Lincoln, Don

Don Lincoln

Notre Dame Department of Physics, Notre Dame, Indiana
Fermi National Laboratory (FNL), Batavia, Illinois

Articles: Symmetry Magazine, Naturalness, 2013
ArXiv: Recent QCD Results
CV (pdf)
YouTubeWhat is supersymmetry?

Second email:  Thursday, August 15, 2019 @ 4:04 PM (updated)

Dear Dr. Don Lincoln:

Thank you for your video,
Why there is something, rather than nothing?”  (other viewpoints)
It really is the most timeless question in both science and philosophy.

That theory of leptogenesis needs testing so we are most interested
in learning the results of your FNAL’s reports!

Next up for us (for our viewing pleasure and learning):
The Deep Underground Neutrino Experiment:
Your video on The science of DUNE:
Global benefits of LBNF/DUNE:

We’ll be looking for your new videos here on DUNE:

Thanks again,


First email:  Thu, Dec 20, 2018 at 9:57 AM

Dear Prof. Dr. Don Lincoln:

Thank you for your work to explain the speed of light. For me,
it appears to be profoundly related to the four Planck base units.

Simple questions, yet not so simple answers:
1. Does Max Planck’s simple formula for Planck Time work:
Planck Time divided by c is equal to Planck Length? It appears to work
(See line 10).
2. Does it follow that Planck Length divided by Planck Time is equal to c ?
It also appears to work. It begs the questions, however, does it also work within an expansion of the four Planck base units using base-2? Here the simple calculation gives us a variable speed notation by notation.

We are still thinking about those preliminary calculations within line 10
of our horizontally-scrolled chart:

Is it just jabber, circular speak, or could the simple logic of these numbers
be trying to tell us something? Thank you.

Most sincerely,

PS. That’s a two-hour drive between Fermi and Notre Dame. I suspect you know those roads very well!

Loll, Renate

Renate Loll


Radboud University High Energy Physics
Institute for Mathematics, Astrophysics and Particle Physics
Nijmegen, Netherlands

Articles: What is space?
Arxiv:   Renormalization   CDT and Cosmology
Video: Emergence of quantum spacetime from causal dynamical triangulations
Wikipedia: CDT

Most recent email: Tuesday, 18 June 2019

Yes, you are back up on our homepage today:
Essentially, inspired by Murray Gell-Mann, I thought you would want to know.

In light of the Ellis Physics on Edge harangue, virtually touching everyone who has been a leading thinker in the past 20 years, right to the final paragraph with Dawid-Rovelli, I repeat the John Wheeler 1986 statement within his article, “How Come the Quantum?” where he says, “Behind it all is surely an idea so simple, so beautiful, that when we grasp it — in a decade, a century, or a millennium — we will all say to each other, how could it have been otherwise?”

These simple numbers may bear him out: 
Simple processes, like Euler’s equations and base-2 notation give us an entire range of unexplored numbers from the second notation to at least the 64th notation. That’s a science unto itself. Pure math, perhaps the string theorists could finally claim a home.

It is easy to write off simplicity, yet someday these numbers will be explored by the likes of somebody as informed as you are. Thank you.

Most sincerely,


Second email: Sunday, 27 January 2019

Perhaps the earlier email (below) was buried. Perhaps this base-2 model is just too absurd to acknowledge. I am just a simple guy following simple logic.

On one of our homepages I suggest that these are our primary assumptions:

1. The Planck base units of length, time, mass and charge describe a real reality.

2. The conceptual door to this infinitesimal universe is where all four Planck base units concresce (grow together, yet individuate) to create a stream of infinitesimal spheres. Though physical, length-time are well below thresholds of measurement, the progression of mass-charge units can be studied. These four units are, in some manner of speaking, the Janus-face of each other and of light.

3. Conceptually, sphere stacking becomes cubic-closest packing; tetrahedrons and octahedrons emergeDoublings beginOur universe emergesTheir numbers eventually begin to define things within our current scientific realities.  This is a natural inflationAnd, it’s not dark.

Since December 2011, I have been carrying on in this light, slowly, intentionally, but naively. I wish somebody of your stature and command of all the academic fields involved would take a moment and put a stop to this effort if it is sheer poppycock.  Thank you ever so much.


First email  21 October 2018

Dear Prof. Dr. Renate Loll:

Thank you for all your work linked (just above), particularly your efforts to discern “…a consistent theory of quantum gravity which describes the dynamical behaviour of spacetime geometry on all scales.”

Our focus has been on the Planck scale. We believe there it has more to contribute than meets the eye.

Between the Planck scale and “CERN-scale of measurements,” there are 67 doublings (or notations or causal sets) of the Planck base units.

[If assume the very first instant of the universe is that which is defined by Planck Time and Planck Length and Planck Mass and Planck Charge and that there is a natural base-2 expansion, the 202nd notation includes the current day and time].

Perhaps it might be better to start at the first doubling and to observe the logical possibilities.

Essentially we’d be building a unified theory of mathematics, yet this one would be based more on John Wheeler’s sense of simplicity (I love his introduction of this article, How Come the Quantum?) than on Robert Langland’s programs. Langland’s needs the plancksphere that both Max Planck and Wheeler anticipated.

Might other factors like Causal Dynamical Triangulations (CDT), Regge calculus, fractal structure, 2-D spacetime, and the flavors of the simplex be included in an appropriate build-out and within an appropriate doubling?

I think that the emergence at the Planck base units, the simplest planckspheres may well account for what we know as dark matter and dark energy. I believe it’s a relatively simple calculation.

Among all the people to whom I write, I suspect you can debunk this concept most quickly; or, you may be surprised at its simplicity and possibility. Of course, the derivative, discrete nature of space-time is necessary and I think we would do well to redefine the infinite with mathematical terminology and anticipate a finite-infinite transformation possibly further defining the renormalization process..

To say the least, I would enjoy hearing from you.

Most sincerely,

PS. I first became aware of your work through the Perimeter Institute’s 2016 conference, Time in Cosmology I write letters to focus my thoughts in conjunction with the thoughts and work of a person who appears to be vibrant, open, in love with life, and filled with questions.

Follow-up (from CDT and Cosmology):
•  Non-renormalizability of perturbative quantum gravity
•  FLRW paradigm:  Physics Beyond the Standard Models of Particles, Cosmology and Astrophysic.
•   Imposing homogeneity and isotropy on spatial slices of constant time t.
•   So-called “backreaction” effect of inhomogeneities on smaller scales on the dynamics of the universe on larger scales
•   “…an explicit realization of a non-perturbative, Planckian quantum dynamics…”

More Work to do (further research):
•  Path integrals and Gaussian fixed point. See Assaf Shomer’s on page 7: “The derivation of the path integral formula in quantum mechanics of a massive particle involves chopping up the quantum evolution into very short time intervals and inserting complete sets of states between them.”
•  Doplicher S, Fredenhagen K, Roberts JE (1995) The quantum structure of spacetime at the planck scale and quantum fields. Communications in Mathematical Physics 172(1):187–220
•  Scale invariance and conformal symmetries

This homepage is called a “how-to” page…

HOMEPAGESJUST PRIOR|1|2|3 |4|5|6|PI|8|9|10|11|12|13|14|15|16|17|187|19|20|21|22|23|24|25|ORIGINAL

Sphere to tetrahedron-octahedron couplet
Planckspheres, cubic-close packing, emergence†

The Emergence of the Universe

By Bruce Camber_  _*Inspiration for this page_ _And, Another Version of this homepage

This website is a study of a model of the universe based on an application of base-2 exponentiation (multiplying by 2 or doublings) that eventually encapsulates-and-relates everything, everywhere, for all time in just 202 notations. This model of the universe starts with Planck Length and Planck Time, the smallest possible measurements, and goes to the largest. It starts with the very first moment in time and goes to this very moment in time.

There has never been a mathematical model of the universe quite like it.

To get an intuitive sense of this model is difficult. Four sacred cows of science need to be reexamined; these are best summarized as continuity, symmetry, harmony and the finite-infinite relation. Continuity applies to the nature of time. Symmetries apply to the structure of space, focusing here particularly on the very small-scale. Harmony is a focus on the dynamics of perfection and imperfection whereby chaos, indeterminacy, creativity, free will and fluctuations all emerge. And, all three are the face of the finite-infinite relation. [1]

The dynamic image at the top of this article opens this analysis. The first sphere is the first instant of space and time with a very specific mass and charge. These numbers were all calculated by Max Planck in 1899 and have been studied in earnest since 2001 when Frank Wilczek wrote a three-part series, “Scaling Mt. Planck” for Physics Today. [2]  When he received his Nobel prize in 2004, these three articles took on the patina of authority.

The next step for scholarship was obvious, but everybody seems to be ignoring it.

The first moment of time is derivative, finite and discrete. Newton’s absolute space and time are sidelined to introduce a new scale of the universe that begins with Planck Length and Planck Time. The focus of that image, including the ellipsis (36 displayed), is the first emergence.” [3]

Seemingly out of nothing – no space, no time – it all starts with just one sphere, defined by the Planck base units and many dimensionless constants, that is followed by another sphere, then another and another…. For now, we’ll call these spheres, planckspheres. If these spheres could be observed — obviously much-much-too-fast-and-too-small to measure — perhaps this process might be described as a line or a string coming out of nowhere, literally defining space and time as it emerges. This is the beginning of time, and this first moment is still emerging, today, at this moment…. It is still creating space/time and the dynamics that are mass/energy (or charge). It is assumed that all four Planck units are inextricably interwoven throughout the 202 doublings [4] (or notations) that bring us to this very moment within this day.

In that light, our first principle is that our Universe begins and is sustained by the dynamics that are defined within Planck Length/Planck Time and Planck Mass/PlanckCharge. Given these are inextricably interwoven, one of our challenges is to loosen, then disentangle all the knots.

Be assured, this is not your daddy’s or your mommy’s sense of time. Here it is a rate of encoding and imprinting on a universe that has no past. It has no future. It is only right now. This instant. Everywhere, everything shares this same moment and this same infrastructure. [5] This first notation is always the same, yet it is always unique just like pi. Impenetrable, there is nothing smaller; and these spheres penetrate and sustain all things.

So, another principle is that time is not a measurement of duration but of processing speed.

Here is the operational nexus between the finite and the infinite. Here is the beginning of an integrated, mathematical model of the universe and a quiet expansion with a most-natural inflation. Here is our little universe displaying its deep-seated order; yet very quickly, it begins to reveal how disorder, chaos, uniqueness, and creativity emerge. [6] Those geometries are well-known and the dynamics within each manifestation are now being explored and will be discussed in subsequent homepages.

Doublings. In the second notation the most basic projective geometry begins to emerge and structure begins building on basic structures [7] that creates a logical continuum from the infinitesimally small scale structures right up to the 67th doubling where now things can, in some sense of the word, be measured by accelerators like CERN in Geneva, Switzerland.

One of the key purposes of this site is to chart a map that takes us right down into these assumed infinitesimal structures.

Academics and scholars have not adopted this model. Questions should be asked  first, about the jump or “quantum leap” from the CERN-scale to the Planck scale. 
To date, there appears to be no other attempt to define this exquisitely small space using a simple application of base-2 notation and a profound respect for the Planck base units. In this study Planck temperature is derivative of mass/charge; so to approach the Planck temperature value, it has been reverse ordered. Just for convenience, it is now started just one notation above the 202nd notation. The logic supporting such a positioning is still being formulated.

Can the deep nature of that “quantum leap” be calculated today using just the four Planck base units and doublings? Could the first doubling from Notation 1 to Notation 2 be the foundation for all doublings?  There are many different types and applications of doublings that have already been well-researched and defined. To learn a little about each, on one page within this site, these key types of doubling will be studied and further researched in light of the continuity equations from the first doubling to the 202nd doubling. [8] Hopefully period-doubling bifurcation, cellular division, double field theory and gauge-symmetry for T-duality-and-doubled geometry, and multiscale modeling and simulations will inform us.

What other kinds of doublings should be considered? The 64 doublings from the Planck scale to just under the CERN-scale (at the 67th doubling) have been well-enumerated through the study of geometric expansions, especially as outlined by the Wheat & Chessboard story. It begs the question, “Is there a logical progression by which numbers and geometries progress?” Does every kind of mathematics, geometry and logic build upon each other? [9]

Given recent scholarship within the studies of prime numbers, the question should also be asked, “What is the role of prime numbers in this expansion?” There are 45 prime numbers between notation 1 and 202; there are 19 primes from 1 and 67. Could each notation that is a prime open a path for more complex mathematics? That question is being pursued within the development of the following pages:

So, even as we study these possibilities, a simple stacking renders our first doubling and an infrastructure for all subsequent doublings. Our centerfold image at the top captures the dynamics of doublings. Cubic-close packing, both face-centered cubic (fcc) and hexagonal close-packed  (hcp), has a rich history beginning in-and-around the 1570s starting with the problem of stacking cannonballs on the deck of a ship. Today there are purely mathematical packing challenges as well as applications of atomic and crystallographic stacking and packing. By starting with planckspheres, this most-simple doubling application becomes discernible as the second,  third, and fourth doublings are assumed. Further, subsequent doublings are assumed right on up to 202nd doubling and the current time.  Yet, something unusual is captured within the 67th doubling, we begin to measure it. That length opens the possibilities of particle physics revealing the potential science of the first 64 steps. It begs the question; is this a logical continuum from the infinitesimally small scale structures up to those being measured by accelerators like CERN?

These planckspheres, a key element of the finite-infinite bridge, are defined by pi, the Planck base units, dimensionless constants and simple logic. Every finite-infinite discussion-and-debate should be re-examined. Though tedious,  it must be re-engaged.  There are too many fine scholars who are being torn up and their logic being shredded to not engage every idea that has been posited throughout human history. All of that is within the 202nd notation. The 197th notation takes us up to 343+ million years. Our first 196 notations open a deep study of the earliest cosmological epochs.

Could this model be in line with Neil Turok’s conclusions that the universe is in a perpetual state of starting? So, yes, I believe planckspheres and every form of emergence up to the 67th notation are keys.

Many people have asked, Why now?

Of course, the question must also be asked, “Is this model overly simplistic and naive?”  Yet, even if so, could this model of the early universe be closer to the truth than the big bang theory? I believe it is. Thank you. -BEC 



Endnotes and Footnotes:

(in process today, 29 June 2018)

[†]   This dynamic image was first introduced within this website on January 4, 2016 in an article about numbers, “Constructing the Universe from Scratch.” It has now become the center point within this analysis. In that initial article, the question was asked, “Which numbers come first and why? Which numbers are the most important to know and understand?” The image was also used within the following articles: Fabric of the Universe (November 20, 2017, just below point #4), Consider how symmetries within the first 67 notations actually create space (Sept. 17, 2017) and Symmetry: Circles-to-Spheres-to-Triangles-to-Tetrahedrons-to-Octahedrons (September 13, 2017.

[1]  The three faces of the finite-infinite relation extend our earlier discussions about David Hilbert’s understanding of infinity and Max Tegmark’s disdain for the word. Continuity-symmetry-harmony are the mathematical-scientific faces of infinity and each face is captured by the dynamics of pi and the emergence of lattice, tetrahedrons and octahedrons, and eventually complex structure.

[2]  Frank Wilczek wrote his three-part series, “Scaling Mt. Planck” for Physics Today, yet has not acknowledged that Planck base units are the best conceptual orientation to start constructing this universe. As a result of this analysis, we will ask him, “Why not?” To our knowledge, the writings within this website are the first to lift up Max Planck’s base units as the starting point for the universe. We are anxious to discover and understand any articles that analyze their place, power and conceptual richness.

[3]  “The first emergence” is a steady stream of planckspheres being uniquely created just like they were in the very first moment. Every notation has a unique function and every notation is evolving at the same time it continues to do what it has done. Here, perhaps are Neil Turok’s perpetual starts of the universe. Here everything, everywhere is built up and emergent from this fabric of the universe, called an aether and/or dark matter and dark energy, that gives this universe its isotropy and homogeneity.

[4]  The Planck base units and dimensionless constants are inextricably interwoven throughout the 202 doublings (or notations) are based on the “Plancksphere” and that analysis is just beginning. I googled the word, for example, on June 25, 2018 with those quotes and there are just nine results. Using two words, “Planck sphere” with the quotes, there are 320 results. And without the quotes there are just over four million combinations that come close. Such results suggest that this is a new or emergent science.

Within our dynamic image about sphere stacking, the tetrahedral-octahedral architecture begins to emerge. Here, the possibilities for getting things inextricably woven together become staggering. By the tenth doubling there are 134,217,728 scaling vertices with which to work. By the 20th notation it catapults to 1.4411519×1017 — there are no limits to the entanglement of strings and knots and yet-to-be-fathomed geometries to create. By the 64th notation those scaling vertices have jumped up to 6.2771017×1057  and the first particle has yet to emerge!

Unless this simple logic is mistaken, there is altogether too much potential to ignore these possibilities and this orientation any longer.

Also, it should be pointed out that Max Planck’s formula for light — you can see it on line 10 of the horizontally-scorlled chart of 202 notations is a special calculation that needs further study.  The fact that these doublings is a form of base-2 exponentiation suggests that our universe is not linear and just might best be defined by Euler’s identity, considered by many mathematicians and physicists to be the most beautiful of all equations.

[5]   Everywhere, everything for all time shares this same moment and this same infrastructure. There are many books and articles about the nature of time. Within this study, most have fallen short. Einstein and Planck opened the door to re-analyze Newton’s earlier conceptual frame of absolute space and time, yet nothing more compelling emerged. Newton continues to define our commonsense logic, but should it? If it is established that period-doubling bifurcation, cellular division, double field theory and doubled geometry, and multiscale modeling all share the same common denominator that starts at the Planck base units, absolute space and time can be placed on the historical shelf as a footnote within the imprinting on the sentience of this universe. More work needed…

[6]  Consider disorder, chaos, uniqueness, creativity and fluctuations. The scholarly community is increasingly confused with the terms, infinite, space and time.  David Hilbert’s simple analysis leaves much to be desired. The infinite can be understood as a logical construct where it is the foundation for continuity, symmetry and harmony. These three perfections should all be understood to be a scientific assertion about the nature of order, relations, and dynamics. The various manifestations of fluctuations can be experienced as disorder, chaos, uniqueness, creativity and human will. The geometry for fluctuations begins with the simple pentastar, a clustering of five tetrahedrons. The next base structure, the icosahedron, is a clustering of 20 tetrahedrons. The dynamics of each will be introduced within future homepages.

[7]  Structures begin building on basic structure.   There are two areas where our analysis is focused. The first is on a notation-by-notation analysis but progress is slow because there is so much mathematical logic to be learned. The other is basic geometries, quantum geometries and dynamic geometries.  Here, too, there is so much to learn and, of course, more to come

[8]  There can be strains of continuity within discontinuity. There can be strains of discontinuity within continuity.  The continuity equations from the first doubling to the 202nd doubling come from within a continuity that envelopes our physical universe, so here, too, there is more to come

[9]  There appears to be a rigorous academic study of the logical construction of concepts, geometries, and equations. Mathematics and geometries do build upon each other! These studies will become our studies and as quickly as possible, each will be integrated within our map of the universe. Yes, there is more to come

“In philosophy, systems theory, science, and art, emergence occurs when “the whole is greater than the sum of the parts,” meaning the whole has properties its parts do not have. These properties come about because of interactions among the parts.” -Wikipedia

This page was started on June 21, 2018 in South San Francisco while on our tour of America. On many occasions Hattie and I been challenged to look at the world and ourselves in new ways. Along our route, we’ve spent time engaging with people:

  • At John Hendrick’s retreat, Gateway Canyon Ranch, an hour south of Grand Junction, Colorado, we discovered his CuriosityStream retreat center. That got me thinking.
  • We were in the highly-overpriced Yellowstone Hotel in Wyoming where the National Park Service is attempting to create a Disney-like experience, highly-controlled-and-organized wilderness. That compressed conflict got me thinking.
  • On our drive to Bend, Oregon, I discovered the Simplot Don plant near Pocatello, Idaho and learned about fertilizers and growth and even that challenged my thinking.
  • In Bend, while visiting with friends, I was challenged again to understand why there is such disparity, both political and economic, within our world.
  • On to Portland, the land of inclusivity, two different sets of friends challenged me to see the world through their eyes. There is so much to process and process it we will until each becomes a homepage.

This homepage was simply to clarify the last three homepages:

Thanks again.


The next homepage builds from this page and from those past homes pages linked just above, and from a page written on July 23, 2016 entitled, Chaos-Order, Indeterminant-Determinant.

Your Small Group For Controversial Discussions

The Nature of the Finite-Infinite Relation

December 2017 Update: April 2018 OVERVIEW  WORKSHOP Session #1  #2  #3 #4 #5 #6 #7 #8 #9  Summary

Convener-Presenter:  This could be you.

Purpose of this group. To develop a special graciousness and openness about life and beliefs, this group is for the people who want to get along with believers and non-believers. Can we find a deeper truth that holds up some new insights that will embrace both sides of an equation by focusing on the nature of the relation. We’ll engage the edges of scientific research and its implications for our current theories about the universe and its origins, and about who we are and the meaning and value of life.

Overview: One of the best sources for a study of the relation between the finite and infinite are the sacred texts within our religious traditions.  Many of us who grew up in the Christian tradition and like typical college students, we tend to reject the old to begin to self-actualize.  Then we begin studying at the limits and boundaries of our knowledge and the challenges can become so daunting, they get left in those undergraduate and graduate classrooms. Personally I went out as far as I could on the edges of physics, working with Bob Cohen, then chairman of Boston University’s physics department, and then with physicists from around the world. I began discovering there are conceptual overlaps between all the departments within the university. The most extreme appeared to be those who were religious and those who demonized all religions.

What can be more different that the texts within The Bible, both Old Testament and the New Testament, and most texts within the scientific community, that is between Genesis 1 and John 1 and Stephen Hawking’s big bang theory.  These sessions are designed to examine concepts within the sciences, philosophy, ethics, and mathematics to see how and where these overlap with concepts about eternity, infinity, light, and love. We start with an integrated view of the universe, and that begins to inform our understanding of the infinite and infinity.

Structure: This small group will have just nine gatherings, no longer than 90 minutes each. A goal for these sessions is to chart a way to empower people to create such a small group study.
• The first two sessions. We will re-examine cosmological models of the universe (2 weeks).
• The 3rd and 4th sessions:  We will explore various ways of approaching an understanding of the finite-infinite relation.
• The 5th and 6th sessions: We will explore a rather different understanding of light, a light that permeates and defines every notation and all of space and time.
• The 7th and 8th sessions.  We will explore the challenges to our understanding of basic concepts like space and time.  Both become finite and transaction oriented.
• The final session: Beyond the summaries, we will be searching for answers to the question, “What do we do now?”

Simple and small goals:  The first goal is to open the door to a very simple orientation to science and faith that (1) works with science and mathematics and (2) allows for, and possibly informs, religious beliefs. The next goal is to explore the entry points between the finite and infinite. Another goal is to explore the physics, philosophy, and psychology of light. If we have even limited success, we’ll all begin to shrink space and time and open up an intimacy with the universe.

Resources to start your own Study Group:

Promo sample to paste on bulletin boards: Please Update the dates, locations and people.
Update: PDF to be printed back-to-back after updating. It creates four 4.25×5.5 inch handouts.
Session 1Models of the Universe   Worksheet #1   S1a   S1b   S1c
Session 2: Models of the Universe
Session 3: Finite-Infinite: Continuity-Symmetry-Harmony
Session 4: Finite-Infinite: Order-Relations-Dynamics
Session 5: Light as defined by the Planck Length and Planck Time
Session 6: Light and time. Ten ways to reconsider the nature of time.
Session 7: Eight Key Ideas
Session 8: Planck Explains Einstein and Redefines Space-Time and Pi.
Session 9: “It’s a wrap.”
1. Always check the homepage of
2. Check for any prior homepages you may have missed.
3. Add to the dialogue: Comment, like, Tweet, Link


Richardson, Louise Mary

Louise Mary RichardsonRichardson

Vice Chancellor
Oxford University
Oxford, England


Second email: July 18, 2020
Dear Ms. Louise Richardson:
Yes, God only knows when we touch another,
and how we learn, and how things change.
My “Louise Mary Richardson” page is here:
It is my note to you from Oct 31, 2017 and
a few references and links to your work.
I just had a chance to re-read my note and was
inspired to visit online the history and story of Mary Aikenhead.
What a very special foundation upon which to see our universe.
I wish you well.
First email: Tue, Oct 31, 2017 at 3:49 PM

Reference:  Forward for Oxford University Press

Dear Prof. Dr. Vice Chancellor Louise Mary Richardson:

Sometimes even Tacitus is wrong. [1] Some age-old “truths” actually hold us back. Two powerful obfuscations came out of the other great British university, particularly from two of their Lucasian Professors, Newton with his absolute space-and-time [2] and Hawking with his infinitely-hot big bang. [3]

Now, I have been reading What Terrorists Want: Understanding the Enemy. And, yes, we have been too slow to create counter narratives to the ideologues of terrorism. I would add that we have also been too slow to challenge conventional paradigms, especially when we find ourselves within circular arguments.

Now, we share a few common experiences. As a kid we would visit Aunt Nellie who worked in the Radcliffe Admissions office. My dad had been a sheet metal worker in the Harvard HVAC group and helped to keep the Mark I and II cooled down in the basement of the Cruft Lab on Oxford Street. While in high school I joined the SDS at Harvard before it was thrown off campus in 1964. By 1969 I was organizing national amendments to end the war in Vietnam with full-page ads in the New York Times and Wall Street Journal, and congressional conferences in Washington, D.C. on global priorities. There wasn’t anything we wouldn’t do.

But something fundamentally was missing.  My driving force was to understand scientific breakthroughs, creativity, and innovation. By 1971 I was onto the EPR paradox [4] and quickly found John Bell [5] at CERN labs. It became obvious that there was something very wrong with our notion of space and time, but we couldn’t break through Newton’s commonsense logic. Hawking was so hooked, the big bang seemed like the only logical choice among cosmological models. It wasn’t. [6] Then, after 100 years of being in an academic closet, the Planck units were re-discovered (2001). Then, in 2011, the first mathematically-integrated chart of the universe was made using the Planck units. Using base-2 from the first moment of physical time to the current time, there were only 202 notations.

That changes everything. Space-and-time are contained. And, now something more fundamental must emerge. Oxford should be on the forefront of understanding what that is. If I were able to assemble an Oxford team, among them would be Harvey BrownArd LouisAlister McGrath, Jirina StoneRichard Swinburne, Roger Trigg, Keith Ward, I.A. Walmsley… and you.

May I follow-up this introduction?

Thank you.

Most sincerely,

Bruce Camber
Austin, Texas

[1]  We seem to settle in with concepts that actually become age-old truths, but these concepts are ultimately flawed. Of course, by and large Tacitus is right:  ‘Truth is confirmed by inspection and delay; falsehood by haste and uncertainty.’ You use the quote within the section, “Challenges” within the  Vice-Chancellor’s Oration 2017
[2] There are comments about the debate between Leibniz and Clarke (Sir Isaac Newton) throughout the website,  For now, you might particularly engage the second point of this page:
[3] There are pages and copies of emails to Stephen Hawking about his Big Bang theory. Ostensibly the argument focuses on the texture of the first fraction of a second of the universe and whether there is “…an infinitely small, infinitely hot, infinitely dense point…”
[4] EPR Paradox, also known as the Einstein-Podolosky-Rosen thought experiment of 1935 opens the question about non-locality and quantum entanglement.
[5] Bell’s Inequality opens the discussion to the widest community within physics and these discussions lead to the conclusions of Nima Arkani-Hamed and Max Tegmark to stop using the concepts of space-time and infinity.
[6] All cosmological models are being called into question.

Read More »

Mersini-Houghton, Laura

Laura Mersini-Houghton

Department of Physics and Astronomy
UNC-Chapel Hill, NC 27599 USA

ArXiv: also many others, including
Predictions of the Quantum Landscape Multiverse, 21 Dec 2016
Practicum: AN ORIGIN STORY (January 23, 2019)
YouTube: How did the Universe Begin? Big Bang Creation Myths (Dec. 2018)

References within this website:
1. Homepage in February 2019:
2. Reference within emails to Stephon Alexander
3. Planck scale to Quantum Fluctuations:

Most recent email: 29 January 2019 at 9:30 AM

Dear Prof. Dr. Laura Mersini-Houghton:

My prior email back in October 2017 (below) was as a result of reading your ArXiv article referenced above with Stephon Alexander of Brown. Since that time, I have had several occasions to read more from your unique perspective.

One of the reasons I was initially attracted to Alexander’s work was the simplicity of his logic. It stood out because in the face of big cosmology, he said that it all either started hot, as with the Planck Temperature, or it started cold as in zero temperature. That was uncharacteristic within the halls of physics. Most had already defaulted to the Lucasians, Newton and Hawking.

We do not.

We are waiting for some scholar with the depth and range that you have to explain why our simple logic of a very cold start and a natural inflation can not work. The numbers generated from simple doublings tell a story that seems to track well with big bang cosmology, yet gives us a very special kind of data that goes well behind what some are calling the epoch of reionization.

Since we can’t get behind that period, why not look at the simple data generated by logic, a cold start, and simple doublings? If it can be pulled into harmony with CMBR measurements, then I think it should be looked at even more closely.

It is not totally crazy if there is some possibility of seeing all these puzzle pieces rather differently.

Thank you.

Most sincerely


First email: Oct 30, 2017, 8:21 PM 


Thank you, Prof. Dr. Stephon Alexander and Prof. Dr. Laura Houghton-Mersini:

I’ve gone through your September 1, 2017 article and have highlighted several spots, particularly,

We are exploring the possibility of an underlying microphysical mechanism that limit contributions to vacuum energy from phase transitions in the early universe, and furthermore which relates the energy of the vacuum to the coupling constants of nature and their hierarchy, in other words to the the Standard Model, in a fundamental way…

In the microphysical scale, if you begin at the Planck units and use base-2, you’ll have those 64-to-67 doublings to the CERN scale which define the very-very early universe. Between the 143rd and 144th doubling the universe is just a second old and the length is the distance light travels in a second. At the 197th we are within our first 500 million years and at the 202 we are now emergent within the Age of the Universe today.

That simple math and simple logic, of course, is too simple for most. You may be surprised, once you are inside those domains, how complex and open it all is.

Thanks again for your article.
Wonderful collaboration!

Most sincerely,


Letters to Stephen Hawking

/Last update: September 27, 2018 We Communicate With Everybody.   Scholars / Specialists

Stephen Hawking & now his foundation

Died: March 14, 2018
Centre for Theoretical Cosmology
Cambridge University, Cambridge, England

CV PhD thesis
YouTube (TED)

References within this website:
• Stephen Hawking was on our homepage.  
• Hawking was the world’s leading advocate for the big bang theory. In 1975 he published his first major book about it. In 2012 we were just starting our rather idiosyncratic studies within this domain. By 2014 we began to realize that our little model just might have key numbers for each epoch as theorized by big bang advocates. Surely if the simplicity of these numbers begins to resonate, we would hope to receive some acknowledgement from someone within the University of Cambridge, Department of Applied Mathematics and Theoretical Physics (DAMTP). 
• Hawking’s “…infinitely small, infinitely hot, infinitely dense point…” full quote.
• Our first email: August 3, 2014

Most recent email: Saturday, 22 September 2018

TO: Stephen Hawking Foundation
RE: Absolute space and time

To whom it may concern:

In 2011 we backed into an excellent STEM tool applying base-2 exponentiation to the Planck base units. We are still struggling to understand each doubling. From the 67th to the 202nd, current science does its work. That is, those notations go from the scale starting at the edges of measurement by accelerators like the Large Hadron Collider at CERN and proceeds to the current expansion, yes, to the size and age of the universe within the 202nd notation. Because the project started in a high school geometry class and was tested among 6th grades in the primary school, we know it is a terrific organizing tool (STEM), but we believe it can be so much more.

Is this the kind of project about which your foundation would like to learn more and might consider supporting? Thank you.

Most sincerely,
Bruce Camber

PS. We have already engaged some of the leading institutes of the world to help with some of the data sets. With your encouragement we would gladly engage centers close to your work, such as the Perimeter Institute of Waterloo, Ontario, to work with us. -BEC

Final Tweet:  Monday, October 17, 2016 and re-opens the 1983 No Boundary Proposal. @tegmark Nice pic of the Mad Hawk

Final email:  Friday, October 7, 2016 at 7:47 PM

Dear Prof. Dr. Stephen Hawking:

Big bang cosmology may not be necessary; a more simple, comprehensive and predictive model may be found in base-2 notation from the Planck scale to the Age of the Universe.  Even the needed inflation is defined within base-2 expansion. It is all so simple, once you know  you know it! Though you and your theory have been attacked since your earliest papers in the 1970s, never has a simple, more comprehensive, alternative model been offered. It has now.

Our offering has slowly evolved since December 2011. We never imagined at that time that we would be coming up inside and behind the big bang cosmology. Never did we imagine that we would engage numbers in such new ways. Never did we imagine that we would have such cause to write to you!

Those who  begin to study the numbers generated by using base-2 from the Planck base units quickly see it. It is that simple.

No less than forty years of research and development, hundreds of thousands of articles, books, conferences, discussions and videos will have to be redressed. It is OK because the big bang has always been problematic at best; it is poor philosophy and rather debilitating psychology.

Intellectual integrity is on the line.  And, it involves the intellectual integrity of the diverse cultures of our world.

I am hoping against hope that you will earnestly look at the numbers. What is wrong with them?   If there is something there, perhaps we can open the doors on a future based on the continuity, symmetry and harmony inherent within this simple model. It will be a sharp contrast with the nihilism inherent within the big bang.

Thank you.
Most sincerely,
* * * * *
Bruce Camber, USA


Our second email:  June 30, 2016 at 5:18 PM

References: Is is possible that a quiet expansion defuses the big bang?

Dear Jonathan (and Prof. Dr. Stephen Hawking):

On June 1 that article (linked just above) to which I referred you earlier this month will finally be our “first draft.” This model, based on a rather quiet expansion of the Planck base units using base-2 exponential notation, begins to redefine the first four epochs that define the start of the big bang theory. The Planck Epoch has become the Planck Moment; the Grand Unification Epoch has become a process and your Inflationary and Electroweak Epochs have also become processes.

Just below, I will insert our introduction from our quite-large, horizontally-scrolled chart and I will post this email within our “Letters” for our 3000+ scholars with whom we communicate around the globe.

Of course, we will inform you and the people of the DAMPT of our progress or lack of it.

I send you our best wishes for your well-being and that of all the DAMPT people,

Most sincerely,

Bruce Camber, USA  and

Redefining the big bang theory through this quiet expansion of 201+ notations:
The following three questions need to be addressed by this simple mathematical model of the universe called Quiet Expansion (QE):
1. Can this quiet expansion defuse the big bang theory? The math within the QE model redefines the first four and most-key elements of the big bang theory (bbt). If it is defused and becomes an historic statement, From Lemaître to Hawking, science can move on within well-prescribed boundary conditions and known parameters. The first four “epochs” of the big bang theory can readily be subjected to redefinition. These “epochs” amount to less than a trillionth-of-a-trillionth a second.
2. Are ethics and values built into the fabric of the universe? The QE model establishes a simple continuity equation from the first moment in time through the Age of the Universe to this day and this moment. These simple mathematical constructions quickly evolve as geometrical constructions and symmetry groups. These become dynamic and harmonic. Continuity, symmetry and harmony are the foundations for a natural value equation deep-seated within the universe. Most every flavor of ethics, morals, and values can be appreciated for what they do and don’t do, and for why they are.
3. How can we more fully understand the finite-infinite relation? This finite-infinite relation is perhaps best described as a study of perfection and moments of perfection and that the geometries and mathematics of imperfection are also better defined and understood as a result.

Planck Moment: The finite-infinite relation most intimately defines the first notation and is necessarily within all notations building from the first. An infinitesimally short duration, it is the beginning that creates space and time and then extends within space and time much like the birthing process. The Planck base units are our simplest-deepest-best description of this moment as of today.

Grand Unification and the Electroweak Processes: Based on the fact that entities and things require a necessary amount of space that only becomes available from the 67th notation and above, the first 60 to 66 notations are foundational to all notations. Using the analogy of the birthing process, all the forms-and-functions, then processes-and-procedures, and then relations-and-systems prior to the actual birthing event, are the first 60 or so notations. Here that finite-infinite relation creates the foundational order, the most basic relations, and many dynamical systems prior to the uniqueness of every reasonable analogue to the birthing event.

The Grand Unification processes continue beyond the 67th notation as specific Unification processes. The electroweak processes now begin to manifest and the measurements given by the big bang theorists can be tweaked and integrated within the quiet expansion model.

Inflationary Processes: Just as there are still many many questions about cellular division, there are even more open questions within this model. However, the force, the infinitesimal amount of energy, available to this process are working ratios of the Planck base units whereby order, relations, and dynamics evolve with a perfect continuity, perfect symmetry, and a deep harmony within every sphere and basic structure. This concept was initially put forth as a philosophical orientation to life, and then it was explored in a post about numbers called, On Constructing the Universe From Scratch (pp.5f).

Our first email: August 3, 2014

My dear Prof. Dr. Stephen Hawking:

I think a high school geometry class, although very rough around the edges with major conceptual leaps, is closing in on a very real, elegant, simple model of the universe that involves base-2 exponential notations to define the boundary conditions from the Planck Length to the Observable Universe including 3D tilings that begin with the tetrahedral-octahedral truss, then considers the parallel construct to music and takes Kepler one step further so we might have some harmony within this little universe.

You may enjoy it:     Thanks.



Hossenfelder, Sabine

Sabine HossenfelderHossenfelder

Frankfurt Institute for Advanced Studies
Frankfurt am Main, Germany

Article(s): Physicist Sabine Hossenfelder Fears Theorists…Scientific American, 2016
ArXiv (48): Rethinking Superdeterminism (13 Dec. 2019)
Books: Lost in Math: How Beauty Leads Physics Astray, Basic Books, 2018 (AAPT Review) (Amazon)
Blog: Backreaction: What is emergence? What does “emergent” mean?
Google Scholar
Homepage  (Research Fellow)

Most recent email: 5 April 2020

Since 2016 I have probably wasted a huge chunk of my time exploring and re-exploring our little base-2 model of the universe from the Planck scale, particularly Planck Time to this moment, our current time, all in 202 notations.

In that same time you’ve gotten a most, prestigious new job, published a most provocative book, Lost in Math with Basic Books (2018), written a dozen technical articles that appear in ArXiv and many of the best journals, have had dozens of articles written about you, and richly extended your blogging within Backreaction. Your production values climb as you continue to extend your YouTube activities and you burn the lines of Twitter. You’re (expletive) incredible. Congratulations. You’ve become a super star!

…and all the while I’ve become more and more idiosyncratic out here inside an Alice-in-Wonderland passage into the Planck’s base units.


Third email: Aug 15, 2018, 8:13 PM (slight corrections)

I don’t come out of my shell too often. Old age is catching up to me.

Regarding our base-2 model of the universe from the Planck units to current time all within just 202 notations or doublings, I am rather sure that you find it all quite idiosyncratic. It is. But, is it going in the right direction? Is it more right than wrong?
How about the simple logic? Is the universe a highly-integrated whole?

Allow me please to include a recent “Ten Functions To Construct Our Universe.” Your comments and criticisms would be highly appreciated.


Ten Functions To Construct Our Universe

202.34 successive doublings of the Planck scale outline our universe.

    1. 202.34 successive doublings of the Planck scale outline our universe. [1][2]
    2.  Doubling mechanisms are built into the universe[1][2][3]
    3. A natural inflation/thrust is within the first moment of space and time. [1]
    4. We are primarily defined by ratios, all the dimensionless constant
      (all appear to be natural bridges between the finite and infinite).
    5. Space, time, and light are more fully integrated. Time appears to be finite. 
      (Length/time continuum suggests this model may actually be on target.)
    6. Consider 64 Unexplored Doublings from the Planck Scale to CERN’s Scale. [1] [2]
    7. One might conclude that it defines an exponential universe.
    8. It quite possibly opens a geometry for quantum fluctuations.
    9. It is becoming clear that infinity needs to be reopened as a key study.
    10. Key concepts like continuity and symmetry, are all reopened for re-evaluation.
Second email: Sat, Jun 30, 2012, 8:13 PM

Hi Sabine –

Thank you for your straightforward response.

It was a genuine question. No trick.
And, you understood the question in the proper
context. I appreciate your answer.

That is what I thought, but I certainly do not
have the depth of knowledge or scholarship
to know with any certainty if life becomes more
than peculiar at that point, i.e. the Planck length.

I was looking for an informed scholar’s
deep-seated insights regarding the functional
nature of the Planck length.

It is so small, so seemingly unknown-but-known,
I decided to explore it in some manner of speaking.
In the first 20 steps of exponential, base-2 notation,
that s-called point, a width/length/height expands to over
one million points (or lines or strings or forms or …. )
and, I assume, a specific length/width/height.

Do you happen to know Ed Fredkin (MIT, Carnegie Mellon, BU)?

He was a long-standing friend of a mutual friend, so while talking about life, I asked him about the Planck length. He responded that exponential, base-2 notation of the Planck length is numerology with physics. Essentially it’s meaningless.

I am not so sure.

If we were to assume that math, particularly simple geometry applies across all space and time, right down to the Planck Length, then those million of points begin to have some value.

Is that a faulty assumption?

I have been thinking about these concepts since
December 2011 while preparing for that geometry class.
I hadn’t seen base-2 from the Planck Length to the edges
of the observable universe — I just thought that I had fallen
asleep in those classes when this topic was introduced,
yet after doing some due diligence, it appears to be
an oversight.

I would dearly appreciate any insight you may add to this
direction of thinking. Thank you.


First email sent: Saturday, June 30, 2012 1:15 AM

Subject: A simple, quick question?
Sabine Hossenfelder, aka Bee

Dear Bee:

I am not a scholar, but I do appreciate good scholarship.

In this past year, I have been introduced to Planck’s length
in my research of basic structure in preparation to substitute for
a high school geometry class (Yes!).

My simple question, “Is there any conceptual error in multiplying
the Planck length by 2, exponential notation from its single point
out to the edges of the observable universe?

That high school geometry class — where I was substituting
for my nephew that day — we found 202.34 notations
or steps or doublings.

A YES or NO answer would be a wonderful starting point.
An explanation of NO would be extraordinarily informative.

Thank you.

Bruce Camber

PS. I am a television producer with over 51 seasons on PBS-TV and
the VOA-TV around the world. I am currently working on early-stage
ideation for a new series that could touch on this question.

Tegmark, Max

Max Tegmark


Professor of Physics
MIT  Kavli Institute
Cambridge, Massachusetts

Article: What scientific idea is ready for retirement?  “Infinity!”
Book: Our Mathematical Universe, Knopf (2014)
Facebook inSPIREHEP PhD Reddit Twitter Website Wiki YouTube

Links above go to a few of Tegmark’s pages on the web.

Links below go to references with this website:
Homepages: With Hawking on the infinite, October 16, 2016
_______________Time Is Always Right Now, This Moment… October 2, 2016
•  ArticlesJuly 2015  The very first reference to Max Tegmark was in December 2012 (that reference is just below). Found in many posts throughout the site, here it is again under the title, “A Simple View of the Universe: Is a simple mathematical and geometrical view of the Universe meaningful or useful?”
December 2012: In 2001 Frank Wilczek (MIT) wrote, Scaling Mt. Planck (Physics Today). In 2006 Wilczek with Max Tegmark (MIT), Anthony Aguirre (UC Santa Clara), Martin J. Rees (Cambridge) focus on 31 key dimensionless constants (ArXiv).
All emails posted below from January 2012 to September 2020 Tegmark is a very busy person and has never responded to these emails. His system did send an automated response to a LinkedIn request in 2014. Because it was automated and has an important link, it’s inserted below.


Most recent email: Tuesday, 1 September 2020

Dear Prof. Dr. Max Tegmark:

On the homepage today is this paragraph:

DEEPER DYNAMICS. Max Tegmark of MIT wants to retire infinity. We want to expand our understanding of infinity. Our key question is to discern how that finite-infinite relation gives rise to infinitesimal spheres, sphere stacking, and cubic-close packing of equal spheres, and how it is that this special mix renders basic geometries, emergence,  and a natural inflation.

My record of my emails to you is here: To come up with such an idiosyncratic point of view, there are essentially about 20 concepts that fall outside the mainstream: I hope you and your family are well and doing fine.




Seventh email: 28 March 2020

Dear Prof. Dr. Max Tegmark:

Along with Nima and Neil, you three constitute a force in physics and are three of my favorites among the legions of the brilliant. Today’s homepage — the unique URL is — has links to you three, plus to one of my very favorite pages,

Our idiosyncratic model of the universe is different:
1. The infinite-finite relation is unique — the infinite is the qualitative expression of continuity (order), symmetry (relations), and harmony (dynamics) while the finite is the quantitative expression of continuity, symmetry, and harmony. For me, any other definition of the infinite has too much historicity that is limited within time.
2.  The initial perfections of the qualitative is challenged by the geometric gap of the five tetrahedral configuration. It becomes the grounds for quantum fluctuations which becomes systemic before Notation-64 where particles and waves begin to manifest.

The fact that the speed of light is confirmed within .01% of laboratory-defined speed at the one second mark between Notation-143 and Notation-144 and then again with a light year between Notation-168-and-169 is sweet.

When it comes to testing new ideas, we are all fools albeit some of us more foolish than others given those quantum leaps and impatience with incrementalism.

I wish you well. We all must try to stay healthy in these very odd times.

Most sincerely,

Sixth email: Thu, Jun 1, 2017 at 5:39 PM

Subject: Fwd: Do our simple mathematics at all jive? I hope so.

Hi Max –

Whenever I quote somebody’s work, I send a copy of that reference.

We all should know your work and your thinking. To that end, we have
a Max Tegmark page within our website (Editor’s note: This page!)

We live in such crazy times and I believe a lot of it has to do with Stephen Hawking’s dystopian, nihilistic bang. Also, to address your desire to throw out infinity, I have offered a redefinition (only highlighted here within this document).

Our naive model has a simple logic, a most-simple start, and simple mathematics. It is all-inclusive yet particularized. And, it also has a simple logical start for infinity, indeterminacy, fluctuations, incompleteness, and imperfections.

So I ask myself, “Why not try to integrate it with the Standard Model of Physics, with quantum gravity, and with the ΛCDM model?” Would you advise us? Thank you.

Most sincerely,
Bruce, as the Editor, answers his own note on 27 March 2020:
“Advise…? So, you want advice? Here’s my advice as a question: What, are you crazy?”

Fifth email Email: Sunday, 2 October 2016 

Max –

Is this a fair summary?  Today, it is our homepage:



PS. We are the simple people — simple model, simple logic, simple math, filling in the continuum from the Planck scale to the CERN-Atlas scale, and then beyond.

Fourth email: 4 August 2016

Hi Max,

Your endearing smile and wonderful openness should have the world on your doorstep.  Congratulations on all that you do.

Of course, the big bang is one of those answers that only a fool would dare question. So, here I stand among the fools. We’re just high school folks; we claim no special status, so maybe we can be excused for being nicely idiosyncratic and naive!

I think you might enjoy seeing the numbers all filled in from the Planck base units to the Age of the Universe using base-2 notation.  Boeke’s Cosmic View looks a little timid by comparison. Even ‘t Hooft’s Time in the Powers of Ten misses too much. If you have a moment — it is looking for a special critique.

Is it solipsistic poppycock?  That chart is big; it is horizontally-scrolled, starts with the five Planck base units (and some simple geometries), and it is  carried out the 200+ notations to the Age of the Universe.  You can follow the changes of each base unit in contrast to the others. There are over 1000 simple-simple-simple calculations. But, simple is good.  It tells a bold and dramatic story but it may have more to do with fantasy than reality… but I don’t think so. I respect you too much to waste your time that way.

Is it possible that the universe started with those infinitesimally small numbers and grew quietly and rather prodigiously and all rather quickly?  Of the 200+ notations, the first second is between 143 and 144.  The first light year is between 168 and 169.  And the first million years between 188 and 189.

That small scale universe, 1-67, could be a new science and math.  Maybe Langlands is on the right path after all.  Below I’ll post some of the other work-in-progress asking for critical review! Thank you.

Most sincerely,

* * * * *

Third email: 22 September 2015 

I am now a groupie of sorts.  Too old and too naive to be deeply informed.

You encourage me with your great spirit while I’ve begun working through your “Dimensionless constants, cosmology and other dark matters.”

From the perplexing place we were within my first note, to the questioning within the third, would you tell us why our basic concept is wrong headed and “to take a break.”
A Simple View of the Universe:

On Developing A Rationale For A Working Model Of The Universe Based On A Quiet Expansion:

Your website is sensational!  Thank you for all that you do to stimulate scholarship and creative thinking!


An automated response: September 22, 2014:

Thanks for your LinkedIn invitation, which I’m going to accept shortly! Although there’s essentially no information on my LinkedIn page, I have an active public Facebook page where you can connect and discuss with me and others intrigued by science and life’s big questions. I very much hope you’ll join me there! Just surf over to the link below and click “like”:
You’ll also find movies, articles and an FAQ for my book at
Second email: May 9, 2013


Max –

I was 20 when you came into this world, I suspect you came in feet first.  So much standing comedy in all that you are and do. It is entirely refreshing. I am enjoying your pages-and-writing immensely.

I am on a search for simple wisdom. I’m a simple person.

But, I do have a seriously silly question for you.  It started when I was asked to substitute for my nephew a couple of years ago. He was to have a second child and I got his five geometry classes for a few days. I wanted to stand them on their head a little, so they actually made models of the “Big Five.” They took a tetrahedron, divided the edges in half, connected the new vertices, and bingo, there is a tetrahedron in each corner and an octahedron in the middle. Then, the same with the octahedron, with six baby octahedrons in the corners and eight tetrahedrons in the faces, all sharing a centerpoint.” That’s a goldmine and you kids have got to go in there and start digging!”

That was the beginning of my regression.  The next time, Stevie wanted to take his bride on a fifth-anniversary cruise and left me with those buggers on the last day of class before the Christmas recess, Monday, December 19, 2011.

Enter “The Big Board – little universe.”

“Come one, come all, see the universe and everything in it from the smallest to the largest measurement in about 202 steps!”

We used the Planck Length and started multiplying by 2.  Within a relatively short time, we had the entire universe looking like a Planck Factory. Everything had a place. Geometry was pervasive. Here was the homunculus of all homunculi. One part Plato, add a little relativistic aether, and mix well into the first sixty steps — nobody seems to have explored 2-to-60, possibly 64 (just before getting hit with any sensibility and a neutrino and quark).

Absolutely crazy?!? Worth exploring further??? Or, shall I tell the kids to come out of that cave?




Bruce  Camber  (part of my life as a television producer)
Small Business School

First email: January 12, 2012


Dear Max,

Please, help to debunk this crazy Alice-in-Wonderland hole that I’ve dropped into….

I am a television producer.  But recently,  I was asked to substitute for a high school geometry teacher, a nephew. He asked me to introduce the kids to Plato’s five. It would be my second time with them, so I had to expand my own horizon a bit for my visit on December 19, 2011.

The first time I had them, back in March 2011, they made icosahedrons out of 20 tetrahedrons. I called it squishy geometry and said that it probably fits into quantum geometries or imperfect geometry somewhere and somehow, but I couldn’t find any online references to it. This link goes to pictures of those icosahedrons.

Then Shechtman comes along with his quasicrystals and five-fold symmetries… I got to thinking about the nesting of tetrahedrons and octahedrons within the icosahedron and wrote up that little note to him (link above).

I thought, “…speculative, fanciful thinking, probably just nonsense.”

Yet, just after that first encounter, I became impatient with my little paper model of a dodecahedron. I took the same pentagonal groups of five tetrahedrons, and attached twelve of them together. I filled it with PlayDoh, then tried to discern what was inside.

A smaller icoshedron was in the center of the thing.  Fascinating for me. No study of it online yet.  I found a name – hexacontagon — but none in the shape of this particular pseudo-dodecahedron.

I’ve been looking inside those five-tetrahedral structures for awhile. A week before that class, I asked, “How far within, how many steps by dividing by 2, would I have to go to get to the range of Planck’s length?” I assumed thousands.  Nope. Just 118 steps! There I was, dividing one meter by 2 and then by 2 again u.s.w until 1.6×10−35 or Planck’s length. Then I thought about the large scale universe and in 91 steps I was out in the range of 1027 meters and the edge of the observable universe.

I hadn’t seen such an application of scientific notation so I made it up and produced a colorful chart for the class:

Where did I go wrong? Is there anything here?