Just Eight Key Ideas


Concepts For A Simple Model Of The Universe

1. 202 base-2 notations (doublings, containers, clusters, domains, layers, sets and/or steps)
2. This Quiet Expansion Is A Natural Inflation. Here’s A Sampling.
3. The speed of light has variable speeds and there is a wide variegation of light.
4. Facelift for Space-time
5. Rebirth of the Finite-Infinite Studies
6. Incommensurables, transcendentals and irrational numbers get real.
7. Continuity-symmetry-harmony creates order, relations and dynamics!
8. A Place For Everything, Everywhere, Throughout All Time

Fabric-Space-Time1. These 202 base-2 notations easily encapsulate the universe.

Multiply by 2. Start with the smallest units of measurement, the Planck Time and Planck Length, multiply each by 2, then the result by 2, and continue right up to the largest possible measurements, the Age of the Universe and the Observable Universe. Though both are still constantly expanding, your result will quickly be a totally, mathematically-integrated model of the universe that includes everything, everywhere, for all time in just 202 notations.

Just one more time: Most scientists and scholars now believe that Planck Length and Planck Time are the very smallest possible measurements. If you double them, then double them over and over again, in just 202 doublings, you will have reached the size of our Universe and you will have gone from the beginning of time to this present moment in time.  It sounds impossible, but the math is the math.

•  Rather special. Though simple logic, simple math, it’s still just a model. As a challenge, take this model as a given, to explore in what ways it could be an outline for the initial structures of the universe. Also, if simple logic and math do not work from the Planck Scale to the CERN scale to the Large Scale Universe, then logic and math should not work anywhere. Continuity is continuity. Order is order.

Eventually we added Planck Charge and Planck Mass to our doublings and continued to study how the numbers and the inherent logic worked together.  We have been exploring this model since December 2011 and have discovered that it seems quite sustainable! No scientists or scholars have seriously challenged it. Of course, it is idiosyncratic and it does raise rather unusual questions. Notwithstanding, the universe within just 202 doublings (clusters, containers, domains, layers, notations, sets and/or steps), so far, actually does seem to cohere 1 (Footnotes/endnotes at bottom).

•  Sweet. By the 31st notation, Planck Mass has increased to 103 pounds. That may be an ideal weight for some, yet in this notation, space and time are still so small that science has always considered these values meaningless.  We do not. Though an entirely novel concept, we take it as a given that there was a time when the universe was just 103 pounds. Though necessarily defined by point free vertices, it already has more active ratios than our imaginations can grasp (1.23794×1027). It exceeded one million vertices by the eighth notation, one billion at the 11th, and one trillion at the 15th, and a quintillion vertices at the 17th notation.  To follow that quiet expansion, look at line 9 in the chart below.  More 1-67a

2. This Quiet Expansion is a Natural Inflation. Here’s a sampling.

•  In this model each notation is more than just a simple doubling. The next notation doubles in size and doubles in content and each notation it would appear is currently defining our universe. As we live with the model, grasping the first notation as the start of the universe and the current notation as our current moment in time, all the notations come alive as a process that gradually builds upon itself, every notation changing and growing because of the others. To think about this very different sense of space-time, I did a sampling of six of the notations somewhat evenly spaced across the 202 notations. Of course, these Planck scale doublings are all predictive numbers. Within these six notations that were sampled, each demonstrates a natural inflation that is a quiet expansion.  A sampling  Prime numbers...2

•  Being natural is good. If one were to wonder about the basis for bifurcation theory, chemical bonding, cellular development, and isotropy-and-homogeneity, we may have found a new opening to explore. Then, if one were ask about the source of this thrust, again I think we may have found another good opening to explore.

The alternative is not pretty, elegant, or logical. Any one of the many theories that use the big bang logic of infinitely dense and infinitely hot are incomplete, unnatural, and riddled with questions. Worse yet, the big bang philosophy and psychology have trashed our culture with a de facto nihilism and dystopia.  It is bad physics. It is bad mathematics. And, it’s bad psychology.

•  Sweet.  (1) The quiet expansion continues its doublings until finally at the 67th the folks at the CERN labs (Geneva) are able to pick up something and our core sciences start to evolve.  (2) Truly sweet is that this natural inflation approximates all the cosmological epochs that were defined by big bang theorists; however, in this model there is no bang.     (3) The 67 notations provides more than enough “room” for every possible system of mathematics to be applied. Remember the 64 doublings within the Checkerboard story!  More  And more...

3. Light has variable speeds and many faces.

Planck’s Equation

•  Planck Length divided by Planck Time equals the speed of light. And, as you might anticipate, with every doubling, that approximation of the speed of light naturally continues. See line 10 within the horizontally-scrolled chart. More

•  That is very special. Light, Time and Length are being redefined by each other and by Charge and Mass.3

Please take note that between the 143rd and 144th notation, the universe is finally one second old and Planck Length has grown to the size defined by the distance that light travels within that second.

Seasonal look at an equation that resets the universe.

It is simple math and simple logic yet it re-engages us to expand and begin to understand a rather extended spectrum of light, of course, well beyond the visible spectrum and well beyond where it has been defined to date.

This work has given new meaning to an old song (1977), “You light up my life.” The very final refrain goes something like this: “It can’t be wrong when it feels so right…” More

•  Sweet.  Here is the first time light, defined by another very simple mathematical formula, can be found within a simple mathematical progression. The formula from Planck predates Einstein’s!  More

4. Space-time is long overdue for a facelift.

•  The Gnarls and Knots of Space-and-Time. Definitively cast in stone in 1686 when Newton released his blockbuster, Principia, time-and-space took on an absolute frame of reference and this view became our commonsense worldview.  It became a realism (and naturalism) whereby our external reality is assumed to exist as it is given and experienced. Both concepts — space-and-time — have been problematic and now some really smart scholars want to throw them both out; we believe it would be better to redefine them in light of our model with its 202 notations. Here, the universe begins within the Planck Scale. Our challenge is to figure out how the universe evolved within those initial notations, and then how it continued to the 202nd notation and to this very second within our expanding universe.

•  It is a very special and rather non-intuitive challenge. There are so many people today who still affirm Newton. They unwittingly do so when one of them looks up into the clear, night skies, observing the panoply of stars, and says, “It goes on forever.” Those wrestling with this new model would say, “We are looking out at our expanding universe. It is still expanding within the 202nd doublings and has been for about 13.82 billion years.”  What happens is that no notation goes away and recedes into a past. Instead, each notation participates in the current definition of the universe and space-and-time, as the fabric of the universe, absorbs every imprint for all time-and-space.

•  Sweet. This new sense of space-time gives it a currency and vibrancy.  The universe has its own clock and as of 2013, the universe was 436 quadrillion, 117 trillion, 076 billion, 640 million  seconds (436,117,076,640,000,000) old.

Let’s turn on the clock.  There are about 31,556,952 seconds per year so at some time we will be adding at least four years of seconds, somewhere over 126 million additional seconds, to bring the total to the current time. A hundred years is just 3.1556 billion seconds. Extend that to 1000 years (31.556 billion seconds), a million years (31.556 trillion seconds), and a billion years (31.556 quadrillon seconds).  Our earth and solar system are approximately 4.5 to 4.6 billion years old.  The estimates for the Milky Way galaxy are about 13.7 billion years (yes, among the original galaxies formed).  Yet, none of it is old; it is all current. All the cosmological epochs are now understood to be ongoing processes of the universe.   More…

5. Let us try to rebirth finite-infinite studies.

 Science and mathematics have made great use the concept of the infinite; philosophers and theologians have as well.  Yet, over the years we have seen how these disciplines tend not to work very well together, especially those elitists among them, particularly among those religionists and theologians who too frequently don’t work well with anybody except their own.

It is no wonder that a few very bold scholars would like to throw out the concept of infinity. It has an awkward personality. It is too big for most of those yellow academic school buses.

•  We suggest a shakedown. First, let us shake out all the concepts that have anything to do with faith statements — these are too often argumentative, emotional, and sometimes even hostile. Within the quiet expansion model, there are several conceptual assumptions that begin to bind the finite and infinite in special-and-heretofore unexplored ways. These concepts include: continuity-order, symmetry-relations, and harmony-dynamics.  Though an unusual combinations of words, some element of each can be readily understood.

 We can do this. The word combinations may be a little gray, but we’ve all used each word at one time or another. Taken together and in this sequence, these words become very rare concepts because each reflects a face of the finite (our beingness, whether it is science, mathematics, psychology, philosophy or religion) and also a face of the infinite.  More   Foundations…   Ethics-and-values…

6. Incommensurables, transcendentals and irrational numbers

 Numbers. Perfect, unshakeable continuity occurs within numbers that are called incommensurables, transcendentals and the irrational. These numbers are never-ending and never-repeating. Our old friend, yes, a very dear friend of every circle and sphere, is Pi.  Its very close cousin is e, for Euler’s number.  Euler’s equation also defines the universe.  It is the heart of our exponential universe. Also, meet Pi once again.

•  Through our Looking Glass. Most looking glasses are mirrors. This looking glass can also be a magnifying glass. Isn’t it unusual that a number can seemingly go on forever without repeating itself and with no special pattern or repetition?  Doesn’t that define a certain kind of uniqueness?  …diversity?  Within this class of numbers there is a group that is also known as dimensionless constants.  There are quite a lot of them. Yet, in all the discussions about the many scholarly blogs, papers, articles and books, there does not appear to be any discussion about how these numbers must define some aspect of infinity.  Isn’t that an oversight? If we take it as a given within our new definition of infinity, this very special kind of continuity and order can also be understood as uniqueness and diversity. That’s rather special.

Now of all the scholars I know, perhaps Clifford Pickover or John Barrow have started a process of looking at infinity in this simpler way; we’ll be digging further into their scholarship. More…

But, for now, let’s see if we can take it one step further. Let us take as a given that these rather unique numbers (1) originate within the infinite, (2) tell us about the nature of the infinite, and (3) define the transformation between the finite and infinite.

•  That’s different and very sweet.  So, we now have an ordered-chaos and a discontinuous-continuity defining our finite universe.  The next step is to look at the symmetry/relations and harmony/dynamics.

7. Continuity-symmetry-harmony create order, relations and dynamics!

Sphere to tetrahedron-octahedron couplet
Creative Commons Share-Alike 2.5 Generic license

•   Pi leads the way. Leading the way out of the infinite is pi. Perfect equal circles, then spheres, then multiple spheres, then stacks of equal and doubled spheres. We are probably within the first ten notations or doublings.  And then, a radius discovers a radius and the first line is created. Then the radii begin discovering radii and lines and dimensionless, point free, vertices are created.  Vertices discover vertices and the first triangles are created. Triangles discover triangles and the first tetrahedron is created. Lines, vertices and triangles discover each other and then the first octahedron is created within the tetrahedron. And, quickly, hexagonal plates are discovered. Triangular plates are discovered.  And diversity begins to move into high gear in a perfectly simple, yet increasingly complex manner. Symmetries abound. Perfection is in the air. But the imperfect and asymmetrical are not far behind.  More…

•   Dynamics.  Euler’s number is somehow holding pi’s hand! The two are working those continuity and symmetry relations and are making a universe one step at a time. More…

•   That is a very special challenge. All shapes and forms and sizes and every manner of symmetry relations are being created. The pulse of energy known as Planck Charge creates a thrust, an energy, a direction, a motion, and soon our little universe is pulsing with activity.  More…

First, called the Planck Scale, it transmogrifies into what some call a Grand Unification.  Here is the first doubling. But for all intents and purposes, it is within a self-discovery mode. Yet, rather quickly (understatement), that self-discovery process organizes and begins what we call the Inflationary Processes right up to and including the 67th notation.  Now declared to be the Electroweak Processes, Planck Charge is huge. Planck Mass is huge. Planck Length has become manageable. Planck Time is still too small to be considered anything other than a placeholder.  More…

•   Sweet.  The rest of the cosmological epochs seem to follow rather naturally in line with the continued expansions (doublings and notations) of these Planck base units. Even Planck Temperature, which was placed at the top of the scale because everything begins simply, is now substantial enough to warm things up and to begin looking like our little universe.  More    And more…

8. A Place For Everything, Everywhere, Throughout All Time

•   The first 60 or so notations will never be observed by our machines. These domains are much too small to be picked up by our measuring devices. If there can be no validation by our machines, then we must rely on logic and mathematics. This special domain has a very special word to describe it; it’s call hypostatic. We actually create a real reality when shared by another. It is a really real reality when shared by many.  As more people adopt that structure, we press meaning and purpose into it.  Then we ask, “Is this helpful? Does it seem to describe a real reality for people within our time?”

•   Yes, this is very special challenge for all of us. Because everything, everywhere, for all time must be logically included on this grid — nothing is exempt —  we will hypostatize a place for philosophy, psychology, mathematics, quantum fluctuations, the cosmological constant, religions, the mind, consciousness, sleep, and qualities. More

•   So we have a bit of work to do.  And, we recognize that this work just started in December 2011 and it is still quite naive and young.  The initial goal was to give our high school students a very special chart to integrate Science, Technology, Engineering and Mathematics (also known as a STEM tool).  Today this project is known as the Big Board -little universe.

That was cool. But now, the real work begins. We know we are onto something and have opened a door that is worth exploring. We’ve begun to study some of the older problems within science with such names as inertial frame of reference, point processes, scalar fields and scalar field theory, and path integral formulation. Many of those subjects are listed on line 11 of our horizontally-scrolled chart.

We struggle with it all most everyday so your advice, insight, and help are most welcomed! Thank you.

Footnotes & Endnotes

1 Time: It is good to be reminded that the first second of the universe is between notation 143 and 144. The estimated 500 million years necessary for galaxy formation takes us up in between notations 197 and 198.

2 Number groups:  We will be studying every prime number as a possibility for a new mathematical system. The obvious, primes from 2 to 199 (3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197), prioritize themselves! The challenge will be to logically build the sequence of systems. It is anticipated that the work of Grothendieck and Langlands (IAS) will contain a few keys. More

3  Quantum fluctuations and imperfections.  We believe the geometry of imperfection begins with the pentastar and the pentastar gap.  Though possible within notations 1-to-40, simple logic suggests that these quantum geometries do not manifest until Systems (first column, eight row) begin organizing.  More

PS.  There may be more footnotes inserted in the forthcoming days. If you are observing changes in the post, it is because this post is edited every day. It will change, and undoubtedly grow a little longer.

Special Thanks

Friends from New Orleans came for a visit. Their two images have been in my mind’s eye as I worked on this page. I have been constantly asking myself, “Is there a way to write this up so they understand it?”   -BEC


We welcome visitors from Belgium, Brazil, Canada, Cambodia, China,  France, Germany, Honduras, the Netherlands, New Zealand, Portugal, Serbia, Singapore, South Africa and Turkey. Yes, all visitors to this site, we welcome you all.

Thumbs Up! Or, “Please Comment.”

We can only grow by helping each other with constructive criticism or reinforcement. A quick little “Thumbs Up” is helpful. If it is “Thumbs down” please send a comment. If you want to just use numbers, -1 for Do not understand, -2 for Confusing and -3 for Disagree.

Our most simple assumptions and insights for an alternative theory:

•  The finite-infinite relation can always be understood more profoundly.
•  The key numbers, functions and geometries recognized by our most-respected scholars all begin their work to define the finite-infinite relations within the very first moment that defines space, time and light.
•  Pi and Euler’s number are the first steps within this understanding and define the very beingness of the universe.
•  The Planck numbers are also part of these first steps and all subsequent steps. More…
•  Multiplying the Planck units by 2 over and over and over again creates a grid or a matrix within which to begin to understand numbers, functions and geometries. The principles of continuity and symmetry become penultimate. Though space-and-time-light are infinitesimal and thought to be meaningless, this is the beginning of a natural inflation and thrust of the universe.

On learning from the work of Sabine Hossenfelder…

Sabine Hossenfelder, HossenfelderFrankfurt 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?
•  The Planck length as a minimal length, January 2012
Google Scholar
Homepage  (Research Fellow)

Most current within this website: https://81018.com/empower/#Sabine

Most recent (fifth) email: 19 June 2021

Dear Prof. Dr. Sabine Hossenfelder:

I am circling back through your work so you’ll see your image along with seven others at the top of the homepage: https://81018.com/ The permanent URL when not a homepage is: https://81018.com/empower/#Scholars

There is a paragraph about your work under “References” that is still being developed.

Other scholars will be directed to it. If you object, I can easily remove the reference to you. If it needs updating or correction, please advise me. I’ll update it as expeditiously as possible. Thanks so much.



PS. My primary reference page to your work is here:

Tweet: 11:25 AM · January 13, 2021 @skdh (SabineHossenfelder)

You are brilliant, a lightbulb for the sun. Our favorites, Kepler and Wilczek, play their violins as we contemplate pi over an Italian dinner. Yes, that simple pi with its deep continuity, those ubiquitous symmetries, and never-ending harmonies, and ask, “Is that all there is…”

My editorial note: Sabine’s book, Lost in Math, is indeed, quite brilliant, but all our complexity within mathematics and physics leads back to pi and the sphere. Add the Planck base units, and apply a bit of base-2 exponentiation, and you have yourself a most-simple beginning of a model of the universe.

Fourth 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 down into 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 “Twelve Key Functions” and “Reconstruct Our Universe.” Your comments and criticisms would be highly appreciated.


202+ successive doublings of the Planck scale outline our universe

  1. 202+ 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 constants (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 so-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 had a little help to find just over
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 E. 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.