PERFECTION STUDIES: CONTINUITY•SYMMETRY•HARMONY GOALS.DECEMBER.2024
PAGES: CHECKLIST.|.REFERENCES-RESOURCES | .RE-READING| EMAILS | IM.| PARTICIPATE | Zzzz
Concepts build on concepts.
Is the baseline a sphere?!?
by Bruce E. Camber
Abstract
Paradigm shifts are major events in human history; but in their process of unfolding, we have failed to recognize simple facts that could have triggered deeper analyses. We’ve made erroneous assumptions* about the basics — geometries, space-time, and the start of the universe — where there is always an abundance of open questions.
The place and importance of spheres, especially infinitesimal spheres, are key.
Though paradigm shifts seem rare, in our recent history, two are currently changing the way we see ourselves and the universe. In 1993 there was the widespread birthing of the internet within the general public. It was a World-Wide-Web where space and time could readily be collapsed or disintermediated. By 2022 privately-held space exploration companies and our space telescopes, especially the James Webb[†], shifted everyone’s attention to the solar system, the Milky Way, and the universe.
Paradigm shifts are stifled because key assumptions haven’t been reviewed:
1. Pi (π). Are the never-ending units of pi either infinite, finite, or both?
2. The facets of pi (π): Are continuity-symmetry-harmony finite or infinite or both?
3. Kurt Gödel & David Hilbert: Is the infinite ubiquitously within the finite?
4. Aristotle’s Gap and gap geometries. What is the basic role of geometry?
5. The universe as a mathematical entity. Are natural units the start of the universe?
6. The universe. Do 202 base-2 notations encapsulate the universe?
7. Time. If the notations are all active now, what is time?
8. Spheres. Do infinitesimal spheres populate the universe?
This page builds on the prior homepage: https://81018.com/thought/ (as in thought experiments) This page was rewritten by ChatGPT and it is on the web for comparison: https://81018.com/ChatGPT-correct/ An index of all ChatGPT rewrites will evolve here: https://81018.com/ChatGPT/
Questions? Help with the next homepage? Basic Structure: Infinitiesimal spheres
Hypotheses follow each question. The first three are about the finite-infinite relation.
1 Pi (π): Are the never-ending units of pi infinite, finite or both? As computing power increased, a threshold was crossed in 1973 when Jean Guilloud and Martine Bouyer calculated over 1 million digits of pi. In 1989 a billion digits were calculated and in 2002, over a trillion.
Continuity is fundamental and foundational within pi (π).
We begin our exploration of key concepts of pi (π) because we think it could cause a paradigm shift. We’ve heard scholars say, “Been there, done that.” Or, condescendingly or indignantly ask, “What does pi (π) have to do the start of the universe?” Instead of stifling deeper questions, we are hoping to trigger questions about continuity principles that open the relation between the finite and infinite.
In 2022 Emma Haruka Iwao calculated and verified over 100 trillion digits of pi. Going on forever, we are now over two hundred trillion. There were 42 records broken between 1973 and 2024. In that time there have been popular analyses like Why life is more interesting with extra pi (Kit Yates, BBC 14 March 2024) and academic writings such as Simple formulas of π in terms of ϕ (Angelo Pignatelli, ArXiv, 28 Feb 2024). None have addressed our questions.
From studying two most simple examples, our questions are: 
“If these numbers are endless, what does it tell us about that modest angle that follows the number 3 — the little .14159265…? Does that angle connect to infinity? 
If that number is a constant, never-ending with no repeating patterns, in what ways can it be finite and infinite at the same time? At over 200 trillion digits, is it the longest documented continuity equation? What is it telling us about continuity? Does that continuity specially define infinity?”
2006: Thomas W. Ferguson recites pi (π) to 3,142,958 decimal places. We can do better. We can understand it more profoundly; and we speculate, “When we do, there’ll be a paradigm shift. We’ll begin to see the universe.”
More… And then there is always more…
_____
2Three facets of pi (π): Continuity-symmetry-harmony appear to be both finite and infinite. Pi (π) is stretches our grasp of fundamentals. The net-net of that formula is a sphere. Its simple definition: “Set of points the same distance, r, from a given point” does not suggest all of its extended range of applications.
Functionally, the sphere acts like a most diverse particle. Perhaps it is the heart of every particle.
Besides redefining continuity, pi (π) renders symmetries and harmonies. Further, with the work of Milnor and Smale, our understanding of spheres as attractors and repellers opens studies of gravity and electromagnetism. And, to that list we now add the concept of perfection. Of course, we added continuity-symmetry-harmony which opens the studies of Fourier, Poincaré, Gauss and others to demonstrate the versatility of pi (π). Plus, there is a wide range of more recent scholars like Phil Davis of Brown University, Frank Wilczek of MIT, Steven Stogatz of Cornell, and Espen Gaarder Haug of Norwegian University of Life Sciences (NMBU) in Oslo who have stretched that work and have added major new insights.
And now, there is a new, younger generation of even more speculative thinkers. There are scholars like Xija Wang of Hunan University in China. We will continue to add even younger, more speculative, creative thinkers as we go on.
Those facets of pi — continuity-symmetry-harmony — are in some manner of speaking both finite and infinite (and we could have begun exploring that hypothesis long ago). The universe is a very different place when you see its perfections within “continuity-symmetry-harmony” and begin to see how they define “order-relations-dynamics” known as “space-time-spacetime moments.”
And, yes, that constitutes a paradigm shift within our paradigm shifts.
_____
3 David Hilbert and Kurt Gödel: Is the infinite ubiquitously within the finite? David Hilbert (1862-1943) was a mathematician-philosopher whose doctoral dissertation was a study of the invariant properties of special binary forms, in particular the spherical harmonic. He wrestled with our deepest understanding of spheres.
His book, Geometry and the Imagination (with Stephan Cohn-Vossen, Chelsea Publishing Company, NY, 1956) describes the eleven essential properties of the sphere. Though he guided the development of mathematical logic, too often his conclusions were too restrictive. For example, he said, “… the infinite is nowhere to be found in reality, no matter what experiences…” Within our emergent model, as described within the above two hypotheses, facets of pi are infinite, and yet the same facets can be found within finite. We readily conclude, responding with an unconventional, “Yes, the infinite is ubiquitously within the finite within every moment of continuity, every moment of symmetry, and every moment of harmony.”
Kurt Gödel (1906-1978) was a logician-mathematician-philosopher who in 1929 wrote one of his signature pieces, the completeness theorem regarding first-order logic, as part of his dissertation at the University of Vienna. Within two years he wrote the incompleteness theorem. The place of pi (π) had no necessary connection to infinity.
Though finally recognized as transcendental, the record of digits had been relatively stagnant since 1858 with Willian Shanks’ record of 527 digits. With the advent of the desk calculator in 1946 it jumped to 620. In 1949 with the help of computers, it jumped to over 1000. In 1958 it went over 10000, in 1961 over 100,000 and in 1973 over one million. After Gödel died, it went up to over a billion digits (1989).
It is a paradigm shift that could well have been established by now. At some time, our scholars could have asked, “If it is never ending, what does it mean?” I think it would have changed their narratives. Infinity, redefined as continuity-symmetry-harmony, was much closer than anyone imagined.
_____
4Aristotle’s Gap and gap geometries. What is the basic role of geometry? Although space is the obvious plenum in which life takes shape, it is a bit puzzling that too often questions about geometry are ignored. The first clear example is Aristotle’s Gap, a discussion that has been reviewed repeatedly within this website.
Our two most substantial discussions to date are here:
• Biased — Aristotle, Newton and Hawking: https://81018.com/biased/ (June 2020)
• Aristotle’s Mistake: https://81018.com/too-simple/ (September 2024)
Three brief periods of academic discussions, one in the 1400s, another in the 1920s, and the most-recent in 2012 (to about 2020), are all corrections to a major conceptual oversight. The scientific community had ignored geometric gaps. The few who know about them, and the fewer yet who think about them, are more inclined to engage sphere packing than anything else.
This paradigm shift could have happened in the 1920s. It didn’t. Old quantum physics would have been simplified to become a radically new physics of the infinitesimal. It wasn’t.
The bigger discussion opens when the questions are asked about what happens at the infinitesimal level. The scale-invariant sphere has a much larger story to tell. When our high school students began building models with natural gaps, students called it “squishy geometry” and then we decided the best name was “quantum geometries.” These were unpredictable and indeterminant. The more we pondered, the more we thought that this was the geometry of quantum fluctuations and indeterminacy.
Nobody would touch it, not even to comment on it. It was too simple. It made science too accessible. It lifted the mysterium and the confusion. And the conclusion was obvious — geometries had a more central role than any of us believed. Paradigms can shift by learning new basics.
_____
5 The universe as a mathematical entity. Are natural units the start of the universe? The natural units of a length and a unit of time defined by the Planck base units can only be accessed by thoughts, logic, math-and-geometry, equations, and the continuities-symmetries-and-harmonies of pi (π).
Our first assumption is that these Planck base units are important numbers to test and explore. We were looking for numbers that might be a starting point of the universe. We were looking at how a base-2 configuration encapsulates the universe in 202 base-2 notations. We were pondering how the first 64 notations are below the ability of our measuring devices to capture. We then found studies that were conceptually rich but not on the grid. Here we found domains for (a).hypothetical particles and (b).functional analyses as uncovered by (c).Langlands programs, (d).string theories, (e).supersymmetries, (f).loop quantum gravity, (g).causal set theory, (h).causal dynamical triangulation, (i).spectral standard model, and non-standard (j).field theories.
There are no less the 64 notations to define a first-level order. A huge domain, we began to try to define vertices, shell particles, shell spheres, basic geometries, continuity equations, symmetry relations, and the dynamics of harmony (as in the Fourier Transform). These numbers are telling a story about the 202 notations; we’ve begun in our limited way to explore them, yet, these concept deserve to be vigorously explored within the academic community. This article is our plea to help us to understand why these concepts are so out of step with the work of our world’s leading scholars. We believe these concepts need critical review and scholarly study.
It is difficult to get scholars to look at materials that originated from a high school geometry class and do not have a proper academic paper trail. Early in the process, we thought it was a good STEM tool. It wasn’t. The concepts were too far outside the mainstream.
Questions about an Exponential Universe. Who among all our scholars — including postdocs, graduate students, undergraduates — might be open to such a concept? Although there are now many scholars who are examining the domain from the Planck scale to the CERN-scale (or electroweak scale), who among them will be open to explore concepts that suggest an exponential universe?
In 2011 we weren’t too keen to engage the circle and sphere. It didn’t seem like much of a building block. The tetrahedron was more interesting. Yet, with just two vertices, the sphere necessarily opened the mysteries of pi. We had begun studying cubic close packing of equal spheres, then the types of Fourier transforms; and, we quickly learned that we had to begin to grasp scale invariance and dimensionless constants more deeply. We’ve begun with the help of some very fine teachers. There is a place for the natural units and it is more substantial than most currently believe.
_____
6The universe. Do the 202 base-2 notations actually encapsulate the universe? Does this progressive, highly-relational flow where everything is related to everything, everywhere, throughout all time actually encapsulate our ever-so large and complex universe? Is it possible?
Hypothesis: “Infinitesimal spheres connect us to everything-everywhere-throughout all time.” That just seems too big a concept for any of us — it is a paradigm shift if-and-when we first see the universe as a highly-integrative whole.
Base-2 notation provides a simple ordering system that provides a foundational and fundamental look at the early universe and its infinitesimal spheres. There is so much activity within the first second (which is within Notation-143), within the much larger picture with all the seconds that follow — 436,117,076,600,000,000 seconds (the first 13.82 billion years) — that just may be enough time to give us all the necessary building blocks to naturally construct our universe as is.
None of these notations are sacrosanct and all of them are constantly changing and none of them would ever be exempt from change. The first 64 notations, which are generated within a duration of just 9.945379×10-25 seconds, is so far removed from any possible measurement, here is a new science and a new context for matter and energy (charge), and for gravity and electromagnetism. And, it is an adjunct science for particle physics, especially for our hypothetical particles and then for the particle zoo.
If these hypotheses appear to hold true, much more work will be done with these last three points. Essentially now that we have the foundations for the greatest diversity of geometries, formulations, and calculations. No part of science or the human experience is exempt, including the role of sleep and the nature of consciousness. Given the current archeological record, these can only exist in Notation-202. Also, we note here that continuity-symmetry-harmony become the basis for valuations. And, valuations become the basis for ethics, and ultimately for morals.
We hypothesize that an infinitesimal primordial sphere is our most conceptually-rich starting point. That sphere is postulated to be the first instance of space-time, matter-energy, and electromagnetism-gravity (each sphere – either an attractor or repeller). It has its never-ending, never-repeating numbers of pi. It has a base symmetry of the sphere, then all the derivative symmetries. And, it has a basic harmonic function of a sphere and then every possible derivative harmony of the spheres. And then, it has base-2 as a starting point for an ever-growing relational nexus which we call our universe.
It all begins with those three characteristics of pi —- continuity-symmetry-harmony —- which are facets of the finite and expressions of the infinite.
More… And, even more:
- The first instance: Pi (π) Shapes Our Universe
- Power of Spheres, Circles and Pi (π)
- The Sphere: Is it the Most-Basic Building Block of our Universe?
- The primordial archetypal sphere
- Acknowledge infinity
_____
7Time. If the notations are all active now, what is time? It’s an open question. Einstein said it is an illusion. Carlo Rovelli, a leading scholar of loop quantum gravity (LQG) along his many other colleagues, take Einstein further and suggest all time is the Now.
Our very different model (than the Big Bang Theory) also suggests that all time is Now. All 202 base-2 notations are always active. Each notation has a natural dependency on the ones that precede it.
We backed into this concept of space-time. It wasn’t part of our family’s philosophical or theological orientations. People ask me, “What is your background? How does it influence you?” At the age of 10 in 1957, my mother and father encouraged me to explore and appreciate other traditions. By 1967 it was an avocation. By 1977 it was a vocation. In today’s world, the most dominant belief system is science and its most dominant philosophy is one of the many flavors of agnosticism and atheism. Our model engages them all. Our core belief is in order-continuity, relations-symmetries, and dynamics-harmonies. All are cornerstones of logic, rational thought, science, and our grasp of the nature of infinity.
Ultimately I believe the deeper truth is within all those hyphens between the finite and infinite.
More… And even more:
- Finite-Infinite: A Nexus of Transformations
- Finite-Infinite: We all so little understand the infinite
- Finite-Infinite: On more fully recognizing the infinite
- Finite-Infinite Bridge: A Nexus of Transformation
_____
8 Spheres. Do infinitesimal spheres populate the universe? Are these perfect? We answer both questions affirmatively. Our name, Center for Perfection Studies affirms it. Within the first 143 notations, the densities and the speed of the transactions render 18.5 tredecillion infinitesimal spheres per second using Planck Time.
We assume that the rate of expansion will be studied to see if it qualifies as a cosmological constant.
The most-simple stacking-and-packing of infinitesimal spheres is perfect. At these densities and those speeds, no gaps are possible. It’s a simple perfection and a new, conceptually-rich domain to explore.
If there are instants when the perfections of this stacking-and-packing penetrate to higher notations, it is even a richer domain to explore. Commensurate with our finest and most memorable experiences, that perfection appears to break through and into the 202nd notation and the current time.
In 1972 I said, “A vision abides… deep within the fabric of life there is an energy, an abiding thrust to make things better, more perfect.”
Here, another paradigm shift is the hypothesis: The Universe starts perfect, then becomes imperfect or creative or innovative. We are foundationally and fundamentally related. Continuity, symmetry, and harmony become the basis for valuations. And, valuations become the basis for ethics, and ultimately for morals.
More…. And even more:
- Ethics and values
- See the prior article about dark matter and dark energy. It is the foundation for this one.
- Within the infinitesimal, Notations 1-64 of the 202 notations, particles begin as spheres that are shaped by those first 64 notations before being observed. The wavelength of light is much larger than the size of these particles. Those current images come from scanning-tunneling electron microscopes cannot and will not get so infinitesimal. Just to be sure of the current state of the art, I am working through the 2023 dissertation (PDF) of Estefania Alves Alves (CEMES/CNRS, 29 Rue J. Marvig, 31055 Toulouse, France).
_____
Resources-References
As references are added, other resources will also be added within this website.
[*] Retrieved: 3 December 2024 – https://81018.com/biased/
[†] Retrieved: 3 December 2024 – https://81018.com/jwst/
[1] a. Retrieved: 3 December 2024 – https://en.wikipedia.org/wiki/Chronology
.___b. Retrieved: 3 December 2024 – https://en.wikipedia.org/wiki/Emma_Haruka_Iwao
.___c. Retrieved: 3 December 2024 – https://81018.com/iwao/
.___d. Retrieved: 3 December 2024 – https://www.bbc.com/future/article/20240313-pi-day
.___e. Retrieved: 3 December 2024 – https://arxiv.org/abs/2403.19684
.___f. Retrieved: 3 December 2024 – https://news.web.baylor.edu/news/story/2024/magic
[2] Retrieved: 3 December 2024 – https://en.wikipedia.org/wiki/Locus_(mathematics)
[3] a. Retrieved: 3 December 2024 – https://en.wikipedia.org/wiki/Binary_quantic
___.b. Retrieved: 3 December 2024 – https://en.wikipedia.org/wiki/Spherical_harmonics
___.c. Retrieved: 3 December 2024 – https://en.wikipedia.org/wiki/Geometry_and_the_Imagination
___.d. Retrieved: 3 December 2024 – https://en.m.wikipedia.org/wiki/First-order_logic
[4] Retrieved: 3 December 2024 – https://en.wikipedia.org/wiki/Quantum_geometry
[5] Retrieved: 3 December 2024 – https://81018.com/chart/
[6] Retrieved: 3 December 2024 – https://81018.com/hypostasis/#Top
[7] Retrieved: 3 December 2024 – https://81018.com/universe-table/
[8] Retrieved 14 November 2024 —- https://81018.com/foundations
_____
Reading and re-reading
What is opened on the desk, on the shelves and on the floor…
• A very nice summary of the advances of pi’s digits
• NASA Jet Propulsion Laboratory: JPL generally use only 15 digits of pi (π) for its highest-accuracy calculations for interplanetary navigation. Isaac Newton, among others, had calculated 16 decimal places by 1666. Pi (𝜋) to 40 digits is enough to compute the circumference of the Milky Way galaxy to an error less than the size of a proton. See: David H. Bailey, Jonathan M. Borwein, Peter B. Borwein and Simon Plouffe, Mathematical Intelligencer, vol. 19, no. 1 (Jan. 1997), pg. 50–57.
• The Mathematics of Harmony and Hilbert’s Fourth Problem: The Way to the Harmonic Hyperbolic and Spherical Worlds of Nature (Paperback – April 17, 2014) by Alexey Stakhov (Author), Samuil Aranson
• Simple formulas of π in terms of ϕ (PDF), Angelo Pignatelli, ArXiv, 28 Feb 2024
• Review. Our scholars pointed me in the direction of spin states and Fourier and harmony. We worked on it a little within these pages — https://81018.com/essentials/ — and now we have reason to come back and study it further. Here is the mathematics of the bridge between the finite and infinite. Here is the mathematics of spin states, gravity, and electromagnetism. There is so much more to learn!
_____
Afterthoughts
Personal reflections.
Starting Points. The world is filled with intelligent people. Most brilliant. There are articles today with hundreds of scholars who have signed on to work that has involved their research. One of those documents that I discovered in 2020 is titled The First Three Seconds; it plays off the title of Steven Weinberg’s The First Three Minutes. Weinberg starts his book at 1/100th of a second. That’s within our Notation-138. The first three seconds is within Notation-144. Three minutes is within Notation-151. Those studies all miss the first two-thirds of all notations, Notation-0 to Notation-134, is where it most formative (and interesting). The first third, Notation-0 to Notation-67, is where the mystery is, but the information is disparate and withino silos.
End points: What seems like an endpoint is also a beginning point. Notation-0 is the transformation between the finite and the infinite. It is where the numbers after the 3, the .14159623… of pi(π) go spiraling off into infinity. The song may be, “May the circle be unbroken” when in actuality, given the formula, no circle is ever complete. Of course, in “the real world,” they are always complete. Properly interpreting it all involves grasping the spin states and other dynamics deep within the interiority of the sphere and knowing that 40 decimal points is all that is necessary to do highly refined work anywhere in the universe. Yet those extra digits are not for naught. In light of infinity, we’ve just begun to analyze them. There will be much more to come!
_____
Emails
There will be emails to many of our scholars about key points.
10 December 2024: Scholars around the world got a similar email as ‘t Hooft below.
9 December 2024: Geradus ‘t Hooft, Institute for Theoretical Physics, Utrecht, Netherlands
4 December 2024: Kenneth Ascher, University of California-Irvine, Irvine, California
December 2024: Select postdocs from around the world.
4 December 2024: John Lennox, Oxford, Oxford, England UK.
3 December 2004: Espen Gaarder Haug, Norwegian University of Life Sciences (NMBU), Oslo
13 November 2024, Lina Necib, MIT, Cambridge, Massachusetts
13 November 2024: Amanda Weltman, University of Cape Town, South Africa
7 November 2024: Vlatko Vedral of Oxford, Oxford, England UK
Much more to come…
_____
IM
There will also be many instant messages to thought leaders about these key points.
Elon Musk: The universe isn’t that big!” https://x.com/elonmusk/status/1864245283472986407
@elonmusk “You’re right. The universe is just 202 base-2 notations from the infinitesimal Planck units to the size and age of the universe.
The math: https://81018.com/chart/
The foundations: https://81018.com/correct/
For more: https://81018.com/pages/
9:05 AM · Nov 19, 2024 @MedvedevRussiaE There are lies and deceptive practices all around us. The problem is with our worldviews. They are all too small. A mathematically integrated view of the universe is the beginning of a reset. https://81018.com is at least attempting to open those discussions.
More to come…
_____
Critique ____ You are always invited.
_____
Keys to this page, correct A verb and invitation!
• This page became the homepage on 3 December 2024 at 6 PM.
• The last update was in April 2025.
• This page was initiated on 20 November 2024.
• The URL for this file is: https://81018.com/correct/
• Current headline for this article: Concepts build on concepts. Is the baseline… a sphere?!?
• Earlier headline All of us have harbored incorrect concepts. Let’s get over it and move on.
• Current teaser* is: All concepts have limits… surprisingly spheres may have the least.
• Prior teaser* is: We’ve all focused on incorrect concepts for a long time…
*Or, wicket, kicker or eyebrow.
_____
This page builds on the prior homepage: https://81018.com/thought/ (as in thought experiments). This page has been rewritten by ChatGPT and it is on the web for comparison: https://81018.com/ChatGPT-correct/
An index of all our ChatGPT rewrites will evolve here: https://81018.com/ChatGPT/
###