An Alternative: The Universe As An Intimate Place


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Warm & Fuzzy or Cold-and-Hostile

By Bruce Camber Key dates   FQXi: In conjunction with this article Today’s work

Summaries. The vastness of space bewilders most of us because our current commonsense understanding of space-and-time is ostensibly Newton’s absolute space and time. It’s challenged by many including our base-2 chart of numbers. We start with Planck Time (and Planck length, mass and charge) and go to the current age and size of the universe in 202 notations or doublings. That horizontally-scrolled chart (34 pages) of just the numbers was completed in 2016. Here space and time are derivative-and-finite. As this data continues to be analyzed, the infinite is necessarily studied and it is also redefined. Within this emerging model, infinity is continuity creating a finite order and time, symmetry creating finite relations and space, and harmony creating finite dynamics and space-time moments. No other definition of infinity or the infinite is engaged. Just 202 notations, domains, jumps or steps might seem intimate enough; yet, in the spirit of John Wheeler, the other prime-number bases (base-3, base-5, base-7, etc) are also explored as a series of possible “wormholes” creating another level of intimacy. Within our projected domain for systems theory, between Notation-50 to Notation-60, the Mind (all forms of consciousness), is being explored. By definition, all notations are always active and building on each other, yet particularly within Notation-202, at the current time, the Now, and the current expansion. Considering the diversity of mathematical and physical systems, it is projected that prime-number notations are also how unique mathematical systems develop at or below Notation-64 and how unique physical systems develop above notation-64. These might be considered matrices within the matrix, or perhaps, subgrids nested within the grid. This picture of the universe is not of a cold-and-hostile place but quite possibly of a warm-and-fuzzy, intimate place. Quick Review  Finite-Infinite

Pythagoras said that all things come to be in accordance with number on the grounds that order in the primary sense is in number and it is by participation in order that a first and a second and the rest sequentially are assigned to things which are counted. – Theano

Introduction. For as long as I can remember we were taught the universe is a vast, empty space. More recently, we learned the universe has over two-trillion galaxies (see Chris Conselice, 2016) with many-more trillions of stars. Either way, it is too big for intimacy. Coming to our rescue is Theano’s Pythagoras who gives numbers a role and stature. In our hyper-networked model* where everything is connected to everything, we hope to open paths that point to a very special intimacy within our universe.

Max Planck’s four base units.1 When we backed into a simple mathematical outline of the universe by applying base-2 to the Planck units, there are just 202 doublings. It all seems quite simple and the 202 notations seem entirely manageable.

Could this be a start to construct a warm-and-fuzzy model of this universe?
We think the answer is “Yes.”

To that end, our first hypothesis is that Planck Time is the first instance of time and that we are now within the earliest part of Notation-202, right up to this day, this moment-and-instant. That gives us a coherent, little mathematical outline of the universe. And, because it all started in a high school geometry class chasing the tetrahedron-and-octahedron back to the Planck numbers, this outline also begins to demonstrate how numbers correspond to simple geometries.

Now, that should be quite encouraging. We know that geometries and numbers are as much a key part of the foundations of physics as particles and waves, so perhaps we are onto something that could become warm and inviting. We ask many people for feedback.

Pi

Pi and Perfections.2 The next hypothesis is that all four Planck base-unit values manifest as an infinitesimal sphere. There is nothing more simple than a sphere. And, the next hypothesis is that there is an endless stream of primordial spheres that follow that first sphere so a natural inflation and simple geometries begin to emerge. More structure, textures, and complexity is observed with all the dimensionless constants that define those Planck units. Eventually even more textures will be added, starting with all the other scientific functions without a necessary length or time dimension. How-why-when-and-where each would manifest is an open question. Notwithstanding, this outline of our universe becomes a working model as more-and-more relations are defined for each notation.

Our hypothesis is that pi (π) is a primary gateway between the finite and the infinite2 and that the qualities of the infinite can be known through the qualities of the sphere. At the Planck base-unit scale, perfect continuity is the never-ending and never-repeating numbers.3 Perfect symmetries can be understood by carefully examining close-cubic packing of equal spheres.4 And, its perfect harmonies are best engaged within the Fourier transform.5  There is something very warm about continuity, symmetry and harmony and here we say, the qualitative expression defines the infinite and the quantitative expression defines the finite.

That is a very different notion of infinity and perfection.

Within this model, however, there are notations that are defined by such perfection and all are prior to the aggregation of the five tetrahedral cluster.6

pentastar

The Tetrahedron and Imperfections. Aristotle (384 BC – 322 BC)  believed the tetrahedron could tile and tessellate the universe.7 It was passed down for at least 1800 years before being debunked. Today we know that an octahedral-tetrahedral couplet is required. Moreover, with just five tetrahedrons sharing a common edge and its two vertices, a natural geometric gap emerges.8 It is proposed that this gap becomes systemic, possibly between Notations 50-60, and opens the first possible systemic fluctuations. Then, around Notation-64 and certainly by Notation-67, systemic fluctuations become measurable and are defined as quantum fluctuations.9

Within this model, quantum indeterminacy now becomes dominant and the universe as we know it continues to unfold. 

Our Fuzzy Universe. In 1945 John Wheeler (Princeton) and Richard Feynman (Caltech) proposed quantum field theory or QFT.10 Very well-defined, QFT, more than Gödel’s incompleteness theorem, captures the deep roots for the unpredictable and indeterminate11 within the sciences, mathematics, logic, linguistics, philosophy, and consciousness. Gödel’s constructions using logic are too limited because he never applied that logic to a base-2 model of the universe12 especially considering the perfections within the earliest notations and the dynamics of the finite-infinite relation.

Finite-infinite bridge. This model creates boundary conditions and parameters. The Planck base units and the sphere define our universe with its initial functions and dynamics. There is no singularity per se; all the equations that define each Planck unit and the sphere are all active and define a bridge between the finite and infinite. This bridge is a key to our understanding the very nature and structures of our little universe.

In that spirit let us go over the basics of this model one more time:

Planck Time

Light and the four Planck base units.13 Planck’s natural units, based on the universal constants of G, ħ, c, and kB, are tested within this model by applying Planck’s simple equation for Planck Time adjusted for the speed of light, c. This highly-integrated chart of numbers defines a consistent variable speed of light throughout the model. It is generally within .01% of the laboratory defined speed of light. The next challenge on this path is to understand more deeply G, ħ, and kB.

Simplicity and complexity within the infinitesimal sphere.14 The product of the finite-infinite relation, the qualities of the infinitesimal sphere tell us about the the most basic qualities of the infinite.[3][4][5] Going larger, the quantitative is further defined. Going smaller the qualitative is further defined.

Perfected systems are possible up to and around Notation-64. Perfected systems are infinitesimal states of being. It would seem, however, that moments or instants of perfection could spark right through to Notation-202.

QFT, quantum fluctuations, and quantum indeterminacy extend from Notation-64 up to and including Notation-202. The first measurable unit of time (attosecond)  is within Notation-84; the first second is between Notation-143 and Notation-144.

The Intimacy of Our Universe

Sphere to tetrahedron-octahedron couplet

Sphere-stacking and cubic-close packing of equal spheres.15  What started around 1587 with Thomas Harriot, then involved Kepler, Gauss, Poincaré and culminated with the most-recent work of Thomas Hales, continues today under many other labels. Seeing how things fit compactly together, has become today’s work to understand the sub-grid physics modeling and the numerical techniques to validate the predictive results of our numerical simulations.

Tetrahedrons enclose an octahedron.

Within this simulation of sphere stacking, the first black circle is perhaps Notation-0 defined by the Planck base units. Notation-1, the first doubling, gives us the green circle (illustrated just above). Now, although difficult to picture, imagine a highly-dense block of these spheres populating every square inch of the universe with octahedrons surrounded by tetrahedrons creating a blank canvas of dimensionality through connections of the centerpoints of circles.  Tiling and tessellating the universe takes on a very new meaning! Imagine if you can that there are literally zillions of these infinitesimal spheres populating every square inch of the universe and this simple tetrahedral-octahedral system, pervasive, is the first level of interconnectivity.

This simple base-2 ordering system quickly becomes complex. Each of the nineteen subsequent prime-number notations — 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, and 61 — introduce even more complex mathematics. The remaining prime numbers — 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 197 and 199 — open physical potentials.

Also, base-2 is just one dynamic of this expansion. This universe appears to be opportunistic so may well use the other prime number bases — base-3, base-5, base-7, base-11, and base-13 (right up on up to base-101 — to introduce yet even more complex functions. Of course, most notations are included within base-3 (there are 67), base-5 (40) and base-7 (28).

One can imagine how any given moment in the universe necessarily involves all 202 notations, yet to experience that moment as a conscious moment, to experience the fullness of a moment within Notation-202, just may actually be limited to specific notations.

We consult with many people. We are always asking for insights, comments, suggestions and criticism. Some of the people to whom we have turned are pictured and linked below.

Stephon AlexanderAlexander
Massimo Amelino- Amelino
Mariah_Carey Carey
Gates Gates
Magueijo Magueijo
Michela Missimi Missimi
Dean Rickles Rickles
Leonard Susskind Susskind
Maryna Viazovska Viazovska

Conclusion. All these concepts are being explored. And, with just this introduction, we open paths for further exploration; there is so much more to be explored. -BEC

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Endnotes and Footnotes

Please note: Most of these endnotes and footnotes are working drafts; a few are still quite rough. Work and rework will continue for awhile longer.

* Hyper-connected construction: The universe like the human brain or the internet, is discussed in many documents throughout this site: This Shifting Paradigm Changes Our Perception Of Everything (October 2014), Everything Starts Most Simply. Therefore, Might It Follow That The Planck Length Becomes The Next Big Thing? (May 2014), On More Fully Recognizing The Infinite (November 2017),  Four Key Missing Pieces from Our Puzzle (December 2019), and On Asking Nobel Laureates Key Questions  (September 2019).

[1] Planck Base Units. The first moment of time in this universe can be called, Planck Time; however, it did not mark the start of the universe all by itself. Planck Length, Planck Mass, and Planck Charge were all happening at the same moment. It is still a very simple start. Things are simple before they become complex. Doubling by stacking is a very simple process, however, it produces a natural inflation.

Follow the numbers. Our chart of numbers was first inspired by following a simple progression of the simplest geometries starting with the tetrahedron and the octahedron within it. But as simple as these two objects are, there is one object that is technically more simple, the sphere. Our intuitions, very early in 2012, was to say, “It all starts with spheres. And, there is a migration path from spheres to the Platonic solids.” We set out to understand what those statements meant if anything at all.

[2] The sphere as perfection and a gateway. Too much mystery and hocus-pocus surround the infinite. It was made even more mysterious when in 1687 Cambridge University Lucasian Professor Isaac Newton incorrectly defined space and time as absolutes. When his book, affectionately known as the Principia, became the primary reference for science, his absolutes became forever and universal, preconditions of all that is. And, even though this point of view became the world’s commonsense embrace of space and time, along with mass and charge, all four need to be put back inside the sphere.

Editor’s comment: Time in a bottle. Jim Croce’s 1973 love song, captured the imaginations of most who listened to it, yet time, I believe, is more logically enclosed with space (length), mass and charge with an infinitesimal sphere. Of course, lyrically, it doesn’t inspire one as much as the old seafaring bottle.

There are within the perfect sphere many equations that define each of the Planck units and equations that define a sphere and sphereness. All the equations are reaching across the finite-infinite bridge or gateway and all of them are about continuity (order), symmetries (relations) and harmony (dynamics). It is quite unlike the imagery of one of my favorite physicists, John Wheeler, when he said, When I became interested in gravitation and general relativity, I found myself forced to invent the idea of quantum foam—made up not merely of particles popping into and out of existence without limit, but of spacetime itself churned into a lather of distorted geometry.”

John Wheeler actually named the two most-basic Planck base units, “Planck Length” and “Planck Time.” Yet, when he thinks about those Planck units, it is in light of the big bang theory. Did he ever consider Planck Length divided by Planck Time is equal to the speed of light? Did he ever consider Planck Time as the first unit of time? Did he ever consider the geometric gap created by five tetrahedrons? To date, we’ve found no records of such inquiries. Yet, he personally knew Gödel and was quoted in a tribute to him by physicists, James E. Peebles & William G. Unruh in Nature, 453, page 50 (2008), “To say Gödel is the greatest logician since Aristotle would be to slight Gödel.” It is wonderful that Wheeler defends Gödel, but it would have been better if they both recognized importance of Aristotle’s mistake and the place and importance of Planck base units.

[3] Never-ending, never-repeating. Obviously not originating from the finite, but equations that are incommensurable, should not be left out in some never-never land. Fundamentally, I believe any number like pi (π) defines the infinite. Though numbers by their nature are finite, certain very special orders of numbers are infinite; so, I am  encouraged to say that this type of ordering is one of the facets of infinity. Of course, people ascribe many other qualities to infinity. We only ascribed continuity (order), symmetry (relations) and harmony (dynamics). Any other quality is solely the choice of an individual and not our concern  here. Within the sciences, especially mathematics and physics, continuity is the first principle for order, and here it is. Simple. Simple. Simple. The sphere comes first.  What else could there be?

Sphere to tetrahedron-octahedron couplet

[4] Close-cubic packing of equal spheres. Had you ever seen this dynamic GIF? It is a key function (so it’s pictured again). Applied to the Planck scale, the first sphere pictured is THE first sphere in the universe. But then look at what happens as the internal dynamics of a sphere “discover” other spheres, geometries (and all of Euclid) begin to emerge.  Sphere stacking begins in earnest.

The very nature of the symmetry of a sphere and these first relations tell us how space, time, mass, and charge are each one of the four most-primary facets of light. Gravitation, temperature, motion… are derivative.

[5] Perfect harmony vis-a-vis the Fourier transform. Can we get inside the sphere and begin to understand all these dynamics?  It is so rich with the entire history of the Fourier transform and all its multitude of applications, and here it is within the very first notations. Here is the epitome of fundamentality. It certainly needs much more analysis and discussion, so of course, there is more to come even within this document.

pentastar250

[6] Five tetrahedral cluster. Something so simple and so geometric, yet so fundamental, I believe it could engender the development of an entirely new science to study the geometry imperfection. Currently there is not even a line or a paragraph about the five tetrahedral cluster within the textbooks of quantum field theory. There are many discussions about tetrahedral configurations (i.e. Quantum Tetrahedra, Mauro Carfora, Annalisa Marzuoli, Mario Rasetti, 2010) and these are now being studied.

Of course, there is so much more to come.

[7] Tile and tessellate the universe. Cambridge University Lucasian Professor Isaac Newton formalized the study of “science” with his publication of his Principia in 1687. He was sure space and time were absolute, forever and universal, preconditions of all that is. He was only partially right. Although his “absolute point of view” continues as the our commonsense embrace of space and time, it is silly today. First, Einstein locked the two together. Then, he locked mass-and-charge together and his mentor, Max Planck, gave us the formulas that tied all four to the speed of light.

We ignore those equations to our peril. Yet, as a result of ignoring Aristotle’s mistake, we fail to see the obvious. Though it took 1800 years to stop repeating his mistake, it still lives on within our refusal to engage the fullness of geometry and its first-and-most-simple imperfection. It takes a tetrahedron and an octahedron to tile and tessellate the universe. We all need to understand this role of that tetrahedral-octahedral cluster as deeply as Newton wanted space and time to be absolute. Geometries and numbers connect the universe.  Here, Aristotle’s 1800 year mistake confronts Newton’s 300 year mistake. It took an Einstein to break that grip. We will know that we are getting successful when Hawking’s infinitely-hot mistake goes cool and becomes an historical footnote.

This outline, a nascent model and construction project, just might help to change things.

The first three epochs of big bang cosmology — The Planck Epoch, the Grand Unification Epoch, and the Inflationary epoch — will eventually be understood notation-by-notation. For example, from 10-44 seconds to 10-41 seconds, Notation-1 to Notation-10 maybe known as the The Initial Processes of Forms. Notation-11 to Notation-20, or 10-40 to 10-38 seconds, might be known as The Initial Processes of Structures. Notation-21 to Notation-30, or from 10-37 to 10-35 seconds might be known as The Initial Processes of Substances. Notation-31 to Notation-40, or from 10-34 to 10-32 seconds, might be known as The Initial Processes of Qualities. Notation-41 to Notation-50, or from 10-31 to 10-29 seconds, might be known as The Initial Processes of Relations. Notation-51 to Notation-60, or from 10-28 to 10-26 seconds, might be known as The Initial Processes of Relations. One might say that these are the domains of perfection or the pure, there is no room or time for the imperfect. Yet, with the initiation of real relations, one could intuit how processes within Notation-202 might effect one of the notations in the 40s and 50s.

Big bang cosmology has barely gotten out of the Planck Epoch, into the Grand Unification Epoch and off to the Inflationary Epoch! The big bang cosmology is built on wishful thinking and not on numbers, mathematical functions, and logic. More to come

[8] Natural geometric gap. Spheres and spherical geometries are the gateway to Euclidean geometry and the most simple tetrahedron.  As we’ve seen with the dynamic image of cubic-close packing of equal spheres, the octahedron manifests immediately.

pentastar

Now, how many notations before the five tetrahedral cluster with its natural geometric gap would find a functional place?  It may be a question of logic that the Langlands programs or string people have answered.

Our research is ongoing.

In this model, it appears that the tetrahedral-octahedral cluster could perhaps be manifest by the fourth notation. It is hypothesized that it becomes the basic building structure for the universe, a core of physical beingness. So, we now ask, “What might happen to create the five tetrahedrons (which are carried into the icosahedron and the Pentakis dodecahedron)?” When might such a combination manifest in the physical universe? It is proposed that this gap becomes systemic, possibly between Notation-50 and Notation-60, and opens the first possible systemic fluctuations, which between Notation-64 and Notation-67, become measurable and are defined as quantum fluctuations per se.

Somewhere near here quantum indeterminacy becomes dominant. More to come….

[9] Quantum fluctuations and quantum indeterminacy. If this mathematical outline and construction is on the right path, quantum fluctuations are redefined. There is a causal efficacy.

I believe we’ve been blinded by basics that were not basic enough; and as a result, we’ve additionally adopted blinders by adopting the mistakes of the luminous and superluminous such as those of Aristotle, Newton, and, yes, even Hawking. Even the best among us make mistakes. And, we all still have much more to learn.

Although Felix Klein (1849-1925) said “Physics is geometry” and John Wheeler (from about 1952 to 1972) also made the statement, “Physics is geometry,” no scholar has brought that geometry down to the initial gap that creates quantum fluctuations, or cubic-close packing of equal spheres for the generation of simple geometries, and then to a primordial sphere itself.

[10] Quantum field theory (QFT). Within this model, we are now exploring a range of notations when-and-where quantum field theory can actually manifest within this universe. We are exploring  whether the perfected notations are a variable and could actually be dependent on the thoughts and activities within Notation-202. One of our little paths within this model just might open QFT to consciousness and the how the qualities of a conscious moment become translated to quantitative entities.

[11] From the Physics to Logic of the Indeterminate. This convergence of three footnotes, 10, 11, and 12, is a direct result of a challenge by the scholarly group, FQXi. They challenge thinkers to engage Gödel, Turing, and QFT, to discern in what ways the most basic principles of all three impact our understanding of undecidability, uncomputability, and unpredictability. For further work within this area, we refer you to this first draft, a response to their challenge.

[12] Gödel, base-2 model and Planck’s units. Gödel didn’t know there could be a mathematical progression from the Planck units in such a manner that unites space, time, matter and energy. Although special relativity pushes the absolutes out of the picture, Gödel gives Newton’s absolute time a place within General Relativity. Given Einstein’s special relations with Max Planck, it is of some interest to note that neither Einstein nor Gödel truly engaged the Planck base units. You would think it might have come up during Gödel’s time as a teacher-professor (1940-1978) at the Institute for Advanced Studies which included those long walks with Einstein. Even with his work on numbering and base-2, Gödel did not clearly demarcate a beginning of the universe but like Einstein, assumes the big bang.


[13] Revisit: Light and the Planck units. Aristotle failed to understand the tetrahedron. Newton failed to understand space and time. And, Hawking failed to understand the Planck base units. Their failures would not be important if they didn’t throw generations of scholars off their search for the truth, for better explanations, and to understand more deeply the way things really relate. I believe we would be so much further along the path of self-understanding had we had a better understanding of the universal constants of G, ħ, c, and kB. Planck’s simple equation for Planck Time gives us the speed of light, c, in 1899, yet we ignored it.

What are we to do with this highly-integrated chart of numbers as it defines a consistent variable speed of light throughout the model? It is generally within .01% of the laboratory defined speed of light.

Yes, quite obviously, our next challenge is go further with c, and to take on G, ħ, and kB.


[14] Revist: Infinite-finite bridge, simplicity-complexity within the infinitesimal sphere. If the most simple sphere is the product of the finite-infinite relation, and if continuity, symmetry, and harmony define the essential qualities of infinite and quantitatively give us the essential quantities of the finite, we have a very different intellectual starting point. So, none of this materials will be easy. Perhaps Planck was right about the absorption rates within the scholarly community. I hope not.

Perfected systems on the same grid as quantum indeterminacy is hard to fathom.

Let me re-iterate: QFT, quantum fluctuations, and quantum indeterminacy extend from Notation-64 up to and including Notation-202. The first measurable unit of time is within Notation-84; the first second is between Notation-143 and Notation-144.

[15] Revisit: The basics. The three key transitions of our thinking begin with 1) spheres, 2).sphere-stacking, and 3) cubic-close packing of equal spheres (ccp). The key people in this emergence span four centuries starting with Thomas Harriot (1587), Kepler (1611), Gauss (1801), Poincaré (conjecture – 1904) and Thomas Hales (1998). Sub-grid physics modeling is one of our continuing research projects:  the numerical techniques to validate the predictive results of our numerical simulations.


Working References & Resources:

Please note: Always a work-in-progress, the following references and resources are still very rough, not even a first draft.  -BEC (May 8, 2020)

1. Simplicity and our historic mistakes: This is the Aristocracy of the Elite.
• Aristotle’s 1800+ year mistake. Tiling/tessellating with the tetrahedron
• Newton’s 300+ year mistake. Absolute space and time.
• Hawking’s 40+ year mistake. An initially infinitely-hot start is certainly a hell-of-a-start.


2. Finite-infinite. From the beginning of time to the Now.
The beginning of time is now included within the Now.
• Gödel finite-infinite relation
• spheres-and-pi
• the limitations of the Planck base units for time, length, mass and charge
Trialogue on the number of fundamental constants, Michael J. Duff,  Lev B. Okun, Gabriele Veneziano


3. The sphere.
It did not result in a theory of everything, but with mathematics it necessarily encapsulated everything, everywhere for all time. It then became mathematics in search of a theory (theoria).


4. Close-cubic packing of equal sphere:
The power of structural modeling of sub-grid scales …
Planck-scale models of the Universe, Fotini Markopoulou
Visualizing a Hypothetical Planck Scale Substructure of realityDugan Hammock


5. Fourier:
•  Visualizing a Hypothetical Planck Scale Substructure of realityDugan Hammock
•  Six easy roads to the Planck scale


6. Five tetrahedral cluster


7. Aristotle’s 1800 year mistake:
• We are redefining space, time, mass and energy. All notations are active and interdependent, all connected through base-2, possibly 67 notations interconnected through base-3, and forty through base-5. Once we get a pathway opened to some of the string theory and Langlands people, it will be fascinating to begin getting their inputs.


8. Newton’s absolute time and space in general relativity, American Journal of Physics 68, 350 (2000); https://doi.org/10.1119/1.19438, Ronald Gautreau

In 1998/99 Merab Gogberashvili published on arXiv a number of articles on a very similar theme. [3] [4] [5] He showed that if the Universe is considered as a thin shell (a mathematical synonym for “brane”) expanding in 5-dimensional space, then there is a possibility to obtain one scale for particle theory corresponding to the 5-dimensional cosmological constant and Universe thickness, and thus to solve the hierarchy problem. It was also shown that four-dimensionality of the Universe is the result of stability requirement, since the extra component of the Einstein field equations giving the localized solution for matter fields coincides with the one of the conditions of stability.


9. Felix Klein (1849-1925) said “Physics is geometry.” John Wheeler from about 1952 to 1972 also made the statement, “Physics is geometry.”


10. QFT as uncomputable and undecidable. Within this model, the universe is an inclusive instance of all things, everywhere, for all time. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always be statements about natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.
https://en.wikipedia.org/wiki/Phase_transition
• https://en.wikipedia.org/wiki/Quantum_critical_point

On Patrick Suppes’ studies – mlfriedman@stanford.edu

Usually a quantum critical point is a point in the phase diagram of a material where a continuous phase transition takes place at absolute zero. In this model, there are 202 notations and it would appear that each has many “quantum” critical points, some superconducting cold and others superconducting hot. “Quantum” is in quotes because it has not been fully defined. If the packet of energy is not measurable and will never be directly measurable with an instrument, is it systemic or quantum?


Jim Peebles, Michel Mayor and Didier Queloz, 2019 Nobel Prize in Physics


Eudoxus, arrived at an answer that, in one form or another, would survive for two thousand years. For mathematical purposes he imagined the heavens as a series of nesting, concentric, transparent spheres…  Aristotle, amended this system. He assumed the spheres were not just mathematical constructs but physical realities; to accommodate the mechanics of an interlocking system, he added counter turning spheres.”


Lincoln Kinnear Barnett, editor and author, Life Magazine, author The Universe and Doctor Einstein, Harper & Brothers, 1948,  and The World We Live In, published by  Life magazine, 1952-1954.  He said, “The gateway to universal knowledge may be opened by the unified field theory upon which Einstein has been at work for a quarter century. Today the outer limits of man’s knowledge are defined by relativity, the inner limits by the quantum theory. Relativity has shaped all our concepts of space, time, gravitation, and the realities that are too remote and too vast to be perceived. Quantum theory has shaped all our concepts of the atom, the basic units of matter and energy, and the realities that are too elusive and too small to be perceived. Yet these two great scientific systems rest on entirely different and unrelated theoretical foundations. The purpose of Einstein’s unified field theory is to construct a bridge between them. Believing in the harmony and uniformity of nature, Einstein hopes to evolve a single edifice of physical laws that will encompass both the phenomena of the atom and the phenomena of outer space. Just as relativity reduced gravitational force to a geometrical peculiarity of the spacetime continuum, the unified field theory will reduce electromagnetic force—the other great universal force—to equivalent status.”


John Wheeler, relativity, and quantum information, C.W. Misner, K.S. Thorne, and W.H. Zurek,  Physics Today, page 40, April 2009


11. Unpredictable and indeterminate. “A theory is a set of formulas, often assumed to be closed under logical consequence. Decidability for a theory concerns whether there is an effective procedure that decides whether the formula is a member of the theory or not, given an arbitrary formula in the signature of the theory. The problem of decidability arises naturally when a theory is defined as the set of logical consequences of a fixed set of axioms.”

“There are several basic results about decidability of theories. Every inconsistent theory is decidable, as every formula in the signature of the theory will be a logical consequence of, and thus a member of, the theory. Every complete recursively enumerable first-order theory is decidable. An extension of a decidable theory may not be decidable. For example, there are undecidable theories in propositional logic, although the set of validities (the smallest theory) is decidable.” – Wikipedia

As families of formal languages mostly have a decidable emptiness problem, the non-emptiness of the intersection of a formal language and a regular language is decidable.” FROM DECIDABILITY TO UNDECIDABILITY BY CONSIDERING REGULAR SETS OF INSTANCES, Petra Wolf arXiv:1906.08027v1, 19 Jun 2019


12. Gödel, base-2 model and Planck’s units.

Time and Causation in Gödel’s Universe (PDF), John Lane Bell, Transcendent Philosophy 3, 2002 gives time its primary status such that time travel becomes a rational conjecture.

Alonzo Church (June 14, 1903 – August 11, 1995) :  “He is best known for the lambda calculus, Church–Turing thesis, proving the undecidability of the Entscheidungsproblem, Frege–Church ontology, and the Church–Rosser theorem.” – Wikipedia

“His proof that the Entscheidungsproblem, which asks for a decision procedure to determine the truth of arbitrary propositions in a first-order mathematical theory, is undecidable. This is known as Church’s theorem.[8]  – Wikipedia

Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation that can be used to simulate any Turing machine. It was introduced by the mathematician Alonzo Church in the 1930s as part of his research into the foundations of mathematics.

When Einstein Walked with Gödel, a video by Robert Wright with Jim Holt, author of the book by the same title, Farrar, Straus and Giroux (May 2018).


13. Revisit: Light and the Planck units. In the first notations, there is such a thrust of light and Planck Charge, continuity-symmetry-and-harmony define everything. The building blocks are spheres and whatever new mathematics can be injected into the emerging forms. A long, long way from particles and waves, dynamic forms (aka automorphic forms)..:
M. Planck, Über irrevesible Strahlungsvorgänge, 1899 S.-B. Preuss Akad. Wiss. 440-480  Google Scholar  M. Planck, 1900 Ann. d. Phys. 1 69  Crossref   Google Scholar  reprinted in Max Planck, Physikalische Abhandlungen und Vorträge, Band I. Friedr. Vieweg. 1958 pp. 560-600, 614-667  Google Scholar


14.  Revist: From Simplicity to complexity within the infinitesimal spheres.


15.  Revisit: Sphere-stacking and cubic-close packing of equal spheres.
•  Sub-grid scale model classification and blending through deep learning (December 2018)
The power of structural modeling of sub-grid scales – application to astrophysical plasmas, Georgiev Vlaykov, Dimitar, Grete, Philipp (August 2015)


  • Modification + divergence-structure + perturbation theory +  spacetime foam
  • Exponential factors + finite.
  • Dynamics generated + the Hamiltonian of general relativity + energy + bounded + stable theory

Please send along your comments or questions:


Header image:

Credit goes to Pablo Carlos Budassi of South Africa where his Facebook, Twitter and YouTube projects are all linked. A high-resolution image is here on Wikipedia under “Universe” (just page up from “See Also“).


Key Dates

This page was initiated on April 5, 2020
Posted online for collaboration: Tuesday, April 7, 2020
Homepage date: April 23, 2020 @ 11:11 PM
Last edit: Wednesday, May 19, 2020

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