CENTER FOR PERFECTION STUDIES: CONTINUITY•SYMMETRY•HARMONY December 19, 2022
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New Orleans: Five high school classes of students — mostly for geometry — were greeted with the chart on the left. It was huge, over seven feet high. Click on the image to see it! It is a mathematical map of the universe.
It didn’t take long for the students to get the knack of it. They were quickly going further and further inside new and unknown spaces. They quickly got smaller than a molecule, then a cell.
Those students had been cajoled to go inside that tetrahedron and octahedron. In your mind’s eye you can do extraordinary things. Shrinking smaller and smaller is one of them. Dividing edges by 2 and connecting the new vertices is another.
Down through the DNA of biology and into the chemistries and its periodic table. Then very quickly we were into particles and waves and fluctuations. Our goal was to reach those natural units that Max Planck defined in 1899. We understood these were the the smallest possible units of space and time. We had come down 45 steps and then uncovered 67 more steps to those Planck units.
Encapsulated Tetrahedrons and octahedrons. All the way down smaller and smaller, every notation is active. It was difficult to discern the archetypal form within each notation. Yet, at Notation-0 it appears to be an infinitesimally-small, sphere.
Vibrant and dynamic, it appears to be the instantiation of the Planck base units and so much more.
From our magical observation deck, we could see those spheres stacking, with new functions with each doubling. From here we could readily look up the 112 steps back into the classroom. In just 90 additional magical doublings or steps or notations, we could see that we would be out to the edge of the expansion of the universe watching the current expansion.
It happens so fast: Tredecillions of spheres per second. We’ve had to double check our numbers over and over again. In just over a second from Planck Time, we were out to Notation-143. In just over a year, Notation-169. And in just over 1000 years, Notation-179. A million years is just over Notation-189 and a billion years, just over 199. If we assume there is one infinitesimal sphere per unit of Planck Time and Planck Length, there are 539 tredecillion spheres per second. If we use Stoney’s numbers, there are 4605 spheres per second.
Here is our universe from the smallest to the largest in 202 steps or doublings or notations. It has its own special logic such that all notations are ongoing, interdependent, and forever.
What’s this all about? Yes, dynamic and logical, this model has numbers and geometries. It has the Planck units. It has a simple algebra; and it is constantly filling with infinitesimal spheres. It is the first time we could see the universe on one highly-ordered, fully-integrated chart. We searched online for the experts’ interpretation of our emergent model, but we couldn’t find such our chart in any textbook or anywhere on the web. So, we turned to the living scholars who would know. Many complimented our work and said something like, “Your chart uses base-2 exponential notation to parse the universe from the smallest to the largest possible measurements.”
We learned that the work was unique. We also learned that the results did not jive with current cosmological theory. This model posits a very smooth, yet highly-integrated beginning of the universe. Here the geometries all fit together perfectly. These geometries tile-and-tessellate without gaps. Yet, we knew that a five-tetrahedral cluster made an object with a gap. Octahedral clusters do the same. Together they make a geometry that has not been discussed in any of the literature. We propose that it is a geometry of quantum fluctuations. It is squishy geometry.
Over our heads and inundated with new information. I consulted with old acquaintances who were scholars — John Conway, Phil Davis, Freeman Dyson, and Lisa Randall, Then we began learning through the work of new people like Frank Wilczek and Stephon Alexander. Work by Jeffery Lagarias and Chaunming Zong, Mysteries in Packing Regular Tetrahedra (PDF), was an indictment on the academic community. Aristotle’s mistake had been ignored and it continues to be ignored within academia. That’s a profound mistake and causes one to pause and ask, “What are some of our other profound mistakes?
Here’s my quick introduction to three:
1. Sphere-to-tetrahedron-octahedron dynamics: Cubic close packing of equal spheres: https://81018.com/ccp/ Scholars have focused on packing densities; very few have focused on the process by which tetrahedrons and octahedrons are created from sphere stacking.
2. Structures created by basic geometries. First, the octahedrons within every tetrahedron is a key. The four interlocking hexagonal plates within every octahedron is another key. Those gaps created by clusters of five tetrahedral clusters and five octahedral clusters are also a key. The gaps created by clusters of twenty tetrahedrons (an icosahedron) are keys as well. It is all unfinished business, whereby we all, especially our scholars, should focus on the place and purpose of each gap. Are these gaps related to quantum fluctuations? That’s a major discussion.
3. The very nature of pi (π): I am no scholar but the mathematics of infinity seems to be a penultimate challenge. There are so few discussions of the place and importance of pi (π) and infinitesimal spheres. I believe that the open questions about the very nature of homogeneity and isotropy of the universe are keys and that Planck units or Stoney units (or the ISO’s equivalent units) will define an approximate rate of expansion so tredecillions of infinitesimal spheres per second fill the universe from the start through to the Now.
These three points are so idiosyncratic, it’ll take time to engage them, absorb them, then use them. It is, however, all very approachable with high school students. We even had our AP class of sixth grade savants get immersed in it; but once our graduates started circling back, we realized that it was too disruptive within the current curriculums. The only hope is within the special integrity of people like you. Might you have any advice for us? How do we proceed? Thank you.
Endnotes & Footnotes
Most of key points already have pages within this website; however, new footnotes may yet emerge.
References & Resources
Key references and resources will be added over time.
• Martin Bridson, Oxford and Clay Institute, December 17, 2022
• Levent Alpoge, Harvard, Cambridge, Massachusetts, December 16, 2022
• Richard J. Fitzgerald, AIP and Univ. Texas-Austin, December 16, 2022
• Alan Guth, MIT, Cambridge, Massachusetts, December 13, 2022
• Gil Lonzarich, Cavendish Lab, Cambridge University, December 12, 2022
• Sankar Das Sarma, University of Maryland, December 11, 2022
• Ana Caraiani, Hausdorff Chair Bonn, Imperial College London, Thurs, 8 Dec, 2022 8:43 AM
• Orli Dahan, Tel-Hai College, Israel, 7 December 2022 @ 2:42 PM
• Elizabeth Gibney, Nature magazine, Tues, Dec 6, 20227:57 PM
Often using Twitter. Criticized, now also using Parler. New IM will be added.
• This page became the homepage on Monday, December 19, 2022.
• The last update was 21 December 2022.
• This page was initiated on 18 December 2022.
• The URL for this file is https://81018.com/December-19-2022
• The first headline for this article: An Alternate Point of View Evolved
Also: Our Big Board-little universe chart began and evolved as a Quiet Expansion, not a Big Bang.
• First byline is: Eleven years ago, from December 19, 2011 to December 19, 2022…