The essence of value-integrity-and-natural law come from facets of nature.

Image of abstract geometric shapes representing continuity, symmetry, and harmony in a mathematical model of the universe.
A cosmic representation highlighting hyper-rationality, featuring spheres, octahedrons, and hexagonal plates, depicting continuity, symmetry, and harmony in an expansive geometric model of the universe.

PERFECTION STUDIES: CONTINUITY•SYMMETRY•HARMONY GOALS..June.2024
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Continuity-Symmetry-Harmony
by Bruce E. Camber, (a first-draft)

Abstract.
Pi (π) is a key equation that defines our universe.[*] The place of that equation goes well-beyond the endless units of pi (π). Though useful within encryption studies and to check the accuracy and efficiencies of next generation computers, the most important facet of that endless equation is that it creates a working model for those continuity equations that encapsulate everything-everywhere-for all time. From the enigmatic-to-the symbolic, and to numerals-and-the-algebraic, pi (π) is scale invariant and opens applications from the smallest to the largest scales. Here, value structures in our universe are still relatively unexplored.[†] Within this website, and especially in these days and times, we consider the three primary facets of pi (π) — her continuities, symmetries, and harmonies — to ask these questions:
1) Is the sphere the most basic building block of our universe?
2) Is pi (π) the most simple equation with the most potential for complexity?
3) Does pi (π) define more equations than any other constant?
4) Is pi’s continuity-symmetry-harmony imparted to everything-everywhere-for all time?
5) Are continuity-symmetry-harmony the foundations for value, integrity, and natural law?

Introduction. Three facets of the sphere — continuity-symmetry-harmony — are not finite or quantitative so we assume (hypothesize and/or hypostatize) these facets define the infinite and the qualitative. And these three facets give rise to value, integrity and natural law.[1]

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 (π) qualifies; it’s an equation that has never-ending results that are always the same and always changing. This continuity is enigmatic.[2]

Symmetry is the second facet of infinity (and of value and natural law). It looks like geometries and is the very nature of a relation. Within the finite it feels like space. Pi (π) qualifies; it’s a symmetry that generates symmetries. It’s an equation that sets up systems of equations.[3]

Harmony is the third facet of the infinite and of value and natural law. It is the very nature of dynamics; and within the finite, it is always cyclical; it has periodicity (even spin) that is experienced as harmonic space-time moments.[4] The numbers of pi (π), the geometries of pi (π), and the equations of pi (π) (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.[5]

Other concepts of the infinite are placed on hold.**
Most are personal definitions that come from personal experiences and family history. That is one’s own business, not ours. If those beliefs help you through life, that is great. Our goal here is to engage those principles and functions that give rise to mathematics, physics, and eventually all the other sciences.

** …until we can learn to be less arrogant and more gracious with our beliefs.

Review: In this model the infinite is profoundly within the finite. It is not finite, but actively imparts qualities to the finite. For those who follow David Hilbert, please stay open. Pi’s three facets of the infinite are really real. These are not just abstractions, but realities of every circle and sphere. These three qualities condition the finite. Everything-everywhere-for all time, is in accordance with numbers, geometries, and equations; and, it all has some manifestation of our three most-basic infinite qualities.[6]

The sphere: the most basic building block of our universe. The most-simple three-dimensional object also becomes its most complex and diverse. Pi (π) is used to define our most essential equations, more so than any other dimensionless or mathematical constant.[7] Yes, this most simple equation has the greatest potential for complexity. Pi (π) is not just a window on the infinite; it is a window on our very being.

A rather different start to grasp the finite-infinite relation, our understanding of the infinite starts with pi (π) and her most infinitesimal circles and spheres. There is free will and within this website it is associated with quantum fluctuations and the geometries of gaps.[8]

Although very simple concepts with which we have been familiar for much of our life, here these concepts become our most basic starting points. It is very different starting point and it takes time before these seeds of a new paradigm begin to germinate. Thank you. -BEC

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References
All these references come from a prior homepage. The focus is always on the same issues. Nevertheless, these will be studied and updated appropriately. Thank you.

[*] Pi (π) – Retrieved 2 June 2024: https://81018.com/starts-2/
[†] Values – Retrieved 2 June 2024: https://81018.com/ethics/
[1] Ethics – Retrieved 2 June 2024: https://81018.com/natural-law/
[2] Continuity – Retrieved 3 June 2024: https://81018.com/instance/
[3] Systems – Retrieved 4 June4 2024: https://81018.com/grasp-2/
[4] Periodicity, cyclicity, spin – Retrieved 5 June 2024: https://81018.com/sphere/
. . . Most speculative – Spin – Retrieved 5 June 2024: https://81018.com/spin/
[5] Perfection – Retrieved 5 June 2024: https://81018.com/perfection/
[6] Infinity – Retrieved 11 June 2024: https://81018.com/exquisite/
[7] Dimensionless – Retrieved 12 June 2024: https://81018.com/2017/06/05/thrust/
Also see: http://81018.com/infinitesimal-composites/
[8] Gap Geometries – Retrieved 12 June 2024: https://81018.com/geometries/

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Reading and re-reading
Many of these references are from the prior homepage, but deal with the same issues as here.

• Aharonov, Yakir and Petersen, Aage, Definability and measurability in Quantum Theory, Ted Bastin, ed., Quantum Physics and Beyond, Cambridge University Press, 1971 https://doi.org/10.1038/069194a0 

• Bell, E. T. , Finite or Infinite?, Philosophy of Science, The University of Chicago, PressVol. 1, No. 1, 1934, pp. 30-49 (20 pages)

• Christian J. Bordé, A consistent unified framework for the new system of units: Matter–wave optics, 2019 christian.borde@obspm.fr

Geometric Relational Embeddings: A Survey, ArXiv, Steffen Staab et al, https://arxiv.org/pdf/2304.11949, Bo Xiong-1 , Mojtaba Nayyeri-1 , Ming Jin-2 , Yunjie He-1 , Michael Cochez-3 , Shirui Pan-4 , Steffen Staab-1,5 from 1-University of Stuttgart, 2-Monash University, 3-VU Amsterdam, 4-Griffith University, 5-University of Southampton

Re-reviewing: https://81018.com/almost/#1f https://81018.com/ai/#CSH https://81018.com/petition/
https://81018.com/third-way/ https://81018.com/infinity/ https://81018.com/ether/ https://81018.com/mistaken/

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Anything new?
Personal reflections.

• 202 notations: First, each notation was determined by spheres encapsulating geometries (tetrahedrons and octahedrons). Numbers were given by natural units calculated by Max Planck (1899). In the model (Figure 1) please note that the three layers of our tetrahedron are literal examples of Notations 112 –113–114. Yet, underpinning that simple base-2 exponential notation are the enigmatic numbers of pi and her spherical geometries. Two sets of numbers, one that comes with spherical shapes and functions and then another that comes with Euclidean shapes and functions, converge. Let’s ruminate on that for awhile.
• Think tanks for scholars: Among the many different consortiums for scholarly research, the Institute for Advanced Studies in Princeton (IAS) is perhaps the best known. Yet, in most institutions, change still comes slowly. Today, there is a consortium of Institutes for Advanced Studies modeled after IAS; it has a growing number of affiliated institutes with leading thinkers from within each country. It helps to put all the creatives in the same place and grow that confidence; progress is still slow.
• The oldest organization of scholars in the USA is the American Academy of Arts & Sciences. It has many leading scholars within mathematics, physics, and astronomy. In countries affiliated with the United Kingdom, these groups are known as a Royal Academy or Royal Society, i.e. Royal Academy of Sciences, New Zealand. Mostly just for recognition, the dynamics for concept formation and development are too little engaged in many of these groups.

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Emails
There will be emails to many of our scholars about key points.

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IM
There will also be many instant messages to thought leaders about these key points.

• 5 June 2024: @JKRowling: Thank you for all that you do. First, you opened the paradigm. It hasn’t shifted, but it’s definitely kicked open from little worldviews. Now… to an integrated view of the universe! Here’s a little map: https://81018.com/stem/ and another of just numbers: https://81018.com/chart/
• Much more to come. In process.

Critique __ You are always invited.

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Keys to this page, integrity

• This page was the homepage from 31 May 2024 through June 10.
• The last update 24 June 2024.
• This page was initiated on 31 May 2024 and is based on https://81018.com/csh/
• The URL for this file is https://81018.com/integrity/
• The headline for this article: Continuity-Symmetry-Harmony
• First teaser* is: Essence of value, integrity, and natural law come from nature

*Or, wicket, kicker or eyebrow.

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