Looking in on the work of Paul J. Steinhardt…


Paul J. Steinhardt
Princeton University
Princeton, New Jersey

ArXiv (over 108 articles)
YouTube: The Myth of Inflation (2021),  A New Kind Of Matter (March 2019), Inflationary Cosmology on trial-2011 and dozens more

References to Steinhardt‘s work within this website:

Most recent email: 8 October 2021 @ 7:05 PM

RE: Still at it! Finally caught up with “Impossible”

Dear Prof. Dr. Paul Steinhardt:

Your book, The Second Kind of Impossible, Simon & Schuster, 2019, resurrects the importance of geometries within the small scale universe. I believe your discoveries, following Daniel Shectman‘s initial quasicrystal work, open a vitally important door. The next door to open is within the infinitesimal universe from the quark-gluon plasma and electroweak scale down to the Planck base units. I just found a group out of Durham University that hosted the 23rd conferences to focus on just that domain. Would geometries become increasing “simple” as we continue to approach Planck Time, i.e. automorphic forms and strings!?!

https://81018.com/hypostasis/ is our most recent speculation about it all. The numbers, of course, we started chasing in 2011: https://81018.com/chart/

I thought you would be interested to learn that I am keeping the fires burning within our most naive-but-logical-and-mathematical model.



Fourth Email: Thursday, 6 March 2021

Your writings are most encouraging. I am so very humbled and I am painfully aware of my naïvetés and limitations. So, I profoundly thank you for opening up the universe for me.

[1] You ask us to be aware of quantum origin.
Remember we backed into this entire domain by following Zeno down inside the tetrahedron and its octahedron. Within just the first 45 steps, we were down within the neutrinos. With another 67 steps, we were down with Max Planck discussing his infinitesimal units. We seemed to break free of the hard quantum fluctuations around Notation-64 and then free of all possible fluctuations around Notation-50. I wanted to call these less harsh fluctuations systemic or ontological (ontic) fluctuations and relate them to thought and consciousness. Again, my naïveté and limitations hold me back. The initial 50 notations I considered a place for pure geometries and numbers and combinatorial optimizations.

[2] Consider those stages when the universe is not inflating.
Those first 64 notations were initially quite upsetting. Struggling as I did, there was little more to suggest than Pati preons. I was just throwing anything I could find up against the wall to see if it would stick! The more obvious — Langlands, string theory — had to be studied. Then came theta functions, Quine* atoms (urelements), axiomatic set theories, etc (line 11 on my chart)… And more recently, causal dynamical triangulation, causal set theory, scalar field theory, loop quantum gravity, and the Spectral Standard Model.

[3] Inflation is about more than exponential expansion.
On that path, it was easy to imagine that every notation was always active, and that the base unit, this infinitesimal sphere (Lemaitre’s atom), is defined by the Planck units. Those first 50-to-64 notations are a precursor to direct measurements. It is a highly-refined, dynamic area where all kinds of mystery could hide. First, the dark stuff. That seemed obvious. The rate of expansion, if we assumed one sphere per Planck unit of time, was hard to imagine but possibly a proper, natural inflation. It certainly felt more logical than Alan Guth’s inflation. Applying base-2 was never some special mathematical magic, but always had “something” making space-and-time even if it was just geometry. But that first object eventually became that infinitesimal sphere that filled the universe and became the new aether whereby everything, everywhere, for all time became connected and its uniformity became the basis for homogeneity and isotropy.

It’s been an evolution. For pi day, I finally said, here is the most basic dimensionless constant of the many that define the first instance, that first infinitesimal sphere, a full 64 doublings from the first particle and wave. There is plenty of time to bring general relativity and gravitation into the equations. Yes, yes, still crazy after all these years!


PS. I once was a dinner guest of Quine’s in his home (as a graduate student)! -BEC

Third Email: Thursday, 9 April 2020

Dear Prof. Dr. Paul Steinhardt:

Thank you for all you do to guide our students and our world’s scholarship. I have enjoyed coming to know you through your writings and videos. You challenge me on every turn!

Notwithstanding, our little idiosyncratic model has not been debunked, just categorized as “idiosyncratic” and it is. There are five general assumptions from which this model emerged. These are as follows:

  • The four Planck base units define the first moment of time.
  • An infinitesimal sphere is the first expression of a physical thing.
  • There is a natural inflation whereby sphere stacking and cubic-close packing of equal spheres creates structure and emergence.
  • There is a finite-infinite relation and the infinite is defined, primarily as a result of discerning aspects of that sphere. It is: (a) continuity and it creates order and the face of time, (b) symmetry and it creates relations and the dimensions of space, and (c) harmony and it creates dynamics and a space-time moment. That is the sum total definition of the infinite (and infinity) and there is a constant working bridge between the finite and infinite.
  • These spheres continue stacking and become an aether and natural inflation. There are just 202 base-2 notations from the Planck Time to the current time. This endless stream of spheres is the current expansion and every notation is always active and present.

I’ll continue to work on this model and will attempt to become more compelling within each step of the way.

In today’s homepage there is a reference to you and the 1999 Structure Formation conference at Cambridge University’s Isaac Newton Institute so I was reminded once again of your most impressive history within this domain.  I thank you.

Most sincerely,


PS.  I recognize that our definitions of time and space are still quite primitive:
https://81018.com/redefinition/#Top  Although Turok, Arkani-Hamed, and Tegmark would never agree with a high school teacher, at least they forcefully raise the questions.

From within my impossibly-deep naivete, even though Planck Mass and Planck Charge are in some sense of the word, quantum, if they are well beyond measurements, might they be re-qualified as more systemic than quantum? I certainly don’t know. There are 64 notations, a virtual universe, between Planck Time-and-Length and actual physical measurements by devices. Wouldn’t it be polite to offer those 64 base-2 notations as a work area for Langlands programs and string theory?
Second email:  Tuesday, March 12, 2019, 1:23 PM
As earlier suggested, I have been trying harder to clarify my first principles. There are five very speculative assumptions (concepts) that form the basis of this idiosyncratic model.

1. Continuity: A simple mathematical grid to order things.  Apply base-2 notation to the Planck base units to encapsulate the universe within 202 base-2 notations. We start at Planck Time and go to the present time.

2.  Symmetry: A simple building block to create relations. Assume the first expression of physicality is the sphere; some have called it a plancksphere; and, back in 1955, John Wheeler called it quantum foam. Apply cubic-close packinghttps://81018.com/number/#Kepler –and form-and-structure become emergent. https://81018.com/circles-spheres/

3. Harmony:  A simple construct for quantum fluctuations and dynamics. Assume basic structures include a five-tetrahedral unit; we have called it a pentastar. It has a gap (0.12838822… radians or 7.356103172… degrees) that also manifests as the twenty-face icosahedron and the sixty-face pentakis dodecahedron. In each the same gaps could readily manifest as quantum indeterminacy by the 64th notation or doubling.

4. Time is derivative. Every notation is always emergent, never-ending, never-the-same. All time is Now. Obviously, within the 202nd notation, there is a perception of past-present-and-future, a sense of time. This notation is 10.9 billion years and only about 2.84 of it has emerged.

5. Re-open the door to define more deeply the concept of infinity. We’ve all got to lighten up a little. It is obvious nobody is making progress within the old-time debate, but some progress just might be made both within mathematics and physics: https://81018.com/infinity/

Summary. It is such a different model, it is hard to engage. It took me the better part of four years to realize in what ways this nascent model could become more than a STEM tool.

Our little history is here: https://81018.com/home/ My story is here; an introduction here.

My request (a plea). I know how idiosyncratic this model and these five constructs are. If the logic and/or mathematics fail, I would be deeply indebted to learn how. If this model is not a possibility, I would like to learn where and how the simple logic and simple math break down so I can give this work a fair burial as a theory and do a better analysis of its STEM possibilities.

Thank you. Thank you so very much.



First email: Wednesday, January 14, 2015, 3:55 PM

Dear Prof. Dr. Paul Steinhardt:

I came upon references to your work within the Kavli Foundation pages and then began reading about the breadth of your work on your own Princeton homepage. We’ve been looking for alternative approaches to understand our earliest universe.

We backed into this work by following simple geometries back to the Planck Length and then out to the Observable Universe. Our work is simple-simple (yes, possibly simplistic) and entirely idiosyncratic. Last month we added Planck Time to our base-2 progression and we are filled with questions.

Have you ever seen the simple compilations of the progressions from the Planck Length and Planck Time (using base-2 notation) to the Observable Universe and Age of the Universe respectively? Based on our initial observations, I think it raises questions about nature of space and time. We can guess. Although we have no conclusive answers, let me admit that we are a little prone to wild speculations and flights of the imagination.

Yet, as high school teachers and students — certainly not experts on the subject by any stretch of the imagination — we still had the audacity last September to begin asking questions. It may all just be an overactive imagination based on simplistic logic. Perhaps this challenge to our understanding of space and time is just too profound for us little folks with such little depth and background in cosmology and astrophysics.

I thought you at least would find such an unusual, rather idiosyncratic approach to these questions to be of some interest. If not, well, sorry to waste your time. However, if you feel that way, I have five classes of high school geometry students and this teacher who would be fascinated to know why.

Best wishes to you and your teams for 2015,

New Orleans
Bruce Camber, Mathematics, Geometry
PS. Given your work with quasicrystals and five-fold symmetries, you may also find this page about tilings and tessellations to be of some interest as well as the following:

  1. The references to your work (just above) for digging down further.
  2. Our “work” began in 2011 in a high school geometry class. That story is here: https://81018.com/home/
  3. This posting of the two progressions side-by-side was done in December 2014: https://81018.com/calculations/
  4. Earlier work from September 2014, mostly questions… one must start somewhere: Did A Quiet Expansion Precede A Big Bang? https://81018.com/2014/09/10/quietexpansion/

Alan Guth’s inflationary theory redefined.*

Left Yellow Arrow
Right Yellow Arrow

Pages: * | Agree | Gravity| Hope | Hypostasis | Mistakes | Pi (π) | Questions | Sphere | STEM | Up

A Radical View of the Inflaton Field
by Bruce E. Camber (first draft)

Lemaître, Hawking, and Guth1 were the most pivotal thinkers to advance a big bang theory. Lemaître died in 1966 at the age of 71; and, Hawking died on Pi Day, March 14, 2018 at the age of 76. Alan Guth now stands alone, the last remaining prime mover, especially with his theory of inflation and its inflaton.

Given that dimensionless constants and their equations are most fundamental keys, we ask, “What ubiquitous, old equation touches the most points within science and mathematics?2 I.suggest that the answer directs us to the best equation to define the first space-time moment within.this universe. And, I believe that equation is pi.

It’s that simple. Notwithstanding, thoughtful work by many scholars has gone into defining inflation and its inflaton. All those insights still hold keys to the universe, just not the keys to the earliest instances of our universe. For those moments, the most-infinitesimal sphere should be a good redefinition of Guth’s inflaton.3

The equations immediately begin to evolve. Basic geometries emerge and continue to evolve for seconds-minutes-hours-days-a-year (and even years). At some key critical point, the definitions by Guth and his collaborators will begin to participate. To determine when will take some study because inflation is dynamically creating the laws of physics as infinitesimal spheres populate the universe.

There are several current disparities to determine an expansion rate so a range is provided. I suspect in reality there has always been a range. Using either the PlanckStoney-or-ISO base units, and by assuming one infinitesimal sphere per unit of PlanckTime, StoneyTime, or a new ISO basetime, there would be a range from around 539-to-4605 tredecillion spheres per second.4 Of course, these are the most infinitesimal spheres possible, at least 50-to-64 base-2 orders of magnitude smaller than the neutrino and are obviously a good candidate for dark energy and dark matter.

That range or rate of expansion, considered a new definition of a cosmological constant, expanding even today, right now, creates a penultimate grid, literally to include everything, everywhere for all time. There are just 202 base-2 notations that outline our universe from the smallest duration of time, doubling each step, to the current time, the Now.5 I believe here is the starting place for group theory, systems theory and at least nine major studies currently not on any grid!

The first infinitesimal sphere has been likened to Lemaître’s primeval atom and Guth’s inflaton. Both the primeval atom and the inflaton field have always been hypothetical. I.believe our very first infinitesimal sphere is a little less hypothetical. The universe has to start with something to create space-time. Yet, our simple postulation goes much further. It is difficult to conceive of a universe totally populated by such infinitesimal spheres. Notwithstanding, even this hypothetical penultimate grid warrants inspection.6

Finite-infinite transformations between the faces of continuity-symmetry-harmony (CSH)7 are assumed. Our focus is on the finite. Defined by CSH, it is the Fourier transform,8 and then configurations of the Poincaré sphere, Poincaré homology sphere, and any-and-all types of spheres as mathematics naturally extends to include each. Only when it becomes possible to “come out” mathematically, building on natural functional dependencies, do these infinitesimal spheres manifest. This would necessarily include studies by Smale and Milnor of spheres as attractors and repellers.

Those new to this site will quickly ask about indeterminacy and quantum physics. Over the years we have struggled with the geometries of indeterminacy.9 It’s a working challenge and very much part of the discussion. So, per usual, I ask, “Where have we gone wrong with our charts, interpretations and prognostications?”10

Thank you. Thanks indeed. -BEC



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

[*] Alan Guth. With this footnote I have asked Alan Guth to consider a new thrust whereby his hypothetical inflaton (and even Frank Wilczek‘s hypothetical axion that Guth adopted) are redefined in the light of infinitesimal spheres and groups of infinitesimal spheres. I’ve proposed that that we first analyse the processes involved by organizing the data about spheres using a base-2 natural expansion. Every law of physics is derivative within a notation between 0 and 202. Base-2 exponentiation is the most-simple way to organize the numbers of spheres with a timestamp and to begin to grasp the unfolding functionalities of spheres and groups of spheres.

There are 202 base-2 notations. The horizontally-scrolled chart of 202 base-2 notations started in December 2011 with just Planck Length. That chart had somewhere around 202 notations. Not until 2016 when we mapped it with Planck Time did we have a more definitive stopping point: 13.79 to 13.81 billion years. The 201st doubling takes Planck Time, 5.391 16(13)×10-44 seconds, out to around 173,272,944,073,600,000 seconds or 5.4908 billion years. If we add up each notation up to the 201st notation, we are one PlanckTime unit shy of 10.98 billion years. Simple math tells us that around 2.8284 billion years has passed since the beginning of the 202nd notation (Calculation: 13.81 minus 10.9816 ≈ 2.8284). It is an important perspective. Our calculation for the UniverseClock helped us along this path. We are now challenged to exegete each notation! We quickly discovered how difficult that notational analysis can be. Here is an introductory pass at Notations 0, 31, 64, 67, 101, 137, 143, 167, 197, 199 and 202.

It all pushes us to redefine time because (1) All the notations are always active. (2) Time does not “pass.” It is. (3) Aging is real. Death is real. Sleep is real. Memory is real. And, all four must be included. Quite a challenge.

[1] Lemaître, Hawking, and Guth. Only Alan Guth has had the advantage to see the 2022 results from the James Webb Space Telescope (JWST). Although Stephen Hawking had access to the results of the Wilkinson Microwave Anisotropy probe from 2001 to 2010 (See: Katherine Freese) and results of the ESA Planck Telescope from 2009 to 2013 (See: George Efstathiou), that data is still a challenge. It has needed the JWST data 330 million years later to provide some perspective. Yet, it is all still a giant jigsaw puzzle… all to discern the very nature of the pieces of that puzzle within the first few minutes of our universe.

Guth is still confident that his group is on the right path, “…that the observational evidence for inflation just keeps mounting up and as things get measured more and more precisely it just gets better and better; so for example, one of the predictions that inflation makes is for the average mass-density of the universe and now that’s been confirmed within a half a percent.” That quote is taken from How Did the Universe Begin? (:18-:31 seconds), Closer to the Truth, 2020. Guth’s inflation is like a chameleon because it is based on just part of the overall construct. Also, see: Why Is There Anything At All?, 2021.

The earliest moments of the universe in the light of big bang theories were generally introduced to the public by Steven Weinberg within his 1977 book, The First Three Minutes. He says on page 5, that “…one-hundredth of a second (is) the earliest we can speak with any confidence” and then adds with aplomb that “the universe was about a hundred thousand million (1011) degrees Centigrade” as if he had observed it in the laboratory. Much later a group of 27 scholars from around the world titled their article, The First Three-Seconds (2020). They had trouble getting behind that first second. Within our chart the first seconds are from Notation-143 and the first hundredth of a second is from Notation-138.

It is all such a blindspot. And the big bang has been blocking a deeper analysis. Inflation has been called into question as has the big bang as a theory itself. It has become entirely obvious that we all need to be thinking more about the results from the ESA Planck Space Telescope in light of the JWST.

Notation-143. By the 143rd doubling of Planck Time (1.202 seconds), we are well into the last third of our chart. Notations 1-67 are virtually unexplored and, to the best of our knowledge, have never been cited as such within scholastic literature. We’ve called it the small-scale universe; perhaps “the infinitesimal universe” would be more appropriate. Notations 67-to-134 have been cited as the human-scale universe while Notations 135-to-202 have been cited as the large-scale universe. By that 143rd notation, on each “first pass” through, the core geometries, mathematics, and physics are being shaped by efficiencies and densities. It seems that there is no time or space for quantum indeterminacy. In that first pass, a perfection is most efficient and most simple. I can well-imagine those efficiencies become precedents and that this “perfection” — currently called smoothness — readily defines the first 330 million years right up to and within Notation-197.

[2] Ubiquitous, old equation. What comes first? The heart of the finite-infinite transformations between the faces of continuity-symmetry-harmony (CSH) is pi. Much of our classic scholarship touches it but has not defined it as CSH. Within this website, the discussion about the finite-infinite is part of many homepages, i.e. the prior homepage on de facto and de jure is one our many finite-infinite discussions. In many places within this website, you will find this declaration:

All other definitions of the infinite are put on hold. Most are personal definitions that come from personal experiences and family history. That is one’s own business, not ours. If those beliefs help you through life, that is great. Our goal here is to engage those principles and functions that give rise to mathematics, physics, and eventually all the other sciences.

from Continuity-Symmetry-Harmony (CSH), 1972

[3] Inflaton definitions. An excellent overview of the range of definitions is with a sampling of ten articles out of over 3700 within ArXiv that use the concept. The most important definition would naturally be from Alan Guth. One such article is Eternal inflation and its implications (PDF), Alan H. Guth, February 2007. Yet, the definitions by other early adopters like Steinhardt, Vilenkin, and Linde, are also key. A sampling of just ten: (1) Arrows of time and the beginning of the universe (PDF), Vilenkin, 2013, (2) Inflationary schism after Planck2013 (PDF), Anna IjjasPaul J. SteinhardtAbraham Loeb, 2014, (3) Inflationary paradigm after Planck 2013 (PDF), Alan H. GuthDavid I. KaiserYasunori Nomura, 2013, (4) The Inflaton Portal to Dark Matter, Lucien Heurtier (PDF), 2017,(5) Could the Higgs boson be the inflaton?, Phys.Lett. B697 (2011) 37-40 (arXiv:1011.4179, Remarks on Higgs Inflation, Michael AtkinsXavier Calmet, 2011, (6) Warm Little Inflaton (PDF), Mar Bastero-GilArjun BereraRudnei O. RamosJoao G. Rosa, 2016, (7) The Minimal GUT with Inflaton and Dark Matter Unification (PDF), Heng-Yu ChenIlia GogoladzeShan HuTianjun LiLina Wu, 2017, and (8) From Cosmic Inflation and Matter Creation to Dark Matter — Journey of the Inflaton? (PDF), B. S. Balakrishna, 2022, (9) The Peebles – Vilenkin quintessential inflation model revisited (PDF), Jaume HaroJaume AmorósSupriya Pan, 2019, and (10) On the behaviour of the quantum Universe anisotropies in a bouncing picture (PDF), Eleonora GiovannettiGiovanni Montani, 2023. Additionally, I include: Paul Steinhardt Disowns Inflation, the Theory He Helped Create, Scientific American, 2014, and Wikipedia’s study of the inflaton because it is a dynamic page.

Reference pages within this site: Guth, Steinhardt, Vilenkin, Linde, Ijjas, Kaiser, Loeb, and Peebles.

From all these (with many footnotes and references within each), I conclude the following:
1. Other than it is pointlike, there is no standard, widely-accepted definition of an inflaton.
2. An inflaton, like an axion, must define a space-time moment or it is not basic enough.
3. I would also add that a first principle to be a first principle, must be mathematically defined.

So, there will be more to come. This article is still a draft; it is in process; insights from all these scholars’ references (above) and most-recent articles will be added over time. -BEC

[4] Tredecillion range: A rather straightforward calculation with Planck Time renders 539.tredecillion spheres per second. With Stoney Time it’s 4605 tredecillion spheres per second. We have requested that the ISO comment on the difference. That such numbers could be an acceptable definition of a cosmological constant will be disputed, especially that it is the root cause of expansion (inflation). In that light, I think the insights of Katherine Freese and Will Kinney about a natural inflation deserve more attention. The question needs to be asked, “What is natural?” The work of Yasunori NomuraTaizan Watari, and Masahito Yamazaki (Berkeley Center for Theoretical Physics), Pure Natural Inflation, 2017 ask, “Does the model of inflation need to be significantly complicated? Is the agreement of ns of the quadratic potential with the data purely accidental?”

The simplest model of inflation V (φ) = m2φ2/2 [A. D. Linde, “Chaotic inflation,” Phys. Lett. 129B, 177 (1983)]—which gives the correct value for the scalar spectral index ns ‘ 0.96—is now excluded at about the 3σ level because of the non-observation of tensor modes.

arXiv:1706.08522v2 [hep-ph] 27 Nov 2017

Remember the little neutrino? The experts (IceCube Neutrino Observatory, the University of Wisconsin–Madison and the National Science Foundation) measure neutrinos say, “About 100 trillion neutrinos pass through your body every second.” More to come

[5] The current time, the Now. The most visited page on this website is titled UniverseClock. It was initiated for a 2017 conference at NASA’s Marshall Space Flight Center in Huntsville. Most people can’t imagine that the universe is only 436 quadrillion, 117 trillion, 76 billion, 600 million seconds old. That computes to about 13.81 billion years. In this model each notation is always active and the universe is constantly building on itself. The simplest equations of the universe become axioms, then first principles, and even laws. Yes, in this model of the universe, the laws of physics are being tested as we go.

The nine major studies that are “not on the grid” are actually on the grid, yet below our ability to measure them. Once each discipline accepts the concept of infinitesimal spheres, I am confident that their mathematicians will quickly work out the new details for their study. Thus, there are many more studies to come.

[6] Penultimate grids open for inspection. I believe it will be helpful to re-engage our current concept of point particles to begin to see them as large aggregations of infinitesimal spheres. Even the concept of points and vertices need to be reconsidered for a very basic redefinition.

Back in high school it bothered me that there was only one definition of a point. I imagined hundreds. The differences between them were in how the ends were secured and what was allowed to pass through them. I saw them all as computing circuits. Clearly the domain of Langlands programs and string theories, this penultimate grid does warrant further study.

[7] Continuity-symmetry-harmony define pi and are defined by pi. Pi defined the finite and infinite and are defined by it as well. In our mind, the realities of pi, continuity-symmetry-harmony, are really real and the foundations of the foundations.

[8] Fourier transform. Every formula that involves pi (starting with the Fourier transform) needs to be re-reviewed in light of CSH and the 202 base-2 notations. Pi is everywhere.

[9] Geometries of indeterminacy. There is a look and feel of quantum fluctuations; the mysteries are all within the geometries. It appears that scholars were first foiled by Aristotle (384-321 BC). Five tetrahedrons create a gap that he missed; and for 1800 years his mistake was repeated by scholars. That is worth pondering. Aristotle was so great it took 1800 years to countermand his mistake. And, iIt is still untouchable. That correction was eventually forgotten until in 1926, a little-known MIT mathematician, Dirk Struik, rekindled that scholarship. Struik’s work did not receive much attention until in 2012 when two scholars, Jeffrey Lagarias and Chaunming Zong, lifted it up again. Yet, these two mathematicians were more interested in packing densities. There is no exploration of the meaning of the gap. Subsequently, in May 2022, the five octrahedral-gap was introduced within this website and questions have been asked of many scholars, “What are these gaps all about?”

[10] Our charts, interpretations and prognostications. Simple logic, simple math, and simple geometries render our charts, interpretations and prognostications. It all awaits critical review, so until then, there will be more to come.


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

 Symmetry in QFT and Gravity (video), Hirosi Ooguri (and Nathan Seiber), 2022
  Mathematically, equations building on natural functional dependencies:
….–  Using math in physics: 5. Functional dependence (PDF), E. F. Redish, Univ. Maryland, 2022
•  Quantum Energy Inequalities along stationary worldlines,
Christopher J. FewsterJacob Thompson, 4 Jan 2023
•  ESA Group (PDF): The universe at 380,000 years
•  Pure Natural Inflation, Yasunori Nomura, Taizan Watari, and Masahito Yamazaki,
Berkeley Center for Theoretical Physics, Department of Physics, 2017
The Friedmann–Lemaître–Robertson–Walker (FLRW) Metric
•  A pedagogical explanation for the non-renormalizability of gravity, (PDF), Assaf Shomer, 2008.
Path integrals and Gaussian fixed point. See Assaf Shomer’s on page 7:
“The derivation of the path integral formula in quantum mechanics of a massive particle involves chopping up the quantum evolution into very short time intervals and inserting complete sets of states between them.”
•  Doplicher S, Fredenhagen K, Roberts JE (1995) The quantum structure of spacetime at the Planck scale and quantum fields. Communications in Mathematical Physics 172(1):187–220
•  Scale invariance and conformal symmetries

Personal projections and ruminations. Standard Model of Cosmology and the Standard Model for Particle Physics: Of the 202 notations, the first 64 notations open a map to make the connections.

There is a place for the some of the big bang numbers but not until after the first few seconds.

Thrust in our universe. In September 2017, I wrote about the thrust in our universe. So now, over five years later, it is time to revisit that article and update it as much as possible. The major update would involve our understanding more about the three facets of pi and how each is a Janus-face for the finite and the infinite. How are the functions of continuity-symmetry-harmony abiding?

Major studies. I have written to Robert Langlands, Ed Frenkel, and others within Langlands programs. They have not yet acknowledged the 202 mathematical notations. Why not? It’s just math and logic. There is no philosophy. There are no agendas. It is what it is, simple math.

I have also written to people within string theory. None have acknowledged the 202 notations.

I believe people are naturally incrementalists. It is more comfortable. The Planck units were ostensibly ignored until 2001 and by that time Hawking-Guth-and-family had a hold on the theory about the start of the universe. With Hawking’s death, that hold has become somewhat more relaxed. With the JWST it’s time to open up the discussions. It will include conformal-quantum-and-scalar field theories (CFT, QFT). Although John Wheeler’s sense of simplicity was a good idea, for most of the octogenarians and nonagenarians, this base-2 model of 202 notations is just too simple. It is too obvious. Yet, maybe not. Prior to Frank Wilczek’s three articles about the Planck scale, Planck’s numbers were aloofly small much like Paul Dirac’s were aloofly big.


In 1980 in Paris at the Institut Henri Poincaré, Jean-Pierre Vigier and I made a six-month study of the EPR paradox in light of the work of Alain Aspect in d’Orsay. Instead of infinitesimal spheres, Vigier had suggested that we use the metaphor of dominos falling. That action-at-a-distance is not instantaneous. Infinitesimal spheres within the packing densities suggested by the Planck-or-Stoney-or-ISO numbers, would be instantaneous.

Mathematics and physics of the finite begin here.


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

25 February 2023, Anna Ijjas, NYU
25 February 2023, Katherine Freese, University of Texas, Austin
23 February 2023, Alexander Vilenkin, Tufts University
12 February 2023, John Moffat, Toronto, Perimeter, Waterloo
10 February 2023, Vladislav Yakovlev, Max Planck Institute for Quantum Optics
8 February 2018, Ian Walmsley, Imperial College of London
3 February 2023, Alan Guth, MIT
31 January 2023, Thomas Sumner, Simons Foundation
30 January 2023, Basil Hiley, University of London (UCL)
29 January 2023, Thomas Lin, Quanta Magazine
27 January 2023, Drew Harrell, Washington Post
26 January 2023, Carl Zimmer, New York Times
25 January 2023, James Sethna, Cornell
24 January 2023, Rebecca BoyleQuanta Magazine
23 January 2023, Rohan Naidu, MIT Pappalardo Fellow


There will also be many instant messages to thought leaders about the following key questions:

  1. Is it possible that the first instance of the universe is defined by Planck’s base units?
  2. Is it possible that the first manifestation of those base units is an infinitesimal sphere?
  3. Might the characteristics of pi describe those spheres?
  4. Might the Fourier Transform impart either electromagnetism or gravitation to each sphere?
  5. Is it possible that one sphere manifests per unit of length and time?
  6. Doesn’t that compute to 539 tredecillion spheres per second using Planck units and 4605 tredecillion per second using Stoney Time?
  7. Is it possible that the densities within the earliest notations are on the order of a blackhole or neutron star?
  8. To create some sense of order with the generation of infinitesimal spheres, may we use base-2 notation?
  9. Using base-2 notation, are there 202 base-2 notations from Planck Time to the current time?
  10. Is it significant that at one second the Planck Length multiple is a very close approximation of the distance light travels?
  11. Is it significant that quantum fluctuations are measured within Notation-67? Notation-72 appears to be the limit of our abilities to measure a duration of time.
  12. Would these notations, 1-64, provide 64 possible redefinitions of a point-particle? (And, I would add a vertex.)

8:45 PM · Feb 1, 2023 @DrOsamaSiddique @Harvard_Law @UniofOxford @IGLP_HarvardLaw There is a type of natural law within pi (π) (https://81018.com/starts-2/) that also creates a mathematically-integrated view of the universe where value comes from its continuity-symmetry-harmony. https://81018.com/values/ March 4, 2023

11:14 AM · Jan 31, 2023 @RBReich Everyone should find their creative thing that makes them happy and brings them joy and ask, “Is there a business in there?” Millions have. We call it small business and it enriches the soul and satisfies the heart and inspires the mind. https://smallbusinessschool.org


Participate       You are always invited.


Keys to this page, inflaton

• This page became the homepage during the early morning of February 4, 2023.
• The last update was February 28, 2023.
• This page was initiated on February 3, 2023 at 11:11 AM
• The URL for this file is https://81018.com/inflaton/
• The initial headline for this article: Infinitesimal Spheres as Inflatons
• First byline: Alan Guth’s inflationary theory redefined.


Also reviewed: Could the Higgs boson be the inflaton?, Phys.Lett. B697 (2011) 37-40 (arXiv:1011.4179, Remarks on Higgs Inflation, Michael AtkinsXavier Calmet, 2011

On following the work of Anna Ijjas

Anna Ijjas, Center for Cosmology and Particle Physics, New York University
726 Broadway, New York, NY, 10003

Articles: What if there was no big bang and we live in an ever-cycling universe?, New Scientist, August 2019; Pop Goes the Universe, Anna Ijjas, Paul J Steinhardt, Abraham Loeb, PMID: 28118351, DOI: 10.1038/scientificamerican0217-32
The philosopher of the Big Bounce (PDF), Big Bang or Big Bounce? Avoiding the Multiverse. A Conversation with Anna Ijjas, Jul 3, 2022
Homepage(s): CV, Falling Walls, Google Scholar

Most recent (third) email: 27 February 2023

Dear Prof. Dr. Anna Ijjas:

Is there a generally accepted definition of an inflaton or the inflaton field?

In my search, the closest thing is Wikipedia and we know that can be questioned. I don’t think there has been any consensus among those who use the term. I make reference to your work here: https://81018.com/inflaton/#3z

Thank you.



PS. Is there any access to your 23 January 2023 presentation at the scientific meeting of the Royal Society, Probing the quantum origin of spacetime? Thank you. –BEC

Second email: 23 December 2022 @ 1:01 PM

Dear Prof. Dr. Anna Ijjas:

In preparation for your upcoming January 2023 talk, Probing the quantum origin of spacetime, for the Royal Society Scientific meeting, if you were to assume that those origins could involve the Planck base units and infinitesimal spheres, you might want to look at the potential role of pi (π) again: https://81018.com/csh/ https://810128.com/seen-unseen/

Best wishes, 



First email: 23 December 2022 at 10:01 AM

Dear Prof. Dr. Anna Ijjas:

Lovely website — https://anna-ijjas.com/ — great continuity, symmetry and harmony!

I watched with amazement as you, Paul Steinhardt and Avi Loeb knowingly stepped well out of line to challenge the orthodoxy of the day. There is no question that you are bold, courageous, and tenacious. I say, “Congratulations on a life well lived even though you have just started out!”

You’ve said, “There is no good evidence that our universe even had a beginning….” I think that’s a finite-infinite question. You can be like Max Tegmark (MIT) and desire to throw out the concept of the infinite. I think a simple redefinition is in order.

Pi (π) best captures that tension. And, I would argue that pi is an expression of the character of infinity and perfection. So, instead of collapsing in about 100 billion years, time is redefined, space is redefined, and we can refocus our attention on first principles and the foundations of the foundations: https://81018.com/almost/ https://81018.com/foundations/ https://81018.com/csh/

I should forewarn you that this construction started in a high school!

Best wishes,




Worldviews are too intransigent. A fully-integrated UniverseView is needed.

Concepts key to an Integrative Universe
by Bruce E. Camber A working draft, in process on this late August day

Intransigence becomes hostility. People from every nation and walk of life are not willing to see a broader, more-inclusive context to grasp the meaning-and-value of life. Limited worldviews clash. Temperatures flare and people fight. A better way is an integrative model of the entire universe within which to know ourselves, our world, and a bit more about our universe.

This outline of an integrative universe uses eight concepts:

#1 Infinite qualities — continuity, symmetry and harmony — shape every-and-all finite quantities, each a dynamic equation and the beginning of spacetime.

The finite-infinite relation is best understood by expanding our understanding of pi. We first learn the first simple equation, the circumference-to-diameter ratio. That’s a start, then it builds from there. As noted in the summary of pi, “…It is our oldest, most-used, mathematical constant, and the ultimate basis for all equations, especially those describing a fundamental principle of our universe.”

There are three facets of pi, however, that are not finite or quantitative so we assume (hypothesize and/or hypostatize) these facets define the infinite and the qualitative.

Continuity is our first facet of infinity. It is the very nature of order. Within the finite it looks like a string of numbers and feels like time. Pi qualifies; it’s an equation that has never-ending results that are always the same and always changing.

Symmetry is the second facet of infinity. It looks like geometries and is the very nature of a relation. Within the finite it feels like space. Pi qualifies; it’s a symmetry that generates symmetries. It’s an equation that generates equations.

Harmony is the third facet of infinity. It is the very nature of dynamics; and within the finite, it is always cyclical (periodicity) and experienced as space-time moments. Pi’s numbers, geometries, and equations (Fourier transform and others) are here within an eternal dance and there’s a domain of perfection which may be experienced as a moment of perfection.

Ultimately, pi is the face of both sides of every equation, one is qualitative (infinite) and the other is quantitative (finite). Let those natural, dynamic relations be natural. Let all your relations breathe and come alive. Be open and engage the harmony of the universe.

#2 There are foundations within mathematics to integrate our Universe.

Are Planck Length and Planck Time real? Among the scholars in this area, they seem to say, “Real enough.”
Are their numbers real? Infinitesimally small, we are prone to say that these are symbolically real and “close enough.”
What manifests first? Pi drives the finite-infinite equations; we consider a size/time invariant sphere that is defined by those Planck base units (numbers). We’ve also used Stoney’s numbers. Both sets of numbers are symbolic placeholders until there is a new consensus among scholars, NIST and ISO.

#3 There are 202 base-2 notations that encapsulate the universe.

Our Story. In December 2011, our high school geometry classes unwittingly made a first pass at defining the universe using base-2 notation starting at the Planck base units. We believed the scholars that the Planck units for length and time were the smallest possible units of space and time. Our conjecture was that they would also be the very first units of spacetime.

We decided to explore. To get down that small, we followed a 4D path inspired by Zeno. We divided the edges of a tetrahedron by 2, and then its internal octahedron and four smaller tetrahedrons, and continued dividing by 2. There were just 112 steps within to the Planck scale. We thought it might feel a bit like Alice’s fall into that rabbit hole as in Lewis Carroll’s Wonderland. But, our walk was highly-ordered, systematic, yet most magical. As we went down deeper and deeper within, it was not at all confusing. Even our shrinking in size each step seemed quite natural.

We rebounded back in the classroom by multiplying the Planck Length by 2. Later we would add Planck Time. And then even later, Planck Mass and Planck Charge. It was extraordinary going from that smallest unit out to the edge of the universe to watch the current expansion, all in just 202 base-2 notations. Yes, from the smallest to the largest sizes and from the first moment of time to 13.81+ billion years later, we had encapsulated everything-everywhere-for-all-time.

#4 It’s an answer to big bang cosmology… but it’s just too simple.

Exponentiation. The entire universe, from the smallest possible measurement to the largest in 202 notations, stretches credulity yet it’s 100% mathematical and predictive. All notations are profoundly related and always dynamic. We were so new and naive about it all, we asked questions of the thought leaders of big bang cosmology, Hawking, Ellis, Guth, Steinhardt… and so many others. “What are we doing wrong?” Nobody was willing to guide us, so we placed the time line for the big bang and our big board, side-by -side. We found only a microsecond’s difference with Hawking cosmology. We were beginning to learn about the problems, so when a scholar labeled our model, idiosyncratic, we knew that his judgement was quick and somewhat flippant. There was — and still is — just too much here to consider.

It has taken ten years to begin to understand why change is difficult to engage. First, there is so, so much vested in the Hawking model. It has stood strong for many years. It began building in 1973 when Hawking and Ellis wrote a thesis, The Large Scale Structure of Space-Time. Every new citation, each new book and movie and video, making reference to Hawking’s big bang cosmology, created a muscular defense around Hawking and his model. Yet, that core belief system could not answer a growing number of questions. It had to choose to ignore others. Second, no new model came along. Still, eventually some of our best scholars broke rank and called more stridently for a new paradigm.

We were late to that party and we had no scholarly credentials, yet our emergent model had clear, simple, and compelling mathematics and logic. Nobody argued that.

#5 The first 64 notations are the foundations.

Those first 64 notations. Although impossibly small, here is a huge infinitesimal domain that is well below the current thresholds of measurement. Unwittingly, all 64 notations, albeit a most-speculative domain, had never been considered. The more we read and studied about the mathematics of Langlands programs, those earliest notations seemed like a natural home. It also seemed like string and M-theory could benefit. Then we began learning about SUSY, and studies like causal set theory (CST), loop quantum gravity (LQG), spectral standard model (SSM), and others. All could benefit. Then came all the hypothetical particles and what we called the Moonshine outliers. They all needed a place to begin working with the two Standard Models. Most naively we raised our hand, “Over here!” Yet, I would guess that we were too simple, too basic, and our grasp so superficial, nobody dared to get too close. We could readily taint their work! I understood… and understand even today.

Consider the obvious. These 64 notations have dimensionality. The conjectured infinitesimal spheres are not “one-dimensional space entities or membranes of higher-dimensional extensions existing in higher-dimensional spaces.” We might say as above, so below, considering that we started with numbers and basic geometries and carry it forward throughout the entire universe.

A new geometry. In May 2022, our simple clear-plastic models opened a new door. We had plenty of images of a five-tetrahedral gap and that work was well-known within small circles of scholars. With various five-tetrahedral models on my desk for several years, one day I asked myself, “Could there be a five-octahedral gap?” In minutes the first models were made; and within the month, we had our first pass at an explanation. A most-challenging composite is a five-tetrahedral gap on the top and bottom with the five octahedral gap in the middle. In June 2022 we began inviting scholars within pure geometry to help interpret where these gaps fit within the larger scholarly models of the universe. My simple thought was that these basic geometries, especially the three with basic gaps — tetrahedrons, octahedrons, and icosahedrons — could be part of the transition from Standard Model of Particle Physics to a new, different, and very-special science of the infinitesimal. The earliest infinitesimal architecture, we conjectured from Notation-0 to Notation-64, would give us that smooth-most-perfect start of the universe and then open a domain, Notations 65-to-67, for quantum fluctuations (our 2017 speculations).

#6 Proposed: Geometries of Quantum Fluctuations

Very few talk about a geometry of quantum fluctuations. When those words were placed in quotes within an online search, the only references that came up in September 2021 were to this website. Yet, when students made tetrahedrons, octahedrons and icosahedrons with those clear plastic models, they naturally dubbed it squishy geometry (also: https://81018.com/squishy/) and quantum geometry.

When pressed on the possible application of these gaps, our scholars seem to avoid those discussions. We can avoid it no longer. It is time to engage the gaps and all their implications for mathematics, physics, chemistry and biology (i.e. synapses).

#7 Pi, One Sphere Per Unit of Planck Time, Cubic Close Packing…

The expanding definition of pi as the actual bridge between the dimensionless constants of the infinite and all finite quantities is a key. Pi and spheres go hand and glove. The first sphere emerges, then one infinitesimal sphere per unit of Planck time. In the first second, we are out to Notation-143 and no less than 539 tredecillion (1042) infinitesimal spheres. In the first year within Notation 169, we would multiply 539 tredecillion by 31,556,952 (seconds per year). Exponential notation has taken over, yet there is a linearity deep within each notation.

For better or worse, the universe has begun.

#8 Next steps: Building consensus

Where do we go from here? Mathematicians and physicists are opening pathways to this domain. It is the domain of finite-infinite transformations where there just happens to be a fair amount of activity. From the esoteric to the basics, magazines like Quanta explore the edges of knowledge. New people are introduced everyday. People like Philipp Dumitrescu call into question the very nature of time. Mary Gaillard, a particle theorist at University of California – Berkeley, asks about the very nature of mass. Peter Scholze pushes forward with his perfectoids in Langlands programs. Although those who define infinity in other ways may disagree, it all seems to boil down to the finite-infinite relation. Many mathematicians are attempting to get beyond David Hilbert and Kurt Gödel and the limitations created by their logic that never entertained the first 64 notations and the perfected states within continuity, symmetry and harmony.


Let’s get beyond our worldviews.

Let us look beyond our little worldviews and consider the universe. In the process of exploring our universe, it was gratifying to find that the International Astronomical Union (IAU) and the United Nations promulgating Universe Awareness, a group that got started in 2004 through the initial work of George Kildare Miley, an Irish-Dutch astronomer and professor at Leiden University’s Observatory. Miley was the Director from 1996 to 2003. Once this page has been gone through several edits, I will introduced these folks to this work and references. Already oriented to a view of the universe, the question is, “Will they be open to the 202 base-2 notations that encapsulate this ever-expanding universe?”

There are many living scholars who have had vision and courage who have helped us begin to break out of our own limited worldviews, people like Frank Wilczek, Robert Langlands, George Ellis, Edward Witten, Helen Quinn, Paul Steinhardt, Sylvester Gates, Alain Connes, and Salvatore Torquato. Of course, there have been many others.

So, as you may well imagine, there will be many more scholars to come who will lead us. -BEC


Endnotes & Footnotes
These Endnotes are placeholders. I anticipate feedback that will open the discussion. Footnotes may be added. -BEC

  1. Infinite qualities — continuity, symmetry and harmony — shape all
    finite quantities. All dynamic equations, here is the beginning of spacetime

    The keys: Qualitative-Quantitative. Continuity, symmetry and harmony are the qualitative; it follows that real numbers that are generated by dimensionless constants constitute the quantitative. So, students, without fully grasping the most-sophisticated work of Hawking, Hilbert, Gödel and so many others over the decades, can understand the outside parameters defined by 202 base-2 notations, then become increasingly sophisticated as they add more and more textures to it. So, we will tarry on unless, of course, we hit a wall where the feedback is deafening and complete.
  2. Foundations for the mathematics to integrate our Universe
    We begin with real numbers. These are the best numbers we have today. They could readily be refined, yet the conceptual boundaries defined by base-2 will be little changed. Notwithstanding, we hold that no page within this website is ever finished. Each can be improved.
  3. The 202 base-2 notations that encapsulate the universe
    Our chart emerged over a five-year period. It took us that long to believe it hadn’t been done and to engage the fullness of it. Beginning in July 2016, the chart stimulated the development of this website for research and another for our secondary schools. That is was all highly-ordered and systematic was surprising and reinforced our basic geometries.
  4. An Answer to Big Bang Cosmology… It’s just too simple and expansive.
    It can’t go on forever. Aristotle had an 1800 year old mistake. We’re less than 100 years into this mistake (Lemaître, 1932; Hawking, 1990). We can begin to clean it up in our lifetime.
     The Large Scale Structure of Space-Time (PDF), S. Hawking and G. EllisCambridge,1973
  5. The First 64 Notations as the Foundations for Everything
    So many possibilities open up, an empowering creativity could become contagious. Ethics could begin to break out all over.
  6. Emergent Geometries of Quantum Fluctuations
    When we know there is far more room to expand, we will. Today we have an index of a bit more than a million total words but collectively use less than 170,000 words, and personally limit ourselves to somewhere around 25,000 words. According to Simon Plouffe, there are 215,000,000 dimensionless constants; to grasp that level of subtlety will require new words and new studies. Entirely new fields of study will emerge.
  7. Pi, One Sphere Per Unit of Planck Time, then Cubic Close Packing…
    A re-engagement with pi and an exponential universe such that every expression understood today will become part of standard curriculum. We know from our teaching and testing with 6th grade students that they can readily grasp these concepts and begin using them immediately.
  8. Next steps: Building consensus
    New leadership worldwide could well be empowered. We already have witnessed how younger scholars have been empowered. Getting the attention of today’s leading thinkers is more difficult. However, people making breakthroughs like Peter Scholze or Philipp Dumitrescu may be more open to simplicity. Then, some within their emeritus status, like Mary Gaillard (Berkeley), may become incrementally bolder and not be so quick to judge the new and the simple.
    Dynamical topological phase realized in a trapped-ion quantum simulator, Philipp T. Dumitrescu, Justin G. Bohnet, John P. Gaebler, Aaron Hankin, David Hayes, Ajesh Kumar, Brian Neyenhuis, Romain Vasseur & Andrew C. Potter, Nature, V.607, pp.463–467, July 20,2022
    International Astronomical Union (IAU) and the United Nations promulgate Universe Awareness, a group that got started in 2004 through the initial work of George Kildare Miley, an Irish-Dutch astronomer and professor at Leiden University‘s Observatory (Director, 1996 to 2003).


References & Resources
A few of the key related works that are studied but not within an endnote or footnote, are added here.

ArXiv: Dark Photon Stars: Formation and Role as Dark Matter Substructure, March 2022 with references to Witten, Wilczek, Kolb, Dimopoulos, Preskill, Fairbairn, Hogan (Carl J.), Garcia-Garcia, and others
Alain Connes, Noncommutativity and Physics: A non-technical review, July 25, 2022 (PDF)
George Ellis, Emergence of time, 2019 with Barbara Drossel and The physics of infinity, Nature Physics, V. 14, Issue 8, p.770-772, 2018
Sylvester Gates, Supersymmetry and Representation Theory in Low Dimensions, Dec. 2020
Robert Langlands, Langlands Program, Trace Formulas, and their GeometrizationEdward Frenkel, 2014
Helen Quinn, BOSE NAS, 20218
Scientific American: The Universe’s Unseen Dimensions, The visible universe could lie on a membrane floating within a higher-dimensional space, (PDF), Georgi Dvali, Nima Arkani-Hamed and Savas Dimopoulos, 20028
Paul Steinhardt
Salvatore Torquato
Frank Wilczek
Edward Witten


There will always be emails to our scholars with questions about their work.

Craig J. Hogan, University of Chicago, August 4, 2022 at 2:00 PM
Jürgen Jost, Max Planck Institute for Mathematics, Leipzig, August 4, 2022 at 11:18 AM
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
Steve J. Carlip, UC-Davis, July 31, 2022
George Ellis, Cape Town, South Africa on July 27, 2022 at 5:01 PM
Helen Quinn, Stanford, on July 27, 2022 at 11:118 AM
Possible: Frank Wilczek, MIT / Paul Steinhardt, Princeton / Sylvester Gates, Brown
Alain Connes, IHES, Paris / Salvatore Torquato, Princeton / Edward Witten, IAS
Robert Langlands, IAS


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

UNESCO, International Banks, Vladimir Putin, Ukraine, Pope, China,


You are always invited to lead a program, Each One – Teach Two.


Keys to this page, as-above-so-below

• This page became a homepage on July 28, 2022.
• The prior homepage is https://81018.com/starting-point/
• The last update was Friday August 26, 2022.
• This page was initiated on July 12, 2022.
• The URL for this file is https://81018.com/as-above-so-below/
• Current headline: Eight Concepts toward an Integrative Universe
• Earlier headlines for this article: The Mathematically-Integrated View of the Universe
• Current byline: Worldviews are too intransigent. A fully-integrated UniverseView is needed.
Other bylines: A good revolution in our time: Old Worldviews to New UniverseView!
The geometry of quantum fluctuationsThe First 64 Notations Out of 202 Are Key
Essential Key: Three Basic Geometries of Quantum Fluctuations
All of us are getting too hostile and intransigent. Let’s embrace the universe.
Let the next revolution begin! Independence from absolute time!











Re-examine Big Bang Enigmas



Does everything start simple before it becomes complex?

In order to begin to explore a natural, highly-integrated mathematical view of the universe, it seems that two of our major conceptual orientations need to be set aside: (1) absolute space and time from Isaac Newton (1643-1727) and (2) the infinitely-hot start of the universe, ostensibly big bang cosmology, as represented by Stephen Hawking (1942-2018).

Our alternative is a natural inflation defined from Planck’s base units to the age-and-size of the universe in 202 base-2 notations or doublings that are always active and are progressively building on each other. Our definitions for space and time are Max Planck’s formulas 1 from 1899 whereby both are quantized, discrete and finite.


Arguments about finite space and time and the finite-infinite relation are part of the earliest recordings of our history. And, those arguments continue today without abatement. Possible answers are still debated with strong opinions on the opposing sides.2

We backed into our understanding slowly by adopting three very different concepts and orientations and, if true, these three may begin to open a new door to explore our universe in ways heretofore undocumented.

The Infinitesimally Small: The Planck base units. We have found no other references to a cosmology whereby the universe is fundamentally defined by applying base-2 exponentiation or doublings to the Planck base units of time, length, mass and charge. These units become the standard units of measurement to define 202 base-2 notations that extend to the age and the size, and the mass and the charge of the universe.

To lift up or debunk these 202 notations is the goal of this project.

Our most naive application of that concept was when we started in December 2011 as a group of mathematics (geometry) teachers and students in a New Orleans high school. Though similar to the 1957 work of Kees Boeke using base-10 (“…to scale of the universe in 40 jumps“), our 2011 group started with a geometry. We divided-by-2 the edges of the tetrahedron and octahedron to discover what we initially thought was a Zeno-like progression. It isn’t. There are limits!

Physical limits. We had discovered those limitations that Max Planck defined in 1899, particularly what is now known as Planck Length and Planck Time. In just 45 divisions we were among the size of particles within the atom. In another 67, we were among the two smallest Planck numbers. Then, to be consistent, we started with the Planck units and simply multiplied-by-2 and in 112 steps we were back to the approximate size of our classroom objects. In another 90 steps we were at the approximate size and age of the universe. We discovered that it took just 202 base-2 doublings or notations 3 to encapsulate the universe. It defined a natural inflation. And, it appears that it could provide a base platform for a grand unified theory of mathematics.

That is enough, yet this nascent model also encouraged questions about the finite-infinite relation and the very nature of infinity.

Early thoughts about cosmology

The Very Large Scale. Our initial introduction to these numbers was just with the Planck Length. We assumed that the first 64+ notations were just prior to the big bang and were defined by the Planck Epoch and the Grand Unification Epoch. The problem quickly became clear that the size, mass, and charge within our nascent model could not support a “big bang.” And there was no reason to think these processes required “infinitely hot.” We obviously needed more data. In 2014 we added a Planck Time progression alongside Planck Length; and then in 2015, we charted Planck Mass and Planck Charge progressions. These numbers described a natural inflation of the universe and our analysis and comparison with the big bang epochs 4 defied the logic of big bang cosmology.

We were challenged, “How do we reconcile these two vastly different models?” We rather slowly realized that there was no reconciliation, so we began to review the logic of our mathematics. We wrote for the advice of those scholars who had made this area of study their life’s work.

At that time, nobody analyzed our work. Nobody engaged its logic. Of course, it is naive; so here, we bring our work forward as logically and consistently as we can and request help from our scholars and scientists to interpret the data. Because we have viewed Max Planck’s formulas in rather unique ways, it should be straightforward to tell us where and how we have strayed from pure logic and math.

Three concepts, three questions:

  1. Basic ConstructDoes simple math-and-logic work consistently everywhere for all times?
    Science believes our universe is homogeneous and isotropic but can not tell you why that is so. Doesn’t this simple math and natural inflation based on the progressive geometries of the tetrahedron and octahedron provide a construct or framework for an initial answer? Does the simple multiplying and dividing-by-2 provide another answer? Though we concluded that these two progressions provided new insights to old questions, we did not want to conclude too-too much so we have always sought the feedback of experts.
    See footnotes 1 through 4.
  2. Basic Shape: What could possibly be the building block at the Planck scale?
    We decided that the most-simple, ubiquitous-but-mysterious building block is the sphere.5 Pi is deep in the heart of most of Planck equations and definitions of dimensionless constants. As a result, we hypothesized that the first notation, perhaps the first, second and third notations, results in an endless generation of spheres. This is the face of the four Planck base units, plus light and the other dimensionless constants involved in the definition of those Planck units. Perhaps not a crystalline clear picture of what is happening at this finite-infinite transformation, it is the best we can do today. Some have call these spheres, “Planck spheres.” That seems appropriate so we have adopted that nomenclature. It seems that these planckspheres do not come “out of nothing” but out of that which we do not define as finite. It could be part of a definition of a finite-infinite bridge. It may also be how the infinite is expressed within the finite without becoming finite.
  3. Basic DynamicsWhat is the the most fundamental doubling mechanism?
    Cubic-close packing 6 is an inherent doubling function whereby geometric structures, particularly the tetrahedron and octahedron, emerge. The thrust 7 to inflate this doubling may well come from Planck Charge, light, and the never-ending, never-repeating numbers of pi and the dimensionless constants. It is instructive to follow any one of the numbers on our horizontally-scrolled chart where the logic flow can be analyzed. 8

Basic functions at the Planck scale

These rather different, simple concepts are possibly enough to start a dialogue. We backed into this model. We claim no genius or depth of knowledge regarding the issues involved. There are open questions that are raised, but at least these first three steps along this path have been presented and our standing request of our readers is to tell us where and how our logic fails and that invitation is open to everyone including you.

Our Challenge: Research baseline questions

  • Who has the best insights about the very nature of the Planck units? We are exploring the work of Paul Steinhardt (ArXiv), Ed WittenAndrei LindeAndreas Albrecht, and others.
  • What is the role of quantum physics in cosmology…isotropy? …homogeneityDAMTP
  • Does space-and-time give rise to quantum effects or is space-time a quantum effect?
  • Do the Planck units have a quantum origin or do they originate from light, the dimensionless constants, and each other?
  • Do the 202 base-2 doublings from Planck base units to the age and size of the universe constitute the infrastructure for a real cosmology?
  • How do quantum effects play a key role in controlling the rate-and-end of inflation?
  • What about all the successes of general relativity?
  • How do you explain the stages meticulously described by Einstein gravity (and in agreement with observations) when the universe is not inflating?”

Endnotes, Footnotes, References & Resources:

1 Max Planck’s formulas. Max Planck’s simple formula for light is part of his pre-definition of Planck Time. I don’t think anybody would dispute its basic logic, but its meaning is not straightforward. Has anybody truly answered the question, “What is light?” Of course, the first 93 doublings are below the visible spectrum (Notations 94 and 95). Notwithstanding, is there an inherent quality of light that presumably remains the same throughout all 202 notations? Certainly the electromagnetic spectrum provides a sense of the characteristics of light from gamma waves, to x-rays to ultraviolent on the infinitesimal side and then from infrared to microwave to radio waves within the human-scale and large-scale side of the spectrum. Yet, there is so much more going on here.

To date, our questions are also focused on the nature of the never-ending, never-repeating dimensionless constants. Do these define a bridge between the finite and infinite?

A key idea. Consider the nature of time. It seems that our Universe Clock, in light of this model, suggests that every second is active and continues to effect the content, the quality, and the substance of this universe. That time doesn’t stand still. It is always changing and it is always the the Now.

2 Strong opinions on opposing sides. We try to avoid religious and theological discussions per se by redefining the very nature of the infinite as continuity, symmetry, and harmony as evidenced with those words highlighted at the top of every homepage. Though several of our homepages extend this insight, perhaps it would be helpful if people could just lighten up a little.

3 The 202 doublings enclose a trifecta to define the universe: (1) encapsulate all the space and time of the universe, (2) define a natural inflation, and (3) provide a base platform for a grand unified theory of mathematics. The result is that space and time are finite, the universe is totally interconnected and integrated, and all mathematics is likewise. The reasons for the homogeneity and isotropy of the universe become self-evident. Our sense of time becomes the Now.

4 Big bang cosmology versus the Quiet Expansion: There are seventeen epochs defined by big bang cosmology. Each is superficially compared to the notations of our Quiet Expansion, also known as a natural inflation. Often just one of the faces of each big bang epoch is used to position the Quiet Expansion alongside it. Eventually all four faces will be used and perhaps the known failures of big bang cosmology can be addressed in new ways.

5 The Sphere: Within this infinitesimally small domain, the sphere becomes known as the Plancksphere and it is being extruded from the finite-infinite relation as a constant stream of spheres, providing no less than 64 doublings up into the domain of particle physics.

It would seem these spheres are the basis of string theoryClumping and stacking, defining space and time and mass and charge, then come the geometries and infinitesimal form, structure, relations, and systems. This is emergence.

6 Doublings: We were in search of the gritty visualization that is not given within descriptive words like base-2 exponential notation, Euler’s perfect number, fractal division and/or bifurcation theory. We all need a visual reference whereby physical processes demonstrate the doubling phenomena that is the natural inflation of this universe. We found it in 2016 within a visualization of cannonball stacking by none other than Johannes Kepler.

Here is our first reference to it: https://81018.com/number/#Kepler

7 Thrust: I have always told myself, “You start small and build on it day by day and finally it progresses and you have something.” Nothing just explodes into beingness. Though an older article now, the focus on thrust will be continued throughout this study.

8 Logic: The numbers within our charts stretch our imaginations; there is no question about that. Yet, this stretching feels productive, like it might lead somewhere special. Our first article is here: https://81018.com/planck_universe/

Our large-scale, notation by notation, effort has been opened up here: https://81018.com/1-202/

Challenge us. Coach us. We need all the help we can get.

Which concept is strongest? Which is weakest?




Today we welcome scholars and visitors from the following countries:

Australia, Brazil, Canada, China, Congo-Kinsasha, Cambodia, Denmark, Estonia, France, Hong Kong, Hungary, India, Malta, Mongolia, Netherlands, Norway, Poland, Russia, Slovaki, South Africa, Switzerland, and the United Kingdom.

Fibonacci and the Golden Ratio

A few references to Fibonacci numbers, 1,1,2,3,5,8,13,21,34,55,89… within this website:

October 18, 2021 11:18 am, Smallest to Largest, https://81018.com/smallest-largest/

What do any of us really know? Are things always simple before becoming complex? It seems to be true, all except around those issues coming out of the big bang theory as promoted by HawkingGuth, and many others. Now, more recently Princeton’s Paul Steinhardt and his coterie have been getting some traction with their quest for a new kind of matter. Dan Shechtman (wiki) before him looked at the small-scale and got his Nobel prize in Chemistry in 2011 for his discovery of quasicrystals, the imperfect geometries based on five tetrahedrons sharing a common edge and lacking a translational symmetry. In our book, it is confined by notation and its respective Fibonacci sequences. Of course, outside of the 202 notations, that statement is meaningless or gobbledegook. The bottomline is arrogance impedes ideas and creativity. Remember Fairbairn‘s comment about “novel approaches.”

Thursday, June 10, 2021: UniverseViews Empower, Worldviews Confine https://81018.com/empower/#Fibonacci

Scale Invariant Sphere Dynamics. From the infinitesimal sphere to the movement of galaxies, pi and phi (circles and Fibonacci sequences), are fundamental dynamics within everything. Pi crosses notations; phi builds within a given notation. This model not only uses numbers and geometries, it uses pi, phi, prime numbers, values, and more where big bang cosmology is based on singularities that do not account for dimensionless constants like pi. The mathematics of materialism generally disregards other systems of engagement. How is it that pi is scale invariant? What are the deep dynamics of spheres? We are trying to learn… we are in the earliest stages of our studies of the Fourier transforms and integral transforms. Of course, we’d welcome any-and-all help to understand these disciplines as well as Steven Strogatz does.

January 14, 2021, Today’s leaders have created many problems. https://81018.com/precis/#Fibonacci

Aristotle’s Mistake: In 2015, my life changed because I came upon a reference to an article titled, Mysteries in Packing Regular Tetrahedra.” That article amazed me. It took over 1800 years to catch Aristotle’s mistake. Yet, along that way, Averroës (Abu al-Walid Mohammad ibn Ahmad al Rushd (1126–1198), Leonardo of Pisa (Fibonacci) (c. 1228), Roger Bacon (c. 1214–1294), and Thomas Aquinas (c. 1225–1274) were among the greats of their time who reinforced his mistake. As a result, none of them would ever know about a most fundamental geometric gap. First, inferred by Johannes Müller von Königsberg (1436–1476), then documented in 1480 by Paul of Middelburg, a professor of astrology in Padua, the discussion was re-birthed by Dirk Struik (MIT) in 1926 while studying in Rome. Most recently, in December 2012, Jeffrey C. Lagarias and Chuanming Zong [also see, May 2020] brought it to life again. Yet, none of these people in their time contemplating that gap ever thought that it just might opened a path to quantum fluctuations, indeterminacy, and imperfection. Such a highly-speculative statement would appear to most physicists today to be uninformed. I do not believe that I would be overplaying my hand to say that this gap makes us all equally human. It is the beginnings of all our imperfections.

Monday, October 20, 2020, Change the Metaphor – Rewrite the History https://81018.com/history/

What could be more basic than waves, particles and fluctuations? How do we relate algebraic geometries (Grothendieck‘s scheme theory), Euclidean geometriesprojective geometrycategory theoryMandelbrot setJulia setMöbius transformationsKleinian groupS-matrix theoryunitarity equationsHermitian analyticityGolden ratio (Phi), the Fibonacci sequencefluctuation theoryratio analysispicubic-close packing of equal spheresring theory, and lattice generation? Out of that group we settled on pi and cubic close-packing of equal spheres at the Planck scale to begin.

Friday, August 23, 2019, We’ve been “top down” too long, https://81018.com/bottom-up/#9f

The first ten notations. There is so much to learn and so little time (our life is short). I’ll be working on this 1-202 chart until I die. Notwithstanding, the Buckingham π theorem is part of our understanding of homogeneity and isotropy; it’s the heart of dimensional analysis. The Buckingham π theorem takes π to the next level along with the pure numbers, i, e, and φ. It is a thrust in the intellectual direction that ratios and equations are real and the things of space and time are derivative.

So, yes, we will continue our studies of those pure numbers, i, e, and φ and  de Moivre numbers, as part of our work on the theory of group characters, and the discrete Fourier transform seeking to justify our belief that all these expressions of mathematics are inherent and active at the Planck scale.

Eventually we want to discuss how these 64 notations open up discussions of concepts within algebraic geometries, projective geometry, Euclidean geometries, category theory, Mandelbrot sets, Julia sets, Möbius transformations, Kleinian groups, S-matrix theory, unitarity, bootstrapping, Hermitian analyticity, the Golden ratio (Phi), the Fibonacci sequence, fluctuation theory, ratio analysis, and ring theory.

May 5, 2012, The original Wikipedia article as written in March 2012, https://81018.com/2012/05/05/wikipedia/#Fibonacci

Qisheng Lin and John D. Corbett, “New Building Blocks…” “According to higher dimensional projection methods, a series of cubic ACs (approximant crystals) exist with orders (q/p) denoted by any two consecutive Fibonacci numbers, i.e., q/p = 1/1, 2/1, 3/2, 5/3 … F n+1/F n (1).” http://www.pnas.org/content/103/37/13589.full


On November 4, 2019 distinguished astrophysicist, Joseph Silk, and his two colleagues, Eleonora Di Valentino and Alessandro Melchiorri (corresponding author), published Planck evidence for a closed Universe and a possible crisis for cosmology. It is the result of their ongoing analysis of the cosmic microwave background radiation (CMBR), mapped by the European Space Agency’s (ESA) Planck satellite. The Silk-diValentino-Melchiorri (SdVM) team looked at the data and concluded, “The Universe May Be A Closed System.” They said:

Planck cosmic microwave background spectra now preferring a positive curvature at more than the 99% confidence level. Here, we further investigate the evidence for a closed Universe from Planck, showing that positive curvature naturally explains the anomalous lensing amplitude, and demonstrating that it also removes a well-known tension in the Planck [ESA] dataset concerning the values of cosmological parameters derived at different angular scales. arXiv:1911.02087  (my emphasis)

Those keywords, a closed universe, were difficult to grasp. A flurry of articles quickly followed, however, nobody else would be analyzing that article in light of our emerging, rather simple model of the universe. Introduced in December 2011, our base-2 exponential model actually does mathematically encapsulate this entire universe within just 202 notations.

Newton and Leibniz did not have the advantage of Leonhard Euler’s work in the 1740s when he first introduced exponentiation to our understanding of the functions of the universe. Nor did they have the advantage of Max Planck’s work in 1899 when he made his calculations that became known as the Planck base units.

My simple hope is that the SdVM observations and conclusions create a real debate that heats up, and eventually that debate becomes a definitive rip in the fabric of absolute space and time. Can we grasp and define the differences between (1) an interval of time, (2) the arrow of time, (3).the flow of time, and (4) the very nature of time?

As a result of this article, we will begin a bit more formal analysis of CMBR. Also, just now, I sent a note to a friend saying, “I believe that most of the confusion within astrophysics today is our understanding of space and time. Those 202 notations are not recognized or understood. People do not know from which notation they are measuring values. We’ll help them discern it, by giving them the speed of light at each notation perhaps within a femtometer so when they start to separate out all the redshift more accurately by gauging it against that particular notation’s speed of light (given that most notations have unique light signatures — line 10 in the chart). Yes, yes, yes I am vaguely aware of the far-reaching implications and simplifications of our universe.

CMB Anisotropies and the Determination of Cosmological Parameters, Efstathiou, G (ArXiv)

Quintessence and Cosmic Acceleration, Steinhardt, Paul J. (PDF)

Exotica in the universe — dark matter, early black hole seeding, the first stars, cosmic microwave background radiation) CMBR, Priyamvada Natarajan

Measuring the Inflaton Coupling in the CMB, Marco Drewes, UC Louvain, Origins – Baryon Asymmetry of the Universe (BAU) (2nd, Summary, PDF) ArXiv (62)

PS. What’s in a name? Several have commented that my name seems to inculcate physics. Since 1965, I often use my initials, BEC, and did so especially in my undergraduate days. Of course, some have associated it with the Bose-Einstein Condensate. Of course within that compression of BEC, all the vowels are the first to be squeezed out and that camber no lift and becomes CMBR.

A possible rapprochement with the naïvetés and simplicity of our youth

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Pages: Blackhole.| C.|.Empower | Hope.|.Mistakes.|.PI (π).|.Redefine.|.Singularity | Sphere. |.TOE.|.Up

Smallest to Largest
by Bruce E. Camber

Durham, UK (2021): Graduate students of the Institute for Particle Physics Phenomenology (IPPP Durham University) were substituting for Sir Peter Higgs. The question (above) for their audience is a major unsolved mystery.

At the IPPP 23rd International Conference from the Planck Scale to Electroweak Scale (June 2021), Prof. Dr. Malcolm Fairbairn of Kings College London presented “Dark Matter Hunting in 2021 – How do you look for something when you don’t know what it is?” His presentation raises key issues about the unsolved mysteries that have surrounded dark matter. On page 70, he challenges us all, “We are well into an era of using novel approaches to learn more about dark matter.”[1]

There were another 20 scholars with similar presentations; each focused on an open question within our smallest-scale universe. Those lectures need close scrutiny (see the endnotes below). The domain from the Planck scale to the Electroweak scale is filled with mystery and unanswered questions.

Princeton physicist and 2019 Nobel laureate James Peebles lifts up such questions as penultimates in physics and cosmology today.

All students are our sacred trust and treasure.

Thinking, learning, and seeing beyond. Students need to be challenged in every way. Yet, we also need to listen carefully to the ways they challenge us. Some of my most inspiring encounters have come from even younger students. In December 2011 and within all the naïvetés of a high school in the USA, we started exploring the infinitesimal. We had discovered a geometric and mathematical path through a tetrahedral-octahedral honeycomb.[2] It dropped down 112 base-2 steps into the Planck-scale. We also went out the 90 base-2 steps to the age-and-size of the universe. That is a total of 202 base-2 steps from the smallest to the largest. Yet, the first 64 base-2 steps stopped us cold. What could be so small? There are plenty of guesses, but nobody knew. And, we didn’t know what we didn’t know.[3]

We had a novel construct. By observing, thinking, and trying hard to be logical, over time we came to several radical conclusions: “That’s a quiet big bang. It’s a natural inflation. Perfectly smooth, it’s the basis for homogeneity-isotropy. Could it be dark matter and dark energy?”[4]

To say the least, we got a bit carried away! And, that is a problem. Nobody would touch it except the kids. [5]

What’s the smallest thing in the universe?

Our students’ response is quick, “An infinitesimal sphere, a little like Lemaître’s primordial atom.” Pushing back, “So what?” The retort is quick. “It’s defined by the Planck base units and there is one Planck sphere per Planck unit of time.” We had worked on the simple math so I asked,”What does that mean?” The answer is still baffling: “One Planck sphere per Planck unit of time computes to 539 tredecillion primordial spheres per second.” That’s a lot of spheres to track. We had our base-2 notation, a map encapsulating everything, everywhere for all time within 202 notations. It was a transformative surprise; it took us over two years to begin to accept the idea that is was a first. And as you’d expect, we were profoundly challenged by the multiplicity of issues it opens up.[6]

As crazy as it all seemed, we weren’t going to duck out. We learned to accept the idiosyncratic and to ask the experts for help. We continued on, but it could no longer be an extracurricular activity for our brightest seniors. They were going on to college and these concepts created too much tension. When I moved out of town, the lights on the project were turned down, yet I’ve continued to look for facts and to make some guesses… it’s a slowly-expanding history. [7]

Asked about the 539 tredecillion infinitesimal spheres per second, a few years before, we had examined questions about thrust and continue to pursue it focused on the infinitesimal thrust of numbers coming through pi and other dimensionless constants like light and Planck Charge.[8]

If Planck’s base units are symbolically the smallest, what could be the largest?

Discovering limits and a range. We became even more controversial. Built into our simple equations is an active finite-infinite relation. We say that only because these continuity equations are never-ending and never-repeating. Like pi (and with pi), all continue to expand.

Those numbers should be the most-dynamic and the largest numbers within each of the general categories within Notation-202 of our horizontal chart. [9]

By staying deep within pi and an ideal sphere, nothing finite is found. There is a sense of continuity, symmetry, and harmony. These simple perfections manifest within the finite yet are not themselves finite. These three are facets of the infinite. Historically the infinite has been defined in numerous other ways. Most are personal matters. We avoid such language and choose only to defer to continuities which manifest as order and is experienced as time, symmetries which manifest as relations and are experienced as space, and harmonies which manifest as dynamics and are experienced as space-time moments. Although still a series of abstractions, there are boundaries and boundary conditions, logic and structure, and the inherent-yet-quite-derivative mathematics and geometries.[10]

Reviews of the model anticipating our ten-year anniversary

Models of the Universe. The original chart followed the Planck Length (December 2011). Then we added Planck Time (2013-2014). Quite naturally we began adding Planck Mass and Planck Charge to our chart in 2015 and 2016. That’s when the extremely-hot Planck Temperature became an extremely-big challenge.

With time/length and mass/charge seemingly the Janus-face of each other, a cold-start seemed more logical than a truly off-the-charts hot start. The four basic Planck units were doubling. It would be truly idiotic if we projected that the temperature doubled with the other facets of the Planck base units. We decided to put that mystery up beyond the current time and we divided it by 2 to give us the results (numbers) in our very first horizontally-scrolled chart.

Review. Anticipating the tenth anniversary of our studies (yes, we formally started on December 19, 2011), it was a good time to re-engage all 1000+ numbers in that chart. For some unknown reason, the inverse square law forced its way into this ideation, “What if you start with Planck Temperature and with each notation the temperature is cut in half? Does that make any sense at all?”

“Be open. Think about it. Be open; be open.”

To get a sense of those numbers I began a new chart that actually begins with Planck Temperature at Notation-0. Instead of multiplying by 2, divide by 2. Though a bit more commensurate with Hawking-style big-bang thinking, it is still entirely idiosyncratic. The approach to absolute zero is too quick. So now we will place the approximate temperature of deep space within Notation-202 and attempt to discern how mathematically we get from Notation-0 to Notation-202. We are currently contemplating the working relation between all the prime-number bases keeping in mind that base-10 has 64-to-65 notations. How many notations using base-3? …base-5? …base-7 …base-11? We’ll do the numbers like we did with base-10.

The thought process went something like this: “Might the thrust required to generate the first infinitesimal sphere to create the first space/time and matter/energy moment require extreme temperature? Perhaps. Is it worth looking at it? Yes. Might the temperature drop by a half with each or the earliest notations with that very small mass? Maybe. Within the first second (Notation-143) as the number of spheres are increasing to 539 tredecillion infinitesimal spheres per second, there just may be some relatively new mathematics perhaps related to laser temperatures that may well be logical. Let’s explore it. It just might work.”

Can we be re-examining the four laws of thermodynamics (0,1,2,3)? Can we grasp the thermodynamics of laser physics? …its spontaneous fluorescence?  Might the inverse square law apply on the first notation? Might there be several different progressions down to the current, average temperature of the universe?


For many, it is all too simplistic. And, perhaps it is. Yet, just maybe it is the simplicity that was within John Wheeler’s dreams and the correlation between reality and numbers that E.P. Wigner so loved. It seems as if this idiosyncratic path is about to become quite a bit more idiosyncratic![11] Thank you.

Editor’s notes: The most dynamic part of this page follows. These are the evolving footnotes, references, emails, and instant messages. Your comments are most welcomed!

This page and the following sections will continue to be updated. A new homepage has been started and it will be released soon.



[1] Scholars. Durham University’s Institute for Particle Physics Phenomenology (IPPP) has achieved global recognition for her work and her graduate students. The seven pictured above are so good they stepped in for Sir Peter Higgs when he became too ill to make a public speech. The IPPP also hosted an event like the 23rd International Conference from the Planck Scale to Electroweak Scale (Planck 2021) where the focus was on some of the most-mysterious, open questions within the smallest scale of our universe. The intent of most conferences is to trigger new insights. That hope is especially true when considering the graduate students and postdocs. Our hope is also in those who make a presentation for a conference. There is nothing like a deadline! By making time fundamental, we experience its derivative nature.

From this 23rd conference, we now have access to the PDFs of the 21 scholars who’ve made a presentation where we can more readily ruminate about such things. Also, their references are always a great resource.

The primary reference to all related emails to these scholars will always be within this footnote:

These 21 scholars come from around the world. Although each focused on probabilities and possibilities, some are closer in spirit to the Fairbairn presentation which challenges us to stretch in new ways. In every instance, my focus is on the nature of that stretching.

In December 2011 we started working to understand the 202 base-2 notations from the Planck scale to the current time. We have come to believe that the first 64 base-2 notations from the Planck scale to what we’ve called the CERN-scale (or Electroweak scale) are the hidden keys to help unlock silos of information that keep the key domains of physics separated. It’s been ten years. There is nothing like a ten-year anniversary to prompt a more critical review.

[2] The tetrahedral-octahedral honeycomb. Not just a speculative vision, here are geometries that open many-many multiple paths to the Planck scale from that simple tetrahedron (sitting on a shelf in the classroom). To give something so simple a little panache, consider those paths to be a tunnel similar to the concept of an Einstein-Rosen bridge (or a wormhole). Though a real reality, not a virtual reality, we’re creating “Zeno goggles” that automatically divide space in half while proportionately and relativistically shrinking the observer.

You’ll observe and experience the 112 steps, going deeper and deeper within. We’ll slow you down as you get to Notation-20. You’ll observe how the tunnel options have gotten fewer and at Notation-10, you’ll observe the actual creation of the tetrahedron and octahedron between Notations 1-5. You’ll actually see the stacking of those 539 tredecillion infinitesimal spheres. Called cubic-close-packing of equal spheres, it’s brilliant. Then you’ll observe how those infinitesimal spheres are popping out of the Planck scale fabric of the universe. That’s a wow!

Seemingly instantly up at Notation-112 where we came in from the classroom, you’ll be given what we call, “Euler-2-exponential goggles.” Here you will see how every notation is multiplied by 2; and in just 90 steps, you will be out to the age-and-size of the universe, watching the current expansion. A show stopper, you’ll see and experience the universe from the smallest to the largest in just 202 steps, notations, sets, jumps… if you haven’t been to our old chart it may be a good time to go.

The new chart has risen!

We all need to look more deeply inside the tetrahedron and octahedron! We all should spend time deep inside the honeycomb. There is nothing simple about a honeycomb.

[3] What do any of us really know? Are things always simple before becoming complex? It seems to be true, all except around those issues coming out of the big bang theory as promoted by Hawking, Guth, and many others. Now, more recently Princeton’s Paul Steinhardt and his coterie have been getting some traction with their quest for a new kind of matter. Dan Shechtman (wiki) before him looked at the small-scale and got his Nobel prize in Chemistry in 2011 for his discovery of quasicrystals, the imperfect geometries based on five tetrahedrons sharing a common edge and lacking a translational symmetry. In our book, it is confined by notation and its respective Fibonacci sequence. Of course, outside of the 202 notations, that statement is meaningless or gobbledegook. The bottomline is arrogance impedes ideas and creativity. Remember Fairbairn‘s comment about “novel approaches.”

[4] Quiet start? Natural inflation? Perfectly smooth? Dark Matter and Energy? What if the universe starts very simply with Lemaître’s primordial atom? In 1927 Lemaître had suggested as much; it was his first idea, a cold-start. We’ve believe it was his best idea. At least 64 base-2 notations before all the complexification of a particle or a wave, here are the pure numbers of a sphere. A little like the Democritus atom, the conceptual study of a sphere is at least 1500 years older and here we are still learning about it! If we take off Planck’s quantum blinders, we might see his numbers more readily and see homogeneity-isotropy in a very different light. We have been fretting about dark matter since Fritz Swicky’s 1933 formal theorem inferring the existence of dark matter.

Dark energy didn’t come into focus until in 1968 the Hubble Space Telescope began collecting the detailed data. Interpreting it all is still up for grabs. With dark matter estimated to be 27% of the universe and dark energy as much as 68%, it is certainly the most enigmatic issue within science today.

Yet, the first 64 notations puts it all in a new light. Here there is a universe of mathematics and geometry that can not be measured with a physical measuring device of any kind. With all these open issues and with so many others that are ever-so-much more problematic, isn’t it time for a radical shift in our constructs for that first septillionth of a second. It sounds like an insanely short amount of time. Within mathematics, one tredecillionth of a second, and that range, a septillionth to a tredecillionth, is another universe unto itself.

[5] Always looking for the start. Fundamental change within our scientific belief systems is difficult. There are too many people, too much history, and way too much money involved with every major theory, whether right or wrong. Scientific research today is big business. Among those at the the top is CERN laboratories. Straddling the border of France and Switzerland, just outside of Geneva, CERN (Conseil Européen pour la Recherche Nucléaire) is a case study unto itself. Initially it involved twelve countries when it began in 1954. Today there are 23 member states, yet associations with virtually every country on the planet and well-over 100,000 research physicists around the world.

It is a very big business. As an organization, percolating out of the darkness and rubble of WWII, it had a bold start involving those twelve European nations. That start is well known. Yet most enigmatically and more importantly, even today the best of CERN are unsure about the first septillionth of a second at the very start of it all.

My first interactions with CERN folks started with Viki Weisskopf (MIT) and Lew Kowarski (Boston University). Weisskopf was Directeur-General from 1961-1965. Kowarski was the first to propose a laboratory for fundamental research; he was tasked with organizing and setting up it up with Raoul Dautry, Pierre Auger, Edoardo Amaldi and Niels Bohr. See: May 1952, Early beginnings

These were all people who understood the evolution of the first atomic weapon and how basic science can quickly become a Hiroshima or a General Electric. Any concepts that might upset these equations must be most compelling and be ready to face stiff, if not fierce, opposition. Yet, in time, the better concepts do rise. We think ours are straightforward.

[6] Redefining the first instant: Lemaître’s primordial atom, one Planck sphere per Planck unit of time. Those two basic assumptions opened the way to this simple calculation — 539 tredecillion primordial spheres per second.

It is Max Planck’s calculation for Planck Time extended to one second.

The results are beyond imagination. Even today, envisioning such numbers is an ongoing challenge. These numbers made their debut within this website in October 2020 and there are still many levels of error-correction yet to be done.

[7] Reaching out for critical feedback. In 1971 I became part of a think-tank on Brattle Street in Harvard Square in Cambridge. Part of the invention-research process was to suspend judgments and accept ideas as given. It wasn’t always easy to do. We are all naturally judgmental people. We are taught to look at new ideas critically. And, it is easy to fall into the trap of arrogance, “How can you be so stupid?” If only we could change that attitude to something like, “Let’s explore that idea and see where it takes us.” Idiosyncratic ideas are not always idiotic! Yet, it takes a bit of courage to approach our experts. So many of them ask, “How can you be so stupid?” After crawling back into our safety zone and hibernating for a bit, we eventually venture out again but with less ambitious goals. That’s why I enjoy the younger students. Some are still actively exploring imaginative ideas. Our goals as teachers should always be to explore such ideas thoroughly. In 2016, it was becoming clear to me that nobody was dealing with our numbers and the logic of base-2, doublings, spheres, stacking and so on. It was such a different paradigm. It was risky business for anyone with a high-standing within the community to come anywhere near it. Though I assured people that their responses would NOT be shared with the public, people were reluctant to be critical, so it became important to me to log my questions and develop a reference page to each scholar’s work. It is a very modest way to try to avoid becoming more of a nuisance and it helped to focus on their work as related to these efforts.

[8] Infinitesimal thrust of numbers coming through pi and all the all the dimensionless constants. Might it manifest as an inherent force within light and the Planck Charge? Might it be a manifestation of the intimate, immediate correlation with the continuity-symmetry-harmony of infinity? Might it be an ongoing, never-ending finite-infinite transformation? Might infinity be the source for the deepest nature of thrust and photons (force bosons)? Of course, we answer all four questions with a “Yes” and then ask, “What is this universe telling us?”

[9] Largest numbers. We are getting a grasp of the smallest numbers. We also can begin to grasp the very largest numbers that define our universe. These numbers give us some assurance that we are on the right path. The universe does, indeed, look more and more like it is base-2 exponential. Yet, again we asked, “In what ways is it also base-3 exponential? …base-5? …base-10? The largest numbers are not far from today’s actual numbers. Is that the roll of the prime numbers?

It all gives us clues and challenges us to fill in the mathematics and geometries.

[10] On infinity. In 1970, by asking questions about perfection in the face of quantum physics and Bell’s inequality equations, continuity-symmetry-harmony seemed like good abstractions. Building on each other, they were general enough yet have relatively specific scientific meaning. Eventually I asked if each could be a facet of the infinite. It didn’t go far because I could not discern a structure or a path from the infinite to the finite until 2011.

Those 202 notations have triggered new thoughts about very old concepts.

[11] From the old guard to the newest thinkers: From Wheeler dreams to Eugene P. Wigner’s extreme trust in numbers, we go to the likes of Tim N. Palmer, and others like Stephon Alexander, Espen Gaarder Haug, Ari Lehto, Ard Louis, Jirina Stone, Frank Wilczek, and Edward Zalta. It would be magical to have them all in a “Zoom-like” session to talk about this page. Yes, we can dream dreams like Wheeler.

With this ten-year review, we re-introduce Planck Temperature, no longer constantly pushing the boundaries out and getting closer to absolute zero, using the more traditional start at the Planck Temperature raises so many new questions for us. Every aspect of our mathematics will be pressed and stretched.

In a rather peculiar way, both models have the same results so that “the real model” of our universe, remains a mystery for another day. Thank you. -BEC


Please let us know if you would like to join us for a “Zoom-like” discussion about it all.

All eleven of these endnotes/footnotes above are being re-edited and textured.





Sir Peter Higgs, Edinburgh: Sunday, November 7, 2021. A quick note about the question the grad students asked their audience on the occasion of substituting for him when he became too ill to present his public lecture.

• Simon White, International Max Planck Research School on Astrophysics at the Ludwig Maximilians University Munich, has been at the forefront of a Cold Dark Matter paradigm. Because scholars like him have been working with cold concepts within a classic big bang model, I have been pushed to ask silly questions like, “Could there be a super-cooling from the Planck Temperature because that phenomena would most likely act like laser thermodynamics. Could the inverse square law apply?” Based on those flights of fancy, I just started another chart that starts with the Planck Temperature within Notation-0 and is divided by 2 to arrive at a radically reduced temperature for Notation-1. It is divided by 2 again for Notation-2. Because it is temperature assumed to be light and not an “infinitely-dense” singularity, but a very dense black light that within Notation-97 becomes visible light. If one Planck Sphere manifests per unit of Planck Time within thirty-one doublings, there are size is still an infinitesimal 3.470762×10-26 meters, the mass is just 103 pounds (46.79 Kilograms). So now we are asking, “What might the temperature be and why?” Within our first horizontally-scrolled chart, it is 4.73×10-18K. In the chart with Planck Temperature within Notation-0, it is 6.597×1022K. The Electroweak Scale requires an estimated temperature of 2×1012 Kelvin to create the Quark-Gluon Plasma (QGP). That’s an important benchmark. It requires 175 MeV per particle. We’ll need help to figure out which notation would be a logical place as another mechanism to force the review of possible mathematics and functions that may be at work.

Malcolm Fairbarin, Kings College London We have started a profile page to follow his work with the International Conferences from the Planck Scale to Electroweak Scale.

Marco Drewes, UC Louvain We will continue to study his work with the IPPP.

A note to the attendees of the IPPP June 2021 conference:

“I see that you were one of the participants in the Planck 2021 IPPP-Durham University conference. I am going through those papers now asking the questions, “What are the most special insights from those 21 scholars? How do we get beyond the Standard Model without getting too far beyond it?”

“Personally, I know that we’ve gone a bit too far because we started at the Planck scale and hypothesized that something like the concept like Lemaitre’s primordial sphere defines the very first moment. I am rather sure Malcolm Fairbarin (linked just above) thinks it is more idiosyncratic than it is a “novel approach.”

“If you would like to take a look, it’s posted here:  https://81018.com/smallest-largest/

“We then applied base-2 notation at the Planck scale to find just 202 notations from Planck Time to this day.The numbers are fascinating — https://81018.com/chart/ — but interpreting those numbers is not easy. Your comments and insights would be treasured.

“Surely more than a “novel approach.” Perhaps “idiosyncratic” is necessary today. Thank you.”

“Most sincerely,

From a student in Spain: Students ask us questions from schools around the world. Here is my response to a question from a biology student with a strong background in physics. He attends Complutense University of Madrid:

“Your English is excellent. Your references and links: Excellent. Your question, Do you know if Arkani-Hamed adopts something similar to Tegmark’s view as well?, is well placed. Those two are so cockily independent and aloof, they might disagree just to disagree. However, I think you nailed them. Like E.P. Wigner (pictured here), all the way back to Pythagoras (See – Theano, On Piety), they are all an inspiration to me. In my deepest being, I believe they are right and you’ll see throughout my work a deep belief in continuity-symmetry-harmony, the qualitative and infinite, always and profoundly giving rise to the finite.  Too much of our being is spent being arrogant. That doesn’t help anyone. Science and religion are full of arrogance so I try very hard to stay open. Any more thoughts and questions, I am all ears!  Thank you.  -Bruce”

In Process: Simons Foundation folks: Leonard Susskind – 2020 lecturer, Patrick Hayden – director, Brian Swingle lecturer – Chaos-Protected Locality, and Juan Maldacena – lecturer, and so many more


October 18, 2021: @BBCScienceNews@bbcnews@BBCNewsnight #RichardSharp Worldviews are incomplete; we all need a highly-integrated view of the universe. We’ve started here: http://81018.com

October 18, 2021: @MiddleEastEye @AlexandraPring Yes, true. Yet, even Gurnah’s work needs to be seen through a very different lens. We’ve all got to grow beyond our simple worldviews to fully integrated views of the universe. Sounds impossible… it’s not. We started here: https://81018.com/hypostasis/
Abdulrazak Gurnah received the Nobel Prize in Literature in 2021.

Other communications are being reviewed from this period and may be added.


Invitations and Collaborations

With whom do we collaborate? You are among thousands of people who visited this page this site this month. Might you ask, “Can I help this effort?” The answer is, “Yes!” Our only thrust is that the foundations of this universe and life itself be seen in light of infinity and the continuity-symmetry-harmony that the infinite engenders. Please, talk to us. Thank you. -Bruce


Key dates for this document, smallest-largest

  • This document was started early on Monday morning, October 18, 2021.
  • First posted for collaborations, late evening, October 18, 2021
  • This page became the homepage, late on Tuesday, October 19, 2021
  • The URL: https://81018.com/smallest-largest/
  • Prior Homepage: https://81018.com/hypostasis/
  • First Headline: The Smallest and the Largest
  • Second Headline: Smallest to largest
  • First Tagline: How do you answer, “What is the smallest thing in the Universe?”
  • Second tagline: A possible rapprochement with the naïvetés and simplicity of our youth
  • Another possible homepage: https://81018.com/tredecillion
  • The most recent update of this page: Monday, 21 March 2022


Concepts that just might change everything…

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Pages: Blackhole.| C.|.Empower | Hope.|.Mistakes.|.PI (π).|.Redefine.|.Singularity | Sphere. |.TOE.|.Up

Eight What-if Questions
by Bruce E. Camber
once in Positano, Italy

  1. What if we live in an exponential universe?
  2. What if the 202 base-2 notations are the most comprehensive-but-simple way to engage the universe from the very first instance?
  3. What if the first 64 notations are an unseen foundational fact?
  4. What if those first 64 notations define a new kind of blackhole?
  5. What if hypostatics grid everything, everywhere, for all time?
  6. What if a sphere is our most conceptually-rich starting point?
  7. What if pi becomes a key to grasp the finite-infinite relation?
  8. What if cubic-close packing (ccp) of equal spheres is a key function of the universe and a foundation of physics?

1 Exponentiation. The 202 base-2 notations are the result of a high school geometry lesson in 2011.1 Over time those eight key concepts above would emerge and be actively explored. Yet, each concept is out of step with today’s scholarship so we’ve asked our world’s leading scholars and their colleagues for their critical review.

It is difficult to get scholars to look at materials that originate in a high school geometry class. Early in the process, we thought it was a good STEM tool. It wasn’t. The concepts were too far outside the mainstream. Although this website provides some feedback, we are now in the process of creating a virtual reality platform of the major theories about the start of the universe and we will include this one so each of our eight key points above receives a larger audience.

Questions about an Exponential Universe. Who among all our scholars — including postdocs, graduate students, undergraduates — might be open to such a concept? Who is examining the domain from the Planck scale to the CERN-scale (or electroweak scale)? Might their concepts suggest an exponential universe?

This article is to answer these questions as succinctly and simply as possible. We build upon a concept that is analogous or similar to Planck Time or StoneyTime. Our primordial sphere is also analogous to Lemaître’s primordial atom.

In 1899 Max Planck first introduced his number for a natural unit of time based in part on fundamental physical constants. That calculation rendered 5.39116(13)×10-44 seconds. In some academic circles, it is the shortest, meaningful interval of time. Those calculations, however, use Planck’s constant and there is a growing group attempting to re-qualify Planck’s base units without the use of Planck’s constant. Yet, even with new numbers, the concept of base units of length, time, mass and charge (energy) stands.

George Johnstone Stoney did his initial calculations in 1874 for a lecture in Belfast.3 His number was similar, but shorter — 4.6054×10-45 seconds. We ask, ”What could possibly be rendered in such a short interval of time? What is the most simple thing?”

Eventually, the circle and sphere were studied.

Circles and spheres are each generated by just two vertices. So, yes, we began wrestling with the mysteries of pi and the nature of a circle and sphere. We’ve begun studying the types of Fourier transforms and quickly learned that we had to begin to grasp scale invariance and dimensionless constants more deeply.

Dynamic spheres open a radical concept. If we are correct and there is a range that begins somewhere around Planck and Stoney’s calculations, and if there is one infinitesimal sphere generated per that infinitesimal unit of time, we have an approximate rate of expansion of the universe. If we use Planck Time, it would be around 539 tredecillion spheres per second. If we use Stoney Time, it would be around 4605 tredecillion infinitesimal spheres per second.

Such numbers seem beyond the scope of imagination. Notwithstanding, if this picture is anywhere close to our real reality, the foundations of exponential notation are established.

Do a general search on ”We live in an exponential universe.” Many pages that are displayed originate from within this website. If our universe is exponential, then the seven concepts that follow are more true than false.

Many articles and this key chart contributed to this article:


2 Base-2 Units. Geometrically and mathematically the 202 base-2 notations are a fact. Here is the most comprehensive-but-simple way to engage the entire universe. From the very first unit of time to the current time, over 13.81 billion years, is within Notation 202.

That very first unit of time is a key that opens doors that have never before been recognized or observed. Of course, Planck, Stoney and in our time, John Ralston, have wrestled with that definition. Notwithstanding, it is a key challenge for our entire academic community throughout the world: Do such base units, defined in the manner of Planck, Stoney, or Ralston, conceptually encapsulate a very first moment of time? We say, “Yes, conceptually, here is the first instance of time.”

In 2011 we backed into the 202 base-2 notations; we certainly had not studied its ramifications. Also, although we had been trying to discern the most simple object, we were reluctant to embrace the circle and sphere. Although we knew about Max Planck’s work, we really had no real insights about Planck Time.

We didn’t even know that cubic-close packing of equal spheres generates tetrahedrons and octahedrons. We knew nothing about Langlands programs and automorphic forms. To say that our learning curve was rather steep is an understatement. Yet perhaps there were some hidden benefits within all of our naïveté.

As we studied and thought about the first 64 notations, we began to experience the stories about the “Wheat and Checkerboard.” What appeared to be an ”infinitesimal nothing” was beginning to look huge and totally dynamic. Then, it appeared even larger; base-2 notation seemed to be a good way to bring some order to it all. Here we had the makings of a geometrical-mathematical science that just might incorporate Langlands programs, string and M-theories, and other promising theories. It just might incorporate many disciplines that have never been on a grid. All the hypothetical particles of SUSY and our standard model of particles just might have a new home.

Obviously these infinitesimal spheres are being generated in a dramatically-explosive yet totally-unobserved-discrete manner. Our simple orientation to the universe was changing and as it did, there were more and more facets to be explored.

Base-2 notation is just an ordering mechanism; it has no causal efficacy. It is just a way to context reality. It logically includes all possible bases. Yes, any other base expansion can ride on top of base-2. In fact, any and all our mathematical formulations can functionally ride on a base-2 platform.

More references:

  1. The first-septillionth-of-a-second to start of the universe: Notations 1-to-64
  2. Built up with planckspheres: An introduction to nine overviews (pages)
  3. The Universe As Extended Planck Base Units
  4. 2015: Early reflections on base-2


3 Causality begins long before particles/waves. No less than 64 notations are all within scales smaller than particles and waves. Perhaps only geometries and mathematics are able to define these notations. The inherent continuity, symmetry and harmony of the sphere appear to give rise to the first dynamical moment.

We’ve been too particle and wave centric for much too long. These new concepts begin to break that logjam. Stymied with so many hypothetical particles, we know our foundational orientation is lacking and those first 64 notations just might challenge us appropriately.

Also, if the base units of Planck and Stoney are metaphorically or conceptually correct, let’s rethink the very beginnings of everything. Why not start very, very simply? If the deep nature of the circle and sphere are entered, the mystery of its continuity, symmetry, and harmony become boldly apparent. Though quantum physics has little to say about each, the evidence for all three is everywhere.

Many writers have suggested that our top-down investigations were missing too much and that we should start from the bottom-up. Yet, the questions must still be asked, “What are the core foundations upon which to build? What is fundamental?’ We answer, “The infinitesimal primordial sphere, the finite-infinite relation, and three finite-infinite functions within the primordial sphere (pi): continuity (order) – symmetry (relations) – harmony (dynamics). Those three finite-infinite functions become the basis for valuations. And valuations become the basis for ethics, and ultimately for morals. Taken altogether, we have the beginnings of the universe.

More references:

  1. From the bottom-up, not from the top-down
  2. Redefine Space, Time, And Infinity
  3. Simple, Logical Concepts
  4. From left to right, we can all be better and do better.


4 Complicate the concept of a blackhole. We agree; it’s a huge stretch. From Einstein to Hawking, the best of the best have been speculating about black holes.* Yet, given speculation is its cornerstone and given the first 64-notations, might there be another kind of blackhole?

Could there be a blackhole that is actually pushing out just below the scales of our measuring devices?

Given all the current anomalies within blackhole studies, it is beginning to look like it’s worth some consideration. Such a radical conclusion has not been entertained within the scholarly community — it has no precedent — but why not take a look? Those first 64 notations are below all our current thresholds of measurement. The time sequence is a bit over one quintillionth of a second. Our current commonsense logic tells us that it is too fast for anything; yet mathematically, it is a lifetime.

Recognizing how current black holes are seen as a sucking up everything, for many reasons, it may also be understood as being an essential foundation which cannot be measured by physical tools, yet, still be a real reality within space and time.

All of these references are recent documents and are still being developed:

  1. Blackhole: Turn the Blackhole Inside Out
  2. Hope: Our hope for you this day
  3. Redefine it all: Where do we go from here?
  4. Singularity: Never Quite Singular
  5. Sphere: First things first

*A consensus document, “Black holes, gravitational waves and fundamental physics: a roadmap”, over 100 authors, IOP Science, June 2019


5 Hypostatics. If quantum fluctuations and all things quantum are measured above the first 64 notations, might the first 64 notations be considered hypostatic. Dating as far back as Plato and Plotinus, the word means “that which stands under” or the essence, or the substance, or underlying reality or fundamental reality.

Might these infinitesimal units of time be called “hypostatic time” and that space becomes ”hypostatic space” and then, of course, hypostatic energy, and hypostatic mass?

The study of substances and a substantial essence was going on well before our current history, and well before what is considered to be the Common Era (CE). Within over 202 notations, this Common Era represents an extremely thin slice of the 10.98+ billion years of Notation-202.

Although the use of CE has been traced back to 1615 to Johannes Kepler, ”annus aerae nostrae vulgaris…”,[a][b]  one might rightly regard all of known human history to be an infinitesimal common era.

Within the perspective of this website, every event with the Common Era is current history, yet within what has become known as ”before the common era” (BCE), the Greeks surely began to wrestle with the concept of hypostasis. What could possibly be substance, essence, and that which stands under? In these days, we well understand how just numbers and geometries compute without particles and waves, as in genomic functions and the functions within artificial intelligence. Waves and particles are involved with the computing systems, but are not themselves that which is computed.

Yes, yes, of course, there will be more to come.

  1. Hypostatic structure starts between the finite and infinite
  2. Hypostatic Way of Learning & Knowing
  3. Perhaps a bit of perfection


6 The infinitesimal sphere appears to be the key. Lemaitre, like so many before him going all the way back to Democritus, called it a “primordial atom.” It is always a sphere. In this model, this sphere is defined by the smallest units of space and time yet it still has all the functionalities of any sphere.

The sphere has continuity and symmetry, and most importantly it has harmonics (dynamics).

An infinitesimal primordial sphere is our most conceptually-rich starting point. That sphere is postulated to be the first instance of space-time, matter-energy, and electromagnetism-gravity (each sphere is an attractor or repeller). It has its never-ending, never-repeating numbers of pi. It has all the symmetries of a sphere. And, it has all the harmonic functions of a sphere. And those three characteristics of pi represent the infinite within the finite.

  1. The first instance: Pi (π) Shapes Our Universe
  2. Power of Spheres, Circles and Pi (π)
  3. The Sphere: Is it the Most-Basic Building Block of our Universe?
  4. The primordial archetypal sphere
  5. Acknowledge infinity


7 Pi, our first clue about the nature of the infinite. Although religions of every kind claim to have an inside-and-direct track of information about the infinite, we will stay within mathematics, geometry, logic, and the foundations of physics. Notwithstanding, we will respect other people’s insights as currently stated.

Our belief and hope is that our information helps the philosophers, the religious, and the theologians to clarify their own beliefs, gesticulations, histories, and postulations.

David Hilbert was possibly just a bit too self-assured with his grasp of the rules of logic. How could he possibly know the depths of infinity such that he could discount some aspect of the infinite that readily manifests within and throughout the finite? Of course, this will be an ongoing subject of this website.

We all grow up within our family’s philosophical and theological orientations. As important as these orientations are to help socialize us, eventually we begin to learn about other traditions. Some of us attempt to build bridges and even to take the best from each tradition to create a new platform of understanding and for reflection. We are possibly thinking, “There has to be a way to respect other traditions without compromising your own or compromising one’s new platform of understanding.” People ask me, “What is your background? How does it influence you?” At the age of 10 in 1957, my mother and father encouraged me to explore and appreciate other traditions. By 1967 it was an avocation. By 1977 it was a vocation. In today’s world, the most dominant belief system is science and its most dominant philosophy is one of the many flavors of agnosticism and atheism. Our model engages them all. Our core belief is in order-continuity, relations-symmetries, and dynamics-harmonies. All are cornerstones of logic, rational thought, science, and our understanding of the infinite.

There are a few within our many cultures and religions who are desperately in search of a bridge of understanding that opens communications, an exchange of ideas, tolerance and trust. I continue to struggle with it all as evidenced within an invocation that I delivered at a birthday party for a friend in Positano, Italy, an event and place that inspired this page.*

Now, all these referenced documents were written over a nine-year period. I’ll be going every through each of them to create a more consistent message for today. Ultimately I believe the deeper truth is within the hyphen between the finite and infinite.

  1. Finite-Infinite: A Nexus of Transformations
  2. Finite-Infinite: We all so little understand the infinite
  3. Finite-Infinite: On more fully recognizing the infinite
  4. Finite-Infinite Bridge: A Nexus of Transformation


8 Cubic-close packing of equal spheres. None of the other current theories for the start of our universe invoke this simple function. The continuity-symmetry-harmony of the sphere are extended throughout those first 64 notations through a finite-infinite relation. Every one of the 202 notations defines a dynamic relation of this universe.

Here is a progressive, highly-relational flow where every thing is related to everything, everywhere, throughout time. We are foundationally and fundamentally related.

Yet, it appears that none of these notations are sacrosanct and all of them are constantly changing and none of them would ever be exempt from change. The first 64 notations, representing about 9.945379×10-25 seconds, is so far removed from any possible measurement, here is a new science and a new context for matter and energy (charge), and for gravity and electromagnetism. There is much more work that will be done on this last point. Essentially now that we have the foundations for the greatest diversity of geometries, formulations, and calculations; no part of science or the human experience is exempt, including the role of sleep (which only exists in Notation-202) and the nature of consciousness. And again, I repeat, continuity, symmetry, and harmony become the basis for valuations. And, valuations become the basis for ethics, and ultimately for morals.

  1. Cubic-close packing of equal spheres
  2. Cubic-close packing
  3. More to come…


Note: This document was started on September 19, 2021 in Positano, Italy overlooking the Amalfi coast; it’s truly an emboldening place! That eighth point has much more work. – BEC



[1] High school geometry lesson. The most wildly-speculative mind should be our high school kids, yet so many become passive, bored, and tired. What might happen within education if there was a growing crescendo of enthusiasm and creativity for scholarly work within each grade throughout our primary and secondary schools? What if by our senior year, the primary role of a teacher was to help context and interpret new ideas? That is the revolution these basic concepts should engender. Let us open up the box for creativity that is increasingly locked up with each passing year of education.

[2] Scholars. Who among us empowers the most insightful thinking, the most inclusive ethical understanding of things, and the most creativity? Those people are our best scholars. We’ve interacted with a few of them. Empowering people to discover their gifts and develop them is a high calling.

[3] George Johnstone Stoney. Our introduction to Stoney was through a short paper by John Barrow (enter the password: Stoney or go to Harvard’s UIRL). I believe Stoney should be acknowledged as the first to experiment with natural units.

[4] A consensus-driven article by 100+ scholars.  The corresponding author, Vitor Cardoso, had his work cut out for himself to get well over 128 signatures on this “roadmap” through the mysteries. When I find important documents like this one, I stop to write to a few of the key authors. Here are leading thinkers and just maybe, these are people who might examine the 202 notations, particularly the first 64 notations at the quark interface to matter where quantum mechanics begins its work.





14 October 2021: @zlj517 There is only one #Earth within the #Universe and China, the USA, Taiwan, and 195 other nations are an inalienable part of it. We have to grow beyond our simple worldviews for a comprehensive view of our universe: https://81018.com It is our key to the future. Note: Thi is just one of the many Chinese leaders to whom I have written. These people need to be hearing from us all. The concepts this leadership is using are still too tight and too limited.

12 October 2012: John L. Hennessy (Chairman), Sundar Pichai (CEO), Ruth Porat (CFO) of Alphabet You’ve been around idiosyncratic concepts; most are relatively complex. Simplicity is more difficult. In 2011 in a New Orleans high school geometry class, I had the kids chase smaller and smaller tetrahedrons and octahedrons by dividing the edges by 2, connecting the new vertices. We thought it was a great STEM tool. The page — https://81018.com/tot/ — goes to is one of our early models. It takes 45 steps within to get to particle physics and another 67 to the Planck scale. If you were to multiply those tetrahedrons by 2,  in just 90 additional steps you’d be out to the approximate size and age of  the universe.  It is a model of the universe using base-2 exponential notation. In 1957 Kees Boeke did a base-10 model that became popular, but not functional. This model becomes functional: https://81018.com/hypostasis/

9 October 2021: Ken Ono, a number theorist at Emory University, Michael Griffin of Brigham Young, Larry Rolen of Vanderbilt, and Don Zagier of the Max Planck Institute of Mathematics are closing in on the Riemann Hypothesis (Wikipedia). Their work is important because all numbers, all equations are being carried forward within base-2, yet the prime numbers open new possibilities. This group and so many other scholars (Langlands programs and M-Theory) also have a role.

8 October 2021: To the Princeton People: Paul Benacerraf and Paul Steinhardt

Riemann, Bernhard (1859), “Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse”, Monatsberichte der Berliner Akademie. In Gesammelte Werke, Teubner, Leipzig (1892), Reprinted by Dover, New York (1953). Original manuscript (with English translation). Reprinted in (Borwein et al. 2008) and (Edwards 1974)

“Let’s get a handle on the Riemann hypothesis. The Riemann zeta function  is made for base-2 notation. We will exegete his 1859 article “On the Number of Primes Less Than a Given Magnitude” in light of base-2 whereby base-3, base-5, and base-7 ride on top of base-2. All prime number notations — there are only 45 primes within the 202 notations — will be initially considered. Notation-199 is a prime-number notation. The next will be Notation-211; it’s assuredly a bit removed from our immediate considerations.

5 October 2021, A note into Pasadena’s ArtCenter College of Design to Heidrun Mumper-Drumm

Much more to come…


There are so many key words and key word combinations. Quite literally hundreds of instant messages will be sent to key thinkers around the world. Although it seems that we’ve become complacent about first principles and our starting points, we all wrestle with these questions every day.


October 12, 2021: @ChaseSupport @Chase We need to grow beyond all our old worldviews by starting over again with a highly-integrated view of the entire universe. Our model — https://81018.com — started in a high school. Continuity-symmetry-harmony become the bedrock of understanding. 

October 7, 2021: Joshua Rothman, @joshuarothman. Rationality is blocked by unexamined concepts that provide erroneous foundations. https://81018.com/duped/ is a quick summary of what I think are the biggest. Here’s our different start: https://81018.com/hypostasis/ Newton’s absolute space and time is our biggest stumbling block.

October 5, 2021: @GuernseyCollege Guernsey, Guernsey, Guernsey — The only way we will ever manage equality-diversity-inclusion is to break free of limited worldviews and work on a mathematically-integrated view of the universe from the first moment of creation to this very day and time: https://81018.com/hypostasis/

October 4, 2021: @xijinping_xi Three fallacies of Western thought became “commonsense” for the world: https://81018.com/duped/ To break free of limited worldviews, we need a fully integrated view of the universe. A start: https://81018.com/hypostasis Mathematically: https://81018.com/chart/

October 4, 2021: @DrEugeniaCheng You’ve got all the right combinations from category theory to pi to infinity. Your music and cooking are a blessing. Now push it through Newton’s absolute space and time, and then through the infinitely-hot bang theory: https://81018.com/hypostasis begins to wrestle.

October 4, 2021: @BorisJohnson To right our little ship, Earth, we’ve got to take charge of Newton’s errors about “absolute” space and time and Hawking’s errors about an “infinitely-hot” big bang: https://81018.com/duped/ Those errors have become the world’s commonsense! https://81018.com/hypostasis/

October 3, 2021: @nickclegg [Facebook VP-Global Affairs] Nick – Let’s really empower leaders by breaking out of little worldviews. We need a fully integrated view of the universe to have depth and perspective and to unleash creativity: https://81018.com/hypostasis is just a beginning. Come on now. Life is short. Make it a work of art!

Communicate: China has become pivotal in our grasp of the transition from global perspectives to those perspectives that embrace the entire universe. Can cubic-close packing (ccp) become more pivotal than politics and parties to grasp the depths of our interconnectedness?

Politics is crazy. Desperation is in the air everywhere.



With whom do we collaborate? Of the thousands of people who visit this site every month, who among them might want to extend the right hand and say, “Let’s work together.” Our only thrust is that the foundations of this universe and life itself be seen in light of infinity and the continuity-symmetry-harmony that the infinite engenders. Please, talk to us. Thank you. -Bruce


Key Dates for this document, Hypostasis

  • This document was started on Sunday, September 19, 2021 in Positano, Italy on the Amalfi Coast.
  • First posted for collaborations: September 20, 2021
  • This page became the homepage: October 6-7, 2021
  • The URL: https://81018.com/hypostasis/
  • The Prior Homepage:https://81018.com/virtual/
  • First Headline: Back to the Basics Second: Eight “What if…?” Questions
  • First Tagline: Concepts that change everything…
  • Another possible homepage: https://81018.com/tredecillion Password: Tredecillion
  • The most recent update of this page: 15 October 2021


For now, the end of this article…

Is there a basic building block of our universe? Might it be a Primordial Sphere, or Infinitesimal-Archetypal Sphere, or First Particle?

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Pages: Blackhole.| C.|.Empower | Hope.|.Mistakes.|.PI (π).|.Singularity | Sphere. |.TOE.|.Up

First things first
By Bruce E. Camber, Started on July 30, 2021. Continued in January 2022
[ Introducing a very special Green Wall ]

Our scholars seem increasingly confident that our universe has a starting point. Notwithstanding, most seem to be holding onto the big bang model, especially the one promoted by Stephen Hawking where he said on PBS-TV in 2016, “Everything in existence, expanding exponentially in every direction, from an infinitely small, infinitely hot, infinitely dense point, creating a cosmos filled with energy and matter.”

Is Hawking saying the entire universe and everything in it had been compressed to an infinitely dense point? I think so; but, I do not think it is true. Hawking was painfully fallible and did not have all the answers. Surely, we all wanted him to have some of the answers.

In 2022, there are very few alternative models. Among them, the work of Paul Steinhardt of Princeton seems to be garnering a fair amount of attention.[1] For me, his model is still not quite simple enough.

Can we just try to define a simple building block?

Most everybody knows that the first physical thing is not an atom. That’s much too complex. It is probably not a particle or wave or a fluctuation — not quite complex enough. There is no amount of colors, shapes, directions, feelings, or charm that may well be part of the overall causal efficacy within a moment of measurement, these each seem quite derivative. What could possibly encompass all those expressions (equations) and have deep causal efficacy? What makes those things be what each is? And, at the same time, could “this something” be magically more simple?

I think that the only thing that might qualify is a sphere, albeit a primordial sphere. Increasingly it seems best to refer to it as the first particle.

Max Planck’s base units. Apply a simple base-2 expansion to Max Planck’s base units and the universe is encapsulated in 202 notations. There are at least 64 steps, base-2 exponentiations, or simple doublings, from the Planck Length to particles that can not be measured. It begs the question, “What is happening between the Planck base units and the electroweak measurements?

Here is the secret universe scholarship has not defined. Here is a conceptual revolution. Many are looking at it. Once defined, it changes everything. Dark energy, dark matter, hidden variables…

Names and Acronyms: Primordial Sphere or Infinitesimal-Archetypal Sphere. We might use “PS” as if we might want to add an addendum or “IAS” (reminding us of the Institute for Advanced Study just down the street from Princeton University). Researching Plancksphere and Planck particle, we are deferring to the first particle because scholars have already use those terms to define a blackhole. Also, the Planck units may get recalculated in light of the scientific advances since 1899.

Base Units. In 1874 George Johnstone Stoney was the first to calculate base units of our universe. In 1899 Max Planck made his calculations. Given Planck’s leadership in the physics community of that day and his working relation with Einstein, his units are best known. Neither are perfect but I say that both are “close enough” to describing a real reality and symbolically both define a first moment of space-time.

Certainly, these figures will be re-calibrated and refined just like the figures for the age of the universe.

Their work became our foundations to begin to define a highly relational universe. We unwittingly backed into the 202 notations of a base-2 grid of the universe. By focusing on Planck Time, in 2014 it was confirmed that there are just 202 notations from beginning of time to today, the Now. The calculation for Planck Time renders a number so small, it is too small to begin to fathom.

We are generally satisfied to measure things within a second. Today, expensive measuring devices measure within a nanosecond, one billionth of a second (10-8). Much more expensive devices measure one trillionth of a second. That’s a picosecond (10-12). A laboratory in Germany, a Max Planck Institute, was the first to measure an attosecond, one quintillionth of a second (10-18). In 2016 they proclaimed measurements in the septosecond range, a trillionth of a billionth of a second (10-21). As infinitesimal as that is, the PlanckSecond is many orders of magnitude smaller (10-44).

What happens at the Planck scale is anybody’s guess. And, there has been a bit of guessing over the years. Logic helps, yet it is often a fool’s paradise. So, I say, “Just stick with the numbers, the dimensionless constants, and all things scale invariant, and even then, be very cautious.”

The Planck Temperature has always bothered me. On November 1, 2021, it started bothering me so much I opened our horizontally-scrolled chart and followed the numbers up and down those 202 notations. Back and forth, back and forth, for some reason, the inverse square law jumped into my simple equation of state and I wondered, “Is that crazy? What is that first moment? Ex nihilo? If the inverse square law applied from Planck Temperature at Notation-0, within 100 notations, it would be within the range of the quark-gluon temperatures. Does that have any logical footing?”

In 2015 Planck Temperature was too difficult, “Put if off into the future. We can deal with it later.”

I put it in Notation-203 and divided by 2. By Notation-0 it was ever so close to absolute zero.

Seven years passed, and later came sooner than expected. Asking, “What would those numbers look like if Planck Temperature is at the beginning (Notation-0)?” Obviously it would not double with the other Planck numbers. Perhaps there is a justification to divide by 2? Maybe the inverse square law could be applied? …surely not with Hawking’s infinitely dense start (his compression of everything from everywhere), but maybe with just light.[2] How might that work?

I took the old chart, made a copy, and began taking those numbers down from the hottest possible start. I asked myself, “Could some kind of extra logic or metalogic help?” With this paragraph and within the context of continuity equations from the smallest to the largest, we begin a process of peeling back the layers of ideation since about 2013 and 2014 as we wrestled with Planck Time, and then 2015 as we wrestled with Planck Mass and Planck Charge. I began thinking about the duration of Notation-202 which is 10.98+ billion years. If the universe is between 13.81 and 14.1 billion years, we’ve only had a small sampling of 3+ billion years of Notation-202 which is currently the notation in which our universe is being defined.

Within systems theory there has to be a rationale for every decision and this was one of the most important that we could make. Is it hot or is it cold? Could it be both? Of course, that’s extremely hot and extremely cold… at the same time? The more I thought about it, the more that an extremely-hot entry point with the inverse square law began to glimmer with possibility. Where is light in all these equations? What is light? What are photons? If Planck Temperature decreases inversely — because there is so-very-little to hold such a temperature — might that open a path for a new inquiry?

So, let us re-explore the question, “Could that kind of infinitely hot start have any cogency?” Could there be a progression within laser thermodynamics [3] that follows the path of Planck Temperature down to the range of the current Cosmic Microwave Background Radiation (CMB or CMBR) where the temperature is about 2.725 degrees Kelvin. That is -270 degrees Celsius or -455 degrees Fahrenheit) between Notations 106 and 107. Might that light be Newton’s perception of absolute space and time? Might Descartes‘ 1637 insight that light is corpuscular have some merit? Today we might imagine these to be infinitesimal spheres that when cooled to a range of the quark-gluon soup (plasma) would mark the beginning of measurable particles. So, we’d then asked within what range along this inverse-scale cooling might there be an actual beginning of the Planck scale doublings? Or, perhaps given this all happens in the range of a femtosecond (quadrillionth of a second), perhaps that Planck Temperature release creates a finite-infinite bridge.

It’s all speculation. Who knows?

To search for an answer, can we engage the study of laser thermodynamics? Could there be two tracks one that is a distant analogue to big bang cosmology’s compression of the entire universe and the other initially related to the explosive number of infinitesimal spheres being generated? Might it approximate our original chart with the temperature increasing exponentially from close to absolute zero? Does that earliest generation of temperature require differential equations to define the two? As usual, “Yes” seems to be the most appropriate answer to many of these hypothetical questions. Thank you.


Endnotes & Footnotes

[1] Attention. A new kind of cyclic universe (PDF), Paul Steinhardt, Anna Ijjas, ArXiv 2019. Also see: Scientific American, Physicist Slams Cosmic Theory He Helped Conceive, John Horgan, December 1, 2014

[2] Light. Opticks, 4th edition, W. Innys, 1730 (PDF), Isaac Newton, ArXiv 2019.

[3] Laser thermodynamics. X. de Hemptinne, “Thermodynamics of laser systems”, Infrared Physics, vol. 25, no. 1, pp. 107–109, (ABS) (IEEE),1985

[More being considered… yes, there is work to be done on these pages.]


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References and Resources

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Key Dates for this article, Primordial