High school is a place to explore basic ideas and soak up information, knowledge, and wisdom. We divided the edges of a tetrahedron, then an octahedron and tiled and tessellated the universe only to discover that it hadn’t been done and was not part of any formal academic program. Wikipedia rejected us in 2012. AAAS rejected us in April 2016. So, now we go back over our logic and math and ask, “What are we doing wrong?”

Since December 2011 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.

The project began by dividing the edges of a tetrahedron in half. We connected the new vertices and discovered a tetrahedron in each of the four corners and an octahedron in the middle. We then divided the edges of the octahedron in half and discovered an octahedron in each of the six corners and a tetrahedron in each of the eight faces. Delighted with the simple complexity, we continued to divide each subsequent object in the same way until we had to resort to paper. By the 40th step we were in the

range of a proton. In another 67 steps we were in the range of the Planck base units. Back up inside the classroom we decided to multiple by 2.

Within about 30 steps we were out to the International Space Station. In less than 70 more steps, we were out to the Observable Universe.

It was a delightful process charting the universe in what we quickly learned was base-2 exponential notation. Not long thereafter we discovered Kees Boeke’s simple work using base-10. It was interesting but not as granular as our work. We thought our work was an excellent Science-Technology-Engineering-Math (STEM) tool so we began sharing it with others within very preliminary web pages, Cf. the Ref. [1].

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The first chart was a 60″ by 11″ board that started with the Planck Length and went to the Observable Universe, Cf. the Ref. [2] so we called 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 a desktop version of the chart was started; it was dubbed, Universe Table, Cf. the Ref. [4]. In December 2014 Planck Time was added to the chart, Cf. the Ref. [5]. Those numbers tracked well with the Planck Length. Now we had a better number, Age of the Universe, to determine when to stop multiplying by 2. Here we discovered that the ratio of of the Planck Length to Planck Time within each of the 201 notations was always within 1% of the speed of light. In February 2015, we added the other three Planck base units to the chart, Cf. the Ref. [6].

Here we discover that each number is a ratio to the others and provides summary data about inherent order within the universe.

The teachers include three of the authors of this paper, Bruce Camber, Cathy Boucvalt, and Steve Curtis and a student, Bryce Estes who represents the many years of students, including a sixth grade class, who have been introduced to these charts.

The very first observation was that each chart is a highly efficient way to organize vast amounts of information. But these charts also raised some rather fascinating questions.

**Questions and Challenges**

First we wondered why couldn’t find some vestiges of these charts within our textbooks or someplace on the World Wide Web. In May 2012 Wikipedia rejected an article we submitted because it was “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? Should this be the first principle within our work?”

The small numbers were impossibly small and the large numbers were impossibly large, yet the 201 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 was that helped to make these numbers more manageable. Yet, it has just taken time. It has been a steep learning curve for our feelings or intuitions about the very nature of a number. We asked more questions, “What are these numbers? What are they 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 notation 201. 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 fermion. 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 column 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 one

second and within an area defined by the earth to the moon. What does that tell us?

Nobody seems 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?

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 become extremely large rather quickly; nevertheless, because the first 60+ notations were not on anybody’s charts of known things with in 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. Are we crazy or what?

**Concluding Questions**

Are these numbers important? Is this model important? 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 why our simple logic and simple math have failed us. Have they?

**References**

1. Big Board-little universe, “Can our entire universe be meaningfully encapsulated within just over 201 base-2 exponential notations?” the basic web page.

http://bblu.org
2. Big Board-little universe, “An exploration of 101 steps from the smallest measurement, the Planck length, to the human scale, and then 101 more steps to the Observable Universe” December 2011

https://81018.com/home
4. Big Board-little universe, “Universe Table – Human Scale”.

5. Big Board-little universe, “UniverseView: Begin at the Planck Time and Planck Length, Use Base-2 Exponential Notation”.

6. Big Board-little universe, “Five Planck Base Units – Vertically scrolled, 204-to-0” February 2015

8. Big Board-little universe, “Five Planck Base Units – Horizontally scrolled, 0-204 to the first second” May 2016.