PERFECTION.STUDIES: CONTINUITY•SYMMETRY•HARMONY GOALS.October.2024
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Foundational Concepts for Cosmology, Physics, and the Public
by Bruce E. Camber

Abstract
In 1874 George Johnstone Stoney introduced the concept of natural units. When used in equations, it results in infinitesimal numbers for space & time (British Association lecture [*], Belfast, Ireland). John Barrow wrote the first summaries of his work. In 1899 Max Planck introduced his own version of those numbers ^[†], again natural units and calculations that render infinitesimal units of space and time. In 2001 Frank Wilczek wrote three articles for Physics Today that interpreted what’s been called, Planck’s numerology, and gave it perspective and substance.^[a] Upon receiving a Nobel Prize in 2004, all of Wilczek’s work received greater scrutiny. Even the international standards organizations took note. Those concepts were finally being studied within the academies of science around the world. With hindsight, it was long overdue. It was about time.

Introduction. Stoney and Planck opened an exquisitely small universe; it’s here patterns can be recognized. As all 202 base-2 notations from the Planck Scale to the Now engage, patterns become models then become paradigms. Today, in our time, there is a convergence with artificial intelligence and it seems to be the perfect time for AI to begin validating the simple logic within-and-between all notations.

In December 2011 our high school geometry classes unwittingly started to learn about it. Planck’s natural units came alive for eighty high school students and three teachers. By multiplying by 2 over and over again, we uncovered the 202 notations that encapsulate everything, everywhere for all time from the start of the universe until this moment, the Now.

Planck’s base units, now updated through the ISO, are pivotal. These concepts can be understood, even though it took scholarly community over 100 years to begin to engage them.

We were exploring the interior of the tetrahedron. By dividing the edges in half and connecting the new vertices, we found four smaller tetrahedrons and an octahedron perfectly nested inside.

We did it again. With each step going within, the number of tetrahedrons would increase by four inside each tetrahedron and by eight inside each octahedron. The number of octahedrons would increase by one inside each tetrahedron, and by six inside each octahedron.

So, at that next step, there would be sixteen plus eight tetrahedrons (24 total), and four plus six octahedrons for a total of 10.

Confirm the count with this image of our model. Click on it to enlarge it.

The question was asked, “How far down inside could we go? How small can we get?

In 45 steps within, we were within the size scales of fermions and within an additional 67 steps, we were down in the domain of the Planck scale.

To check our work, we used Planck’s units to return. We multiplied by 2 over and over again. Within 112 doublings, we had returned to the scale of our classroom. We then continued multiplying by 2. In another 90 doublings we were out beyond the age of the universe and the approximate size of the universe.

It became a beguiling fascinating chart of numbers.

To create images of these models at each step, we will continue by using AI-tools that can generate geometries and geometrical structures. Once those AI models are working, additional capabilities will be mapped from the Planck base units.

It has been over ten years thinking about that chart (as well as others we have created). We have emerged with eight hypotheses — all closely related — ostensibly to begin to formulate thought experiments that can demarcate forms and functions at the Planck scale:

• The Planck units define an infinitesimal sphere.
• Spheres at the Planck scale define a perfection.
• Perfection is defined by the continuity-symmetry-harmony within pi(π).
• The universe is tiled and tessellated by Planck spheres.
• A grid of Planck-scale spheres define the infinitesimal universe.
• Planck-scale physics and mathematics are defined by pi(π).
• Continuity-symmetry-and-harmony of pi (π) render the homogeneous and isotropic.
• There are also geometries of imperfection (going back to Aristotle).

All eight hypotheses are “what if” questions and are linked to one of our pages where the discussion has been opened. As a result of this article either those pages will be further developed or a new page’ will be started to focus on just that hypothesis alone.

These hypotheses are at densities and durations defined by the Planck scale physics and mathematics. That presents a special challenge and for that reason we are encouraging everybody to go back to the original documents of Stoney and Planck to get acquainted with many of the creative and novel approaches to these concepts and numbers.

Results. Not all scholars have found the work of Stoney, Planck, Barrow, and Wilczek to be compelling. There are questions about causal efficacies. These eight hypotheses above may provide a tipping point for some. If these become compelling through the use of AI tools, there will be further analysis by others.

If all eight hypotheses can be mapped into an AI project, it should become compelling for many others. To that end, we repeat the hypotheses and links and add a few comments.

[1] The Planck units define an infinitesimal sphere. We began our studies of spheres in 2012 through Philip Davis, a Brown University applied mathematics professor and one-time lead mathematician for the National Institute for Standards and Technology. We earnestly began to learn about the richness of the sphere and pi(π).

Spheres can be as exotic as any of the fundamental particles. Include the functionalities of sphere stacking and cubic close packing of equal spheres and the Fourier transform and these hypothesized spheres could mimic the functionalities of any of the hypothetical particles.

“What is Planckscale physics?” asked Harvard’s Cumrun Vafa. He says, “We have no idea.” Yet, many people have had many ideas; and, to all those ideas, we hypothesize these eight concepts and the need to figure out how to test each of them.

[2] Spheres at the Planck scale define a perfection. In 2019 Nobel Laureate, P. James Peebles of Princeton said, “…we have no good theory of such a thing as the beginning.” Peebles was one of the world’s experts on the mapping of the Cosmic Microwave Background Radiation (CMB, CMBR).

There are two reasons we have hypothesized that the universe within the earliest notations is perfect: 1) The nature of pi(π) and symmetry. Circles and spheres are the face of perfection. 2).There is no wiggle room. The densities and durations are made for perfections. The densities are that of a neutron star and durations are too short. Even at Notation-64, the durations are less than a yoctosecond, one trillionth of a trillionth of a second.

Each of the eight hypotheses are held together by the other seven hypotheses.

[3] Perfection is defined by the continuity-symmetry-harmony within pi (π). Every Pi Day, March 14, was a challenge to understand pi (π) more profoundly. In 2022 the feature-functions within pi (π) were seen as a constant that defined both the finite-and-infinite and the quantitative-and-qualitative. These were on the divide; the hyphens between the two concepts defined the divide. Not only did it seem like a reasonable hypothesis, it became a primary hypothesis of the project. It will be fun to learn and see how these concepts get incorporated into and by AI.

Though these eight hypotheses are self-referential, they incorporate the infinite and qualitative.

[4] A grid of Planck-scale spheres define an infinitesimal universe. A calculation is made. If one plancksphere is generated for every Planck Second, over 18.5 tredecillion spheres per second are generated. Infinitesimal spheres at the Planck scale fill the universe. That they could be the actual source of dark matter and energy would solve a major mystery.

This model has to resolve big problems. It needs a base of eight hypotheses!

[5] The universe is tiled and tessellated by Planck spheres. Though hard to imagine, the universe is entirely “held together” by infinitesimal spheres. It puts a different spin on causal efficacies. This takes me back to discussion with Jean-Pierre Vigier in 1980 when we talked about causal efficacies and action at a distance. We were not thinking about a grid of spheres defined by the Planck scale whereby the entire universe — everything, everywhere for all time — is networked. It would require having all eight hypotheses working at the same time.

[6] Planck-scale physics and mathematics are defined (a) by pi(π), (b) by spheres, and (c) by tetrahedrons-and-octahedrons. Cubic-close packing of equal spheres is the dynamic image that summarizes those moments, especially including the emergence of the Platonic solids and Euclidean geometries. These redundancies within the eight hypotheses ties it all together.

[7] The continuity-symmetry-and-harmony of pi (π) renders the homogeneity and isotropy that is an essential quality of our universe. Again, it is an hypothesis that this causal efficacy is fundamentally ingrained in the very being of all that is, and as a result, it creates the value equations for all that is; it lays the foundations for ethics. This was an unexpected benefit. If the foundations of ethics can be affirmed through the simple formula for pi (π), perhaps major conflicts could be avoided.

If these eight hypotheses are laying such foundations, there should be redundancies.

[8] There are also geometries of imperfection. Indeterminacy starts with geometries that create spaces; they do not fit together perfectly. Five tetrahedrons sharing a common edge create a 7.35610317+ gap. It is been named after Aristotle because he thought one could tile and tessellate space perfectly with the tetrahedron.

That mistake threw off academics for about 1800 years before it was discovered in the 1400s. But then, it was only reviewed six hundred years later. Given its history, one could readily conclude that it is a trivial issue. The subject was again reviewed in 2012 but it received minimal citations. Yet, hardly trivial, we have hypothesized that it could redefine the foundations of quantum physics as a “geometry of gaps.” It is a geometry of indeterminacy and unpredictability. In our more speculative moments we can see how other facets of life will follow including Life itself. Could a gap be responsible for the inanimate becoming animate? Could consciousness follow? …sentience? …creativity and emotions?

All this appears to be given with those spaces that do not fit perfectly.

These are our eight hypotheses.

Now the challenge is to have AI test the logic and viability of each of these eight hypotheses. If they hold water and the notations work as 202 interdependencies, all time is now. All notations are always active and it becomes a plausible model of the universe.

That would be an extraordinary validation. Thank you.

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Resources
As references are added, other resources may also be added

[*] Stoney units. Published in 1881 and retrieved 30 September 2024: The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, LII. On the Physical Units of Nature. By G. Johnstone Stoney, DS, FRS, Vice President, Royal Dublin Society, February 26, 1881

[†] Planck Units. Notation for Planck Length and Planck Time: Retrieved 30 September 2024. Go to Section 164, Natural Units, pages 205-208.

[a] Frank Wilczek. Retrieved 30 September 2024; https://81018.com/wilczek/

Please note: Physics Today is the flagship publication of the American Institute of Physics (AIP). There is no free access to these three seminal papers. To facilitate an understanding of his work a homepage will be developed that quotes extensively and provides a basic introduction to the three articles. -BEC

[1] Hypothesis I. Retrieved 1 October 2014, https://81018.com/particle/

[2] Hypothesis II. Retrieved 1 October 2014, https://81018.com/a-perfect-start/

[3] Hypothesis III. Retrieved 1 October 2014, https://81018.com/csh/

[4] Hypothesis IV. Retrieved 1 October 2014, https://81018.com/exquisite/

[5] Hypothesis V. Retrieved 1 October 2014, https://81018.com/structure/

[6] Hypothesis VI. Retrieved 1 October 2014, https://81018.com/facts-guesses/

[7] Hypothesis VII. Retrieved 1 October 2014, https://81018.com/2024-piday/

[8] Hypothesis VIII. Retrieved 1 October 2014, https://81018.com/gap-geometry/
Reference to Aristotle: https://81018.com/too-simple/

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Reading and re-reading
What is opened on the desk, on the shelves and on the floor.

• Facts and Speculations in Cosmology, Jayant Narlikar & G. Burbridge, Cambridge University Press 2008

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Afterthoughts
Personal reflections.

Artificial Intelligence (AI) has a learning curve and it’s not always straightforward:

1. The first AI platform to be initiated was IBM Watson. Got hung up within IBM watsonx Assistant.
2. ChatGPT recommends Blender, 3D modeling software to create and manipulate Platonic solids.
3. Tinkercad by Autodesk. 3D design tool to create/customize 3D models, including Platonic solids.
4. GeoGebra: Dynamic mathematics software that includes tools for constructing geometric shapes, including Platonic solids, in both 2D and 3D.
5. Wolfram Alpha: Explore properties of Platonic solids, visualize them, and even get mathematical insights.
6. MATLAB: If you’re into programming, you can create and visualize Platonic solids using code.
7. Python.

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

12 October 2024: Tejaswi Venumadhav Nerella, UC Santa Barbara, CA
11 October 2024: Theo Grundhöfer, Würzburg, Germany
9 October 2024: Espen Gaarder Haug, NMBU, Oslo, Norway
9 October 2024: Timothy Palmer, Oxford University, Oxford, England
9 October 2024: Andrei Linde, Stanford University, Stanford, CA
6 October 2024: James Glimm, Stony Brook, NY
6 October 2024: Gregor Kasieczka, Universität Hamburg, Germany
5 October 2024: Cora Dvorkin, Harvard, Cambridge, MA
5 October 2024: P. James Peebles, Princeton, NJ
4 October 2024, Pumla Gobodo-Madikizela, Stellenbosch University, South Africa
4 October 2024, Gustavo Joaquin Turiaci, University of Washington, Seattle, WA
2 October 2024: Cumrun Vafa, Harvard — https://81018.com/facts-guesses/ — Cambridge, MA
1 October 2024, Jayant Narlikar, IUCAA. Pune, India
1 October 2024, Jesse Thaler, MIT, IAIFI, Cambridge, MA

More to come…

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

5:23 PM · Oct 2, 2024: cnnbrk (CNN Breaking News) The world is a mess because we do not have a perspective of the universe to guide us. There are 202 notations that relate everything, everywhere for all time — https://81018.com — explains it. Continuity, symmetry and harmony become the baseline of behavior.

More to come…

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Critique ____ You are always invited.

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Keys to this page, infinitesimals

• This page became a homepage, October 2: https://81018.com/infinitesimals/
• The last update was 11 October 2024.
• This page was initiated on 11 September 2024.
• The prior homepage is https://81018.com/interdependencies/
• The next homepage: https://81018.com/vision/ Password: Vision ( in process)
• The URL for this file is https://81018.com/infinitesimals/
• The headline for this article: Radical Concepts for Cosmology, Physics, and the Public.
• First teaser* is: Emergence of the concept of natural units and an infinitesimal universe

*Or, wicket, kicker or eyebrow.

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