Asking for help from the editors of AAAS, Nature, Scientific American…


.New STEM tool delights, but raises questions

by Bryce Estes,1  Cathy Boucvalt,2  Steve Curtis,and Bruce Camber,4  New Orleans, LA 70123 USA
Please note: At the time this article was first written back in 2015, Bryce Estes was a high school senior, and his math and science teachers were Cathy Boucvalt, Steve Curtis, and Bruce Camber. They asked editors, scholars, and each other, “What is wrong with our simple logic and simple math?”


Homegrown STEM tools can be inspirational and ours was no exception.  In our geometry classes we divided the edges of a tetrahedron in half and discovered the four smaller tetrahedrons in each corner and an octahedron in the middle. We then divided the edges of that octahedron in half and found the smaller octahedrons in the six corners and eight tetrahedrons, one in each face. Like Zeno, we continued the process of dividing by 2. In 45 steps (on paper only), we were in the area of the CERN-scale of particles and waves and in 67 more steps going further within, we were in the Planck scale. We then used the Planck Length for our edge, then multiplied by 2. In 112 steps we were back to the classroom’s original objects. It is simple, straightforward, just a bit of commonsense, and an historic first.

Yet we were in for an even bigger surprise.

We kept multiplying by 2. In just another 90 steps or doublings, we were out to the Age of the Universe and the Observable Universe. That’s just 202 base-2 steps! And it seems, by definition and with our simple logic, that this model includes everything, everywhere for all time.

Your can check the numbers. We posted and updated our chart:

We dubbed our little model “the perfect STEM tool.” Even our AP sixth grade science class understood it! But, when we sent our little STEM project to Scientific American, they ignored us. Even Wikipedia rejected our summary as “original research.” The AAAS Science magazine and Nature magazine rejected us without comment. We’ve written to a diversity of scholars and even they are reluctant to comment. So, we’re going back over our logic and math, asking, “What are we doing wrong?

As an introduction, this is how we describe our work:

A small group of high school students and a few of their teachers have been trying to figure out what to do with an all-encompassing-but-simple mathematical and geometrical model. Findings to date are presented with the hope that the academic-scientific community can tell us how best to proceed with our very simple charts.

Our Brief History from December 19, 2011

Yes, this project began by simply dividing the edges of a tetrahedron in half. Delighted with the simple complexity, we had models, but quickly had to resort to calculations on paper. Everyone should chart the universe! We quickly learned it is called base-2 exponential notation. Not long thereafter, Kees Boeke and his base-10 Cosmic View came to our attention. It was entertaining but not as granular as our base-2 outline. We first thought our work was an excellent Science-Technology-Engineering-Math (STEM) tool so began sharing it with others through our early web pages, Cf. the Ref. [1]. Our first chart was a 60″ by 11″ board that started with the Planck Length and went to the Observable Universe, Cf. the Ref. [2].

We dubbed our little project, Big Board-little universe.

Because we didn’t know where to stop, we got a little help with our calculations, Cf. the Ref. [3]. A year later we started a desktop version dubbed Universe Table, Cf. the Ref. [4]. We then added Planck Time to the chart, Cf. the Ref. [5]. Those numbers tracked well with the Planck Length. Also, the Age of the Universe, 13.81 to 14.1 billion years, was no longer a mysterious number and it gave us a place to stop our “multiplying by 2.” We then discovered that the ratio of of the Planck Length to Planck Time within each of the 202 notations was always within .1% of the speed of light. We quickly asked, “What does that mean?” and knew it would be an open question for a while.

We then added the other two Planck base units to the chart, Cf. the Ref. [6]. Now, there are so many things to discover, our heads were spinning. Each notation is filled with data to analyze. Although each chart is a highly efficient way to organize vast amounts of information, these charts raise rather fascinating questions.

Questions and Challenges

At first we wondered why we couldn’t find some vestiges of these charts within our textbooks or someplace on the World Wide Web. Then, when Wikipedia rejected our article as “original research,” Cf. the Ref. [7], we asked, “Isn’t all this information somewhere within the academic world?” Stepping back from our charts, we asked, ”Isn’t each column of the chart a very basic continuity equation from a Planck base unit to its largest possible measurement? Isn’t continuity the bedrock of order? Shouldn’t this be the first principle within our work?”

The small numbers were impossibly small and the large numbers were impossibly large, yet the 202 notations were relatively manageable. The nagging question was, “Is there a problem with our logic and math?” It was exponential notation that helped us get comfortable with both extremes and it helped make these numbers more manageable. When we learned a little about Leonhard Euler’s equation, we decided that we lived in an exponential universe! It has taken time. It has been a steep learning curve; we now have feelings or intuitions about the very nature of a number!

We asked more questions,  “What are these numbers telling us about the universe and ourselves?” The geometries started simple, but became exceedingly complex. We asked, “What is geometry? How is space necessarily defined? Does it require all the Planck base units? Does it require the extended Planck units?”

The human family seems to dominate the middle of this chart, yet the time epoch for humanity’s existence is entirely within a very small slice within Notation-202. What is the correlation, the working relation, between the current time and the other notations? Are all notations concurrent, active and forever? What does that imply about the nature of space and time? When the chart is divided into thirds, the small-scale universe is extremely small. It goes from the Planck Length to about the size of the quark.

This particular view of the small-scale universe is virtually unknown yet it has a substantial amount of data waiting to be properly analyzed. We reached out to many of the finest scholars for their inputs. Everybody seemed puzzled.

The human scale and large scale did not seem to challenge our simple logic until the “time line” was observed, particularly the figures at one second, Cf. the Ref. [8]. What does it mean that the Planck Length multiple is the distance light travels in a second? Well over two-thirds of all the notations are within that first second and within an area defined by the earth to the moon. What does that tell us?

Nobody seemed to know what to do with these charts. So, to get some scrutiny, online articles, blogs and emails, Cf. the Ref. [9] were written.

Feedback has been limited. How can that change?

We did get some very helpful suggestions. Prof. Dr. Freeman Dyson (email, Cf. the Ref. [10]) recommended that we use dimensional analysis and scaling laws to determine the number of possible vertices starting at the Planck base units. The numbers became extremely large rather quickly; nevertheless, because these first 60+ notations were not on anybody’s charts of known things within space and time, we concluded that these vertices must be shared by the entire universe and have something to do with homogeneity, isotropy, the very nature of symmetry and the symmetry of nature, and the cosmological constant.

It was easy to ask ourselves, “Are we crazy or what?”

Concluding Questions

Are these numbers important? Is this model a reasonable STEM tool? We believe these numbers are trying to tell us something very new and rather special so we will continue writing blogs about our ideas, intuitions, conjectures, and sometimes rather-wild speculations until we learn if our simple logic and simple math have failed us. We are now trying to understand how continuity-order and symmetry-relations, then harmony-dynamics, are truly bedrock principles of Science, Technology, Engineering, and Mathematics.

A sad, perhaps tragic footnote

In December 2011 we didn’t know what we didn’t know. By December 2012 a few of our best students, recently-graduated seniors, now going to Tulane and Loyola just down the street, dropped back by their favorite high school. They told us that their professors had never seen a base-2 progression like ours. The students were confused and so were we. It did not take too long to realize that this work was indeed out of the mainstream. It even seemed like our little mathematical and geometric model was a bit seditious. It raised too many questions. Within a year, we became cautious. Within two years, even more cautious, and within three years, we stopped teaching about the model. We were learning how very seditious an idea can be. At that time this project became my sole cause, “We’ve got to figure out what’s going on here.” –BEC

Footnotes and References

  1. Big Board-little universe, “Can our entire universe be meaningfully encapsulated within just 202 base-2 exponential notations?” The first web page:
  2. Quiet Expansion, “An exploration of 202 steps from the smallest measurement, the Planck length, to the Observable Universe”
  3. Some Calculations and Thoughts Regarding Measurement by Joe Kolecki, NASA scientist, retired:
  4. Universe Table – Human Scale:
  5. Big Board-little universe, “UniverseView: Begin at the Planck Time and Planck Length, Use Base-2 Exponential Notation.”
  6. Five Planck Base Units – Vertically scrolled, 204-to-0:
  7. The original Wikipedia article: 
  8. Five Planck Base Units – Horizontally scrolled:
  9. A working Index of articles:
  10. Freeman Dyson:


Challenge us. Coach us. We need all the help we can get.


1 Bryce Estes 2 Cathy Boucvalt – 3 Steve Curtis – 4 Bruce Camber –