On identifying keys to our Universe

Many Questions and Possible Answers
by Bruce E. Camber (first draft

Abstract
Answers to well-framed questions open doors to more explorations and study, and then to more questions. If not, there is usually a logical flaw in either the question or the answer. Our world and her people need answers to many open questions about our universe. So, to that end, we will reframe questions and examine different answers about our universe.

Introduction
Where is the most logical place to begin a mathematical model of our universe?

We had a natural predisposition toward geometries. We were well into our introductory studies of the tetrahedron and octahedron when we discovered the 202 base-2 notations from Planck Time to the Now. We had been following the embedded geometries going deeper and deeper inside by dividing each of the edges in half and connecting the new vertices. Within 45 steps down into that scale, we were at the size of fermions and bosons. We continued. In 67 more steps within, we were down inside the Planck Scale. That space seemed to be a most natural order and the Planck base units seem worthy to be considered a logical place to begin the mathematical modeling of the universe. A reasonable answer seems to be: the Planck Base Units (PBU).^[1]

Did the universe start with dimensionless constants (and natural units)? Possibly, yet with more!

The Planck scale is defined by dimensionless constants and natural units. Increasingly it is regarded as a real domain of physics; we believe its numbers convey real information. We believe it is a worthy place to explore the possibility that a quantifiable universe had its start with these units.^[2]

Are these the smallest possible units of space-time? …believed to be.
Isn’t it logical that the smallest unit of anything would precede the larger units? Yes.

At that smallest scale:^[3] The Planck Length gives us a place to stop getting smaller and smaller. The current time gives us a dynamic place to consider the process of getting larger and larger. With all those natural units and dimensionless constants, we learned about Euler’s base-2, exponential notation, the Planck base units, pi (π) and key issues with cosmology. And, with all that data, our emergent model has a much more simple logic than the configurations of Lemaître, Hawking, or Guth. At the same time our model appears to address the same key issues that the Big Bang addresses plus many difficult open issues.

At the very smallest interval of that 3D Zeno-like walk deep down inside the tetrahedron and octahedron, we recognized Planck time as the chronon, the first unit of time. We then recognized today, the current time, as the Now. And with that to define this dynamic scale, we had a new chart; people told us it was a first — “It’s an original.” There were just 202 notations from the smallest unit of time to the largest. That chart raised hundreds of new questions, plus it had a smooth beginning. And, it also had an exponential expansion right from the start. It seemed like it was made to address the new observations coming in from the James Webb Space Telescope (JWST).

So, does this model of the universe start at the Planck scale? Yes.

Although the Planck scale is confusing to many — Cumrun Vafa of Harvard asks, “What is Planckscale physics?” And immediately concludes, “We have no idea.”^[4] (TASI, 2015). Notwithstanding, in 2001 in Physics Today, Frank Wilczek (MIT) had plenty of ideas. Others have as well. Our approach, we believe, opens the Planck scale to everyone. It’s the universe in numbers and geometries! Our most-recent work area is usually the homepage which is here: https://81018.com

What should we do with those who reject all but particles and waves?

Max Planck had a pessimistic answer to that question: “They’ll die.” Einstein cajoles us — arrogance is out. Integrity is in. Yet, there is plenty of pressure within today’s scientific and scholarly communities to come up with a new physics that is ”Beyond the Standard Models and the Lambda CDM.” Yet, among our most distinguished physicists, there are many within the old school who echo the words of Partha Ghose when he says,”The fundamental building blocks of the universe can only be bosons and fermions.” Particle physicists want to begin with particles unless, of course, they decide to become “a.pre-particle physicist-and-geometer.” Although particles, waves, and fluctuations are at the limits of our measuring abilities, it does not preclude grasping things that cannot be directly measured.

What could possibly manifest at the first moment of space time?
What is that thing?^[5]

• Might we decide that the most-simple thing is an infinitesimal sphere? Yes.
• Might the old pi and simple pi (π) render new insights? Yes.
• Might there manifest one infinitesimal sphere for each unit of Planck Time? Yes.
• Might the universe be a grid of infinitesimal spheres
many magnitudes smaller than the neutrino or quark and these spheres bind everything, everywhere for all time? As difficult as it may seem, I say, “Yes, it might.”
• Might Langlands Programs, string-and M-theory and so many others fill in the gap between the Planck scale and particle phenomenology? Yes.

The answers to those five little questions is an emphatic, “Yes!“

At one time to suggest “…everything, everywhere for all time…” would seem foolhardy. That all changed in 2022 with the release of the movie, Everything Everywhere All at Once.^[6] A movie about the multiverse, it garnered 264 awards, including seven Oscars (Best Picture, Best Director, Best Actress, Best Supporting Actress, Best Supporting Actor, Best Screenplay, and Best Film Editing). The concept of “everything, everywhere, for all time” has become part of the public dialogue. Instead of a multiverse which cannot be proven or disproven at this time, here we engage our own universe and our encounters within it.

Do the qualities of pi (π) and spheres beg questions about infinity and perfection?^[7]

There is something about the never-ending numbers, the longest continuity equation possible, that’s still ongoing right now, richly defined by pi (π), that tells us about infinity and the nature of numbers and order. There is something about circles and spheres with their perfect symmetries that tell us about the very nature of shape and relations. And, there is something about the Fourier Transform and the harmony of the spheres the give us all of our dynamics, our spacetime moment and light. In this model, it is assumed that continuity-symmetry-harmony define infinity and the qualitative.

The Planck base units are the beginning of the quantitative and define an infinitesimal sphere as a primordial building block of the universe.

Also, the qualitative opens the way to values and valuations.

What about quantum physics and indeterminacy?

Aristotle did not understand tiling and tessellating the universe. He thought with just the tetrahedron one could fill the universe perfectly. It takes both the tetrahedron and octahedron. His mistake went unchallenged for about 1800 years and by that time, it was obviously deeply ingrained within the mind of academia. In 1926 D. J. Struik, an MIT mathematician, wrote about it. Then, in 2012 the AMS published an article about it and awarded the authors, J. Lagarias & C. Zong, the Conant prize in 2015. People still ignore their conclusions and nobody appears to be thinking about its ramifications. There is a natural gap within our basic geometries and there can be no perfection when those gaps are included within any construct. These gaps have a direct relation to quantum mechanics, fluctuations, indeterminacy and probability. So, moments of perfection are rare yet not impossible. Further, among the earlier notations, 1-64, there are surely many domains of perfection.

2. Materials & Methods. Materials include the Planck base units and spheres. The methods include the extensive use of pi (π) and the mathematics of base-2 exponential notation. Stoney or ISO base units could have been used; the Planck units are well known and studied.^[x]

3. Results. A diversity of results, possibly the most disconcerting for our scholarly community are:

(a) The universe as a grid of infinitesimal spheres
Sphere dynamics at the infinitesimal scale inform everything, everywhere for all time. There have been very few other people making such a statement. Neutrinos are small. Trillions pass through us every day. These spheres are many orders of magnitude smaller than a neutrino. They are as many as 64 base-2 notations smaller, yet it would seem all are packed at such a high density, it might be described as a finite-infinite gateway where continuity-symmetry-harmony are the connectors.
(b) The redefinition of infinity and the infinite is difficult for most. The qualities of pi, continuity-symmetry-harmony, manifest within the finite yet these qualities define the infinite. For many years, infinity has been out-of-bounds. It is a concept that was to be avoided. When we began working with the concept of that infinitesimal sphere, scale invariance became a reality and those three facets of pi began looking more and more like a good redefinition of the infinite.
(c) The discovery that just 202 base-2 notations encapsulate the universe. We rhetorically asked ourselves, “What else could Planck Time be other than the first moment of time and Notation-0 or Notation-1? At the top of the chart is Notation-202. It is over 10.98 billion years in duration. The universe is about 13.81 years old. That opened up the universe so we could begin to explore it. We’ve barely made a scratch on the surface. That range has everything to teach us. We first turn to nine disciplines within functional analysis that are not on the grid.
(d) Domains of perfection below the first 64 notations. Quantum physics was introduced to the world by Max Planck and had he respected his numbers, all natural units, and had he suggested that those units define the universe, he and his colleagues could have done our base-2 chart in and around 1900. It didn’t happen, but it can happen now. The first 64 notations are such a short duration — a yoctosecond or a trillionth of a trillionth of a second — and the densities are so high — on the order of a neutron star — the geometries of perfection are efficient and there is no time or space for inefficiencies. Our guess is that the earliest structures of the universe were perfectly uniform. The first second is within Notation-143, the first year within Notation-169, and the first 1000 years within Notation-179. We would only be guessing when the first geometry of a gap and quantum fluctuations began. Some day it might be an interesting calculation to make.
(e) All notations are always active. And, all notations are actively contributing to the look, feel and functionality of the universe today, right Now. Ostensibly time is redefined. Although the results of the past are part of our definition today, the past has no real status except as it presents itself today. ~

There have been 35 seemingly new concepts that have emerged from these studies.

Also, these five results follow the logic of our fifteen questions but are not currently acknowledged within our scientific and scholarly communities. Yet, these five results have a coherent logic, so our analysis of them will continue.

4. Conclusions and Discussion. Answers to to well-framed questions tend to open new areas for exploration and discovery, and then for new questions to evolve. This work was consistent. There were many direct challenges to old theories. Some of them could be immediately tested and some were actually validated. Yet, each validation raises many more new questions. As it is, there could be an eruption of creativity until every notation becomes well-defined. Even today, each has only been initially defined with a few actual numbers.

Here are a few of the conclusions that are paradigmatic and could cause a shift:

(a) Grids: In 2013 Frank Wilczek encouraged our earliest efforts to understand the Planck scale. Within his book, The Lightness of Being: Mass, Ether, and the Unification of Forces (2008), he talks about a grid but does not attempt to define it mathematically. That work reminds me of discussions I had with Jean-Pierre Vigier back in 1980 at the Institut Henri Poincaré in Paris. Vigier was trying to define a grid, but the concept of infinitesimal spheres at the Planck scale was not a consideration. Wilczek’s is at least actively talking about the grid but is well-removed from the Planck base units.

The grid that we are proposing is entirely based on the simple logic of “one sphere per unit of Planck Length and Planck Time.” Max Planck defined it such. It has its own formula. And, that formula can be tested and it actually validates the initial presumptions of this emergent theory.

(b) Infinity: The historic debates about the finite-infinite are endless. Simplifying what we know about the infinite to the equations of pi seems like a bit of common sense. Giving infinity the status of the qualitative makes it personal and immediate. Relegating the finite to only that which can be measured or inferred quantitatively is simple logic.

(c) 202 for the universe. That the place and importance of simple geometries that opened this entire explorationof our universe should not be minimized. Our naive work was a substantial step beyond the base-10 work of Kees Boeke. We were looking for causal efficacies. We always used most-simple geometries. Structure, energy, and action were all around us. This wasn’t just 202 notations that captured everything, everywhere for all time, it was a living, breathing, expanding universe.

(d) Perfection. We have all been told that the universe is fundamentally statistical, probabilistic, and indeterminate. It has been sold in the public square since about 1925. Five generations have struggled with these concepts. Each successive generation appeared to be increasingly comfortable with the conclusions. It is a most peculiar task to be re-introducing the a perfected-state within space-time, a concept that has been beaten down over the ensuing century. We all talk about something being perfect, but intellectually we “knew” it was not. Quantum theory told us so. No longer. Not only might there be instants of perfection with perfect continuity-symmetry-harmony, the earliest domains within the earliest notations might actually be too fast and too dense for the freedoms of imperfection.

(e) The Now: All notations are always active. The major proponent of loop quantum gravity, Carlo Rovelli, has declared to the world that all time is Now. Within this model of the universe, we see all 202 notations actively involved with the sustaining and evolution of the universe. It stands to follow that all time is now.

Lee Smolin wrote a book, The Trouble with Physics (2007), where he declares that to the degree that string theory rises is the degree that science falls. Smolin argues effectively throughout the 392 pages of his book, that physics is missing something. Ultimately there is no real causal efficacy within string and M-theories. A savage indictment is, among many different issues, dark matter and dark energy. To that, I would add, that some of our biggest and oldest theories, even more destabilizing to the human psyche, also need to be modified, then re-enlivened.

To say the least, we’ve got some to work to do. Thank you. –BEC

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Author Contributions. Bruce E. Camber is currently the sole author of this article. He readily acknowledges that this is part of an ongoing analysis of the inability of big bang cosmology to account for observations through the JWST. He is always available for 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 encouraged our studies 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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Review of the fifteen questions

Where is the most logical place to begin the mathematical modeling of our universe?
Should we start with dimensionless constants (and natural units)?
Are these the smallest possible units of space and time?
Isn’t it logical that the smallest unit of anything precedes the larger units?
Does this model of the universe start at the Planck scale?
What should we do with those who reject all but particles and waves?
What could possibly manifest at the first moment of space time?
What is that thing?
Might we decide that the most-simple thing is an infinitesimal sphere?
Might old and simple pi (π) render new insights? Yes, little old pi (π)?.
Might there manifest one infinitesimal sphere for each unit of Planck Time? Result? Crazy?
Might the universe be a grid of infinitesimal spheres magnitudes smaller than neutrinos?
Might Langlands Programs, string-and M-theory and so many others fill in the gap between the Planck scale and particle phenomenology?
Do the qualities of pi (π) and spheres beg questions about infinity and perfection?
What about quantum physics and indeterminacy?

References (more to come)

[1] Planck Base Units (PBU). Retrieved 6 March 2024: https://81018.com/planck-base-units/

Comparison: Hawking’s singularity, a compression of everything, everywhere, for all time throughout the universe: Retrieved 6 March 2024: https://81018.com/calculations/

[2] Dimensionless constants and natural units.
Dimensionless constants, cosmology and other dark matters, Max Tegmark (MIT), Anthony Aguirre (UCSC), Martin J Rees (Cambridge), Frank Wilczek (MIT), (2005) ArXiv: https://arxiv.org/abs/astro-ph/0511774v3 (PDF)

[4] “What is Planckscale physics? We have no idea.”video, Cumrun Vafa, Lecture 3, Missing Corner (TASI, 32:27 min.), Theoretical Advanced Study Institute (TASI), University of Colorado at Boulder, 2015
• Pessimism: Retrieved 8 March 2024 – Max Planck – https://81018.com/max-planck/
• Einstein: Retrieved 8 March 2024 – https://81018.com/arrogance/
• Integrity: Retrieved 8 March 2024 – https://81018.com/einstein-bronze/#Quote
• Standard Models: Retrieved 8 March 2024 – https://81018.com/beyond-standard-model/
> Planck Units: Physics Beyond The Standard Model?, Arpan Dey, Journal of YP, August, 2020
> Planck-scale physics: facts and beliefs, Diego Meschini, ArXiv, Jan 2006.
• Ghose: Retrieved 8 March 2024 – https://81018.com/ghose/

[5] Infinitesimal spheres Retrieved 8 March 2024, https://81018.com/sphere/
• Pi (π): Retrieved 8 March 2024, https://81018.com/csh/
• One: Retrieved 8 March 2024, https://81018.com/tredecillion/
• Grid: Retrieved 8 March 2024, https://81018.com/grid/
• So many others: Retrieved 8 March 2024, https://81018.com/functional-analysis/

[6] Everything Everywhere All at Once Retrieved 8 March 2024: https://en.wikipedia.org/wiki/Everything_Everywhere_All_at_Once

[7]. Continuity, Retrieved 9 March 2024: https://81018.com/perfection/

Pi (π) Day

Endnotes & Footnotes (personal reflections)
There are over 2000 pages within this website; much of it is repetitious, because of the belief that by going over things, justione more time, a new insights or idea will present itself.

[1] Attempts to answer the question about the emergence of the universe: https://www.simonsfoundation.org/event/origins-of-the-universe-2022/

[2] An Alternative Theory of Everything: Classical Quantum Physics, Jean Louis Van Belle, 2020

[3] Perhaps more to come…

Resources (to come)
Key resources will be added within this website.

[1] Continuity and Infinitesimals, John Lane Bell, Ontario, Stanford Encyclopedia, First published Wed Jul 27, 2005; substantive revision Wed Mar 16, 2022 https://plato.stanford.edu/entries/continuity/ partially from Reflections on the Axiomatic Approach to Continuity. In: Ferreira, F., Kahle, R., Sommaruga, G. (eds) Axiomatic Thinking II, pp.131-143, Springer, 2022

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Emails (to come)
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.

14 March 2024: @OpenAI Pursue continuity-symmetry-harmony:
• Identifying keys to our Universe: https://81018.com/tighter/
• Qualitatives: https://81018.com/qualitative/
• Number Theory: https://81018.com/numbers-numbers-numbers/
• From the smallest to largest scales in physics: https://81018.com/reformat/
• Pi Day: https://81018.com/2024-piday

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Critique. Your comments are most helpful. These five pages work together:
• From the smallest to largest scales in physics: https://81018.com/reformat/
• On identifying keys to our Universe: https://81018.com/tighter/
• The Qualitative: https://81018.com/qualitative/
• Pi Day: https://81018.com/2024-piday/
• Number Theory: https://81018.com/numbers-numbers-numbers/

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Keys to this page, tighter

• This page became the homepage even though “under construction.”
• The last update was 14 March 2024.
• This page was initiated on 24 February 2024.
• The URL for this file is: https://81018.com/tighter/
• The headline for this article: Many Questions, Possible Answers
• First teaser* is: On identifying keys to our Universe.

*Or, wicket, kicker or eyebrow.

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Redefining the Universe Through Mathematics

On identifying keys to our Universe

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