### GO TO: Transformations between the finite and infinite

https://81018.com/transformation/ for the basic conscresence.

### GO TO: *A new STEM tool delights, but raises difficult questions*

https://81018.com/stem/ for an update about our STEM activities.

*A new STEM tool delights, but raises difficult questions*

#### GO TO: *Tiling and Tessellating the Universe: A Great Chain of Being*

https://81018.com/2014/12/01/tiling/ for a review of how we got to this page.

*Tiling and Tessellating the Universe: A Great Chain of Being*

#### GO TO: *Everything Starts Most Simply. Therefore, Might It Follow That The Planck Length Becomes The Next Big Thing?* https://81018.com/2014/05/21/propaedeutics/ which was an early article.

*Everything Starts Most Simply. Therefore, Might It Follow That The Planck Length Becomes The Next Big Thing?*

#### GO TO *Simple facts* https://81018.com/simple-facts/; it introduces some of our earlier work (1997-2011).

*Simple facts*

**This page will be reworked as an even more simple introduction to the face-to-face intersections of tetrahedrons and octahedrons.**

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?”

**Introduction**

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.

**History**

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.

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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.

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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].

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].

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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.

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**Questions and Challenges**

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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?

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What does that imply about the nature of space and time?

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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.

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**Concluding Questions**

**References**