PERFECTION STUDIES: CONTINUITY•SYMMETRY•HARMONY GOALS.April.2024
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Different Approach to Number Theory
by Bruce E. Camber (working first draft)
Abstract. Number theory starts with the first instance of space-time. Hypothesized: It is rendered or defined by both pi (π) and the Planck’s natural numbers; the first sphere is the first whole number and the first moment of space-time. Numbers originate as the inexplicable numbers of pi(π). Dynamic numbers are constantly working. With no end to pi’s continuity-symmetry-harmony, a finite-infinite relation is infused, “…everywhere within everything for all time.” Functional numbers are an equation to do a job. Numerals represent a thing, i.e. a sphere. In the next instant of PlanckTime there are two equal spheres. Two (2) is defined as a whole number.
Key words: numbers, dynamic numbers, numerals, functional numbers, whole number…
1. Introduction
The very first numbers within this universe did not happen by chance. There is a deep-seated interiority of numbers that has not yet been recognized within number theory simply because our simple logic tells us that our numbers were actually invented or created by humans and not by an abstraction like pi (π).
Yes, here we are saying that the actual numerals, 0-1-2-3-4-5-6-7-8-9-0, may have come later but before 0-1-2-3-4-5-6-7-8-9 could exist, there was, and still is, a natural advent of numbers that defines the very nature of continuity and order, then defines the very nature of symmetry and relations, and is always defining harmony (fine tuning) and the very nature of dynamics. This is an emergent definition of pi (π) that necessarily involves the finite-infinite relation. These numbers, we propose, actually originate from somewhere other than the finite. If it is the infinite by default, then let it define the infinite! We can then explore to see if that definition is helpful!
From Archimedes to today’s folks, we’ve moved onto a fast track. Sometime before 212 BC Archimedes defined the well-known first few digits of π (pi). Chinese mathematicians, Zu Chongzhi and Zu Gengzhi, defined the well-known 3.14159 in-and-around 500 AD. In our time, those never-ending digits are on a fast-track for growth. In 2020 Timothy Mullican of Huntsville, Alabama verified 50 trillion places for π (pi). In 2021 there were 62.8 trillion digits verified by Thomas Keller at the University of Applied Sciences of the Grisons in Switzerland. Then in 2022, Emma Haruka Iwao of Seattle gave us over 100 trillion verified digits of pi. Perhaps the next target will be 314 trillion,159 billion… then, we’ll move into the quadrillion counts with another generation of computers. These are a never-ending, never repeating pattern of numbers, always different, always the same… one might say that these numbers are an oxymoron or perhaps a compressed conflict being beyond comprehension yet making everything comprehensible. We’ll call them the first infinite number set.
These numbers, of course, appear to be the calculations of humans with the assistance of computers and algorithms. The three — calculations, computers and algorithms — do not hold even the smallest candle to π (pi). Logically, at one Planck sphere per unit of Planck Time, there would be over 18.5 tredecillion spheres per second. With so many combinatorial possibilities, we might readily conclude that π (pi) is a long way from giving up all of her secrets. Yet, as our first formula to beget spacetime, our universe has a fundamentally exponential start and that is the first function of the universe. Addition and subtraction appear to be derivative and localized within a notation.
Admittedly a most counter-intuitive approach to number theory, these functions of π (pi) define the nature of the number. Pi (π) gives each number its order, relations, and dynamics. All we did was name and label each in combinations of 0-1-2-3-4-5-6-7-8-9-10. Thank you. -BEC
Editor’s note: This page may become our first truly collaborative page on this website. This article is now open for collaborations. Want to help? Send a note by email [that is camber (at) 81018.com] or complete this form.
2. Materials and Methods
This is a thought experiment which primarily uses logic and mathematics. However, the 202 base-2 notations that encapsulate the universe from Planck Time to Now encompass both materials and methods; the 202 notations create a working, mathematical model of the universe. This model demonstrates the essential role of dimensionless constants like pi (π) and its three primary functions, continuity-symmetry-harmony. It includes spheres and sphere dynamics, period doubling bifurcations, and the emergence of basic geometries. Yet, number theory is the core of this work whereby the origin of our base numbers, 0-1-2-3-4-5-6-7-8-9-10, is explored. The primacy of multiplication-division over addition-subtraction is also introduced. The place of natural units like Max Planck’s base units, Stoney units, or ISO units, hold keys to reconstruct the universe most simply, but integratively and comprehensively such that truly simple equations can become exceedingly complex very quickly.
3. Results
We take as a given the natural units of Max Planck (other natural units will be engaged in future studies). Assuming PlanckTime is the first unit of time, base-2 notation is applied which results in 202 base-2 notations from the Planck Time until the Now. The first measurable unit of time had been within Notation-74 which contains one zeptosecond (10-21). The yoctosecond (10-24) within Notation-64 appears to be on the threshold of measurement and quantum fluctuations.
Footnote: Now part of many research programs around the world, most often building on the prior work of the Max Planck Institute of Quantum Optics in Garching (Germany) and the earlier work of Ahmed Hassan Zewail of Egypt, known as the “father of femtochemistry” and a Nobel laureate (1999).
The structure and substance of those first 64 notations become the focus. What is there and how does it contribute to the foundational structure of the universe? It would seem impossible to go further. Yet, we slowly began to consider that first moment with the definitions of each base unit as given. What can we say about it? Each base unit has a value. What might those values represent? After much debate, it is decided that the scale invariant sphere with just two vertices qualifies. We take as a given that the sphere is the most simple structure in the universe. We know that it is profoundly and inextricably bound to pi (π); and that pi (π) is inextricably bound to its three facets, continuity-symmetry-harmony. We know that those three facets do not appear in the finite world per se and the three qualities are not finite. The more we studied those three qualities the more they seem to capture the concept of infinity. Like dimensionless constants, we take as a given that continuity-symmetry-harmony are not finite and are the best possible description of the infinite. We then take it as a given that these concepts necessarily open the finite-infinite relation.
Functional numbers: Continuing our initial examination of numbers in 2016, there are simple functional numbers such as perfect numbers, hyperperfect Numbers, elementary symmetric polynomials (named)… every number can be the result of an equation and every equation defines a relation. It starts from a single, simple symmetry and continues to become complex. The ISO has certified that the speed of light is constant at 299,792,458 metres per second. It is a special functional number that may in fact be a variable. Many such numbers, the constants of science, are now being re-examined in the same light. Every number must be re-examined, examined, and conditionally understood within the context given.
Dynamic numbers: These numbers never stop and they include all irrational numbers and equations with these irrational numbers. That list includes pi, phi, Kepler’s conjecture, and e = 2.718… Euler’s natural exponential function ( f(x) = ex ) (also, Euler’s constant), and then Feigenbaum’s 4.669… Cliff Pickford describes Feigenbaum’s constant as having “…properties of dynamical systems with period-doubling. The ratio of successive differences between period-doubling bifurcation parameters approaches the number 4.669 … , and it has been discovered in many physical systems before they enter the chaotic regime. It has not been proven to be transcendental, but is generally believed to be.”
Studies of these numbers will continue and we will return to references from Cliff Pickover (Pickover is at Zmail.com), Martin Rees (Six Numbers) and others throughout the references, footnotes and resources.
Number Systems. There are any number of formulations of number theory; the following outline is just one example:
Number classifications and theory. We have just started our walk into number theory. With so many classifications, one can readily understand why there is confusion. Our start here is from a very different point of view. We’ll just have to see what the market says about the approach. In the interim, if we take our approach as a given, we can begin counting infinitesimal spheres, begin considering the perfections of simple geometries that perfectly fill each other and allow for a reductionism that works in one direction and an expansion that works in the other.
Spheres. That first infinitesimal sphere has mass, charge, space and time. The more that it is considered, we take it as given that that the first sphere is at Notation-0 and that there will be one sphere for every expansion of that PlanckTime and PlanckLength. Again, that rate of expansion calculates to be at 185+ tredecillion spheres per second. The three-dimensional calculation is still being debated. Could it fill about the area defined by the orbital path of the International Space Station? It would appear that such an expansion would be exceedingly smooth but robust enough to have stars and galaxies form well within the 300 million years currently observed by the James Webb Space Telescope (JWST).
Sphere stacking and sphere dynamics. The packing and stacking of spheres is an ongoing study. This we know. Tetrahedrons and octahedrons are generated. The other platonic solids are then generated. There is a geometry of perfection where objects are perfectly-filled and there are no spaces. There is a geometry of imperfection where gaps are necessarily defined. We take as a given that the first 64 notations are so fast and so dense that perfectly-filling is easier and quicker than creating gaps. One of our current studies is of the best densities for gaps to begin to manifest. An hypothesis is that relativity is set by the geometries of the perfectly-filling objects and quantum physics is set by the geometries of the gaps created by tetrahedrons, octahedrons, dodecahedrons and icosahedrons and there is a constant weaving between them.
A little perspective. These thoughts and hypotheses (whereby things are taken as given) have been discussed within this website since 2012. More recently these were reduced to five concepts that were proposed to the Lawrence-Livermore National Laboratory-National Ignition Facility (LLNL-NIF) for the control of nuclear fusion and to many of the scholar-scientists among studies currently not on the grid. Today’s grid misses the first 64 notations. Big bang theories have blocked the view of the infinitesimal wherein the universe gets a broader view of functional analysis which we hypothesize is necessary for controlled nuclear fusion.
The LLNL-NIF is reintroducing the concept of perfection and particularly perfected states within spacetime.
4. Conclusions and Discussion
This is a thought experiment we believe is worthy of further consideration. If it can have a role in opening the discussions between scholars and scientists about perfected states in spacetime, we might make faster progress to solve the clean energy crisis with all its potential negative and positive economic impacts. We might make faster progress in our understanding of our relation to the globe, the sun, the solar system, the Milky Way, and the universe. We may discover the nascent value equations within continuity-order, symmetry-relations, and harmony-dynamics such that crime begins to fall and educational values increase. Thank you. -BEC
Author Contributions. Bruce E. Camber is currently the sole author of this article. He acknowledges that it is an idiosyncratic interpretation, so he will always make himself available for corrections and 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 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 confirmed our understanding of the Planck base units with his many articles and books and was an uplifting spirit.
Conflicts of Interest. There have been no known conflicts of interest.
[*] Base-2 notation applied to the Natural Units of Max Planck: A 2016 Chart, https://81018.com/chart/ retrieved on January 30, 2024
[†]Spheres. https://81018.com/sphere/ Retrieved January 30, 2024
[a] Max Planck, The Theory of Heat Radiation, Translator: Morton Masius, 1914 See “Natural Units” pp 205-207, open source ebook, release date, June 18, 2012 https://www.gutenberg.org/files/40030/40030-pdf.pdf retrieved January 30, 2024
[b] Rate of expansion: 185+ tredecillion spheres per second, https://81018.com/tredecillion/ retrieved January 30, 2024
[c] A metrological approach to quantities that are counted and the unit one, Richard J C Brown, 2021, IOP Publishing, Metrologia 58 035014 DOI 10.1088/1681-7575/abf7a4
[d] Five pages for our studies of dimensional and dimensionless analysis:
• Freeman Dyson, emails, https://81018.com/dyson/#First retrieved on 3 April 2024
• Dimensional Analysis, https://81018.com/dimensional/ retrieved 3 April 2024
• Constants, https://81018.com/tighter/#Constants retrieved 4 April 2024
[e] Rates of expansion: https://81018.com/tredecillion/ retrieved 3 April 2024
[f] Geometries: https://81018.com/geometries/ retrieved 6 April 2024
[g] Functional analysis: Retrieved on 6 April 2024: https://81018.com/functional-analysis/
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Resources
As the references are studied, additional resources are suggested.
- Inflationary Cosmology after Planck 2013, Andrei Linde, https://doi.org/10.48550/arXiv.1402.0526, 2014
- Max Planck Institute of Quantum Optics: https://twitter.com/MPI_Quantum
- Time, Constants and Fundamental Symmetries (TCFS). https://www.mpq.mpg.de/6903579/11-german-japanese-cooperation-for-highest-precision-extended?c=2342
- Prof. Dr. Klaus Blaum, MPIK; Prof. Dr. Thomas Udem, MPIQ; Dr. Ekkehard Peik, PTB Department time and frequency; Dr. Stefan Ulmer, RIKEN Fundamental Symmetries Laboratory
- https://en.wikipedia.org/wiki/Closed-form_expression#Comparison_of_different_classes_of_expressions
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Endnotes & Footnotes
Personal reflections.
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Emails
There will be emails to many of our scholars about key points.
• Of course, there will be a follow-up of the February emails.
• The March listing is slowly being compiled!
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IM
There will also be many instant messages to thought leaders about these key points.
20 March 2024: @mcuban Our problems as a people stem from little worldviews. We need a mathematically-integrated view of the universe and the most simple and comprehensive is base-2 from the Planck base units to the age of the universe. Just 202 notations! https://81018.com
Critique. Your comments are most helpful. There are five pages working together:
• From the smallest to largest scales: 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/
Keys to this page, numbers-numbers-numbers
• The last update was 14 February 2025.
• This page was initiated on 11 January 2024.
• The URL for this file is https://81018.com/numbers-numbers-numbers/
• First headline for this article: Let’s All Learn A Few Basic Numbers
• First teaser* is: 0123… The origination of a number before it is a number.
• Current headline: A Different Orientation to Numbers
• Current teaser* is: 0123… Numbers defined before anyone knew about them
*Or, wicket, kicker or eyebrow.
Final author-editor notes: Reading this Abstract to this page, “Numbers-numbers-numbers” requires a bit of patience. It’s a stretch. The page is a first draft so I thank you for being here. So much of this topic is new to me. If you are a number theory person, might you be able to help? Available to talk? Send your telephone number within those comments. -Bruce
Review then delete: If each unit of PlanckTime generates one sphere, within ten units of PlanckTime, depending on which counting metrology[c] is invoked, there could be as few as ten spheres. There are so many other equations within that first sphere, with each subsequent sphere there may well be other dynamic expansions. It would appear that this would be the fastest, most-dense expansion possible — 18.5 tredecillion spheres per second. We’re consulting the wizards; but, for example, if the Fibonacci sequence is somehow invoked, with the next Plancksphere, Fibonacci spheres may have start to form. A natural doubling mechanism may well be initiated such that along with those two Planckspheres, a base-2 definition of spheres becomes emergent. Then, respecting Freeman Dyson’s comment to us about dimensional analyses (“…multiply by 8…”), there may well be spheres that look like points or vertices.[d] Quite possibly, a key will be that rate of expansion.[e] Whatever the sphere that is defined by these natural units, all are most-densely packed. Scale invariance at work, all the edges and centerpoints of new spheres are instantly in a relation to each other. Perfect triangles are created, then perfectd tetrahedrons, then perfect octahedrons.[f] Numbers become functional. Symmetries are defined. And, with just those initial Planckspheres, many symmetries are defined. As these symmetries begin to interact, there are the first dynamics of interior relations. Then, with every prime number notation, it appears that new equations could manifest. Basic formulae to guide our expansion are manifest within those first 64 notations. We are now exploring if primary work has been done (functional analysis) by those disciplines not currently on the grid.[g]
Editor’s note: So, yes, the unpacking of these counting metrologies continues. (the 202 base-2 notations from Max Planck’s natural units to the age and size of the universe today.* Hypothesized is that those Planck numbers best describe an infinitesimal sphere.† Taken as a given, this is the first instance of spacetime (Notation-0). Max Planck calculated those numbers in 1899[a] and each number is a ratio and an equation of dimensionless constants. Within the sphere, there are numbers from equations for units of time, length, mass and charge. Instantly three very different types of numbers manifest: dynamic numbers, functional numbers, and numerals.
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