A little like pi, your continuity-symmetry-harmony is unique-but-universal.

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The Known Unknowns
by Bruce E. Camber
a working draft

Ideas and concepts can be powerful even when they don’t have a name. We grow up inside ideas and concepts about which we know nothing, but everybody shares them. Assumed, unquestioned, pervasive, these become part of our world’s culture. Though pervasive, some of these concepts are simply wrong. I call them the known unknowns.

Three such concepts were introduced here in May 2020 (opens a new page to that earlier article). Although known to a few and unknown to most, the first was considered to be a fact but it was wrong. For the better part of 2400 years, although wrong, what is right is still not understood. The other two are common sense and our task is to show that both make no sense at all. Here the known is confused, seemingly known, but actually unknown or profoundly mistaken.

Geometries surrounds us; we know that. There is one geometry from Aristotle that was wrong in his time and it is still wrong today. It went unchallenged for about 1800 years.[1] When it was first understood to be wrong in 1435, the intelligentsia discussed it — Aristotle made a mistake — but then it was largely forgotten for close to 500 years. In 1926 a little-known Dutch-American, MIT mathematics professor, Dirk Jan Struik [2], resurrected that 1435 research and tried to re-opened the door. It barely cracked. In 2012 Jeffrey Lagarias and Chaunming Zong tried opening the door again. It’s now 2022 and that actual gap in our universe has barely been explored. “What does it mean to scientific theory?” And more pointedly, I ask, “Could that gap have something to do with quantum fluctuations? Are the very footings of quantum mechanics determined by the geometries of a gap?”

I believe the quick and easy answer is, “Yes.” The longer answer opens many current debates. Our position here is a bit different because everything is in context with the 202 base-2 doublings from the Planck Time to the current time, right Now. The first 64 notations are orders of magnitude too small to be measured; and, as such, these 64 notations are not yet recognized by our scholars and scientists. Infinitesimal in duration and size, those 64 notations are projected to be largely pre-quantum. Here we project there are perfections of sphere dynamics defined by qualities of the infinite — continuity-symmetry-harmony — and, if these statements are anywhere close to reality, it’s a paradigm shift.[3]

What is the possibility? Not as far-fetched as it first seems, here quantum fluctuations are reduced to a simple geometry. Aristotle thought we could tile the universe with tetrahedrons. Necessarily, octahedrons are also required. Our children with clear plastic models of both readily understand it, yet many university professors without those plastic models do not.

In our time, sphere packing has become a question about packing densities. That’s well and good, but there is so much more. When we go inside that question, we naturally begin to wonder how that 7.3561+ degree gap effects us and our universe.

I believe Aristotle’s mistake taints our intellectual capacities and stunts inquiry. Geometry became a ninth-grade study that was replaced by algebra and calculus for the next three years. We weren’t told about cubic-close packing of equal spheres. We weren’t told about the emergence of tetrahedrons and octahedrons. We weren’t told about that 7.3561+ degree gap that gave us the space to fluctuate, be free, have choice, be creative. It was missed. Geometry became bewildering, a Grassmannian hiding in the weeds.[4] And, as a people, we were not empowered.

We all make mistakes. Some are quite big. Yet, it is within our mistakes that we can learn the most. So, we thank Aristotle. And, we thank all the scholars who have tried to open that door. It needs to be opened as wide as possible. It is real and it makes a difference. As a people and a global culture, when we finally embrace it, I predict that we will begin awakening from one of our many dogmatic slumbers.


The second big mistake was made by an equally famous person — Isaac Newton. And, my mother would say it “…was a doozey!”

In his 1687 Principia, his abiding masterpiece that changed the world and officially opened science to become science, he embedded concepts so deep it encouraged arrogance to breathe and come into its fullness. He encouraged us to see space-and-time as absolutes. Space-time held the aether; space-time existed before the aether. Space-and-time may well pre-exist all existence, but, absolute, eternal and infinite, those two are not.

The words, space-time, are just not big enough. And, we all grew up thinking, “That’s all there is.”

Some of us got a little religion along the way, but up against science, it was weak. It didn’t give us a progression for growth and discovery. Religions were soft and squishy. We weren’t introduced to the mysteries of continuity equations that never stopped, were constantly changing, but always the same. Most of us were not introduced to the deep insides of perfect spheres that stack and pack and create tetrahedrons and octahedrons. We were never introduced to Joseph Fourier and his transform that created harmony, spin states, and then a deep-and-abiding harmony with many flavors. We weren’t introduced to the infinitesimal, to Max Planck and his base units, and to Euler’s simple base-2 expansions.

We never learned that space-and-time was derivative. Newton’s many successes convinced us otherwise and we failed to recognize the fundamentality of continuity-symmetry-harmony, these three seemingly give rise to space-and-time and are best known through pi (π). These three do not fight with the universals of most religions. These three are the peacemakers for which humanity has yearned throughout our many centuries of wars and our abundance of other forms of barbarity and banality.

Newton’s absolutes have us bound up within a misplaced concreteness that blocks the paths to a more gentle and abiding universe all of which can be quickly discovered within the sphere, yes, right there with pi, quite universal and infinite.


The stories about our tragic mistakes do not end with Newton. In our own time, we have built upon Aristotle and Newton, compounding mistakes that to this day, cause a lot of pain and very bad behavior.

“How did it all begin?” is a question that opens abiding mysteries.

Enter Stephen Hawking. While he was alive, it was difficult to raise questions about his version of the big bang theory. Given his battle with Lou Gehrig’s disease (ALS), we all readily understand why there were so many people who were so very protective of him. Yet, the start of this universe is such an open question and there are always so many new ways to engage the question, there is no place for arrogance, just openness.

Can an idea spark a nihilism within our consciousness? Hawking pulls Aristotle and Newton’s arrogance into the 21st century. Arrogance takes over. And, eventually the dystopian curtains open and there is no rhyme or reason for anything.

As you can see from some of the links above, my first introduction to these thoughts was back in 2017 which had culminated with my 2020 reflections about the effects of these three formidable scholars, “We reach for the stars, but we’re conceptually blocked…” As much as science has its reservations about infinity, and mathematicians like David Hilbert and physicists like Max Tegmark truncate its influence, we only need to look at the dimensionless physical constants and mathematical constants like pi (π) to experience an alternative.

How did it all begin?” is such an open question, a known unknown, it just might be helpful to re-engage the concept of infinity.


Before we do, please, put all definitions of the infinite on hold. Some are cultural; most are personal 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. Our access to the infinite is through dimensionless constants like pi (π). There are many discussions about it within this website. Here, continuity-symmetry-harmony stand out as universal and infinite, yet with very specific finite applications. Here is a bridge between perfection and imperfection, between the finite and infinite. Here is a bridge to ethics and value.

Science and theology (or its many religions) can share common foundations; and when we do, we will become a kinder and gentler people. Thank you.


PS. I’ll keep revisiting this line of thinking but I need help, so, of course, your comments are most welcomed. -BEC



[1] Unchallenged for about 1800 years. It has been closer to 2400 years before anybody insisted on asking about the meaning of that gap created by five tetrahedrons sharing a common edge. Let’s all insist on it today. This work was earlier introduced within this an article entitled, duped.
Jeffrey C. Lagarias & Chuanming Zong, Mysteries in Packing Regular Tetrahedra(PDF), American Mathematical Society (AMS), December 2012

[2] Dirk Jan Struik. An MIT mathematician and self-described atheist and Marxist socialist, Struik is best-known for his work, A Concise History of Mathematics. He was a key reference for Lagarias and Zong for their 2012 article (noted just above). The Wikipedia summary and an overview by Tufts University professor, Boris Hasselblatt, provide a good introduction to his life and work. Here within this one person, are the two great tensions of our time, capitalism/marxism and atheism/theism. And, within Struik’s hand is the forward-slash that instead of dividing these four basic belief systems, just might have become hyphenated and these disparate systems might have found some common ground.

The challenge of our time is to grasp the very essence of that forward-slash.

[3] Paradigm Shift. The concepts of time and space are fundamentally changed. The concept of the universe shifts from linearity to exponential, whole, and dynamically-integrated-and-inter-related. The concepts of infinity, the infinitesimal, perfection, and the hypostatic become really real. More…
Footnote: Thomas Kuhn, The Structure of Scientific Revolutions, University of Chicago Press 1962

[4] Geometry became bewildering. Some concepts are difficult. It is the job of our scholars to make them simple. The concept of a Grassmannian is difficult enough, yet when we surround it with even more abstractions, one might say that the meaning is indeed hiding in the weeds.
Grassmannian, retrieved from Wikipedia, February 15, 2022

More… The Penultimate Perfections of Pi


References / Resources  ________ Prior / Next

• Quantum fluctuating geometries and the information paradox (PDF), Rodolfo Gambini, Rodrigo Eyheralde, Miguel Campiglia, Jorge Pullin, 2017

• What every physicist should know about string theory, Ed Witten, Physics Today, 68, 11, 38 (2015)https://doi.org/10.1063/PT.3.2980

• Oriti, Daniele, Approaches to Quantum Gravity: Toward a New Understanding of Space, Time and Matter, 1st ed.; Cambridge University Press: Cambridge, UK, 2009. [Google Scholar] a Researcher at the Max Planck Institute for Gravitational, Physics, Potsdam, Germany, working on non-perturbative quantum gravity. Also, at the Perimeter Institute for Theoretical Physics, Canada; Institute for Theoretical Physics at Utrecht University, The Netherlands; and Department of Applied Mathematics and Theoretical Physics (DAMTP), University ofCambridge, UK. See: Spin foam models and group field theory approach to quantum gravity.

Nima Arkani-Hamed, Spacetime, quantum mechanics and positive geometry at infinity – Nima Arkani-Hamed (2019, video lecture, International Conference “String-Math 2018” of the Tohoku Forum for Creativity, Tohoku University.)

Sergio DoplicherKlaus FredenhagenJohn E. Roberts, The quantum structure of spacetime at the Planck scale and quantum fields (ArXiv), Commun.Math.Phys. 172 (1995) 187-220, Mar 2003



• Prof. Dr. Shamit Kachru, Stanford
• Natalie M. Paquette, Institute for Advanced Studies, Princeton, New Jersey
Prof. Dr. Tim Palmer, Oxford
• Prof. Dr. Miranda C.N. Cheng, Amsterdam
Prof. Dr Barbara Drossel, Germany with George F R Ellis, Emergence of time, Nov. 2019
David Romero Abad and José Pedro Reyes-Portales, Lima, Peru
• Prof. Dr. Chiara Macchiavello, Pavia, Italy
• Prof. Dr. George F. R. Ellis (many emails)(overview)
• Prof. Dr. Natalia Berloff, Cambridge (England) and Skoltech, Moscow
• Prof. Dr. Alexander Petrovich Kuleshov, Skoltech, Moscow
• Prof. Dr. Andrew Chi-Chih Yao, Tsinghua, Beijing
Audrey Azoulay, DirectorGeneral, UNESCO



@zlj517 Lijian Zhao – Now is the time to move from limited worldviews to an integrated view of the universe: http://81018.com Otherwise we will have more of the same. I’ll keep you posted on our China efforts.

@kendricklamar Ten Years In the Limelight. Ten Years to Influence Millions. Ten Years to Lay down tracks of Insight. All within a little lifetime. All within. All within. But there’s so much more. Take in the universe. Drop the little worldviews. http://81018.com is a start.

@bluemeridianp What holds us back are our limited worldviews when a highly-integrated, mathematical view of the universe empowers. http://81018.com is just a start. We re-open a dynamic finite-infinite bridge: https://81018.com/almost/ a key to it all.

Key dates for this document, cause