CENTER FOR PERFECTION STUDIES: CONTINUITY•SYMMETRY•HARMONY • GOALS.•.March.2020*
HOMEPAGES:.ASSUMPTIONS|BOTTOM UP|DARK| INFINITY | MAP|Transformations
Background. In 1960 E.P. Wigner, Princeton physicist and Nobel Laureate, 1963, wrote The.Unreasonable Effectiveness of Mathematics in the Natural Sciences.1 In this article Wigner beholds the elegance of mathematics and how it helps to define our perceptions with miraculous accuracy. This deep respect, even reverence, for mathematics and numbers goes back to the Pythagorean schools (circa 500 BC), then even further back to the old Hindu masters (circa 800 BC), Babylonian sages (1900 BC) and Egyptian seers (circa 4200 BC).
From about 1900 BC forward, most of these “numbers-people” were mystified and challenged by the mathematics of the circle, the sphere, and the magic of pi (π). There is a unique perfection within pi with its never-ending, never-repeating numbers.
As of 2020, that ratio now has over 31.4 trillion digits, a calculation that was set up by Emma Haruka Iwao.2 It ran from September 22, 2018 to January 21, 2019, yet it will never finish. Within this model, all those numbers of every circle-and-sphere are: (1).the face of perfection, (2).a definition of the infinite, (3).a finite-infinite bridge, and (4).the penultimate continuity equation. There is a fundamental ordering of numbers, a deep symmetry of relations-and-geometries, and the opening of basic dynamics within harmonic functions.
We conclude, “If we are to understand this universe, we must start with pi.”
Pulling everything together. At no time in our human history has the entire physical universe, literally everything, everywhere, for all time,3 been logically and mathematically encapsulated. Yet, because logic and mathematics fit together, hand and glove, the logic inherent with the Planck base units gives us an actual beginning of the universe. By applying simple mathematics, base-2 exponentiation, to those base units we have another ordering system. Today, right now, this very moment in time, is the current expansion of the universe AND the ever-changing endpoint of the universe AND the current age of the universe.
Natural base units. In 1874 in Dublin, George Johnstone Stoney began his calculations to define natural units. Then, in 1899 in Berlin Max Planck4 did his own calculations. The concept of a natural units was finding a place within academia. These very special numbers and formulas also give us the best possible starting point of the universe. Natural units are defined by universal dimnesionless constants.
Though ostensibly ignored for over 100 years, in 2001 an MIT physics professor, Frank Wilczek,5 wrote three articles for Physics Today that began the current, deeper explorations. Wilczek, awarded the Nobel prize in Physics in 2004, lifted Planck’s numbers out of numerology-and-obscurity and into scientific respectability. The logic and simplicity of these numbers are now beginning to be refined.
Since 2011, I have been exploring the question, “Can we meaningfully multiply these Planck numbers by 2?” We unwittingly applied base-2 to the Planck Length while working on a geometrical progression that started by going deeper and deeper inside a tetrahedron. Wilczek and Freeman Dyson6 both encouraged our explorations.
Planck Time in 2013 and 2014. Now, also following Planck Time, I asked, “If this is the smallest possible unit of time, doesn’t it follow that it is also the first unit of time?”
Asking for a critical review and hearing no objections, I concluded that the Planck base units describe the most-logical starting point of this universe. The expansion of the universe, today, right now, is widely-studied and well-documented by many of our best scholars. As a result of that work, this universe is understood to be between 13.799-to-13.81 billion years. Some have it as high as 14.1 billion. Of course, there are a few who push it much higher and a few lower. As of today, we accept and use 13.81 billion years.
I believe that a rather profoundly underrated problem within our scholarship (and even within our faith statements) is the scope of the platform within which we make our observations and pronouncements. The old guard called it a Weltanschauung,7 yet we all know our little world evolves within a much larger universe. I would say that all so-called worldviews are by definition too small. Until we context our belief systems within an ordered, integrated, mathematical universe, our scope is too limited, too confined.
Base-2 Exponential Notation. By applying base-2 (doublings) to the Planck scale, we can rediscover this universe, now parsed and parameterized within just 202 notations. That little chart — https://81018.com/chart/ — requires much more work; nevertheless, it is a start.
Finite-Infinite. When we envision the universe in all that we do, our encapsulated finite universe begs the question about the infinite. One of the first ways we begin to know about the infinite is through our never-ending, never-repeating universal constants beginning with pi (π).
Pi and the very nature of light are within the core that defines those Planck units.
The Beginning and the Perfections of a Sphere. The universal sphere is the first expression of physicality that remains outside the boundaries of measurement for as many as 64 doublings. Here the perfections of continuity, symmetry and harmony define physical space. Here, there is a perfection within our physical world that is rendered as homogeneous and isotropic. Here is a domain forever and always beyond the reach of quantum indeterminacy and chaos theory.
1 E.P. Wigner Like those writings of Frank Wilczek about the Planck scale, once a professor receives a Nobel prize, the earlier writings take on a special significance. With this page and reference, I will start a new group of pages, Letters to those who ideas live on. Of course, E.P. Wigner and other key Nobel Laureates will be among those to whom I write. With the simple gift of pi (π), we construct a very different approach to the universe, yet one, given his writing within The Unreasonable Effectiveness of Mathematics in the Natural Sciences that I believe Wigner would approve.
2 Emma Haruka Iwao is a 2008 graduate of the University of Tsukuba (Japan) and today works for Google in Seattle, Washington. She set up the systems within the Google cloud and her automated calculations began churning digits on September 22, 2018 and ran until January 21, 2019 when they symbolically stopped it at 31.4 trillion digits, way-way-way beyond the actual number, 31 trillion, 415 billion, 926 million, 535 thousand, 897. That’s just 14 units. Think of all the pages of numbers those 14 digits represent. Let’s figure it out.** (Does over 8 billion pages of numbers sound about right?) It is arguably the longest actual definition of continuity in the world.
3 Everything, everywhere, for all time: Not a “theory of everything” but the mathematics for everything is further modified to be sure nothing is overlooked; “for all time everywhere” has been added just to start a debate. Once everything, everywhere, for all time is inscribed, can a theory be far behind?
4 Max Planck: The initial Father of Quantum Physics, Max Planck was Einstein’s mentor and Germany’s foremost physicist after whom over 80 research institutes have been named. For his work on quantum theory, Planck became a Nobel Laureate in 1918, Einstein in 1921 and Niels Bohr in 1922.
5 Frank Wilczek: Picking up on Richard Feynman and Paul Dirac’s anxiety about fundamental constants and how the universe coheres, Frank Wilczek was driven to open his own search to understand the fundamentals of physics in a new way. His study and use of Planck’s constant led him to the dig through Planck’s own struggles with the basics 100 years earlier. Wilczek is among a very select group to re-kindle interest in basic units, natural units, and fundamental physical constants. Others, like John Barrow (Natural Units Before Planck, Quarterly Journal of the Royal Astronomical Society, Vol. 24, P. 24, 1983) and C. Alden Mead (UMinn), were earlier adopters. In 1959, Mead wrote an article to build a case that Planck length and time are fundamental units. That work was largely rejected (C. Alden Mead: Observable Consequences of Fundamental-Length Hypotheses, Physical Review, N4, March 25, 1966, p.990-1005, doi:10.1103 / PhysRev.143.990). It is interesting to note that in 1989 Mead became a fellow of the American Physical Society and in 2012 he was awarded the Wigner medal.
6 Freeman Dyson: I visited with Freeman Dyson in 1979 at the Institute for Advanced Studies, just down the street from Princeton. At that time he was considered the sage of IAS, a collaborator with Einstein, and an insider of the Manhattan project.
7 Weltanschauung. There is a fair amount of confusion around the concept of a Weltanschauung (Wikipedia). Four categories — postpositivism, constructivism, advocacy/participatory, and pragmatism — are the four classic worldviews. Others ascribe seven different categories: Theism, Atheism, Pantheism, Panentheism, Deism, Finite Godism, and Polytheism. One group is from the perspective of the finite and the later from the infinite. None have an integrated, mathematical view of the universe. And, each position is held by various groups of self-assured people throughout the world. It is no wonder why we are so contentious, confused, and on edge.
8 Domain of perfection. Today we would say that this domain will be primarily under the 64th notation. Here, perhaps the scholars among Langlands programs, string theory, and loop quantum gravity research will have the best possible insights to localize and specify the functionalities within each domain or notation. Also, applicable is the 2007 work of Howard Georgi within his concepts of “Unparticle Physics.”
Imperfection. The pentastar, Pentakis dodecahedron, and icosahedron use the same simple combinations of basic geometries. Logic tells us that that our opportunistic universe would have manifest the most simple within the very earliest notations. These are very basic geometric figures. With just five tetrahedrons, sharing that edge at the centerpoint, if the faces remain exact, there is a gap between them. If not, there are “stretched” angles and faces. Yet, if that gap is not part of a larger system, there is no possibility that quantum fluctuations begin. We project that it is only within actual systems, projected to be between Notations-50 and Notation-64 is where those gaps actually become fluctuations and that indeterminacy (and unpredictability, uncomputability and undecidability) become an operational modality.
Also, I believe consciousness and sleep will find a variable place within these domains from Notation-1 to Notation-64.
- General relativity theory, quantum theory and chaos theory enter the equations at some point prior to the Notation-67 where these faces of our universe become dominant. Yet, within our mathematics of everything, everywhere, for all time, those first 64 notations have been largely unexamined. The mathematics of string theory, Langlands programs, and loop quantum gravity have a long and sophisticated history. Here we project that they all have a home.
- A lack of critical review of this model by our scholars is problematic. To encourage it, emails and tweets are sent and the key claims from within this study since December 2011 have been summarized.
- A redefinition of the infinite: More recently, we have redefined the infinite as the qualitative expression of continuity (order), symmetry (relations), and harmony (dynamics) while the finite is the quantitative expression of continuity (order), symmetry (relations), and harmony (dynamics).
- Today Steven Strogatz of Cornell University carries on the spirit of E.P. Wigner. Strogatz book, Infinite Powers (Houghton-Mifflin, 2019) engages infinity masterfully while loving its calculus. His article, Why Pi Matters, The New Yorker, March 13, 2015, is one of best Pi Day articles ever written. A prolific author, his classic book, The Joy of x, could have been titled “A Love Story.” He captures the allure, mystery and power of mathematics.
- Part of the dynamics of this article is the Foundational Questions Institute (FQXi). I prepared a sister article to this one. Under the constraints of their deadlines, it was submitted too early and it is now a (PDF) on the FQXi website. Technically it did not convert well from HTML to Pages (Apple’s word processing to a PDF). This PDF on our website is a little closer to how it was intended to look and feel (PDF). –BEC
Here are just a few of the recent tweets and emails during this period.
1. Closely-associated with other homepages, this article will continue to be updated. Among a few of the related are Twelve Formulas (Aug 2019 and Feb. 2020), Transformation (Aug. 2019), Bottom-up (Sept. 2019), Map the Universe (Oct. 2019), Finite-Infinite Bridge (Nov. 2019), Our young, cosmological model (Dec. 2019), A Simple View (Jan. 2020), Claims (Feb. 2020) and Imperfections (March 2020).
2. Further research: https://arxiv.org/abs/1110.5634
“Thus, knowledge-building in cosmology, more than in any other field, should begin with visions of the reality, and passing to have a technical form whenever concepts and relations in between are translated into a mathematical structure.” -Francisco Jose Amaral Vieira
Not far from date line, close to the equator, here it most often becomes “the next day” at Noon in London and 8 AM in New York City. The difference is always contingent on Daylight Savings adjustments.
First, how many characters across? Can we agree on 75?
How many lines down? Can we agree on 52?
That would give us about 3900 characters per page.
6 (just 16 down)
… and so on. Yes, about 75 characters across and 52 characters down or 3900 characters per page out of 31,415,926,535,897 (31415926535897) is a book of about 8,055,365,778 or just over 8 billion pages.
If you appreciate what we are doing here, please “like” and “share” this page. Thank you.
Key Dates for this page named Perfection
This page was initiated on 12 February 2020
It became a top post or homepage: 24 February 2020
The URL for this page is https://81018.com/perfection/
Last edit: Sunday, June 6, 2021