PERFECTION STUDIES: CONTINUITY•SYMMETRY•HARMONY GOALS.September.2024
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Aristotle’s Mistake
By Bruce E. Camber (a first draft)
Abstract
Partially corrected mistakes from our past create confusion in the present. Aristotle’s 1800+ year mistake, though caught in the 1400s, was mostly ignored by academia.[*] When resuscitated in 1925 and 2012, the analyses were incomplete.[†] This article is an attempt to more fully analyze Aristotle’s mistake, then how it is being compounded with Newton’s fundamental mistake.[a] Then, it gets even further compounded with our incomplete understanding of Max Planck’s introduction of natural numbers and a quanta of energy.[b] As it gets even further compounded, quantum mechanics is incomplete, Einstein is incomplete, cosmology is incomplete, dark energy-matter is incomplete, and the very foundations of our sciences are incomplete. It’s no wonder the world is confused about the nature of life and there is so much divisiveness.[c]
Key words: Errors, mistakes, compounded errors, incompletes, Struik, Senechal, Aristotle, Lagarias, Zong, American Mathematical Society (AMS), continuity, symmetry, harmony, symmetry-breaking, super-symmetries, Bridson, Euclid, Euler, dark matter, dark energy…
About this study: A continuation of earlier studies, Mistakes (2017), Aristotle’s Mistake.(2022), and Mistaken (2024)…
Introduction. Errors, verifiable errors, when ignored by academia, create conceptual roadblocks ahead. It was true in the 1400s when Aristotle’s mistake was first uncovered. When Dirk Struik (1925, Gottingen; 1926, MIT) wrote about it (translation from Dutch, Majorie Senechal, 1980), it was more true.[1] And,.it became critically true when Jeffrey Lagarias and Chaunming Zong wrote about it in the 2012 American Mathematical Society Bulletin.[2] In 2015 Lagarias-Zong received the AMS Levi L. Conant Award for their work; but now, it has been all but forgotten and not many scholars are aware that the universe cannot be tiled and tessellated with just tetrahedrons.
It may seem like trivial pursuit, yet it will be argued here that it is a keyway to grasping the deepest realities that shape us.
As we seemingly race into cataclysmic times, the question is asked, “How could a simple mistake in geometry lead us so far down a path whereby key countries are becoming increasingly hostile and even neighbors become more intransigent, and even hostile, with each other?”
Research. Tiling and tessellating the universe. An error introduced by one of the world’s most influential scholars in history, Aristotle (384-322 BC), trivializes the importance of the topic. Assumed to be right for over 1800 years, then virtually ignored for another 600 years, trivializes the issue even further.
It is time for a resurgence and restoration of the place and importance of basic geometry.[3]
Grasping the nature of symmetry and symmetry-breaking is a key part of our current studies and dialogue. Shape dynamics, causal dynamic triangulation, loop quantum gravity, and super-symmetries, are just a few applications of geometry in new and robust ways. I am guessing, but given the numbers of citations to the Lagarias-Zong AMS article, few of our scholars are aware of Aristotle’s error. First, it takes one octahedron-to-two tetrahedrons to perfectly fill space and to begin to tile and tessellate the universe. Second, five tetrahedrons (or five octahedrons) sharing an edge, create a 7.356103172+ gap.[4]
The first observation is that on a fundamental level space-time can be perfectly filled. The second observation is that again on a most fundamental level, there is a geometry of imperfection.
Now, compound Aristotle’s mistake with Newton’s most fundamental mistake: absolute space and time. It is the commonsense worldview; space and time are the plenum or container of the universe. Even scientists, mathematicians and physicists who have engaged Einstein’s theories still affirm those absolutes when a finite universe view would be closer to the truth.[5]
Still debated, space-and-time, space-time, or spacetime are all derivative. …of what? Light.
Enter quantum mechanics. Max Planck got a little attention with the introduction of natural units, the ever-so-small units of time and length. His idea of a quantum of action received much more; it became the foundation for what became known as the old quantum theory. It was a new discipline; and over the next 60 years, the debates settled down around the most influential thinkers. Open questions gave rise to new disciplines. String theory among them, never was there a debate about Struik’s work or Senechal’s translation of it. Geometry was yet to regain enough stature and Struik’s work was ignored.
Enter Lagarias and Zong. Neither Lagarias nor Zong expressed an interest in speculating about the nature of the gap and how it might manifest as a physical phenomenon. In December 2022 I wrote to Martin Bridson (Oxford mathematician and head of the Clay Institute of Mathematics) to ask his opinion.[6] He was ready to move beyond discussions about packing densities; I suggested exploring a link to quantum fluctuations, however, that note is my most recent follow-up.
A major stop-gap to that discussion is the Big Bang theory. Until theorists realize that a base-2 natural inflation and expansion of the universe is a more forgiving-and-creative model of the universe, scholars will continue to be reluctant to get into any conversation that naturally leads to questions about the voracity of the theory. These questions create too much pressure on too many issues all at once.
Results. Confusion. Aristotle did not know basic facts of emergent geometries. He did not have perfect tetrahedrons in his toolkit. He did not and could not test his guess that a tetrahedron could be used to tile and tessellate the universe. The only way to do it with a tetrahedron is to use it with an octahedron. There is magic in the perfections when two tetrahedrons get together with one octahedron to fill space with no gaps.
Aristotle made a mistake; and by the time of Isaac Newton, Plato’s forms were not the focus. As much as the work of Euclid was respected, nobody had an intuition that cubic-close packing of equal spheres could render tetrahedrons and octahedrons. The perfect internal constructions of these two most basic objects were not discerned; nobody was asking what was perfectly enclosed within them.
Newton made a mistake. Leibniz was trying to persuade him to adopt a more relational view of space-time but they were instead hardening their positions; they were in a psychological war to determine who created the first calculus. Notational wisdom was just on the horizon. The work of Euler came too late for either Newton or Leibniz to begin to grasp the scale of the universe.
The universe is a container. It has a beginning and it has an end, the current time. It is not a classic reductio ad absurdum, but the calculation of those natural units that define the first moment would not be published until George Stoney (1874), Max Planck (1899), and the ISO (2019). And the first container, the base-10 work of Kees Boeke wasn’t introduced until 1957. It had books, films (Smithsonian, IMAX) and many webpages done about it. Our container was introduced in 2011. It is a base-2 model which is 3.333+ times more granular than base-10; it has several geometries, a calculus, natural units, and more. There are 202 base-2 notations that include everything, everywhere, from the beginning of time to this moment right Now.
The first second takes us up to Notation-143. It is like a big bang without the bang. It’s like inflation, a fraction slower, but within this model there are those first 64 notations to study for the first time and a new way to look at those notations up to the very first second of our universe. This is a model (outline) of the start. Then, it becomes a study of how those 143 in the next 59 notations bring us well beyond our current 13.8 billion years.
Academia has not yet fully embraced Planck’s base units, bifurcation theory, pi (π), and all the mathematics involved with spheres.[7] It’s just too much. It is just too difficult to go back to the basics and start all over again. We can’t be absurd to ourselves, even though we know — we truly know — that intellectual integrity insists on it.
Dark-to-Light. The 202 base-2 notations are a key. The first 64 notations are below our measuring capabilities. The densities are too high and the time is too short. If we go to where our densities are highest — the center of revolving spheres such as solar systems and galaxies — and assume there are 64 non-local notations to go, we are challenged to see a very simple dark energy and dark matter in a radically different way.
Within pi (π) are the continuity-symmetry-harmony conditions that define it. In the face of David Hilbert and so many others, it’s the best possible description of the finite-infinite transformation. If taken as given, even more fundamental questions are opened.
Conclusions. We have generally accepted the concept of the Planck scale and those dimensionless constants that establish each of their values. We have a ways to go before we see our universe as a grid of infinitesimal spheres, the most dense of which are deep within every galaxy, solar system, planet and moon that defines our universe. We have been, in fact, looking right in the face of dark matter and dark energy since 1884 when Lord Kelvin first speculated about it.
Out here where things are not quite so dense, there is the universe as we see it. You are designing it right now… with your thoughts, words and deeds. It’s all dynamic. It’s all Now. It’s all connected and profoundly inter-related. And, it is all constantly conditioned by the continuities, symmetries, and harmonies within pi (π).
Harmony? It’s not just a nicety. It is much more than “what singers do.” Since Fourier it has become one of the fundamentals of science.
So, yes, it is true. If only we could teach the world to sing in perfect harmony, we could begin to surround everybody with fundamental beauty so there would be no wars, no taking of human life, but just unmitigated creativity, insights, and making things fascinating. Thank you. -BEC
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References
As references are added, other resources will also be added within this website.
[*] Mistake ignored. Retrieved 3 September 2024: https://81018.com/biased/#Aristotle
[†] Analyses incomplete. Retrieved 3 September 2024: https://81018.com/precis/#Zong
[a] Newton’s mistake. Retrieved 3 September 2024: https://81018.com/biased/#Newton
[b] Quanta of energy Retrieved 3 September 2024: https://81018.com/biased/#Hawking
[c] Value of life and hostility. Retrieved 3 September 2024: https://81018.com/value/
[1] Struik/Senechal. Retrieved 3 September 2024: https://81018.com/struik/
[2] American Mathematical Society Retrieved 3 September 2024: https://81018.com/ams/
[3] Geometry’s resurgence. Retrieved 3 September 2024: https://81018.com/identity/
[4] Gap Geometries. Retrieved 3 September 2024: https://81018.com/gap/
[5] First 64 Notations. Retrieved 3 September 2024: https://81018.com/64-notations/ (2018)
[6] Martin Bridson. Retrieved 4 September 2024: https://81018.com/bridson/#Fifth.
[7] Spheres. Retrieved 4 September 2024: https://81018.com/starts-2/
[8] More to come!
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Reading and re-reading
What is opened on the desk, on the shelves and on the floor.
• A review of ISAAC NEWTON ON MATHEMATICAL CERTAINTY AND METHOD. Niccolò Guicciardini. xxvi + 422 pages. The MIT Press, 2009 by Paolo Mancosu, professor of philosophy at the University of California, Berkeley, Newton’s Toolbox.
• Duff, M. J. (2014). How fundamental are fundamental constants? (ArXiv-PDF), Contemporary Physics, 56(1), 35–47. https://doi.org/10.1080/00107514.2014.980093
• Thomas Thiemann, “The fabric of space: spin networks” in: Einstein Online Band 01 (2005), 01-1029 , professor of physics, Erlangen University. Loop quantum gravity.
• 23 – 24 January 2023, Probing the quantum origin of spacetime, Royal Society
• Rakshit P. Vyas & Mihir J. Joshi, Implications of New Quantum Spin Perspective In
Quantum Gravity (PDF), Department of Physics, Saurashtra University, Rajkot, India
(7 December 2022)
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Afterthoughts
Personal reflections.
Every large-scale structure that revolves around others is a candidate for dark matter – dark energy. Not at the visible level, but deep within the cores of moons, planets, suns (of solar systems), and the center of galaxies will be an even deeper concresence of the first 64 notations from its respective start.
There’ll be more to come…
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Emails
There will be emails to many of our scholars about key points.
• 5 September 2024: Martin Bridson, Mathematics Institute, Oxford Uiversity, England
• 6 September 2024: Sergio Mujica, ISO, Geneva, Switzerland
• 6 September 2024: Chaunming Zong, TCAM, Tianjin, China
• 7 September 2024: Jeffrey C. Lagarias, Ann Arbor, Michigan
• 7 September 2024: Marjorie Senechal, Smith College, Hahn Institue, Northampton, MA
• 8 September 2024: Michael James Duff, Imperial College, London
More to come…
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IM
There will also be many instant messages to thought leaders about these key points.
07 September 2024: @DavidAFrench (NYT) All our narrow little worldviews tie us in knots. To see the really big picture, adopt a mathematically-integrated view of the universe. Start at the Planck base units, apply base-2. You’ll have an outline in 202 notations. It works. https://81018.com
4:28 PM · Sep 9, 2024 @AdrienneLaF (Executive Editor, The Atlantic) What is truly delimiting is that we have such small worldviews when the entire universe is our home. Let’s break out. Begin with a mathematically-integrated universe view. It’s just 202 base-2 notations from the Planck Base Units: https://81018.com
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Critique ____ You are always invited.
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• This page become the homepage on 4 September 2024.
• The last update was 8 September 2024.
• This page was initiated on 2 September 2024.
• The URL for this file is https://81018.com/too-simple/
• The headline for this article: Aristotle’s Mistake Bites Us Today
First headline: Still Compounding Our Mistakes.
• Current teaser: We seldom get it right the first time, but we’ve been wrong for 2400 years!
• First teaser* is: Too easy. Too simple. Too Good To Be True. Too much to ask.
*Or, wicket, kicker or eyebrow.
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