Intransigence becomes hostility. People from every nation and walk of life are not willing to see a broader, more-inclusive context to grasp the meaning-and-value of life. Limited worldviews clash. Temperatures flare and people fight. A better way is an integrative model of the entire universe within which to know ourselves, our world, and a bit more about our universe.
The finite-infinite relation is best understood by expanding our understanding of pi. We first learn the first simple equation, the circumference-to-diameter ratio. That’s a start, then it builds from there. As noted in the summary of pi, “…It is our oldest, most-used, mathematical constant, and the ultimate basis for all equations, especially those describing a fundamental principle of our universe.”
There are three facets of pi, however, that are not finite or quantitative so we assume (hypothesize and/or hypostatize) these facets define the infinite and the qualitative.
Continuity is our first facet of infinity. It is the very nature of order. Within the finite it looks like a string of numbers and feels like time. Pi qualifies; it’s an equation that has never-ending results that are always the same and always changing.
Symmetry is the second facet of infinity. It looks like geometries and is the very nature of a relation. Within the finite it feels like space. Pi qualifies; it’s a symmetry that generates symmetries. It’s an equation that generates equations.
Harmony is the third facet of infinity. It is the very nature of dynamics; and within the finite, it is always cyclical (periodicity) and experienced as space-time moments. Pi’s numbers, geometries, and equations (Fourier transform and others) are here within an eternal dance and there’s a domain of perfection which may be experienced as a moment of perfection.
Ultimately, pi is the face of both sides of every equation, one is qualitative (infinite) and the other is quantitative (finite). Let those natural, dynamic relations be natural. Let all your relations breathe and come alive. Be open and engage the harmony of the universe.
• Are Planck Length and Planck Time real? Among the scholars in this area, they seem to say, “Real enough.”
• Are their numbers real? Infinitesimally small, we are prone to say that these are symbolically real and “close enough.”
• What manifests first? Pi drives the finite-infinite equations; we consider a size/time invariant sphere that is defined by those Planck base units (numbers). We’ve also used Stoney’s numbers. Both sets of numbers are symbolic placeholders until there is a new consensus among scholars, NIST and ISO.
Our Story. In December 2011, our high school geometry classes unwittingly made a first pass at defining the universe using base-2 notation starting at the Planck base units. We believed the scholars that the Planck units for length and time were the smallest possible units of space and time. Our conjecture was that they would also be the very first units of spacetime.
We decided to explore. To get down that small, we followed a 4D path inspired by Zeno. We divided the edges of a tetrahedron by 2, and then its internal octahedron and four smaller tetrahedrons, and continued dividing by 2. There were just 112 steps within to the Planck scale. We thought it might feel a bit like Alice’s fall into that rabbit hole as in Lewis Carroll’s Wonderland. But, our walk was highly-ordered, systematic, yet most magical. As we went down deeper and deeper within, it was not at all confusing. Even our shrinking in size each step seemed quite natural.
We rebounded back in the classroom by multiplying the Planck Length by 2. Later we would add Planck Time. And then even later, Planck Mass and Planck Charge. It was extraordinary going from that smallest unit out to the edge of the universe to watch the current expansion, all in just 202 base-2 notations. Yes, from the smallest to the largest sizes and from the first moment of time to 13.81+ billion years later, we had encapsulated everything-everywhere-for-all-time.
Exponentiation. The entire universe, from the smallest possible measurement to the largest in 202 notations, stretches credulity yet it’s 100% mathematical and predictive. All notations are profoundly related and always dynamic. We were so new and naive about it all, we asked questions of the thought leaders of big bang cosmology, Hawking, Ellis, Guth, Steinhardt… and so many others. “What are we doing wrong?” Nobody was willing to guide us, so we placed the time line for the big bang and our big board, side-by -side. We found only a microsecond’s difference with Hawking cosmology. We were beginning to learn about the problems, so when a scholar labeled our model, idiosyncratic, we knew that his judgement was quick and somewhat flippant. There was — and still is — just too much here to consider.
It has taken ten years to begin to understand why change is difficult to engage. First, there is so, so much vested in the Hawking model. It has stood strong for many years. It began building in 1973 when Hawking and Ellis wrote a thesis, The Large Scale Structure of Space-Time. Every new citation, each new book and movie and video, making reference to Hawking’s big bang cosmology, created a muscular defense around Hawking and his model. Yet, that core belief system could not answer a growing number of questions. It had to choose to ignore others. Second, no new model came along. Still, eventually some of our best scholars broke rank and called more stridently for a new paradigm.
We were late to that party and we had no scholarly credentials, yet our emergent model had clear, simple, and compelling mathematics and logic. Nobody argued that.
Those first 64 notations. Although impossibly small, here is a huge infinitesimal domain that is well below the current thresholds of measurement. Unwittingly, all 64 notations, albeit a most-speculative domain, had never been considered. The more we read and studied about the mathematics of Langlands programs, those earliest notations seemed like a natural home. It also seemed like string and M-theory could benefit. Then we began learning about SUSY, and studies like causal set theory (CST), loop quantum gravity (LQG), spectral standard model (SSM), and others. All could benefit. Then came all the hypothetical particles and what we called the Moonshine outliers. They all needed a place to begin working with the two Standard Models. Most naively we raised our hand, “Over here!” Yet, I would guess that we were too simple, too basic, and our grasp so superficial, nobody dared to get too close. We could readily taint their work! I understood… and understand even today.
Consider the obvious. These 64 notations have dimensionality. The conjectured infinitesimal spheres are not “one-dimensional space entities or membranes of higher-dimensional extensions existing in higher-dimensional spaces.” We might say as above, so below, considering that we started with numbers and basic geometries and carry it forward throughout the entire universe.
A new geometry. In May 2022, our simple clear-plastic models opened a new door. We had plenty of images of a five-tetrahedral gap and that work was well-known within small circles of scholars. With various five-tetrahedral models on my desk for several years, one day I asked myself, “Could there be a five-octahedral gap?” In minutes the first models were made; and within the month, we had our first pass at an explanation. A most-challenging composite is a five-tetrahedral gap on the top and bottom with the five octahedral gap in the middle. In June 2022 we began inviting scholars within pure geometry to help interpret where these gaps fit within the larger scholarly models of the universe. My simple thought was that these basic geometries, especially the three with basic gaps — tetrahedrons, octahedrons, and icosahedrons — could be part of the transition from Standard Model of Particle Physics to a new, different, and very-special science of the infinitesimal. The earliest infinitesimal architecture, we conjectured from Notation-0 to Notation-64, would give us that smooth-most-perfect start of the universe and then open a domain, Notations 65-to-67, for quantum fluctuations (our 2017 speculations).
Very few talk about a geometry of quantum fluctuations. When those words were placed in quotes within an online search, the only references that came up in September 2021 were to this website. Yet, when students made tetrahedrons, octahedrons and icosahedrons with those clear plastic models, they naturally dubbed it squishy geometry (also: https://81018.com/squishy/) and quantum geometry.
When pressed on the possible application of these gaps, our scholars seem to avoid those discussions. We can avoid it no longer. It is time to engage the gaps and all their implications for mathematics, physics, chemistry and biology (i.e. synapses).
The expanding definition of pi as the actual bridge between the dimensionless constants of the infinite and all finite quantities is a key. Pi and spheres go hand and glove. The first sphere emerges, then one infinitesimal sphere per unit of Planck time. In the first second, we are out to Notation-143 and no less than 539 tredecillion (1042) infinitesimal spheres. In the first year within Notation 169, we would multiply 539 tredecillion by 31,556,952 (seconds per year). Exponential notation has taken over, yet there is a linearity deep within each notation.
For better or worse, the universe has begun.
Where do we go from here? Mathematicians and physicists are opening pathways to this domain. It is the domain of finite-infinite transformations where there just happens to be a fair amount of activity. From the esoteric to the basics, magazines like Quanta explore the edges of knowledge. New people are introduced everyday. People like Philipp Dumitrescu call into question the very nature of time. Mary Gaillard, a particle theorist at University of California – Berkeley, asks about the very nature of mass. Peter Scholze pushes forward with his perfectoids in Langlands programs. Although those who define infinity in other ways may disagree, it all seems to boil down to the finite-infinite relation. Many mathematicians are attempting to get beyond David Hilbert and Kurt Gödel and the limitations created by their logic that never entertained the first 64 notations and the perfected states within continuity, symmetry and harmony.
Let’s get beyond our worldviews.
Let us look beyond our little worldviews and consider the universe. In the process of exploring our universe, it was gratifying to find that the International Astronomical Union (IAU) and the United Nations promulgating Universe Awareness, a group that got started in 2004 through the initial work of George Kildare Miley, an Irish-Dutch astronomer and professor at Leiden University’s Observatory. Miley was the Director from 1996 to 2003. Once this page has been gone through several edits, I will introduced these folks to this work and references. Already oriented to a view of the universe, the question is, “Will they be open to the 202 base-2 notations that encapsulate this ever-expanding universe?”
There are many living scholars who have had vision and courage who have helped us begin to break out of our own limited worldviews, people like Frank Wilczek, Robert Langlands, George Ellis, Edward Witten, Helen Quinn, Paul Steinhardt, Sylvester Gates, Alain Connes, and Salvatore Torquato. Of course, there have been many others.
So, as you may well imagine, there will be many more scholars to come who will lead us. -BEC
Endnotes & Footnotes
These Endnotes are placeholders. I anticipate feedback that will open the discussion. Footnotes may be added. -BEC
- Infinite qualities — continuity, symmetry and harmony — shape all
finite quantities. All dynamic equations, here is the beginning of spacetime.
The keys: Qualitative-Quantitative. Continuity, symmetry and harmony are the qualitative; it follows that real numbers that are generated by dimensionless constants constitute the quantitative. So, students, without fully grasping the most-sophisticated work of Hawking, Hilbert, Gödel and so many others over the decades, can understand the outside parameters defined by 202 base-2 notations, then become increasingly sophisticated as they add more and more textures to it. So, we will tarry on unless, of course, we hit a wall where the feedback is deafening and complete.
- Foundations for the mathematics to integrate our Universe
We begin with real numbers. These are the best numbers we have today. They could readily be refined, yet the conceptual boundaries defined by base-2 will be little changed. Notwithstanding, we hold that no page within this website is ever finished. Each can be improved.
- The 202 base-2 notations that encapsulate the universe
Our chart emerged over a five-year period. It took us that long to believe it hadn’t been done and to engage the fullness of it. Beginning in July 2016, the chart stimulated the development of this website for research and another for our secondary schools. That is was all highly-ordered and systematic was surprising and reinforced our basic geometries.
- An Answer to Big Bang Cosmology… It’s just too simple and expansive.
It can’t go on forever. Aristotle had an 1800 year old mistake. We’re less than 100 years into this mistake (Lemaître, 1932; Hawking, 1990). We can begin to clean it up in our lifetime.
The Large Scale Structure of Space-Time (PDF), S. Hawking and G. Ellis, Cambridge,1973
- The First 64 Notations as the Foundations for Everything
So many possibilities open up, an empowering creativity could become contagious. Ethics could begin to break out all over.
- Emergent Geometries of Quantum Fluctuations
When we know there is far more room to expand, we will. Today we have an index of a bit more than a million total words but collectively use less than 170,000 words, and personally limit ourselves to somewhere around 25,000 words. According to Simon Plouffe, there are 215,000,000 dimensionless constants; to grasp that level of subtlety will require new words and new studies. Entirely new fields of study will emerge.
- Pi, One Sphere Per Unit of Planck Time, then Cubic Close Packing…
A re-engagement with pi and an exponential universe such that every expression understood today will become part of standard curriculum. We know from our teaching and testing with 6th grade students that they can readily grasp these concepts and begin using them immediately.
- Next steps: Building consensus
New leadership worldwide could well be empowered. We already have witnessed how younger scholars have been empowered. Getting the attention of today’s leading thinkers is more difficult. However, people making breakthroughs like Peter Scholze or Philipp Dumitrescu may be more open to simplicity. Then, some within their emeritus status, like Mary Gaillard (Berkeley), may become incrementally bolder and not be so quick to judge the new and the simple.
Dynamical topological phase realized in a trapped-ion quantum simulator, Philipp T. Dumitrescu, Justin G. Bohnet, John P. Gaebler, Aaron Hankin, David Hayes, Ajesh Kumar, Brian Neyenhuis, Romain Vasseur & Andrew C. Potter, Nature, V.607, pp.463–467, July 20,2022
International Astronomical Union (IAU) and the United Nations promulgate Universe Awareness, a group that got started in 2004 through the initial work of George Kildare Miley, an Irish-Dutch astronomer and professor at Leiden University‘s Observatory (Director, 1996 to 2003).
References & Resources
A few of the key related works that are studied but not within an endnote or footnote, are added here.
ArXiv: Dark Photon Stars: Formation and Role as Dark Matter Substructure, March 2022 with references to Witten, Wilczek, Kolb, Dimopoulos, Preskill, Fairbairn, Hogan (Carl J.), Garcia-Garcia, and others
Alain Connes, Noncommutativity and Physics: A non-technical review, July 25, 2022 (PDF)
George Ellis, Emergence of time, 2019 with Barbara Drossel and The physics of infinity, Nature Physics, V. 14, Issue 8, p.770-772, 2018
Sylvester Gates, Supersymmetry and Representation Theory in Low Dimensions, Dec. 2020
Robert Langlands, Langlands Program, Trace Formulas, and their Geometrization, Edward Frenkel, 2014
Helen Quinn, BOSE NAS, 20218
Scientific American: The Universe’s Unseen Dimensions, The visible universe could lie on a membrane floating within a higher-dimensional space, (PDF), Georgi Dvali, Nima Arkani-Hamed and Savas Dimopoulos, 20028
Craig J. Hogan, University of Chicago, August 4, 2022 at 2:00 PM
Jürgen Jost, Max Planck Institute for Mathematics, Leipzig, August 4, 2022 at 11:18 AM
Sir Peter Knight, Imperial College London, August 2, 2022, at 3:320 PM
Peter Scholze, Max Planck Institute for Mathematic, Bonn, August 1, 2022 at 4:51 PM
Steve J. Carlip, UC-Davis, July 31, 2022
George Ellis, Cape Town, South Africa on July 27, 2022 at 5:01 PM
Helen Quinn, Stanford, on July 27, 2022 at 11:118 AM
Possible: Frank Wilczek, MIT / Paul Steinhardt, Princeton / Sylvester Gates, Brown
Alain Connes, IHES, Paris / Salvatore Torquato, Princeton / Edward Witten, IAS
Robert Langlands, IAS
Here will also be many instant messages to thought leaders about key points.
UNESCO, International Banks, Vladimir Putin, Ukraine, Pope, China,
• This page became a homepage on July 28, 2022.
• The prior homepage is https://81018.com/starting-point/
• The last update was Friday August 26, 2022.
• This page was initiated on July 12, 2022.
• The URL for this file is https://81018.com/as-above-so-below/
• Current headline: Eight Concepts toward an Integrative Universe
• Earlier headlines for this article: The Mathematically-Integrated View of the Universe
• Current byline: Worldviews are too intransigent. A fully-integrated UniverseView is needed.
• Other bylines: A good revolution in our time: Old Worldviews to New UniverseView!
• The geometry of quantum fluctuations — The First 64 Notations Out of 202 Are Key
• Essential Key: Three Basic Geometries of Quantum Fluctuations
• All of us are getting too hostile and intransigent. Let’s embrace the universe.
Let the next revolution begin! Independence from absolute time!