PERFECTION STUDIES: CONTINUITY•SYMMETRY•HARMONY GOALS..September.2024
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Pi (π): 3.14159… and the Planck base units
By Bruce E. Camber (a working, first draft)
Abstract.
Pi (π) is the most-precise, dynamic number in our universe.* Pi (π) is also the most-versatile equation of the universe.† Historically, among the earliest records of study-and-work to know pi (π) was that of Archimedes (c. 287 – c.212 BC); and ever since, the study of pi (π) has become more and more precise, but there is still much to learn. The values of pi do not change. Computers now generate and verify trillions of new numbers, but what does it mean?
Among all the equations and numbers of the universe, pi (π) is hypothesized to be the first possible number-and-equation and the most-inexplicable and enigmatic of the first numbers because it is the bridge equation between the finite-and-infinite.
Another set of equations, the Planck base units (or the BIPM–ISO equivalents), result in natural numbers which we hypothesize to be the second set of numbers. These numbers merge and manifest as an infinitesimal physical sphere. That sphere is defined by pi (π) and no less than four continuity equations: Planck Time, Planck Length, Planck Mass, and Planck Charge. The never-ending numbers of pi (π) generate a sphere, one at a time, each starting with 3.1415… and these spheres render whole numbers. It starts with the first sphere, then counting begins with the second, the third, the fourth, the fifth, the sixth and so on. Then, among all these numbers our prime numbers are identified. Within the first instants of the start of the universe, we have four sets of numbers defining reality.
Key words: Pi (π), 3.1415…, spheres, 1,2,3,4,5… numbers, number theory, Planck base units, Planck Time, Planck Length, Planck Mass, Planck Charge, prime numbers, 202 base-2 notations, automorphic forms, Langlands programs, string theory, M-theory, perfection-imperfection, prime numbers, prime…
Introduction. In that imaginatively creative time just on the edge of sleep in the early morning hours, it occurred to me that even the first moment of time is richly identified by a range of numbers. There were so many different numbers, geometries, and equations, it was difficult to keep track of them all.
Based on an hypothesis that the first moment of space-time is defined by the Planck base units and these numbers manifest as a sphere which is pi (π), it begged the questions, “How could the never-ending numbers of pi (π) be before the beginning? Do numbers like the Planck natural units define the first moment of physicality? How do these numbers group-merge-transform-manifest?”
Research: Counting. We hypothesize the generation of spheres gives us the whole numbers; start with the first sphere, then the first counting begins — 2, 3, 4, 5, 6, 7, 8, 9, 10… Then, those Planck natural units give us an exacting physicality. And finally, some of the numbers of each sphere are further identified by prime numbers and then, within and by base-2 notation.
It would seem that every moment has nine forms of identity: (1) the numbers of pi (π), (2) spheres (geometries), (3).number of spheres, (4-5-6-7) the four continuity equations of Planck units, (8).prime numbers, and (9) a Planck-defined notation (1-202). Taken altogether, it defines the infinitesimal. [1]
It may seem a bit premature to hypothesize that these prime numbers mark historic events and that an early such event would be the development of an imperfection and the first fluctuations as defined by the geometries of gaps. Other events would be the evolution of galaxies, our Milky Way being the one within which we are most familiar.
In our first analysis of numbers in 2016, we were in search of the key numbers that defined our universe. Pi (π) was #1. In our second analysis, we started learning a little about number theory and began reaching some of the conclusions that are in this article.[2]
The first continuity equation, pi (π), begets the first physical continuity equation, Planck Time. It.imparts order and numbers [generated by the never-ending numbers of pi (π) with no-repeating patterns]. The second continuity equation for physicality, Planck Length, imparts relations, symmetries, and geometries. The third and fourth continuity equations of physicality, Planck Mass and Planck Charge, impart harmonies (Fourier transform), the dynamics of every moment in the universe.
Other Planck numbers will continue to be analyzed. Yet, for now, that is the primary identity of the first moment; however, there is more.
Although mathematicians discovered prime numbers, the primes and their functionalities predate that recognition. Prime numbers were with the universe within the 2nd, 3rd, 5th, 7th, 11th and subsequent prime notations. Hypothesized is that these prime numbers mark on-going events, i.e. gap geometries imperfections, galaxies, etcetera.
Results. Our sense of numbers continues our number theory discussions and postulations:
1. The sphere, which is pi (π), is the first manifestation of space/time.
2. The Planck natural units define the first moment of space/time.
3. Base-2 notation is applied to the numbers-events (generating a chart of everything everywhere).
4. Keys dynamic events throughout the universe and their notations are a prime number.
The modern sense of time based on units of equal durations, such as a second (which gave us our UniverseClock), are human conventions. These numbers necessarily come much later in Notation 202 within the human era.
Notation-0 to Notation-1: The first result of pi (π) are the physical dimensions of the Planck base units. That would be Notation-0 to Notation-1: the penultimate transformation. Then come base-2 and the second notation.
Here we hypothesize automorphic forms. It is number-to-shape centric.[3]
Notation-2: Automorphic Forms. The oldest, most-thorough study of this domain of mathematics is the work of Robert Langlands and what has become known as Langlands Programs. Conceptually opened with a letter in 1967 and formalized with an article in 1970, today many of the best mathematicians in the world are focused on this work. The difference is that here we set the entire program within pi (π) and its functions of continuity, symmetry, and harmony. This definition of the infinite is key.
Next, as one might imagine, closely-related to forms but thing-centric, we hypothesize strings.[4]
Notation-3: String and M-theory. Although a well-developed theory over as many years as Langlands programs, it, too, was not on the grid of 202 Notations. It did not have pi (π) within its initial foundations; and, as a result, it did not give continuity, symmetry and harmony a necessary role to define its foundations. Among its early conceptual thinkers are Edward Witten and Steven Weinberg (deceased). Many followed, all with voluminous publications: Michael Duff, Juan Maldacena, Hermann Nicolai, Dean Rickles, Joseph Polchinski (deceased), Nathan Seiberg, Cumrun Vafa, and Gabriele Veneziano. Early work of Shing-Tung Yau is being engaged.
For the next notations based on primes, we turn to the list of those disciplines that define some aspect of functional analysis. These disciplines represent many of our finest scholars who have introduced us to the study of the infinitesimal.[5]
Notation-5: Perfection-Imperfection. Recognizing the abundance of geometries that are emergent within the just this time scale, it is hypothesized that only those geometries that are perfectly fitting have time to manifest. Even as late as the 64th notation, just below the thresholds of physical measurements, the time scale is in yoctoseconds, one trillionth of a trillionth of a second. It is not until we get into Notation-143 do we find a second. There is reason to believe that by the time a second has manifest, precedence is being manifest so the universe continues within its perfections. That hypothesis clearly remains an open study.
Conclusions. We will continue to examine all 202 base-2 notations (from the first moment of the universe assumed to be at Planck Length and Planck Time to this very moment in time assumed to be the Now); and of course, the logic and mathematics that follows. Something like the Planck units define that first moment in time. Whatever these units are, it is hypothesized that these manifest as an infinitesimal sphere, and the next moment is defined by two infinitesimal spheres, and the third moment is defined by four, the fifth moment by eight, the sixth by sixteen, the seventh by 32, the eighth by 64, the ninth by 128 and so on. Here are the fundamental building blocks of the universe uniquely defining each moment within one-an-emergent-universe.
The sphere applies the numbers of pi (π) and the sequential numbers of the Planck’s natural units (or their equivalent), along with the numerals of sphere counts, then prime numbers, and then a base-2 ordering schema. These numbering systems are the beginning of the uniqueness of everything. At the same time the inexplicable numbers of pi are revealing continuity as the first among equals, there is a convergence of many numbers to describe this exacting moment. There are no less than three other continuity equations that are launched at the same time. The first, Planck Time, the numbers are new type of number, a new ordering. The second, Planck Length, is a geometry, particularly symmetry. The third and fourth for Planck Mass and Planck Charge, introduce dynamics, a simple harmony (Fourier transform). Each equation is necessarily and inextricably related as a whole. Nevertheless, we will continue our survey of other Planck base units within each notation.
There is a rate of expansion and it seems to be divided by 2 from step to step. Each sphere is uniquely numbered, the first generation of whole numbers. Prime numbers are among them. Some of them, we will discover from prime number experts, are very special.
The very nature of a number is created with a correspondence to an infinitesimal sphere which is further related by a particular notation.
The definitions of prime numbers do not change, but now there is a necessary relation to a notation. Numbers that are not prime are also related to a notation and a sphere count. Now, Freeman Dyson suggested that we apply dimensional analysis and that the spheres increase by a factor of 8. In light of how we are approaching numbering and the place of sphere generation, Dyson’s advice will continue to be re-reviewed. A special “Dyson” calculation is line 9 within our chart.
While we are working on these formulations, we will be looking to answer the question, “We can approximate the time, the number of the notation, and the number of the spheres. Is there a correlation between the look and feel of the prime number with the continuity, symmetry, and harmony within that notation?” What is the function of Notation-169 (marking a year)? What is the function at one second between Notation-143 (.60116 seconds) and Notation-144? What about the yoctosecond at the 64 to 67 notations? Eventually, we’ll look at every notational prime number to relate it to a point in time (even as that point moves along through time) and its function(s).
Thank you. -BEC
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References
References are added for at least a month after becoming the homepage.
[*] Most-precise number. Retrieved on 17 August 2024: https://81018.com/perfection/
[†] Most-versatile equation. Retrieved on 17 August 2024: https://81018.com/starts-2/
[1] The infinitesimal. Retrieved on 14 August 2024: https://81018.com/engimatic/
[2] The same conclusions that are in this article. Retrieved on 14 August 2024: https://81018.com/numbers-numbers-numbers
[3] Number-to-shape centric. Retrieved on 14 August 2024: https://81018.com/langlands_programs/
[4] Thing-centric strings. Retrieved, 14 August 2024: https://81018.com/strings/
[5] All Infinitesimals. Retrieved, 14 August 2024: https://81018.com/reformatting/#List
Reading and re-reading
What articles are opened on the desk, shelves and even the floor…
- Shing-Tung Yau. Essentially the base-2 system of 202 notations from the Planck base units or their equivalents, provides cover-and-context for the Calabi conjecture and the Calabi-Yau manifold, particularly within the first 67 notations of the 202. These 67 notations are referred to as the Infinitesimal Systems.
- Cusack PTE (2017), Continuous or Discrete?, J Generalized Lie Theory Appl, 11: 257. doi:10.4172/1736-4337.1000257
- Xerxes D. Arsiwall, Hatem Elshatlawy, Dean Rickles, Pregeometry, Formal Language and Constructivist Foundations of Physics Mirror, 2023 (PDF)
- Oliver Brammen, Uncertainty Principles on Harmonic Manifolds of Rank One, https://arxiv.org/abs/2408.16324 https://arxiv.org/pdf/2408.16324
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Afterthoughts
Personal reflections.
The interface between 3.1415… and Planck numbers… and Primes
25 August 2024: Research begins on a definition of pi as a continuous line, not just a circumference, because on the second rotation the line is separated at the circumference by a Planck Length or its equivalent. Yes, it is anticipated that there will be a robust expansion of the definition of pi (π).
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Emails
There will be emails to many of our scholars about key points.
Maybe more to come tomorrow (or tomorrow’s tomorrow)…
31 August 2024: Oliver Brammen, Ruhr-Universität, Bochum, Germany
30 August 2024: Claudia deRham, London, England
29 August 2024: Boris Lishak, Sydney, Australia
29 August 2024: Giuseppe Dattoli, Rome, Italy
28 August 2024: Shing-Tung Yau, Harvard & Tsinghua, Cambridge & Beijing
28 August 2024: Leonard Mlodinow, Caltech, Pasadena, CA
28 August 2024: Lee Smolin, Perimeter Institute, Waterloo, Ontario, Canada
27 August 2024: Dean Rickles, University of Sydney, Australia
22 August 2024: Andrea Gawrylewski, Scientific American, NYC
17 August 2024: Ed Witten, IAS, Princeton, NJ
15 August 2024: Robert Langlands (IAS), Ed Frenkel (Berkeley), Ngô Bảo Châu (Chicago)
15 August 2024: Andrei Linde, Stanford, California
15 August 2024: John Lennox, Oxford, England
30 July 2024: Postdocs and associates of IAIFI, Cambridge, MA
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IM There will also be many instant messages to thought leaders about these key points.
28 August 2024: @PhysInHistory The simple appears simplistic. Actually it’s elegant. Complexity occurs quite quickly. In less than a full yoctosecond, the universe has become complex. Yoctosecond, a trillion of a trillionth of a second, spans four notations within the infinitesimal. https://81018.com/the-firsts/
27 August 2024: Physics In History Pi (π), the most-precise, dynamic number in our universe and also the most-versatile equation of the universe. Could it have been the very first equation of the universe creating an infinitesimal sphere? Might our universe be built with those spheres starting at the Planck scale? I am learning lots of physics as a result but the process is slow because of my age (77)! See https://81018.com/identity/ @PhysInHistory
19 August 2024: Phil Donahue dies today and his interview with Milton Friedman bubbled up. Phil and Milt would benefit from an integrated universe view and the transcendental generation of ethics and values.
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Critique __ Your insights and comments are always most welcomed.
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• This page became the homepage on 15 August 2024.
• The last update was on 3 September 2024.
• This page was initiated on 4 August 2024.
• The link for this file is: https://81018.com/identity/
• Current headline: Pi (π): 3.14159… and Planck base units
• Earlier headlines: (1) Exact, (2) First Identity: Dynamic Numbers universe…
• Current teaser: The numbers and equations that define the finite-infinite transformation also defined the very first instant of this universe.
• Second teaser: The very first numbers to define our universe…
• First teaser* is: Identity, Numbers, Prime Numbers, Geometries, and Equations.
*Or, wicket, kicker or eyebrow..
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NUMBERS THAT START OUR UNIVERSE
1. Pi (π)
2. The Planck natural units
3. Numbers of Infinitesimal Spheres
4. Numbers with base-2 expansion of continuity-symmetry-harmony
5. Whole numbers
6. Prime numbers
First Identity: Dynamic Numbers
Pi (π): 3.14159265358979323846264338327950…
Planck base units
Numbers as numbers
Numerals: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18…
Primes: 2, 3, 5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,
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, 199…
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