “If the tension is real, it may signal a new physics beyond the standard model.” 

The Hubble constant is the cosmological parameter that sets the absolute scale, size and age of the universe; it is one of the most direct ways we have of quantifying how the universe evolves.” – Wendy Freedman (video), Introduction (PDF), ArXiv, July 2019

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

Of course, our suspicion is, “Yes, of course.”

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



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

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

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

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


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

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



Back editing today… especially those footnotes. October 22, 2020

This posting is being updated today and throughout this week.


Endnotes and Footnotes

*10,000,000,000,000,000,000,000,000,000,000,000,000,000,000± Planckspheres per second
Here is the current expansion of our universe. Already an impossibly large number to grasp, if multiplied by the total seconds of the universe, it would give us an approximate total number of Planckspheres within the universe which constitute the physical foundations of the universe. It is a rather novel concept! It is such a different vision of the old concept of the aether (we’ll need to revisit Michelson-Morley) and Wilczek’s matrix or grid, perhaps we should add it to our list of claims or novel concepts. -BEC

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

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

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

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


[2] Out-of-the-box thinkers regarding the meaning and value of the Planck base units.
[2a] C. Alden Mead (UMinn) In 1959 he began his struggle to publish his work about the Planck Length. Though finally published in 1964, the article, Possible Connection Between Gravitation and Fundamental Length Phys. Rev. 135, B849 (10 August 1964), was ignored by the scholarly community. Planck Length commanded no respect as a fundamental unit of length.
[2b] John Barrow (1982): With a depth and range of scholarship, and a sensitivity to young students, my first letter to John Barrow in 2013 was an earnest request for help, “What do we do with these numbers?” It was followed by many more letters and I have often wondered what he thoughts about this rather naive attempt to shoehorn everything-everywhere-for all time into 202 notations. Barrow died on September 26, 2020.
[2c] Thanu Padmanabhan: His 1985 article — Physical significance of planck length (PDF) — captured my attention. His nonperturbative approach produced a quantum cosmological model free from singularities and the horizon problem. I was very surprised and gratified to see that his article was published so early in his career. He was just 28 years old (born March 10, 1957). Yet, with guidance from India’s renown astrophysicist, Jayant Vishnu Narlikar, he has been a most prodigious scholar.
[2d] Frank Wilczek (2001) became a Nobel Laureate in 2004, yet he continued his wide-eye, open and enthusiastic approach to the unknowns within life. He was one of the first of those within his caliber who encouraged our explorations. His three articles about Planck units truly opened the door for the rest of us.


[3] Three Minutes to Three Seconds. The general population and many of our best scholars hold the positions spelled out in 1976 within the book, The First Three Minutes, by Steven Weinberg. A Nobel laureate and one of our most cited scholars, Weinberg still missed over two-thirds of the most fundamental structures of the universe. In June 2020, twenty-seven leading scholars from around the world argue most convincingly about the early structures of the universe. As a tribute to Weinberg, their article was titled, The First Three Seconds: A Review of Possible Expansion Histories of the Early Universe, (June 2020). Forty-four years after Weinberg’s popular work, they admit that there is still an abundance of mystery within the first three seconds. More

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


[4] Brandon Brown wrote the book, Planck: Driven by Vision, Broken by War, OUP, 2015. Prof. Dr. Brandon Brown of the University of San Francisco has become a foremost Max Planck scholar. These comments came from his 2015 book published by Oxford University Press. Here was one of the most formative personal relations in history that continues to influence our sciences. Though it appears that Planck was unable to break out of Newton’s commonsense worldview, Einstein made some progress. Yet, he was wrapped up in his own vision. With the help of Max Planck Institutes and people like Brandon Brown, a dialogue about the Planck numbers may yet be uncovered. To date, there is no record of it.


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

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


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

Editor’s note: Every day, this work is re-read and edited. The Footnotes and every section that follows are the focus of today’s work (Wednesday, October 21, 2020 at 5:03 PM USA-CST).

[7] Today’s Experimental and Observational Environments.

Experimental result cannot be explained by the Standard Model (SM): Non-zero masses for the neutrinos (elementary particles traveling close to light speed, electrically neutral, and weakly interacting. The SM assumes that they are massless. Therefore, particle physics now explores a new physics beyond the SM.

The Standard Model is not a complete description of Nature: it does not account for dark matter, dark energy, gravity, or neutrino masses and mixings. There are also remain many features of the Standard Model itself which are not understood, and which may find their answers in speculative ideas beyond the Standard Model such as supersymmetry, large extra dimensions, and/or extended Higgs sectors.

Conspiracy of BSM physics and cosmology, Maxim Yu. Khlopov. Nov 2019:   The only experimentally proven evidence for new physics is the effect of neutrino oscillations, but the physical nature of neutrino mass is still unknown. “… the conspiracy of Beyond the Standard model (BSM) Cosmology [1] is puzzling taking into account the plethora of nontrivial cosmological consequences of BSM particle models. ” page 7  Yakov (YaB) Zeldovich:  ”…though the probability for existence of these phenomena seems low, the expectation value of their discovery can be hardly overestimated”.


[8] Crisis in the Foundation of Mathematics

8. The Crisis in the Foundations of Mathematics, José Ferreirós, Universidad de Sevilla 2008, 2011 https://personal.us.es/josef/pcmCrisis.pdf



1. Wendy Freedman, Professor of Astronomy & Astrophysics, Univ. Chicago
1a. November 2020: Is There a Crisis in Cosmology? A New Debate Over the Value of H0
1b. Measuring and Understanding the Universe, https://arxiv.org/abs/astro-ph/0308418

2. April 11, 2019, Marclay’s Clock: 24-hour installation highlights a modern obsession with time, Jean-Michel Johnston, University of Oxford

3. In 1925, the great mathematician, David Hilbert wrote, “We have already seen that the infinite is nowhere to be found in reality, no matter what experiences, observations, and knowledge are appealed to.” Even today, many scholars would agree, but perhaps Hilbert and those scholars are mistaken.


Also see: Not all mathematical advances relating to π were aimed at increasing the accuracy of approximations. When Euler solved the Basel problem in 1735, finding the exact value of the sum of the reciprocal squares, he established a connection between π and the prime numbers that later contributed to the development and study of the Riemann zeta function:
1. https://en.wikipedia.org/wiki/Pi#Complex_numbers_and_Euler’s_identity
2. https://en.wikipedia.org/wiki/Pi#Number_theory_and_Riemann_zeta_function


Emails (just a few)

TO: Marios ChristodoulouAndrea Di BiagioPierre Martin-Dussaud
RE: An experiment to test the discreteness of time
Did you know that there are 202 base-2 notations
from the Planck base units to the current day and size of the universe?
To follow the numbers: https://81018.com/chart/
History: https://81018.com/home/  (We’re just a bunch of high school people fooling around with a tetrahedron and the octahedron and tetrahedrons within it, and so on down.)
112 steps to the Planck Lengthhttps://81018.com/tot/
Current explanation: https://81018.com/world/

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

3. Andreas Battehberg, Entering the field of zeptosecond measurement, Nov-2016


Tweets (just a few)

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

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


Zzzzs (afterthoughts)

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

Register your comments


Key Dates for this document, The-Three

This article was initiated on Tuesday, September 21, 2020
The-Three was first posted for collaborations on October 3, 2020.
The-Three become the top post (homepage) on October 16, 2020.
Last update: Thursday, October 22, 2020
The Prior Homepage: https://81018.com/world/
The URL for this page: https://81018.com/the-three/
The initial tagline:  “Countdown: Three Minutes, Three Seconds, Three Nanoseconds…”
Initial image byline: “Time, tortured, pulled away from its space and their family, mass-and-energy, and light.”
Image tagline: Fibonacci Time is linear and limited with linear space, linear mass-and-energy, and light

Image by Mikhail Leonov. April 11, 2019, Marclay’s Clock and what might be called, “Fibonacci Time.”

Overduin, James

James Overduin

Towson University, 8000 York Road, Towson, MD 21252

Articles: What If There Were No Gravity? – Scientific American
ArXiv: Waves and causality in higher dimensions with Paul S. Wesson .
——Scaling Relations for the Cosmological “Constant” in Five-Dimensional Relativity, 2014.
——Finite cosmology and a CMB cold spot, 2006
Book(s): Principles of Space-Time-Matter: Cosmology, Particles and Waves in Five Dimensions with Paul Wesson
Google Scholar
Homepages (Towson)
YouTube: Why do we need a single theory of physics?

First email: 18 September 2020

Dear Prof. Dr. James Overduin:

Your significant work with Paul Wesson has come to my attention. I must say, “Congratulations.” You did so much work together I had to create a reference page just to keep things straight: https://81018.com/2020/09/17/overduin/

Now I am hoping that you can help interpret your colleague’s quote within a Wikipedia article about the Planck units. Though I am not a scholar, I do ask questions about the presuppositions that we all bring to bear on any conceptual frame of reference. I have four:
1) What is the assumed understanding of the nature of time? …of space?
2) What, if anything, is assumed about the finite-infinite relation?
3) How is light defined?
4) How are quantum fluctuations defined?

Of course, these questions are never easy to answer and finding even a semblance of an answer is often difficult.

With all your work, I am confident there is clarity within all four areas and that information will help me to understand Paul Wesson’s comments about the proper handling of the Planck units.

This particular track of my work began back in 2011 in our high school geometry classes where we were examining how tetrahedrons and octahedrons can readily tile and tessellate going within smaller-and-smaller and going out larger-and-larger. We got carried away using base-2 notation. We also got carried away with Euler and Zeno and Planck… and, yes, also with pi, spheres, sphere stacking and cubic close packing of equal spheres.

We mapped the universe! Now it is time to reel it in and get real.

I need another week or so with all your writings so I can frame my questions most carefully in light of your joint work with Paul Wesson. Would you object to another email sometime soon? Thank you.

Most sincerely,


PS. I’m working to tighten up (at least a little) this article: https://81018.com/continuity/BEC

RE: 9-12 Geometry class STEM tool puzzles us.

National Council of Teachers of Mathematics

NCTM is the world’s largest mathematics education organization
1906 Association Drive, Reston, Virginia 20191

First email: September 10, 2020, 6:02 PM 

RE: Mathematically mapping the universe
Yet, even our best 6th graders appreciated this STEM tool!

Hi –

Homegrown STEM tools can be inspirational and ours was no exception.  In our geometry classes we divided the edges of a tetrahedron in half and discovered the four smaller tetrahedrons in each corner and an octahedron in the middle. We then divided the edges of that octahedron in half and found the smaller octahedrons in the six corners and eight tetrahedrons, one in each face. Thinking a bit like Zeno, we continued the process of dividing by 2. In 45 steps (on paper only), we were in the area of the CERN-scale of particles and waves and in 67 more steps going within, we were within the Planck scale. We then used the Planck Length and Planck Time, multiplied by 2, and in 112 steps we were back out to the classroom’s original objects but we were at a fraction of a fraction of a second. In just another 90 steps or doublings, we were out to the Age of the Universe and the Observable Universe.

Just 202 doublings. We wondered about our simple logic. Did we just mathematically include everything, everywhere for all time?

It was much more granular than Kees Boekes 1957 work using base-10 to chart the universe in 40 jumps. Ours was based on Planck base units and it had a de facto geometry.

We dubbed our model “the perfect STEM tool.” Even our AP sixth grade science class understood it! But, when we sent our little STEM project to Scientific American, they ignored us. Even Wikipedia rejected our summary as “original research.” The AAAS and Nature magazines rejected us without comment. We’ve written to a diversity of scholars and even they are reluctant to comment.

So, we’re going back over our logic and math, asking, “What are we doing wrong?

Perhaps there is someone out there who could help us?

Thank you.

Most sincerely,

PS. This could be signed by the head of our math department, plus one of our best students, plus our physics teacher. -BEC

Long-term goals and short-term actions

Prior Post|Claims|Endnotes-Footnotes|References|Emails|Tweets|Afterthoughts

Our Highly-Integrated Universe View

by Bruce E. Camber

The Story. On December 19, 2011 our New Orleans high school math classes were introduced to the Big Board – little universe. Considered a new STEM tool, our simple goal was to share our chart to get some critical feedback. When this project started, it was a simple geometric progression that went from our desktop down inside to the Planck Length and then out to the Observable Universe (all by using base-2 notation, i.e. dividing or multiplying by 2). It took 202.34 progressive doublings from one end to the other. A simple logic tells us that it necessarily includes everything from everywhere throughout all time.

To populate the chart with examples is an ongoing challenge that still requires the help of scholars and experts. In the years of analysis that have followed, larger goals of the project (and this website) became increasingly clear. The first four listed became our focus. Then there is a listing of all eight goals, within the order of their emergence. Along this path, it became evident that there are concepts that might help our scholars either affirm or debunk this process.1 That help would be a welcomed relief.

If these concepts are all misleading silliness,2 let’s put them all in a box with big bold warning labels and an explanation!

To trigger such an analysis, we’ve emerged with four primary goals positioned as questions.

Four primary questions

Sphere to tetrahedron-octahedron couplet
Sphere-stacking &
cubic-close packing

1. Shall we unplug the big bang theory?
It’s on life support. We can replace the strained logic of “infinitely hot, infinitely dense” with a natural inflation. If Neil Turok’s “perpetual starts” concept is the first notation where infinitesimal spheres manifest, these 202.34 mathematically-integrated doublings begin with the logic of pi and a simplicity that further defines light, space-time and mass-charge, and infinity. We start with the Planck base units and go to this very moment of time. Homepage  More  Chart

2. Can we redefine space and time?
Going back to Isaac Newton, we reconsider his treatment of space and time as absolutes. Defined here as discrete, finite, and quantized, there are many references. His debate with Leibniz through his associate, Samuel Clarke, is revisited time and again. Because it is the world’s de facto commonsense view, there has to be much more pointed analysis of Newtons work. Also, there are analyses in light of infinity defined by continuity, symmetry and harmony, natural inflation, and consistent scholarly requests  to redefine both!

3. Can we develop a science of the infinitesimal?
The first 67 doublings (out of the 202.34) have never been formally recognized as such by the academic community. Always taken as a whole, it has been thought to be too small for much of anything except perhaps for strings. Notwithstanding, if each doubling is considered an area for mathematics and geometries, those first 67 steps could become a new frontier for exploration. We might even postulate a place for consciousness on this grid.  More…

4. Can we grasp an inherent ethics of the universe?
Deep within the essence of our charts, three qualities and functions within pi seem to define the Janus-face of the finite and the infinite transformation: (1) continuity that creates order and time, (2) symmetry that creates relations and space, and (3) harmony that creates dynamics, a space-time moment, and a range of perfection. Are these the foundations for ethics?  More…

Stretching for such far-reaching answers creates a fair amount of self-doubt and questioning. Our progress has been a very slow evolution. Each speculative insight is naturally based on many smaller steps.

Progression of goals: all short-term actions

1. Introduce a highly-integrated, very-simple mathematical model of the universe (where Planck Length is assumed to be the very first expression of space) and proceed by doubling Planck Length and then each result, 202.34 times to the current size of the universe. Once we had our first simple chart, we began to seek the advice and counsel of leading scholars. Here are some key dates:
December 2011: Create a chart of the universe based on mathematical and geometric sequences: https://81018.com/big-board/
December 2011 to this day: Seek the insights of scholars, friends, and others. Emails were sent to some of the world’s finest living scholars and to people who command the attention of large groups of people: https://81018.com/alphabetical/
January 2012: Write up a description of the discovery process for publication whereby everything, everywhere, for all time is encapsulated. First draft: https://81018.com/first/
March 2012: Write up a description for Wikipedia. First draft of this article: March 2012 Published on Wikipedia: April 2, 2012 Taken down: May 2, 2012 URL
September 2012: Write up an article for publication whereby everything, everywhere, for all time is encapsulated. The first draft of this article: https://81018.com/planck-length-time/

2. Ask questions about the infinitely-hot and infinitely-dense Big Bang Theory using these four Planck base units, Planck Length-and-Planck Time, and Planck Mass-and-Planck Charge of the Big Board-little universe project with its 202+ steps thereby charting the universe with a natural inflation.
September 2014: With a bit of reluctance, we raised our first questions about the big bang theory: https://81018.com/2014/09/10/quietexpansion/
April 2016: Develop a chart using the Planck base units, Planck Length-and-Planck Time, and Planck Mass-and-Planck Charge, from the first moment of time to the current day. The first draft of this article: https://81018.com/chart/ This chart just might become a series of books and a banner for classrooms. An extended article in June 2016: https://81018.com/2016/06/01/quiet/
August 2017: Study the logic of this sampling of groups of numbers of Planck Length-and-Planck Time, and Planck Mass-and-Planck Charge; Steps 31, 67, 101, 137, 167, and 199 were selected: https://81018.com/planck_universe/  I’ll rework it until published as a journal article.

3. Introduce and further develop the first 67 doublings from the Planck scale to the CERN-scale as a hypostatic domain for mathematics, consciousness, and the preconditions for systems, particles, waves, and quantum fluctuations.
October 2015:  The first 67 notations as key missing links: https://81018.com/smallscale/
September 2017: The introduction of the concept of a hypostatic domain – Hypostatic structure starts between the finite and infinite: https://81018.com/hypostatic/
December 2017: The concept of a transformation nexus between the finite and infinite is introduced whereby the mathematics of dimensionless constants are progressively applied throughout the 202 notations. This concept comes right out of my work from 1971 through 1980. It is just starting to be developed within the first ten notations: https://81018.com/1-202

4. Further develop our understanding of light in relation to space and time within each of the 202 doublings. Light is defined on both sides of the visible spectrum:
December 2016:  What is light?  https://81018.com/c/
December 2016: Be a light in the world.  https://81018.com/2ten/

5. Introduce and further develop a definition of the infinite that is continuity that begets order, symmetries that beget relations, and harmonies that beget dynamics2020
•  November 2014:  The first look
•  December 2014:  Second look
October 2016:  Homepage
•  February 2018:  Finite & Infinite (Homepage)

6. Recognize the emergence of ethical and qualitative judgments. Whereas the big bang theory encourages a solipsism and nihilism, this redefinition of the finite-infinite as continuity, symmetry and harmony encourage values: https://81018.com/values

7. Further develop a philosophy and psychology of the dynamics of finite space-time such that people begin to see that each step from 1-202 is active and full and each continues to define its unique flavors of space-and-time. Nothing is static and everything, everywhere for all time is inter-related. This work is on the priority list to be developed: https://81018.com/ten/

8. Further develop the mathematics within each of the 202 steps as a progressive evolution tying all mathematics and geometries to physics, chemistry and biology and to systems that define our universe, i.e. cosmology and even theology: https://81018.com/1-202


Endnotes & Footnotes

[1] Yes, we are asking our scholars to help debunk this model. First, we’ve written letters and emails and we post occasional tweets. I try not to bother our scholars too much. To that end, I keep track of those communications.

If this model is not debunked, we could begin re-using it in the classroom!

[2] Yet, these new concepts could be red flags to help our scholars debunk this model. I created a list of radical departures and idiosyncratic concepts to help them to begin to see where our assumptions, claims and presuppositions could be mistaken. After a few years of speculations, it became evident, “These are idiosyncratic concepts and are necessary to construct this model of the universe. Because the feedback from our scholars was so tentative, I thought this list of twenty-or so concepts just might help to identify red flags.



  1. Freeman Dyson was an old friend and critic of this work; he is missed. He had a special integrity. He wasn’t afraid to be wrong. He didn’t easily go along with the crowd. But like the rest of us, he did fall in love with some of his own ideas. For our scholars that is a special challenge. My wife, Hattie, is always saying, “We can’t be absurd to ourselves.” As a result it is difficult for all of us to embrace any concept that might challenge our own sacred worldviews. Today, worldviews are just too small. We all need to see ourselves in light of the universe.
  2. Sabine K. D. Hossenfelder is a special character within the physics community. She really knows the fundamentals and she is a thinker and a risk-taker. I am rather sure Freeman Dyson would affirm her bold spirit. On Twitter, she is @skdh and there she reviews a book by @JimBaggott, Quantum Reality: The Quest for the Real Meaning of Quantum Mechanics, Oxford University Press, 2020 Both of them are entirely engaging, but the first thing that I look for is their concept of space and time, then the finite-infinite relation, and then I look to see what they do with the Planck base units and their recognition of Aristotle’s 1800 year mistake. Without those four pieces of the puzzle, conclusions are necessarily limited. Now, to find people talking about all these things, I look closely at all the other links SKDH gives us: #withscience #sciencemagazine #physics #quantum



  1. Hermann Nicolai works closely with Krzysztof Antoni Meissner of Poland and together with George F.R. Ellis, they wrote a most seminal piece: The physics of infinity, Nature Physics, Volume 14, Issue 8, p.770-772, 2018. I had written to both Ellis and Meissner about it so felt perhaps Nicolai might respond with some pointed criticism of this work.
  2. Mathematically Mapping The Universe. A wide diversity of people receive our emails. Here is one to the publication, Mathematics Teacher: Learning and Teaching PK-12 of the National Council of Teachers of Mathematics (NCTM). Their web pages encourage people to submit a problem. Ours came right out of high school! We hope the gatekeeper, Dr. Allyson Hallman-Thrasher, allows it to be printed or included within their webpages.



15 September 2020: Dr. Martha @CenteredVoice #UnlockPotential Yes, how do we break free of little worldviews that entrap us within circular arguments? Might a mathematically-and-geometrically integrated view of the universe help? Perhaps I am a bit too cautious here, but I believe so. https://81018.com/ is a start. https://81018.com/solipsism/ is a result.



Wikipedia, Planck Units: Because Planck Time and Planck Length are our starting points, this entire piece within Wikipedia is being studied over and over and over again. The focus is here: “This is why Planck units or any other use of natural units should be employed with care. ” Referring to G = c = 1…” Also, see what Paul S. Wesson wrote — “Mathematically it is an acceptable trick which saves labor. Physically it represents a loss of information and can lead to confusion.”[1]

Given that Wesson’s quote above was initially posted in March 2018, we know this topic is under careful scrutiny. Our challenge to their authors would be the inherent presuppositions brought to the discussion within their concepts of space and time (in light of Newton’s absolutes), their inherent understanding of the finite-infinite correspondence, their understanding of light, and their understanding of quantum fluctuations.BEC


Key Dates for Goals-2

An article, Goals, was first initiated on Sunday, March 5, 2018.
Goals was a top post (homepage) on March 18, 2018.
Updated as Goals-2, a homepage on September 14, 2020
Last update: Thursday, September 17, 2020
The prior homepage: https://81018.com/just-a-second/
The URL for this page: https://81018.com/goals-2/
Related Page: https://81018.com/universe/
The initial tagline: Long-term goals and short-term actions