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Finite-Infinite Relations Within An Infinitesimal Sphere

by Bruce E. Camber (working draft)

**Introduction**. The *References *section of this homepage is comprised of articles being used to help shape the page. A key question is always about the starting point or provenance of a concept. A morning fog lifted when it hit me, “Of course, most concepts are not set within a dynamic finite-infinite relation, nor do they have a necessary connection to dimensionless constants like pi or to infinitesimal spheres and base-2 exponentiation.” Notwithstanding, I conclude that these are the necessary precursors to the definition of any one concept and then to the integration of that concept into a larger picture. *

Our finest scholars may ask, “How so?” And my most-simple answer would be, “…because each is a precursor.” That is, *if and only if* the first instantiation that creates physical spacetime is an active finite-infinite relation defined by pi, which necessarily is continuity-symmetry-harmony, then it follows that everything is shaped by all these inherent relations. † A naive, simple logic tells us that it is so. –BEC

**The Thesis**. Key comments by leading scholars can take awhile to compute. Take, for example, the comments by 2019 Nobel Laureate James Peebles when he stated that we do not have a theory of the start of the universe. I asked, “Isn’t that the role of the big bang theory?” Peebles rightly claims that Stephen Hawking’s favorite theory did not account for the very beginning. It does not describe the very first instant of the universe. Neil Turok made that clear.

If the first instant of the universe necessarily involves a finite-infinite relation, then all equations are necessarily derivative of it. If the first equation of that finite-infinite relation is pi, then all subsequent equations are necessarily derivative of it. If always and in every way set within base-2 exponentiation, one might ask what difference it makes. Of course, we need to find out.

**The first expressions of pi provide a bit of assurance that these conclusions might work**.

**The Antithesis**. The thought leaders of the Standard Models, one for Particle Physics and the other for Cosmology, will object. Some within Langlands Programs, string and M-theory, SUSY and the expositors — CDT, CST, LQG, SSM, and the Moonshine outliers — may protest loudly. And, the logicians may protest, too. People like Edward Zalta have unique starting points, yet none quite so compelling to capture the imaginations of the aforementioned groups of scholars.

But, the finite-infinite and pi… One asks, “How can something so simple be overlooked for so long?”

**The Synthesis**. Nothing changes with any of those cited studies. They each get an addendum, the first 64 notations below all current thresholds of measurement, prior to quantum fluctuations, and starting with base units as infinitesimal spheres. Here that elusive starting point is defined by pi, other dimensionless constants, and is shaped by continuity-symmetry-harmony. Plus, every concept today gets the overall dynamics within the structure of the 202 base-2 notations.

It’ll be easy for many to associate their studies with definitions that include pi. Most have simple possible relations with base-2. And then, all the facets included within each unique study become facets within a notation, within many notations, or within all notations.

**Conclusions**. Our synthesis is slowly progressing; it needs the help of scholars. To that end, we will continue our efforts to engage such integrative thinkers from around the world where their studies truly define key parts of the whole. Thank you. -BEC

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Endnotes & Footnotes

There may not be many because all these points already have pages within this website.

* A dynamic finite-infinite relation, pi, infinitesimal spheres, and base-2 exponentiation: The conjecture is that this universe is defined by that which is fundamentally continuity-symmetry-harmony of the infinite whereby those facets of pi manifest as an infinitesimal sphere, applying the Planck scale units of time, length, mass and charge (or the earlier calculations by Stoney or other more accurately calculated equivalents), at a rate of one sphere per primordial unit of time like Planck’s or Stoney’s. That manifestation of the base Planck units includes all their dimensionless constants of the infinite. Sphere stacking and cubic-close packing of equal spheres begins the initial, very smooth (no gaps) geometries of the universe. *More to come* on dimensionless constants and Baez–Wilczek–Aguirre–Rees–Tegmark–Wikipedia–NIST–Plouffe…

† Precursors, all those inherent relations: For the standard model for particle physics, John Baez required 26 dimensionless constants. Wilczek, Aguirre, Rees and Tegmark required no less than 31. Wikipedia identified 104 dimensionless constants. The National Institute for Standards & Technology (NIST) had identified over 300 (PDF – 2008, SI Report). And, Simon Plouffe has through algorithmic programming identified over 200 million dimensionless constants. There is nothing in the universe not touched by dimensionless constants.

*More*… on mathematical formulations, model-and-proof theory, real realities, infinitesimal circuitry, five gates as five plates with multiple lines and nodes

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References & Resources

A few of the key related works that are studied but not within an endnote or footnote, are added here.

• Thomas Hales, Univ. Pittsburgh: A formal proof of the Kepler conjecture (Jan. 2015) (PDF)

• John Harrison: Complete publications list

• Okuma, R., Kofu, M., Asai, S. *et al.* Dimensional reduction by geometrical frustration in a cubic antiferromagnet composed of tetrahedral clusters. *Nat Commun* **12, **4382 (2021). https://doi.org/10.1038/s41467-021-24636-1

• Edward N. Zalta, Principia Logico-Metaphysica, Stanford University, with Daniel Kirchner, Freie Universität Berlin and Uri Nodelman, Stanford University. May 5, 2022

http://mally.stanford.edu/principia.pdf

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Emails

There will always be emails to our scholars with questions about their work.

Emails this week include to the following:

• Prof. Dr. Simon Plouffe, Quebec and France, July 17, 2022

• John J. Harrison, Cambridge and Amazon Web Services, July 11, 2022

• Prof. Dr. Vladimir Drinfeld, University of Chicago, July 7, 2022

• Prof. Dr. William Goldman, University of Maryland, July 7, 2022

• Dr. Toyin Alli, University of Georgia, July 7, 2022

• Prof. Dr. Thomas Banchoff, Brown University, July 7, 2022

• Prof. Dr. W. Hugh Woodin, Harvard University, July 7, 2022

• Dr. Boris Lishak, University of Sydney, July 7, 2022

• Prof. Dr. Jeanetta Jackson, Tennessee State University, July 7, 2022

• Dr. Heidi Schweingruber, National Academy of Science, July 7, 2022

• Prof. Dr. Noam Elkies, Harvard University, July 7, 2022

• Prof. Dr. Dan Knopf, University of Texas, Austin, July 7, 2022

• Prof. Dr. Deidra Coleman, Wofford College, July 7, 2022

• Prof. Dr. Salvatore Torquato, Princeton University, July 6, 20222

• Dr. Julia Collins, ECU, Joondalup, Australia, July 5, 2022

• Dr. Oliver Janzer, ETH Zurich, July 5, 2022

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IM

There will also be many instant messages to thought leaders about key ideas.

6:20 PM · Jul 26, 2022·@FBI Hunter Biden should become national study at every level. He’s an all-American boy. What went wrong? In that process, we all need to break free of limited worldviews and engage the 202 base-2 notations that encapsulate the universe — see https://81018.com

If asked, “What went wrong?” the quick answer is “Solipsism devolved into narcissism devolved into nihilism.”

5:04 PM · Jul 21, 20 @MichaelEDyson The equality we all seek is hidden behind by billions of little worldviews when an entire view of a highly-integrated (even mathematically so) universe is needed whereby your pain becomes my pain. My start at it: https://81018.com/

10:16 AM · Jul 21, 2022 @wallacemick Governments do not work well or efficiently. Governments inculcate the limited worldviews of those within them. If we are ever to evolve, a transition to a highly integrated view of the universe is needed. A start on such a view is here: https://81018.com

10:54 PM · Jul 19, 2022 @hollykrieger Have you ever seen a gap created by **five octahedrons**? Computer graphics programming and geometric construction kits miss it (just like the tetrahedral gap): https://81018.com/15-2/ That five-tetrahedral gap is identical and above and below it.

**July 18, 2022 **(through LinkedIN): “Are you aware of the five-octahedral gap? It is the same as the five-tetrahedral gap that Aristotle missed. https://81018.com/15-2/ is an image and https://81018.com/geometries/ is the beginning of an explanation. Your comments would be valued.” Talat Rafiq, PhD, Applied Mathematics, Gujrāt, Punjab, Pakistan

Researching: Fermions on the Honeycomb Lattice and Tetrahedral-octahedral honeycomb

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Participate

You are always invited.

We needed to focus on the good, grasp the moments of perfection, and limit imperfections that become solipsistic or evil. Unfortunately religions do not give us very clear answers. Yet, it turns out that science doesn’t either.

Mathematics gives us some clarity. There are dimensionless constants and foremost among them is pi (π). These are values not defined by a person, but defined by the universe. And, I will add defined by infinity as well. It seems that pi (π) gives us the best insights. And, those insights give us a new definition of infinity — continuity-symmetry-harmony. These facets define infinity and become the basis of our ethics and our grasp of value otherwise we become solipsistic.

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Keys to this page, *starting-point*

• This page became the homepage on July 12, 2022. It is “under construction” even today.

• The last update was July 21, 2022.

• This page was initiated on July 12, 2022.

• The URL for this file is https://81018.com/starting-point

• The headline for this article: Finite-infinite Relations Starting With An Infinitesimal Sphere.

• First byline is: The starting point of all concepts must include pi to bridge the finite-infinite.

• 2nd byline: Dimensionless constants, bridge the finite-and-infinite for all concepts.

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