PERFECTION STUDIES: CONTINUITY•SYMMETRY•HARMONY GOALS.10.March.2024
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Defining the Qualitative
by Bruce E. Camber
A working draft, March 2024
Abstract. We take as a given that the nature of pi (π) may be further defined at the Planck scale by assuming that the Planck base units (natural units) manifest the first moment of space-time as an infinitesimal sphere. It is the most simple three-dimensional object yet one that necessarily manifests three qualities — continuity, symmetry and harmony.* Given this infinitesimal sphere is defined by units of Planck Time, Planck Length, Planck Charge and Planck Mass, a rate of expansion can be calculated. If we take as a given that there is one infinitesimal sphere for each unit of Planck Time, there would be 18.5 tredecillion spheres per second generated.† This would be a rather simple start of the universe. With these relatively basic assumptions, the universe starts uniformly and smoothly and that its expansion is immediate. By definition pi (π) preconditions everything within spacetime. Many orders of magnitude smaller than the neutrino, those infinitesimal spheres necessarily form a grid (sphere stacking and packing) that connects everything, everywhere, for all time. It is a very different perception of the roles of pi (π) than is currently studied in schools today.
Given this redefinition, three facts-features-functions of pi (π) can be recognized:
1. Continuity-numbers-order are created by her endless equation.
2. Symmetry-shape-relations are given with the perfections of her circles and spheres.
3. Harmony-spacetime-dynamics are given by Fourier’s transform, periodicity, and spin states.
Introduction. Of course, pi (π) is the oldest-known equation and our most-ubiquitous equation within mathematics. It is the only mathematical equation with its own global day of recognition. As known as it is, there is still more to be explored within pi (π). Within our work, because big bang cosmology eliminates pi (π) from immediate consideration, big bang cosmology was placed on hold. Having already observed simple geometries to the Planck scale, it was time to explore how those infinitesimal spheres could precondition everything within space and time with continuity, symmetry and harmony. And because continuity-symmetry-harmony did not appear to be finite, we began to ask, “What if those three are a key part of the definition of the infinite?” We also began to explore those qualities as a bridge between the finite and infinite. It is all quite up in the air.
Currently, in this model of the universe, the infinite is defined as continuity-symmetry-harmony. All other definitions of infinity are placed on hold.
Early in our studies, we were confronted with a very unusual history lesson that Aristotle made a mistake within most-basic geometries and that mistake was not discovered for 1800 years. Five tetrahedrons sharing an edge create a gap of 7.3561+ degrees. We then learned about dodecahedral and icosahedral gaps. We asked the experts, “Could these gaps be related to quantum fluctuations?” There was no response. Too obvious, we just assumed that quantum fluctuations are the result of the geometries of gaps. Nobody has told us otherwise. Given current measurements by CERN, we know that fluctuations are within Notations 65-67. It appears that the first geometric gaps were observed in the 15th century and they are now well-documented.
(Mysteries in Packing Regular Tetrahedra with Jeffrey Lagarias and Chuanming Zong, (PDF), AMS, 2012)
The study. This model of the universe started in 2011 in a high school geometry class that studied how tetrahedrons and octahedrons are perfectly enclosed within each other. Realizing there could be an infinite regress or expansion, Zeno’s paradox was first explored. It took 45 steps to the particle scale and 67 additional steps to the Planck scale. Following the expansion of Planck Time, there were 112 steps to the nanosecond and just 90 additional steps out to the current time (202 notations). Our first conclusion was that we had developed the most comprehensive STEM tool possible. Then we realized that this scale introduces a new physics at the shortest length-and-times but because it uses base-2 exponentiation, it relates it all to the physics at the largest lengths-and-time. Several charts were developed. By 2016 a horizontally-scrolled chart emerged. Throughout this time, scholars from around the world were asked, “Where is the flaw in our logic?” No answers were forthcoming.
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A lingering question was about the origins of continuity, symmetry, and harmony. As a feature-function of pi (π), is that all there is? Each can be quantified, qualified, and idealized. There is a certain perfection deep within each. We decided that either they are the best possible definition of the infinite or a bridge between the finite and infinite. That judgment is still out as we explore both options. It seems for sure, that the three define the qualitative; and as qualitatives, each instantiates the face, then the substance of value. We explored that idea and found it helpful. There was so much within this model of the universe that was helpful, we decided it was time to see if any of those scholars who had become editors thought it warranted attention by their readership. It would be my first article within such a publication.
Results. Because it was the 125th anniversary edition of The Physical Review (July 1893), the editors of Physical Review D (PRD), Urs Heller and Erik Weinberg, were celebrating and wrote the article, Physics at the Shortest and Longest Scales, October 2018 (Volume 27, Number 9) and because Alan Guth’s 1981 article is the most cited in PRD, it seemed that the PRD would be the logical place to submit this article.
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Where else might we submit this article? Your suggestions would be very seriously considered! How about to Sir John Maddox at Nature? If only he were alive… yet Magdalena Skipper , the current Editor, might find it of interest.
The next paragraphs and conclusions are yet to be written! So, yes, there will be more to come…
Author Contributions. Bruce E. Camber is currently the sole author of this article. He acknowledges that it is a reformat of big bang cosmology so he will always make himself available for corrections and discussions.
Acknowledgments In 2011 Steve Curtis and Cathy Boucvalt were fellow teachers and very helpful and supportive; and, a student, Bryce Estes, was an inspiration especially with his Science Fair project, Walk the Planck. Freeman Dyson introduced me to dimensional analysis and offered constructive criticisms and became a guiding light. Frank Wilczek at MIT reviewed our most-primitive understanding of the Planck base units and was an uplifting spirit.
Conflicts of Interest. There have been no known conflicts of interest.
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Keys to this page, facts-features-functions
• This page may become a homepage on 10 March 2024.
• The last update: 22 February 2024
• This page was initiated on 14 February 2024.
• URL: https://81018.com/facts-features-functions/
• First headline: Defining the Qualitative
• Teaser (wicket-kicker-eyebrow): Three relatively unexplored facts-features-functions of pi (π)