CENTER FOR PERFECTION STUDIES: CONTINUITY•SYMMETRY•HARMONY GOALS.November..2018
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The First Three Minutes Revisited

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BY BRUCE CAMBER  Related pages: Overview, Open Letter, Dark Matter/dark energy

Abstract: For his classic book, The First Three Minutes (1976), Steven Weinberg begins his analysis of the beginning of the universe at 1/100 of a second. Too much comes before that time and he misses the possibilities of key constructions that might help us to understand the current problems of elementary particles within a continuum that relates to the current problems of cosmology.  If, for example, we were to consider the first moment of time to be Planck Time, a simple continuum for this discussion is a base-2 application whereby there are 202 notations or doublings that totally encapsulate the universe. That first hundredth of a second is within the 138th notation. The conclusion is that to begin to understand this continuum requires knowing something about notations 1 to 138, especially the first ten or so, the most formative notations.

I. Introduction

Steven Weinberg and his book, The First Three Minutes. By the time Weinberg begins his analysis at the first hundredth of a second, already too much has happened. The key steps occur closest to something like the Planck Scale. Yet, Weinberg is a critical thinker so we naively invited him to take a look at the first 138 mathematically-defined steps that preceded the first 100th of a second. There are a total of 202 steps (doublings), each a successive doubling from the four Planck base units, Length-Time-Mass-Charge, to the size and age of the universe today (“the Now”).

In  2016, his Theory Group at the University of Texas-Austin received an NSF research grant for “String Theory and Quantum Field Theory: From the Planck Scale to the Hubble Scale.” This group, by definition, is now examining Quantum Field Theory (QFT) down to the Planck Scale. In 1980 Weinberg co-authored an article with Edward Witten, “Limits on massless particles.” They had to look down into the Planck Scale yet they never calculated that there were at least 64 base-2 steps that were out of bounds for all of our measuring devices. The Weinberg-Witten theorem, one of the results of that collaboration, opened the Standard Model of particle physics, yet we anticipate that the first 64 of the 202 notations (doublings, steps, etc.) will open it further.

II. Tools

Beyond Measurement. A rather different approach is needed to get inside those first 64 notations.  Logic, commonsense, a sense of simplicity, mathematics, a highly-unified theory of mathematics, and the basic-basics of physics — constants, universals and the nature of infinity – are a few of the proposed tools. Yet, red flags pop up everywhere. For many physicists, universals spells philosophy and it is not welcomed. And, for even more physicists, the nature of infinity is highly problematic.  A tough sell.  Of the most elite thinkers within the sciences, and Weinberg is assuredly among them, there is very little patience with anything that looks like religion.

Universals, constants and infinity.  And, the hot button is infinity. Physicists do not want to invoke any aspect of theology and the use of the concept of infinity is avoided at all costs. On the surface, that’s smart. Renormalization is smart. Steven Weinberg’s reformulation of  the processes of renormalization is smart.  But, if it is academic elitism, blinders are put on our sciences.

So, of all of these tools on hand, perhaps simplicity will open a reasonable path forward.

III. Simplicity

Simplicity, John Wheeler Style. In 1981, Steven Weinberg was cajoled to leave Harvard for the University of Texas-Austin by a most distinguished physicist who also had roots in Princeton. That was John Archibald Wheeler. In 1986, Wheeler wrote these words, “Behind it all is surely an idea so simple, so beautiful, that when we grasp it — in a decade, a century, or a millennium — we will all say to each other, how could it have been otherwise?”

A possible passageway to simplicity just may be this application of base-2 to the Planck base units based on these observations made over the years:

1. Everything, everywhere, for all time is encapsulated by starting with the Planck base units, doubling each, then doubling again and again, 202 times to the Age of the Universe and the size of our universe.  “That’s inclusive.”
2. A natural inflation is defined by these numbers.  “Now, that’s a challenge.”
3. A formula for light-time-and-space according to Max Planck: light is equal to Planck Length divided by Planck Time.  “Planck’s formula appears more basic than Einstein’s!”
4. The Now. All notations are always active and deeply-and-profoundly interrelated. Though the first-64 notations are beyond our ability to measure, there are still four numbers in each notation to study. “What is time? Space? Mass? Charge? See #3 above.”
5. Plancksperes. If simplicity is what we need, let us consider how the four Planck base units could manifest first within space-time as spheres. “It is simple and ubiquitous… pi.”
6. Infinity is defined by pi as continuity/order, symmetry/relations, and harmony/dynamics.
7. Emergence may begin with sphere stacking and the thrust within those base units.
8. An infinite number of symmetry groups are possible within the first-64 notations.
   Even today, it happens in one picosecond (just 10^-12 seconds or one-trillionth of a second).

That should be enough to get us going!  -BEC

PS.  There is a comment field just below. If you would like to help, we encourage your comments.

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Endnotes, footnotes, resources, references

First draft: 31 October 2018.  

• John Archibald Wheeler (1911-2008), How Come the Quantum? from New Techniques and Ideas in Quantum Measurement Theory, Annals of the New York Academy of Sciences, Vol. 480, Dec. 1986 (p.304–316), DOI:10.1111/j.1749-6632.1986.tb12434.x 

• Weinberg, Steven; Witten, Edward (1980). “Limits on massless particles”. Physics Letters B. 96 (1–2): 59–62. Bibcode:1980PhLB…96…59W. doi:10.1016/0370-2693(80)90212-9.  Personal note to both Weinberg and Witten: “If there are no massless particles, just particles whose mass is below the thresholds of measurement, how does this change these calculations?”

• Robert Brandenberger, Jerome Martin: “The trans-Planckian problem also appears in inflationary cosmology. The cosmological scales that we nowadays observe, correspond to length scales smaller than the Planck length at the onset of inflation.”

• From Wikipedia: In 1979 Weinberg pioneered the modern view on the renormalization aspect of quantum field theory that considers all quantum field theories as effective field theories and changed the viewpoint of previous work (including his own in his 1967 paper) that a sensible quantum field theory must be renormalizable.^[15] This approach allowed the development of effective theory of quantum gravity,^[16] low energy QCD, heavy quark effective field theory and other developments, and it is a topic of considerable interest in current research.

• L.V. Laperashvili,  H.B. Nielsen  and B.G. Sidharth, Planck Scale Physics, Gravi-Weak Unification and the Higgs Inflation  https://arxiv.org/pdf/1503.03911.pdf

• Michael Kachelriess, Quantum Fields: From the Hubble to the Planck Scale (Oxford, 1st Edition)

• Achim Kempf, On the Structure of Space-Time at the Planck Scale,  and Hilbert space representation of the minimal length uncertainty relation (1995), Perimeter Institute, Waterloo

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Notes:

Source for Einstein’s quote, “…the pursuit of truth and beauty is the sphere in which we are permitted to remain children all our lives.”
See Pierre Cartier note from 4 October 2018.
See Ellis note on Defending the Integrity of Physics

Steven Weinberg died: July 23, 2021 Born: May 3, 1933
Weinberg Theory Group, University of Texas – Austin, Austin, Texas

ArXiv (6): What Happens in a Measurement? (2016)
Books:  The Quantum Theory of Fields I, II, III, Cambridge Univ. Press, 1995
•  Gravitation & Cosmology, Wiley, 1972
•  The First Three Minutes, Basic Books, 1977
•_Facing Up, Harvard University Press, 2001  and dozens more.
CV (PDF)
Homepage
inSPIRE^HEP
Nobel Laureate: 1979 Nobel Lecture
Research: String Theory and Quantum Field Theory: From the Planck Scale to the Hubble Scale
Wikipedia
YouTube

Citations within this website: Weinberg Theory Group
•  Where do we go from here?
•  From Perfection to Imperfection
•  The First Three Minutes Revisited

Key associates: Willy Fischler, Jacques Distler, Can Kilic, Sonia Paban (IAS), and Vadim Kaplunovsky

Last email: July 13, 2021 at 9:28 PM

Dear Prof. Dr. Steven Weinberg:

I believe there is a direct correspondence between the breakdown of values throughout our world and the inadequacies of our scientific models. I can hear you reply, “Utter nonsense,” so I beg your patience. Our scientific models are a key part of our worldviews and if they are wrong or too narrowly focused, our beliefs become solipsistic. If the universe is mathematical and highly-integrated, then our understanding of that starting point, now over 13.8 billion years, is key.

Might we consider Max Planck’s base units a starting point? Why not?

Of course, those units are derivative of other key numbers. If we take as a given that Max’s 1899 calculations of his base units are close enough, at least as a symbolic description, how might these initial conditions manifest as the first instant of the universe? …perhaps an infinitesimal sphere? If not these numbers, are there any numbers and calculations that would be more fundamental?

Do you believe Max’s 1899 calculations of his base units are “close enough” to an accurate description of the parameters of the first instant of the universe? If not, are there any such calculations that would be? I believe John Ralston of the University of Kansas is working on recalculations. Thanks.

Most sincerely,

Bruce

See: https://81018.com/empower/

Third email: 30 March 2020 at 4 PM

Dear Prof. Dr. Steven Weinberg:

Of course, you are one of the most cited scholars in our time so I recognize that my little references are just a nuisance. I will be going deeper within your concept of a grand reductionism. From Planck Time to this moment, the Now, all ordered by base-2 exponentiation (assuming a doubling of the numbers of planckspheres for each of the 202 notations so an infinitesimal aether becomes the underlayment of the universe) seems rather “grand” though totally idiosyncratic! But given these days and times of sheer idiocy, I ask, “Why not?”

I’ll insert the two references below so you can see them, albeit slightly out of context.

I wish you continued excellent health in these strange days,

Bruce

PS. The two most recent references are found here:
https://81018.com/imperfection/#1b, /imperfection/#2f (reconstructed below):

Consider the four equations and their numbers for space (length), time, mass and charge.  We ask, “If the Planck Length and Planck Time are the smallest possible units of length and time, does it follow that these are also the first units of length and time? [1]

Does it follow that these equations, with all their dimensionless constants, come together to become the very first moment of physicality?” Unwittingly we had opened the “CDM of the universe” and wondered if Steven Weinberg would consider it a “grand reductionism.” [2]
We started as everything does — simple. We take very little steps and ask simple questions. We try to respect all the scholarship that has gone on before us. When we become confused, we step back to something more simple. So, it was with deep respect that we engaged the CDM approach to the universe. We read that Steven Weinberg (book, Facing Up) might call this model, “a grand reductionism.” We continue wrestling with his work and with these other scholars:

Beyond the Dynamical Universe: Unifying Block Universe Physics and Time as Experienced, Silberstein, Stuckey, McDevitt, Oxford (2018)  https://www.relationalblockworld.com/

Personal note: In 1979 I first met Steven Weinberg at his office in Jefferson and Lyman Labs at Harvard. He did not yet have his Nobel prize, but The First Three Minutes was out.

My overview page: https://81018.com/weinberg/ Thanks. -BEC

Second email: 29 October 2018

RE:  The First Three Minutes Revisited

Dear Prof. Dr. Steven Weinberg:

Our first conversation in your office in Lyman Labs (1979) was about The First Three Minutes.* Please observe that out of the 202 base-2 notations from Planck Time to the Age of the Universe, the 1/100th of a second is within the 138th notation and the third minute is within the 151st notation well after two-thirds of the total information. The first light year is within the 169th notation. The first million years is within the 189th notation. The first billion years is within the 198th notation. The 202nd represents about 10.98 billion years of which only about 2.9 billion years has come to be.

I would be interested to hear your thoughts about this rather idiosyncratic chart! Thank you.

Most sincerely,
Bruce
****************
Bruce Camber
http://81018.com

PS. These are the key points that have emerged from this chart. Obviously, it is all a quite stretch!

1. The universe is encapsulated by 202 base-2 notations from the Planck units
   to this moment and day and current size of the universe, and by definition that includes everything, everywhere, for all time.
2. A natural inflation is defined within the unfolding numbers of each doubling.
3. Max Planck teaches us that light is equal to Planck Length divided by Planck Time.
4. The universe appears to be exponential; Leonhard Euler’s mathematics apply.
5. All notations are always active and deeply-and-profoundly interrelated.
   The first 64-notations are below the thresholds of measurement.
6. The geometries for imperfection might beget quantum physics-and- fluctuations.
7. The four Planck base units manifest first within space-time as spheres.
8. Emergence might begin with sphere stacking and the thrust within those base units.
9. The never-ending, never-repeating generation of spheres could be a finite-infinite bridge.  All the dimensionless constants that define the base units could be as well.
10. Continuity/order, symmetry/relations, and harmony/dynamics might define  infinity.
11. These qualities of infinity seem to impart “an ethical bias” within the structure of universe.
12. Basic concepts like dark energy and dark matter could possibly be addressed.
    Even old concepts like a point can be revisited.

*We also talked about the display project at MIT and my work to summarize your work. There were 77 living scholars selected from around the world and you were among them.

First email in a long time: 1 January 2015

RE: Planck’s Time & Length, The First Three Minutes, and Time in Powers of Ten

Dear Prof. Dr. Steven Weinberg:

Unwittingly we have begun working with Planck Time. We started with the Planck Length on December 19, 2011.

Our high school geometry classes over here in New Orleans backed into a model of the universe using base-2 exponential notation. We multiplied the Planck Length and Planck Time by 2 until we got out to the Observable Universe and the Age of the Universe respectively. Here is a link within our work on a science fair project: https://81018.com/plancktime/ (original) (current)

It took just 202 notations or doublings and it all started because we went inside a tetrahedron, halving the edges, connecting those vertices to discover the four smaller tetrahedrons, one in each corner and an octahedron in the middle. We did the same with the octahedron (finding the six smaller octahedrons in the corners and eight tetrahedrons, one in each of the eight faces) and we didn’t stop until we were somewhere around the Planck Length.

The fascinating thing we discovered along the way is what we are calling “the really-real small-scale universe.” It has a geometry and a systemic order (numbers and symmetries). Nobody seems to know much about it although analyzed throughout human history and called the aether (ether), vinculum, plenum, matrix, grid, continuum, firmament and hypostases. If we divide this little mathematical-geometric universe into “thirds” as the small-human-large scale, the small-scale universe finally has some definition but now it only takes us up to size of the fermions and bosons.

What do you think? Just poppycock? Nonsense?

If it is nonsense, please, please tell us why and we can go back to normal and get on with our life. If not… I thank you.

Most sincerely,
Bruce
—————–
Bruce E. Camber

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Historical footnote: My First letter, 7 March 1979

_________________________________________________
The Quantum Theory of Fields, Vol. I and II by S. Weinberg,

• Review within ArXiv by Dharam Vir Ahluwalia
• inspire^HEP

CENTER FOR PERFECTION STUDIES: CONTINUITY•SYMMETRY•HARMONY• USA•GOALS•September.2019
HOMEPAGES: ASSUMPTIONS|DARK|EMERGENCE| INFINITY|Inflation|Letter| REVIEW|Transformation

On Asking Nobel Laureates Key Questions^*

Ada E. Yonath

Steven Weinberg

Barack Obama

Kip Thorne

Donna Strickland

Gerardus ‘t Hooft

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by Bruce Camber, working draft, initiated in August 2019
Related: Base-2, Dark, Lemaître, Questions, Structure, Subjects-Objects, Time, Transformation

Background. In 1969 I worked for a group that developed new priorities for the USA. One of my jobs was to do the initial research and compile data, including one-on-one interviews with scholars from around the world.¹ These were people who had expert knowledge and key insights about a pivotal subject for our time. That experience served me well.

When my attention turned to creativity, invention, scientific anomalies, and paradigm shifts, the 1935 Einstein-Podolsky-Rosen thought formula ² became my most obstinate-and-key challenge. Something wasn’t right.  It became an on-going challenge to determine what was missing. For the next ten years I called on some of the best who might have new key insights. By 1980, it became entirely obvious, I was going in circles. It was time to earn a living. I backed off knowing eventually somebody would breakthrough.³

In 2011, thirty-one years later, something finally hit me; I was helping a high school teacher in our extended family with his geometry classes. That early story is now well-told; a very-simple mathematical model of the universe emerged.⁴  It had just 202 base-2 notations (successive doublings) of the Planck base units whereby the first notation is the first moment of time. The 202nd notation holds this day (the Now). That 202nd notation also holds all of human history as well as the current expansion of the universe. Fresh from an experience of working with over 100 school kids who seemed to grasp it all, I began asking questions of everyone else.

Potential breakthrough. I’d ask, “Did we back into a new paradigm?  Is it _right or wrong?” ⁵

Nobody had an answer. A few made one or two-word comments. So, what does one do? Ask the smartest among us? …Nobel laureates? Surely they are among our best; so why not? Of course, these laureates are all extremely busy and in high demand. And, to be fair, we also know that they don’t have all the answers. Just look at our world’s problems. Look at how very nasty we can be with each other. Obviously, there is something we haven’t quite grasped. And, my suspicion is that even the smartest among us haven’t a clue how to answer our most vexing questions. Yes, I’m still asking the same questions that I asked in 1979 for a “first principles” project at MIT.

Yet, what if this rather radical re-engagement of our starting points opens a new door? Could it become a major paradigm shift? We know that every one of the concepts that give meaning and value to our life can still be improved even if a concept seems complete unto itself. Our world is filled with silos of information that do not readily communicate with other silos of information.

Our basic premise — a very different starting point — shows how everything is related to everything. There is connective tissue. There is an aether. There is a a grid or matrix. So, we will ask questions until our simple little starting point is either more fully understood or discredited. To date, it seems that those 64 doublings from the Planck Scale to the CERN-scale, if examined, just might give us access to new answers.

Three levels of engagement became increasingly clear: (1) cubic close packing of equal spheres and sphere stacking from the Planck scale, (2) period doubling bifurcation at the Planck scale and (3) the Fourier transform at the Planck scale.⁶

Let’s critically evaluate it. To that end, I have sent notes, emails, and tweets to many Nobel laureates, six of whom are pictured above (each picture is linked to a discussion that then goes to recent letters to them). At no time has any one of them said, “Yes, let’s look into this further.” That could change.

The Future. We will not rest until we know how it is that we are wrong.  Our simple paradigm of reality is based on the following concepts:

• Continuity (order). All time is now.⁷ There is no past or future. There are 202 notations that encapsulate our universe, and every notation is active, different, and encodes every thought, word and deed of every person and every change of every thing. Notations 1-201 are fully symmetric and 202 becomes symmetric, possibly individually through sleeping.
• Symmetry (relations). The primary real.⁸ Space and time are derivative, albeit fundamental relations. Mass and charge are also derivative, albeit fundamental relations. Each of the 202 base-2 notations have different parameters that defines it, yet base-2 (doublings) are held in common by all notations. And, it logically seems all notations are active in the current definition of who we are and why we are.
• Dynamics (harmony). Networks.⁹ There is a plenum, an aether, grid or matrix of planckspheres. It fills the universe within those 202 notations and this is the basis of homogeneity-and-isotropy, dark matter-and-dark energy and moments of perfection also known as harmony.  Notations 1 to 64 are the basis of the continued expansion of the universe.

Leading-edge thinking. Of the eleven Nobel Laureates pictured on this page, questions have already been raised with eight. Those letters to each are linked from the discussion about each below. More questions will be pursued. Any answer will be deeply appreciated and analyzed. Additional questions will be raised. Questions with those laureates listed just below will also be raised.  Others will be asked, especially those who carry on the traditions of laureates who have died. 

Either our simple construct is true or it is not.
And, either way, we will learn a lot about mathematical logic.

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Much more research to come…

• The Nobel Prize in Physics 2016: David J. Thouless, F. Duncan M. Haldane and J. Michael Kosterlitz “for theoretical discoveries of topological phase transitions and topological phases of matter”

• The Nobel Prize in Physics 2015: Takaaki Kajita and Arthur B. McDonald “for the discovery of neutrino oscillations, which shows that neutrinos have mass”

• The Nobel Prize in Physics 2008:  Yoichiro Nambu “for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics”

• The Nobel Prize in Physics 2004:  David J. Gross, H. David Politzer and Frank Wilczek “for the discovery of asymptotic freedom in the theory of the strong interaction”

• The Nobel Prize in Physics 2003: Alexei A. Abrikosov, Vitaly L. Ginzburg and Anthony J. Leggett “for pioneering contributions to the theory of superconductors and superfluids”

• The Nobel Prize in Physics 2001: Eric A. Cornell, Wolfgang Ketterle and Carl E. Wieman “for the achievement of Bose-Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the condensates” 

The study of critical insights of scholars is a key…

Marie Curie

Gérard Mourou

Frank Wilczek

Barry Barish

Rainer Weiss

Katherine Freese

Endnotes, Footnotes, References and Resources

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A basic premise of this website: Every concept can be improved even if it seems complete.
* Six Nobel laureates. Pictured at the top of this page (with another five just above this section endnotes, footnotes, etc.) have all been asked key questions about our simple, mathematical  (base-2) model of our universe. Letters to each are linked below. Plus, there are many others among our listings of people who have also been contacted about this work.

Ada E. Yonath (Email) is included because she never gave up. Who can claim 25,000 trials over ten years? Not many people. Most of us would have given up. But, Ada had an insight, a hunch, an inner driving motivation. She may have gotten discouraged, but she would not be deterred. So, who better to ask about the very nature of life? There is a huge discussion within biology — genomics, RNA/DNA, protein, bioinformatics, back to the simple archaea family.  How-when-where does it begin? How is it sustained? How would you answer our questions to her? In our base-2 model, life as we know it today doesn’t begin until the 202nd notation. Only 2.83 to 3 billion years of this notation has unfolded. Also, the earth is just 4.543 billion years old, the sun 4.6 billion and the Solar System 4.51 billion! That all began in the 201st notation!

Steven Weinberg  (Email & Letters) was awarded his share of a Nobel prize in 1979. Even before that time, he did not suffer fools gladly. This special assurance of knowing what is right and who is wrong often bristles people, but I rather enjoy such folks. I continue to nudge this ever-so-famous emeritus professor and his group of scholars working on basic theory through a grant from the National Science Foundation, Department of Energy. As expansive and detailed as their knowledge is, I think they have a limited view of the possibilities between the Planck scale and fundamental particles. In our model dark matter and dark energy emerge within those first 64 notations, well-below the thresholds of actual measurement! Just because these theorists have never considered that there could be “the first 64 notations,” it is easily written off as poppycock!

Barack Obama (Letter and emails) was awarded the Nobel Peace Prize. It was controversial at the time and  continues to be so. Notwithstanding, our former president is included here because with the Prime Minister of Israel, Benjamin “Bibi” Netanyahu, and the Ayatollah Seyyed Ali Khamanei of Iran, they were all introduced to our work, particularly where it invokes continuity, symmetry and harmony, the quantitative/qualitative faces of this project. This value dimension is a key part of the project. This note was to invite them to challenge the incompleteness of religious hermeneutics and the our understanding of the finite-infinite relation. Although this work now falls to all thoughtful world leaders, I believe it should be a component of every Nobel Peace Prize, i.e. an intellectual contribution to our understanding of, and need for, an ever-improving quality of life for everyone.

In his Nobel speech, Obama said, “To say that force may sometimes be necessary is not a call to cynicism – it is a recognition of history; the imperfections of man and the limits of reason… We do not have to live in an idealized world to still reach for those ideals that will make it a better place… Let us reach for the world that ought to be – that spark of the divine that still stirs within each of our souls.” My comment: I think we can go deeper.

Kip Thorne (Letters) has allowed his knowledge to be challenged by everyday people. He has had a primary role with the development — writing, production, and follow-up — of the 2014 movie, Interstellar. Our hope is that with his unique sense of openness, he will eventually tell us where, how, and why our model could work within the world of physics and even general science.

Donna Strickland (Email) was awarded her share of the Nobel Prize in 2018 within key areas of laser technologies. Who better to ask the question, “What is light?”  Much more than visible light, the rest of the electromagnetic spectrum doesn’t look like light. Can we understand light in new ways from the four Planck base units? We think so.

Gerardus ‘t Hooft (Email) in 2011 with his Dutch colleague, Stefan Vandoren, wrote the heart of their book, “Time in Powers of Ten: Natural Phenomena and Their Timescales.” Translated into English by Saskia Eisberg-t’Hooft and republished in 2014, it was a natural sequel to the 1957 work of another Dutch educator, Kees Boeke with his book, “Cosmic View: The Universe in 40 Jumps.” ‘t Hooft became a Nobel Laureate in 1999. Though our work has not been embraced by our Dutch friends, it also has never been challenged.

Frank Wilczek (Emails, meetings) was the first Nobel laureate to teach us about Max Planck and the nature of the Planck scale. His articles and books are everywhere within this website and our offices. He has not yet shut us down and at times, he has encouraged us.

Rainer Weiss (Email) is a new Nobel Laureate and his LIGO experiments are being heavily analyzed and discussed. He has spent a lifetime focused on the subject. For us to ask him to consider a completely different set of starting principles was a bit presumptuous. But, one never knows. A seed may have been planted.

Katherine Freese (Email) is not a Nobel laureate but there is good reason to think that she could become one. In 1999 principal thought-leaders among cosmologists and theoretical physicists were called in to make sense of inflation. They haven’t. Here we find the work of somebody who has. She further opened her study of natural inflation (appears to have begun in 1991).  She seems like the kind of person who might consider asking what natural inflation would look like if it were to begin at the Planck scale. If she and her associates were to find a natural, exponential inflation that redefines time, she would be in line for a Nobel prize and I would be most pleased.

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¹ New priorities for the USA. Cold-calling is an essential part of business growth and it seems also to be true about intellectual growth. To grow we have to risk a little. Science advances incrementally and most often it is slow and even arduous. Paradigm shifts are very rare. Yet that “cold calling” modus operandi prevailed and served me well.  A little more history…

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² The 1935 Einstein-Podolsky-Rosen. Commonly referred to as the EPR paradox, my first encounter in 1970 was through David Bohm when a friend introduced me to his work with Aharonov from 1957. As one thing always leads to another, soon we were studying his other 1957 article about “…Paradox of Einstein, Rosen, and Podolsky.” There were 77 scholars whose insights I especially sought out.  

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³ Something new will come. That’s the creative process. Sometimes you just have to “back off until something hits you.” We had gone over the details incessantly. We asked the question, “What are we missing?”  We didn’t know. We had continuity-symmetry-and-harmony, but also Bell’s inequalities, quantum fluctuations and action-at-a-distance. It was enigmatic!

____________________

⁴ A mathematical model of the universe. Long before we had that simple model, I had questions for everyone.  A mathematical physicist, Patricio Letelier, told me in and around 1976, that strings were the smallest constituents of matter. We were all working on our PhDs at Boston University and even at that time I was thinking that string theory had something to do with a finite-infinite bridge. Though renormalization was helpful in getting specific mathematical equations to work, it did not mitigate or truncate the concept of infinity, especially if we redefine infinity as continuity (order), symmetry (relations) and harmony (dynamics). In 2011 we quickly discovered that our 202 base-2 notations were not part of current academic thinking. Base-10 (Kees Boeke’s 1957 work and the ‘t Hooft – Vandoren 2014 work) was, yet it was also functionally aloof and not granular enough. We began to tell the unfolding of our 2011 story, “Isn’t this remarkable? What’s happening within those first 64 notations?” We had questions for everyone, but at least, we had a STEM tool! 

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⁵ …a new paradigm? …not even wrong? It took seven years (2011-2018), but the light is shining a little more brightly. Then, in July 2019 the homepage article (herein to be known as “the transformation homepage“) just seemed to open it all up. There was a concrescence of concepts. At no time had those concepts been applied to the Planck scale. As it was happening, it just seemed right. So, our rather radical re-engagement of these starting points is either right or wrong.  I’ll give it until August 31 — “Let’s go over that just one more time” — and we’ll begin submitting that article to professional publications. When they reject it, we will plead for some explanations. Maybe we can get some conceptual clarity.

My 1979 MIT project is finally back in business!

____________________

⁶ Three faces or forms of the transformation. From among all the concepts examined over the years, three unlikely, principal concepts emerged for our transformation homepage: 
1. Cubic close packing of equal spheres (and sphere stacking) from the Planck scale
2. Period doubling bifurcation at the Planck scale
3. The Fourier transform at the Planck scale

Literally, taken together, I will guess that all three will touch most every academic discipline.  I cannot see how it could be otherwise.

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⁷ Three infinite functions of the transformation. Of the principal concepts within that Transformation homepage, our paradigm for infinity will be applied.  The first is continuity (order) whereby all time is now. 

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⁸ Symmetry (relations). A primary real. Instead of running away from the concept, we embrace infinity. With only a superficial analysis of pi, people like David Hilbert are challenged. When we begin to explore space and time as derivative, what becomes fundamental is clear — the relations. Mass and charge are also derivative, albeit fundamental relations. These 202 base-2 notations each have different parameters that define it, yet base-2 (doublings) are held in common by all notations. And, it logically seems all parameters are active in the current definition of who we are and why we are.

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⁹ Dynamics (harmony). Networks. There is a plenum, an aether, grid or matrix of planckspheres. It fills the universe within those 202 notations and this is the basis of homogeneity-and-isotropy, dark matter-and-dark energy and moments of perfection also known as harmony. Within every second of our universe, there are 143 notations that pulsate, like a heart beat, expanding the universe.

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More editing to come.

References & Resources

Reference/Resource #1. David Bohm in his book, Causality & Chance in Modern Physics, 1957, pages 163-164, said: “Thus, in the last century only mechanical, chemical, thermal, electrical, luminous, and gravitational energy were known. Now, we know of nuclear energy, which constitutes a much larger reservoir. But the infinite substructure of matter very probably contains energies that are as far beyond nuclear energies as nuclear energies are beyond chemical energies. Indeed, there is already some evidence in favour of this idea. Thus, if one computes the “zero point” energy due to quantum-mechanical fluctuations on even one cubic centimetre of space, one comes out with something of the order of 10³⁸ ergs, which is equal to that which would be liberated by fission of about 10¹⁰ tons of uranium.”

Reference/Resource #2. A seminal work, Discussion of Experimental Proof for the Paradox of Einstein, Rosen, and Podolsky, D. Bohm and Y. Aharonov, Technion, Haifa, Israel Phys. Rev. 108, 1070 – Published 15 November 1957 (Received May 10, 1957 [PDF]

Reference/Resource #3. On of the most seminal works in physics, On the Einstein, Podolsky and Rosen Paradox [PDF], J.S. Bell, Physics Vol. 1, No. 3, pp. 195—200, 1964

Spacetime

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Challenge us, coach us. We need all the help we can get.  I’d be pleased to hear from you. -BEC

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A Radical View of the Inflaton Field
by Bruce E. Camber (first draft)

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 Planck–Stoney-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 Ijjas, Paul J. Steinhardt, Abraham Loeb, 2014, (3) Inflationary paradigm after Planck 2013 (PDF), Alan H. Guth, David I. Kaiser, Yasunori 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 Atkins, Xavier Calmet, 2011, (6) Warm Little Inflaton (PDF), Mar Bastero-Gil, Arjun Berera, Rudnei O. Ramos, Joao G. Rosa, 2016, (7) The Minimal GUT with Inflaton and Dark Matter Unification (PDF), Heng-Yu Chen, Ilia Gogoladze, Shan Hu, Tianjun Li, Lina 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 Haro, Jaume Amorós, Supriya Pan, 2019, and (10) On the behaviour of the quantum Universe anisotropies in a bouncing picture (PDF), Eleonora Giovannetti, Giovanni 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.

So, there will be more to come. This article is still a draft; it is in process; insights from all these scholars’ references (above) and most-recent articles will be added over time. -BEC

[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 Nomura, Taizan 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 n_s 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.

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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. Fewster, Jacob 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.

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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 Boyle, Quanta Magazine
23 January 2023, Rohan Naidu, MIT Pappalardo Fellow

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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

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Participate       You are always invited.

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Keys to this page, inflaton

• 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/
• The initial headline for this article: Infinitesimal Spheres as Inflatons
• 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 Atkins, Xavier Calmet, 2011

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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, pi (π) 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 pi (π) 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.

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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

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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 Boyle, Quanta Magazine
23 January 2023, Rohan Naidu, MIT Pappalardo Fellow

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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/

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Participate       You are always invited.

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Keys to this page, pi-π

• This page became the homepage on January 27, 2023 at about 8:42 PM.
• 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/
• The headline for this article: Pi Defines the Finite and Infinite.
• First byline is: Filename changed to “pi-π” because pi-pi was already engaged.

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CENTER FOR PERFECTION STUDIES: CONTINUITY•SYMMETRY•HARMONY October 2022
Pages: Agree | Gravity| Hope | Hypostasis Mistakes | PI (π) | Questions | Sphere | STEM | Up
THIS PAGE: CHECKLIST | FOOTNOTES | REFERENCES EMAILS | IM | PARTICIPATE | Zzzz’s

Reason to believe ..
by B.E. Camber Working first draft
Go to an easier read: No links/notes

Abstract. Base-2 exponentiation symbolically begins with the Planck scale, the first possible moment in time, and in 202 doublings defines this current moment in time.^[*] Base-2 groups diverse studies such as exponentiation, bifurcation theory, fractal geometries, and cellular growth. It’s becoming a working model based on simple logic, geometries, and algebra, initially based on spheres, tetrahedrons, and octahedrons. It begins with natural units and is driven by pi (π). Its 202 predictive, base-2 notations totally absorb big bang cosmology.[†] This mathematically-integrated view of the Universe addresses key issues that big bang cosmology cannot. Five examples follow.

I. Smoothness. The James Webb Space Telescope images have raised anxieties that the early universe is too smooth for our working understanding of the dynamics of big bang cosmology.^[1] The transition from smooth to lumpy is not a problem within our 202 base-2 notations. In this model geometric gaps do not become systemic until later in the unfolding of the universe.^[2] The earliest notations begin perfectly smooth because it starts with the most simple geometries that tile and tessellate this universe perfectly.^[3]

II. Time: The first minute, first second, and first zeptosecond. The first minute of the universe is within Notations 149-150.^[4] The first second is between Notation 143-and-144. Zeptoseconds (1×10^-21) are between Notation 65-and-67. And, Notations 1-64 are opened for definition!

Eminent scholars, Sean Carroll ^[5] of John Hopkins and James Peebles ^[6] of Princeton (Nobel laureate, 2019, and a pioneer of cosmic microwave background radiation research) articulate the importance of defining the first minute of the universe. In June 2020 twenty-seven scholars wrote “The First Three Seconds: A Review of Possible Expansion Histories of the Early Universe” (arXiv:2006.16182 [astro-ph.co]). It focused on emergence, yet they were unable to define the first minutes of our universe.

The zeptosecond is on the cusp of quantum fluctuations. The first notations begin with the natural units that were defined by Max Planck in 1899 ^[7] and George Johnstone Stoney ^[8] in 1874. It is a natural grid. As each notation builds on the prior notations, the geometries, numbers and relations necessarily redefine the nature of time.^[9] Those first 64 notations have been unwittingly defined by experts within Langlands programs, string theory, and like disciplines ^[10], but big bang cosmology hides any access to those first notations.

III. Quantum fluctuations and quantum physics. The study of a geometry of quantum fluctuations over the years has been limited.^[11] A most-simple place to start is to recognize the tetrahedral gap that Aristotle did not see.^[12] That gap is real. And, there are others that are ignored. Add to it our octahedral gap and then the icosahedral gaps.^[13] Here are possibilities for fluctuations. Big bang cosmology has no simple geometry and certainly no geometry for chaos and indeterminacy. Our mathematically-integrated view of the Universe begins with the inherent geometries of doublings that perfectly tile and tessellate; plus, it has a geometry for fluctuations that is inherently indeterminant. One of our primary studies is to grasp the varieties of gaps and the probabilities for each manifestation within a given notation.

IV. A natural inflation and dark energy and dark matter. Dark matter and dark energy are below all possible thresholds of direct measurement. The indirect effects have been well-regarded since the work of Lord Kelvin (1884), Jacobus Kapteyn (1922), Jan Oort (1932) and Fritz Zwicky (1933). That mystery prevails.^[14] Big bang cosmology blocks the view of both the geometries of perfection and of imperfection. Initially there are no gaps as spacetime is dynamically created. Within this mathematically-integrated view of the Universe, a natural inflation starts with the most simple infinitesimal sphere, sphere stacking, and cubic-close packing of equal spheres. Tetrahedrons and octahedrons naturally and smoothly tile and tessellate the earliest universe.

If taken as a given that one infinitesimal sphere is generated per unit of length and time, the rate would range from 539-to-4609 tredecillion spheres per second.^[15] Of course, that range is established by Planck Time and Stoney Time.

V. Finite-infinite, quantitative-qualitative. Big bang cosmology has no finite-infinite relation and makes no distinction between the quantitative and the qualitative. It does not posit the smallest physical unit of spacetime. It makes no statements about pi (π), nor recognizes the essential faces of pi (π): continuity (ordering), symmetry (relating) and harmony (making dynamic).^[16] Naturally, the ubiquitous dimensionless constant that generates the natural units for Planck and Stoney is pi (π). We hypothesize that these three faces of pi (π) define the qualitative and the infinite. Within big bang cosmology the Planck Epoch and a singularity are the baseline whereas within our mathematically-integrated view of the Universe, it is the simple perfections of the infinitesimal sphere, then spheres, and then tetrahedrons and octahedrons.

Thank you. -BEC

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Endnotes & Footnotes
Most of these points, already have pages within this website, are linked from here.

[*] 202 predictive, base-2 notations. Initiated in 2011, this chart drives this model.

[†] Simple concepts: Spheres, tetrahedrons, octahedrons and doublings. This project began in 2011 in a New Orleans high school geometry class. Here’s an early assessment. Rather surprisingly, it readily absorbs big bang cosmology ( https://81018.com/calculations/ ).

[1] Smooth to lumpy. An early article, The Lumpy Universe, by a group within NASA’s Goddard Space Flight Center is written for students from 14 years old and up. The Imagine Team is an effort headed by Dr. Barbara Mattson and the segment, Imagine the Universe, addresses the current concerns within cosmology and astrophysics. It raises those issues that are pushing the scientific-academic community to re-imagine big bang cosmology.

Embedded links (URL):
Article: https://imagine.gsfc.nasa.gov/science/questions/lumpy.html
Team: https://imagine.gsfc.nasa.gov/people/lcteam.html
Project Leader: https://imagine.gsfc.nasa.gov/people/mattson.html

[2] Systemic gaps and fluctuations. Too dense and too fast to accommodate fluctuations, it is hypothesized that quantum fluctuations do not initially manifest until much later than the first minute which is within Notation-144. It is also hypothesized that these gaps, once systemic, will work back into prior notations and are currently at least within Notation-67. Further, it is hypothesized that there is also a geometry of gaps for consciousness and the mind.

[3] Tile and tessellate this universe with no gaps. Throughout mathematical and geometric history, tilings and tessellations have challenged the human mind. Kepler was the first to make it a systematic study (Harmonices Mundi). The simplest 3D tessellation is with the tetrahedron and octahedron. Within this model it shapes the first instant of the universe resulting first in a sphere, then a systematic expansion of spheres (see #15 below), sphere stacking, and then what is known as close-cubic packing of equal spheres. Here is the starting point within Notation-0.

[4] Notations 1-202: This chart of 202 notations began in 2011. It became a horizontally-scrolled chart in 2016. It may take several generations to fill out even the first level of notations. It may well take many more generations to tie all the notations together in a dynamic unit. Notwithstanding, elementary school children can (and have) effectively engaged the chart to see the order within our universe.

[5] Sean Carroll. He is listed among the scholars to whom we turn for insight and help. Based on the videos we have watched and from his writings, we readily speculate that Sean is a bit like Steven Weinberg. When Weinberg got impatient with a person with whom he disagreed, he would say, “Utter nonsense.” I suspect the response from Sean Carroll would be similar. Yet, we’ll continue to write to him!

[6] James Peebles. Of course, most Nobel laureates are swamped with correspondence. There are just too many people hoping to grab their attention. James Peebles is older now and still very active looking at astronomical phenomena that are “off the beaten track.” In that light, our strategy has been to catch him by surprise in hopes that he might rethink the concepts of space-time-and-infinity with us.

[7] Max Planck. There are current challenges to Max Planck’s base units yet the results of those challenges are still being evaluated. We are following the work of John Ralston, Espen Gaarder Haug, and Tim Palmer as each impacts our thinking about the Planck constant, the Planck base units, and the dimensionless constants.

[8] George Johnstone Stoney. Not many people pay attention to the scholarly work of Stoney. We do because we have been encouraging a deep review of all this work and the ISO–CODATA–NPL–NIST standards for all the units involved.

[9] Redefining Time. The most disconcerting notion to emerge from this work is to discover that in some manner of speaking all time is now. Although physicists like Carlo Rovelli, Max Tegmark, and Julian Barbour, claim time is an illusion, within the 202 notations linear time is associated with just that period of time experienced prior to sleep (when it is recompile into the whole). We say that time is exponential; time is an equation and all notations are always active.

[10] Langlands programs, string theory, and like disciplines. There are no less than nine disciplines currently, yet unwittingly, addressing these first 64 notations. None of their scholars has formally recognized the 202 notations and none are formally on the grid. They are further linked here: Langlands programs, string theory (including M-Theory, F-theory, type II and its offshoots), supersymmetry (SUSY), loop quantum gravity (LQG), causal dynamical triangulation (CDT), causal set theory(CST), field theories (QFT, CFT, LFT), spectral standard model (SSM), hypothetical particles, and a few more.

[11] Quantum fluctuations. A search on the words, “geometry of quantum fluctuations,” renders just ten results on October 5, 2022. There has been no geometry of fluctuations based on simple geometries of gaps. Our page, geometries, is our announcement of our intention to pursue this domain of study beginning with the geometries of gaps within the most simple structures.

[12] Aristotle’s blindspot. This history serves to remind us to be somewhat reserved about our conclusions. Life is short, but our words may well live on. Aristotle’s arrogance is all of us. Aristotle’s mistake is profoundly all of us.

[13] Gaps. The initial study of the five-octahedral gap was part of the /geometries/ efforts in May 2022 when we announced our intention to pursue this domain of study. We were even able to create a model of what we believe is the first five-octahedral gap — 81018.com/2022/05/19/five/ — that then coupled with the tetrahedral gaps — 81018.com/gap/ — becomes a new object — 81018.com/15-1/ — which has been tentatively named, triantahedron, for a thirty-sided object. We’ll see if it works.

[14] Historical figures who first recognized dark energy-dark matter. Thousands of scholars have subsequently tried to explain the dark energy and dark matter. The big bang hides people’s access to answers. To say that it is the abundance of infinitesimal spheres below the boundaries of measurement is just an introductory overview and a direction for a more complete answer.

[15] 539-to-4609 tredecillion spheres per second. When I surveyed the initial formula in September 2021, it seemed simple and logical enough. Yet, to begin to imagine the emergence of 539 tredecillion spheres per second is simply beyond my grasp. This is the opening of a new domain of study. The range is a placeholder for more refined figures to come.

[16] Continuity-symmetry-harmony. The heart of this study began with simple geometries but backed into the infinitesimal sphere by backing into the very nature of pi (π) and finding the three faces of a perfected state in spacetime, continuity, symmetry, and harmony, all deeply inherent within pi. This is our essential story and it will be told and retold many more times to come.

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

• Reason to believe by Rod Stewart, Lyrics by Tim Hardin

• Diego Rapoport, The Geometry of Quantum Fluctuations II (Quantum Gravity and Ergodicity), in “Proceedings of the International Workshops on the Frontiers of Mathematics, Physics and Biology”, Monteroduni, Italy, August 1995 vol. 2, G. Tsagas (ed.), Hadronic Press and Ukraine Academy of Sciences, 1996

• Two Questions:
(1) Is the smoothness of the JWST’s earliest universe a cause for concern? It seems some are concerned that it cannot be supported by big bang cosmology. Sean Carroll says, “…dark energy made the universe smooth out and accelerate, but it didn’t stick around for long.”
(2) Is the Guth-defined inflation cause for concern? Most of the old guard like ‘t Hooft, seem fine with the one-time exception that inflation was an expansion of space itself so extralogical assumptions apply.

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Emails
This is a representative selection of our notes to scholars asking about the substance of this article.

• Matilde Marcolli, Caltech, Pasadena
• Elizabeth Gibney, London
• Suzy Lidström, Texas A&M, 15 October 2022
• Monika Schleier-Smith, Stanford, 15 October 2022
• Natalie Wolchover, Simons Foundation, Quanta Magazine, NYC, 14 October 2022
• Fedele Lizzi Naples, Italy, 15 October 2022
• James Peebles, Princeton, 12 October 2022
• Edward Zalta, Stanford, 12 October 2022
• Andrew Chi-Chih Yao, Tsinghua, Beijing, China, 11 October 2022
• Edward (Rocky) Kolb, Univ. Chicago, Kavli, Fermilab, October 11, 2022
• Sean Carroll, John Hopkins, October 11, 2022
• Fabienne Casoli, Paris Observatory, 10 October 2022
• John C. Mather, NASA Goddard Space Flight Center, October 9, 2022
• William Bailek, Princeton, 7 October 2022
• Frank Wilczek, MIT, 7 October 2022

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IM
There will also be many instant messages to thought leaders about the general thrust of this article.

10:08 AM · Oct 21, 2022 @FreelanceAstro @NYTimes @BBC @NPR @SciAm @QuantaMagazine @Undarkmag My note to you is really to all people who are exploring the edges of knowledge and our understanding. Isn’t simple better than complex? https://81018.com/chart/ https://81018.com/stem/ https://81018.com/reason/

1:35 PM · Oct 20, 2022 @GeraldoRivera @KellyannePolls @IvankaTrump Come on, Geraldo. You don’t have to incite folks with words like jingoism. You’re bigger than that. Little worldviews get little people saying little things. Get an integrated view of the universe. Be a leader: https://81018.com/

• 2:04 PM · Oct 14, 2022 @GoryErika It will take a bold journalist to explore the “new physics” coming back with the images of smoothness from the James Webb Space Telescope. It is too radical for most: https://81018.com/reason/ (Perhaps “after the big bang” will get redefined).

• 3:37 PM · Oct 9, 2022 @kanyewest The big bang theory (BBT) is coming down. It’s on a smooth decent on the JWST – James Webb Space Telescope – and within the deep continuity, symmetry and harmony of the universe. A BBT alternative working model is here: https://81018.com Give a shout for more. -BEC

• 8:43 AM · Oct 8, 2022 @NatashaBertrand Biden needs a new model of who he is and why he is. “The Biden Family” is not a model. A mathematically-integrated view of the universe is. Base-2 exponentiation (doublings) starting at the Planck base units is: http://81018.com is a simple start. All continuity equations!

Editor’s note: Continuity is the first principle of order. The second is symmetry whereby a relation is created. The third is harmony, where there are multiple symmetries within a dynamic moment. We need all three, but continuity will at least get us on a level playing field.

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Participate

You are always invited.

_____

Keys to this page, reason

• This page became the homepage on October 8, 2022. It is still under construction.
• The last update was October 17, 2022.
• This page was initiated on October 4, 2022.
• The URL for this file is https://81018.com/reason/
• The headline: Reason to believe (lyrics by Tim Hardin, sung by Rod Stewart).
• First byline: Anything that comes “after the big bang” will be damaged.
• Next byline: Smoothness, the first minute, fluctuations, dark energy-matter, finite-infinite….

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Just as an aside, it appears that the adoption cycles of a major idea require no less than three generations and quantum theory is no exception. New theories have new truths but are not absolute truth and not “all truth for all time.”

Avi Loeb, The Center for Astrophysics, Harvard University, Cambridge, Massachusetts

Articles by Avi
ArXiv (741): Overview of the Galileo Project, August 2022; Direct Measurement of Cosmological Parameters from the Cosmic Deceleration of Extragalactic Objects, 1998, plus more.
Books: Extraterrestrial, 2021
Homepage(s): Google Scholar, IAS, inSPIRE^HEP Scientific American, Smithsonian, Wikipedia
Publications: Quote (in the header just above): Our Unexpectedly Smooth Universe May Point To New Physics, Govert Schilling, Sky & Telescope, July 31, 2020
Twitter: National Cathedral…
YouTube: CNBC, TOE

First email: 10 September 2022 @ 3:29 PM (an updated version)

Dear Prof. Dr. Avi Loeb:

You are open to idiosyncratic concepts. The question is, “…just how idiosyncratic?” Our work all started with simple math and geometry in a high school and I do not think it will be a waste your time to review a bit of our work.

By the way, we share some commonalities.

In 1972 at Harvard I worked with Arthur Loeb back within the Philomorphs. In the attic of Sever Hall, geometry was everything; Bucky Fuller was part of it.  In 1975 with Arthur McGill over in the Divinity School, we studied Austin Farrer’s Finite and Infinite and it seared in my mind with the need for a better, more encompassing definition of infinity.

Later, in 1979 I was invited by Steven Weinberg to come by his Lyman office. My last note to him was just ten days before his death. With my mixed bag of studies, continuity-symmetry-harmony were not particularly meaningful to him, but he didn’t call it utter nonsense to my face! He would with these two articles: First three minutes revisited and Dark Matter-Dark Energy.

So I ask, “Might we take the Planck base units as the symbolic representation of the first moment in time? Might we apply base-2 to those units to create a chart with boundaries and parameters?” There are just 202 base-2 notations from that first moment to this day. From Notation-1 to Notation-143, essentially the first second, it captured and is currently capturing all but a microsecond of classic big bang cosmology.

Much more recently I found that continuity-symmetry-harmony describe the three faces of pi and, of course, pi is involved with the most pivotal equations of physics. Might pi also define the first units of space-time? …an infinitesimal sphere?  If so, that sphere emerges about 64 notations from the first measurements of quantum fluctuations.

May I go on?  Thank you.

Most sincerely,

Bruce

PS. Eleonora Di Valentino (and colleagues at Snowmass 2021) also raised the spectre that S8 could be calling for a new physics. -BEC

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Note: John Langeloth Loeb Jr. CBE is another Loeb in my life. An American businessman, former United States Ambassador to Denmark, and former delegate to the United Nations, he is an advocate for religious freedom and separation of church and state. In 2009 he founded the George Washington Institute for Religious Freedom located in Rhode Island. He is another very impressive Loeb! -BEC