There are three simple oversights within our academic pursuit that, if opened up for a wider discourse, might help to overcome basic problems within the sciences and humanities today.

1. What is the simple geometrical structure of interior space?

What is inside the tetrahedron? …the octahedron? …the icosahedron? …the dodecahedron? …the square. Although most think the square is well known, there is still much to be learned even within it. The interior structures within the other basic solids are readily known by a few specialists of nested geometries, yet hardly known at all even within disciplines like architecture, chemistry, cosmology…

2. Do geometries nest within each other from the smallest to the largest?

Math and geometry in some manner of speaking apply to all space and time from the smallest space to the largest. These geometries are necessarily inter-related. How? Why? Where?

To develop this discourse, begin with the smallest calculated unit within space and time; most scientists know it as “The Planck length.”

What happens when you multiply Planck Length by 2 and each subsequent result by 2? That question was only answered in a high-school, geometry class as recently as December 19, 2011. That story is here. Both teacher and students could not believe that they were doing original research. It is just too simple and basic. But, they searched the World Wide Web and found no references. Then they began searching through scholarly journals. They assume, even if it is out there somewhere, it is not commonly used or understood. Perhaps it is a little like the space frame; it was first developed by Alexander Graham Bell while working with basic structures from 1886 to 1922 at his summer home in Beinn Bhreagh, Nova Scotia. No special importance was given to it other than for designs of box kites.

In the 1950s, and quite unaware of Bell’s earlier work, Buckminster Fuller developed the same space frame but immediately began putting it to work. The architectural and construction communities adopted Fuller’s work for truss design and infrastructure applications. Yet, within the general scientific community, it still had no special significance.

Perhaps it should.

The space frame is a partial representation of another basic structure. Push two space frames together so the squares all match up, and a series of tetrahedral-octahedral-tetrahedral (TOT) chains are created. By doubling the space frame, each square becomes stronger with four additional equilateral triangles to hold its form. Also, there are two internal channels created whereby an internal chain, half the size of the original, can readily be aligned within each.

This structure occurs naturally in mineralogy, yet it has not been extended within the other scientific disciplines.

3. In what ways could these basic structures and the doubling of points from the Planck Length cohere?

Theoretical physics has a rich and deep history of using mathematics to model physical realities. Particle physics extended naturally from experimental physics and the search for fundamental particles within nature.

The Planck length has played an important role within both domains especially with those people focused on topics such as black hole entropy, string theory, multiverses, and a theory of everything. The simple idea of multiplying the Planck length by two has not been a focus of study. Perhaps it should be.

It was discovered that there are 202.34 notations from the Planck Length to the edge of the observable universe. A NASA physicist helped with that calculation. It renders 202+ notations (or steps or doublings) which hereinafter are called Planck Numbers, 1-to-202+.

Initially these notations were readily segmented as small scale (PN1 to PN67), human scale (PN68 to PN135), and large scale (PN135 to PN202+). Yet, upon reflection, those ranges need more study.

Questions around parameters and boundary conditions remain quite fluid.

Also, within the small and large scale, there are additional segmentations that might initially help to see the whole. At this time, the small scale is from PN1-to-66 that sets the first limit at the Fermi point or fermi particle (PN66). Perhaps the Small Scale could be divided into seven layers, just like the Open Systems Interconnection of the International Standardization Organization (OSI of the ISO) whereby initially we take every ten notations as a layer and see if anything can be more deeply discerned..

Though the focus of that work will initially be the very-small scale, the entire chart from PN1 to PN202+ will continue to be our study.

Illustrations follow…

Tetrahedron’s simplest parts

Octahedron’s simplest parts