##### by Bryce Estes,^{1} Cathy Boucvalt,^{2} Steve Curtis,^{3 }and Bruce Camber,^{4} (2015) New Orleans, LA 70123 USA

Please note that at the time this article was first written, Bryce Estes was a high school student, 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?”

**Abstract**

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 half-sized tetrahedrons in each corner and an octahedron in the middle. We then divided the edges of the octahedron in half and found half-sized octahedrons in the six corners and eight tetrahedrons in each face. Like Zeno, we continued the process of dividing by 2, and within 45 steps (on paper only), we were in the area of the CERN-scale and within 67 more steps within, we were in the Planck scale. We then multiplied the original objects multiplied by 2 and within 90 steps we were out to the Age of the Universe and Observable Universe. That included everything, everywhere for all time. We dubbed it “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 this summary as “original research.” The AAAS and Nature magazines rejected us without comment. So, now we go back over our logic and math and ask, “What are we doing wrong?”

**Introduction**

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.

**History**

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 we discovered Kees Boeke’s simple work using base-10. It was interesting but not as granular as our work. We first 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].

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]. We then added Planck Time to the chart, Cf. the Ref. [5]. Those numbers tracked well with the Planck Length and Age of the Universe was no longer a mysterious number and it gave us a place to stop 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. What does that mean?

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 went 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**

First we wondered why couldn’t we could not find some vestiges of these charts within our textbooks or someplace on the World Wide Web. When Wikipedia rejected our article about it 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 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 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 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 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 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 or continuity and order are truly bedrock principles of Science, Technology, Engineering, and Mathematics.

**References**

1. Big Board-little universe, “Can our entire universe be meaningfully encapsulated with- in just over 201 base-2 exponential notations?” the basic web page. https://81018.com/home

2. Quiet Expansion, “An exploration of 202 steps from the smallest measurement, the Planck length, to the Observable Universe” http://81018.org

3. *Some Calculations and Thoughts Regarding Measurement* by Joe Kolecki, NASA scientist, retired: https://81018.com/kolecki/

4. Universe Table – Human Scale: https://81018.com/universe-table/

5. Big Board-little universe, “UniverseView: Begin at the Planck Time and Planck Length, Use Base-2 Exponential Notation”. https://81018.com/plancktime/

6. Five Planck Base Units – Vertically scrolled, 204-to-0: https://81018.com/chart4/

7. The original Wikipedia article: https://81018.com/2012/05/05/wikipedia/

8. Five Planck Base Units – Horizontally scrolled: https://81018.com/chart

9. A working Index of articles: https://81018.com/index

10. Freeman Dyson: https://81018.com/dyson