Continuity: A first principle

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

Pi & Continuity Are the Finite & the Infinite

by Bruce E. Camber

Introduction. Our simple model of the universe has roots down into the most-familiar-but-ever-so-elusive, dimensionless constant called pi.1 Never-repeating, never-ending, transcendental, and incommensurable, pi informs us about the very nature of the finite and the infinite. By placing trust in the universal nature of pi and by applying Leonhard Euler’s base-2 exponentiation to the key derivative numbers that Max Planck calculated in 1899, we create a highly-integrated, mathematical model of the universe that includes everything, everywhere for all time.

This model has just 202 dynamic notations.2 Also known as doublings, in this model each notation is forever dynamic and constantly building on each other. Highly-ordered, there is a perfect symmetry within notations 0-to-201 and an asymmetry within notation 202 because this notation is, in part, defined by the edge of our expanding universe. Time is derivative, discrete, and quantized; ostensibly a highly-unique Now. So, as straight-forward as this model may seem, it retains plenty of mystery.

There is a substantial downside in using pi. It has over 4000 years of baggage dating back to ancient schools in Babylonia, China, Egypt and India. Today that all manifests in many forms including occult schools and mystery religions. And as complex as that seems, we’ll still forge ahead and attempt to figure this out. We just might be able to demythologize some of those mysteries! Notwithstanding, we’ve got to be bold to get outside of our old absolute boxes.

Ultimate or penultimate? Yes, what if pi’s continuity, symmetry and harmony,3 are ultimates, not penultimates? Could these three primary facets of pi actually be the primary facets of infinity?

Continuity comes within its numbers and gives us a sense of order and time. Symmetry comes within its shapes and gives us our dimensionality, space, and our sense of relations. Harmony (or harmonic functions) comes within its internal dynamics — hardly empty and entirely lively — gives us our space-time moments. None exist per se within space and time, yet every moment of space and time is derivative of these three facets.

Possible Conclusion. Perhaps that’s all there is. That’s our container universe and that’s the infinite. Why not?

Reflections. On the surface it seems to be a much more simple and a bit nicer place than the universe that Stephen Hawking and all the big bang cosmologists have given us. In this model there is a domain of perfection — continuity-symmetry-harmony — that defines the first notations. It is always there, the foundation and essence of homogeneity and isotropy. Then, there are also domains for indeterminacy, uniqueness, and creativity, and finally a domain for quantum indeterminacy. It is a very different universe than Hawking’s universe, yet that difference is only within the first fractions of a second. All the other data throughout big bang cosmology is easily and totally absorbed by our Mathematically-Integrated Model of the Universe.

Continuity as an ultimate. First, we were dumbfounded to find nothing on the web that examined the continuity equations from the first possible moment in time, 13.81 billion years ago, to this very day, hour and moment in time. Though well-aware of work done in 1957 in Holland by a secondary school teacher, Kees Boeke, his base-10 work was incomplete. First, he only found 40 of the 63 possible notations. He had no geometries and he did not start with the Planck units. And, there was no discussion of the finite-infinite relation. These are all keys. There was also no discussion about the nature of time. And, that’s another key.

Furthermore. It would seem that these continuity equations do not end at the first instant of the physical universe. Wouldn’t you think that there is a bridge or transition phase from the finite to the infinite and from the infinite to the finite? Aspects of every equation that defines.those first Planck units as infinitesimal spheres just might be a bridge.

And, perhaps there are two bridges, one where the simple sphere emerges and the other the edge of the current expansion.

A Diversity of Continuity Equations. In 2014 we added Planck Time. In 2015, we added the other Planck base units.  When we began to see the epochs of big bang cosmology emerge within our numbers, we knew something important was happening. To make it easier to analyze the numbers, in April 2016 we initiated our horizontally-scrolled chart. Besides the natural inflation (especially within the first second of the life of this universe), continuity equations seem to be bustin’ out all over.

Undaunted, we’ve continued our explorations. Something felt right about this work. It was simple. It was logical. It was mathematical. It included all time and all space. That’s not just simple, but elegant and yes, even beautiful, so we push onward asking for your help to understand this work just a little better. Thank you. – BEC


What if… Yes, if time is discrete, quantized, and derivative, how do we deal with it?


Example. If time is continuously discrete, how would it effect the work of all the galaxy counters? Remember back in 2016 when there were joint announcements about trillions of galaxies? Scholar-scientist from the Centre for Astronomy & Particle Physics of Nottingham in England, Chris Conselice, was leading that charge.

Hardly a trivial question, I did my own calculations. If we redefine time, it will be fun to re-open questions about our current methods to count galaxies. -BEC


Endnotes and Footnotes



1. Never-ending and never-repeating. Back in 2016 when we looked in on the pi-research of the day, we found a fascinating amount of work. One of our analyses of it all became a homepage (or top-posting).

The work of Emma Haruka Iwao was reviewed. She’s the one who did 31.4 trillion calculations of the units of pi. Pi is not finite. Yet, every application of pi is. Here, pi is our penultimate continuity equation.

ccp: We also had discovered cubic close packing of equal spheres and period doubling bifurcation. Though it has now been since 2017, our studies  are still in their early stages. We are constantly inviting scholars to help.

2. 202 dynamic notations.
Particularly fascinating to consider is the place of all the dimensionless constants like pi within this chart of the universe and how all dimensionless constants become continuity equations that bind the finite and in finite. Of course, the infinite here is known as continuity, symmetry and harmony.

3. Pi’s continuity, symmetry and harmony. The suspicion is that every dimensionless constant harbors these three facets of our very being. It is one of the many open questions we are engaging. Hopefully some experts, real scholars can help us. As we get more insights, the three documents that are highlighted on each homepage, CONTINUITYSYMMETRYHARMONY will be updated. Thank you.





1. Chris Conselice, Nottingham University on nature of time
Overduin2. James Overduin wrote a tribute to the work of  Paul S. Wesson in Physics Today, 15.Jan.2016. In the prior homepage (top posting), I referenced Wesson’s work especially where he was quoted in Wikipedia, particularly his caution about how we engage the Planck units. No such advice shall go unheeded!

This email to Prof. Dr. James Overduin (pictured above) is to open the door to see if he can help expand on Wesson’s caution (see “Afterthoughts” just below).



September 13: @lhsideris “Gifford Lectures? Science-theology?? We’ve got to get out of our little worldviews and attempt a mathematically-integrated view of the universe.
Our approach:
History: Worth pursuing further? Quite idiosyncratic, but…
Reference: Lisa Sideris, assistant professor at the McGill School of Environment (MSE) and Faculty of Religious Studies.

September 18: @RichardWike Director of Global Attitudes Research @pewresearch Richard, In a hyper-connected global community where cultural adoption is immediate, our tensions reflect the world. A highly-integrative, mathematical view of the universe — — maybe could provide a new platform for building consensus. Yes, “maybe.”

September 18: @georgesoros @OpenSociety @Thomas1774Paine @maddow @Heritage @realDonaldTrumpHow can we all be so far off? Answer: Limited worldviews. We’ve missed the universe. It anchors us. It gives us perspective. It’s a just a small start.”

September 22: Al Ewing Writes Comics  @Al_Ewing  “Will you be working to further develop the conceptual framework for the plurality of the Ultimate as in the Ultimates? Usually associated with the Infinite, the Penultimates become all the derivative dimensionless constants. Let’s teach some philosophy and physics along the way.


Zzzzzs (Afterthoughts)

  1. I am still working on the quote from Paul Wesson that appears in Wikipedia, Planck Units. Though Wesson has died, his colleague and frequent co-author, James Overduin, is at Towson University and I am reading as much as I can about their understanding of the Planck units, the nature of space and time, and the definitions of light, quantum fluctuations, and infinity. –BEC
  2. Just reviewed this email to Jamie Farnes from July 5. I am not sure if he received it. Does anybody know Jamie?
  3. What about that tweet (just above) to the extremes of our political world? I so dislike politics. It brings out the worst in people. I really believe if we were always thinking in context with the universe, we would be asking “Does what I am doing and thinking have continuity, symmetry and harmony? If not, why not? Can we do it differently and be more sensitive and more inclusive? This model seems to enliven the concept of a living history. There is no past; there is only the potential to make a positive or negative impact on our little universe. -BEC


Key Dates for Continuity

This article was initiated on Saturday, March 11, 2017
Continuity became a homepage on September 18, 2020.
Last update: Saturday, October 8, 2022
The Prior Homepage:
The URL for this page:
The initial tagline: Continuity: A first principle



Max Planck


Stephen Hawking


Kees Boeke


Christopher Conselice



Haruka Iwao



Our universe may not be as mysterious as our academics and scientists have made it out to be. There are just 202 notations that encapsulate the universe. From slightly different perspectives, these notations may also be known as archetypes, categories, clusters, containers, domains, fundamental ratios, groups, layers, sets, or steps.