First, we stretched well beyond our comfort zones. We started with the two key numbers, Planck Length – 1.61619926×10-35 meters or .000 000 000 000 000 000 000 000 000 000 000 016 161 992 6 meters and the size of the observable universe: 8.79829142×1026 meters or 879,829,142,000,000,000,000,000,000 meters
There are many numbers in between the two. Each “0” represents a major base-10 transformation; and within each base-10, there are three or four base-2 notations. Though some say that the Planck Length is a special type of singularity, it has a specific length. Yet, that length is so small, for about 100 years, it was virtually ignored by the entire scientific community. Perhaps a better way of looking at the Planck Length is through the lense of geometry. If we make it one of Alfred North Whitehead’s point-free vertices of a specific length, each time we multiply by two we grow the size as well as the number of vertices.
The Numbers of Vertices at Key Notations Between 1 and 65. If we were to assume that the Planck Length is a vertex, unusual concepts flow. First, consider the generation of vertices just by multiplying by 2, then each result by two, over and over again. By the tenth doubling there are 1024 vertices. By the 20th doubling, over a million more are added. On the 30th, another billion+ are added. Then, comes another trillion+ at the 40th, a quadrillion+ at the 50th notation and a quintillion+ at the 60th. At the 61st there are another 2+ quintillion vertices added. These vast arrays and systems of vertices cannot be observed.
This is the domain of postulations and hypostatizations. Consider this concept: going within from about the 65th notation, the domains begin to be shared. More and more is shared by everything as the Planck Length approaches. Each notation organizes uniquely, yet within groups. And these natural groupings reflect all the diversity within all the notations 65 and higher. It seems that the mathematics of cellular automaton may figure into the first 20 or 30 notations. We start with the most basic Forms, then Structures, which become the pre-structure for Substances, archetypes for Qualities, then Relations, then the Mind. We turn to systems theory, group theory, and set theory to discern the order of things.
Perhaps there are five hot spots for immediate research: * Notations 1-20 and the foundations of cellular automaton and fractal geometries by using the functions created by more than one million vertices * Notations 50-60 and the foundations of the Mind, logic, psychology, memory, thought, epistemology and learning with over 500 trillion vertices at the 59th notation and then another quintillion+ vertices within the 60th notation. * Notations 60-80, the emergence of the particles and atoms and the most basic structures of all physical matter * Notations 100-103, the emergence of the human life and most all life as we know it * Notations 135-138, the transition to the Large-Scale Universe with the possibilities of uncovering pathways to the Einstein-Rosen bridges and tunnels also known as wormholes. Key references for more: The numbers
Facts & Guesses. The Facts are what is measurable and what fits within each domain. The Guesses are about what goes on with those domains (aka steps, notations, layers or doublings) especially those that remain blank. Is there a pattern, especially a cyclic pattern that manifests in another notation? We followed Max Planck where he took the constants of nature, starting with the speed of light to calculate the smallest number. We took the age of the universe, with some help from scientists, to learn the largest calculation of a length, the Observable Universe. Making sense of these numbers is another story. So, over the forthcoming weeks, months and years, we will be looking even deeper.
Vertices as building blocks. If we take it as a given that that the Planck Length is also a vertex, by the second doubling, there are four vertices, just enough for a tetrahedron. By the tenth doubling there are 1024 vertices. The number doubles each notation. By the 20th doubling, over a million more are added. On the 30th, another billion+ are added. Then, comes a trillion+ at the 40th, a quadrillion+ at the 50th notation and a quintillion+ at the 60th. At the 61st there are another 2+ quintillion vertices. What does it mean?
The simplest geometries yield a deep-seated order and symmetries throughout the universe. Those same simple geometries also appear to provide the basis for asymmetry and the foundations of quantum fluctuations and perhaps even human will.
Observations. 1. Social media begins at Step 119, which is within the size of a home. It also involves several steps for the actual transmission of information within wires, to satellites, and stored within computer hardware. All of those details are not as important as what I have posted. 2. We all live, work, and enjoy life usually within a 100 mile radius of our home. That involves steps 120 to 133. What happens outside of those steps is not important to me. 3. To me, my friends are the most important people on earth. 4. If we give Barack Obama (United States), Vladimir Putin (Russia), and Xi Jinping (China) time together, they will work out their differences and focus on ways to help the world. 5. I would like to travel to Washington, DC, Moscow, and Beijing to learn, first-hand, how these governments work. 6. No nation should consider itself to be the best; we all need to strive to get along with everyone. 7. The Big Board-little universe was driven by geometry first and base-2 exponential notation second, which is fascinating. That the entire universe has the possibility of having that deep-seated geometry in 202-to-205 steps is especially intriguing. 8. Given that each notation is related by geometries and numbers, the parameters of continuity and symmetry take on new meaning. 9. The Big Board-little universe makes astrophysics and cosmology more approachable. 10. The transition from one notation to the next must involve and creatively use all the universals and constants that we currently understand. This opens another possible world for exploration and speculation.
Big Board-little universe: This chart was developed in December 2011.
Let us start with the two key numbers:
1. The Planck Length: 1.61619926×10-35 meters which is 0.0000000000000000000000000000000000161619926 meters
2. The Observable Universe: 8.79829142×1026 meters or 879,829,142,000,000,000,000,000,000 meters
Max Planck gave us the first number. The second number is the Planck Length doubled, then doubled, then doubled again and again. Just 202 times, the figure approximates the generally-accepted, current estimates for the size of the universe. Our number is generated from simple math and the Planck scale. The generally accepted estimate is generated within the university and that process is much more complex!
There are many numbers in between the two. Each “0” represents a major base-10 transformation; and within each base-10, there are three or four base-2 notations. Though some say that the Planck Length is a special type of singularity, it has a specific length. Yet, that length is so small, for about 100 years, it was virtually ignored by the entire scientific community. Perhaps a better way of looking at the Planck Length is through the lenses of geometry. If we make it one of Alfred North Whitehead’s point-free vertices of a specific length, each time we multiply by two we grow the size as well as the number of vertices.
This is the domain of postulations and hypostatizations. Consider this concept: going within (from 1-to-65) from about the 65th notation down to Notation-1, more and more is shared by everything especially the Planck Length base units.
Each notation organizes uniquely, yet within groups. And these natural groupings reflect all the diversity within all the notations 65 and higher. It seems that the mathematics of cellular automaton may figure into the first 20 or 30 notations. We start with the most basic Forms, then Structures, which become the pre-structure for Substances, archetypes for Qualities, then Relations, then the Mind. We turn to systems theory, group theory, and set theory to discern the order of things.
Perhaps there are five hot spots for immediate research: * Notations 1-20 and the foundations of cellular automaton and fractal geometries by using the functions created by more than one million vertices * Notations 50-60.The foundations of the Mind, logic, psychology, memory, thought, epistemology and learning with over 500 trillion vertices at the 59th notation and then another quintillion+ vertices within the 60th notation. * Notations 60-80. The emergence of the particles and atoms and the most basic structures of all physical matter * Notations 100-103. The emergence of the human life and most all life as we know it * Notations 135-138. Transition to the Large-Scale Universe with the possibilities of uncovering pathways to the Einstein-Rosen bridges and tunnels also known as wormholes. Key references for more: The numbers.
Facts & Guesses. The Facts are what is measurable and what fits within each domain. The Guesses are about what goes on with those domains (aka steps, notations, layers or doublings) especially those that remain blank. Is there a pattern, especially a cyclic pattern that manifests in another notation? We followed Max Planck where he took the constants of nature, starting with the speed of light to calculate the smallest number. We took the age of the universe, with some help from scientists, to learn the largest calculation of a length, the Observable Universe. Making sense of these numbers is another story. So, over the forthcoming weeks, months and years, we will be looking even deeper.
Editor’s note: When this page was first posted in 2014, it was part of a high school Science Fair project. At this point at the end of the article, there was a link to take ta little survey. Eventually a link will be restored to a new survey, but not today!
In 2011 we encountered very large and very small numbers that were all necessarily related, a real continuum, for our Big Board-little universe project. We asked over and over again, “What does it mean?”
In the middle of the chart, from Notations 80-to-140, were numbers with which we had worked in the past . The very small numbers, truly infinitesimals, ranged from Notations 1-to-64. The very large numbers ranged from Notations 140-202.
My first steps to analyze the nature of a number was back in 2016. I had been reminiscing about Pythagoras and his affections for numbers when I found a reference to an article about Theano (his wife, daughter, or confidant). It challenged my prior understanding. Too important, I started a new article, On Constructing the Universe from Scratch, with that key quote from her.
Numbers are first and foremost relational. They appear solitary, but there is a necessary relation to every number that surrounds it or in any way is incorporated with it. Numbers bear our identity and the identity of everything since the very beginning of space and time.
Here are a few other pages about numbers within this website:
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.
I invite you to explore an alternative model for the emergence of our universe. -BEC
1. With numbers we 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.”
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. With geometries we 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 stepsto the edges of the universe. We were more than flummoxed; it was all too simple.
By 2014 our current workingchart 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, within dynamics we 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. We 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.
Infinity is continuity, symmetry and harmony, nothing more and nothing less. Categorically, that’s it for now.
5. We 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. A place on this grid for the consciousness-values-and-The Mind
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 (guessed, imagined, hypostatized) 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.
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]
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.
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).
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.
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?
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.
“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 the 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 Bohr, Erwin Schrödinger, Werner 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: https://81018.com/foundations/ •Perfections of Pi: https://81018.com/perfection/ •The Start: https://81018.com/starts-8/ •Center for Perfection Studies: https://81018.com/center/
[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.
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, Poincaré… The 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!
Mansoora Shamim’s Hypothesized, Reified, Hypostasized Numbers: I was stopped short with the work of Mansoora Shamim at CERN labs. On her way to her PhD she did seminal work at University of Oregon and Kansas State University. She didn’t name the squark or gluino, but she helped to keep these two mathematically-defined concepts alive.
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. Please do a word search of this website on her first name, Mansoora.
Robert Laughlin, Stanford, A Different Universe, Reinventing Physics from the Bottom Down, 2005 On page 120 he says, “The word “ether” has extremely negative connotations with theoretical physicists because of its past association with opposition to relativity. This is unfortunate because, stripped of these connotations, it is rather nicely captures the way most physicists today actually think about the vacuum.”
A Dynamical Theory for Massive Supergravity, S. James Sylvester, 2013 In 1971, about when theories about supersymmetries began to emerge, S. James Gates was at MIT. His 1977 PhD thesis was the first at MIT that studied supersymmetries. He has written over 157 papers and several books about it. SUPERSPACE or One thousand and one lessons in supersymmetry, 1983, written with three colleagues, was his first book about it all; the index begins on page 542. At no time did they stop to ask about dimensionless constants, or the role of pi and the Planck numbers. A little like Johnny Lee’s song, Looking for love in all the wrong places, they did not know that there are continuity and symmetry equations that extend well below all possible measurements of space and time. Though infinitesimal and beyond our measurements, the mathematics is still there.
Footnote: There are many other related pages currently being developed. Most have a security wall requiring a password because these pages are still early-stage developments. If you are interested in helping to develop this model, please request the URL and passwords to join this effort
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.
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 — https://81018.com/start/) and by misleading concepts of space and time (https://81018.com/biased/#Newton) and by a failure of Aristotle in basic geometry, a mistake that was repeated for over 1800 years (https://81018.com/biased/#Aristotle). 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
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.
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: http://81018.com 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. http://81018.com 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)
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: https://81018.com 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: http://81018.com It is easy and calming, too!
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
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!
The Planck Length is the smallest. The largest length is the Observable Universe.
This may well be the first time you will have seen the entire universe notated on a chart, all numerically and geometrically ordered, in a very granular relation.
Here are two simple charts with simple mathematics (doublings or base-2) that render a simple model that opens many questions.
The Planck Length is not a point because it has length. Points do not have length. And, if you were to multiply that length over and over again by 2, anywhere over 202.34 times, you will go out to the largest possible length, the Observable Universe. Called exponential notation, it is a very simple scale of the universe.
It is hard to believe, yet the simple math tells the story. This project uses that range, 202.34 to 205.11 because even though math can be exacting, our knowledge of the age of the universe is not.
First, these ordered relations by numbers and geometries for so few notations are already helping students to understand the relations between disciplines. Looking up or looking within, there is a sense of real order where there was chaos.
Notes about Look-and-feel and Navigation: If a little thumbnail of any picture is displayed, simply refresh your browser and the full-size version should paste in. Also, if any of the letters from right column, the Archives and Meta are bleeding through the image of the Universe Table, please open your window larger (possibly to full screen). Usually if you click on the last sentence in each description you will go to the next page.
Key Surprises: First, just the very small number of notations was a surprise. When we started at one meter and got down to the size of a proton in about 50 steps (at that time, we were dividing each notation in half), it seemed hard to believe. Then, when we got in the range of the Planck Length in another 66 steps, it was puzzling. When we went to the large scale and found only another 90 or so notations, we were flummoxed.
The universe divided in thirds. The old logic of the Small Scale, the Human Scale, and the Large Scale universe is in play, yet here the start points are quite different than the historical use of those terms. Here the very logical range for each is defined by simple math. What does it mean to look at the totality of the universe and it in thirds.
The simple geometries. If the Planck Length is defined as a single vertex at notation 1, by step 60, it becomes a major structural enterprise. The proton-fermion-electron appear to manifest at step 66. This small scale universe of geometry and numbers is unexplored. Perhaps it is the first step for a science and basic logic for perfected states within this continuum.
Background: An FQXi call for papers has forced us to focus on the raw power of mathematics to anticipate the structure of real realities. If there is mathematical cohesion, there is probably a real physical reality that it describes. Matching them up and learning where and how such a unit of mathematical cohesion fits within the larger frameworks is the challenge. More…
[15] Base-2 and Prime-Number Notations. We see the simple progression of numbers within our base-2 system. In light of it, how should we engage base-3? Wouldn’t that base-3 expansion necessarily be in sync with base-2? Might the expansion look more linear, going to Notation-201 in 67 jumps not just 3, 9, 27, 81? If base-5 is necessarily related by the base-2 foundation, might it require 40 jumps to get to Notation-200?
Each prime number will require analysis. The mathematics and geometrics could vary from prime number notation to prime number notation. There may be different iterations. For example, would prime number 7 within the base-2 system move forward via Notations 14, 21, 28, 35, 42… and finally end up on Notation-196 in 28 steps?
Metaphorically speaking, perhaps we should think of these primes to be like an express train to its highest notation closest to 202, then a transfer on a local train, would then bring the effects into the present moment within Notation-202.
Again, let us ask, “What would be the effect of being necessarily tied to the base-2 platform?” Might it affect each base differently? A prime-number notation like 11 might be guided by its relation with base-2 to progress to Notation 198 (11×18) in 18 steps. Might there be a special equation of state at Notation 121 (11×11)? Prime number 13 might jump to Notation 195 in 15 steps. Would it also have some interactive qualities with the progression of 5? 17 jumps to 188 in 11, 19 jumps to 190 in 10, 23 to 184 in 8, and 29 to 174 in 6.
31 goes to 186 in six jumps. 37 goes to Notation 175 in five jumps. Just what is that passageway is anybody’s guess.
What happens with Notations-41, 43 and 47? How about 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, and 101? The nineteen primes thereafter — 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 197, and 199 — are themselves an especially unique place within the universe.
Each new notation initially replicates all prior notations, yet each evolves with its unique functionality.
Another key questions is about symmetry. Does each notation that is “completely filled” with planckspheres within its base-2 platform become fully symmetrical? Notation-202 which is being populated now as the current expansion, may well be literally filling up with planckspheres and is necessarily asymmetrical and directional.
Obviously, we are just being speculative, playing with ideas.
Introduction: Our work started innocently: “Let’s challenge Zeno’s paradox.” The wall in this instance was defined by Max Planck in 1899 with four natural units defined by dimensionless constants: Planck Length, Planck Time, Planck Charge and Planck Mass. When we applied base-2 to these Planck units, we had our numbers in 202 doublings. That was straightforward. Understanding those numbers is a vastly different story. Our focus shifted, “How can we understand the place and importance of what appears to be the largest possible continuum from the Planck base units to the most current state of the four most basic facets of reality: Planck Time to the Age of the Universe, Planck Length to the size of the universe, Planck Mass to the total mass of the universe and Planck Charge to the total energy of the universe at this moment.
Process. It would be a formidable task had we not applied base-2 exponentiation — a big word for doublings — that start at the Planck base level and rather quickly progress to their maximums in and around 202 notations.
We were surprised that the number of doublings was so small. It appears impossible, yet you can readily follow the numbers on either this horizontally-scrolled chart ( https://81018.com/chart/ ) or the vertically-scrolled chart ( https://81018.com/chart4/ ). That horizontal chart starts with the Planck base units and scrolls, left to right, to the current time. The vertical starts with the current time and scrolls down to the Planck scale.
Results. Apparently these charts, just simple mathematics, are the first time anyone has actually charted the entire universe as a continuum; and, by definition, by starting with the Planck scale and essentially multiplying by 2 over and over and over again, this picture of the universe has a simple logic and it is highly-integrated and ordered by definition. Notwithstanding, within our study of numbers and geometries, this model can also account for the chaos and indeterminacy of quantum physics and her fluctuations.
Key ideas come together to establish the relations between continuity, symmetry and harmony as the basis for creating order, relations and dynamics with a clear perception of value, values, and ethics, and even states of perfection, and thus the name of this little research center.
Worldviews limit perspective 