To the Editors of Scientific American

Most recent email: Friday, 26 January 2018

What if

What if the old worldview, often called the Weltanschauung, is too small. In these times we all need a highly-integrated view of the entire universe!

What if Hawking is wrong when he says that we started from , “…an infinitely hot, infinitely dense point” but instead we started simply, but infinitesimally at the Planck base units of Length and Time, and at the very small Planck Mass and Planck Charge, and we quietly expanded exponentially?

~Note:  A new chart emerges from the Planck Time to the Now. It has only 202 base-2 notations. There is enough granularity to see if the numbers cohere and carry some logic.

What if all these simple numbers within our new chart provide a credible path, a natural inflation imposing a certain isotropy-and-homogeneity throughout the universe?

What if this natural inflation actually works for electroweak baryogenesis within the current Standard Model of Big Bang cosmology, i.e. the only parts of that theory being discounted are the initial conditions and the Inflationary Epoch?

~ Note: The new chart at least posits credible concepts and numbers for the expansion.

What if we’ve had it wrong since 1716 when Leibniz forfeited the debate to Newton (he died) regarding absolute space and time; and, his insight that space-time-light are all profoundly relational?

~Note: The first second of the universe emerges between notations 143 and 144 where the Hadron Epoch picks up out of the total 202 notations to the current Age of the Universe.

I thought you might enjoy these questions.

Most sincerely,

Third email: 5 June 2017

Dear most-distinguished editors:

In December 2011 our high school geometry class was following the simple logic of base-2 exponentiation. We had discovered an infinite regression, or at least what seemed like such, going inside the tetrahedron and octahedron. Within the tetrahedron, by dividing each edge in half, there are four half-sized tetrahedrons in the corners and an octahedron in the middle. Inside the octahedron, dividing each edge in half and connecting those new vertices, there are six half-sized octahedrons in each corner and a tetrahedron in each of the eight faces.

How far within can we go? Where would Zeno stop? Where would Max Planck stop?

We had fun mapping the universe using base-2 notation. We were quite surprised to find there were less than 40 steps within to get down to the size of particle physics and just another 67 steps within to get down to the Planck scale. The next day we multiplied by two. In about 95 steps we were out to the Observable Universe.

We didn’t know what we didn’t know. Are we doing something wrong? Where does our logic break down?

We were glad to find Kees Boeke’s base-10 work, but found no base-2. We kept looking for almost a year and discovered bits and pieces, but no map of the universe using base-2 with its very special granularity. For the past five years we continued poking at our map. We added Planck Time, then the other Planck base units and said, “Voila. A Base-2 Map of the Universe.” Totally predictive, it is 100% simple mathematics but it tells a radically different story about the universe. Starting with the Planck base units and all the constants that define each, this “singularity” is more like an “alphabet-and-number soup” it has so many equations defining it. Naturally inflating, it seems to encapsulate all the appropriate epochs of the big bang without a bang.

It is all a bit much to swallow; it is altogether too simple; and hardly anybody has truly wrestled with it. We must be doing something wrong, but what? Thank you.

Most sincerely,

Bruce Camber
New Orleans

Endnotes/Footnotes: To date, no scientific publication has printed this simple letter. So we ask again, “What are we doing wrong? What are we missing? What is so sacred about big bang cosmology that a more simple explanation could not at least be explored, discussed, and if need be, discounted.”

Second email: 5 November 2013

RE:  A proposed Article for Scientific American

Possible Titles: (1) Might the Planck Length be the next big thing? (2) From a Weltanschauung to Universe View

The subject of the article: We answer the question, “How can we go from our Weltanschauung to a Universe View using base-2 geometric notation from the Planck Length to the Observable Universe in 202.34 to 205.11 notations (doublings or steps)?”

How you would tell the story of this subject: The story tells itself. It all started in a high school geometry class exploring how four tetrahedrons and an octahedron perfectly fill a larger tetrahedron and six octahedrons and eight tetrahedrons perfectly fill the octahedron. We had those models in front of us when the question was asked, “How far within can we go?” The answer, “Not far.” Within 50 steps we were as small as a proton and within the next 65 steps we were bumping into the Planck Length. The next day we did the simple math going out and found around 90 notations to get into the range of the Observable Universe.

We tried to find this information on the web. No go. We wrote up as a Wikipedia article. It was published for a month, then deleted within a week as “original research.” So, then we just started putting it up on websites were we could. The majority of the work is now on WordPress.

The practical and theoretical significance of this subject: Today’s information glut is so chaotic and overwhelming, it seems that it actually depresses creative thinking. So, our hope in sharing this simple little table is that students will feel empowered to search for new insights to understand this universe more deeply and as we do, to instill some optimism about our common future.

How this article would differ from previous coverage of the topic (if any) in Scientific American or other media: We have tried to find it. We have sent out hundreds of emails asking people for help to explain its significance or lack of significance. It just appears to be an academic oversight. Of course, Kees Boeke and the Morrison duo (Phil & Phyllis were old friends) and the Huang boys have done a great job using base-10 to create a scale of the universe, but it is not granular or relational enough, but most importantly they did not start and incorporate with nested geometries throughout..

Your credentials for writing about the topic:
1972: Studied with Arthur Loeb (Carpenter Arts Center, Harvard)
1973-1980: Robert S. Cohen, Milic Capek, Abner Shimony, John N. Findlay et al (Boston University Graduate School and Boston Studies in the Philosophy of Science)
1996-2000: Studied with Ted Bastin, John S. Bell, David Bohm, Olivier Costa de Beauregard, J.P. Vigier et al regarding the EPR Paradox;
1979: Worked with 77 leading scholars for a display project on first principles at MIT for a conference, Faith, Science and the Future
2002: Daylong session with John Conway on interiority of platonic solids
2011: Guest substitute teacher for high school geometry and in 2012 studies the works of Frank Wilczek and Roger Penrose.

Any other information that you think would make the article interesting to our audience. Since January 2012 we have been inviting critical comments and review by posting the following articles in WordPress:

1. Universe Table, An Ongoing Work There are between 202.34 and 205.11 notations from the Planck length to the Observable Universe. This table focuses on the Human Scale, notations 67 to 134-138. The Small Scale (1 to 67-69) and Large Scale (134-138 to 205) will follow after the dynamics and substance for the footnotes have been completed for this first table.

2. Propaedeutics for an article A very rough draft for a journal article to analyze where we are in our work on this table and the Big Board – little universe

3. Concepts & Parameters The first iteration was published in January 2012 within the Small Business School website.

4. Big Board – little universe Version was first used in a classroom on December 19, 2011 and it was first published on the web in January 2012 within the Small Business School website while the current version,, was posted in September 15, 2012. Links to the best current research within each notation are being documented and will be added.

First email:  16 May 2012

RE: How would you tell the story of this subject?

We’ve been on a discovery/uncovering process.

It all started while I was substituting for my nephew’s five high school geometry classes…

The practical and theoretical significance of this subject
An unexpected plot unfolded: We found 117 steps going from the smallest measurement, the Planck length, to the human scale, and then 85+ more steps out to somewhere near the edge of the observable universe, all just by multiplying the Planck length by 2, and then the subsequent results by 2.

We looked for it on Wikipedia, but didn’t find it. The auto-responder said something like, “We don’t have such an article. You can create it or ask for it to be created.”

So, we decided to tell our story. Within two weeks an MIT fellow and Wikipedia editor started a campaign to delete it as original research. What? ….from a high school class? “It is all common knowledge. They’re just silly,” we concluded. But in two weeks it was deleted. We thought, “Well, we couldn’t find any direct references to using Planck’s length multiplied by two at each step to create a scale of the universe… maybe it just hasn’t been done!”

So, we started asking around. First, we asked the first AAAS (American Academy of Arts & Sciences). They pulled a blank. The second AAAS (American Association for the Advancement of Science) thought it a bit unusual for a high school class, but didn’t quite follow the simple logic, and said,. “Sorry I can’t be of more help.”

A NASA physicist was the first to confirm Wikipedia’s “Original Research” judgment and he also helped us to calculate the number of exponentiations or steps to scale the universe from the smallest to the largest. We learn it was just 202.34 doublings.

Here is his story behind NASA’s Joe Kolecki’s calculation:

How this article would differ from previous coverage of the topic (if any) in Scientific American or other media:
You have covered the Powers of Ten with Phil and Phyllis Morrison but not the Powers of Two as related to the Planck length.

Our goal now: Try to grasp the meaning of it. Open a discussion about it. Really see the entire universe in 202+ steps, all necessarily related notations.

We dubbed, this project, “Big Board for our little universe.”
There is a graphic of our work to date on this page:

There you will find this introduction:
“Perhaps this work could be called, “From praxis-to-theoria.” It is a working project. And, yes, it all started in a high school geometry class with a substitute teacher (family member) suggested to the class that they found out how many nested platonic solids would be contained in a meter before bumping into the Planck length. Because we were dividing by two, base-2 exponential or scientific notation — that’s the praxis — was used. We were there at the smallest measurement (Planck length) in just 117 steps.

“Well, what happens when you multiply by two? How many steps to the edges of the observable universe? We needed help on that so engaged a NASA scientists and the results of the BOSS (Baryon Oscillation Spectroscopic Survey). We were there in virtually no time at all. A little over 85 steps. The entire universe, from to the smallest to the largest , represented in just 202+ steps was just too elegant to keep to ourselves.”

Of course, we were studying geometry so every point was seen as a vertex for doing constructions. From a point to a line to a triangle, then a tetrahedron, octahedron, icosahedron, cube and dodecahedron, we could readily see these forms building upon each other and within each other and we could imagine, and some day we hope to postulate functions thgat inter-related these geometries. Though on our first pass through it all, we had a lot of blank lines, we are working now to fill these lines with facts or conjectures (ideas and concepts aka theoria). Eventually real data will be added.

The original chart was put together in just a week (December 12-19, 2011); the simplest math errors have been corrected in later versions. Hopefully each notation will be under the guidance of scholars and students doing research within a particular notation.

Credentials for writing about the topic:
1. High school Geometry, substitute teacher
2. Gadfly: I was a doctoral candidate in the ’70s at Boston University. My focus was on the EPR paradox.
3. Prior to that work: I was part of a think tank, Synectics Education, in Cambridge, and was part of Arthur Loeb’s Philomorphs Group at Harvard.
4. Politics: For a couple of years I had occasional dinners at the Morrision’s home at MIT (Phil & Phyllis) where we worked on the ways to reduce the Pentagon’s budget.
5. Scholars. I worked a bit with Lew Kowarski at BU and he cleared the way for my first visit with John S. Bell at CERN in 1974. Later, after getting to know Victor Weisskopf, I returned for a second visit in 1977. I also visited with David Bohm in London on that trip. In 1980 I studied with JP Vigier and Olivia Costa de Beauregard at the Institut Henri Poincaré in Paris on the work of Alain Aspect at the Institut de Optics in d’Orsay. In 1979, working with the chancellor of MIT and the World Council of Churches in Geneva, I organized a first-principles display project of 77 of the world’s leading-living scholars:addressing the question, “What is Life?” in the spirit of Erwin Schrodinger’s earlier work. Reference:

Your Acknowledgement: “Generally speaking, SCIENTIFIC AMERICAN presents ideas that have already been published in the peer-reviewed technical literature. We do not publish new theories or results of original research.”

My response: There is nothing really new here. Good scientists know the Planck length much better than we do. Of course, base-ten scientific notation has been used for over 50 years — — and even 14-year olds make beautiful web pages about it.

Base-2 exponentiation, using the powers of two, is simply more granular and more relational.


To look at the Wikipedia article that was deleted:

Thank you.

Please note: The links have been updated as of September 2018.