Grasp numbers and systems that define our Universe

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An Integrated View of the Universe
Empowers Any-and-All Worldviews
by Bruce E. Camber
(email about this page)

Abstract. Things start simple. Our base-2 outline of the universe starts with the first instance of space-and-time. For now, Max Planck’s base units are taken-as-given and assumed to manifest as a primordial sphere, defined in part by key dimensionless constants which are all used to calculate Max’s historic results. These units also define a rate of expansion (assuming one primordial sphere per Planck unit of time). The role of pi, a dynamic bridging of the finite-infinite, as well as basic geometries and quantum fluctuations are explored. Issues within big bang theories are also explored. We invite you to explore an alternative model for the emergence of our universe. -BEC

Introduction: Eight key points constitute the foundations of this emergent model of the universe: (1).Key Numbers, (2).Key Geometries, (3).The Heart of Dynamics, (4).Finite-infinite and all our dimensionless constants, (5).Perfections, (6).Imperfections, (7).Mind-values-consciousness, and (8).Everything, everywhere, for all time. A discussion about each point follows.

1. Numbers to grasp continuities, order, and time

Numbers define: Assumed are primordial numbers like those calculated by Max Planck (1899) and by George Stoney (1874). Today’s scholars like John Ralston (University of Kansas) advocate for new calculations based on current knowledge, yet Planck’s base units, taken as given, open a conceptual model for the initial conditions, parameters, and boundaries of our universe. Planck’s numbers will be tweaked. His calculations are based on dimensionless constants. Natural units have a special status and give us a metaphorical-yet-clear start of the universe. If the current calculations for the age of the universe are also taken as given, we have a duration and an endpoint we might call, “today’s expansion,” the Now, and even “the current point.”

Yes, take as a given, base units define a first instant and that instant is always active to the current time.

Between the smallest number and largest number is every possible second and every possible part (infinitesimals) of every second. It is all encapsulated, numbered, and accounted; and, simple boundaries and the largest-possible scale are established. [1]

2. Geometries to grasp symmetries, relations, and space

Shapes define the look-and-feel of the first instant. Lemaître intuited a primordial atom. Within our emerging theory, it is an infinitesimal primordial sphere defined by dimensionless constants starting with pi (π). Pi reaches beyond the finite and provides our first look at the nature of the infinite. Pi, a key dynamic ratio, is never-ending and never-repeating, always the same and always changing. Everybody knows pi yet it seems that very few know it well.

Geometries work. In 2011 in our high school geometry classes, we chased tetrahedrons and octahedrons, going within, smaller and smaller. From our classroom model to the Planck length there were just 112 base-2 steps by dividing the edges by 2 and connecting the new vertices until we were about the size of the Planck’s length.

Of course, when we multiplied the Planck Length by 2, there were 112 steps back up into the classroom and just 90 more steps to the edges of the universe. We were more than flummoxed; it was all too simple.

By 2014 our current working chart of 202 notations began taking shape. We engaged the far-reaching Langlands programs. We studied a bit of string theory and its M-theory. When we finally learned about cubic-close packing (of equal spheres), we began thinking that we just might be onto a different model of the universe. Ours had simple numbers, well-explored and generally-understood concepts, and potentially every possible geometry from the first instant, i.e..the very start of the universe. [2a]

Within the heart of our geometries. Planck’s infinitesimal numbers push us into a very different logic. Here dimensionless constants dominate. And, among all the constants, pi dominates. And, there we identified three facets of pi, continuity, symmetry, and harmony. How could such a dimensionless constant be finite? Is “never-ending and never-repeating” finite?

Intuiting the essence of pi. Quickly we ran into the closed-or-open universe debates. So, we postulate that the universe is finite and infinity is totally other. We postulate that infinity is the source for pi and the other dimensionless constants such that pi reaches between the finite and the infinite. Then, we postulate that pi’s first finite manifestation is a primordial sphere — the first sphere and first thing in the universe.

Imputing boundaries and boundary conditions. Base-2 is a most simple means to sort all the seconds and parts of a second that define our universe. Symbolically and analogically, we’ve used Planck’s numbers from his 1899 calculations to create our working chart of the universe. And yes, the result is the 202 notations to encapsulate the universe — all time, all space, everything, everywhere. Perhaps a little like a DNA sequence, here numbers and shape define it all. [2b]

3. And, dynamics to grasp continuities-symmetries in motion

We assume all notations are always active. Each builds on the prior; therefore, only the current notation, 202, has time asymmetry. That key issue is being addressed in several ways, albeit it’s one of our youngest issues among many open issues within this emerging theory. [3a]

The number of notations, of course, is not the key. The concept of a grid from the first moment to this day is. Again, using Planck Time, we go from the first moment to the first second. Out of 202 notations, the first second is within Notation-143. The first light year is within Notation-169. Then, we go 370,000 years (Notation-187) for recombination, to 300 million years (Notation-196) for large-scale structure formation, to the first billion years within Notation-198 to this very time right now (Notation-202). And, yes, these numbers outline aether theories (and that would even include lattice Higgs theories).

The stacking and packing of spheres is a key activity and a natural inflation. By following the progression of Planck Charge and Planck Mass, we find that there is enough temperature for the Quark-Gluon Plasma (QGP) between Notations 135-and-136. Using Euler’s base-2 exponential notation, from a cold start (very close to absolute zero), the QGP begins within the first second of the start of the universe.[3b]

Natural Inflation: One primordial sphere per primordial unit of length. The thrust for an expanding universe starts with one primordial sphere per unit of primordial time. If the expansion is then calculated for just the first second, using Planck’s base units, PlanckTime generates 539-tredecillion spheres per second. Those numbers are necessarily woven together with Planck Mass, Planck Charge, and the speed of light. If we were to use StoneyTime, it would generate 4605-tredecillion spheres per second.[3c]

4. Assume a necessary, always-active, finite-infinite relation.

Finite-infinite. Many scholars say that infinity is messing up science. Perhaps their concept of infinity is incomplete. Perhaps they do not think about the origins of dimensionless constants. Now, we have a very large number of infinitesimal primordial spheres per second coming from somewhere. If we say “infinity” most scholars will have a problem. Yet, if we say that pi is the concrescence of continuity, symmetry and harmony, and that looks like a sphere, there may be fewer problems. If we say that the qualities of continuity, symmetry and harmony define the infinite, perhaps we should stop and contemplate that.

Think. Reflect. Be gracious… because that is exactly what is being asked of every scholar-scientist-student.

Infinitesimals. Creating a transitional logic, infinitesimals challenge us to begin to grasp the dynamics between the finite and infinite. If on one hand we open the definition of the infinite and on the other we radically limit its scope, we might begin to understand how infinitesimals relate to strange things like blackholes, singularities, multiverses, and all our hypothetical particles proposed over the years.

Science is the continuity and symmetry that start within the sphere. And, science is also the harmony that is found deep within the sphere’s Fourier Transform. Continuity has simple values: order… memory. Symmetry has more complex values: relations… balance. And harmony has the most complex values: continuities-and-symmetries in motion. It is life, consciousness, and perhaps all our other values, even hope and love.

Continuity-symmetry-harmony define pi. They also characterize the infinite. [4]

Infinity is continuity, symmetry and harmony, nothing more and nothing less. Categorically, that’s it for now.

5. Assume domains of perfection...

Facing quantum fluctuations. In light of the 202 notations, the focus is first between Notation-64 and Notation-67, a range within which current research detects fluctuations. It begs the question about what is happening between Notations 1-and-64. If cubic-close packing is generating basic geometries within densities that are on the order of neutron stars (based on Planck’s numbers), one can imagine that only the most efficient combinations of points, lines and geometries manifest. There is a thrust of simple perfections; yet, there are also many more factors to analyze that could interrupt a flow of the geometries of a simple perfection. [5]

6. We all know there are domains of imperfection.

Indeterminacy and quantum fluctuations are inherent in our universe. Yet, many people are unaware of the gap created by five tetrahedrons sharing a common edge and how within the infinitesimal scale it opens the way to fluctuations. If systems begin to manifest around Notation-50, there could be many notations where indeterminacy prevails but is too infinitesimal to be measured..[6]

7. There’s a place on this grid for the Mind-consciousness-values.

Further considering the continuity, symmetry and harmony within pi. Throughout our brief history as a civilization, the wise among us have said something like, “Truth sets you free.” Surely the best of science has empowered us. The best of science has liberated the human mind. Yet, freedom is a value-laden word. What is continuity? What is symmetry? What is harmony? Are all three necessarily what defines both the first sphere and the concept of freedom?

Pi, spheres, infinitesimals and notations are well-known parameters within science yet apparently at no time have these three been applied to the first instance of the universe. Also, the progression, Notations 1-to-64, has not been formally engaged within academia. Within one of our early charts, we made groups of ten notations and postulated the following:
1. Forms (like Langlands programs/automorphic forms) develop in the first ten notations, 2-11.
2. Archetypal Structures develop in the next ten, from Notations 11-20.
3. Archetypal Substances develop in the next ten, Notations 21-30.

Here within these thirty notations might be the hypothetical particles that mirror the particles within the Lambda Cold Dark Matter (ΛCDM) model and the Standard Model for Particle Physics.

4. From Notations 31-40, Archetypal Qualities are given a place along the grid.
5. And from Notations 41-to-50, Archetypal Relations are postulated.
6. From those five groups, Archetypal Systems are then postulated (Notations 51-60). Here within these notations was the beginning of systems theory, the Mind, consciousness and values. It is all physical. Yet, the physical systems measured by our most sensitive devices like the Large Hadron Collider can only measure effects from around Notation-65 and larger.

The first 64 notations. We will continue to explore how these infinitesimal spheres manifest the Fourier transforms and all other integral transforms. These dynamics are so rich, surely here are the very keys for electromagnetism-and-gravity and the yoke that ties them together. [7]

8. Everything-everywhere always affects everything-everywhere.

Our history is so short, so minuscule, and we’re on a step learning curve. And, describing this infinitesimal universe has been problematic. Now, we are not scholars, certainly not a cosmologist nor astrophysicist. We are high school people, but that has not stopped us from discovering Tim N. Palmer of Oxford and his work with Invariant Set Theory, or Simon White of the International Max Planck Research School on Astrophysics in Munich who is developing a Cold Dark Matter paradigm, or Alain Connes (and company) regarding their Spectral Standard Model.

We’ve asked for advice from many people — “What are we doing wrong?” “Is this a theory of everything? How can it have only a picosecond difference with the big bang theory? We have so many more questions. [8]

Where pi has continuity from the first moment of time to the current time, phi (φ) has a very different ordering principle that appears to be limited by notation. There may be other kinds of fluctuations where these two ordering principles seat together. It is ideation that is currently being explored.

Many brilliant scholars have been working on these problems from quite a different perspective. None have acknowledged the simple outline created by the 202 base-2 notations. To say the least, our first 64 notations are enigmatic. Although infinitesimal, Notations-65-to-67 are on the edge of our measuring capabilities of our finest instruments (i.e. the LHC, CERN, Geneva).

Notwithstanding, we can apply logic and intuit the dynamics of Notations 1-to-64. Here is the basis for a natural inflation and homogeneity and isotropy. Here is dark energy and dark matter. Yet, here, too, is a domain of perfection prior to quantum fluctuations. And, yes, our universe looks-and-acts like its exponential.

We recognize how idiosyncratic such statements are. For many our work would naturally be characterized as crackpottery. Yet, this is just our beginning. If we take the base units as defined by Planck or Stoney, densities are in the range of neutron stars and blackholes. It is a very different picture of our expanding universe. Yet, the enigmatic and idiosyncratic may be necessary to open new paradigms of who we are and why.

Thank you. -BEC

For more: 12-question survey, presuppositions, universe clock, twelve key concepts, first Instants, pi challenge



Concepts and ideas. On my path, I have met a few of our finest living scholars. All struggle. It’s never easy even though a few make it look easy. Many of us do not have the finesse of others and our work is written off too quickly. There are so many ways to interpret a data set like the chart of 202 notations. When the data doesn’t cohere or leaves questions unanswered, theories provide temporary work-arounds. Our theory has been known by many names. Big Board-little universe captured the sense that space and time are disintermediated and the two need to be redefined. Quiet Expansion was our simple way to distance ourselves from the Big Bang. Yet, our most descriptive was the “Mathematically-Integrated View of the Universe.” This model, to my knowledge, is the only one that outlines the universe with mathematics — both numbers and geometries — with causal efficacy from the first instance to this very moment. There are thirty presuppositions. If, in some manner, these are engaged, we believe there could be a profound intellectual awakening and possibly a resurgence of ethics. -BEC



[1] Numbers, Boundaries & Parameters. First, we have a start time around 13.8 billion years ago. Then we have our current time. Just like DNA, every moment has its own unique identify within the universe. Every instant using base-2 notation is part of key continuity equations. Like the 31 trillion digits of pi (31,415,926,535,897) (See the work of Emma Iwao) that are never-ending and never-repeating (always changing and always the same), here is the heart of our horizontally-scrolled chart of the universe. Of course, the first continuity equation is Planck Time to the current time. Planck Length to the size of the universe is next. Then, Planck Mass to the total mass of the universe and Planck Charge to the total charge in the universe follows. A bit much, the veracity of such a concept is questioned and explored throughout this website.

Keep questioning everything. We get bored and dull if we don’t. For many years (and within some quarters, even today) if you questioned the big bang, you’d be laughed out of the room. Part of our problem is our arrogance that cuts off intellectual discussion. For example, many scholars are sure that science is value neutral. That’s just a bit of silliness. Its deepest definitions exude value and values. Eventually we’ll realize that we have adopted old constructs that impede our thinking and our sciences. Here are what may be considered the biggest three:
Hawking’s infinitely-hot big-bang start holds us back. It blocks a cold start.
Newton’s cosmology of absolute time and space suffocates us. It blocks the current point.
Aristotle’s failures with geometry truncate creativity, blocks our grasp of indeterminacy and creativity, and diminishes geometry in general. This story is one of the deep failures of scholarship.

Current work: Fine Structure Constant and Pi. Scholars have been challenged and mystified by these two physical constants. They should be. Inherent in both are starting points for the universe. I am now working through the scholarship of Jeff Yee, author of The Relationship of the Fine Structure Constant and Pi (June 2019) and of Giuseppe Dattoli, the author of The fine structure constant and numerical alchemy, 2010. Yee has clearly stated, “…the fine structure constant is derived from a geometric ratio of surface areas, as a result of vibrations in a lattice with a body-centered cubic arrangement.” Then later, “The fine structure constant can be derived in terms of pi due to a ratio of geometric shapes, possibly the result of the motion of something that fills empty space.” He’s on it!

Written within my mind’s eye, “We should not underestimate the place, position, and power of pi!” We still have many open questions within number theory.

[2a] Geometries have been making a comeback. Topology, shape theory, representation theory, category theory, Langlands programs, string theory (M-theory) and supersymmetries (SUSY) are all mathematical formulations that have a place on our grid. Base-2 is the simplest grid. Mathematical realities are precursors of physical realities. These (and many other) disciplines need the first 64 notations out of the 202 that outline the universe and redefine space-time and infinity. A simple function like cubic-close packing of equal spheres can take its place as a most-simple, key function of our universe. Why not?

[2b] Continuity is numbers. And, numbers define a face of continuity. Inculcating the spirit of Pythagoras, we first turn to Theano, On Piety (as reported by Thesleff, Stobaeus, and Heeren), “…he did not say that all things come to be from number; rather, in accordance with number – on the grounds that order in the primary sense is in number and it is by participation in order that a first and a second and the rest sequentially are assigned to things which are counted.”

Big bang cosmology lacks continuity. First, it’s too hot. Problematically, it tries to cool things down too quickly. Then, it runs out of energy. And, it fishtails with inflationary excuses.

An infinitesimal sphere defined by dimensionless constants has a metaphorical equivalent in every level of science and within each notation. The universe would appear to be constantly testing, changing, and evolving to be more efficient or “more integrated.” It is not difficult to imagine. Stephon Alexander’s group, The Autodidactic Universe, is working on it.

It is, however, very difficult to imagine that one primordial sphere is generated for every unit of an infinitesimal primordial length. That’s a tall order, but it is logically coherent. The net-net is the generation of a phantasmagorical number of infinitesimal primordial spheres per second. Every second something on the order of the area defined by the path of the International Space Station is manifest (seemingly out of nothing). Within a year, an area about the size of our solar system is created.

So, again, our essential challenge is to re-engage our understanding of the nature of infinity and to give it some breathing room without all the poetry and mythopoetics.

Our model sometimes called the Quiet Expansion, is a mathematical — both numerical and geometrical– model of the universe and it is entirely predictive. Just silliness? Please let us know: 12-question survey for this article.

[3a] Scholars like Neil Turok make similar claims. I thought for sure that Neil Turok and his colleagues, Feldbrugge and Lehners, would quickly embrace our model. They did not. One of their claims is that the universe acts like it is constantly starting. Within big bang cosmology, such a claim is counter-intuitive. Within a cold-start model, it at least has a chance to work. They reached their conclusions from a totally different path. Our first note to them was back in 2016, but they have had nothing to say to us. I think if they could point to something that was wrong, one of them would have said as much. Also, it is natural that close-knit groups evolve with specialized language and concepts which those outside their group do not fully understand.

In his book, A Different Universe (page 120-121), Robert Laughlin, a Nobel laureate, cautions us about the aether. It is a tainted concept. Notwithstanding, an aether at the Planck scale is not your father-or-mother’s aether.

New Physics Beyond the Standard Model (Wikipedia). Stymied for so long, Beyond the Standard Model has its own acronym now, BSM. It has become its own special category of study. And, it should be. We’ve all got to push the edges of our understanding of things. These studies are all too important to be left in the hands a few elite scholars. Among those who cannot yet imagine a new physics based on infinitesimal spheres that are defined by the Planck scale, an excellent read is John Ellis‘ May 2021 ArXiv article from the Andromeda Proceedings (BSM-2021 Conference, Zewail City, Egypt), SMEFT Constraints on New Physics Beyond the Standard Model (PDF). The Center for Fundamental Physics (CFP). In collaboration with the Faculty of Engineering and Natural Sciences at Sabancı University, this online international conference was titled, “Beyond Standard Model: From Theory to Experiment (BSM-2021)” and it ran from March 29-April 2, 2021. It seems to me that a conceptual; stumbling block goes back to the general acceptance of concept that the infinite is nowhere found within the finite (Hilbert). Of course, we start with pi. Is it finite or infinite? We observe the continuity of its never-ending, always the same, forever-changing numbers. …finite or infinite? We observe its perfect symmetry. Is it finite or infinite? Now, how about the sphere’s inherent Fourier transforms? Are those harmonic functions finite or infinite? Both? A dynamic bridge between the two?

[3b] 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.

[3c] Expanding Universe. This model of the universe has a very natural inflation. It is naive on the surface — one primordial sphere per primordial unit of length and time — the result is bewildering. How can we begin to imagine what 539-tredecillion spheres per second means? If necessarily woven together with Planck Mass, Planck Charge, and the speed of light, it is a radically different model of who we are and why. That finite-infinite relation becomes penultimate.

[4] Scientific truth. The influence of Tegmark, Arkani-Hamed, and Turok on our thinking is substantial. Until we are able to grasp a better definition of space, time and infinity, all scientific truth is relative or incomplete. Continuity-symmetry-harmony have an “extra” scientific truth. Derived from dimensionless constants that are not finite, these qualities beg the questions about the very nature of infinity. Over the centuries, scholars and religionists have built up the concept of infinity. Perhaps all that we can definitively know are the three basic concepts. Why not?

[5] Perfection. The concept of perfection was increasingly minimized as quantum theory developed. All the greats of physics were involved. Starting with Max Planck, Albert Einstein, Niels BohrErwin SchrödingerWerner Heisenberg, and Max Born, concepts like the uncertainty principle, indeterminacy, and quantum entanglement were increasingly mathematically formulated and began dominating scientific thought. In 2001 Frank Wilczek scrutinized Planck’s base units and caused them to be lifted up and re-examined. It wasn’t until December 2011 that we did our little geometric progression backing into Planck’s base units. Not until 2015 did we begin examining the numbers assuming that the first instance was an infinitesimal sphere and that pi defined three facets of perfection within the sphere. And because those spheres are the footings and foundations of each base-2 notation, the concept of perfection and a place for perfection has been re-introduced within a very different framework:
 Foundations Within Foundations:
 Perfections of Pi:
The Start:
 Center for Perfection Studies:

[6] Imperfection. In 2011 in those high school geometry classes, we made models of the five-tetrahedral star, the icosahedron and the Pentakis dodecahedron; we called it squishy geometry. The pieces do not perfectly fit together. There are natural gaps. Aristotle made a mistake that was reinforced by academic thinking for over 1800 years. Even after the mistake was discovered in the 15th century, it had to be rediscovered in 1926 and then again in 2010; and still, there has been no general debate about the significance of five-tetrahedral star and its gap. Here is one profound imperfection built into the very geometries of the universe and it is largely ignored. Here is one critical gap and a place for quantum physics. There are possibly several other equally important places that will be discussed in future homepages. This is a topic of ongoing analysis.

[7] Transformations. Within the panoply of “big bang” cosmologies, the Fourier transform is ignored. Pi and the simplest geometries are as well. If we are to create a working theory, it seems that it should start simple and begin building as best we can using simple concepts. In our model of the universe, the most basic tools of mathematics and science are, by design, all used progressively, building off of one another. In this model there is a place for Langlands programs. There is a place for point-free geometries. There is a more fundamental place for binary functions, scalar field theory and Lagrangian field theory. It is all a bit much for high school people, yet our intuitions help to guide us.

[8] Out on the edge. We have asked questions of the eight scholars pictured — Stephon Alexander (Brown Univ.), Mansoora Shamim (CERN), Nima Arkani-Hamed (Institute for Advanced Study-IAS), Sabine Hossenfelder (Frankfort IAS), Ard Louis (Oxford), Emma Haruka Iwao (Google), Thanu Padmanabhan (Inter-University Centre for Astronomy and Astrophysics), and Claudia de Rham (Imperial College London) — each represents a facet of what might be called bleeding-edge research. Earlier Sylvester Gates had been pictured. A result of our engagement with their work is the linked resource page with our notes and emails. Some scholars, people like Renate Loll and Lee Smolin (Causal Dynamical Triangulation or CDT), have never responded to our emails, so progress with CDT has been slow.

……Stephon…….Mansoora……..Nima……….Sabine………Ard………Emma………Thanu….. …..Claudia

These eight scholars have inspired us. This website is an open dialogue with leading scholars, scientists, and students who think about things like space, time and infinity. These eight scholars are well-known to the people who frequent this website. Each has a reference page to their work, especially as it applies to introducing a new model for the start and growth of our universe. With all the brilliance within academia over the years, it is inexplicable that our base-2 model originated within a high school geometry class. In 2011 we were just following the path down inside a tetrahedron and octahedron to the Planck base units. It was that simple. Today, we will document those efforts by scholars who are beginning to use analogous constructs. _


  • Stephon Alexander: The Autodidactic Universe (PDF), 2021: The universe learns its own laws by exploring a landscape of possible laws (a class of matrix models) and constantly evolves. Stephon Alexander has his six co-authors. Their work has a few parallels with the elemental principles of our model: 1) each notation builds on the prior, 2) all notations are always active, 3) there is a dynamic, never-ending relation between the finite and infinite, 4) the facets of pi help us to understand a perfection within the finite which is the perfection of the infinite which is continuity-symmetry-harmony, and 5) continuity-symmetry-harmony are facets of the infinite creating, the order, relations and dynamics within the most infinitesimal spheres.
  • Ard A. Louis: Generalization bounds for deep learning, Guillermo Valle-Pérez, Ard A. Louis, arXiv:2012.04115v2, December 2020 With some caution, it seems that our theory complies with the requirements for a theory for deep learning, i.e. such a theory would readily scale with data complexity. In our theory we eventually scale to include everything everywhere for all time. We’ve become a de facto school to capture the differences between the architectures within the first 64 notations. It is entirely computable on the surface and we are confident it will accommodate the differences between any and all optimization algorithms. We had been familiar with prior work by Ard Louis and from his December 2020 ArXiv article (linked above) we will now turn to others within the deep learning space.
  • Thanu Padmanabhan: Planck length: Lost + found, Thanu Padmanabhan, Elsevier, Science Direct, Physics Letters B, Volume 809, 10 October 2020. Thanu Padmanabhan has been focused on the Planck scale as long as anybody living today. It is a domain of the mind. It cannot be reached by anything other than logic and mathematics. One might think that at such an infinitesimal scale, there is an absolute convergence of time, space, matter and energy. It all becomes a singularity. It is a viewpoint now echoed throughout the scholarly world. For me, it begs the question, “What are Planck’s four base unit calculations? Shall we ignore them?” I don’t think so. Padmanabhan tells us that a “relativistic point particle is a zero dimensional object.” I am not so confident. Even though these calculations look like a “point” particle, all the dynamics of the dimensionless constants that define those units are theoretically scale invariant; those characteristics or qualities do not go away. The classically-schooled scholars still think in terms of the qualities of particles and waves when those calculations are quite obviously much smaller than any wave or particle measurement. We can only know that these physical things exist mathematically. As high school people we found that there are no less than 64 base-2 steps to get into the most infinitesimal Planck scale state. It would seem that each step defines a very unique reality. There’ll be more to come regarding his comments about the (Feynman) propagator and his 1988 examination of the conceptual framework for blackholes.
  • Claudia de Rham: Although much of Claudia de Rham’s work is co-authored with others and they use specialized language within the very unique conceptual settings of astrophysics, her videos and interviews tend to be more general and generally more self-aware and critical of their collective progress. She is her own best critic and has a delightful sense of humor, so as we go forward, we’ll try to weave a path between her public expressions and her very challenging research. So, yes, here there’s more to come as well.
  • Nima Arkani-Hamed. He may forever be known by his lecture in Cornell on October 6, 2010 and for his statement, “Spacetime is domed.” It provoked lots of discussion. I say that a key to a transformative concept of spacetime is to establish its boundaries, then its boundary conditions. We have a symbolic or metaphorical start with Planck’s units. If we accept as a given that the calculations for the age of the universe are close enough, we have a range. If we apply a mathematical construct, Euler’s base-2, we have a process. It is simple and builds on prior work: period doubling bifurcation, Feigenbaum’s constant, PoincaréThe 202 notations become functional. The first second comes out within Notation-143. The first light year is within Notation-169. The first billion years emerges toward the end of Notation-198. Every notation builds of the priors. All time is active. All space-and-time share that emergence and thus spacetime is being redefined. There’s an alternative.
  • Emma Haruka Iwao: The Endless Number. It took the single-minded dedication of Emma Haruka Iwao to singlehandedly introduce the world to the largest possible number in all of creation. From her early childhood she has had a fascination with pi. She may not be Archimedes, yet her work runs circles around him. She has pulled pi out of the finite. And, we proclaim that it is the bridge between the finite and infinite. We further claim that the facets of pi — continuity-symmetry-harmony — are the very definition of the infinite. That’s it. Stop there. Science does not need the millions of books about infinity and the infinite. Pi gives us the infinite in a nutshell and Emma Iwao pushes our nose right into it. Here is where we should begin our theories about the start of the universe!

You’ll find squarks and gluinos in the pages of the Standard Model of Particle Physics but both remain illusive. Why? Could it be that all the mathematics that define these hypothesized particles are just “too infinitesimal” for the Large Hadron Collider? Dr. Mansoora Shamim just might be able to tell us so. She may be the one who opens a path to and down smaller through Notation-64.


Communications: Emails

1. Short emails to those mentioned within the article: Simon White, Tim.Palmer, Renate Loll, and Lee Smolin. We started with Stephon Alexander, Mansoora Shamim, Nima Arkani-Hamed (also on a recent homepage), Sabine.Hossenfelder, Ard Louis, Emma Iwao (recently on another homepage), Sylvester Gates, Thanu Padmanabhan and Claudia de Rham.

2. Email to Robert Laughlin: “It may be a very different universe.” Deep inside the tetrahedron (and its octahedron within), this dynamic GIF showed us how both were derived from spheres (cubic-close packing and sphere-stacking). When we started to follow pi back to its source, continuity-symmetry-harmony were deep within. Acknowledging a symbolic starting point (defined by some analogue to the Planck Length and Planck time), space and time became derivative, finite, and quantized. When Newton’s absolutes are tamped down, a dynamic finite-infinite relation opens up. Here, pi, as the key dimensionless constant, is quantitative in practice while her infinite expression is qualitative. We had a start of the universe with a single, infinitesimal sphere, Lemaitre’s 1927 long-sought-for primeval atom.

3. Emails while hammering on the homepage: Inspirations come from many places. First, there are all the many collaborators and co-authors mentioned within our scholars’ published works, plus there are journalists and world leaders who cause us to write. For example, Guillermo Valle Perez is a co-author with Ard Louis. Then, I receive an email soliciting money for the Obama Library. A special listing of a range of people will evolve as each are sent emails about how our work is related to their work.

4. Google: “Break free of little worldviews.” Get the entire universe. Get access to a simple logic. Pi holds clues that opens it all up. Pi is continuity, symmetry and harmony. Continuity-symmetry-harmony is a bridge between the finite and infinite. Learn more here.

5. WordPress: The purpose of this work and website is to break the impasse created by infinitely-hot big bang theories (versus a cold start — and by misleading concepts of space and time ( and by a failure of Aristotle in basic geometry, a mistake that was repeated for over 1800 years ( As a result of this effort, wouldn’t it good to have an intellectual awakening around integrative thinking, a resurgence of ethics, and a hypersensitivity about the nature of our walk in this universe. To that end, many.emails are sent to key academic thinkers and leaders throughout the world. -Bruce


Communications: Instant Messages

A complete left turn, I sent Reed Hasting (co-CEO of Netflix) a note to congratulate him for his past ten years of hard-fought successes. Yet here, I recommend that he incorporate an integrated view of the universe in all that he does.

@AppleEDU With all of Apple’s culture, you should be leading the way to break us all out of parochial worldviews and into a mathematically-integrated view of the universe so when we think it is in context with all time, all space, everything, everywhere!

Nature Magazine

Magdalena Skipper writes, “Confronting gender bias in Nature’s journalism – at Nature, we know we need to continue to work hard to eliminate gender & other biases.” To which I sent the following Tweet.

@Magda_Skipper No surprise. So going forward, empowering all people is the name of the game. To do it, we’ll all need to break through our limited worldviews so we totally engage the universe, everything, everywhere for all time: No surprise indeed!

Simon Ainslie, NEOM “The thrust for perfection is built into the very fabric of the universe. Continuity-symmetry-harmony, the essence of the circle and sphere, are infinite qualities that are the foundations of the finite, the first moment. To open a way to a sustainable future, build on these three universals defined by the oldest equation in our common history, pi. is a small start on a model of the universe that uses such logic, mathematics, and physics. Until we break through our limited worldviews, our ethics and values will also be limited. Thank you. -Bruce ( A message through Linked IN)

@petertallack @sciencefactory You just might enjoy knowing about a model of the universe using base-2 and starting with an infinitesimal sphere defined by the Planck base units. It has a rather natural inflation, all within just 202 notations. It’s an exponential universe!

@rweingarten Of course, “honest history” is perspectival. Our problem is our little worldviews all have differing vanishing points. Only a highly integrated view of the universe has the long history and greatest perspective: is just a start. Note: Randi Weingarten is the president of American Federation of Teachers and in a recent speech she said that she wants her teachers to engage accurate history. In light of the universe, the record of human activity beginning in the 4th millennium BC is all current events. And, very little of it is a pretty picture, but it does tell us who we are to date. Have we changed? Have we grown? How much better can we become? Many, many people are trying hard to keep us growing, learning, and doing good. In this model of the universe, that thrust is built into the universe. See more.

@philipbull Beyond ΛCDM: Problems, solutions, and the road ahead, Physics of the Dark Universe. Thinking about your collective work here: Under References, there is a link to your site. The primary page regarding it all is here:

Then there are all the short spontaneous ones like these: @brianmclaren You need an integrated view of the universe… part epiphany, a little MEGO, but a bit of fun: Or, like this: @lsarsour@CoriBush@AOC Yes, yes, yes, but we need a new context for this atonement. Our little worldviews are clashing all the time. A step out of that foray is an integrated view of the universe — just 202 simple base-2 notations. Our start on it: It is easy and calming, too!


A few final words

In 1980 in Paris at the Institut Henri Poincaré, one day I would be in discussions with Jean-Pierre Vigier and the next day with Olivier Costa de Beauregard. They were polar opposites. We focused on the 1935 EPR Paradox and Bell’s inequality equations. By the time I returned to Boston University later that year, I thought, “Nobody has an answer. You could spend your life spinning in circles.” I collected my books at BU and continued walking. I went back to a business that I had started ten years earlier. Little did I know that by helping out in a high school geometry class (December 2011), all these issues would be reopened. It would take me at least five years to get reoriented to learn what today’s scholars were saying. They’ve made some progress. Many new concepts have been introduced. But unanswered is the question, “How does it all cohere?” Solutions to key issues are still outstanding. I do not have that much more time in my life so I have asked quite a few scholars, “What’s wrong with this picture?” referring to our 202 base-2 notations, “Is it a framework, an outline within which to work, or not?” I believe it is. –BEC



There are many ways to be involved:

  1. Tweet or email the link to this page to those who you believe would be interested.
  2. Complete a survey. There are two surveys, both using simple Yes / No / Maybe answers.

We would celebrate if you could take time to answer the questions of either survey! Copy the questions to an email and send them in with your answers and comments!


Key Dates for this article, Empower

  • This document: Started on Thursday, June 10, 2021 @ 7 AM
  • First posted for collaborations: June 10, 2021 at 2 PM
  • It also became a homepage: June 14, 2021 at about 6 PM
  • The URL:
  • The Prior Homepage:
  • First Headline: Defining a new model of the universe
  • Second headline: Grow Beyond Those Limited Worldviews, Adopt an Integrated View of the Universe
  • Third headline: An Integrated View of the Universe Enlivens Any and All Worldviews
  • First Tagline: Empowering scholars, scientists, and students of every kind
  • Second Tagline: Eight Steps: Scholars, scientists, and many students are helping us.*
  • Third tagline: Towards An Integrated Understanding of our Universe
  • Another tagline: Let’s go deep and be all-inclusive in our understanding of this Universe.
  • Another tagline: Opening boundaries and parameters to context more of our Universe
  • Today’s tagline: Attempting to grasp the numbers and systems that define our Universe
  • Possibly the next homepage: Password: Tredecillion
  • The most recent update of this page: Saturday, September 11, 2021.
    Earlier, added 3c. August 30, 2021, added Ellis reference.