An analysis of the 202 notations or doublings of the Planck base units

RE: Our horizontally-scrolled chart of the universe

We backed into our map of the entire universe
defined by 202 geometric and mathematical relations.
by Bruce E. Camber (October 2018)

History. This website began back in December 2011 with work in a high school geometry class in New Orleans. We had first observed how the tetrahedron is perfectly filled with four half-sized tetrahedrons (one in each corner) and an octahedron (revealing one triangular face in the center of each of the four faces of the tetrahedron). We then observed how the octahedron was perfectly filled with six half-sized octahedrons (one in each corner) and eight tetrahedrons (one in each face). We observed how the two objects together perfectly fill space, theoretically tiling and tessellating the universe. The question was asked, “How far within can we go?” By filling each tetrahedron and octahedron with smaller and smaller tetrahedrons and octahedrons, we discovered the smallest limits. By multiplying each by 2, and the result by 2, over and over again, we reached the upper limit.Once we defined those boundaries, we began re-examining the processes.

202 notations or doubling or groups or steps. In just just three steps within, we had so many tetrahedrons and octahedrons, we turned to paper! Within just 45 steps going within, we were down into the sizes that CERN Labs (Geneva) measures. Within another 67 steps within, we were facing the Planck Wall and realized that this is where Zeno had also finally reached a limit.When we multiplied our objects by 2 to get bigger, we were equally surprised that we reached the approximate size of the universe in just over 90 steps, all successive doublings. That we mapped the entire universe in 202 doublings with geometries and multiplication by 2 was as satisfying as it was mystifying.

Mystery. First, we couldn’t find any references to it on the web! We did find Kees Boeke’s base-10 and that was some comfort, but where is our more granular base-2? How could something so simple be new?Then we asked the question, “Does this geometry represent anything in reality?” It is symbolic, of course, but in many different ways, it is also observable. We’ve kept that question open.

A STEM Tool. Now, both surprised and a bit perplexed, we asked,”What can we do with this nascent model?” We decided to share our map of the universe with other schools. For us, it seemed like an excellent STEM tool.

Summary. In this first mapping of the universe, we de facto discovered the Planck Length, base-2 notation, a rather overwhelming continuum of geometries, and a delightful way of ordering information along a scale of the universe.But, we still had a lot of work to do. First, we started to learn about the other Planck base units. How would they track with the Planck Length expansion? We could not even begin to guess. We are told that we live in an expanding universe, so we realized that we would have to keep track of the top numbers and the expansion. We also asked, “What comes before the Planck units?” We didn’t have a clue.

It took us three years to be somewhat convinced that what we did was original. So far, all that we know is that we backed into a base-2 chart of the universe and have now started to learn about the Planck base units…

Return to the chart

Related Webpages

December 2011:

Learning Geometry

Original chart

Working Index

January 2012:

Early Questions

First Overview

Early ideas


Letters to
Scientific American

Wikipedia Rejection

Simple facts


Start Simply

Big Bang Questioned

Planck Time


Planck Mass &
Planck Charge

Big Bang Questioned


Chart of the Universe
AAAS Science
Magazine rejection