# Gauss, one of the great mathematicians of history (an emerging document)

Johann Carl Friedrich Gauss: In 1587 the most efficient stacking of cannonballs was addressed by Thomas Harriot and then in 1611 by Johannes Kepler. It took over 200 years before Johann Carl Friedrich Gauss actually started to prove these conjectures and about another 200 years before the conjectures were more formally proven by Thomas Hales (website) and his people (2014). This question about density had become a key mathematical challenge, deemed by David Hilbert in 1900 to be the eighteenth problem; there appears to be no references to the size of the spheres. For example, I would ask, “Is it possible to have a sphere the size of the Planck Length?” Given the ineffable work of pi, I would argue, “Yes,” and begin sphere stacking at the Planck scale.

Fourier series, transform: The goal here is to bring everyday physics and mathematics to bear to grasp the foundations of our universe so there is nothing esoteric or extra-logical about it. How very satisfying it will be if key mathematicians throughout our history, people like J. Kepler, C.F.Gauss, T.C. Hales (cubic-close packing),  Poincaré-Feigenbam (period doubling bifurcation), and Fourier-Dirac-Strogatz (Fourier transform), are responsible for the concepts that describe and predict the behaviors of our infinitesimal universe.

Cubic close packingOur knowledge of cubic close packing goes back to Thomas Harriot (circa 1587), Johannes Kepler (circa 1611),  and Johann Carl Friedrich Gauss (circa 1801). More recently, through the work of Thomas Hales (1998, 2014), we learned that these scholars were each proven to have calculated a very good approximation of sphere-packed densities . Also, notably, in the 2010 Wikipedia’s summaries of this discipline inspired a programmer to create a simple, but highly-informative simulation of sphere stacking.1

Path integrals and Gaussian fixed point. See Assaf Shomer’s on page 7: “The derivation of the path integral formula in quantum mechanics of a massive particle involves chopping up the quantum evolution into very short time intervals and inserting complete sets of states between them.”

http://slideplayer.com/slide/4427954/ Physics 213: Gauss

In the letter, Langlands described a way to extend some of Carl Friedrich Gauss’ pioneering work on prime numbers. Number theorists before Gauss had noticed a hidden relationship among primes: that all the primes that can be formulated as the sum of two squares (for instance, 2^2 + 1^2 = 5 or 3^2+2^2 = 13) have a remainder of 1 when divided by 4, but didn’t know if it held true in all cases Quanta magazine reported. Gauss proved this idea in what’s now known as the quadratic reciprocity law.

Langlands took Gauss’ work and showed that the prime numbers that can be expressed as the sum of numbers raised to the third or fourth power (such as 1^3+2^3+4^3=73) can be tied to the distant mathematical realm of harmonic analysis. (This kind of analysis includes Fourier transforms, a mainstay tool used by scientists and engineers to analyze signals that have a periodic nature, such as sound waves or electromagnetic radiation spectra.)

November 2018 (update):  “Generate n points at random in d-dimensions where each coordinate is a zero mean, unit variance Gaussian.” from Foundations of Data Science, 2.1 page 12

# Pi (π) is the concrescence of continuity, symmetry and harmony.

## Pi (π), a key way to infinity

by Bruce E. Camber

Background: No other mathematical symbol is recognized with its very own celebration and holiday. In 1988 the Exploratorium, a San Francisco museum, celebrated “Pi Day” and set a precedent for eating pies and pizza decorated with pi’s symbol and endless numbers. An historic moment, in 2009 that day was recognized as a national holiday in the USA. In November 2019 Pi Day was adopted by the United Nations (UNESCO) as the International Day of Mathematics.* The day is becoming more of a general celebration of the extraordinary power of mathematics in our lives. More detailed studies of pi|(π) are taking a backseat. This posting is a simple precaution… Pi (π) is more powerful than we think. Hidden within that ratio of the circumference of a circle to its diameter is the keyway to the universe and infinity..BEC

Key words: Pi (π), Pi Day, International Day of Mathematics, continuity, symmetry, harmony, quantum fluctuations, 539 tredecillion spheres per second, everything-everywhere-for-all-time, sphere-stacking, and cubic-close packing of equal spheres

We should not lose focus of our studies of the very nature of pi (π) especially her perfections that reveal a deeper essence of this ubiquitous equation.

Pi(π) is the concrescence of continuity, symmetry, and harmony from which all circles and spheres evolve. That opens key points to explore further:

Perfect functions of the circle and sphere: Continuity is the never-ending, never-repeating numbers of pi. Symmetry is a seemingly magical, deeper nature within those numbers that become relations which become perfect circles and spheres. And, harmony is an even deeper dynamic nature of the sphere. First explored in 1820 by Joseph Fourier, his work reveals a basic harmony of every sphere.

If taken as a whole, continuity-symmetry-harmony are a finite-infinite transformation point, a perfection, and an expression of both the finite and infinite. Our ongoing studies of the finite-infinite relation are here.

Our scholars continue to build on Fourier’s insights. Visit with Poincaré, Gauss, Planck, Einstein, Smale, Milnor and others who have uncovered even more exacting relations with pi. Continuity defines time; symmetry defines space, and harmony defines the dynamics of space-time.

Perfected states within space-time. The Planck base units were defined by Max Planck in 1899 using dimensionless constants which render natural units and a vision and definition of the smallest possible units of space and time. Logic tells us that the smallest are also the first, the most-simple starting points. At the bottom of the graphic on your right there is Planck Time and Planck Length where the first infinitesimal-and-perfect spheres emerge. An expansion rate, one sphere per unit of Planck Time and Planck Length, is hypothesized.

If so, 539 tredecillion spheres per second are generated. Base-2 notation is applied to investigate basic relations. The result is 202 notations (or doublings) to explore that encapsulate the universe.

The numbers are time stamped with sphere-stacking.

Cubic-close packing of equal spheres further geometrizes each number. In the first notations, there is an absence of gaps. The basic geometries all fit perfectly.

By studying Aristotle’s mistake with tetrahedrons, we learn about basic geometric gaps. Associated with quantum fluctuations, it is hypothesized that these do not manifest until at least Notation-50.

Langlands programs and string theory are further defined.

Then the known equations that define our foundations begin to emerge. By the 202nd notation, the universe as we know it — everything, everywhere for all time — is encapsulated and all intimately connected by infinitesimal spheres that are many orders of magnitude smaller than the elusive neutrino (of which about 100 trillion pass through our bodies every second according to the Smithsonian).

All 202 notations are always active. Some scholar-scientists say “all time is now.” Each notation adds definition. As we go down the scale, there is increased particularity and coherence. The only possible singularity is at the very beginning, and even then, it is a convergence of equations. Exacting definitions of the infinitesimally small evolve, first through sets, then groups, and then obviously working systems that involve all 202 notations.

Logically there is a domain with no gaps. Perfectly-fitting geometries are hypothesized to come prior to the possible emergence of quantum fluctuations.[2]

Values. These perfectly-fitting geometries might account for the first 50 notations where the continuity-symmetry-harmony of the spheres where the extreme densities create no gaps and this becomes the basis for values.

If this were to become a new platform for mathematics, the world would change because mathematics would be pushing us to explore the meaning and value of life as expressions of continuity, symmetry and harmony.

The positions and functions of infinitesimal spheres, especially the generation and labelling of every sphere after the first, would be the beginning of a new paradigm for the sciences. We would begin to recognize the tools to fill in the gaps between the Planck Scale and the Electroweak Scale (and between the Lambda Cold Dark Matter model or the Standard Model for Cosmology and the Standard Model for Particle Physics). Yet, it all begs the question, “What is the role of light within each notation? Is it what holds it all together (as in e=mc2)? Is it the deepest part of continuity- symmetry-harmony? Is it the beginning of values and ethics?

None of those questions are beyond our imaginations and our capabilities to answer. Thank you.

____________________________________________________________

Endnotes & Footnotes
All these points already have pages within this website.

[*] Einstein’s birthday and the day of Hawking’s death. Many historians mention that the day, March 14, has unusual symbolic meaning. Two of the most influential people of our time seem to be pointing at pi (π) as if saying, “Pi (π) is a key.”

[1] Pointing beyond circles and spheres. Between the finite-infinite transformation and between the faces of continuity-symmetry-harmony (CSH) are equations. Many equations converge within the numbers that make up the Planck base units. Although there are alternatives to the Planck numbers (Stoney, Ralston, and ISO numbers), Planck’s have become a standard. Eventually we will probably be using new ISO base units, yet the results will be very similar. The convergence of equations is the point. It is the necessary convergence of the finite-infinite. It also appears to be the beginning of values and even our sense of ethics.

Bringing the infinite into the equation is difficult for many. Within this website, you will find this declaration:

All other definitions of the infinite are put on hold. Most are personal definitions that come from personal experiences and family history. That is one’s own business, not ours. If those beliefs help you through life, that is great. Our goal here is to engage those principles and functions that give rise to mathematics, physics, and eventually all the other sciences.

from Continuity-Symmetry-Harmony (CSH), 1972

CSH is the infinite and the finite. Its first expression as the finite is the Planck base units. The first expression of those units is an infinitesimal sphere. This is an unprecedented definition of the finite-infinite relation. Doing a simple calculation with Planck Time, assuming one sphere per unit of Planck Time, renders 539 tredecillion spheres per second. That may well be considered a new definition of the cosmological constant. To begin to grasp that natural expansion, apply base-2 notation and the first second, manifests within Notation-143. The first year manifests within Notation-169. The first 1000 years manifest are within Notation-179. The first million years manifest within Notation-189 and the first billion years within Notation-199.

These 202 base-2 notations functionally outline the universe; having been studied within and throughout this website, there’s more: https://81018.com/inflaton/#202

Fourier transform. Every formula that involves pi (starting with the Fourier transform) needs to be re-reviewed in light of CSH and the 202 base-2 notations. Pi is everywhere.

[2] Geometries of indeterminacy. There is a look and feel of quantum fluctuations; the mysteries appear to be within all the geometries. Perhaps scholars were first foiled by Aristotle (384-321 BC). Five tetrahedrons create a gap that he missed; and for 1800 years that mistake was repeated by scholars. It is worth pondering. Aristotle was so great it took 1800 years to countermand his mistake. And, it is still untouchable. That correction was eventually forgotten until in 1926, a little-known MIT mathematician, Dirk Struik, rekindled the scholarship. Struik’s work did not receive much attention until in 2012 when two scholars, Jeffrey Lagarias and Chaunming Zong, lifted it up again. Yet, these two mathematicians were more interested in packing densities. There is no exploration of the meaning of the gap. Subsequently, in May 2022, a five octrahedral-gap was first introduced to the world from within this website and questions were asked of many scholars, “What are these gaps all about?”

Our charts, interpretations and prognostications. Simple logic, simple math, and simple geometries render our charts, interpretations and prognostications. It all awaits critical review, so until then, there will be more to come.

Review and summary of at least ten new ways to look at pi:

1. A closer-look at Continuity-Symmetry-Harmony
2. Pi, the primary clue about the Finite-infinite relation
3. Planck’s base units defining the most infinitesimal spheres
4. No less than seven new perspectives: Fourier, PoincaréGaussEinsteinSmaleMilnor and many others
5. 539 tredecillion infinitesimal spheres per second
6. Sphere-stacking
7. Cubic-close packing of equal spheres
8. Infinitesimal spheres populating the universe and making everything-everywhere-for-all-time
9. Responsible for the first fluctuation and the geometries of quantum fluctuations
10. 202 notations always active
11. Continuity-symmetry-harmony become a foundation for values.
12. Filling in the gaps between Planck Scale and the Electroweak Scale and between Lambda Cold Dark Matter model (or the Standard Model for Cosmology) and the Standard Model for Particle Physics

_____

References & Resources
As references are studied, these references and other resources will be updated.

Pi (π): Dimensional analysis, scale invariance, functional dependencies
Symmetry in QFT and Gravity (video), Hirosi Ooguri (homepage) and Nathan Seiber), 2022
Mathematically, equations building on natural functional dependencies:
….–  Using math in physics: 5. Functional dependence (PDF), E. F. Redish, Univ. Maryland, 2022
•  ESA Group (PDF): The universe at 380,000 years
https://www.esa.int/Our_Activities/Space_Science/Planck/Planck_reveals_an_almost_perfect_Universe,2009
•  Pure Natural Inflation, Yasunori Nomura, Taizan Watari, and Masahito Yamazaki,
Berkeley Center for Theoretical Physics, Department of Physics, 2017
The Friedmann–Lemaître–Robertson–Walker (FLRW) Metric
•  Scale invariance, conformal symmetries, and asymptotic freedom.

Of the 202 notations, the first 64 notations open a new map to make the deeper connections. There’ll be a place for the some of the big bang numbers but not until after the first few seconds (Notation-143 and higher).

Thrust in our universe. In September 2017, I wrote about the thrust in our universe. So now, over five years later, it is time to revisit that article and update it as much as possible. The major update would involve our understanding more about the three facets of pi and how each is a Janus-face for the finite and the infinite. How are the functions of continuity-symmetry-harmony abiding?

Major studies. I have written to Robert Langlands, Ed Frenkel, and others within Langlands programs. They have not yet acknowledged the 202 mathematical notations. Why not? It’s just math and logic. There is no philosophy. There are no agendas. It is what it is, simple math.

I have also written to people within string theory. None have acknowledged the 202 notations.

I believe people are naturally incrementalists. It is more comfortable. The Planck units were ostensibly ignored until 2001 and by that time Hawking-Guth-and-family had a hold on the theory about the start of the universe. With Hawking’s death, that hold has become somewhat more relaxed. With results from the James Webb Space Telescope (JWST), it’s time to open up the discussions. It will include conformal-quantum-and-scalar field theories (CFT, QFT). Although John Wheeler’s sense of simplicity is a good idea, for most of the octogenarians and nonagenarians, this base-2 model of 202 notations is just too simple. It is too obvious. Yet, maybe not. Prior to Frank Wilczek’s three articles about the Planck scale, Planck’s numbers were aloofly small much like Paul Dirac’s were aloofly big.

#

In 1980 in Paris at the Institut Henri Poincaré, Jean-Pierre Vigier and I made a six-month study of the EPR paradox in light of the work of Alain Aspect in d’Orsay. Instead of infinitesimal spheres, Vigier had suggested that we use the metaphor of dominos falling. That type of action-at-a-distance is not instantaneous. Infinitesimal spheres within the packing densities suggested by the Planck-or-Stoney-or-ISO numbers would be instantaneous. Also, in this period, an equal amount of time was spent with Olivier Costa de Beauregard.

Do the mathematics and physics of the finite begin here?

_____

Emails
There will be emails to many of our scholars about the key points.

29 March 2023: C.S. Unnikrishnan, DIAT (Pune)
26 March 2023: Christoph Sorger, IMU, University of Nantes
25 March 2023: Michael Spannowsky, Durham
25 March 2023: James Warren, NIST, DC
21 March 2023: CIMPA’s educators throughout the world
14 March 2023 Audrey Azoulay, UNESCO, Paris*
3 March 2023: David F. Robinson, Kings College (London)
2 March 2023: Steven Strogatz, Cornell
2 March 2023: Kevin Dykema, National Council of Teachers of Mathematics
2 March 2023, Pi Day Puzzle to many of those already contacted
1 March 2023, Edward F. Redish, Univ. of Maryland
25 February 2023, Anna Ijjas, NYU
25 February 2023, Katherine Freese, University of Texas, Austin

_____

Many instant messages to thought leaders.

3:49 PM · Mar 9, 2023 @TheAtlantic @marinakoren You won’t believe this history of the universe. https://81018.com/chart/ It’s too simple. Base-2 notation from the Planck scale: https://81018.com/stem/ Pi day celebrations shed some light, too. https://81018.com/continuity-symmetry-harmony/

7:46 AM · Mar 9, 2023 @TonomusNEOM Three levels of cognition: continuity, symmetry, harmony work together within pi and define the finite-infinite relation: https://81018.com opens that door. “Let’s pi… work together.”

9:22 AM · Mar 4, 2023 @DrOsamaSiddique @Harvard_Law @UniofOxford @IGLP_HarvardLaw Natural law can be found within the fundamentals of pi (π): https://81018.com/continuity-symmetry-harmony/ The relation becomes the primary real. Editor’s note, also see: https://81018.com/values/ https://81018.com/oxford/ https://81018.com/harvard/

4:00 PM · Mar 2, 2023 @RushHolt Pi Day is coming up on March 14. I think we’ve underestimated the importance and place of pi (π): https://81018.com/

1. Is it possible that the first instance of the universe is defined by Planck’s base units?
2. Is it possible that the first manifestation of those base units is an infinitesimal sphere?
3. Might the characteristics of pi describe those spheres?
4. Might the Fourier Transform impart either electromagnetism or gravitation to each sphere?
5. Is it possible that one sphere manifests per unit of length and time?
6. Doesn’t that compute to 539 tredecillion spheres per second using Planck units and 4605 tredecillion per second using Stoney Time?
7. Is it possible that the densities within the earliest notations are on the order of a blackhole or neutron star?
8. To create some sense of order with the generation of infinitesimal spheres, may we use base-2 notation?
9. Using base-2 notation, are there 202 base-2 notations from Planck Time to the current time?
10. Is it significant that at one second the Planck Length multiple is a very close approximation of the distance light travels?
11. Is it significant that quantum fluctuations are measured within Notation-67? Notation-72 appears to be the limit of our abilities to measure a duration of time.
12. Would these notations, 1-64, provide 64 possible redefinitions of a point-particle? (And, I would add a vertex.)

_____

Editor’s Note: Putin’s Heart and Mind.All people who instigate violence against another have not learned the basics about life. Arrogance and crudeness block paths for light and understanding. UNESCO is about shining light wherever there is a problem in the world. They need to illuminate Vladimir Putin’s heart and mind. They can reach him. He is ill and facing death; he just may be receptive to their words about education,

_____

• This page became a working homepage at 8 AM on March 2, 2023.
• The last update was March 21, 2023.
• This page was initiated on February 24, 2023 at 7 AM.
• The URL for this file: https://81018.com/continuity-symmetry-harmony/
• A headline: A Global Celebration of Mathematics
. . Sub-header and link: Our Call to Expand Our Understanding of Pi (π) for Pi Day 2023
• First byline: Pi Day points us beyond circles and spheres.

____

# For immediate release:

Introduction: A working draft of the press release — https://81018.com/pointing/ — was first written for academics then it was toned down to become a general press release and its purpose was greatly expanded. A goal is to have several versions of that article, each weighted for particular audiences. The next audience to reach are the online-broadcast-printed news outlets so they run a press release a few days after March 14. That version will be emerge here, then a new release of 500 words will be done. The goal is to stir people to talk about entirely new dimensions of pi.

A new version for academics with the benefit of feedback will be done.

This press release may be run anywhere in the world on any publication, news broadcast, or website. It may also be re-written to eliminate footnotes.

For immediate release:
Center for Perfection Studies, Austin, Texas. Contact: Bruce E. Camber

Background: Bruce Camber, the Managing Director of the Center for Perfection Studies in Austin, Texas, has been critical of most Pi Day celebrations. He has advocated that Pi Day be addressed by further considering the three functions that define it: continuity, symmetry, and harmony. “A core part of science is to define its functional dependencies; yet dimensional analysis starting at the Planck base units and extending through to electroweak scale has been virtually ignored. It’s an Achilles Heel for science and humanity.”

In 2016 the Center Perfection Studies did the first mathematical map of the universe that starts with the Planck base units and goes to the current time. It is a base-2 map with 202 notations. In 1957 Kees Boeke did a base-10 map of much of the universe that captured the widespread attention (credits within films, Cosmic Zoom, National Film Board of Canada, 1968; Powers of Ten, Charles and Ray Eames, 1968; and Cosmic Voyage, IMAX  and Smithsonian National Air & Space Museum, 1996).

“The difference between base2 and base-10 is that our base-2 map encourages scholars to look for the functional dependencies,” Camber went on, “There is causal efficacy between notations. Dimensional analysis is a key.”

History: In 1988 Larry Shaw of the San Francisco science museum, Exploratorium, started the first known Pi Day celebration. By 2009 Pi Day was recognized as a national holiday in the USA. In November 2019 UNESCO adopted Pi Day as the International Day of Mathematics. The challenge each year is to do something significant on that day and progress beyond pie-eating contests and the recitation of some part of the 100-trillion known digits of pi (calculated using Google Cloud in 2022 by Emma Haruka Iwao).

The Center for Perfection Studies believes that Pi Day could be a rapprochement to explore the first principles of pi and to better define the very nature of pi. That it has real potential to define common foundations that could bring people together. heretofore has not been explored. The Center is seeking to partner with UNESCO (emails to Audrey Azoulay, Director-General, and David Atchoarena, Director, UNESCO Institute for Lifelong Learning, Hamburg, Germany) to make Pi Day a true International Day of Mathematics.  The center’s most simple math — multiplying by 2 — encapsulates the universe within just 202 notations (https://81018.com/chart/).

In the center’s study, pi (π) is defined by continuity, symmetry, and harmony. Circles and spheres are derivative. There are no less than ten key points that they ask people to consider:

• Three perfect functions have not taken together as a functional whole. Continuity is the never-ending, never-repeating numbers of pi. Symmetry is the deeper nature within those numbers that become relations which become circles and spheres. And, harmony is an even deeper dynamic nature of the sphere that was first opened in 1820 by Joseph Fourier. A most simple harmony is found within every sphere. p;
• Taken as a whole, continuity-symmetry-harmony are both finite and infinite.
• Our scholars continue to build on Fourier’s insights. Visit with Poincaré, Gauss, Planck, Einstein, Smale, Milnor and many others who uncovered even more exacting relations with pi. Yet, at its core, continuity defines time; symmetry defines space, and harmony defines the dynamics of space-time.
• Perfected states within space-time. The Planck base units defined by Max Planck in 1899 use dimensionless constants which render natural units and a vision and definition of the smallest possible units of space and time. Simple logic holds the smallest are also the first, the starting points of our universe.At the bottom of the graphic on your right there is Planck Time and Planck Length where the first infinitesimal-and-perfect spheres emerge. Using Planck’s numbers, one sphere per unit of Planck Time and Planck Length is logically defined. There are just 202 doublings to explore to encapsulate the known universe. These numbers keep the score.
• At that rate, 539 tredecillion spheres per second are generated.
• Those numbers are timestamped with sphere-stacking.
• Then the numbers are geometrize with cubic-close packing of equal spheres. In the first notations, there is an absence of gaps. The basic geometries all fit perfectly. It is hypothesized that quantum fluctuations cannot manifest until at least Notation-50.
• Langlands programs and string theory are further defined with pi.
• Then the known equations that define our foundations emerge. By the 202nd notation, we have our universe, everything, everywhere for all time, all intimately connected by infinitesimal spheres.
• All 202 notations are always active. Many scientists say “all time is now.” Each notation adds definition. As we go down the scale, there is increased particularity and coherence. The only possible singularity is in the very beginning, and even then, it is a convergence of equations. Exacting definitions of the infinitesimally small, first start within groups, and then obviously become part of a working system that involves all 202 notations.
• Logically there is a domain with no gaps. Perfectly fitting geometries exists prior to the emergence of quantum fluctuations.[2]
• Values. Those perfectly-fitting geometries may possibly account for the first 50 notations where the continuity-symmetry-harmony of the spheres creates no gaps and becomes the basis for value.

Camber concludes, “With all this as a platform, Pi Day could be turned in to an extraordinary International Day of Mathematics. It could become an exploration of the positions and functions of infinitesimal spheres, particularly the generation and labelling of every sphere after the very first. And, it just might begin to fill in the gaps between the Planck Scale and the Electroweak Scale as well as between the Lambda Cold Dark Matter model (or the Standard Model for Cosmology) and the Standard Model for Particle Physics.”

“It is not beyond our imaginations and our capabilities. Thank you.”

____________________________________________________________

Endnotes & Footnotes & Graphics
These points already have pages within this website.

[1] Pointing beyond circles and spheres. Between the finite-infinite transformation and between the faces of continuity-symmetry-harmony (CSH) are equations. Many equations converge within the numbers that make up the Planck base units. Although there are alternatives to the Planck numbers (StoneyRalston, and ISO numbers), they’ll use the same dynamics (and equations). Eventually we will probably be using new ISO base units, yet I expect the results will be very similar. That convergence of equations is the point. It is the necessary convergence of the finite-infinite. It’s also the beginning of value.

Bringing the infinite into the equation is difficult for many. Within this website, you will find this declaration:

All other definitions of the infinite are put on hold. Most are personal definitions that come from personal experiences and family history. That is one’s own business, not ours. If those beliefs help you through life, that is great. Our goal here is to engage those principles and functions that give rise to mathematics, physics, and eventually all the other sciences.from Continuity-Symmetry-Harmony (CSH), 1972

CSH is the infinite and the finite. Its first expression as the finite is the Planck base units. The first expression of those units is an infinitesimal sphere. This is an unprecedented definition of the finite-infinite relation. Doing a simple calculation with Planck Time, assuming one sphere per unit of Planck Time, renders 539 tredecillion spheres per second. That could be considered a new definition of the cosmological constant. To begin to grasp that natural expansion, we apply base-2 notation and the first second, manifests within Notation-143. The first year manifests within Notation-169. The first 1000 years manifest within Notation-179. The first million years manifest within Notation-189 and the first billion years within Notation-199.

The only place where these 202 base-2 notations that functionally outline the universe have been studied is within and throughout this website. For more: https://81018.com/inflaton/#202

Fourier transform. Every formula that involves pi (starting with the Fourier transform) needs to be re-reviewed in light of CSH and the 202 base-2 notations. Pi is everywhere.

[2] Geometries of indeterminacy. There is a look and feel of quantum fluctuations; the mysteries are all within the geometries. It appears that scholars were first foiled by Aristotle (384-321 BC). Five tetrahedrons create a gap that he missed; and for 1800 years his mistake was repeated by scholars. That is worth pondering. Aristotle was so great it took 1800 years to countermand his mistake. And, it is still untouchable. That correction was eventually forgotten until in 1926, a little-known MIT mathematician, Dirk Struik, rekindled that scholarship. Struik’s work did not receive much attention until in 2012 when two scholars, Jeffrey Lagarias and Chaunming Zong, lifted it up again. Yet, these two mathematicians were more interested in packing densities. There is no exploration of the meaning of the gap. Subsequently, in May 2022, a five octrahedral-gap was first introduced to the world from within this website and questions were asked of many scholars, “What are these gaps all about?”

Our charts, interpretations and prognostications. Simple logic, simple math, and simple geometries render our charts, interpretations and prognostications. It all awaits critical review, so until then, there will be more to come.

A Review-Summary of least ten new ways to look at Pi Day in this universe:

1. A celebration of Continuity-Symmetry-Harmony
2. Pi is the primary clue about the Finite-infinite relation
3. No less than seven new perspectives: FourierPoincaréGaussMilnor and many others
4. Planck’s base units begin to define those infinitesimal spheres.
5. 539 tredecillion infinitesimal spheres per second
6. Sphere-stacking
7. Cubic-close packing of equal spheres
8. Infinitesimal spheres make everything, everywhere, for all time yet start with Langlands programs and string theory.
9. All the known equations that define our foundations emerge.
10. 202 notations encapsulate our universe, all defined by pi.
11. A domain with no gaps, then comes the first fluctuation and the geometries of quantum fluctuations
12. A foundation for values
13. Filling in the gaps between Planck Scale and the Electroweak Scale and between Lambda Cold Dark Matter model (or the Standard Model for Cosmology) and the Standard Model for Particle Physics
• Audrey Azoulay, Director-General, UNESCO (speeches, 2023) (in Iraq) “Mathematics, with its many technical applications, now underpins all areas of our lives. Together with algorithms, mathematics plays a key role in artificial intelligence and technological disruptions – and, as we address global issues such as the COVID-19 pandemic and climate change, we are reminded of the importance of mathematics in responding to the challenges of our time.”
• Hiraku Nakajima, Secretary General of the International Mathematical Union, Hausvogteiplatz 11A, D-10117 Berlin, Germany
• Andreas Matt, Managing Director of IMAGINARY and of the IDM
• Christiane Rousseau, Chair of the IDM Governing Board
• Djamel Eddine Cheriet, Vice-President of the Algerian Mathematical Society,
• National Institute for Mathematical Sciences, Korea
• European Mathematical Society
• Helge Holden, former secretary-general of the International Mathematical Union

###

# Pi points well beyond circles and spheres.

by Bruce E. Camber

History: The first Pi Day celebration was in 1988 (San Francisco science museum, Exploratorium). By 2009 it was recognized as a national holiday (USA). And, by November 2019 Pi Day was adopted by the United Nations, particularly UNESCO, as the International Day of Mathematics.

What had been a focus on pie-eating and reciting some part of the 100-trillion known digits of pi (π) is increasingly becoming a celebration of the power of mathematics in our lives. However, we shouldn’t lose focus of our studies of the very nature of pi (π) especially her perfections that reveal a deeper essence and purpose of this ubiquitous equation.

Pi (π) is the continuity, symmetry, and harmony from which all circles and spheres evolve. That statement opens at least ten key points to explore:

• Three perfect functions. These are currently not taken together as a whole and with their functional dependencies: Continuity is the never-ending, never-repeating numbers of pi. Symmetry is a deeper nature within those numbers that become relations which become circles and spheres. And, harmony is an even deeper dynamic nature of the sphere, first explored in 1820 by Joseph Fourier. He revealed a most simple harmony can be found within every sphere.
• Taken as a whole, continuity-symmetry-harmony are finite and infinite. Some may want to say that it is an expression of both the finite and infinite. Our summaries of documents regarding infinity
• Our scholars continue to build on Fourier’s insights. Visit with Poincaré, Gauss, Planck, Einstein, Smale, Milnor and others who have uncovered even more exacting relations with pi. Yet, at its core, continuity defines time; symmetry defines space, and harmony defines the dynamics of space-time.
• Perfected states within space-time. The Planck base units defined by Max Planck in 1899 use dimensionless constants which render natural units and a vision and definition of the smallest possible units of space and time. Simple logic says that the smallest are also the first, the most-simple starting points. At the bottom of the graphic on your right there is Planck Time and Planck Length where the first infinitesimal-and-perfect spheres emerge. Could one sphere per unit of Planck Time and Planck Length define a rate of expansion?
• If so, 539 tredecillion spheres per second are generated. To grasp some order, apply base-2 notation. The result is 202 notations (or doublings) to explore that encapsulate the known universe. These are the numbers that keep the score for something. What?
• Those numbers are timestamped with sphere-stacking.
• Then the numbers are geometrized with cubic-close packing of equal spheres. In the first notations, there is an absence of gaps. The basic geometries all fit perfectly. By following Aristotle’s mistake with tetrahedrons, we learn about basic geometric gaps. Associated with quantum fluctuations, it is hypothesized that these do not manifest until at least Notation-50.
• Langlands programs and string theory are further defined.
• Then the known equations that define our foundations begin to emerge. By the 202nd notation, we have our universe, everything, everywhere for all time, all intimately connected by infinitesimal spheres.
• All 202 notations are always active. Many scientists say “all time is now.” Each notation adds definition. As we go down the scale, there is increased particularity and coherence. The only possible singularity is at the very beginning, and even then, it is a convergence of equations. Exacting definitions of the infinitesimally small evolve, first through sets, then groups, and then obviously working systems that involve all 202 notations.
• Logically there is a domain with no gaps. Perfectly fitting geometries exist prior to the emergence of quantum fluctuations.[2] Notations 0-to-50 have been proposed.
• Values. Those perfectly-fitting geometries may possibly account for the first 50 notations where the continuity-symmetry-harmony of the spheres creates no gaps and this could be the basis for values.

If this were to become a new platform, UNESCO could change the world through mathematics by having us all truly begin to explore the positions and functions of infinitesimal spheres, especially the generation and labelling of every sphere after the first. Perhaps we will begin to fill in the gaps between the Planck Scale and the Electroweak Scale as well as between the Lambda Cold Dark Matter model (or the Standard Model for Cosmology) and the Standard Model for Particle Physics. Yet, it all begs the question, “What is the role of light within each notation? Is it what holds it all together (as in e=mc2)? Is it the deepest part of continuity- symmetry-harmony? Is it the beginning of values, ethics, and even love-versus-hate?

None of those questions are beyond our imaginations and our capabilities. Thank you.

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Endnotes & Footnotes
All these points already have pages within this website.

[1] Pointing beyond circles and spheres. Between the finite-infinite transformation and between the faces of continuity-symmetry-harmony (CSH) are equations. Many equations converge within the numbers that make up the Planck base units. Although there are alternatives to the Planck numbers (Stoney, Ralston, and ISO numbers), Planck’s have become a standard. Eventually we will probably be using new ISO base units, yet I’ll suggest the results will be very similar. The convergence of equations is the point. It is the necessary convergence of the finite-infinite. It also appears to be the beginning of values and even our sense of ethics.

Bringing the infinite into the equation is difficult for many. Within this website, you will find this declaration:

All other definitions of the infinite are put on hold. Most are personal definitions that come from personal experiences and family history. That is one’s own business, not ours. If those beliefs help you through life, that is great. Our goal here is to engage those principles and functions that give rise to mathematics, physics, and eventually all the other sciences.

from Continuity-Symmetry-Harmony (CSH), 1972

CSH is the infinite and the finite. Its first expression as the finite is the Planck base units. The first expression of those units is an infinitesimal sphere. This is an unprecedented definition of the finite-infinite relation. Doing a simple calculation with Planck Time, assuming one sphere per unit of Planck Time, renders 539 tredecillion spheres per second. That may well be considered a new definition of the cosmological constant. To begin to grasp that natural expansion, we apply base-2 notation and the first second, manifests within Notation-143. The first year manifests within Notation-169. The first 1000 years manifest within Notation-179. The first million years manifest within Notation-189 and the first billion years within Notation-199.

These 202 base-2 notations functionally outline the universe have been studied within and throughout this website. For more: https://81018.com/inflaton/#202

Fourier transform. Every formula that involves pi (starting with the Fourier transform) needs to be re-reviewed in light of CSH and the 202 base-2 notations. Pi is everywhere.

[2] Geometries of indeterminacy. There is a look and feel of quantum fluctuations; the mysteries appear to be within all the geometries. Perhaps scholars were first foiled by Aristotle (384-321 BC). Five tetrahedrons create a gap that he missed; and for 1800 years that mistake was repeated by scholars. It is worth pondering. Aristotle was so great it took 1800 years to countermand his mistake. And, it is still untouchable. That correction was eventually forgotten until in 1926, a little-known MIT mathematician, Dirk Struik, rekindled the scholarship. Struik’s work did not receive much attention until in 2012 when two scholars, Jeffrey Lagarias and Chaunming Zong, lifted it up again. Yet, these two mathematicians were more interested in packing densities. There is no exploration of the meaning of the gap. Subsequently, in May 2022, a five octrahedral-gap was first introduced to the world from within this website and questions were asked of many scholars, “What are these gaps all about?”

Our charts, interpretations and prognostications. Simple logic, simple math, and simple geometries render our charts, interpretations and prognostications. It all awaits critical review, so until then, there will be more to come.

Review and summary of at least ten new ways to look at pi:

1. A celebration of Continuity-Symmetry-Harmony
2. Pi as the primary clue about the Finite-infinite relation
3. Planck’s base units defining the most infinitesimal spheres
4. No less than seven new perspectives: FourierPoincaréGaussEinsteinSmaleMilnor and many others
5. 539 tredecillion infinitesimal spheres per second
6. Sphere-stacking
7. Cubic-close packing of equal spheres
8. Infinitesimal spheres populating the universe and making everything, everywhere, for all time
9. Responsible for the first fluctuation and the geometries of quantum fluctuations
10. 202 notations always active
11. Continuity-symmetry-harmony become a foundation for values.
12. Filling in the gaps between Planck Scale and the Electroweak Scale and between Lambda Cold Dark Matter model (or the Standard Model for Cosmology) and the Standard Model for Particle Physics

Please note for March 2023: Work continues, yet a new homepage has been started. The sections below, also used in prior homepages, may also be reworked.

Thank you. -BEC

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References & Resources
As references are studied, these references and other resources will be updated.

Pi (π): Dimensional analysis, scale invariance, functional dependencies
Symmetry in QFT and Gravity (video), Hirosi Ooguri (homepage) and Nathan Seiber), 2022
Mathematically, equations building on natural functional dependencies:
….–  Using math in physics: 5. Functional dependence (PDF), E. F. Redish, Univ. Maryland, 2022
•  Quantum Energy Inequalities along stationary worldlines,
Christopher J. FewsterJacob Thompson, 4 Jan 2023
•  ESA Group (PDF): The universe at 380,000 years
https://www.esa.int/Our_Activities/Space_Science/Planck/Planck_reveals_an_almost_perfect_Universe,2009
•  Pure Natural Inflation, Yasunori Nomura, Taizan Watari, and Masahito Yamazaki,
Berkeley Center for Theoretical Physics, Department of Physics, 2017
The Friedmann–Lemaître–Robertson–Walker (FLRW) Metric
•  A pedagogical explanation for the non-renormalizability of gravity, (PDF), Assaf Shomer, 2008.
Path integrals and Gaussian fixed point. See Assaf Shomer’s on page 7:
“The derivation of the path integral formula in quantum mechanics of a massive particle involves chopping up the quantum evolution into very short time intervals and inserting complete sets of states between them.”
•  Doplicher S, Fredenhagen K, Roberts JE (1995) The quantum structure of spacetime at the Planck scale and quantum fields. Communications in Mathematical Physics 172(1):187–220
•  Scale invariance and conformal symmetries

Of the 202 notations, the first 64 notations open a new map to make the deeper connections. There’ll be a place for the some of the big bang numbers but not until after the first few seconds (Notation-143 and higher).

Thrust in our universe. In September 2017, I wrote about the thrust in our universe. So now, over five years later, it is time to revisit that article and update it as much as possible. The major update would involve our understanding more about the three facets of pi and how each is a Janus-face for the finite and the infinite. How are the functions of continuity-symmetry-harmony abiding?

Major studies. I have written to Robert Langlands, Ed Frenkel, and others within Langlands programs. They have not yet acknowledged the 202 mathematical notations. Why not? It’s just math and logic. There is no philosophy. There are no agendas. It is what it is, simple math.

I have also written to people within string theory. None have acknowledged the 202 notations.

I believe people are naturally incrementalists. It is more comfortable. The Planck units were ostensibly ignored until 2001 and by that time Hawking-Guth-and-family had a hold on the theory about the start of the universe. With Hawking’s death, that hold has become somewhat more relaxed. With results from the James Webb Space Telescope (JWST), it’s time to open up the discussions. It will include conformal-quantum-and-scalar field theories (CFT, QFT). Although John Wheeler’s sense of simplicity is a good idea, for most of the octogenarians and nonagenarians, this base-2 model of 202 notations is just too simple. It is too obvious. Yet, maybe not. Prior to Frank Wilczek’s three articles about the Planck scale, Planck’s numbers were aloofly small much like Paul Dirac’s were aloofly big.

#

In 1980 in Paris at the Institut Henri Poincaré, Jean-Pierre Vigier and I made a six-month study of the EPR paradox in light of the work of Alain Aspect in d’Orsay. Instead of infinitesimal spheres, Vigier had suggested that we use the metaphor of dominos falling. That type of action-at-a-distance is not instantaneous. Infinitesimal spheres within the packing densities suggested by the Planck-or-Stoney-or-ISO numbers would be instantaneous. Also, in this period, an equal amount of time was spent with Olivier Costa de Beauregard.

Do the mathematics and physics of the finite begin here?

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Emails
There will be emails to many of our scholars about the key points.

14 March 2023 Audrey Azoulay, UNESCO, Paris*
3 March 2023: David F. Robinson, Kings College (London)
2 March 2023: Steven Strogatz, Cornell
2 March 2023: Kevin Dykema, National Council of Teachers of Mathematics
2 March 2023, Pi Day Puzzle to many of those already contacted
1 March 2023, Edward F. Redish, Univ. of Maryland
25 February 2023, Anna Ijjas, NYU
25 February 2023, Katherine Freese, University of Texas, Austin

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Many instant messages to thought leaders.

3:49 PM · Mar 9, 2023 @TheAtlantic @marinakoren You won’t believe this history of the universe. https://81018.com/chart/ It’s too simple. Base-2 notation from the Planck scale: https://81018.com/stem/ Pi day celebrations shed some light, too. https://81018.com/pointing/

7:46 AM · Mar 9, 2023 @TonomusNEOM Three levels of cognition: continuity, symmetry, harmony work together within pi and define the finite-infinite relation: https://81018.com opens that door. “Let’s pi… work together.”

9:22 AM · Mar 4, 2023 @DrOsamaSiddique @Harvard_Law @UniofOxford @IGLP_HarvardLaw Natural law can be found within the fundamentals of pi (π): https://81018.com/pointing/ The relation becomes the primary real. Editor’s note, also see: https://81018.com/values/ https://81018.com/oxford/ https://81018.com/harvard/

4:00 PM · Mar 2, 2023 @RushHolt Pi Day is coming up on March 14. I think we’ve underestimated the importance and place of pi (π): https://81018.com/

1. Is it possible that the first instance of the universe is defined by Planck’s base units?
2. Is it possible that the first manifestation of those base units is an infinitesimal sphere?
3. Might the characteristics of pi describe those spheres?
4. Might the Fourier Transform impart either electromagnetism or gravitation to each sphere?
5. Is it possible that one sphere manifests per unit of length and time?
6. Doesn’t that compute to 539 tredecillion spheres per second using Planck units and 4605 tredecillion per second using Stoney Time?
7. Is it possible that the densities within the earliest notations are on the order of a blackhole or neutron star?
8. To create some sense of order with the generation of infinitesimal spheres, may we use base-2 notation?
9. Using base-2 notation, are there 202 base-2 notations from Planck Time to the current time?
10. Is it significant that at one second the Planck Length multiple is a very close approximation of the distance light travels?
11. Is it significant that quantum fluctuations are measured within Notation-67? Notation-72 appears to be the limit of our abilities to measure a duration of time.
12. Would these notations, 1-64, provide 64 possible redefinitions of a point-particle? (And, I would add a vertex.)

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[*] Putin’s Heart and Mind: All people who instigate violence against another have not learned the basics about life. Arrogance and crudeness block paths for light and understanding. UNESCO is about shining light wherever there is a problem in the world. They need to illuminate Vladimir Putin’s heart and mind. They can reach him. He is ill and facing death; he just may be receptive to their words about education,

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• This page became a working homepage at 8 AM on March 2, 2023.
• The last update was March 20, 2023.
• This page was initiated on February 24, 2023 at 7 AM.
• The URL for this file: https://81018.com/pointing/
• The eventual headline: A Global Celebration of Mathematics
. . .Sub-header and link: Our Call to Expand Our Understanding of Pi (π) for Pi Day 2023
• First byline: 14 March 2023: Pi Day points us beyond circles and spheres.

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# Alan Guth’s inflationary theory redefined.*

CENTER FOR PERFECTION STUDIES: CONTINUITY•SYMMETRY•HARMONY March.2023
| | STEM | Up
|

Lemaître, Hawking, and Guth1 were the most pivotal thinkers to advance a big bang theory. Lemaître died in 1966 at the age of 71; and, Hawking died on Pi Day, March 14, 2018 at the age of 76. Alan Guth now stands alone, the last remaining prime mover, especially with his theory of inflation and its inflaton.

Given that dimensionless constants and their equations are most fundamental keys, we ask, “What ubiquitous, old equation touches the most points within science and mathematics?2 I.suggest that the answer directs us to the best equation to define the first space-time moment within.this universe. And, I believe that equation is pi.

It’s that simple. Notwithstanding, thoughtful work by many scholars has gone into defining inflation and its inflaton. All those insights still hold keys to the universe, just not the keys to the earliest instances of our universe. For those moments, the most-infinitesimal sphere should be a good redefinition of Guth’s inflaton.3

The equations immediately begin to evolve. Basic geometries emerge and continue to evolve for seconds-minutes-hours-days-a-year (and even years). At some key critical point, the definitions by Guth and his collaborators will begin to participate. To determine when will take some study because inflation is dynamically creating the laws of physics as infinitesimal spheres populate the universe.

There are several current disparities to determine an expansion rate so a range is provided. I suspect in reality there has always been a range. Using either the PlanckStoney-or-ISO base units, and by assuming one infinitesimal sphere per unit of PlanckTime, StoneyTime, or a new ISO basetime, there would be a range from around 539-to-4605 tredecillion spheres per second.4 Of course, these are the most infinitesimal spheres possible, at least 50-to-64 base-2 orders of magnitude smaller than the neutrino and are obviously a good candidate for dark energy and dark matter.

That range or rate of expansion, considered a new definition of a cosmological constant, expanding even today, right now, creates a penultimate grid, literally to include everything, everywhere for all time. There are just 202 base-2 notations that outline our universe from the smallest duration of time, doubling each step, to the current time, the Now.5 I believe here is the starting place for group theory, systems theory and at least nine major studies currently not on any grid!

The first infinitesimal sphere has been likened to Lemaître’s primeval atom and Guth’s inflaton. Both the primeval atom and the inflaton field have always been hypothetical. I.believe our very first infinitesimal sphere is a little less hypothetical. The universe has to start with something to create space-time. Yet, our simple postulation goes much further. It is difficult to conceive of a universe totally populated by such infinitesimal spheres. Notwithstanding, even this hypothetical penultimate grid warrants inspection.6

Finite-infinite transformations between the faces of continuity-symmetry-harmony (CSH)7 are assumed. Our focus is on the finite. Defined by CSH, it is the Fourier transform,8 and then configurations of the Poincaré sphere, Poincaré homology sphere, and any-and-all types of spheres as mathematics naturally extends to include each. Only when it becomes possible to “come out” mathematically, building on natural functional dependencies, do these infinitesimal spheres manifest. This would necessarily include studies by Smale and Milnor of spheres as attractors and repellers.

Those new to this site will quickly ask about indeterminacy and quantum physics. Over the years we have struggled with the geometries of indeterminacy.9 It’s a working challenge and very much part of the discussion. So, per usual, I ask, “Where have we gone wrong with our charts, interpretations and prognostications?”10

Thank you. Thanks indeed. -BEC

###

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Endnotes & Footnotes
All these points already have pages within this website.

[*] Alan Guth. With this footnote I have asked Alan Guth to consider a new thrust whereby his hypothetical inflaton (and even Frank Wilczek‘s hypothetical axion that Guth adopted) are redefined in the light of infinitesimal spheres and groups of infinitesimal spheres. I’ve proposed that that we first analyse the processes involved by organizing the data about spheres using a base-2 natural expansion. Every law of physics is derivative within a notation between 0 and 202. Base-2 exponentiation is the most-simple way to organize the numbers of spheres with a timestamp and to begin to grasp the unfolding functionalities of spheres and groups of spheres.

There are 202 base-2 notations. The horizontally-scrolled chart of 202 base-2 notations started in December 2011 with just Planck Length. That chart had somewhere around 202 notations. Not until 2016 when we mapped it with Planck Time did we have a more definitive stopping point: 13.79 to 13.81 billion years. The 201st doubling takes Planck Time, 5.391 16(13)×10-44 seconds, out to around 173,272,944,073,600,000 seconds or 5.4908 billion years. If we add up each notation up to the 201st notation, we are one PlanckTime unit shy of 10.98 billion years. Simple math tells us that around 2.8284 billion years has passed since the beginning of the 202nd notation (Calculation: 13.81 minus 10.9816 ≈ 2.8284). It is an important perspective. Our calculation for the UniverseClock helped us along this path. We are now challenged to exegete each notation! We quickly discovered how difficult that notational analysis can be. Here is an introductory pass at Notations 0, 31, 64, 67, 101, 137, 143, 167, 197, 199 and 202.

It all pushes us to redefine time because (1) All the notations are always active. (2) Time does not “pass.” It is. (3) Aging is real. Death is real. Sleep is real. Memory is real. And, all four must be included. Quite a challenge.

[1] Lemaître, Hawking, and Guth. Only Alan Guth has had the advantage to see the 2022 results from the James Webb Space Telescope (JWST). Although Stephen Hawking had access to the results of the Wilkinson Microwave Anisotropy probe from 2001 to 2010 (See: Katherine Freese) and results of the ESA Planck Telescope from 2009 to 2013 (See: George Efstathiou), that data is still a challenge. It has needed the JWST data 330 million years later to provide some perspective. Yet, it is all still a giant jigsaw puzzle… all to discern the very nature of the pieces of that puzzle within the first few minutes of our universe.

Guth is still confident that his group is on the right path, “…that the observational evidence for inflation just keeps mounting up and as things get measured more and more precisely it just gets better and better; so for example, one of the predictions that inflation makes is for the average mass-density of the universe and now that’s been confirmed within a half a percent.” That quote is taken from How Did the Universe Begin? (:18-:31 seconds), Closer to the Truth, 2020. Guth’s inflation is like a chameleon because it is based on just part of the overall construct. Also, see: Why Is There Anything At All?, 2021.

The earliest moments of the universe in the light of big bang theories were generally introduced to the public by Steven Weinberg within his 1977 book, The First Three Minutes. He says on page 5, that “…one-hundredth of a second (is) the earliest we can speak with any confidence” and then adds with aplomb that “the universe was about a hundred thousand million (1011) degrees Centigrade” as if he had observed it in the laboratory. Much later a group of 27 scholars from around the world titled their article, The First Three-Seconds (2020). They had trouble getting behind that first second. Within our chart the first seconds are from Notation-143 and the first hundredth of a second is from Notation-138.

It is all such a blindspot. And the big bang has been blocking a deeper analysis. Inflation has been called into question as has the big bang as a theory itself. It has become entirely obvious that we all need to be thinking more about the results from the ESA Planck Space Telescope in light of the JWST.

Notation-143. By the 143rd doubling of Planck Time (1.202 seconds), we are well into the last third of our chart. Notations 1-67 are virtually unexplored and, to the best of our knowledge, have never been cited as such within scholastic literature. We’ve called it the small-scale universe; perhaps “the infinitesimal universe” would be more appropriate. Notations 67-to-134 have been cited as the human-scale universe while Notations 135-to-202 have been cited as the large-scale universe. By that 143rd notation, on each “first pass” through, the core geometries, mathematics, and physics are being shaped by efficiencies and densities. It seems that there is no time or space for quantum indeterminacy. In that first pass, a perfection is most efficient and most simple. I can well-imagine those efficiencies become precedents and that this “perfection” — currently called smoothness — readily defines the first 330 million years right up to and within Notation-197.

[2] Ubiquitous, old equation. What comes first? The heart of the finite-infinite transformations between the faces of continuity-symmetry-harmony (CSH) is pi. Much of our classic scholarship touches it but has not defined it as CSH. Within this website, the discussion about the finite-infinite is part of many homepages, i.e. the prior homepage on de facto and de jure is one our many finite-infinite discussions. In many places within this website, you will find this declaration:

All other definitions of the infinite are put on hold. Most are personal definitions that come from personal experiences and family history. That is one’s own business, not ours. If those beliefs help you through life, that is great. Our goal here is to engage those principles and functions that give rise to mathematics, physics, and eventually all the other sciences.

from Continuity-Symmetry-Harmony (CSH), 1972

[3] Inflaton definitions. An excellent overview of the range of definitions is with a sampling of ten articles out of over 3700 within ArXiv that use the concept. The most important definition would naturally be from Alan Guth. One such article is Eternal inflation and its implications (PDF), Alan H. Guth, February 2007. Yet, the definitions by other early adopters like Steinhardt, Vilenkin, and Linde, are also key. A sampling of just ten: (1) Arrows of time and the beginning of the universe (PDF), Vilenkin, 2013, (2) Inflationary schism after Planck2013 (PDF), Anna IjjasPaul J. SteinhardtAbraham Loeb, 2014, (3) Inflationary paradigm after Planck 2013 (PDF), Alan H. GuthDavid I. KaiserYasunori Nomura, 2013, (4) The Inflaton Portal to Dark Matter, Lucien Heurtier (PDF), 2017,(5) Could the Higgs boson be the inflaton?, Phys.Lett. B697 (2011) 37-40 (arXiv:1011.4179, Remarks on Higgs Inflation, Michael AtkinsXavier Calmet, 2011, (6) Warm Little Inflaton (PDF), Mar Bastero-GilArjun BereraRudnei O. RamosJoao G. Rosa, 2016, (7) The Minimal GUT with Inflaton and Dark Matter Unification (PDF), Heng-Yu ChenIlia GogoladzeShan HuTianjun LiLina Wu, 2017, and (8) From Cosmic Inflation and Matter Creation to Dark Matter — Journey of the Inflaton? (PDF), B. S. Balakrishna, 2022, (9) The Peebles – Vilenkin quintessential inflation model revisited (PDF), Jaume HaroJaume AmorósSupriya Pan, 2019, and (10) On the behaviour of the quantum Universe anisotropies in a bouncing picture (PDF), Eleonora GiovannettiGiovanni Montani, 2023. Additionally, I include: Paul Steinhardt Disowns Inflation, the Theory He Helped Create, Scientific American, 2014, and Wikipedia’s study of the inflaton because it is a dynamic page.

Reference pages within this site: Guth, Steinhardt, Vilenkin, Linde, Ijjas, Kaiser, Loeb, and Peebles.

From all these (with many footnotes and references within each), I conclude the following:
1. Other than it is pointlike, there is no standard, widely-accepted definition of an inflaton.
2. An inflaton, like an axion, must define a space-time moment or it is not basic enough.
3. I would also add that a first principle to be a first principle, must be mathematically defined.

[4] Tredecillion range: A rather straightforward calculation with Planck Time renders 539.tredecillion spheres per second. With Stoney Time it’s 4605 tredecillion spheres per second. We have requested that the ISO comment on the difference. That such numbers could be an acceptable definition of a cosmological constant will be disputed, especially that it is the root cause of expansion (inflation). In that light, I think the insights of Katherine Freese and Will Kinney about a natural inflation deserve more attention. The question needs to be asked, “What is natural?” The work of Yasunori NomuraTaizan Watari, and Masahito Yamazaki (Berkeley Center for Theoretical Physics), Pure Natural Inflation, 2017 ask, “Does the model of inflation need to be significantly complicated? Is the agreement of ns of the quadratic potential with the data purely accidental?”

The simplest model of inflation V (φ) = m2φ2/2 [A. D. Linde, “Chaotic inflation,” Phys. Lett. 129B, 177 (1983)]—which gives the correct value for the scalar spectral index ns ‘ 0.96—is now excluded at about the 3σ level because of the non-observation of tensor modes.

arXiv:1706.08522v2 [hep-ph] 27 Nov 2017

Remember the little neutrino? The experts (IceCube Neutrino Observatory, the University of Wisconsin–Madison and the National Science Foundation) measure neutrinos say, “About 100 trillion neutrinos pass through your body every second.” More to come

[5] The current time, the Now. The most visited page on this website is titled UniverseClock. It was initiated for a 2017 conference at NASA’s Marshall Space Flight Center in Huntsville. Most people can’t imagine that the universe is only 436 quadrillion, 117 trillion, 76 billion, 600 million seconds old. That computes to about 13.81 billion years. In this model each notation is always active and the universe is constantly building on itself. The simplest equations of the universe become axioms, then first principles, and even laws. Yes, in this model of the universe, the laws of physics are being tested as we go.

The nine major studies that are “not on the grid” are actually on the grid, yet below our ability to measure them. Once each discipline accepts the concept of infinitesimal spheres, I am confident that their mathematicians will quickly work out the new details for their study. Thus, there are many more studies to come.

[6] Penultimate grids open for inspection. I believe it will be helpful to re-engage our current concept of point particles to begin to see them as large aggregations of infinitesimal spheres. Even the concept of points and vertices need to be reconsidered for a very basic redefinition.

Back in high school it bothered me that there was only one definition of a point. I imagined hundreds. The differences between them were in how the ends were secured and what was allowed to pass through them. I saw them all as computing circuits. Clearly the domain of Langlands programs and string theories, this penultimate grid does warrant further study.

[7] Continuity-symmetry-harmony define pi and are defined by pi. Pi defined the finite and infinite and are defined by it as well. In our mind, the realities of pi, continuity-symmetry-harmony, are really real and the foundations of the foundations.

[8] Fourier transform. Every formula that involves pi (starting with the Fourier transform) needs to be re-reviewed in light of CSH and the 202 base-2 notations. Pi is everywhere.

[9] Geometries of indeterminacy. There is a look and feel of quantum fluctuations; the mysteries are all within the geometries. It appears that scholars were first foiled by Aristotle (384-321 BC). Five tetrahedrons create a gap that he missed; and for 1800 years his mistake was repeated by scholars. That is worth pondering. Aristotle was so great it took 1800 years to countermand his mistake. And, iIt is still untouchable. That correction was eventually forgotten until in 1926, a little-known MIT mathematician, Dirk Struik, rekindled that scholarship. Struik’s work did not receive much attention until in 2012 when two scholars, Jeffrey Lagarias and Chaunming Zong, lifted it up again. Yet, these two mathematicians were more interested in packing densities. There is no exploration of the meaning of the gap. Subsequently, in May 2022, the five octrahedral-gap was introduced within this website and questions have been asked of many scholars, “What are these gaps all about?”

[10] Our charts, interpretations and prognostications. Simple logic, simple math, and simple geometries render our charts, interpretations and prognostications. It all awaits critical review, so until then, there will be more to come.

_____

References & Resources
As references are studied, key references and other resources will be added.

Symmetry in QFT and Gravity (video), Hirosi Ooguri (and Nathan Seiber), 2022
Mathematically, equations building on natural functional dependencies:
….–  Using math in physics: 5. Functional dependence (PDF), E. F. Redish, Univ. Maryland, 2022
•  Quantum Energy Inequalities along stationary worldlines,
Christopher J. FewsterJacob Thompson, 4 Jan 2023
•  ESA Group (PDF): The universe at 380,000 years
https://www.esa.int/Our_Activities/Space_Science/Planck/Planck_reveals_an_almost_perfect_Universe,2009
•  Pure Natural Inflation, Yasunori Nomura, Taizan Watari, and Masahito Yamazaki,
Berkeley Center for Theoretical Physics, Department of Physics, 2017
The Friedmann–Lemaître–Robertson–Walker (FLRW) Metric
•  A pedagogical explanation for the non-renormalizability of gravity, (PDF), Assaf Shomer, 2008.
Path integrals and Gaussian fixed point. See Assaf Shomer’s on page 7:
“The derivation of the path integral formula in quantum mechanics of a massive particle involves chopping up the quantum evolution into very short time intervals and inserting complete sets of states between them.”
•  Doplicher S, Fredenhagen K, Roberts JE (1995) The quantum structure of spacetime at the Planck scale and quantum fields. Communications in Mathematical Physics 172(1):187–220
•  Scale invariance and conformal symmetries

Personal projections and ruminations. Standard Model of Cosmology and the Standard Model for Particle Physics: Of the 202 notations, the first 64 notations open a map to make the connections.

There is a place for the some of the big bang numbers but not until after the first few seconds.

Thrust in our universe. In September 2017, I wrote about the thrust in our universe. So now, over five years later, it is time to revisit that article and update it as much as possible. The major update would involve our understanding more about the three facets of pi and how each is a Janus-face for the finite and the infinite. How are the functions of continuity-symmetry-harmony abiding?

Major studies. I have written to Robert Langlands, Ed Frenkel, and others within Langlands programs. They have not yet acknowledged the 202 mathematical notations. Why not? It’s just math and logic. There is no philosophy. There are no agendas. It is what it is, simple math.

I have also written to people within string theory. None have acknowledged the 202 notations.

I believe people are naturally incrementalists. It is more comfortable. The Planck units were ostensibly ignored until 2001 and by that time Hawking-Guth-and-family had a hold on the theory about the start of the universe. With Hawking’s death, that hold has become somewhat more relaxed. With the JWST it’s time to open up the discussions. It will include conformal-quantum-and-scalar field theories (CFT, QFT). Although John Wheeler’s sense of simplicity was a good idea, for most of the octogenarians and nonagenarians, this base-2 model of 202 notations is just too simple. It is too obvious. Yet, maybe not. Prior to Frank Wilczek’s three articles about the Planck scale, Planck’s numbers were aloofly small much like Paul Dirac’s were aloofly big.

#

In 1980 in Paris at the Institut Henri Poincaré, Jean-Pierre Vigier and I made a six-month study of the EPR paradox in light of the work of Alain Aspect in d’Orsay. Instead of infinitesimal spheres, Vigier had suggested that we use the metaphor of dominos falling. That action-at-a-distance is not instantaneous. Infinitesimal spheres within the packing densities suggested by the Planck-or-Stoney-or-ISO numbers, would be instantaneous.

Mathematics and physics of the finite begin here.

_____

Emails
There will be emails to many of our scholars about the key points.

25 February 2023, Anna Ijjas, NYU
25 February 2023, Katherine Freese, University of Texas, Austin
23 February 2023, Alexander Vilenkin, Tufts University
12 February 2023, John Moffat, Toronto, Perimeter, Waterloo
10 February 2023, Vladislav Yakovlev, Max Planck Institute for Quantum Optics
8 February 2018, Ian Walmsley, Imperial College of London
3 February 2023, Alan Guth, MIT
31 January 2023, Thomas Sumner, Simons Foundation
30 January 2023, Basil Hiley, University of London (UCL)
29 January 2023, Thomas Lin, Quanta Magazine
27 January 2023, Drew Harrell, Washington Post
26 January 2023, Carl Zimmer, New York Times
25 January 2023, James Sethna, Cornell
24 January 2023, Rebecca BoyleQuanta Magazine
23 January 2023, Rohan Naidu, MIT Pappalardo Fellow

_____

IM
There will also be many instant messages to thought leaders about the following key questions:

1. Is it possible that the first instance of the universe is defined by Planck’s base units?
2. Is it possible that the first manifestation of those base units is an infinitesimal sphere?
3. Might the characteristics of pi describe those spheres?
4. Might the Fourier Transform impart either electromagnetism or gravitation to each sphere?
5. Is it possible that one sphere manifests per unit of length and time?
6. Doesn’t that compute to 539 tredecillion spheres per second using Planck units and 4605 tredecillion per second using Stoney Time?
7. Is it possible that the densities within the earliest notations are on the order of a blackhole or neutron star?
8. To create some sense of order with the generation of infinitesimal spheres, may we use base-2 notation?
9. Using base-2 notation, are there 202 base-2 notations from Planck Time to the current time?
10. Is it significant that at one second the Planck Length multiple is a very close approximation of the distance light travels?
11. Is it significant that quantum fluctuations are measured within Notation-67? Notation-72 appears to be the limit of our abilities to measure a duration of time.
12. Would these notations, 1-64, provide 64 possible redefinitions of a point-particle? (And, I would add a vertex.)

8:45 PM · Feb 1, 2023 @DrOsamaSiddique @Harvard_Law @UniofOxford @IGLP_HarvardLaw There is a type of natural law within pi (π) (https://81018.com/starts-2/) that also creates a mathematically-integrated view of the universe where value comes from its continuity-symmetry-harmony. https://81018.com/values/ March 4, 2023

11:14 AM · Jan 31, 2023 @RBReich Everyone should find their creative thing that makes them happy and brings them joy and ask, “Is there a business in there?” Millions have. We call it small business and it enriches the soul and satisfies the heart and inspires the mind. https://smallbusinessschool.org

_____

_____

• This page became the homepage during the early morning of February 4, 2023.
• The last update was February 28, 2023.
• This page was initiated on February 3, 2023 at 11:11 AM
• The URL for this file is https://81018.com/inflaton/
• First byline: Alan Guth’s inflationary theory redefined.

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Also reviewed: Could the Higgs boson be the inflaton?, Phys.Lett. B697 (2011) 37-40 (arXiv:1011.4179, Remarks on Higgs Inflation, Michael AtkinsXavier Calmet, 2011

# The necessary Janus-face of pi-π and thus of all things*

Is pi (π) both finite and infinite?
by Bruce E. Camber (first draft)

James Webb Space Telescope1 (JWST): The JWST is challenging everyone who studies his/her/its findings. I predict that it will push the Standard Model of Cosmology2 well-beyond the formulations and justifications for big bang theories. Lemaître, Hawking, Guth3 and followers have had to ignore the most basic formula of science, pi (π), as well as the key dimensionless constants in order to make big bang cosmology appear to work.

An article, Standard Model of Cosmology Survives a Telescope’s Findings, by Rebecca Boyle4 was published on January 20, 2023 in Quanta Magazine.5 It focuses on the people and issues shaping this Standard Model. However, if we place all those issues within our 202 base-2 notations6 from Planck Time to this moment in time, our predictive, mathematical model would readily begin to absorb and transform the sense of logic within big bang thinking. The continuity equation from Planck Time to the current day is perhaps the most-basic continuity equation there is. The progression of numbers from the very-first moment of the universe to the very-first second7 of the universe is within our Notation-143[8] out of the 202. It is a “must-study” progression. It is a look at the earliest universe unlike any proposed. It has Planck units (numbers), geometries, logic, a built-in thrust9, and a host of studies10 yearning to be on that grid.

Penultimate grid.11 In this model key symmetry-and-harmonic functions, the essence of the finite-infinite transformation, give rise to a real cosmological constant that within Notation-0 emerges as an infinitesimal sphere. Assuming one Planck sphere per unit of Planck Time and Planck Length, within the first year )which is within Notation-169), the mathematics of this universe is already showing signs of greatness. Starting with Planck Mass at 2.176.470(51)×10-8 (kg), within just over one year our universe is already 1.628×1042 kg. As a comparison, our sun is estimated to be 1.989×1030 kg. Even with Jupiter, the sun is estimated to be 99.5% of the total weight of the Solar System. This expansion is clearly inflation. The entire Milky Way has been estimated (Sloan Digital Sky Survey). Currently it is thought to have a total mass of around 6×1042 kilograms. And, within the first year, the universe has densities in the range of neutron stars and blackholes. With just the first year, we can begin to understand why and how the universe is quite so large in 13.8 billion years.

This trajectory for the universe has a commonsense logic based on a simple mathematical progression that is emulated by nature everywhere.

From that first infinitesimal sphere, tetrahedrons and octahedrons naturally emerge. Fourier kicks in. Inherent harmonic functions of the Fourier transform should readily inspire because, yes, here is a place for Langlands programs and for string and M-theory, and loop quantum gravity and all the hypothetical particles. Here is a place of all those disciplines that are not on the grid. There’s even a place for Smale and Milnor with their attractors and repellers.

Here is a model of the earliest universe where our thinking is least developed. And, it offers a new challenge and opportunity. It’s a new opening of possibilities.

When the Boyle/Quanta article came out, I had been reflecting on the Scientific Method and how currently we all de facto assume the big bang. Of course, de jure is the counterpoint and I was particularly looking at pi and the dimensionless constants to provide foundations for natural law. It was increasingly clear that pi’s continuity-symmetry-harmony were descriptions of both the finite and infinite and de facto was finite and de jure was infinite. Although the Boyle article gives a passing reference to the big bang, that theory has nothing to do with the results of the JWST and it really doesn’t change any of the conclusions made by Boyle. She has given us an excellent introduction to some of the key challenges the JWST is making. It is not about the Standard Model. It is about the first microseconds and minutes and years and how the universe began so smoothly.

It is an article to which I will return and watch as a wonderful encapsulation of this moment in time.

Thank you. –BEC

Editor’s Note: Obviously this article was inspired by Rebecca Boyle and her article in Quanta Magazine. This homepage evolved from my note to her. -BEC

###

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Endnotes & Footnotes
All these points already have pages within this website. Another 14 footnotes are being added…

[*] PI (π). In this website, always has a face of the infinite and a face of the finite. When focused too much in either direction, we lose our bearings. For this posting, we had first named it, pi-pi, but quickly discovered there was a hip-hop recording named, Pi-Pi, by Milli Music, director, Shane Creative. Their recording of pi-pi opens with the lyrics, “Only you can bring the demon home.” So, here’s a viewer warning: drugs, sex, and darkness and nothing to do with circles or spheres was our first encounter with Pi-Pi. Our next, another recording named, Pi-Pi-Pi, is humorous and it is all about Pi Day and the circumference of the circle with a very light touch.

My work with started in 1961 in high school. But it took a much later high school geometry class to begin the progression from the Planck units using base-2 that resulted in 202 notations. Those notations truly opened the discussion around the question, “What is the first thing to manifest in this universe?” After a false start, we’ve settle on an infinitesimal sphere defined by those Planck units. However, we are also open to using the Stoney units or new ISO units. Arguably, studies of pi began between 2500 to 5000 years ago. Euclid’s Elements was published around 300 BC. So with so much focused study over such a long period of time, of course, we think we have milked it dry. The opposite is true. We’re making slow progress to grasp its deepest, broadest, highest, most-comprehensive meaning.

[1] JWST. The James Webb Space Telescope is technically named for the head of NASA from 1961 to 1968. Huge progress was made during the Mercury, Gemini, and Apollo programs under his leadership. Yet, it could be argued that the array of sixteen hexagonal mirrors of this telescope is more like a she than a he. In the spirit of the time, I think the pronouns, he/she/it, are probably suitable. Wikipedia‘s summary of this work is an ongoing venture that is often updated with new information.

[2] Standard Model of Cosmology doesn’t care how the universe started. The more comprehensive it is the better. The more mathematical it is, the more compelling. If the model includes some of the key concepts of the big bang, yet not its time line or its place of importance, so much the better. The 202 base-2 notations do all that and so much more; so of course, we’ll come back to this footnote “for more” as we attempt to build a connection between the it and the Standard Model for Particle Physics.

[3] Lemaître, Hawking, Guth were the most pivotal thinkers to promulgate the big bang. Of course, Lemaître is long dead, and the very few who knew him are now close to the end of life. Hawking died on Pi Day, March 14, 2018. I can well-imagine he had had enough. Photo-op after photo-op, it is hard to be a celebrity and even consider doing serious science. Our infinitesimal sphere just may be a very good definition of Guth’s inflaton. It is creating the laws of physics as it populates the universe which based on either Planck‘s or Stoney’s base units could anywhere from 539-to-4605 tredecillion infinitesimal spheres per second… More to come.

[4] Standard Model of Cosmology Survives a Telescope’s Findings, R.Boyle, Quanta, Jan. 2013 Rebecca Boyle has written an excellent article. She gives the big bang passing acknowledgement yet focuses on the current tensions in cosmology created by the results of the JWST. The focus has to be on the results of real research. And, the focus is to answer the question, “How can the universe look like these images 330 million years from the start?” Although the base-2 expansion from a single infinitesimal sphere is dramatic, it is orderly and entirely geometrical and mathematical. It is consistent with the JWST’s findings… More to come. Standard Model of Cosmology Survives a Telescope’s Findings, by Rebecca Boyle

[5] Quanta Magazine Thomas Lin started the publication in 2012 and Quanta Magazine has already won the 2022 Pulitzer Prize in Explanatory Reporting and the 2020 National Magazine Award for General Excellence. The magazine is primarily sponsored by the Simons Foundation which is also responsible for the Flatiron Institute in NYC (Wiki), Simons Center for Geometry and Physics at Stony Brook, and hundreds of programs related to the advancement of scientific knowledge. James Simons used the power of mathematics to understand the markets and trading and made billions. His investment in Quanta Magazine is richly paying back.

[6] 202 base-2 notations. The horizontally-scrolled chart of 202 base-2 notations started in December 2011 with just Planck Length. That chart had somewhere around 202 notations. Not until we mapped it with Planck Time did we have a more definitive stopping point: 13.79 to 13.81 billion years. The 201st doubling has taken Planck Time, 5.391 16(13)×10-44 seconds, around 173,272,944,073,600,000 seconds or 5.4908 billion years. If we add up each notation up to the 201st notation, we are one unit of Planck Time shy of 10.98 billion years. Simple math tells us that just 2.8284 billion years has passed since the beginning of the 202nd notation (Calculation: 13.81 minus 10.9816 ≈ 2.8284). It is an important, hard-earned perspective. Our calculation for the UniverseClock helped us along that path. We are now challenged to exegete each notation! We quickly discovered how difficult that notational analysis can be: 0, 31, 64, 67, 101, 137, 143, 167, 197, 199 and 202.

There is a place for the big bang numbers but not until after the first few seconds.

[7] The very-first second. One might think that the very-first second of the universe is well understood. It’s not. Steven Weinberg within his 1977 book, The First Three Minutes, says on page 5, that “…one-hundredth of a second (is) the earliest we can speak with any confidence” and then adds with great aplomb that “the universe was about a hundred thousand million (1011) degrees Centigrade” as if he had observed it in the laboratory. Then there is a group of 27 scholars from around the world who titled their article, The First Three-Seconds. They didn’t get anywhere close to the first second. It is such a blindspot.

[8] Notation-143. Then, there is Notation-143, or the 143rd doubling of Planck Time, and we are well into the last third of our chart. Notations 1-67 are virtually unexplored and, to the best of our knowledge, had never been cited in our scholastic literature. We’ve called it the small-scale universe when perhaps The Infinitesimal Universe would be more appropriate. Notations 67-to-134 have been cited as the human-scale universe while Notations 135-to-202 have been cited as the large-scale universe. By that 143rd notation, on the first pass through, the core geometries, mathematics, and physics have been shaped by efficiencies and densities. There is no time or space for indeterminacy. In that first pass there is only perfection. It is the most efficient and the most simple. I can well-imagine those efficiencies become precedents and that perfection, currently called smoothness, readily defines the first 330 million years right up to and within Notation-197.

[9] Thrust in our universe. In September 2017, I took a stab at my first real article about the thrust in our universe. So now, over five years later, it is time to revisit that article and update it as much as possible. The major update would involve our understanding that the three facets of pi are each a Janus-face for the finite and the infinite. Another major update will include the continuity-symmetry-harmony functions that are abiding.

[10] Major studies not on the grid. I consider nine major studies not on the grid. I have written to Robert Langlands, Ed Frenkel, and others within Langlands programs. They have not yet acknowledged the 202 mathematical notations. Why not? It’s just math and logic. There is no philosophy. There are no agendas. It is either correct or not.

I have also written to people within string theory. None have acknowledged the 202 notations. Why not?

I believe people are naturally incrementalists. It is more comfortable. The Planck units were ostensibly ignored until 2001 and by that time Hawking-Guth-and-family had a choke hold on the theory about the start of the universe. With Hawking’s death, the choke hold has become somewhat more relaxed. With the JWST it’s time to breathe again. Of course, conformal-quantum-and-scalar field theories (CFT, QFT) have holds on all the old-timers within the industry. You can imagine that each night they are hoping that they may see a breakthrough before they die. Yet, although John Wheeler’s sense of simplicity was a good idea, for most of the nonagenarians, this base-2 model of 202 notations is just too simple. It is too obvious. Yet, prior to 2001 and Frank Wilczek’s three articles about the Planck scale, Planck’s numbers were aloofly small in a similar way that Dirac’s were aloofly big.

Perhaps a little more to come…

[11] Penultimate grid. The first infinitesimal sphere has been likened to Lemaître’s primeval atom and Guth’s inflaton. Both are hypothetical. Our very first infinitesimal sphere is a little less hypothetical because it has a geometry, a mathematics (an algebra), and a deep-and-abiding logic. The universe has to start with something to create space-time. Of course, our postulation that our universe is totally populated by such infinitesimal spheres is also hypothetical. Notwithstanding, this hypothetical penultimate grid warrants inspection. Although the finite-infinite transformations between the faces of continuity-symmetry-harmony (CSH) are assumed, our focus is on the finite. The finite is first defined by CSH, then defined by the Fourier transform, and the Poincaré sphere, and then the Poincaré homology sphere. Any and all types of spheres are included as potential spheres waiting for their mathematics to evolve (be possible, come out). This, of course, would include Smale and Milnor’s spheres, attractors and repellers.

In 1980 in Paris at the Institut Henri Poincaré, Jean-Pierre Vigier discussed (and I listened) the EPR paradox in light of the work of Alain Aspect in d’Orsay. Instead of infinitesimal spheres, Vigier had suggested using the metaphor of the dominos which was not instantaneous. Infinitesimal spheres with the packing densities suggested by the Planck-or-Stoney-or-ISO numbers, would be instantaneous. Mathematics and physics begin here.

Please note: Today, more of the linked words or expressions may still become a footnote. Today is indeed February 3, 2023.

_____

References & Resources
As these references are studied, key references and resources will be added.

•   The Friedmann–Lemaître–Robertson–Walker (FLRW) Metric
•  Path integrals and Gaussian fixed point. See Assaf Shomer’s on page 7: “The derivation of the path integral formula in quantum mechanics of a massive particle involves chopping up the quantum evolution into very short time intervals and inserting complete sets of states between them.”
•  Doplicher S, Fredenhagen K, Roberts JE (1995) The quantum structure of spacetime at the Planck scale and quantum fields. Communications in Mathematical Physics 172(1):187–220
•  Scale invariance and conformal symmetries

_____

Emails
There will be emails to many of our scholars about the key points.

31 January 2023, Thomas Sumner, Simons Foundation
30 January 2023, Basil Hiley, University of London (UCL)
29 January 2023, Thomas Lin, Quanta Magazine
27 January 2023, Drew Harrell, Washington Post
26 January 2023, Carl Zimmer, New York Times
25 January 2023, James Sethna, Cornell
24 January 2023, Rebecca BoyleQuanta Magazine
23 January 2023, Rohan Naidu, MIT Pappalardo Fellow

_____

IM
There will also be many instant messages to thought leaders about the following key questions:

1. Is it possible that the first instance of the universe is defined by Planck’s base units?
2. Is it possible that the first manifestation of those base units is an infinitesimal sphere?
3. Might the characteristics of pi describe those spheres?
4. Might the Fourier Transform impart either electromagnetism or gravitation to each sphere?
5. Is it possible that one sphere manifests per unit of length and time?
6. If so, doesn’t that compute to 539 tredecillion spheres per second using Planck units and 4605 tredecillion units per second using Stoney time?
7. Is it possible that the densities within the earliest notations are on the order of a blackhole?
8. To create some sense of order with the generation of infinitesimal spheres, may we use base-2 notation?
9. Using base-2 notation, are there 202 base-2 notations from Planck Time to the current time?
10. Is the calculation significant at one second where that Planck Length multiple is a very close approximation of the distance light travels in that second?
11. Is it significant that quantum fluctuations are measured within Notation-67? Notation-72 appears to be the limit of our abilities to measure a duration of time.
12. Would these notations, 1-64, provide 64 possible redefinitions of a point-particle? (And, I would add a vertex.)

11:14 AM · Jan 31, 2023 @RBReich Everyone should find their creative thing that makes them happy and brings them joy and ask, “Is there a business in there?” Millions have. We call it small business and it enriches the soul and satisfies the heart and inspires the mind. https://smallbusinessschool.org

8:45 PM · Feb 1, 2023 @DrOsamaSiddique @Harvard_Law @UniofOxford @IGLP_HarvardLaw There is a type of natural law within pi (π) (https://81018.com/starts-2/) that also creates a mathematically-integrated view of the universe where value comes from its continuity-symmetry-harmony. https://81018.com/values/

_____

_____

• The last update was February 3, 2023 in the morning.
• This page was initiated on January 23, 2023 at 8:42 AM
• The URL for this file is https://81018.com/pi-π/
• First byline is: Filename changed to “pi-π” because pi-pi was already engaged.

_____

# On studying the work of Steve Carlip, Ricardo Mosna, and João Pitelli

Steven Jonathan Carlip, Department of Physics
University of California
, Davis, CA 95616, USA
Ricardo A. Mosna and João Paulo M. Pitelli, Departamento de Matematica Aplicada

`Second email: Friday, March 3, 2023 at 5 PM `

Gentlemen:

Have you ever seen a five-octahedral gap? https://81018.com/2022/05/19/five/#Gap. We’ve found no references to it and computer-aided design does not properly compute it. I would enjoy reading an article from you about the relation of these gaps to quantum fluctuations. It seems that scholarship has ignored the natural starting points within pi (π), especially if the cosmological constant is computed based on the Planck base units. Wouldn’t it be around 539 tredecillion infinitesimal spheres per second? It seems we make things too complicated before we start. A deeper study of pi (π) might help lay proper foundations: https://81018.com/pointing/ which today is the homepage: https://81018.com/

Thank you.

Most sincerely,

Bruce

PS. My reference page to your work is here: https://81018.com/carlip/
https://81018.com/mosna/
https://81018.com/pitelli/
****************
Bruce E. Camber

`First email: Sunday, July 31, 2022 at 8:45 AM. (Update: March 3, 2023)`

Dear Professors/Doctors Steve Carlip, Ricardo A. Mosna, and João Paulo M. Pitelli:

In ArXiv Steve Carlip,  Ricardo A. Mosna and João Paulo M. Pitelli came to my attention first. In a search today there are not many articles that have geometry and quantum fluctuations in the same sentence. So, very quickly, I saved your article so I could read it at my leisure and study your references, especially given your background in physics and mathematics through Harvard, IAS, and UC-Davis.

As points of reference, in 1979 I had a project at MIT and got Steven Weinberg and Sheldon Glashow involved. A friend of mine from Boston University, Patricio Letelier, was a Chilean mathematical physicist and professor at University of Campinas (UNICAMP). I suspect your colleagues knew him or of him. I created a Wikipedia entry about him (See: View History, August 20, 2019).

My background within academia is incomplete. I have also become biassed by discovering in 2011 that there are just 202 base-2 notations from the Planck scale to the current time (and size of the universe). Also in 2022, I found a five-octahedral gap that complements the five-tetrahedral gap that Aristotle made infamous. One of the results is a very different take on transitions to non-Gaussianity within the first 64 notations along the way to quantum fluctuations.

I just started a page about this note. It’s still rough but it’s the only way I can keep track of the work of scholars to whom I write. Our work will strike you as rather odd, but you may have some “first-impressions” and advice for us and that is why I write to you.  I’ll be using your work to further develop my thoughts to follow-up this page: https://81018.com/geometries/

Most sincerely,

Bruce

PS. I think I remember seeing you at a UC-Davis conference that touched on the EPR that I dropped in on back in 2018. Also, looking at Steve Carlip’s ArXiv publications, it is gratifying to see so many articles where he is the single author. Also, I grew up in the shadows of Harvard. When still in high school in 1964, I joined the Harvard SDS. Later, in 1971, I was with Arthur Loeb and his group called the Philomorphs in the attic of Sever Hall. In 1975 I was over at the Harvard Divinity School with Arthur McGill where we engaged Austin Farrer’s Finite and Infinite

I may have crossed paths with Steve Carlip more than once! -BEC

# The Geometric Fluctuations as understood by Carlip, Pitelli, and Mosna

Editor’s Note: Started on Saturday, July 30, 2022; in process.

Quantum Fields, Geometric Fluctuations, and the Structure of Spacetime, 21 Sep 2018 (v1), last revised 17 Dec 2020 (v4) PDF

S. Carlip, Department of Physics, University of California, Davis, CA 95616, USA
R. A. Mosna and J. P. M. Pitelli, Departamento de Matematica Aplicada, Universidade Estadual de Campinas, 13083-859, Campinas, Sao Paulo, Brazil

`First email: Sunday, August 1, 2022`

TO: Joao Paulo Manoel Pitelli
cc: Ricardo A. Mosna, Steve Carlip

Gentlemen:

Your workCarlipMosnaPitelli — regarding geometric fluctuations has come to my attention. There are not too many articles that have geometry and quantum fluctuations in the same sentence. So, very quickly, I saved it out so I could read it at my leisure and study all your references.

Now a friend of mine from Boston University, Patricio Letelier, was a Chilean mathematical physicist and professor at University of Campinas (UNICAMP). I created a Wikipedia entry about him (see: View History, August 20, 2019) a few years ago. I suspect you knew him or knew of him.

When Patricio got his PhD, I went back into a business that I had started six years earlier (so my background within academia is incomplete). I returned to my earlier work quite by accident when helping a nephew by taking his geometry classes for a few days. That was back in 2011. We were having fun with embedded geometries when we rather unwittingly uncovered the fact that there are just 202 base-2 notations from the Planck scale to the current time (and size of the universe). We thought it was a good STEM tool. For years, the first 64 notations up to particle physics eluded us. We could not imagine what was there. Then, we learned a little about Langlands programs and I returned to memories of late night discussions about string theory with Patricio. More recently I uncovered an octahedral gap commensurate with the five tetrahedral gap. Together they struck me as a possible gate in quantum computing. I also began thinking about transitions to non-Gaussianity within those first 64 notations.

I fully agree that our work is entirely odd, a wiffle ball coming out of left field. But I thought you’d be interested to see this page about that it: https://81018.com/geometries/ Of course, I would be most fascinated with your initial comments, no matter how harsh or direct you’d like to be!

Thank you.

Warmly,

Bruce

_____

# On learning a little about the work of Thomas Francis Banchoff…

Thomas Francis Banchoff, emeritus professor, Brown University, Providence, Rhode Island

Articles: The Best Homework Ever, 1996
ArXiv: The Gauss map of polyhedral vertex stars (PDF), 2019
Books:
• Beyond The Third Dimension investigates ways of picturing and understanding dimensions below and above our own. Ranging from Egyptian pyramids to the nineteenth-century satire Flatland to the paintings of Salvador Dali, Scientific American Library, Freeman 1990 (Review)
• Differential Geometry of Curves and Surfaces, Thomas F. Banchoff, Stephen Lovett, Aug 5, 2022
• Flatland: The Movie Edition, 2008
CV
Homepage(s): Brown University, Beyond The Third Dimension, MAA
Publications
Twitter: @BanchoffF Congrats, PBS-Lanier, Dalí-Vassilieva, TinyGeometry-Third Dimension
Wikipedia

(born April 7, 1938)

Thomas Banchoff is referenced here: https://81018.com/starting-point/#Emails

`Second email: July 16, 2022 at 5:05 PM`

Dear Prof. Dr. Thomas F. Banchoff,

Again, let me say a profound congratulations on such a diverse and full life (as evidenced above).

I got stuck in elementary things and didn’t move very far forward. During a visit with John Conway in the Spring 2001, he accused me of being hung up on the octahedron-and-tetrahedron and he was right. Finally, it was your colleague at Brown, Phil Davis, who dislodged me from the tetrahedron to the sphere in 2012, but It didn’t last long. When I found the work with cubic-close packing of equal spheres, I was back into octet things. When I learned about Aristotle’s 1800-year old mistake, it was an eye-opener. I thanked Lagarias and Zong profusely for their work, but both were reluctant to speculate on the nature of that five-tetrahedral gap of 7.35610317+ degrees.

Work within a high school geometry class also complicated matters. My nephew was the head of the math department in his high school and the geometry teacher. On a couple occasions he had me take over to introduce the platonic solids. I had boxes filled with clear-plastics models of octahedrons and tetrahedrons that I had manufactured (a silly idea). We were able to make clusters of that tetrahedral gap and then went on to make a twenty-tetrahedral icosahedron and then even the Pentakis dodecahedron. We called it squishy geometry, imperfect geometry and quantum geometry. Of course, I wanted to associate it with quantum fluctuations and the interstitial area between the imperfect geometries with gaps and perfect geometries without gaps.

To complicate matters in 2011, these classes learned about the Planck scale and the idea that Planck had calculated the smallest possible unit of time and length. On December 19, 2011, the students followed the embedded geometries of the tetrahedron and octahedron back to Planck’s length. Much later we went back to Planck Time. It was 45 steps down into particle physics and another 67 steps to the Planck units. Going out, doubling all the way, there were an additional 90 steps for our map of the universe of just 202 base-2 steps. Empowered by it, I asked Freeman Dyson and Frank Wilczek about its efficacy. We were encouraged to continue our explorations. We didn’t get very far. It was labelled idiosyncratic by John Baez. It was a non-sequitur and Hawking ruled, so we backed down.

Just recently, I put the five octahedrons together and found that it, too, has a gap. Confirming with geometers that it is an identical gap, I began studying the two together. Salvatore Torquarto agreed with me that it is simple and that it has not been studied much beyond what I did within my initial overview.

Might you add your thoughts? Do you think it could be important? …within the infinitesimal? Thank you.

Warmly,

Bruce

PS. Please excuse my long email. I only wish I could say it all more succinctly. I was especially impressed to see that photo of you and Dali, I copied it out and attached it here. May I use it on our overview page about you and your work? -BEC

`First email: July 7, 2022, 3:28 PM`

Dear Prof. Dr. Thomas Banchoff,

We have been working with the Platonic geometries in our high school and cannot find any references online to a very simple geometric figure of five octahedrons, all sharing a centerpoint (and three sharing two  faces with another octahedron and two sharing only one face). It is a very interesting image when the five-tetrahedrons are added on the top and bottom. That stack has 15 objects sharing the centerpoint. I took the picture below just a few weeks ago but, to date, it appears that there is no scholarship about it.

Have you seen any scholarly analysis of it?  Thank you.

Warmly,

Bruce

PS The URL: https://81018.com/15-2/
Preliminary analysis: https://81018.com/geometries/

Thanks. -BEC

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This actual file was once /a34/ and this information is part of /a31/

Every prime number has its own flavor and personality. There are over 101 different types identified by Wikipedia editors. Are there mathematical experts within the studies of the functionality of prime who could help guide our thinking? Is it possible that each prime introduces a new mathematical set? Is this set properly described by set theory? Is each notation, within itself, defined by set theory and each transformation to the next notation defined by group theory?

To begin the process of answering these questions. We’ve made guesses regarding the ordering of the emergence of numbers, forms and functions within each prime. This listing comes from line 11 of the chart and an article about numbers.
2 • Euclidean geometries, starting with pi and cubic-close packing of equal spheres and lattice generation
3 • Bifurcation theory, including the Feigenbaum constant, and the various manifestations of the theory
5 • Golden ratio (Phi), the Fibonacci sequence and the nature of addition; five-fold symmetries, indeterminacy, the imperfect, fluctuation theory, and ratio analysis
7 • Computer automata theory with John Conway and Stephen Wolfram (this may be a special application of bifurcation theory)

13 • Algebraic geometries

23 • S-matrix theory, unitarity equations, Hermitian analyticity, connectedness

# Searching for the start of our infinitesimal universe

CONTINUITYSYMMETRYHARMONY
Pages: Blackhole | C.|.Empower | Hope.| Mistakes.|. PI (π) |.Redefine |.Singularity | Sphere |.TOE.|.Up
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Introduction. Using simple mathematics (doublings), basic geometries, logic, and commonsense, we found 202 base-2 notations from Planck Time to this day. Within that scale, there is a domain of the infinitesimal. It appears that the smallest, first “things” of the universe are her base units, Planck Length and Planck Time. Virtually ignored for over 100 years after their formulation in 1899, these two Planck units have become de facto ISO standards that define two of the core concepts within our sciences. The largest “things” within this infinitesimal scale — particle physics and quantum fluctuations — are well-studied. Both are measurable and a key part of the corpus of today’s science. If we are ever to build consensus within the sciences, we’ve got to look at our core concepts and agree, “These are core concepts” and “this” is what each means. When we agree, we can begin to build access paths to all of our current applied sciences.

The Tetrahedron and Octahedron. Our path to these two concepts was a bit unusual. We were studying the tetrahedron in high school and we decided to explore its interior structure by dividing each edge by 2 and by connecting those new vertices. We found four smaller tetrahedrons, one in each corner, and an octahedron in the middle. We went further within all five objects.

Within that octahedron we found smaller octahedrons, one in each of its six corners, and tetrahedrons, one in each of its eight faces. We could see how we could tile and tessellate all space using both the tetrahedron and octahedron. We could also see that we could go further within each object, so we did. By our 45th time dividing by 2, we were observing lengths used within particle physics and within the measurement of quantum fluctuations. We continued to go deeper inside. Another 67 times dividing by 2, we were using numbers on the order of the Planck Length. We then used the Planck Length as our edge, and multiplied it by 2. In 112 doublings we were back in the range of our original tetrahedron. We continued. Within another 90 doublings the numbers approximated the size of the universe. At that time we learned there are 202 base-2 notations from the smallest to the largest possible measurements (a story).

STEM. We thought it was the penultimate STEM tool and began sharing it with other math teachers. Nobody had seen a base-2 chart and many pointed to similarities with Kees Boeke’s 1957 base-10 chart. Eventually we began to accept the thought that this base-2 chart just might be an original. We knew it was idiosyncratic; it was not part of any cosmological model.

Although the best scholars within the sciences have wrestled with many hypotheses about the infinitesimal scale, most of the scale can not be measured directly. The best possible approach for now is through logic and math (which, of course, includes geometry). Among the more powerful tools within this domain are natural units and the first documented work to develop natural units was by George Johnstone Stoney in 1874 in Dublin, Ireland. In 1899 Max Planck did his first calculations. In our time in 2022, the units by Planck are better known than those by Stoney.

Here are natural numbers that describe “something” within the earliest universe. Over time, we have come to believe this “something” is the starting point of this universe.

The Key Question: What does that starting point of the universe look like? Although we had natural units, we used two Platonic solids, the tetrahedron and octahedron, to tile and tessellate the universe. We had not asked if there was a particular form those Planck or Stoney natural units might take.

Circles and spheres. These are the most simple constructions — two vertices — yet not until we actually saw how tetrahedrons and octahedrons emerge from spheres were we ready to concede the role of “the starting point” to a primordial, infinitesimal sphere. The dynamic image of cubic-close packing of equal spheres found in Wikipedia opened that door. Images of the Fourier Transform pushed unexpected new frameworks for thought about spheres.

The Nature of a Sphere. To begin to know the sphere, one must know pi (π) and getting to know pi is not trivial. It may well be the oldest, best-known, most-used mathematical equation; I believe we have barely scratched its surface. A key subject within all of mathematics, and although discussed within this website, only within the first few months of 2022 have the more penetrating aspects started to become apparent.

Continuity, symmetry, and harmony. I first developed that working progression from simplicity to complexity in 1971 to describe “a perfected state within space-time.” Pi wasn’t an issue. The development of a moment of new insight was. Yet, as a result of these studies of spheres, I see that perfection is perfection and the progression from continuity to symmetry to harmony is also described by the three most basic facets of the sphere. Of course, within one’s mind’s eye, the sphere is always perfect. Those three qualities, continuity-symmetry-harmony, are deep and abiding studies within academia, however, the study of harmonic functions is its youngest, and the Fourier Transform is its science.

Wild-and-crazy Speculations. There are no less than five Wikipedia dynamic images that are being studied and speculations are being made. For example, the Fourier Transform imparts electromagnetic or gravitational qualities within each infinitesimal, primordial sphere [1]. Further, there are 539-to-4605 tredecillion spheres per second (one primordial sphere per primordial unit of time). Although such speculations are not yet recognized within the academic community, we’ve continued. Each sphere has a natural functionality of continuity-symmetry-harmony as given within pi (π) and her Fourier transform.[2] Here a finite-infinite boundary (or bridge) is defined.[3] Here each sphere manifests with its own flavors and functions which begins as an attractor or repeller.[4] As our universe expands very rapidly, those first 64 notations continue to provide unique foundations for Langlands programs, string-and-M theory, hypothetical particles, SUSY, and so much more.

Of course, these points are all idiosyncratic, unconventional, and a necessary paradigm shift. In this model gravity and electromagnetism begin to be created in the first notations. Each results from a Fourier Transform and these transforms are scale invariant.

I believe it could be the beginning of a new science and I think a good name for it is one that has been around for millennium, hypostatics, which can be loosely translated as “That which stands under” or “the foundations of the foundations.” If we start at the very beginning, within the very first moment, we can watch the universe construct itself with all the working mathematics that has already been developed. Every type of sphere could tells us something about our earliest structures. Every process will have a place. These 64 to 67 notations hold the penultimate puzzle pieces. Just maybe, this may could become an introduction to the start of a new science of the infinitesimal universe. Thank you. -BEC

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[1] Each infinitesimal, primordial sphere. Somebody has to postulate it! Also, perhaps the initial conditions of “sphereness” are best described as an attractor sphere (even more fundamental than a hypothetical particle) or repeller (or repellor) sphere. Why not? It was in this discovery of the attractor scholarship that I also discovered two of its primary thinkers, Steve Smale of the University of California, Berkeley, and John Milnor of Stony Brook, Institute for Mathematical Sciences. Immediately I began to think these scholars might be able to shed light on my questions in recent emails to David Kaiser of MIT and Karen Uhlenbeck of IAS.

While engaging the work of John Milnor to define an attractor, I began thinking about the models of the Fourier Transform and those actions, although considered scale invariant, most scholars seem to hesitate to move that invariance into the infinitesimal scales. There is no hesitation here because within our base-2 chart of the universe, the infinitesimal scale of quantum fluctuations within Notation-67 quickly drops below all thresholds of direct measurements. The inclination today is to assume that Notation-1 is the manifestation of the first infinitesimal sphere and Milnor’s work describes part of the processes within that sphere.

[2] The Fourier transform. Scale invariant, these infinitesimal spheres adopt what amounts to attractor- and-repeller functionalities and these functionalities, building upon each other, manifest differently within each notation. The possibilities for complexity and uniqueness are staggering and most bewilderingly. Much more to come

[3] The finite-infinite boundary (or bridge). Pi is under-appreciated and little understood. The absolute mystery of pi is that it defines both the finite and the infinite, all within three concepts-not-3000 volumes. The inexplicable never-ending, never-repeating, always-changing, always-the-same qualities are beyond comprehension yet here can be summarized in a word, continuity, and its function is to create order. A simple formula that renders the most complex qualities is enigmatic enough, pi-and-its-spheres define space uniquely and perfectly and that is called symmetry and it is the first working relation. The majesty of that perfection is barely grasped and is profoundly unappreciated. The third quality has only been engaged for a short time in human history, perhaps a bit by Kepler, Gauss, Euler, Fourier, and Poincaré, yet new applications seem to emerge daily. Here are the dynamics of a moment, particularly the deepest, most intimate dynamics of motion that bring everything alive, is best summarized as harmony. Everything qualitative is infinite and everything quantitative is finite. A bridge of dimensionless constants connect the two. We have so much to learn and even more to begin to understand and truly appreciate. More… Even more…

[4] Spherical functionalities: From attractors and repellers, to electromagnetism and gravity. The functionalities of spheres is a young science within one of our oldest studies. Yes, the most-basic functionality of pi (π) is within the first 67 notations of the 202 that currently encapsulate the universe. Of the 67, the first ten notations are the foundations of a new science. It is well beneath the domain of quantum fluctuations as well as any direct measurement. These are the foundations under the known foundations; we’ve referred to this domain as hypostatic, for “that which stands under,” and here we take that to be continuity, symmetry, and harmony. Here are the essences, the first principles, and the starting point for every possible application and understanding of spherical functionalities.

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References & Resources

Auslander, J., Bhatia, N.P., Seibert, P., Attractors in dynamical systems (PDF), NASA-CR-59858. 1964.
• Mohsen KhodadiKourosh Nozari Fazlollah HajkarimOn the viability of Planck scale cosmology with quartessenceEur. Phys. J. C 78, 716 (2018). https://doi.org/10.1140/epjc/s10052-018-6191-4
• John Willard Milnor (1985). “On the concept of attractor”. Communications in Mathematical Physics99 (2): 177–195. doi:10.1007/BF01212280 (excellent bibliography). Wikipedia
• Gideon Rosen, “Abstract Objects”, The Stanford Encyclopedia of Philosophy (Spring 2012 Edition), Edward N. Zalta (ed.)(Also, see Zalta, Edward, Principia Metaphysica, online PDF manuscript, 2022)
• Steve SmaleThe Emergence of Function, ArXiv, 2016
• Steve Smale, The mathematics of time Springer-Verlag, New York-Berlin, 1980. ISBN 0-387-90519-7
• David Tong, Classical Dynamics (PDF), University of Cambridge Press, Part II Mathematical Tripos, 2004, 2015
• Within this website: Transformations (2019)

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Emails

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IM

2:07 PM · May 5, 2022 @BillGates, @sundarpichai (Apple CEO) The best cosmologists-physicists, people like Princeton’s James Peebles, Nobel Laureate 2019, say we do not have a theory for the first microseconds of the universe. Perhaps your most brilliant people can work on it: https://81018.com might be helpful place to start.

2:17 PM · May 1, 2022 @FinitePhysicist Can the finite be quantitative and the infinite be qualitative? Does pi (π) (and how it never ends) tell us about continuity, a perfect sphere about symmetry, and its harmonic functions about dynamics? https://81018.com/

2:06 PM · May 1, 2022 @Pontifex Teach us to grasp the infinite. Rediscover pi (π) and how it never ends (continuity) and its symmetry is perfect, and its harmonic functions pervasive. There’s the infinite, all qualitative, and the finite is quantitative: https://81018.com You can do it. We can!

1:15 PM · Apr 26, 2022 @CERNCourier On July 10, 2021 your tweet was about the next generation of detector designs. What about the Planck scale? It is so far beyond detectors, a new approach is needed. The first 64 notations of 202 base-2 that contain the universe need study: https://81018.com/chart/

4:08 PM · Apr 9, 2022. @anabelquanhaase We’re caught by three historic errors, one by Aristotle: https://81018.com/duped/ another by Newton, and also by Hawking as understood by his co-author Neil Turok: https://81018.com/bbtheory/ We’re confused because our grasp of the foundations is wrong. Also, see: https://81018.com/quan-haase/

Looking back…

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Keys to this document, hypostatics