A possible rapprochement with the naïvetés and simplicity of our youth

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Smallest to Largest
by Bruce E. Camber

Durham, UK (2021): Graduate students of the Institute for Particle Physics Phenomenology (IPPP Durham University) were substituting for Sir Peter Higgs. The question (above) for their audience is a major unsolved mystery.

At the IPPP 23rd International Conference from the Planck Scale to Electroweak Scale (June 2021), Prof. Dr. Malcolm Fairbairn of Kings College London presented “Dark Matter Hunting in 2021 – How do you look for something when you don’t know what it is?” His presentation raises key issues about the unsolved mysteries that have surrounded dark matter. On page 70, he challenges us all, “We are well into an era of using novel approaches to learn more about dark matter.”[1]

There were another 20 scholars with similar presentations; each focused on an open question within our smallest-scale universe. Those lectures need close scrutiny (see the endnotes below). The domain from the Planck scale to the Electroweak scale is filled with mystery and unanswered questions.

Princeton physicist and 2019 Nobel laureate James Peebles lifts up such questions as penultimates in physics and cosmology today.

All students are our sacred trust and treasure.

Thinking, learning, and seeing beyond. Students need to be challenged in every way. Yet, we also need to listen carefully to the ways they challenge us. Some of my most inspiring encounters have come from even younger students. In December 2011 and within all the naïvetés of a high school in the USA, we started exploring the infinitesimal. We had discovered a geometric and mathematical path through a tetrahedral-octahedral honeycomb.[2] It dropped down 112 base-2 steps into the Planck-scale. We also went out the 90 base-2 steps to the age-and-size of the universe. That is a total of 202 base-2 steps from the smallest to the largest. Yet, the first 64 base-2 steps stopped us cold. What could be so small? There are plenty of guesses, but nobody knew. And, we didn’t know what we didn’t know.[3]

We had a novel construct. By observing, thinking, and trying hard to be logical, over time we came to several radical conclusions: “That’s a quiet big bang. It’s a natural inflation. Perfectly smooth, it’s the basis for homogeneity-isotropy. Could it be dark matter and dark energy?”[4]

To say the least, we got a bit carried away! And, that is a problem. Nobody would touch it except the kids. [5]

What’s the smallest thing in the universe?

Our students’ response is quick, “An infinitesimal sphere, a little like Lemaître’s primordial atom.” Pushing back, “So what?” The retort is quick. “It’s defined by the Planck base units and there is one Planck sphere per Planck unit of time.” We had worked on the simple math so I asked,”What does that mean?” The answer is still baffling: “One Planck sphere per Planck unit of time computes to 539 tredecillion primordial spheres per second.” That’s a lot of spheres to track. We had our base-2 notation, a map encapsulating everything, everywhere for all time within 202 notations. It was a transformative surprise; it took us over two years to begin to accept the idea that is was a first. And as you’d expect, we were profoundly challenged by the multiplicity of issues it opens up.[6]

As crazy as it all seemed, we weren’t going to duck out. We learned to accept the idiosyncratic and to ask the experts for help. We continued on, but it could no longer be an extracurricular activity for our brightest seniors. They were going on to college and these concepts created too much tension. When I moved out of town, the lights on the project were turned down, yet I’ve continued to look for facts and to make some guesses… it’s a slowly-expanding history. [7]

Asked about the 539 tredecillion infinitesimal spheres per second, a few years before, we had examined questions about thrust and continue to pursue it focused on the infinitesimal thrust of numbers coming through pi and other dimensionless constants like light and Planck Charge.[8]

If Planck’s base units are symbolically the smallest, what could be the largest?

Discovering limits and a range. We became even more controversial. Built into our simple equations is an active finite-infinite relation. We say that only because these continuity equations are never-ending and never-repeating. Like pi (and with pi), all continue to expand.

Those numbers should be the most-dynamic and the largest numbers within each of the general categories within Notation-202 of our horizontal chart. [9]

By staying deep within pi and an ideal sphere, nothing finite is found. There is a sense of continuity, symmetry, and harmony. These simple perfections manifest within the finite yet are not themselves finite. These three are facets of the infinite. Historically the infinite has been defined in numerous other ways. Most are personal matters. We avoid such language and choose only to defer to continuities which manifest as order and is experienced as time, symmetries which manifest as relations and are experienced as space, and harmonies which manifest as dynamics and are experienced as space-time moments. Although still a series of abstractions, there are boundaries and boundary conditions, logic and structure, and the inherent-yet-quite-derivative mathematics and geometries.[10]

Reviews of the model anticipating our ten-year anniversary

Models of the Universe. The original chart followed the Planck Length (December 2011). Then we added Planck Time (2013-2014). Quite naturally we began adding Planck Mass and Planck Charge to our chart in 2015 and 2016. That’s when the extremely-hot Planck Temperature became an extremely-big challenge.

With time/length and mass/charge seemingly the Janus-face of each other, a cold-start seemed more logical than a truly off-the-charts hot start. The four basic Planck units were doubling. It would be truly idiotic if we projected that the temperature doubled with the other facets of the Planck base units. We decided to put that mystery up beyond the current time and we divided it by 2 to give us the results (numbers) in our very first horizontally-scrolled chart.

Review. Anticipating the tenth anniversary of our studies (yes, we formally started on December 19, 2011), it was a good time to re-engage all 1000+ numbers in that chart. For some unknown reason, the inverse square law forced its way into this ideation, “What if you start with Planck Temperature and with each notation the temperature is cut in half? Does that make any sense at all?”

“Be open. Think about it. Be open; be open.”

To get a sense of those numbers I began a new chart that actually begins with Planck Temperature at Notation-0. Instead of multiplying by 2, divide by 2. Though a bit more commensurate with Hawking-style big-bang thinking, it is still entirely idiosyncratic. The approach to absolute zero is too quick. So now we will place the approximate temperature of deep space within Notation-202 and attempt to discern how mathematically we get from Notation-0 to Notation-202. We are currently contemplating the working relation between all the prime-number bases keeping in mind that base-10 has 64-to-65 notations. How many notations using base-3? …base-5? …base-7 …base-11? We’ll do the numbers like we did with base-10.

The thought process went something like this: “Might the thrust required to generate the first infinitesimal sphere to create the first space/time and matter/energy moment require extreme temperature? Perhaps. Is it worth looking at it? Yes. Might the temperature drop by a half with each or the earliest notations with that very small mass? Maybe. Within the first second (Notation-143) as the number of spheres are increasing to 539 tredecillion infinitesimal spheres per second, there just may be some relatively new mathematics perhaps related to laser temperatures that may well be logical. Let’s explore it. It just might work.”

Can we be re-examining the four laws of thermodynamics (0,1,2,3)? Can we grasp the thermodynamics of laser physics? …its spontaneous fluorescence?  Might the inverse square law apply on the first notation? Might there be several different progressions down to the current, average temperature of the universe?


For many, it is all too simplistic. And, perhaps it is. Yet, just maybe it is the simplicity that was within John Wheeler’s dreams and the correlation between reality and numbers that E.P. Wigner so loved. It seems as if this idiosyncratic path is about to become quite a bit more idiosyncratic![11] Thank you.

Editor’s notes: The most dynamic part of this page follows. These are the evolving footnotes, references, emails, and instant messages. Your comments are most welcomed!

This page and the following sections will continue to be updated. A new homepage has been started and it will be released soon.



[1] Scholars. Durham University’s Institute for Particle Physics Phenomenology (IPPP) has achieved global recognition for her work and her graduate students. The seven pictured above are so good they stepped in for Sir Peter Higgs when he became too ill to make a public speech. The IPPP also hosted an event like the 23rd International Conference from the Planck Scale to Electroweak Scale (Planck 2021) where the focus was on some of the most-mysterious, open questions within the smallest scale of our universe. The intent of most conferences is to trigger new insights. That hope is especially true when considering the graduate students and postdocs. Our hope is also in those who make a presentation for a conference. There is nothing like a deadline! By making time fundamental, we experience its derivative nature.

From this 23rd conference, we now have access to the PDFs of the 21 scholars who’ve made a presentation where we can more readily ruminate about such things. Also, their references are always a great resource.

The primary reference to all related emails to these scholars will always be within this footnote:

These 21 scholars come from around the world. Although each focused on probabilities and possibilities, some are closer in spirit to the Fairbairn presentation which challenges us to stretch in new ways. In every instance, my focus is on the nature of that stretching.

In December 2011 we started working to understand the 202 base-2 notations from the Planck scale to the current time. We have come to believe that the first 64 base-2 notations from the Planck scale to what we’ve called the CERN-scale (or Electroweak scale) are the hidden keys to help unlock silos of information that keep the key domains of physics separated. It’s been ten years. There is nothing like a ten-year anniversary to prompt a more critical review.

[2] The tetrahedral-octahedral honeycomb. Not just a speculative vision, here are geometries that open many-many multiple paths to the Planck scale from that simple tetrahedron (sitting on a shelf in the classroom). To give something so simple a little panache, consider those paths to be a tunnel similar to the concept of an Einstein-Rosen bridge (or a wormhole). Though a real reality, not a virtual reality, we’re creating “Zeno goggles” that automatically divide space in half while proportionately and relativistically shrinking the observer.

You’ll observe and experience the 112 steps, going deeper and deeper within. We’ll slow you down as you get to Notation-20. You’ll observe how the tunnel options have gotten fewer and at Notation-10, you’ll observe the actual creation of the tetrahedron and octahedron between Notations 1-5. You’ll actually see the stacking of those 539 tredecillion infinitesimal spheres. Called cubic-close-packing of equal spheres, it’s brilliant. Then you’ll observe how those infinitesimal spheres are popping out of the Planck scale fabric of the universe. That’s a wow!

Seemingly instantly up at Notation-112 where we came in from the classroom, you’ll be given what we call, “Euler-2-exponential goggles.” Here you will see how every notation is multiplied by 2; and in just 90 steps, you will be out to the age-and-size of the universe, watching the current expansion. A show stopper, you’ll see and experience the universe from the smallest to the largest in just 202 steps, notations, sets, jumps… if you haven’t been to our old chart it may be a good time to go.

The new chart has risen!

We all need to look more deeply inside the tetrahedron and octahedron! We all should spend time deep inside the honeycomb. There is nothing simple about a honeycomb.

[3] What do any of us really know? Are things always simple before becoming complex? It seems to be true, all except around those issues coming out of the big bang theory as promoted by Hawking, Guth, and many others. Now, more recently Princeton’s Paul Steinhardt and his coterie have been getting some traction with their quest for a new kind of matter. Dan Shechtman (wiki) before him looked at the small-scale and got his Nobel prize in Chemistry in 2011 for his discovery of quasicrystals, the imperfect geometries based on five tetrahedrons sharing a common edge and lacking a translational symmetry. In our book, it is confined by notation and its respective Fibonacci sequence. Of course, outside of the 202 notations, that statement is meaningless or gobbledegook. The bottomline is arrogance impedes ideas and creativity. Remember Fairbairn‘s comment about “novel approaches.”

[4] Quiet start? Natural inflation? Perfectly smooth? Dark Matter and Energy? What if the universe starts very simply with Lemaître’s primordial atom? In 1927 Lemaître had suggested as much; it was his first idea, a cold-start. We’ve believe it was his best idea. At least 64 base-2 notations before all the complexification of a particle or a wave, here are the pure numbers of a sphere. A little like the Democritus atom, the conceptual study of a sphere is at least 1500 years older and here we are still learning about it! If we take off Planck’s quantum blinders, we might see his numbers more readily and see homogeneity-isotropy in a very different light. We have been fretting about dark matter since Fritz Swicky’s 1933 formal theorem inferring the existence of dark matter.

Dark energy didn’t come into focus until in 1968 the Hubble Space Telescope began collecting the detailed data. Interpreting it all is still up for grabs. With dark matter estimated to be 27% of the universe and dark energy as much as 68%, it is certainly the most enigmatic issue within science today.

Yet, the first 64 notations puts it all in a new light. Here there is a universe of mathematics and geometry that can not be measured with a physical measuring device of any kind. With all these open issues and with so many others that are ever-so-much more problematic, isn’t it time for a radical shift in our constructs for that first septillionth of a second. It sounds like an insanely short amount of time. Within mathematics, one tredecillionth of a second, and that range, a septillionth to a tredecillionth, is another universe unto itself.

[5] Always looking for the start. Fundamental change within our scientific belief systems is difficult. There are too many people, too much history, and way too much money involved with every major theory, whether right or wrong. Scientific research today is big business. Among those at the the top is CERN laboratories. Straddling the border of France and Switzerland, just outside of Geneva, CERN (Conseil Européen pour la Recherche Nucléaire) is a case study unto itself. Initially it involved twelve countries when it began in 1954. Today there are 23 member states, yet associations with virtually every country on the planet and well-over 100,000 research physicists around the world.

It is a very big business. As an organization, percolating out of the darkness and rubble of WWII, it had a bold start involving those twelve European nations. That start is well known. Yet most enigmatically and more importantly, even today the best of CERN are unsure about the first septillionth of a second at the very start of it all.

My first interactions with CERN folks started with Viki Weisskopf (MIT) and Lew Kowarski (Boston University). Weisskopf was Directeur-General from 1961-1965. Kowarski was the first to propose a laboratory for fundamental research; he was tasked with organizing and setting up it up with Raoul Dautry, Pierre Auger, Edoardo Amaldi and Niels Bohr. See: May 1952, Early beginnings

These were all people who understood the evolution of the first atomic weapon and how basic science can quickly become a Hiroshima or a General Electric. Any concepts that might upset these equations must be most compelling and be ready to face stiff, if not fierce, opposition. Yet, in time, the better concepts do rise. We think ours are straightforward.

[6] Redefining the first instant: Lemaître’s primordial atom, one Planck sphere per Planck unit of time. Those two basic assumptions opened the way to this simple calculation — 539 tredecillion primordial spheres per second.

It is Max Planck’s calculation for Planck Time extended to one second.

The results are beyond imagination. Even today, envisioning such numbers is an ongoing challenge. These numbers made their debut within this website in October 2020 and there are still many levels of error-correction yet to be done.

[7] Reaching out for critical feedback. In 1971 I became part of a think-tank on Brattle Street in Harvard Square in Cambridge. Part of the invention-research process was to suspend judgments and accept ideas as given. It wasn’t always easy to do. We are all naturally judgmental people. We are taught to look at new ideas critically. And, it is easy to fall into the trap of arrogance, “How can you be so stupid?” If only we could change that attitude to something like, “Let’s explore that idea and see where it takes us.” Idiosyncratic ideas are not always idiotic! Yet, it takes a bit of courage to approach our experts. So many of them ask, “How can you be so stupid?” After crawling back into our safety zone and hibernating for a bit, we eventually venture out again but with less ambitious goals. That’s why I enjoy the younger students. Some are still actively exploring imaginative ideas. Our goals as teachers should always be to explore such ideas thoroughly. In 2016, it was becoming clear to me that nobody was dealing with our numbers and the logic of base-2, doublings, spheres, stacking and so on. It was such a different paradigm. It was risky business for anyone with a high-standing within the community to come anywhere near it. Though I assured people that their responses would NOT be shared with the public, people were reluctant to be critical, so it became important to me to log my questions and develop a reference page to each scholar’s work. It is a very modest way to try to avoid becoming more of a nuisance and it helped to focus on their work as related to these efforts.

[8] Infinitesimal thrust of numbers coming through pi and all the all the dimensionless constants. Might it manifest as an inherent force within light and the Planck Charge? Might it be a manifestation of the intimate, immediate correlation with the continuity-symmetry-harmony of infinity? Might it be an ongoing, never-ending finite-infinite transformation? Might infinity be the source for the deepest nature of thrust and photons (force bosons)? Of course, we answer all four questions with a “Yes” and then ask, “What is this universe telling us?”

[9] Largest numbers. We are getting a grasp of the smallest numbers. We also can begin to grasp the very largest numbers that define our universe. These numbers give us some assurance that we are on the right path. The universe does, indeed, look more and more like it is base-2 exponential. Yet, again we asked, “In what ways is it also base-3 exponential? …base-5? …base-10? The largest numbers are not far from today’s actual numbers. Is that the roll of the prime numbers?

It all gives us clues and challenges us to fill in the mathematics and geometries.

[10] On infinity. In 1970, by asking questions about perfection in the face of quantum physics and Bell’s inequality equations, continuity-symmetry-harmony seemed like good abstractions. Building on each other, they were general enough yet have relatively specific scientific meaning. Eventually I asked if each could be a facet of the infinite. It didn’t go far because I could not discern a structure or a path from the infinite to the finite until 2011.

Those 202 notations have triggered new thoughts about very old concepts.

[11] From the old guard to the newest thinkers: From Wheeler dreams to Eugene P. Wigner’s extreme trust in numbers, we go to the likes of Tim N. Palmer, and others like Stephon Alexander, Espen Gaarder Haug, Ari Lehto, Ard Louis, Jirina Stone, Frank Wilczek, and Edward Zalta. It would be magical to have them all in a “Zoom-like” session to talk about this page. Yes, we can dream dreams like Wheeler.

With this ten-year review, we re-introduce Planck Temperature, no longer constantly pushing the boundaries out and getting closer to absolute zero, using the more traditional start at the Planck Temperature raises so many new questions for us. Every aspect of our mathematics will be pressed and stretched.

In a rather peculiar way, both models have the same results so that “the real model” of our universe, remains a mystery for another day. Thank you. -BEC


Please let us know if you would like to join us for a “Zoom-like” discussion about it all.

All eleven of these endnotes/footnotes above are being re-edited and textured.





Sir Peter Higgs, Edinburgh: Sunday, November 7, 2021. A quick note about the question the grad students asked their audience on the occasion of substituting for him when he became too ill to present his public lecture.

• Simon White, International Max Planck Research School on Astrophysics at the Ludwig Maximilians University Munich, has been at the forefront of a Cold Dark Matter paradigm. Because scholars like him have been working with cold concepts within a classic big bang model, I have been pushed to ask silly questions like, “Could there be a super-cooling from the Planck Temperature because that phenomena would most likely act like laser thermodynamics. Could the inverse square law apply?” Based on those flights of fancy, I just started another chart that starts with the Planck Temperature within Notation-0 and is divided by 2 to arrive at a radically reduced temperature for Notation-1. It is divided by 2 again for Notation-2. Because it is temperature assumed to be light and not an “infinitely-dense” singularity, but a very dense black light that within Notation-97 becomes visible light. If one Planck Sphere manifests per unit of Planck Time within thirty-one doublings, there are size is still an infinitesimal 3.470762×10-26 meters, the mass is just 103 pounds (46.79 Kilograms). So now we are asking, “What might the temperature be and why?” Within our first horizontally-scrolled chart, it is 4.73×10-18K. In the chart with Planck Temperature within Notation-0, it is 6.597×1022K. The Electroweak Scale requires an estimated temperature of 2×1012 Kelvin to create the Quark-Gluon Plasma (QGP). That’s an important benchmark. It requires 175 MeV per particle. We’ll need help to figure out which notation would be a logical place as another mechanism to force the review of possible mathematics and functions that may be at work.

Malcolm Fairbarin, Kings College London We have started a profile page to follow his work with the International Conferences from the Planck Scale to Electroweak Scale.

Marco Drewes, UC Louvain We will continue to study his work with the IPPP.

A note to the attendees of the IPPP June 2021 conference:

“I see that you were one of the participants in the Planck 2021 IPPP-Durham University conference. I am going through those papers now asking the questions, “What are the most special insights from those 21 scholars? How do we get beyond the Standard Model without getting too far beyond it?”

“Personally, I know that we’ve gone a bit too far because we started at the Planck scale and hypothesized that something like the concept like Lemaitre’s primordial sphere defines the very first moment. I am rather sure Malcolm Fairbarin (linked just above) thinks it is more idiosyncratic than it is a “novel approach.”

“If you would like to take a look, it’s posted here:  https://81018.com/smallest-largest/

“We then applied base-2 notation at the Planck scale to find just 202 notations from Planck Time to this day.The numbers are fascinating — https://81018.com/chart/ — but interpreting those numbers is not easy. Your comments and insights would be treasured.

“Surely more than a “novel approach.” Perhaps “idiosyncratic” is necessary today. Thank you.”

“Most sincerely,

From a student in Spain: Students ask us questions from schools around the world. Here is my response to a question from a biology student with a strong background in physics. He attends Complutense University of Madrid:

“Your English is excellent. Your references and links: Excellent. Your question, Do you know if Arkani-Hamed adopts something similar to Tegmark’s view as well?, is well placed. Those two are so cockily independent and aloof, they might disagree just to disagree. However, I think you nailed them. Like E.P. Wigner (pictured here), all the way back to Pythagoras (See – Theano, On Piety), they are all an inspiration to me. In my deepest being, I believe they are right and you’ll see throughout my work a deep belief in continuity-symmetry-harmony, the qualitative and infinite, always and profoundly giving rise to the finite.  Too much of our being is spent being arrogant. That doesn’t help anyone. Science and religion are full of arrogance so I try very hard to stay open. Any more thoughts and questions, I am all ears!  Thank you.  -Bruce”

In Process: Simons Foundation folks: Leonard Susskind – 2020 lecturer, Patrick Hayden – director, Brian Swingle lecturer – Chaos-Protected Locality, and Juan Maldacena – lecturer, and so many more


October 18, 2021: @BBCScienceNews@bbcnews@BBCNewsnight #RichardSharp Worldviews are incomplete; we all need a highly-integrated view of the universe. We’ve started here: http://81018.com

October 18, 2021: @MiddleEastEye @AlexandraPring Yes, true. Yet, even Gurnah’s work needs to be seen through a very different lens. We’ve all got to grow beyond our simple worldviews to fully integrated views of the universe. Sounds impossible… it’s not. We started here: https://81018.com/hypostasis/
Abdulrazak Gurnah received the Nobel Prize in Literature in 2021.

Other communications are being reviewed from this period and may be added.


Invitations and Collaborations

With whom do we collaborate? You are among thousands of people who visited this page this site this month. Might you ask, “Can I help this effort?” The answer is, “Yes!” Our only thrust is that the foundations of this universe and life itself be seen in light of infinity and the continuity-symmetry-harmony that the infinite engenders. Please, talk to us. Thank you. -Bruce


Key dates for this document, smallest-largest

  • This document was started early on Monday morning, October 18, 2021.
  • First posted for collaborations, late evening, October 18, 2021
  • This page became the homepage, late on Tuesday, October 19, 2021
  • The URL: https://81018.com/smallest-largest/
  • Prior Homepage: https://81018.com/hypostasis/
  • First Headline: The Smallest and the Largest
  • Second Headline: Smallest to largest
  • First Tagline: How do you answer, “What is the smallest thing in the Universe?”
  • Second tagline: A possible rapprochement with the naïvetés and simplicity of our youth
  • Another possible homepage: https://81018.com/tredecillion
  • The most recent update of this page: Monday, 21 March 2022


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