• Big Board - little universe   Ten-page Tour: Introduction   #1,  #2,  #3,   #4,   #5:  #6,  #7,  #8,   #9  &  #10
• Early-stage lesson plans for middle and upper schools (called "BiBo-lu)
• Simple Math: 205+ Exponential Notations from the Planck Length
• Analysis of the story A simple history of these high school geometry classes

Editor's Note: This page is an exploratory to obtain constructive criticism. The work is not part of any normal curriculum. That makes it speculative even though it is based on the simplest mathematics and geometries. If it should spark a comment, "It is not even wrong." and that is you; if you can, please tell us what or why it is not even wrong. Based on the work of Max Planck and Plato, this table uses the familiar format within chemistry to order information. That table evolved over 100 years to a working format (1871, Dmitri Mendeleev), then it has taken all these intervening years to refine it. Though the similarities might provide a little comfort factor, this table is based entirely on the principle of continuity extended from the Planck Length following nested Platonic geometries out to the edges of the Observable Universe. The first 60+ notations (doublings or steps) cannot be measured. Each is hypothesized, possibly hypostatized and instantiated.

- Bruce Camber (Email)

Introduction. The Big Board-little universe  was first used in class on December 19, 2011. This Universe Table (a full-sized version is just below) began a year later for those same high school geometry classes. The big board measures 62"x10" and it is just too big and awkward for desktop work.   The table is designed to be printed on 8.5"x11" paper and displayed on a smartphone. Now, the origin of these two charts can be found by looking inside a tetrahedron and an octahedron. Half-sizes of both objects can perfectly fill each other. The question was asked, "How far can we go inside each by dividing in half over and over again?" The simple answer is, "Not very far." Within 50 steps we were at the size of a proton. Within another 65 steps we were at the Planck Length. This particular table was created by multiplying the smallest possible length -the Planck Length- by 2 until we got to the edges of the Observable Universe. Distinguished scientists have helped us. One scientist calculated as few as 202.34 notations (doublings or steps) from the smallest to the largest. Another calculated 205.11.

We use both figures. Within over 202 notations, here is a simple view of the universe, highly-ordered and structurally integrated from the smallest to the largest measurements of a length, all within a geometrically homogeneous group.

Examples. Initially the examples came mostly from the Paul Falstad's Scale. Then over the following year other objects of special interest to students were selected. Each should be within the range of the notation defined as no less than 50% smaller or no more than 50% larger than that particular Planck multiple.  As we go forward, every entry will have footnotes and links for further explanation and exploration.

Exhausting. Today's information glut is so chaotic and overwhelming, it seems that it actually depresses creative thinking.  So, our hope in sharing this simple little table is that students will feel empowered to search for new insights to understand this universe more deeply and as we do, to instill some optimism about our common future.

Notice the first 66 notations. In light of the Planck Length doublings, this is rather new ground. Here, there are very few facts and many, many guesses. And, we believe that there are many more surprises to be found throughout this chart. One might readily conclude that all the surprises are new domains for research and study.