## A Working Resource Page. Please be careful in here. It’s an archeological dig.

###### by Bruce Camber Initiated in August 2019

**Editor’s notes**: All pages marked as “Working Page” or “In Process” are still quite rough. This page qualifies. Your comments and suggestions will always be welcomed. -BEC

**61-to-67: Preparticles, Elementary Particles, Particles**

- PRIMES: 61, 67 (all primes open for the new, transformational testing)
- Base-3: Multiply each notational number by the base number. Notation-61 would have only Notation-183 and Notation-67 only Notation-201.
- Within the notations 61-to-65 the face and functions of elementary particles would be shaping up for emergence.

## 51-to-60: Systems

- PRIMES: 53, 59 (There can be no base-4, base-5 or higher.)
- Notation-59: Base-3 also opens Notation-177
- Notation-53: Base-3 also opens Notation-159

*Systems*-systems theory, including all the studies of consciousness.^{9h}- References and resources:

## 41-to-50: Relations

- PRIMES: 41, 43, 47
- Notation-41: Base-3 opens Notation-123 and Notation-164
- Notation-43: Base-3 opens Notation-129 and Notation-172
- Notation-47: Base-3 opens Notation-141 and Notation-188

- Versus the derivative,
*subject*and*object*, were intuited within Notations 41-to-50.^{9f} - Possibly within some one of these ten notations, and probably not one of the primes, a geometry of imperfection emerges, the simple object created by five tetrahedrons with its gap of 0.12838822 radians (a 7.356103 degree gap).
^{9g} - Fluctuation Compressibility Theorem and Its Application to the Pairing Model

## 31-to-40: Qualities

- PRIMES: 31, 37
- Base-3, Base-4, Base-5 and Base-6 opens additional up additional related notations. There are no higher bases possible.
*Qualia*(or*pure*qualities) was also imagined between Notations 31-and-40^{9e}

## 21-to-30: Substances

- PRIMES: 23, 29
- Base-3, base-4, base-5, base-6, base-7, and base-8 open related notations.
- Aristotle’s concept of
*Ousia*or*Substances* - Kerr and Kerr-Schild metrics (1963)
- A precursor of the Periodic Table was intuited
^{9d} - The word “quine” was coined by Douglas Hofstadter in honor of Willard Van Orman Quine’s work on indirect self reference and the resulting Quine’s Paradox…

## 11-to-20: Structures

- PRIMES: 11, 13, 17, 19
- Base-3 through base-18 open related notations
- A Bourbakian sense of
*structures*was engaged for the next ten notations.^{9c} - Double Poles and Nonexponential Decays
- Nuclear Optical Model for Virtual Pions
*A Kind of Collapse in a spacetime model*by Maximo Garcia-Sucre, Scientific Philosophy Today: Essays in Honor of Mario Bunge edited by J. Agassi, Robert S. Cohen page 47: “On preparticles we say that they are unchangeable physical structure.”

## 1-to-10: Forms

- 0: Mass – PLANCK MASS: 2.176.470(51)×10
^{-8}(kg) - 10: 2.22874×10
^{-5 }kg - PRIMES: 2, 3, 5, 7
- Base-3 through base-10 are straightforward calculations. Above base-10 is also possible and will be explored.
- What do we know about forms?
- Automorphic
- Plato’s concept of
*forms*was first instantiated for the first ten notations.^{Go to 9b} - 2π Decay of the K02 Meson Consider the mass of the meson and all other particles and begin sorting them by mass and/or charge. This will involve redefining parts of the current Standard Model of Particle Physics. Pions are the lightest mesons and, more generally, the lightest hadrons.

**Doublings**. In this data stream, a third approach to these concepts is the study of period doubling, bifurcation theory, coming full-circle with our first, most-simple, doubling mechanism, cubic close packing of equal spheres. Here that mechanism is described as *stacking*. There are other types of doublings, but there appears to be no other doubling mechanism *per se*.

In Finland, physicist Ari Lehto claims that the period doubling mechanism is a universal property of **nonlinear dynamical systems** and that it governs the buildup of structures; he says, “…from the intrinsic properties of the elementary particles to the large scale systems with cosmological dimensions.” In our model here, Lehto is asked to consider those notations or doublings prior to elementary particles.

Lehto writes, *“The mechanism that indicates a high degree of order in nature is not a part of the prevailing theories but it could give a major contribution to our understanding of the physical reality and the origin of the invariant properties and structures of matter.” *^{9i}

**The Fourier transform**^{10}

^{10}

True confessions.^{10} Because I do not have anything close to what would be considered a baseline for writing this analysis, the following postulations are simply my guesses more than based on a deep-and-rich understanding of these functions.

http://cogs.indiana.edu/people/profile.php?u=dughof

**Symmetries in motion**. The circle-sphere dynamics now transition from basic geometries, to symmetries in motion.

**The work** of a wide range of people, from Pythagoras (c. 570 – c. 495 BC) to Feynman (1918-1988) to Strogatz (1959- ) to today’s thinkers and tinkerers within music theory, may find a key function and a new paradigm within the Fourier transform understood from the Planck scale.

There is an *inner transformation* (pictured, above right) that I would equate to electromagnetism, Maxwell’s equations and Faraday’s intuitions. Then there are the *outer transformations* which I would equate with the *de facto* dialogue between Newton and Einstein and the current wrestlings regarding our understanding of gravity and loop quantum gravity (LQG).

See Sir Martin Rees’ *Just Six Numbers*.

**The internal and external dynamic of spheres**. The three dynamic images above are each, in their very special ways, based on our most ubiquitous, never-ending, never-repeating, dimensionless constant, pi.

If in the first emergence there are endless strings of spheres, could it also be a face of Planck Charge, Planck Mass, Planck Length and Planck Time? If the secondary emergence is that inner transformation, in what ways is it the face electromagnetism and an expression of Planck Time, Planck Length, Planck Mass and Planck Charge? If the third emergence is the outer transformations, in what manner of speaking is this the face of gravity and yet another expression of Planck Time, Planck Length, Planck Mass and Planck Charge?

**History should be our guide**. How could so many applications not be tied to the fundamentals of our beginning?

## A *foundational* mathematics and physics^{11}

**The foundations-of-foundations**: **A Quick Summary**. If the first 64 notations are taken as a given, they certainly do not describe physical reality as we experience it or understand it today. Most people have a *de facto* absolute plenum of space and time within which everything exists and has its being. Within this model of the universe, the infinitesimal spheres create space, time, mass and charge and these stack, causing a period doubling, thus causing dynamic symmetries to evolve with uniquely defined dynamics at each notation. Those notations or doublings defined by a prime number have an additional uniqueness to interject entirely new dimensionless constants into the overall doubling equations. It seems to follow that from one of these notations Langlands programs would begin to evolve, and then from another, string theory would evolve with its unique language and functions. The nineteen prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67 whereby base-2 begins at 2, and our science of particles and waves begins at 67. What begins at 3? …at 5? …at 7? Which dimensionless constants can be applied; and then upon which of those can more mathematical structures be developed?

Perhaps a number theorist like Akshay Venkatesh of the Institute for Advanced Study can help us. Perhaps we need to go back and reintroduce ourselves to Robert Langlands, Ed Frenkel and other thought leaders among the Langlands group (Robert Kottwitz, Stephen Gelbart, Thomas Hales, Gerard Laumon, V.G. Drinfeld, D. Gaitsgory and others). Perhaps we need to reintroduce this conjecture to our string theory, thought leaders like Edward Witten and Gabriele Veneziano and those testing their conjectures like Krzysztof Cichy….

**Language**. Because these first 64 notations appear in every way to be below the thresholds of measurement of space and time, there is a need to attempt to simplify set theory with language, words and expressions, that capture the forms and functions that give rise to the realities we can measure. Wouldn’t it be fascinating to begin to be able to make distinctions between reification, instantiation, hypostatization, and hypothesization? It just may be possible.

**Dimensionless constants**. All the key dimensionless constants, particularly those considered to be necessary for the *Standard Model for Particle Physics*, will have a very special role, especially when each is considered a bridge between the finite and infinite. ^{11}

**Finite-Infinite**^{12}

Although lightly approached within several documents within this website, it is now increasingly obvious that the mathematics, science and philosophy of renormalization^{12} needs to be further explored. To deny infinity is to know infinity. So, infinity, both mathematical and conceptual, can be uniquely and independently known through the use of renormalization within any of the sciences, especially physics, and mathematics.

Since the renormalization work of Dyson, Feynman, Schwinger and Tomonaga (1947-50), Nikolay Bogolyubov, Stueckelberg and Petermann (1953) and the work of Wilson, Kadanoff, Fisher (1965 and 1975), scholars have developed ways to capture points within equations whereby infinity becomes equal to 1. Each is a possible clue. Beginning with with Freeman Dyson’s work in and around 1947, renormalization continues to be refined and expanded. In 1973 the Coleman–Weinberg potential was introduced. Like Weinberg (1993), Dütsch (2013) and others continue that effort.

As with dimensionless constants, every new twist for renormalization demarcates a possible new entry point along the grid especially within the first 64 doublings, yet including the twenty-five primes between 67-and-199: 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, and 197.

Renormalization was a welcomed relief from having to wrestle with infinity. Also, because the concept of infinity was so often associated with religious belief, it was a relief from those discussions as well. Some of our leading scholar-physicists went so far as to advocate that space, time and infinity be retired from academic inquiries. Within this model, these three pivotal concepts are further defined and refined. First, the simple doublings create continuity equations for each of the Planck base units creating a heretofore unrecognized definition of order, relations (symmetries) and dynamics (harmonics) that redefine the infinite and apparently bind the finite and infinite.

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