Getting to know our Universe, the seen and unseen

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An All-Natural View ___
___by Bruce E. Camber, Working first draft

We’ve underestimated Planck’s base units, infinitesimal spheres, and pi (π).
These appear to be among the penultimates of physics and mathematics.

I. Planck Base Units. Practically ignored for about 100 years, in 2001 Frank Wilczek[1] put Planck’s base units on a fast track for adoption by our scientific community, yet those Planck units remain enigmatic and are still questioned by some. In 2011 our high school geometry classes[2] peeled back some of the mystery by blazing a path of geometries and simple mathematics (dividing by 2) to Planck’s base units. We uncovered 202 doublings or notations[3] from the first possible moment of time to our current time.

We were told that it was the first base-2 chart of the universe. Logically that chart includes everything, everywhere for all time. It builds on itself. All notations are active. Space and time are redefined. Our universe is perpetually starting. And, there is no need for big bang cosmology.[4]

We were exploring the tetrahedron and octahedron[5]. Rather unwittingly we also had to learn about base-2 exponential notation[6] and along that way, we discovered the universe.[7] There are 112 steps from our classroom model down to the Planck base units, and then, just 90 steps going out to the current time. We used the generous estimate of 13.81 billion years to approximate the age and then the size of the universe. Quite naive, those simple calculations were not made thinking about theories of the origins of our universe.

“It is just simple math — doubings — dividing or multiplying by 2.”

So what does one make of all those numbers?
We turned to our scholars and experts for help.[8]

II. Infinitesimal spheres. First, we considered the Planck base units to be Notation-0 and we asked the question, “What would that look like?” Many scholars and experts say, “A singularity.”[9] But, that is difficult to imagine. In 1927, Georges Lemaître said, “A primeval atom.”[10] In 2011, our class of high school geometers said, “A primordial sphere” and today we say, “An infinitesimal sphere.”

There is nothing simple about the first sphere. The Fourier transform[11] opened the door on complexity. Steve Smale and John Milnor‘s work with attractors and repellers[12] opened it further. The deep-seated continuities-symmetries-harmonies[13] of pi, opened the qualitative and the infinite most fundamentally. Pi is ubiquitous; it is used to define the most fundamental equations that define our universe.

So, where is pi within the big bang theory?
And the answer it seems is, “It’s nowhere to be found

Scalar fields.[14] At the 67th notation, 7.95630×10-24 seconds is much too small for any possible measurement of time. The corresponding length, 2.38509×10-15 meters, is on the cusp of possible length measurements. As a result, we hypothesize that Notations 0-to-64 define scalar fields that can be used by Langlands programs, string theories, SUSY, loop quantum gravity, and all those other disciplines currently not on the grid. Every moment grows with numbers and geometries to uniquely define it as it adds notations. These are scalar fields for everything, everywhere for all time.

Expansion or inflation. We assume there is one infinitesimal sphere per unit of Planck Time and Planck Length. It’s a key assumption. Within the first second, there would be 539 tredecillion spheres.[15a] The 1874 calculations by George Johnstone Stoney render 4609 tredecillion spheres per second.[15b] Given the first second of the universe is between Notations 143-and-144 and represents over two-thirds of all notations, it became obvious that the earliest universe is the focus of this study.

In just the first day, if we were to line up all those spheres, we would be out to around the gravitational edge of our solar system. Someday that statement may become significant. Today, it is an observation. And for now, we need to be doing cubic calculations (and, that will be done).

The first year is between Notations-168 and 169. The first million years is between Notations 188-and-189. And, the first billion years is between Notations 198-and-199.

As we studied the dynamics of sphere stacking and packing going back to Kepler and Harriot, we also discovered the dynamics of close-cubic packing of equal spheres[16] whereby tetrahedra and octahedra are generated and perfectly fill space. There is a natural inflation that is homogeneous and isotropic. The earliest densities create a thrust to continue to perfectly fill space. It’s the path of least resistance.

It is smooth and it is within the realm of possibilities that it could remain smooth for 200+ million years and out to the current observations of the James Webb Space Telescope[17] (JWST). Although there are many potential gaps for fluctuations[18], we will wait for more results from the JWST and the judgments of their experts.[19]

III. Pi (π). If we accept a sphere as given, and recognize that pi is its leading dimensionless constant, we can learn about the finite-infinite relation. The discrete-numerical-quantitative is finite. And, the continuous-geometrical-qualitative is infinite. Pi (π) gives us continuity, symmetry, and harmony[20], preconditions for order, relations, and dynamics, and the essence of the finite-infinite relation[21]. The key to it all is within pi and its perfected states in space-and-time.[22] And because this model is inherently respectful of people and things, no matter the religion, philosophy or total lack thereof, we do not, at this time, feel a need to go any further with our examination of the infinite.

Perfected-states in space-time was part of my early research of the EPR paradox[23]. Given its deeper relations with the Planck base units and within pi, it can be readily integrated with everything, everywhere, for all time, now discretized with numbers and geometries. Plato and Pythagoras may celebrate. Loop Quantum Gravity and all studies not on the grid [24] may want to celebrate because time is redefined and the grid is extended and opened up substantially. Again, all notations build on each other and are always active. Time’s arrow is relegated to an infinitesimal slice of the current time within Notation-202 and, most unusually, it seems to be associated with a recompile during the sleep cycles of all sentient beings.

Our chart with its 202 base-2 notations is slowly becoming a model and our hope is that you will help us to understand it. In this world of Planck’s base units, infinitesimal spheres, and pi, it appears to use less extralogic and seems less idiosyncratic than Alan Guth’s inflation and his hypothetical inflaton.[25]

Within our emerging model of the universe, there is no need for hypotheticals. Thank you. Thank you very much. -BEC


Endnotes & Footnotes
Most of these points already have pages within this website.

[1] Wilczek. Webpages: Frank Wilczek
Physics Today, 312. Scaling Mt. Planck I: A View from the Bottom (June 2001)
Physics Today, 321. Scaling Mt. Planck II: Base Camp (Nov 2001)
• Physics Today, 328. Scaling Mt. Planck III: Is That All There Is? (August 2002).

Endnotes (BEC Comment): In Frank Wilczek’s latest work, Fundamentals: Ten Keys to Reality, I was disappointed that he used the words, “after the Big Bang.” With its current raft of problems, I had hoped that Wilczek would have been inclined to hold back from reaffirming the big bang. Even after ten years I recognize that he’s not quite ready to affirm a natural inflation with base-2 notation, the Planck base units, infinitesimal spheres, and pi, yet even after two one-on-one discussions and countless emails, I still have hopes that maybe someday he will. He must somehow believe that the Planck base units are remotely related to the bing bang singularity. If we ever meet again, I’ll ask him that question.


[2] 2011 high school geometry Webpage:

Endnotes (BEC Comments and Questions): We started with geometry and math and followed Zeno in a three-dimensional way. It seems strange that in ten years nobody has commented about that 112-step walk down to the Planck scale. It is a natural progression. The final 67 notations should fascinate every geometry student and teacher. It is a most simple math and geometry. On one hand, I ask, “Why is everybody ignoring it?” and then on the other, “What am I failing to grasp?” I acknowledge that the Planck base units have only been on the ascendancy since 2001. The Big Bang Theory had over twenty solid years of undivided attention from 1979 to 2001. In that time, any doubter was chastised into complacency and declared idiosyncratic at best.

I caution myself, “This isn’t going to be easy! Look how much investment there is each year within sciences based on after the big bang. It’s mind-numbing.”


[3] A Chart of 202 Base-2 Notations  Webpage:

Endnotes (BEC Comments) : This chart was based on earlier charts, the first being from 2011. There has been a steady progression of charts yet the focus today is on our horizontally-scrolled chart that was started in 2016. It has a long way to go before we will be happy with it. The biggest challenge is the first 64 notations where we fully expect to integrate those studies currently not on the grid (See Footnote 24 below). We also hypothesize scalar fields are defined within those first 64 notations.


[4] No Big Bang, a key idea. Webpages:

Endnotes: Scholars have been calling for a fundamental redefinition of space and time. A most credible scholar, Neil Turok, occupies the Higgs Chair at Edinburgh, says the universe acts like it is perpetually starting. It is. And, of course, it cannot be perpetually starting as a big bang. It can perpetually start as an infinitesimal sphere. The big bang will slowly be put on ice and we will slowly and more logically re-engage infinity.


[5] Tetrahedrons and Octahedrons (always have four hexagonal plates). Webpages:

Endnote: (BEC Comments): The most-simple interior parts of the tetrahedron — a tetrahedron in each corner and an octahedron in the middle — can be readily visualized, but we don’t. We do not grasp the interior parts of the most simple of Plato’s five solids. Its internal octahedron is a key element for our general education. It should be the subject of study within elementary schools. It’s not.

Even one of the world’s greatest geometers had to buy time when asked, “What objects most simply and completely fill the octahedron? Of course, John Conway knew the answer, but it wasn’t spontaneous. All of us should be able to answer that question easily by the time we are in the sixth grade. We all should know about the four hexagonal plates that crisscross through the octahedron. We all should know about the square plates as well. The octahedron and tetrahedron are the essence of stability and in this model of the universe, it is a key element of the overall architecture. Here is a fundamental oversight in our general education.


[6] Everything, everywhere, for all time. Webpage:

Endnotes: Those 202 notations start with the smallest working units of space-and-time and then expand to the largest possible units of space and time. Logically, doesn’t that include everything, everywhere for all time? If not, why not? For many of the notations, we have started a special page to begin to drill down into it. For example, at one second:


[7] Mapping the Universe: A STEM tool. Webpage:


[8] Scholars and experts. Webpage:

Endnotes: Over the years we have turned to the finest scholars we could find. Direct mail, text messages, and tweets have been sent. Believe it or not, this list (linked) is a small percentage of all the people who have contacted.


[9] Singularity Webpages: and gravitational and others

Endnotes: If all our notations are always active, this model redefines the nature of space and time. It defines a very different notion of a singularity. Our page about singularities was started in 2017; and with this reference, more attention will be given to the topic:


[10] Primeval atom of Lemaître. Webpage:ître/

Endnotes: In 1927 Lemaître made his first postulations about a primeval atom and a cold start of the universe. Initially we replied that it was a primordial sphere. Perhaps the best concept is that of an infinitesimal sphere.


[11] Fourier transform. Web page:

Endnotes: Open the door on complexity. There is nothing simple about the first sphere.


[12] Smale-Milnor. Webpages: and

Endnotes: Smale and Milnor‘s work with attractors and repellers opened the initial complexity even further.


[13] Fundamentals. Webpages:

Endnotes: The deep-seated continuity-symmetry-harmony within pi most fundamentally opened the qualitative and the infinite. Pi is everywhere. It is pivotal within the most fundamental equations that define our universe.


[14] Scalar Fields. Webpage: and theory

Endnotes: With this webpage, scalar fields are introduced. It seems natural. We will be seeking help from experts in this field. Since it is a hypothetical field, we expect the experts will also mostly be involved with the definition of dark energy and dark matter.


[15] Tredecillion. Webpage:

Endnotes: Something like the following quote has been said in many different ways by many different people, “Inflation causes growth at an exponential rate and is due to a hypothetical scalar field that has never been directly observed. Expansion is basically just the general-relativistic version of inertia and requires no new physics.”

An appeal has been made to the International Standards Organization (ISO) to open an analysis of these different results from Planck and Stoney. We will advocate that the work of John Ralston and Espen Gaarder Haug be part of that assessment, especially of our understanding of the Planck constant.

George Johnstone Stoney. At least 26-years before Max Planck, natural units were introduced by Stoney. These units are part of the great unsolved problems within physics.


[16] CCP and a natural inflation. Stacking spheres sounds relatively innocuous. It is not. It may well be the most basic building block for space and time. Wikipedia’s section on face-centered cubic (FCC), also called cubic-close packed, and hexagonal-close-packed (HCP) introduces a dynamic graphic that demonstrates how tetrahedra and octahedra are perfectly generated and perfectly fill space from stacking spheres. We brought that work down into the infinitesimal. We also recognized that this is a natural inflation that becomes the basis for homogeneity and isotropy. Here was our initial look at perfected states that define space-time. Here was our initial introduction to Aristotle’s mistaken geometry and the geometries of quantum fluctuations.


[17] James Webb Space Telescope. Webpage:


[18] Fluctuations. Webpages: Also, the prior homepage.

Endnotes: The issue of quantum fluctuations has been scratched by a few. First, I believe there are no less than two general flavors of fluctuations, physical and mental. And within those two, there all are at least six flavors each that are geometrically determined: tetrahedral, octahedral, tetrahedral-octahedral, icosahedra A, icosahedral B, and dodecahedral. This very early introduction started with this page, That these studies pick up where Aristotle failed us is important. Aristotle made a most basic error in geometry that great scholars repeated for 1800 years. Talk about setting scholarship back a few years and we still haven’t come out of it. Aristotle tainted geometry and its place within our intellectual landscape.


[19] JWST Experts. Webpage:


[20] Continuity, symmetry, and harmony Webpages:


[21] Finite-infinite. Webpage:

Endnotes: The essence of the finite-infinite relation and the beginning of an ethics.


[22] Perfected-states in space-time. Webpage:

Endnotes: There is an infinitesimal perfection within the physical world. This is a major correction to quantum theory and controversial. However, if the first notations have no fluctuations and are smooth, it does suggest a new physics and we hypothesize that it is within the first 64 notations.


[23] Einstein, Podolsky Rosen 1935. Webpage:


[24] Loop Quantum Gravity and others. Webpages: (1) (2) (3) (4) (5) (6) (7) (8) and (9) 


[25] Guth and his inflaton Webpage:


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

The Known Unknowns. Initiated in 5 February 2022.

The Resilience Project, Initiated in October and last updated on 2 November 2022

The First 64-Notations. URL:

Bounce of Nothing (PDF) (Conference Presentation PDF), Isabel García García, KITP, UC Santa Barbara, 2020, 2021

Bubble collisions in the very early universe, S. W. Hawking, I. G. Moss, and J. M. Stewart, Phys. Rev. D 26, 2681, 15 November 1982


There will be emails to many of our scholars.

• Isabel García García, KITP, UC Santa Barbara, 28 October 2022 at 11 PM 
• Andronikos Paliathanasis, Oct 28, 2022, 5:48 PM 
• Quick notes to Robert DiSalle, Espen Haug, Tomonori Totani, and Denis Weaire:
   “Your page on our site has been seeing some activity today!” 27-28 October 2022
• Richard J. Fitzgerald, Editor, Physics Today, AIP Publishing, 11:10 AM, October 26, 2022
• Frank Wilczek, MIT, 25 October 2022 at about 1:34 PM


Often using Twitter. Criticized, now also using Parler.

9:04 PM · Nov 2, 2022: @TheOnion Pictures from the James Webb Space Telescope challenge big bang cosmology. The pictures of the early universe are just too smooth! An alternative model: mathematical-geometrical doublings of Planck base units, the first moment of time to this day all in 202 notations:

November 1, 2022: Parler #1: We’ll all be moving from the old-and-tired big bang theory (with its inherent nihilism) to an integrated mathematical-and-geometric view of the universe. First, start with the base units by Max Planck. Apply base-2 notation and in just 202 all-natural doublings, we’ll go from the first moment of time to this day. It is an easy, yet unprecedented map of the universe and a special continuity-symmetry-and-harmony because it all starts with an infinitesimal sphere  and pi (π):  
• 12:11 AM · Oct 30, 2022 @tim_cook (Apple, CEO) I think Einstein was closer to the truth when he said arrogance was the bigger danger. Hawking was rough on anybody who dared to question the big bang theory. Now, the James Webb Space Telescope is! A more simple-complete theory:
• 2:29 PM · Oct 25, 2022 Sergio Mujica@ISOSecGen Secretary-General of ISO
• 4:57 PM · Oct 26, 2022 John Brockman, @brockmanincOur worldviews are too small and an integrated view of the universe seems impossible. It’s not. Start at the Planck base units. Apply base-2 and in 202 notations you have the outline: And, tells a good story.


Participate…     You are always invited.


Keys to this page, penultimates

• This page became a homepage at 10:30 PM, 25 October 2022.
• The last update was 6 November 2022.
• This page was initiated on 8 October 2022.
• The URL for this file is
• The headline for this article: An all natural view of the universe
• First byline is: Getting to know our Universe, the seen and unseen