CENTER FOR PERFECTION STUDIES: CONTINUITY•SYMMETRY•HARMONY. GOALS.JUNE 2021
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Preface: Three years ago I reviewed the work of these three creatively-aggressive and confident scholars. Pictured again, just above, all theoretical physicists, Max Tegmark of MIT, Neil Turok of Perimeter Institute, and Nima Arkani-Hamed of the Institute for Advanced Studies (IAS) have been asking the scholarly community to redefine space, time, and infinity. For them, the processes involved with renormalization do not go far enough.
Max throws out infinity. Nima throws out space and time! Neil tries to redefine all three. They ask, “What is more fundamental? What are our preconceptions? What concepts abide?”
A very different start: I’ve proposed to them that we use quite general concepts but with very specific meanings within the infinitesimal; that is continuity, symmetry and harmony. There has been no general academic discussion about the deepest roots of each of these concepts within pi (π), circles, spheres, the infinitesimal, and infinity. To open such a discussion is one of the goals of this article.
This re-definition imputes fundamentality to each concept: 
1. Continuity begets order begets numbers which beget time.
2. Symmetry begets relations which beget geometries which beget space.
3. Harmony begets dynamics which begets systems which begets space-time.
Continuity-symmetry-harmony, taken as a whole, first redefines how we understand the infinite and then how the infinite defines pi and other key dimensionless constants, and how these define the first infinitesimal, primordial sphere which becomes the first instance of the finite such that space and time are derivative, discrete, and quantized.
Although infinity has been used and abused throughout history, our goal is to define it most simply, logically, mathematically, and scientifically. As a result, there are many discussions about the finite-infinite relation through this website.
About exploring 81018.com. I invite you to flip back through the past homepages. Notice the yellow arrows above, to the left and right of our secondary header. The arrow on the left will take you back through the homepages, one at a time, all the way back to July 2016. The arrow on the right will take you to a summary page with a date stamp, title, and embedded link to the same group of pages.
Our most creative-yet-contentious scholars within academia drive this site. Add to the three above, the 2019 Nobel laureate, James Peebles, challenged me with his comment, “…we have no good theory of such a thing as the beginning.” The result is a most-simple nine-step progression: Five concepts to start the universe and four concepts to grow the universe.
Most labs like CERN can readily measure within a nanosecond of the first instance of creation. Within our base-2 chart (map) of the universe, a nanosecond (a trillionth of a second or 10–12 s) is defined within Notations 114-117. Even the yoctosecond range, one trillionth of a trillionth of a second (10–24 s), can be logically explored within Notations 65-67. That leaves us with the pivotal notations between 1-and-65 yet-to-be explored and discussed within the academic community. It may not be possible until at least some of these thirty unique presuppositions are assumed.
Pi Days: In my analysis for Pi Day 2021, we build on those three primary facets of pi. A key part of that analysis was to see pi as the gateway between the finite-and-infinite and as a gateway for all key dimensionless constants. Then most importantly, we hypothesize that the first manifestation that creates space-time, mass-charge, and electromagnetism-gravity is an infinitesimal, primordial sphere.
This primordial sphere is what Lemaître characterized as a primordial atom. In this model it never disintegrates and it is defined by dimensionless constants that renders six quantities all expressed within units analogous to the base units of Stoney or Planck.
Another key part of that analysis is to conclude that the rate by which primordial spheres are created is one sphere per primordial unit of time. Thrust comes within charge and light. The rate per second is predetermined by the calculations of PlanckTime (539-tredecillion spheres per second) or StoneyTime (4605-tredecillion spheres per second) or a yet to be determined primordial time.
To impute some order within this extraordinarily robust expansion, we applied base-2 to the units of Length/Time, Mass/Charge, and Electromagnetism/Gravity. Base-2 is a natural grouping. Though dealing with the same primordial spheres, the dynamics within each notation are being uniquely defined. Each notation continues building upon base-2, but just the next notation opens a base-3 organizational dynamic. The fifth notation opens base-5. The seventh notation opens base-7, and so on.
For now, we are primarily focused on base-2.
A very special chart of the universe emerges. It maps a natural inflation or a thrust within our universe such that every unit is accounted and related. There are just 202 steps, base-2 notations or doublings to create our first totally mathematical map of the universe from the very first moment to the Age of the Universe today and to the size of the Observable Universe right now.
If we follow the constructions of the Planck units and the Stoney units, the spheres per unit of mass and charge are at density levels of a blackhole and neutron star. These so-called “blackholes” are building the universe. It is a simple logic to conclude,
That chart is here: https://81018.com/chart/ Around the 67th doubling we begin to measure particles in space. This is a rather small section that is perhaps best described as “the CERN scale.” Not until the 84th doubling, can we finally measure a unit of time. Up between the 143rd and 144th doubling comes the first second of our universe; by the 169th doubling comes a light year. Within the 189th doubling we have what happens with one million years of processing. By the 199th doubling an aeon (billion years) shapes our universe. Within the 202nd doubling, we emerge with a rather complete map of a logical and highly-integrated mathematical — numerical and geometrical — universe.
If we review just a small sampling of those 202 doublings, there is a logic and a flow with over 1000 real numbers to examine. An initial analysis — https://81018.com/planck_universe/ — of six sets of numbers, somewhat evenly distributed across the 202 notations, individually and as a whole, support the logic of a quiet expansion; plus the numbers support the current definitions of the cosmological epochs better than the guesstimates and estimates from within the infinitely-hot start proposed by Guth, Hawking and so many other scholars. A rather lengthy analysis is here: https://81018.com/2016/06/01/quiet/ An actual comparison with the epochs of big bang cosmology is here: https://81018.com/calculations/
Though idiosyncratic and quite unlike current scholarship, to open a discussion, I have created a page of long-term and short-term goals to analyze: https://81018.com/goals/ The next step is to continue to consult with imaginative-but-scholarly mathematicians to discern if there are mathematical and geometrical processes that build off of the most simple and most-used dimensionless constants that might define the first ten notations.
Because this work originated back in 2011 within a New Orleans high school — https://81018.com/home/ — it has not been seriously reviewed by the scholarly community. All these web pages are an attempt to begin to write for publication in order to have some recognized scholar finally tell us, “You’re wrong and these are the reasons.” Or, perhaps, “You’re getting close but need these course corrections.” Or, “How novel! Keep it up.”
Our hope is that somebody like James Peebles might say, “You are cutting a new path. I may not understand it, but you are not wasting our time.” Until we hear such words, we will continue to learn from scholars like Edward Zalta (Stanford) in order to use his Computational Metaphysics and logic to analyze our numbers more closely.
There is much more work to be done. https://81018.com/hypostatic
 Three Highly-Speculative Scholars. Max Tegmark (emails), Neil Turok (emails), and Nima Arkani-Hamed (emails), are three of the world’s most vocal theoretical physicists. Stephen Hawking died on Pi Day 2018 and left the world without a scientific ambassador. Our homepage that day referenced the BBC’s report, the place of pi within our scholarship, and a new page of tweets and links about Hawking’s death. Each of our three scholars could replace Stephen Hawking as a spokesperson to explain the results of current scientific research about our universe.
 Envision the very start of the universe. This article is a re-write of our 2018 article which was an open letter to scholars around the world. It is a follow-up of two postings about the thrust of the universe and its natural inflation — https://81018.com/thrust/ and https://81018.com/ni/ — that are especially evident in the first 67 doublings, 1-to-67, of the 202 doublings from the first instance to the current time, the Now. Current research reaches down into Notations 65 to 67. The first 64 notations have never before been recognized as such by our scholarly community. We hypostatize and hypothesize that 1-to-64 is strictly a geometrical and logical domain where pure mathematics reigns. It is a place for a hypostatic science that bridges the finite and infinite. With only mathematics and logic, those 64 notations could even provide new metaphors for those involved in religion and philosophy which just might help our cultures abide, yet it is not the initial intent of this website (or this article).
 Continuity-Symmetry-Harmony: These three re-definitions impute fundamentality to each concept such that space and time are obviously derivative of all three. Also, each concept cannot and does not stand alone. These are the three facets of infinity, pi, and the primordial sphere. Continuity is order; it is numbers and it is time. Symmetry inculcates all of continuity; it is relations; it is geometries, and it is space. Harmony inculcates continuity and symmetry and it is at the heart of all dynamics and it is a system and it does define space-time.
 Finite-Infinite Relation. Metaphorical-and-romantic language can be understood in many conflicting ways. Let us work to define infinity and the infinite in the most simple scientific terms and scientific principles that appear to be the most abundant, most simple forms and functions of matter, energy, and life. To that end, three pages become our working documents:
- https://81018.com/infinity/ infinity qua infinity
- https://81018.com/infinitesimal/ infinity in transition
- https://81018.com/infinity-summary/, a sampler
 Renegades. Scholars who are willing to stick their necks out all need to be congratulated. But, unfortunately, we eventually tend to lift these people up with prizes and honorary degrees. They begin to think, “Maybe I am smarter than everybody else.” Such arrogance is the beginning of their downfall. We are all prone to mistakes and stupidity. That’s the face of chaos and indeterminacy. We all need to be constantly correcting each other and forgiving each other.
 P. James E. Peebles, Princeton, Nobel Laureate 2019. In 1982, James Peebles opened the path that laid the foundations for the standard model of cosmology or the ΛCDM. As a scholars’ scholar, he knows that the gap between the first instance and the first billionth of a second is huge and must be further examined. Our proposal is here. There are many scholars who have been trying hard to conjure the first trillionth of a second. Do a quick search of “the first trillionth second” and you’ll discover several thousand references. During his acceptance speech while receiving the Nobel prize, Peebles took the opportunity to remind his fellow scholars that there are many open questions within the big bang theory and it has no account for the first instants.
 Assumptions and Presuppositions. Back in 2013 while working with high school students, I said that we all had to become increasingly comfortable with extremely-small and extremely-large numbers. These were the next frontiers. To ignore them would be the height of arrogance. That the nations’ governing bodies for standards in science continue to ignore the need to define and name six groups of fractions is a reflection of our cultural and scientific arrogance. It is reflected in the comments about penultimate status of particles, waves, fluctuations and the like.
 Primordial Sphere. The most simple manifestation of physicality, an infinitesimal sphere, is the manifestation of the three facets of pi, a perfect continuity-symmetry-and-harmony. Here the ideal becomes real.
 Numbers like those from Planck or Stoney. Currently ignored by those with big bang sympathies, the very concept of a base unit is scientifically and philosophically enigmatic for many academics. Perhaps it takes the naïveté of a high school teacher to ask questions from a less-committed, less-than-informed platform. In March 2021 John Ralston’s work regarding the Planck constant finally began sinking in. Ralston, a physicist working out of the University of Kansas, had identified Planck’s limited perspectives and advocated for better numbers independent of Planck’s understanding of first principles held 1899. We await such recalculations from scholars like Ralston. If possible, we will use those figures to recalculate all the figures within our horizontally-scrolled chart that currently starts at the Planck base units and in 202 doublings or notations come to the current time and size of the universe.
 Tredecillion Per Second. This calculation has been a bit mystifying right from its inception. We have been about seven years now attempting to grasp the differences between the big bang theory and our own cold-start theory. We had called our theory a Quiet Expansion to contrast it with the Big Bang. Yet, now we are confronted with well-over a tredecillion spheres per second. Of course, well below the thresholds for sound waves, the question was asked, “Is there ever any sound involved?” Because every notation builds on the prior notations and all build upon a foundation of infinitesimal primordial spheres, there can be no sound. Yet, obviously, at some point there is sound. The “how’s” and “why’s” of the evolution of sound will be an important part of these studies.
The size of one primordial sphere is given by a primordial length. In our primary example, that is the Planck Length. We have only recently begun to explore what it might look like as a StoneyLength. Before going too far with Stoney, we await the possibility of using a RalstonLength!
 Dark matter and dark energy. The entire scientific community is flummoxed that such a far-reaching, key question has gone unanswered for so long. It is our hope that through their incremental work, they will begin to define the first 65 notations, giving both Langlands programs and string theory and her many offshoots a place on a fully-integrated grid of our universe.
- 2012 Breakthrough Prize in Fundamental Physics, Nima Arkani-Hamed, Institute for Advanced Study
- Oct. 7, 2015, Neil Turok Public Lecture, The Astonishing Simplicity of Everything
- 2002 Parallel Universes, by Max Tegmark, Scientific American, and 100 years of Quantum Mysteries, with John Wheeler, 2001
- Dec. 1, 1982, Large-scale background temperature and mass fluctuations due to scale-invariant primeval perturbations, P. James E. Peebles, Princeton, The Astrophysical Journal, 263: L1-L5
- The Physics of Infinity, George FR Ellis, Krzyztof Meissener, Herman Nicoalai, Volume 14, August 2018, pp 770–772.
- Emergence of time, George F R Ellis and Barbara Drosse, 2018 (PDF)
Recent emails have been sent to James Peebles, Neil Turok, Nima Arkani-Hamed, and Max Tegmark regarding our references to their work. I also alerted Emily Wilson, the editor-in-chief of the New Scientist, of my notes to James Peebles and Dan Hooper (Kavli, Fermilab, and University of Chicago). Most recently Jens Niemeyer of Göttingen received a note about his mapping project of the first trillionth of a second. At the very least we can learn the differences between a picosecond (10−12) which is a trillionth of a second, the femtosecond (10−15), an attosecond (10−18), the zeptosecond (10−21) and the yoctosecond (10−24), a trillionth of a trillionth of a second. We will continue to ask our national institutes for standards to name six groups of fractions from that yoctosecond to include: 1) up to 10−27 then, 2) 10−30, 3) 10−33 4) 10−37, 5) 10−40, 6) 10−43, and finally to the PlanckSecond (10−44), or StoneySecond (10−45), or a yet-to-be-defined LemaitreSecond (also a primordial second). -BEC
Additional notes will be sent to every scholar who is referenced within this article.
28 May 2021: @BrigidHains In December 2011 our high school geometry class followed the simple logic of base-2 exponentiation https://81018.com/home/ with a tetrahedron with its octahedron in the middle: https://81018.com/tot/ Eventually we encapsulated the universe in just 202 notations! https://81018.com/chart/ You might enjoy it.
31 May 2021: @Magda_Skipper (Editor, Nature) “Are you aware that we had no theory for the first fraction of a second of the universe? James Peebles (Princeton) noted it within his 2019 Nobel (physics) acceptance speech. I checked it out and others of his caliber agree. https://81018.com/starts/ is a theory!” (and, includes the first instant and, of course, the first trillionth of a second) @Magda_Skipper
A few more tweets will soon be added.
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- This document was started on May 25, 2021
by copying key parts of Redefinition, March 2018.
- First posted for collaborations: May 25, 2021
- It also became a homepage: May 25, 2021
- The URL: https://81018.com/envision/
- The Prior Homepage: https://81018.com/starts/
- First Headline: Redefine Space, Time And Infinity!
- First Tagline: Envision the universe: What concepts are key?
- Possibly the next homepage: https://81018.com/tredecillion Password: Tredecillion
- The most recent update of this page: June 4, 2021