CENTER FOR PERFECTION STUDIES: CONTINUITY•SYMMETRY•HARMONY • GOALS.•.February.24-25,.2019
HOMEPAGES:.ASSUMPTIONS|BOTTOM UP|DARK| INFINITY | MAP-THE-UNIVERSE|Transformations

Starting With Mathematical Perfections

3.141592653589793238462643383279502884+

by Bruce Camber In Process: Click on the little yellow arrows pointing left and right (just above) to go to related homepages.

Background. In 1960 E.P. Wigner, a Princeton physicist (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.

The ratio for those numbers now has over 31.4 trillion digits, a calculation set up by Emma Haruka Iwao.²  It ran from September 22, 2018 to January 21, 2019 and it is not finite. Within this model, those numbers and the circles-and-spheres are the face of (1) perfection, (2) a definition of the infinite, and (3) a finite-infinite bridge. There is a fundamental ordering of numbers, a deep symmetry of relations and geometries, and the opening of basic dynamics with 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 — everything, everywhere, for all time³ — 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. Applying simple mathematics, base-2 exponentiation, to those base units gives us another ordering system; and, today, right now, this very moment in time, is the current expansion of the universe as well as the ever-changing endpoint of the universe and the current age of the universe.

Planck base units. In 1899 Max Planck⁴ grasped these special numbers and formulas that give us the best possible beginning point of the universe. These numbers are all natural units, defined by universal physical constants. Though practically ignored for over 100 years, in 2001 Frank Wilczek⁵ of MIT 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 no longer argued.

Since 2011, I have been exploring the question, “Can we multiply these Planck numbers by 2?” We unwittingly applied base-2 to Planck Length while working on a geometrical progression that started by going deeper and deeper inside a tetrahedron. Wilczek and Freeman Dyson⁶ both encouraged that exploration.

Planck Time. Now, also looking at Planck Time, we 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 critical review and hearing no objections, we finally concluded that the Planck base units describe the most logical starting point of this universe. The current expansion of the universe today, right now, is deeply studied and well-documented. 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 go with 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. Until we context our belief systems within an ordered, integrated, mathematical understanding of the 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.

And, here this finite-infinite relation creates a domain of perfection.⁸

Although general relativity theory, quantum theory and chaos theory seem impossibly discordant, within our mathematics of everything, everywhere, for all time, there is a substantial, heretofore unexamined domain, made for mathematics, the likes of string theory and Langlands programs; here is the very core of homogeneity and isotropy.

Herein are very new possibilities for convergence and for more deeply understanding ourselves and this universe. Because of the lack of critical review by our scholars, we have summarized the claims suggested, proposed, and made within this study (since December 2011).

Our redefinition of the infinite: The infinite is a 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).

Thank you. –BEC

Footnotes, endnotes, references and resources

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.

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 is 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 which over 80 research institutes have been named after him. 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 first 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 on the Manhattan project.

Today, his legendary status is still waxing.

⁷ Weltanschauung.  There is a fair amount of confusion around the  concept of a Weltanschauung (Wikipedia). Some ascribe four categories — postpositivism, constructivism, advocacy/participatory, and pragmatism to describe our worldviews. Others ascribe seven very different categories: Theism, Atheism, Pantheism, Panentheism, Deism, Finite Godism, and Polytheism. One group is from the perspective of the finite and the laer 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 Langlands programs people and string theory people may have the best possible insights to localize and specify the functionalities within each domain or notation. The pentastar, dodecahedron, and  icosahedron, may manifest within very earlier notations, they will be a geometric figure with a gap or with “stretched” angles yet if these are not part of a larger system, there is no possibility that quantum fluctuations begin. We project that it is only within systems where those gaps actually become fluctuations that indeterminacy (unpredictability, uncomputability and undecidability) become an operational modality. Also, consciousness and sleep will find a place within this domain from Notation-1 to Notation-64.  Much more work to come…

###

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), and Claims (Feb. 2020).

This page was initiated on 12 February 2020
First homepage date: 24 February 2020
Last edit: Monday, February 24, 2020