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 abouttheories of the origins of our universe.

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

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.”

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

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

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.

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.”

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.

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.

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.

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: https://81018.com/a143/

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.

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: https://81018.com/singularity/

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.

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.

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.

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, https://81018.com/geometries/ 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.

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.

• 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

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IM Often using Twitter. Criticized, now also using Parler.

Abstract. Base-2 exponentiation symbolically begins with the Planck scale, the first possible moment in time, and in 202 doublings defines this current moment in time.^{[*]} Base-2 groups diverse studies such as exponentiation, bifurcation theory, fractal geometries, and cellular growth. It’s becoming a working model based on simple logic, geometries, and algebra, initially based on spheres, tetrahedrons, and octahedrons. It begins with natural units and is driven by pi (π). Its 202 predictive, base-2 notations totally absorb big bang cosmology.[†] This mathematically-integrated view of the Universe addresses key issues that big bang cosmology cannot. Five examples follow.

I. Smoothness. The James Webb Space Telescope images have raised anxieties that the early universe is too smooth for our working understanding of the dynamics of big bang cosmology.^{[1]} The transition from smooth to lumpy is not a problem within our 202 base-2 notations. In this model geometric gaps do not become systemic until later in the unfolding of the universe.^{[2]} The earliest notations begin perfectly smooth because it starts with the most simple geometries that tile and tessellate this universe perfectly.^{[3]}

II. Time: The first minute, first second, and first zeptosecond. The first minute of the universe is within Notations 149-150.^{[4]} The first second is between Notation 143-and-144. Zeptoseconds (1×10^{-21}) are between Notation 65-and-67. And, Notations 1-64 are opened for definition!

Eminent scholars, Sean Carroll ^{[5]} of John Hopkins and James Peebles ^{[6]} of Princeton (Nobel laureate, 2019, and a pioneer of cosmic microwave background radiation research) articulate the importance of defining the first minute of the universe. In June 2020 twenty-seven scholars wrote “The First Three Seconds: A Review of Possible Expansion Histories of the Early Universe” (arXiv:2006.16182 [astro-ph.co]). It focused on emergence, yet they were unable to define the first minutes of our universe.

III. Quantum fluctuations and quantum physics. The study of a geometry of quantum fluctuations over the years has been limited.^{[11]} A most-simple place to start is to recognize the tetrahedral gap that Aristotle did not see.^{[12]} That gap is real. And, there are others that are ignored. Add to it our octahedral gap and then the icosahedral gaps.^{[13]} Here are possibilities for fluctuations. Big bang cosmology has no simple geometry and certainly no geometry for chaos and indeterminacy. Our mathematically-integrated view of the Universe begins with the inherent geometries of doublings that perfectly tile and tessellate; plus, it has a geometry for fluctuations that is inherently indeterminant. One of our primary studies is to grasp the varieties of gaps and the probabilities for each manifestation within a given notation.

IV. A natural inflation and dark energy and dark matter. Dark matter and dark energy are below all possible thresholds of direct measurement. The indirect effects have been well-regarded since the work of Lord Kelvin (1884), Jacobus Kapteyn (1922), Jan Oort (1932) and Fritz Zwicky (1933). That mystery prevails.^{[14]} Big bang cosmology blocks the view of both the geometries of perfection and of imperfection. Initially there are no gaps as spacetime is dynamically created. Within this mathematically-integrated view of the Universe, a natural inflation starts with the most simple infinitesimal sphere, sphere stacking, and cubic-close packing of equal spheres. Tetrahedrons and octahedrons naturally and smoothly tile and tessellate the earliest universe.

If taken as a given that one infinitesimal sphere is generated per unit of length and time, the rate would range from 539-to-4609 tredecillion spheres per second.^{[15]} Of course, that range is established by Planck Time and Stoney Time.

V. Finite-infinite, quantitative-qualitative. Big bang cosmology has no finite-infinite relation and makes no distinction between the quantitative and the qualitative. It does not posit the smallest physical unit of spacetime. It makes no statements about pi (π), nor recognizes the essential faces of pi (π): continuity (ordering), symmetry (relating) and harmony (making dynamic).^{[16]} Naturally, the ubiquitous dimensionless constant that generates the natural units for Planck and Stoney is pi (π). We hypothesize that these three faces of pi (π) define the qualitative and the infinite. Within big bang cosmology the Planck Epoch and a singularity are the baseline whereas within our mathematically-integrated view of the Universe, it is the simple perfections of the infinitesimal sphere, then spheres, and then tetrahedrons and octahedrons.

[1] Smooth to lumpy. An early article, The Lumpy Universe, by a group within NASA’s Goddard Space Flight Center is written for students from 14 years old and up. The Imagine Team is an effort headed by Dr. Barbara Mattson and the segment, Imagine the Universe, addresses the current concerns within cosmology and astrophysics. It raises those issues that are pushing the scientific-academic community to re-imagine big bang cosmology.

[2] Systemic gaps and fluctuations. Too dense and too fast to accommodate fluctuations, it is hypothesized that quantum fluctuations do not initially manifest until much later than the first minute which is within Notation-144. It is also hypothesized that these gaps, once systemic, will work back into prior notations and are currently at least within Notation-67. Further, it is hypothesized that there is also a geometry of gaps for consciousness and the mind.

[3] Tile and tessellate this universe with no gaps. Throughout mathematical and geometric history, tilings and tessellations have challenged the human mind. Kepler was the first to make it a systematic study (Harmonices Mundi). The simplest 3D tessellationis with the tetrahedron and octahedron. Within this model it shapes the first instant of the universe resulting first in a sphere, then a systematic expansion of spheres (see #15 below), sphere stacking, and then what is known as close-cubic packing of equal spheres. Here is the starting point within Notation-0.

[4] Notations 1-202: This chart of 202 notations began in 2011. It became a horizontally-scrolled chart in 2016. It may take several generations to fill out even the first level of notations. It may well take many more generations to tie all the notations together in a dynamic unit. Notwithstanding, elementary school children can (and have) effectively engaged the chart to see the order within our universe.

[5] Sean Carroll. He is listed among the scholars to whom we turn for insight and help. Based on the videos we have watched and from his writings, we readily speculate that Sean is a bit like Steven Weinberg. When Weinberg got impatient with a person with whom he disagreed, he would say, “Utter nonsense.” I suspect the response from Sean Carroll would be similar. Yet, we’ll continue to write to him!

[6] James Peebles. Of course, most Nobel laureates are swamped with correspondence. There are just too many people hoping to grab their attention. James Peebles is older now and still very active looking at astronomical phenomena that are “off the beaten track.” In that light, our strategy has been to catch him by surprise in hopes that he might rethink the concepts of space-time-and-infinity with us.

[7] Max Planck. There are current challenges to Max Planck’s base units yet the results of those challenges are still being evaluated. We are following the work of John Ralston, Espen Gaarder Haug, and Tim Palmer as each impacts our thinking about the Planck constant, the Planck base units, and the dimensionless constants.

[9] Redefining Time. The most disconcerting notion to emerge from this work is to discover that in some manner of speaking all time is now. Although physicists like Carlo Rovelli, Max Tegmark, and Julian Barbour, claim time is an illusion, within the 202 notations linear time is associated with just that period of time experienced prior to sleep (when it is recompile into the whole). We say that time is exponential; time is an equation and all notations are always active.

[11] Quantum fluctuations. A search on the words, “geometry of quantum fluctuations,” renders just ten results on October 5, 2022. There has been no geometry of fluctuations based on simple geometries of gaps. Our page, geometries, is our announcement of our intention to pursue this domain of study beginning with the geometries of gaps within the most simple structures.

[12] Aristotle’s blindspot. This history serves to remind us to be somewhat reserved about our conclusions. Life is short, but our words may well live on. Aristotle’s arrogance is all of us. Aristotle’s mistake is profoundly all of us.

[13] Gaps. The initial study of the five-octahedral gap was part of the /geometries/ efforts in May 2022 when we announced our intention to pursue this domain of study. We were even able to create a model of what we believe is the first five-octahedral gap — 81018.com/2022/05/19/five/ — that then coupled with the tetrahedral gaps — 81018.com/gap/ — becomes a new object — 81018.com/15-1/ — which my wife, Hattie Bryant, named the eikosihedron. We’ll see if it works.

[15] 539-to-4609 tredecillion spheres per second. When I surveyed the initial formula in September 2021, it seemed simple and logical enough. Yet, to begin to imagine the emergence of 539 tredecillion spheres per second is simply beyond my grasp. This is the opening of a new domain of study. The range is a placeholder for more refined figures to come.

[16] Continuity-symmetry-harmony. The heart of this study began with simple geometries but backed into the infinitesimal sphere by backing into the very nature of pi (π) and finding the three faces of a perfected state in spacetime, continuity, symmetry, and harmony, all deeply inherent within pi. This is our essential story and it will be told and retold many more times to come.

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

• Reason to believe by Rod Stewart, Lyrics by Tim Hardin

If I listened long enough to you I’d find a way to believe that it’s all true Knowing that you lied straight-faced while I cried Still, I look to find a reason to believe

Someone like you makes it hard to live without Somebody else Someone like you makes it easy to give Never think about myself

If I gave you time to change my mind I’d try to leave all the past behind Knowing that you lied straight-faced while I cried Still, I look to find a reason to believe

Please note: These are all the lyrics; two paragraphs repeat. Life is fair; it breaks everyone’s heart be it with love or beliefs (ideas and concepts).

• Diego Rapoport, The Geometry of Quantum Fluctuations II (Quantum Gravity and Ergodicity), in “Proceedings of the International Workshops on the Frontiers of Mathematics, Physics and Biology”, Monteroduni, Italy, August 1995 vol. 2, G. Tsagas (ed.), Hadronic Press and Ukraine Academy of Sciences, 1996

• Two Questions: (1) Is the smoothness of the JWST’s earliest universe a cause for concern? It seems some are concerned that it cannot be supported by big bang cosmology. Sean Carroll says, “…dark energy made the universe smooth out and accelerate, but it didn’t stick around for long.” (2) Is the Guth-defined inflation cause for concern? Most of the old guard like ‘t Hooft, seem fine with the one-time exception that inflation was an expansion of space itself so extralogical assumptions apply.

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Emails This is a representative selection of our notes to scholars asking about the substance of this article.

Editor’s note: Continuity is the first principle of order. The second is symmetry whereby a relation is created. The third is harmony, where there are multiple symmetries within a dynamic moment. We need all three, but continuity will at least get us on a level playing field.

Just as an aside, it appears that the adoption cycles of a major idea require no less than three generations and quantum theory is no exception. New theories have new truths but are not absolute truth and not “all truth for all time.”

The BIPM also convenes the General Conference on Weights and Measures (CGPM). A diplomatic event, the 27th general conference is Tuesday, 15 to Friday 18 November 2022, at the Palais des Congrès de Versailles (10 rue de la Chancellerie, 78000 Versailles, Yvelines) in France.

You have to be a delegate to attend. You have to be an official representative of a member state .

We have requested through NIST and CODATA these international standards bodies name six groups of numbers between the yoctosecond and the Planck scale. This is all simple, basic math for the infinitesimal. All six groups are mathematically-defined notations and often used. The numbers start just after the already recognized (and often used) yoctosecond and go down to the smallest recognized size, the Planck Second. We are also requesting that the Planck Second be formally recognized.

Status: Although great planning is going into the 27th CGPM conference, it needs to go further. It appears from the Draft Resolutions that only two extensions will be considered beyond the already officially recognized yoctosecond (See your PDF document, “SI Concise summary”, page 3, Table 3. Those two extensions (and subs) are 10^{−27} (ronto) and 10^{−30} (quecto) (page 22).

You will miss the opportunity to officially name 10^{−33}, 10^{−36}, 10^{−39} and 10^{−42}. The 10^{−42} group includes 10^{−44} PlanckTime.

Recommendation: Whichever organization, probably CODATA, submitted this naming proposal, send it back and ask that they call emergency meetings to virtually gather and name these other four domains and resubmit before November 1.

You would not want to miss an opportunity to do a job well.

Background: The naming conventions for the infinitesimal have become exquisitely important since Frank Wilczek (Nobel, 2004) wrote a series of articles about the Planck scale for Physics Today. Very quickly, the importance of the Planck scale in theoretical physics became entirely evident to most working within these domains.

I am available to answer any questions, but must apologize that my French has not improved since 1980 when I studied with Olivier Costa de Beauregard and Jean-Pierre Vigier at the Institut Henri Poincaré. Thank you.

Warmest regards,

Bruce

PS. Here is how these are displayed within Wikipedia:

One yoctosecond = 1×10^{-24}

One xonosecond = 1×10^{-27 }(You will set a new standard with rontosecond.)

One vecosecond = 1×10^{-30 }(You will set a new standard with quectosecond.)

One mecosecond = 1×10^{-33} Increasingly used and in question.

One duecosecond = 1×10^{-36} Increasingly used and in question.

One trecosecond 1×10^{-39} Increasingly used and in question.

One tetrecosecond = 1×10^{-42 }Increasingly used and in question.

Abstract. Our evolving theory posits a most-simple start of our Universe by applying base-2 notation (multiplying by 2) to the Planck-or-Stoney base units.^{[*]} The entire universe is mapped within 202 notations that logically and mathematically encapsulate everything, everywhere for all time.^{[†]} That’s the outline. Structures are the next issue. Given the utter simplicity of the sphere and its total dependency on pi (π), hypothesized is that those base units first manifest as an infinitesimal sphere. All natural units, that sphere is projected to be the first moment of time.^{[a]} Assuming one sphere per unit of time and length, anywhere from 539-to-4605 tredecillion infinitesimal spheres per second manifest.^{[b]} Those infinitesimal spheres, an obvious candidate for dark matter-and-energy, have been filling our universe from the beginning. It creates a grid.^{[c]} A radically different scenario (to big bang cosmology), this grid outlines systems for our universe. We began in 2011 in a New Orleans high school geometry class.^{[d]} Initially considered to be a most comprehensive STEM tool, it was idiosyncratic because it didn’t start with the big bang.^{[e]} Ours is a quiet expansion. All notations are always active. Initially we started with the simple tetrahedron and octahedron until a scholar convinced us the sphere was more fundamental.^{[f]} We then learned about the history and deep dynamics of close-cubic packing of equal spheres (ccp) and its generation of tetrahedral-octahedral structures.^{[g]} It is smooth; there are no-gaps at the start of this model of the universe. There is a perfection of the three faces of the sphere, continuity-symmetry-harmony. ^{[h]}

Background: Since the 1980s the big bang theory (BBT) has been the default theory within cosmology; and whether we know it or not, it profoundly impacts us all. There’s a generation of scholars who have known nothing else. So, this effort to lift up a different theory is admittedly ambitious. We do it not to be different or competitive, but because we think our theory answers more questions while being more inclusive, more comprehensive, more kind, more liberating, more integrative, and a bit less judgmental. Also, we are not alone. There are others; highly-respected scholars have said, “The BBT is wrong.” ^{[1]}

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Our plan of action for our base-2 model is to study big bang problems and scientific paradoxes to see if our quiet expansion might address them. Big bang advocates like Sean Carroll are so sure of its veracity, he has made statements like, “…it is true that there is no point doubting the Big Bang model.” But then, he goes on to confess, “The first minute is a little bit up for grabs.”^{[2]}

The first minute is everything. In our model even the first second and zeptosecond are everything!

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The model. There are a total of 202 base-2 notations that go from the first moment of time until today. It is 100% simple mathematics. The first second (between Notations 143-and-144) involves over two-thirds of all notations. Carroll’s first minute is between Notations 148-and-149. The first year, a light year, is between Notations 168-and-169. Each notation confirms the mathematics of the speed of light; the Planck Length (or multiple of it) is the distance light travels in Planck Time (or the corresponding multiple of it).

Hotspot. Results from the James Webb Space Telescope (JWST) are pouring in. While most astrophysicists are looking for some way to participate, we’re looking for new challenges to big bang cosmology as we’ve understood it. These old galaxy records are telling us something new: GN-z11 galaxy, discovered in 2015, held the record for seven years by going back to within 400 million years “after the big bang.” That would be 13.4 billion years ago. GLASS-z13, a galaxy found in July 2022, went back to 352.3 million years after the start. That would be 13.4577 billion years ago. A bit later in July 2022 the CEERS-93316 galaxy was observed and it goes back to 235.8 million years after the start. That would be about 13.556 billion years ago.

Astrophysicist Dr. Rebecca Bowler (Manchester), reporting through the Cosmic Dawn Center of the Niels Bohr Institute at the University of Copenhagen and of the National Space Institute at the Technical University of Denmark, comments, “Already we’ve found more galaxies in the very early Universe than computer simulations predicted, so there is clearly a lot of open questions about how and when the first stars and galaxies formed.”

The logic of it all. The 202-notations build on each other. No notation is ever complete. The universe evolves together. What is happening to time? Every notation is sharing it equally. Within the first minutes, everything is okay. But in Notation-169, there is a year’s distance from Notation-1. If Notation-1 is still active and participating in making Notation-169, they share the same time and same moment. The same is true with Notation-179 at 1000 years, 189 (1,000,000 years), 199 (1,000,000,000 years). All notations are involved with the unfolding of Notation-202. Space-time becomes a very different concept. These two no longer separate us. They are dynamically involved with everything all of the time.^{[8]}

That is even a lot for me to process.

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Counting galaxies is not as straightforward as we think. In October 2016 NASA, European Space Agency (ESA), and the Royal Astronomical Society (RSA) jointly announced a tenfold increase in our galaxy count to over two trillion galaxies in today’s universe. Although some astrophysicists continue to use the old estimate of 100-to-200 billion galaxies, Dr. Chris Conselice bumped that number up to two trillion based on Hubble data.^{[9]} And now, we know with the JWST, those numbers are increasing. The JWST is exuding new questions. Along with many old questions, the big bang theory will be hard pressed to answer them.

Perhaps a little exercise will help. 13.82 billion years may seem like a long time. But, if we convert it to seconds, the results is 436,117,076,600,000,000 or 436 quadrillion seconds.^{[10]} In that time, does the big bang theory account for all the stars and planets and its smoothness? Some scholars are already saying, “No,” especially as the JWST seems to be reaching further and further back in time.

Perfectly smooth. In our simple model, from Notation-1 to about Notation-64, the universe is perfectly smooth for a reason. The geometries are perfectly filling.^{[11]} There is no “lumpiness.” There are no quantum fluctuations. The essence of homogeneity and isotropy are instantiated here. From Notation-64 to Notation-134, the essentials of our physical world manifest. From Notation-134 to Notations 194, the foundations for our Solar System and Milky Way emerge. From Notation-194 to Notation-202 large scale structure formation evolves. It is all happening in this moment of time within Notation-202. sustained and dynamically related to every other notation. We cannot add the observed galaxies together as we go back in time. We would be looking at the same galaxies as each is being shaped within that given point in time.

That statement can be tested and this theory, a quiet expansion, can be either thrown out or further studied.

_____

Notations. To date, the Hubble and the JWST only analyze data from the last seven notations: 1. Notation-202 starts at 10.9816+ billion years. There’s only been about 2.8394 billion years of churn. 2. Notation-201 starts at 5.4908+ billion years and goes 5.4908 billion years adding unique substance and structure to the universe, and continues today within Notation 202 and with all shorter notations. 3. Notation-200 starts at 2.744+ billion years and uniquely goes 2.744 billion years adding its unique substance and structures but today functions with and within all other notations. 4. Notation-199 starts at 1.3727+ billion years. It first builds on Notations 1-198 and then extends and builds Notation 200, then 201, and now 202 for about another 11 billion years. 5. Notation-198 at 686.806+ million years, is an extension of Notations 1-197, then becomes symmetrical with all those notations, and that symmetry now extends into Notation-202. 6. Notation-197 at 343.15+ million years is where GN-z11, GLASS-z13 and the CEERS-93316 galaxies were discovered. Interpreting that data correctly will be a challenge. 7. Notation-196 at 171.5+ million years and it today, right now, functions within all other notations.^{[12]}

A Prediction. Among all the pressure points on the big bang theory, I predict the pressure from the James Webb Space Telescope will become so pervasive, alternatives will be demanded. Smoothness at the start is in our favor; at some point in time, among all the alternatives, our model and theory will be critically reviewed and some of several possible alternatives will begin to grow in stature. And, as one of them does, using words like “after the Big Bang” will slowly wane, then stop being used. Living documents will be updated, and then the term will disappear except for within our historical documents.^{[13]}

We’ve contrasted our model with the big bang by calling it a “Quiet Expansion.” Because its simplicity allows for diversity and complexity, I am hopeful that the work within this website will stimulate some discussion that helps the process along to grasp how it is that we go from an infinitesimal sphere to a galaxy to our universe.

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

[*] Base Units. We start with two “natural-units gurus,” George Johnstone Stoney with his base units and Max Planck with his. The ISO and NIST may eventually come up with even better numbers. When base-2 notation is applied, these numbers are a parallel construct and by Notation-202 end up in essentially in the same moment.

[†] Another Map of the Universe. “The most detailed map ever created of the cosmic microwave background…” of the universe was done in 2009 when the Planck satellite measured the CMB (Cosmic Microwave Background radiation or CMBR). Scholars like George Efstathiou, director of the Kavli Institute for Cosmology at the University of Cambridge, believe it is “380,000 years after the big bang.” For us, time and temperature are works-in-progress; there are so many open questions. Our little map of 202 notations “mathematically encapsulates everything, everywhere for all time” so we are working to grasp the fullness of the Efstathiou 380,000 years, and his time-stamp, “after the big bang.”

In our model, all notations are always active and time is fundamentally redefined; the universe is foundationally exponential.

[a] Infinitesimal Spheres. So once there is a mathematical map of the universe, the question is raised, “What does that first moment look like?” The focus returns to the derivation of the natural units by G.S. Stoney and Max Planck. The most consistent and fundamental part of those equations is pi. So, we assume pi with its special numbers that are endless, totally-changing, and always the same. One enigmatic statement follows others. There are the perfections of sphere; its internal and external symmetries are bewildering. There are the harmonic functions of spheres. There is a deep and inherent energy of spheres. There are electromagnetic and gravitational factors. And, the list goes on. Spheres are magical. The centerpoints come alive. So, an infinitesimal sphere is projected to create the first moment of time.

[b] Tredecillion. If we assume there is one infinitesimal sphere per unit of Planck or Stoney length and Planck or Stoney Time, very large numbers result.

[d] High School. We all want our children to succeed. We all know education is a vital part of it and science-math education is a key. Yet, the big bang theory obfuscates and confuses, and the scholarship around it just doesn’t empower. We must all be grateful for all efforts by scholars to educate the public. But most important is educating the children. Since 2011 we have been pleading with scholars around the world to tell us what is wrong with our model. None have. After hundreds of emails and ten years, I have concluded there is nothing “wrong” with our model; it is just wildly idiosyncratic but we believe it is on the right path.7 That it came out of a high school also suggests that all educators on all levels need to be brought into the mainstream of research. There can be no elitism within scholarship. There is a place for simple observations like ours.

[e] STEM. It is a problem that this first article about it all has been rejected by over a dozen publications without comment. Initially I thought the errors were so egregious it just wasn’t worth their time. Yet, out of hundreds of scholars who have been asked to comment, a few would have pointed out something if they could, so we continue to follow and build upon the geometries, the numbers, and the logic.

[f] Geometry. This project started as a study of the most simple tetrahedron and octahedron. Together they fill space perfectly. Separately, they are the first step within the domain of quantum fluctuations. Our students and faculty need to know these simple geometries, how they work together and what they are capable of doing alone.

Prof. Dr. Philip Davis of Brown University finally convinced us that the sphere was more simple and fundamental. That opened a much deeper analysis of circles, spheres, and pi (π).

[g] CCP. We need a section in our geometry book: Close-cubic packing of equal spheres (ccp). Here begins the generation of tetrahedral-octahedral structures. Here geometry takes its place as a key function of our universe. It is relevant and a key critical part of who we are.

That the Chinese Communist Party shares those initials is fortuitous. There are several Chinese scholars who follow our work yet politics taints scholarship. We become overly sensitive to power struggles (politics) when the most important thing is the veracity of a concept and how it coheres with others. This work is important because it crosses political lines and looks for common ground and we find it within the sphere and pi as the hyphen between the finite-infinite and quantitative-qualitative. We know that hyphen is continuity-symmetry-harmony which is an expression of the first dynamic – the manifestation of an infinitesimal sphere, the second dynamic – sphere stacking, and the third dynamic – cubic-close packing of equal spheres.

[h] Perfections. This exploration began by going inside the tetrahedron and octahedron down to the Planck base units. We learn about geometry, mathematics (base-2), and about natural units and their formulae. We ostensibly learn a little about a continuity-symmetry-harmony that is shared by everything, everywhere throughout all time. We learn about smoothness, no gaps, and perfection and that becomes the centerpiece of this model and theory.

____

[1] Big Bang Theory is wrong. There are real experts who believe the big bang theory, as constituted by Hawking–Guth and others, is wrong. Their colleague, Neil Turok, says it as if the universe is actually in a perpetual state of big bangs. Turok’s co-author, Job Feldbrugge says, “Our research implies that we either should look for another picture to understand the very early universe, or that we have to rethink the most elementary models of quantum gravity.” Notation-0 within our model is the start, and it is perpetually starting.

J. Feldbrugge (Perimeter Institute), J.L. Lehners (Max Planck Institute for Gravitational Physics and Albert Einstein Institute), and N. Turok (Perimeter Institute), “Inconsistencies of the New No-Boundary Proposal,” arXiv:1805.01609 (PDF), Universe 4 (2018) no.10, 100. _________________________

Our theory is more liberating because it starts with things that we know, simple geometries and simple math, then goes out and includes everything for all time. Thus, it’s also more integrative and inclusive. And, it is a bit less judgemental because it includes the qualitative. It is a theory with heart and feelings that doesn’t promote nihilism.

Sean Carroll, a distinguished professor at Caltech, occupies Richard Feynman’s office and uses his desk! He has a natural impatience, yet he seems to be earnestly seeking the truth so I try to understand his logic. His big bang theory is not quite the Hawking-Guth model, yet it’s not yet clear to me how he would differentiate. We know quite assuredly he would not start with the Planck base units, or use base-2 notation, infinitesimal spheres, and 202-notations; and, he would not affirm a no-gap perfection of substance-and-structure within the first 64-notations given through geometries of sphere-stacking. The first minute is between Notations 148-and-149. The first second is between Notation-143 and Notation-144. The zeptosecond (1×10^{-21}) is between Notations 65-to-67, the range of first measuring quantum fluctuations. There’s a lot of work to do to interpret those notations properly.

If each notation is always active, these observations aren’t past, but are the activity within the current day within a specific notation. As commented within earlier homepages, a re-interpretation of the redshift is also in order. We have a lot to learn.

[4] Cover-Ups We have found unwitting cover-ups. First, the big bang theory unwittingly covers up the pathway to a quiet expansion. It took the naïveté of high school people to follow basic geometries down into the Planck scale, apply base-2, map the universe, and then rather innocently ask, “What do we do with this?”

Second, in much the same way, quantum physics emerged and slowly affirmed the primacy of its fluctuations and indeterminacy without ever being able to explain those roots or origins. It got established as rigorous theory with a huge unknown for its start. It, too, became an unwitting cover up.

While learning about spheres, we were introduced to a tetrahedral gap and learned about a third cover-up initiated by Aristotle. He made a mistake and scholars didn’t catch it for 1800+ years. Even today, scholars do not know what to do with the geometric gap that Aristotle missed. That gap breaks the perfect filling of space. In the process of that study, we also uncovered a heretofore unrecognized octahedral gap. We work with perfect tetrahedrons and octahedrons, so once the question was asked about five octahedrons sharing a common centerpoint, it took minutes to see the exact same gap as with five tetrahedrons.

We then found more subtle coverups. Our most popular interactive geometry software (IGS) and their dynamic geometry environments (DGEs) easily accommodate these gaps. Never programmed for these gaps, it’s a little like Aristotle’s failure. We also discovered that the geometric construction kits like the Zometool also would not display these gaps. Further analysis of both software systems and construction kits is underway.

[5] Extralogic. Within the circles of people who study logic, there are rules and conventions. There is also extralogic that can be a little like religion and look like Guth’s inflation. MUCH MORE TO COME… See Ed Zalta.

[6] Arrogance. I enjoy Einstein’s quote. It’s true, but arrogance is endemic to the many insecurities of the human family and scholars are not exempt from them.

[7] Hotspot: James Webb Space Telescope (JWST). If we do not have a construct for the first second, there is no way that we will have the first year or the first million years (Notation 189) correct. Observational technology reaches back in between Notation 196-to-197; that 13.556 billion years is 235.8 million years “after the big bang.” The big bang theory misses all the most formative processes of the universe. The JWST started capturing data in July 2022. It sits within a dynamic tension out on the L2 (Lagrange Point 2) about 1.2 km from earth. The Planck satellite mission, also within L2, has been working since 2009. In all probability, the JWST will do equally well, if not better. We have many years to be capturing data to help us determine the real realities of this universe. We look forward to more of the work of Rebecca Bowler and the Cosmic Dawn Center. They are building on a long history about which we are now learning: List of the most distant astronomical objects.

[8] Time. In our model of the universe all notations are always active. Each builds off of the other. There is a dynamic reach from the first notation to the 202nd. It is fully symmetric from Notation-1 to Notation-201 and to just a small sliver of 202. Time is always right Now. In that light, the galaxy counters may well want to re-think their galaxy count. The looking back may be notational. We may be witnessing activity within a notation today. That is a very difficult concept to wrap one’s mind around.

So, if the electroweak processes are based on the Fermi scale whereby one fermi equals 1×10^{-13} cm or about .00000000000010 centimeters, if it were observable, we’d be looking at today’s activity within Notation-73.

We’ll continue struggling with the logic of it all.

[9] Galaxy Counting. Some astrophysicists like Mario Livio continue to use the old estimate of 100-to-200 billion galaxies even though in 2016 Dr. Chris Conselice bumped that number up to two trillion based on Hubble data. Today some speculative folks are saying that the number is yet much higher.

If all time is now, and there is only a infinitesimal sliver of time that is directional, all these estimates need to be revisited.

[10] 436 quadrillion seconds or a little more closely, 436,117,076,600,000,000, introduces a new reality that it all has to happen within 436 quadrillion seconds. It is the next group of numbers after a trillion. When looked at in this way, 13.82 billion years doesn’t seem much time at all.

[11] Perfections. Quantum theory became the de facto background of our universe through the 1920s and ’30s. In our model, the universe starts out perfectly smooth with no gaps. Quantum physics has little possibility of breaking into the model until quantum geometries become systemic. We suspect in the first pass through the first second within Notation-143, there is too much thrust and density for any of the quantum geometries to manifest. Did it take a year, 1000 years, or a million-or-a-billion years? I wouldn’t hazard a guess. Yet, once there is a system whereby quantum fluctuations begin, I suspect it then works its way back to Notation-67 where it first becomes measurable. This domain will become an entirely new area of mathematics and physics. I call it hypostatic.

[12] Notations. GN-z11 galaxy, discovered in 2015 in the Ursa Major constellation, held the record for seven years by going back to within 400 million years of the start. That would be 13.4 billion years ago. GLASS-z13, a galaxy found in July 2022, went back to 352.3 million years after the start. That would be 13.4577 billion years ago. A bit later in July 2022 the CEERS-93316 galaxy (ArXiv) was observed and it goes back to 235.8 million years after the start. That would be about 13.556 billion years ago.

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

CMBR, Dark Matter-Dark Energy: We’ll be looking into the 1960’s data of Arno Penzias and Robert Wilson from the Holmdel Horn Antenna. CMB. We’ll even be going back to the 1933 computations of Fritz Zwicky of Caltech. He had a way of calling people he didn’t like spherical bastards. Given our idiosyncratic approach, I suspect we’d get lumped with them! There’ll be much more to come.

“…space-time itself does expand faster than the speed of light” and “…how it is possible that there may be galaxies that are almost 100 billion light years apart.” – Gerardus ‘t Hooft (Nobel, 2019)

Extralogical: “…the bulk of extant mathematics is believed to be derivable logically from a small number of extralogical axioms, such as the axioms of Zermelo–Fraenkel set theory (or its extension ZFC), from which no inconsistencies have as yet been derived. Thus, elements of the logicist programmes have proved viable, but in the process theories of classes, sets and mappings, and higher-order logics other than with Henkin semantics, have come to be regarded as extralogical in nature, in part under the influence of Quine‘s later thought.”

GN-z11: After seven years, attention is shifting to CEER-93316 and the JWST. However, in 2016 it was Pascal Oesch (Yale, Geneva) and Gabriel Brammer (Niels Bohr Institute) who reported their 2015 findings and have been the voices of GN-z11. If our model has any viability, these two would be excellent minds to reconsider what the redshift is tell using if all time is now. We’ll keep you posted. There’ll be much more to come!

Other professors with whom I have worked from long-long ago: Phil Morrison, Noam Chomsky, Marvin Minsky, Gian-Carlo Rota and Jay Forrester (with Dennis Meadows and Club of Rome). More to come about Jerome Friedman, Leonid Levitov, Seth Lloyd, Joe Pickett (MIT OCW), and Isadore Singer.

The James Webb Space Telescope (JWST)^{[1}^{]} is finding so many new galaxies, people are again asking, How is it possible? Are there too many galaxies and not enough time? Should we redefine time? Possibly there’s a better way to interpret the redshift data. ^{[2]} Perhaps we are unwittingly double-counting (or more). Is our understanding of galaxy formation too incomplete? What if this universe is fundamentally exponential? Could base-2 notation be a key to it all? ^{[3]}

Time redefined. A dynamic equation that makes numbering possible

Einstein and others tell us that time is not absolute. It’s finite. Not to be confused with a second or some part of it, time is also dynamic. Time is an equation; it makes numbering possible. And as a result, it makes measurement possible. Seconds-minutes-hours-days are all human conventions. Simple equations make time, i.e. one infinitesimal sphere per unit of infinitesimal dimensionless constants and it all manifests as space-time. Time is the result of equations that render Planck units. Yet these current numbers are still just placeholders. NIST and the ISO could adjust those values. Even the 1874 calculations by Stoney could be used to help determine a new set of values based on current data.

Base-2 applied to the symbolic Planck units goes from the first possible moment of the universe to the current time in just 202 highly-integrated, richly-mathematical notations. It is no longer spaceship earth; it’s spaceship universe. We are intimately one; and, we create space-time as we go.

The first notation opens the finite-infinite relation and the most logical manifestation is within pi. Here we find pi’s continuity, symmetry, and harmony which manifests as the finite-infinite, a quantitative-qualitative bond (relations and/or equations). Those three faces of pi create sphericals, and those geometries stack, create space, then together perfectly fill space by creating tetrahedral-octahedral packing based on symmetries-as-relations, then harmony-as-dynamics.

Imperfection — discontinuity, asymmetry and dissonance — comes.

Again, the domain encapsulated by the first groups of notations would be perfectly filled and smooth (no gaps) until there is a formation of the five tetrahedral and five octahedral gaps. A speculation is that due to compression (densities), these geometries would be encapsulated and not become systemic. We know, however, that at some point there comes a notation with encapsulated gaps that becomes systemic, giving rise to quantum fluctuations. And then, those fluctuations begin to reach down into the prior on-going notations (we’re beginning to learn how all notations are always active).

Concepts that could help open historic worldviews that confine us:

Simple mathematics. Looking at those 202 base-2 notations from the Planck base units to the current time, the first 64 notations are below thresholds of measurement and are the subject of the nine studies cited just above.

Redefine time. Newton’s concept of absolute time has been our common-sense worldview for about 300 years and the alternatives are not common sense. We can’t give up. We need to redefine time. It is a major hurdle for most of us. We can do it.

Finite-and-infinite. This Janus-faced relation has been controversial throughout time. Let’s define it as the quantitative-qualitative in light of those three faces of pi and in light of the first 64 notations. Historic and personal issues regarding infinity are placed on hold.

Perfection-imperfection. There has been a lack of engagement with (1) the geometries and physics of perfections, particularly of continuity-symmetry-harmony where there are no gaps, and (2) imperfections, where there are fluctuations (our constructions are all formative and being developed) and squishy or quantum geometries within an idealized Euclidean base.

The nature of sleep cycles. Within sentient and thinking things, there is a constant process by which linear time is recompiled within exponential time and the current moment of the universe. Notation-202, the Now, is always on the edge of the current expansion, could appear to be a time asymmetry but is forever being recompiled within the whole as everything that sleeps does within an infinite cradle of continuity-symmetry-harmony.

Conclusions A hypostatic geometry, hypostatic physics, and hypostatic science

Of course, the word, hypostasis, is loaded with a prehistory that is not ignored, but could be. If today, right now, is the only time that is really real, it seems that we could engage the word as given within its meaning of “that which stands under” or perhaps “the foundations of the foundations.” It is about giving those first 64 notations a special name and definition. It’s a pre-physics that is still physics. It’s a most seminal geometry of nodes, lines and faces that are always dynamic, interactive, testing, defining, creating… and so much more. Scholars have spent their lifetime feeling, contexting, and writing about the subject. They each know a face of that mathematics. They have the textures and refinements. So, let us turn to them and ask, “Can you tell us more? Can you all work together? Might those five bullet-points just above help?”

Endnotes & Footnotes There may be more endnotes than footnote because all these points already have pages within this website.

* All these new images from the JWST, such as the Carina Nebula pictured above, enliven cosmology by bringing people out beyond our limited world, beyond our Solar System, into the Milky Way, into our Local Group, and even beyond into the Virgo Supercluster. The Carina Nebula is located in an arm of theMilky Way and is approximately 8,500 light-years from Earth. It all seems so vast and confusing until it is placed within the our 202 base-2 notations where our basic assumptions of space and time are challenged.

[1] James Webb Space Telescope (JWST) follows the work history of the Hubble Space Telescope. In 2016 Prof. Dr. Christopher Conselice defended a two-trillion galaxy estimate from his analysis of the Hubble data. He believed that number was consistent with big bang cosmology as understood by Stephen Hawking and his followers. Other respectable astrophysicists like Mario Livio (Space Telescope Science Institute, Baltimore) have not disputed the Conselice estimate but hold to a more conservative number between 100 and 200 billion. Notwithstanding, the JWST will continue to put pressure on that count and on the adequacies of classic big bang theories. Also, it will be anyone’s guess what is behind all the blindspots between us and the rest of the universe. The New General Catalogue of Nebulae and Clusters of Stars and other deep sky objects will become the largest document in the universe!

[2] Our understanding of the redshift (color, distance, frequency, light, time and wavelength) just might be challenged. We will start a pointed study of the redshift as currently understood.

[3] Counting within base-2. As noted in the prior homepage, just one sphere doubled, then doubled again and again, 64 times or 2^{64} (our Notation-64) would amount to over 18,446 trillion infinitesimal spheres. At one second (as noted in just the prior paragraph of that homepage) is 539 tredecillion spheres per second. We have just scratched the surface in our quest to learn about exponential notation and all the possible counting schemas. The possibility of trillions of galaxies with quadrillions more planets has begun to peep into our spheres of plausibility.

Possibly more to come…

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

Longing for the Harmonies, Frank Wilczek and Betsy Devine, W. W. Norton, 1988 Editor’s note: More true today than at any time, Frank and Betsy’s dedication quote to Amity and Mira, sets the tenor of this book, “…awaken our understanding and longing for the harmonies” (which comes directly from Kepler).

Mapping the Heavens, Priyamvada Natarajan, Yale University Press, 2016 Editor’s note: The Cosmic Microwave Radiation provides the makings of a map of the universe and our abundance of space telescopes (Hubble, WMAP, and JWST being among the most well-known) provides the data. We rather timidly believe, however, that the most comprehensive map, from the first instant of the universe until this moment, is the one that we started in 2011 as a high school STEM project. An ordered set, continuous-but-discrete, fully-integrated within 202 notations, it truly is a very special outline to begin mapping the heavens.

There is so much insecure arrogance in our world. One would think with all that we don’t know and all we learn every day about the depth and breadth of what we don’t know, well, wouldn’t you think we’d become a little more reflective and introspective.

Abstract. A model of the universe is introduced, based on simple logic, mathematics, and geometries, created by parsing the universe into 202 base-2 notations.* It starts with Planck Length and Planck Time and goes to today’s size and age of the universe. Those Planck’s units are placeholders, symbolically the very first units of everything, everywhere for all time. Our hypothesis about the look and feel of the first moment that defines space and time, posits the sphere and pi to be the most logical. Qualities and quantities are manifest. The qualities appear infinite and perfect and are represented by continuity, symmetry and harmony, the primary three qualities of spherical geometries. Through cubic-close packing of equal spheres, tetrahedrons and octahedrons are rendered, perfectly filing space; it’s a smooth beginning with no gaps. At a point in time five tetrahedrons share a center point to create a gap and fluctuations emerge. Five octahedrons create the same gap, and together they create many kinds of gaps, and the probable beginnings of quantum physics. This a very different, simple model that needs the courtesy of a critical review. Here, too, is a most-comprehensive STEM tool that lays out the first second (Notation-143), the first millennium (Notation-179), and the first billion years (Notation-199). Notation-202 is 10.9816 billion years in duration; less than 2.83 billion years has manifest. This simple model absorbs big bang cosmology.^{†} After discussions (with charts and other graphics), our savants from our sixth-grade classes began to grasp it, so your comments and questions are always welcomed. Thank you. -BEC

Key words: Time, space, mathematical models, geometric models, pi, spheres, tetrahedrons, cubic-close packing, octahedrons, perfection, imperfection, continuity, symmetry, harmony, 202 base-2 notations, integrated UniverseView, Frank Wilczek, Carl Hogan, Joanne Baker, Nature Magazine, time, space-time, Max Planck Institute…

Consider a simple concept of time.

What do we believe about time? In a limited survey, a commonsense belief is that time goes on forever. In this model time is finite. Most people have an intuition about a second. Possibly it is the most-used, shortest duration of time. There are 60 seconds in a minute, 60 minutes in an hour (3600 seconds), 24 hours in a day (86,400 seconds), and 365 days per year (31,536,000 seconds). Factor in Leap Year with its 366 days, we’re up to 31,556,952 seconds. Multiply that by 10 billion years for 31,556,952,000,000,000 seconds. Factor in 13.82 for a generous estimate for the billions of years, and that would give us 436,117,076,640,000,000 seconds. That’s from the very start of the universe to this day with some room for error. For Isaac Newton time goes on forever. Again, within this simple model, time is finite. The universe is somewhere around 436 quadrillion seconds from the very first moment of time to this day, right now.^{1}

Consider everything, everywhere, for all time.

The story of our first new idea that we uncovered has been told and retold many times. It is the story of the 202 base-2 notations from the Planck base units up to Now. We came up with a simple chart for length — https://81018.com/big-board/ — and lived with it for several years. Then we added Planck Time, and a year later we added Planck Charge and Planck Mass. It.was difficult to follow the numbers on each line so in 2016 a horizontally-scrolled chart emerged — https://81018.com/chart/ — and then a website so we all could access it at anytime.

That new chart literally came alive. We had observed how each notation was building on the prior notations. There was a causal efficacy; the geometries, pi, dimensionless constants, and cubic-close packing were tying each notation together. At some point it became apparent that all notations had to be active all the time. That was a steep learning curve. We had to ask ourselves, “If that’s true, then what is time?” We started at the Planck base units and assumed Planck Time is the smallest unit and the first unit. That work in 2017 was part of a NASA Space App exploration at their facility in Huntsville.^{2}

We thought we had emerged with our own homegrown STEM tool and began sharing it with other schools. It came with our rough outline of the universe in 202 base-2 notations. We had slowly started learning a bit more cosmology and theoretical physics; Frank Wilczek’s books were helping to guide us and there were people like Freeman Dyson who tried to keep us on the straight and narrow.

That the first second wasn’t until Notation-143 was quite surprising. We surmised, “This chart is mostly about the first second of the universe after that very first instant when it all began. This model is mostly about the infinitesimal.” One of the many ah-ha moments was when we asked, “Isn’t that the first second of the universe even as it unfolds today?” It was a puzzling question to ask. We began to see that the universe is almost fully symmetric. It appeared to have a dynamic, causal, working relation back to Notation-0 and up to Notation-201. I thought, “That puts a lot of pressure on Notation-202, especially the current time. All the peculiarities of time symmetries and asymmetries have to be within Notation-202.”

Plus, there were so many other questions. Where does gravity come in? How does inflation work here? What about quantum indeterminacy and fluctuations? Is it a quanta of energy or a dynamic relation? What are blackholes and dark energy-and-matter?

We knew we had a long way to go before we could truly tackle those well-known unknowns. At that point, we were trying to figure out the geometries and numbers for those first few notations. We were being pushed to study pi and infinity more closely.

Reconsidering the nature of pi and infinity

The concept of Infinity has been a problem for the world. Self-assured people have come up with special concepts and stories about the very nature of infinity. Told for many generations, those stories have become a key part of a family’s traditions. Not only are these the stories of Mom-and-Dad, but from the generations; “This must be the truth. Absolutely so.” That kind of assurance can become arrogance; and when it does, it becomes a problem. It is often difficult to discuss new ideas and concepts if there is limited or no openness. So I asked myself, “Is there a way to respect those stories but have mathematical and scientific concepts that everyone might embrace and about which these should not offend, even if an atheist?”

Our attention increasingly focused on pi.^{[3],[4],[5]}

We concluded that it had been undervalued and under-analyzed among our scholars. It provides a pivot point between the finite and infinite. It is a natural connection. It is a key part of so many basic equations that describe fundamental things and nobody was talking about those keys or essence as a starting point. The more I learned about Hilbert, Gödel, and infinity, it seemed a simple redefinition was in order. They didn’t have those early notations to challenge them. Let pi provide the simple bifurcation whereby the infinite is qualitative with its continuity/order, symmetry/relations, and harmony/dynamics. And, the finite is the quantitative. It’s measurable. The more time we spent with pi, the more challenging and exhilarating it became. The most speculative jump we made was to consider that a natural inflation could be assumed at a rate of one infinitesimal sphere per infinitesimal unit of time and space. Using the Planck numbers that calculated out at 539 tredecillion spheres per second. Using Stoney’s numbers renders 4609 tredecillion spheres per second. The nature of that inflation, explored in an earlier homepage about thrust, is slowly being expanded and pi is leading the way.

Consider these the foundations of our foundations.

The first 64 notations are currently below possibilities for physical measurements. Might these be considered the foundations of the foundations? If primordial spheres manifest at the Planck scale and there are 64 base-2 doublings before anything can be measured, isn’t that a new domain, a major amount of space? Just one sphere doubled 64 times would amount to over 18,446,744,073,709,551,616 infinitesimal spheres. It may be too small for arrogance but perfect for Langlands, string-and-M theory, SUSY, hypothetical particles… and so much more.

And finally, consider simple complexity.

On the cusp of the finite-infinite relation. It looks simple, but there is nothing simple about a sphere. Her numbers go on forever, always changing and always the same. Those symmetries appear simple, but are the expression of those endless numbers. Attractors and repellers are seemingly in the fiber of its being. The Fourier Transform and dimensionless constants are quite literally everywhere. One might say that the sphere is a bundle of nerves, infinitesimal but profoundly alive. Here is the continuity-order, symmetry-relations, and harmony-dynamics within the perfections of the infinite unfolding within everything quantitative. The perfectly perfect is hypostatic. Simple configurations of five tetrahedrons or five octahedrons come together and become a gateway for fluctuations, imperfection, and creativity.

The new is opened. A deeper complexity is defined. And, there is so much more to learn, do and explore. Thank you.

We especially welcome your comments and insights. Thanks again.

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Endnotes & Footnotes These points have already been made within pages within this website.

A key part of this chart is between notations 64-and-67 where quantum fluctuations become dominant. There comes a place when the composition of measuring devices and the people using them interfere with the measurement. As we go smaller, it becomes increasingly difficult. There will be three zones: 1).Not measurable, 2).Transitional area, and 3).Measurable. The area that is not measurable has had major studies some of which are noted here.

Note: The tetrahedrons and octahedrons used in these models have an actual place along the Notations 0-202. The length of the side is about 2.5 inches with is between Notations 111-and-112 (1.65 to 3.3 inches). The models are representational, not literal and become structural within Notation-1 and are infinitesimally present within Notation-202.

[1] It is always right now: No matter how large the numbers or how small the numbers, right now, this moment, is the only time there is. Any number brings us into the scale at that moment.

[5] Ethics. This platform of continuity-order, symmetry-relations, and harmony-dynamics readily creates a many-sided valuation that on closer inspection appears to be an ethical model as well. We have an ever-deeper sense of what solipsism, narcissism, nihilism, and dystopia are.

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

Emails To scholars around the world, their writings help clarify issues and inspire us.

• Joanne Baker, Nature Magazine, August 4, 2022 • Craig J. Hogan, University of Chicago, Enrico Fermi Institute, August 4, 2022 • Jürgen Jost, Max Planck Institute, Leipzig, August 4, 2022M • Sir Peter Knight, Imperial College London, August 2, 2022, at 3:320 PM • Peter Scholze, Max Planck Institute for Mathematic, Bonn, August 1, 2022 at 4:51 PM

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IM There will also be many instant messages to thought leaders about these ideas and concepts.

@the_xijinping This very simple model of the universe is based on simple mathematics, geometries and logic — https://81018.com — whereby continuity, symmetry and harmony becomes the basis for ethics and value — https://81018.com/ethics/ — and rises above politics.

Li Keqiang, Xi Jinping, Li Zhanshu, Wang Yang, Wang Huning, Zhao Leji, and Han Zheng Editor’s note: We all need to start files our communications to all leaders! We will do it. -BEC

I discovered your article, Symmetries of the Primordial Sky, and was immediately attracted to it and immediately went and opened the ArXiv edition.

Fascinating. Engaging. At about that time, I had set aside my writing to Joanne Baker of Nature magazine; and now, thinking of your work, you were inspiring me to be bolder.

As I read your abstract, I could hear myself saying, “Check. Right. Right. Right. Check…” So, now I need to dig into the article and also look at all your other work to see just how bold I can be if I were to write to you. Eventually, you’ll know, but for now, maybe we can be friends.

So, I just did a brief survey of your work. First, “Congratulations on all that you have done. You have done quite a sweep of the world and the universe! As a sequel of Symmetries… I think you could begin to answer some of our many unanswered questions.

You begin the dialogue with the reader, “The world works according to two all-encompassing theories…” and you are so right. Our world has done well with those two theories. Our universe, on the other hand, demands that the two come together.

First, let’s push our understanding of time. We are all so infinitely Newtonian when finite seconds do just fine. Here’s is our look at what we called, The Universe Clock. We start at the Planck base units and assume Planck Time is the smallest unit and the first unit. That work in 2017 was part of a NASA Space App exploration at their facility in Huntsville. We thought we had emerged with our own homegrown STEM tool and began sharing it with other high schools. It came with a rough outline of the universe in 202 base-2 notations. We had started learning a little cosmology and theoretical physics; Frank Wilczek’s books were helping to guide us and an old friend, Freeman Dyson, was trying to keep us on the straight and narrow.

Yet, there was something fundamentally wrong with our model. It didn’t cotton with big bang cosmology. It had at least 64 notations before particle physics and CERN’s measuring devices. Our little model was puzzling yet logical. How could we be so far off and out of step?

I decided that pi was our stumbling block. It was tied up inside so many fundamental equations that describe fundamental things and nobody was talking about its essence and as a starting point. The more I learned about Hilbert, Gödel, and infinity, it seemed a simple redefinition was in order. Might pi provide the simple bifurcation whereby the infinite is qualitative that is continuity/order, symmetry/relations, and harmony/dynamics and finite is the always a quantitative expression?

It gave me a slight reprieve so our 202 notations could stand, and time and space could be inadvertently redefined so all notations could become always active. There is so much more that we’ve slowly uncovered, but I have already overstayed a de facto time allocated to emails such as this. So let me say, “Thank you, thank you, thank you for all that you do, and for taking time to write about the Symmetries of the Primordial Sky. I have questions, but on my continued survey of your work, I know you do not have the time. So, let me ask for permission to write again. Thank you.

Most sincerely,

Bruce

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Symmetries of the Primordial Sky Abstract (PDF): Quantum field theory, which is generally used to describe the origin of large-scale gravitational perturbations during cosmic inflation, has been shown to omit an important physical effect in curved space-time, the nonlocal entanglement among quantized modes from their gravitational effect on causal structure. It is argued here that in a different model of quantum gravity that coherently preserves nonlocal directional and causal relationships, primordial perturbations originate instead from coherent quantum distortions of emergent inflationary horizons; and moreover, that causal constraints account for approximate symmetries of cosmic microwave background correlations measured at large angular separations, which are highly anomalous in the standard picture. Thus, symmetries already apparent in the large-angle CMB pattern may be unique signatures of the emergence of locality and causal structure from quantum gravity.

Questions related to approach to QFT: 1. Does QFT apply to Planck scale physics? 2. Might the profoundly infinitesimal universe (below the measurements of CERN) be perfectly smooth? 3. Might quantum physics be a question of geometry? More to come…