3. 2. 1. 0: Minutes, Seconds, Nanoseconds, Picoseconds… Plancksecond!

Prior Post|Claims|Endnotes-Footnotes|References|Emails|Tweets|Zzzz

A Most-Basic Building Block of the Universe:
One Plancksphere per Plancksecond *

by Bruce E. Camber Related: World – HistoryExpansionFirst InstantConsciousness

In 1899 Max Planck calculated numbers for Planck Length & Planck Time.1 Max Planck knew he was onto something significant, but he couldn’t quite make it work. One can imagine that he had hoped that the young Einstein could help. Surely Einstein opened new doors to explore, but his were different. And, we have learned over the years that all big ideas and concepts incubate slowly.

Within Max Planck’s equations, space-and-time are necessarily yoked. One is always a face of the other and a primary characteristic of light. As such, both are also yoked to mass-and-charge. Planck and Einstein redefined the very nature of space-and-time, and mass-and-energy. In so doing, they unwittingly redefined the finite and infinite.

A goal of this article will be to examine how this could be so. We start with one of the world’s oldest, best-known, and most-used mathematical constructs, pi, along with her circles and spheres. Most of us have not explored how in some manner of speaking these three are derived from continuity-symmetry-harmony. Another intention of this posting is to see how pi-circles-and-spheres generate space, time, and geometries.

This work is slowly evolving out of presuppositions that have also slowly emerged.


Max Planck ignored his own calculations.2 Perhaps he didn’t know what to do with them. It took out-of-the-box thinkers, a bold scholar like C. Alden Mead, to open that door. In 1959 he wrote about the place of the Planck scale. Leading first-principles scholars like John Barrow (1982) and Thanu Padmanabhan (1985) also began wrestling with the Planck units. Frank Wilczek finally broke open the Planck scale to the world in 2001 with a series of articles in Physics Today.

More recently scholars around the world have wrestled with the meaning and value of the Planck Scale. Most top-level posts within this website attempt to be deeper exploration of  those issues.

The four formulas for the Planck base-units

Too small to measure, Planck Length and Planck Time redefine the infinitesimal. It appears nothing is meaningfully smaller, shorter or faster.

When the Planck base units are re-envisioned to create a base-2 chart from the smallest to the largest measurements of space and time, it becomes increasingly evident (1) neither space-nor-time are absolute, (2) time-and-space are Janus-faced, correlated with the Janus-face of mass and energy, and (3) all the notations are, even today, generating one Plancksphere per Plancksecond.

There are around 64 notations (doublings) before waves, particles, and fluctuations. Sixty-four successive doublings of the Planck Length and Planck Time are enough space and time to do a lot of mathematics-and-geometry, but key leaders within the academic-intellectual community think it’s too small for much of anything.

Older, Slower Studies 3

The First Three Minutes.3 In this 1976 book Steven Weinberg begins his study of the universe at about 1/100 of a second after the big bang. That is Notation-138 within our horizontally-scrolled chart. There are 202 base-2 notations or doublings from Planck Time, the very first infinitesimal moment of the universe, to this very day. And, yes, there are just 202 simple doublings.

We all know that life is about doublings. Every living thing doubles in some special way. Yet, Weinberg could not explore from Notation-1 to Notation-137. Though the Planck units have been around since 1899, that progression of Planck doublings did not come out until 2011. To date, we know of no other model of the universe that starts and builds  on the Planck base units initially manifest as an infinitesimal sphere.

The First Three Seconds: A Review of Possible Expansion Histories of the Early Universe, (June 2020). Twenty-seven leading scholars from around the world collaborated on a composite article about the first three seconds. The very first second is between Notation-143 and 144. They, too, assumed an infinitely-hot start of the universe so their first three seconds are shrouded in mystery. They didn’t explore the concept of a cold-start model which was first proposed in 1927 by Lemaître when he began to share his earliest thoughts about the beginnings of this universe, so they, too, missed a lot of possible action between Planck Time and that first second.


Planck-Time Transformations
________________5.391 16(13)×10-44 seconds________________

New ideas take time to incubate.4 Max Planck first wrote about Albert Einstein’s new ideas back in 1905. Years later, after Planck died in 1947, Einstein wrote to Planck’s widow about his special memories with Max yet acknowledged how general relativity and quantum theory would, for now, have to stand awkwardly together. These two seemingly irreconcilable pillars of modern physics have continued to stymie the world so much so that the world’s people, especially her leading scholars, have been quite unsure of space and time.

We inherited our commonsense worldview from Isaac Newton.5 So with all due respect and for a very long time, we’ve believed that time and space are absolute.

It seems most people still do. To stray from that bit of so-called commonsense is not easy. If space and time are not absolute, then what is? What holds it all together?

What’s in the heart of every Planck Time transformation? The Planck scale is a different scale but it may not be as strange as so many scholars seem to think today. As a result of our studies of this model since December 2011… though still fuzzy, some clarity is becoming apparent.


Pi’s Continuity-Symmetry-Harmony

A Possible Domain of Perfection.6 Learning a bit more about pi, going over it one more time — even attempting to go inside it — finally my old 1972 definition of a moment of perfection seemed relevant. Inherent within the many definitions of pi is continuity, symmetry and harmony. There is the continuity of the never-ending, never-repeating numbers, the perfect symmetry of the circles and spheres, and special internal and external dynamics, harmonics, introduced to us through the Fourier transform.

Continuity-symmetry-and-harmony are such key concepts, there are links to those three facets of reality at the top of every homepage or top posting within this site.

Where do these concepts reside? Or, could the three be the container for everything, everywhere, for all time? Here the answer is a cautious “Yes.”


Finite & Infinite

Simple logic tells us that the very first spheres are still being pushed forward.7 By going over those progressions of the doublings, over and over again, it slowly became apparent that each notation is always active. Each builds on the prior notations. Time is a face of light, the Janus face of space. So, along with the oldest-most-popular mathematical construct, pi, all of the dimensionless constants became our focus.

If these special equations and relations do not reside within the finite, might we assume that they are somehow aspects of the infinite? Can the infinite be brought into the finite without becoming finite? What connects the finite and infinite? Quite puzzling, it behooves us to ask, “In what ways might David Hilbert have been wrong about his conclusion regarding the finite-infinite relation?”

Simple logic seems to tell us there is an ever-so-active, rather intimate bridge between the finite and infinite. By definition, the finite is the quantitative. Perhaps we should be thinking about the infinite as the qualitative. So, we now propose (and have begun exploring the idea) that this bridge is defined by all the dimensionless constants and the infinite is the qualitative face of reality and beingness.

We’ve all been taught that the infinite is some abstract superlative that is not part of our immediate reality. Here, quite the opposite, it appears that the infinite is not only an intimate part of our experience, it is the experience of the experience that can not be defined by space and time. It is defined by ratios and relations. And, the infinite is experienced as some expression of continuity, symmetry and harmony. That’s a perfection and it appears to extend into the finite.

Yet, recognizing the transitioning from spheres to tetrahedrons and octahedrons, somewhere along that progression of notational doublings, the most simple tetrahedral gap, just five tetrahedrons sharing a common edge, would be among the many combinations that would be tested. My suspicion is such a gap doesn’t become part of fabric of the universe until as late as the first three seconds up within Notation-143, Notation-144 and Notation-145 and then over time, that structure begins working its way back to earlier notations between 48 and 64.

It is a new topic opened for discussions and analyses. Again, in this model, we shall give the infinite everything qualitative. We’ll give the finite everything that is quantitative. And within this model of the universe, quite obviously the quantitative and qualitative co-exist quite well together.

Yet, those age-old questions about good and evil are implied.8 Might we say that all qualities that do not reflect continuity, symmetry and harmony (but do reflect discontinuity, asymmetry, and disharmony) are perspectival and are actively impressed within the very fabric of this dynamic universe? The implications are so far-reaching. More…


Nanosecond to Plancksecond (Planck Time)
(10-9 seconds, the nanosecond is just one billionth of a second)

A long, long way from the Nanosecond to the Plancksecond.9 Our mathematically-defined chart of the universe captures the nanosecond within Notation-114 at 1.1197×10-9 seconds. Notation-115 is 2.2395×10-9 seconds, Notation-116 is 4.479×10-9 seconds, and Notation-117 is 8.958×10-9 seconds.

That encompasses the first four groups of nanoseconds of the universe. The related length scale is in the domain in which most of life takes place. Here time is dynamic right back to the first instant.  Each notation defines the look and feel of the universe within that notation.

Wouldn’t you think that our entire universe shares this moment in time? If it is true for the first 116 notations, it may well be true for the next 86 notations.

A nanosecond is equal to 1000 Picoseconds. The Picosecond (10-12) is followed by the Femtosecond (10-15), the Attosecond (10-18) and the Zeptosecond (10-21 which is within Notations-74-to-77).

The accuracy of time determination. The greatest accuracy achieved to date, the zeptosecond, was achieved in 2016 by a collaboration of three groups: Max Planck Institute of Quantum Optics (MPQ) in Garching, Technical University of Munich (TUM) and Ludwig Maximilian University (LMU) of Munich. They captured the timescale of photoionization. They were the first to make such a short determination of a unit of time. That followed their earlier work to establish the attosecond under the MPQ leadership of Ferenc Krausz and Vladislav Yakovlev.

The measurement of the Zeptoscond, just one sextillionth of a second — that’s a trillionth of a billionth of a second — is work led by a laser physicist, Martin Schultze. It is truly a measurement by devices, not just a mathematical calculation, and Schultze steps us back into Notation-74 to Notation-77 within our horizontally-scrolled chart.

On to Planck Time. As fast as it is, that zeptoscond is still rather slow when compared to 10−44 seconds given within Planck Time. Next will be the Yoctosecond (10−24), just one septillionth of a second (10−24). Within our chart, the Yoctosecond ranges from Notations 65-to-67.

No Names. The actual words for the next six categories (or groups) down to the Planck scale do not yet exist. Hardly trivial, until each group has a name, they have a limited identity and study of them is more difficult.

The last International System of Units (SI) categories to be added were in 1991. It may well be time to call them back together again. They need to name those next six new groups: 10−27, 10−30, 10−33, 10−36, 10−39, and 10−42 seconds. Planck Time at 5.391 16(13)×10-44 seconds is within the 10−42 seconds’ expansion. It could be named a Plancksecond or PlanckSecond. To date, that combination of words has only been used casually to refer to an extremely short period of time.


Stretching Credulity Even Further

The four base units in lockstep.10 There is literally no room for error within the first groups of notations. It would seem that even with the abundance of scaling vertices, 8.5 billion within Notation-12, and 5.902958×1020 vertices at Notation-24, the thrust of precision would keep everything perfectly aligned. Yet, we know by Notation-64 with its 6.2771017×1057 scaling vertices, quantum fluctuations are emerging. That’s well-established fact.

Consciousness is also a fact.11 We assume it is within the earliest sixty notations. Back in and around 2016, our guess for consciousness was that a primitive consciousness might emerge as early as Notation-48 and that domain could be considered a place for the introduction of a type of fluctuation. We are now researching to see if there may be a better nomenclature already established to distinguish the emergence of various kinds of fluctuations. At Notation-48 there are 2.2300745×1043 scaling vertices. It may well be the area in which we begin our search for the first manifestations of a gap integral to creating a system for the five most primitive perceptions.

Review. These Planck spheres manifest the most complete sense of continuity, symmetry and harmony possible. Sphere stacking would be generating “pure” tetrahedrons and octahedrons. Yet, within each doubling, new dynamics are introduced.

Prime numbers. 12 Rather casually proposed in a few sentences and brief paragraphs in earlier postings is the role of the prime numbers. There are 45 prime notations within the 202 notations that currently encapsulate the universe. There are just nineteen primes within the first 67 notations. The postulation is that each prime supports a new mathematical system that initiates even more diversity and complexity. As within computer programming, there is an order of operations based on the logic of mathematical expression. Each expression gives us clues about our universe and their ordering and we need to pay attention to all of them.

The Hubble Constant.13 Reviewing the work of Wendy L. Freedman, Professor of Astronomy and Astrophysics at the University of Chicago, I learned about their standing enigma — the two values for the Hubble Constant. The editors at PSW Science ask, Is There a Crisis in Cosmology? A New Debate Over the Value of H0. For a November 6, 2020 Zoom webinar with Prof. Dr. Wendy Freedman, PSW Science comments, “If the tension is real, it may signal a new physics beyond the standard model.”

The Hubble constant is the cosmological parameter that sets the absolute scale, size and age of the universe; it is one of the most direct ways we have of quantifying how the universe evolves.” –Wendy Freedman (video), Carnegie-Chicago Hubble Program. VIII. (PDF), ArXiv, July 2019

Astronomers make observations and have an observational framework. We have a strictly mathematical framework.

  1. Can the two work together? Can their observational data work with this simple mathematics?
  2. Can the observational data work if the concept of time is derivative and finite?
  3. Can the observational data tolerate infinity defined as continuity, symmetry, and harmony?
  4. Would the Hubble Constant work with 201 fully-symmetric notations in one manner and with an asymmetric Notation-202 in another manner? That is, might the Hubble measurements that are within Notation-202 be different from any measurement that is within Notations-0-to-201?

Of course, our suspicion is, “Yes, of course,” observation and mathematics most often concur.

We know how idiosyncratic this model of the universe is. We also know how simple and logical it is. We also know there are over twenty assumptions, all departures from the academic norms, that have been made since 2011. With this posting, we’ll add another: Time measurement varies between the 202nd notation and all other notations. Notation-202 feels directional and seems linear; it is asymmetric. Notations 1-201 are all symmetric and each notation has been “filled” with infinitesimal spheres that are defined by the Planck base units.



Fundamental key question, “Is the universe open or closed?”14 In 2017 a most-helpful work by Joseph Silk, Challenges in Cosmology from the Big Bang to Dark Energy, Dark Matter and Galaxy Formation (2016) had come to my attention. In a quick note of thanks and an introduction, I asked for help, “Where did we go wrong?” More recently, I discovered a provocative article that he had written with two others, Planck evidence for a closed Universe and a possible crisis for cosmology (Nov. 2019). With this work I awkwardly engaged his question, “Is the universe an open or closed system?” I was confused; and an email to Joseph Silk, Alessandro Melchiorri, and Eleonora di Valentino (November 2019) certainly reflects that confusion; and rather predictably, that confusion continues to this day.

It seems the answer to their question is “perspectival, yet fundamentally open.” The five dynamics of pi push our faculties to imagine what these small-scale dynamics look like within the largest-possible scale, i.e., the size and age of the universe at this moment in time.

Emergence, Inflation, Acceleration.15 The other dynamic in all these equations is within light. In one of her earliest articles by Eleonora Di Valentino, with her co-authors Alessandro Melchiorri, Valentina Salvatelli, and Alessandra Silvestri, wrote Parametrised modified gravity and the CMB Bispectrum (ArXiv 2012). They conclude, “Cosmic acceleration is one of the major challenges faced by modern cosmology and understanding the very nature of what is sourcing, it is the main focus of up-coming and future cosmological experiments.”

What has happened in the intervening eight years?

Those comments reflect the blinding problems created by big bang cosmology that seem far more approachable within our mathematically-integrated view of the universe. In our simple model, there is a natural inflation, a thrust of the universe, that can all be seen within the numbers of our chart of the universe and these generally approximate the majority of big bang epochs.


Continuity, symmetry and harmony are three facets of reality that define both the finite-and-the-infinite, as well as light, space-and-time and pi-circles-and-spheres.

Old mysteries become evidence as new mysteries are uncovered. Thank you. –BEC




Endnotes and Footnotes

*  One plancksphere per plancksecond, and if Planck Time is equal to 5.391 16(13)×10-44 seconds:

*539,116,000,000,000,000,000,000,000,000,000,000,000,000 planckspheres per second

That number would be the top end. It should be equal to the current expansion of our universe. There are so many dynamics within the first few steps… notwithstanding, it is already an impossibly large number to grasp. We should also consider an even larger number by  multiplying it by the total number of seconds since the start of the universe. That would give us an approximate total number of Planckspheres within the universe and it would constitute the physical foundations of the universe. It’s a rather novel concept and such a different vision of the old aether. We’ll need to revisit Michelson-Morley and Wilczek’s matrix or grid. Perhaps we should add it to our list of claims or novel concepts. -BEC


[1] The Speed of Light and the Nature of Light in a Very Different Light: 202 Notations.
Light defines (1) each notation, (2) space-time, and (3) mass-energy. Yet, in this model of the universe, each is defined even more fundamentally by continuity, symmetry, and harmony. The speed of light is defined within each notation as well. When we first started exploring the numbers for these Planck Length doublings, we had no idea that we would find a simple correlation between Planck Length and Planck Time. Then, we started thinking about Planck’s formulas, particularly the more simple expression for Planck Time:

Our first reflections began in 2012. By 2014 we began to grasp how well all the numbers worked together. Those formulas worked! We looked for articles by experts but could find no references. Yet, right there on the page, simple mathematics was validating the relation. We began to realize that light is a much broader category than photons, just as photons are a much broader category than visible light.

The results of that simple act of division — Planck Length divided by Planck Time is equal to the speed of light — was nowhere to be found so we began writing it up. Planck’s formula in light of the 202 notations, the instantiation of the sphere as the first expression of space-time, mass-energy, and the building of geometries (cubic close packing), and 64 to 67 notations to quantum fluctuations, particles, and waves, extends the deeper definitions of light as an aether, matrix and grid.

Planck’s calculations render the speed of light more accurately than the 2019 SI number or ISO number (299,792,458 m⋅s). More


[2] Max Planck ignored his calculations from 1899. It would take out-of-the-box thinkers to give meaning to those four Planck base units.

[2a] C. Alden Mead (UMinn) In 1959 he began his struggle to publish his work about the Planck Length. Though finally published in 1964, the article, Possible Connection Between Gravitation and Fundamental Length Phys. Rev. 135, B849 (10 August 1964), was ignored by the scholarly community. Planck Length commanded no respect as a fundamental unit of length.

[2b] John Barrow (1982): With an extraordinary depth and range of scholarship, and a sensitivity to young students, my first letter to John Barrow in 2013 was an earnest request for help, “What do we do with these numbers?” He never commented about my naive attempt to shoehorn everything-everywhere-for all time into 202 notations. Barrow died on September 26, 2020.

[2c] Thanu Padmanabhan: His 1985 article — Physical significance of planck length (PDF) — captured my attention. His nonperturbative approach produced a quantum cosmological model free from singularities and the horizon problem. I was very surprised and gratified to see that his article was published so early in his career. He was just 28 years old (born March 10, 1957). Yet, with guidance from India’s renown astrophysicist, Jayant Vishnu Narlikar, he has been a most prodigious scholar.

[2d] Frank Wilczek (2001) became a Nobel Laureate in 2004, yet he continued his wide-eye, open and enthusiastic approach to the unknowns within life. He was one of the first of those within his caliber who encouraged our explorations. His three articles about Planck units truly opened the door for the rest of us.


[3] From Three Minutes down to Three Seconds. It seems that most within the general population and many of our best scholars hold the positions spelled out in 1976 within the book, The First Three Minutes, by Steven Weinberg. A Nobel laureate and one of our most cited scholars, Weinberg still missed over two-thirds of the most fundamental structures of the universe.

In June 2020, twenty-seven leading scholars from around the world argued most convincingly about the early structures of the universe. A tribute to Weinberg, their article was titled, The First Three Seconds: A Review of Possible Expansion Histories of the Early Universe, (June 2020). Forty-four years after Weinberg’s popular work, they acknowledge the abundance of mystery within the first three seconds. More

Those are the magical three seconds that open up to an entirely new and profoundly simple universe.


[4] Yes, New Ideas Do Take Time To Incubate, Sometimes Centuries. Those “seemingly irreconcilable pillars” have been screaming at us for over one hundred years, “It’s incomplete. You’re missing key parts.” So instead of going in circles with the same parameters trying to do a different thing, break the circle so it becomes a spiral and find those missing parameters! Our simple guess is the first 67 notations.

Brandon Brown wrote the book, Planck: Driven by Vision, Broken by War, OUP, 2015. He is Prof. Dr. Brandon Brown on the University of San Francisco campus and he has become a foremost Max Planck scholar with his comments and analysis from his 2015 book published by Oxford University Press. The Planck-Einstein relation was one of the most formative personal relations in history and one of the reasons their silos stand today is because physics has not fully embraced mathematics and mathematics hasn’t fully embraced physics. Arrogance and turf wars keep them apart. The first 64-to-67 notations are grounds for reconciliation; and with it, I predict will come the birth of entirely new science.

Though it appears that Planck was unable to break out of Newton’s commonsense worldview, Einstein made some progress. Yet, he was wrapped up in his own vision. With the help of Max Planck Institutes and people like Brandon Brown, an actual dialogue between Planck and Einstein about the Planck base numbers may yet be uncovered. To date, there is no record of it. If the two of them really focused on those Planck numbers, they just might have discovered those 64-to-67 notations prior to particles, waves, and fluctuations.


[5] “Commonsense is not so common.” It took the intellect of Sir Isaac Newton to define perhaps the most widely-held “commonsense” worldview which today makes very little sense at all. That is, of course, Newton’s claim that space and time are absolute. To this day, it is still pushed forward by respectable scientists and philosophers among us. For me it stands as one of history’s most egregious intellectual mistakes that has created walls and silos within our current picture of the universe. The expression has been credited to several — Voltaire (1764), poet and political writer, Nicholas Amhurst (1726), and a Roman poet, Decimus Iunius Iuvenalis (aka Juvenal, Book III of Satires, circa AD 181). It has become so true, today it’s a truism!

We have missed something most fundamental.

Tensions are real and there are many reasons why these tensions are signals for what people have in so many different ways characterized as a “new physics beyond the standard model.” That expression has been repeated so often, it now has its own acronym, BSM.

More to come: breaking though commonsense and the BSM


[6] Perfection and possible degrees of perfection. We have all experienced a moment that was profoundly moving. Possibly it felt transcendent. Some might call it a moment of perfection. In 1971, confronted with such, I attempted to describe them in the most general mathematical and scientific terms that caught the spirit of such an experience — continuity-symmetry-harmony. I quickly learned that all experiences are within space and time and Newton’s container universe was the generally-accepted, commonsense description of such. It wasn’t enough for me, so I took on those conditional expressions — continuity-symmetry-harmony — to evaluate all new information about the structures of reality. So within quantum physics, I gravitated toward quantum chaos theory and the EPR paradox and what has become known as quantum entanglement.


[7] The very first spheres are still being pushed forward. Hard to believe, of course, but so much about this sphere generation is hard to believe. There is no name for 1044 spheres. One could say, “Somewhere just under a trillion-trillion-trillion-trillion.” It doesn’t compute easily. Then, if we are to imagine that amount per second, it becomes rather unfathomable. Nevertheless, very large and very small numbers are the next steps for all of us to begin to grasp the boundaries of this universe. More


[8] Qualitative, values, ethics, morals, aesthetics. Continuity, symmetry and harmony became the basis to make valuations: What is good? What is better? And, what is the best? These valuations are perspectival. They slide around plancksecond-by-plancksecond, second-by-second, day-by-day, and year-to-year. So even though seemingly arbitrary, there are aggregations of value which also become a basis for judgement and evaluations such that a quantitative value may be assigned to an experience, an artform, or performance, and especially to things. More


[9] Scale of Infinitesimal Measurements: From Nanosecond to Plancksecond. The six groups of numbers between the Yoctosecond and the Planck Time need formal names that everybody within the global scientific community recognizes.

The group responsible for such standards is CODATA, the Committee on Data of the International Science Council (ISC). They are charged to improve the availability and usability of data within all areas of research. Having a name for these infinitesimal measurements is the first step in having the reality of these dimensions become adopted science. I have asked many of the members of their Executive Committee to take up that cause. More


[10] Four Planck base units in a base-2 notational lockstep: At this point, we can only use our intuition and logic to construct the very nature of simplicity and perfection. Langlands programs and string theory may help yet those disciplines will have to incorporate, then evolve out of the functions of pi, circles, and sphere. They’ll have to find places into which they can pick up and integrate all their earlier work, accommodating the four Planck units working together. In this model, each of these initial 64-to-67 notations represent unique opportunities, relations, and functions. More

As we continue this analysis, it will be coming increasingly important that the six groups of scales of the universe with no names, be named officially-and-formally by the ISO and CODATA and all their consultative entities like NISTBIPM, and standards groups within 141 other countries. Prior to quantum fluctuations, there are these clusters of measurements that have no name: 10−27, 10−30, 10−33, 10−36, 10−39, and 10−42 seconds. As we observed earlier, Planck Time at 5.391 16(13)×10-44 seconds is within the 10−42. More


[11] Consciousness: We know where the brain is located, but we do not know how where the mind is located nor are we profoundly sure how the brain/mind relation works. The first experts to whom I turned for insights about these issues was John Eccles. His report with Karl Popper is The Self and Its Brain (Springer, 1977). It set the stage for me. The next was Roger Penrose, author of The Emperor’s New Mind (Oxford, 1989) and Shadows of the Mind (Oxford, 1994). Their genius is clear and their concepts robust, yet neither Eccles nor Penrose were able to define a grid within which the mind and brain were in concert.

Enter Computational Neuroscience. While an undergraduate in-and-around 1957, Stephen Grossberg posited nonlinear differential equations for neural networks. One could say that it was a stroke of genius as well as a deep-seated intuition. Grossberg was among the first to begin to define computational neuroscience. Yet, the scientific community has been limited without a simple grid that includes everything, everywhere, for all time, including consciousness. The first grid by Kees Boeke used base-10; and though digital, it encouraged analogical thinking with no causal efficacy. Here within a base-2 grid, causality is driving the exploration.


[12] Prime numbers: Prime numbers have a key role within encryption technologies today, but one might still ask, “Is that all there is? Could primes be playing a more fundamental and pivotal role within the structure of things?” We think so. To that end, as an exploration, we would assign the first 19 primes — 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, and 67 — to absorb the expansion of structures and functions within Mathematical Systems Theory  (Also, see the text of that title by Diederich Hinrichsen and Anthony J. Pritchard, Vol. 48, 2005).  Prime elements and irreducible elements, prime ideas, group theory There will be more to come.


[13] Two values for the Hubble constant: In lectures and papers, Wendy Freedman is an expert and leading scholar regarding all things related to the Hubble Constant. She says, “Our value of the Hubble constant, Ho = 69.8, with statistical and systematic uncertainties of 0.8 and 1.7 km/sec/Mpc, respectively, falls midway between the value obtained from the Planck Cosmic Microwave Background analysis, and that obtained using Cepheids.” Freedman has not seen our base-2 scale from the Planck Time, assumed to be the first moment of time, to our current time. Nor has she seen the comparative analysis with the big bang epochs. She is also unaware of the difference between Notation-202 and the first 201 notations. Using the simple logic of this simple model of the universe, the age of the area in the universe being measured will render one result for all images within 2.82+ billion years and another Hubble Constant for all images within areas older than 2.82+ billion years (perhaps as high as 3.2 billion). More to come


[14] Open or closed: Joseph Silk is highly-regarded within the Astrophysics and Cosmology community. His overview gave me a chance to go over the basics just one more time, and ask myself, “What am I missing? Why is our idiosyncratic theory so wrong and the big bang theory so right?”

So, I empathize with those people who started within this industry back in the 1970s. Now fifty years later, those people (like me who are now over 70 years old) remember when there was a certain respect for Sir Fred Hoyle’s steady-state theory as an alternative, competitive theory to the big bang. Since that time investments in the big bang theory skyrocketed and reached an all-time high under the leadership of Stephen Hawking. With its many unresolved problems exacerbated by time and with the Planck base units finally becoming recognized, the value of big bang cosmology is falling. Those who have invested heavily in it cannot be absurd to themselves. Yet, we all know that which is more-true-than-false prevails.

Of course, these kinds of transitions are not easy.

I was glad to discover that second article by Joseph Silk with his two younger colleagues. There is an honesty to their question and we need to explore these kinds of questions. For me, it helped to shape the finite-infinite analysis, especially our focus on dimensionless constants: finite, infinite or in that hyphen between the two. This time, however, it shaped that quantitative-qualitative analysis; and so far, it feels good and seems to work.


[15] Inflation, expansion: A young, Italian astrophysicist, Eleonora diValentino, was part of the “Closed or Open?” discussion with Joseph Silk (just above). In 2014 she was asking key question about  cosmic acceleration, particularly “…the very nature of what is sourcing it…” She appears to be the next generation of the Wendy-Freedman-types who are in search of fundamental truth; these are  people who expect that their quest will never ever finish. As an academic exercise, we are going to focus on a joint article,  Parametrised modified gravity and the CMB Bispectrum (ArXiv 2012) where Eleonora Di Valentino and her co-authors Alessandro Melchiorri, Valentina Salvatelli, and Alessandra Silvestri arrived at that conclusion. The study now is to answer the question, “How can you believe in big bang cosmology when you have done this analysis and made these conclusions?”  So, yes, there is more to come


References & Resources

  1. Planck scale: A special page of references and resources will be dedicated to exploring the work of people like Serge Timashev of the Karpov Institute of Physical Chemistry (Moscow) with his ArXiv article, The Planck numbers and the essence of gravitation: phenomenology (2017),  and Ronald J. Adler of Hansen Experimental Physics Laboratory (Gravity Probe B Mission) of Stanford University with his ArXiv article, Six easy roads to the Planck scale (2010).
  2. Wendy Freedman, Professor of Astronomy & Astrophysics, Univ. Chicago, November 2020: Is There a Crisis in Cosmology? A New Debate Over the Value of HAlso see: Measuring and Understanding the Universe, https://arxiv.org/abs/astro-ph/0308418 
  3. HubblesiteGalaxies Used To Calibrate The Hubble Constant
  4. April 11, 2019, Marclay’s Clock: 24-hour installation highlights a modern obsession with time, Jean-Michel Johnston, University of Oxford Also in Nexus NewFeed
  5. In 1925, the great mathematician, David Hilbert wrote, “We have already seen that the infinite is nowhere to be found in reality, no matter what experiences, observations, and knowledge are appealed to.” Even today, many scholars would agree, but perhaps Hilbert and those scholars are mistaken.
  6. Research: “Primordial adiabatic and Gaussian perturbations
  7. Is a time symmetric interpretation of quantum theory possible without retrocausality? Matthew S. Leifer and Matthew F. Pusey
  8. Not all mathematical advances relating to π were aimed at increasing the accuracy of approximations. When Euler solved the Basel problem in 1735, finding the exact value of the sum of the reciprocal squares, he established a connection between π and the prime numbers that later contributed to the development and study of the Riemann zeta function.  Fore more:
    Complex numbers and Euler’s identity
    Number Theory and RZF
  9. October 24, 2020 at 12:22 pm · Reply to “Infinity Is Not The Problem” Does the qualitative reside within the finite? Could the perfection of the sphere be an example? Is pi an example? I’ve been playing with it within an examination of the Planck scale: https://81018.com/the-three/   Might all the dimensionless constants be the bridge between the finite and infinite
  10. Experimental result cannot be explained by the Standard Model (SM): Non-zero masses for the neutrinos (elementary particles traveling close to light speed, electrically neutral, and weakly interacting). The SM assumes that they are massless. Therefore, particle physics explores a new physics beyond the SM.
  11. The Standard Model is not a complete description of Nature: it does not account for dark matter, dark energy, gravity, or neutrino masses and mixings. There are also remain many features of the Standard Model itself which are not understood, and which may find their answers in speculative ideas beyond the Standard Model such as supersymmetry, large extra dimensions, and/or extended Higgs sectors.
  12. Conspiracy of BSM physics and cosmology, Maxim Yu. Khlopov. Nov 2019: The only experimentally proven evidence for new physics is the effect of neutrino oscillations, but the physical nature of neutrino mass is still unknown. “… the conspiracy of Beyond the Standard model (BSM) Cosmology [1] is puzzling taking into account the plethora of nontrivial cosmological consequences of BSM particle models. “
  13. Yakov (YaB) Zeldovich: ”…though the probability for existence of these phenomena seems low, the expectation value of their discovery can be hardly overestimated” (ArXiv, Conspiracy of BSM physics and cosmology, Maxim Yu. Khlopov, Nov. 2019
  14. The Crisis in the Foundations of Mathematics, José Ferreirós, Universidad de Sevilla 2008, 2011 https://personal.us.es/josef/pcmCrisis.pdf
  15. Proyecto Hephacos, 2014:
  16. Is The Universe Finite? PBS, sponsored by Brilliant, 2019


Emails (just a few)

1. Marios Christodoulou, Andrea Di Biagio, Pierre Martin-Dussaud, An experiment to test the discreteness of time

2. Wendy Freedman, Kavli Institute for Cosmological Physics, Astronomy & Astrophysics University of Chicago

3. Andreas Battehberg, Entering the field of zeptosecond measurement, Nov-2016

4. Bonnie Carroll, Secretary General, CODATA. Calculator


Tweets (just a few)

@Pontifex What you are saying is actually backed up by a mathematical-and-scientific model of the universe. There are just 202 base-2 notations from the Planck units to the current-time-and-size of the universe: https://81018.com/chart/ Also: http://81018.com

@lori_deschene You’ve got good spirit, a good heart… now we have to break free of our little worldviews and get a highly-integrated, mathematical view of the universe (all within 202 base-2 notations). http://81018.com Everything we say and do affects the universe.


Zzzzs (afterthoughts)

What works survives. Every possible geometric combination that works provides form, function, structure, and then substance, relations, and networks of relations. What works best, survives. The universe, the penultimate opportunist, is creating something big that requires solid foundations. Perhaps somewhere around Notation-50, our universe begins to experiment with those five tetrahedrons with its built-in gap. Out of an abundance of shapes and configurations, the five tetrahedral structure is surrounded by perfectly manifesting forms and structures. Within a moment, that gap comes alive. Perhaps as early as Notation-50, the gap becomes a structural system, and then becomes a systemic fluctuation. Just a guess, the first expression of these systemic fluctuations just might be considered a primitive consciousness. By Notation-67, when it can be measured and “observed”, it will be defined as a quantum fluctuation.

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Key Dates for this document, The-Three

Image by Mikhail Leonov, April 11, 2019, Marclay’s Clock and what could be called, “Fibonacci Time.”
We are all so confused about time. How about Fibonacci Time? Linear, limited yet still light.