First email: 22 August 2018
Dear Prof. Dr. David Nolte:
Do we trust simple logic and math?
Our high school classes in New Orleans were studying the interior geometries of the tetrahedron by dividing each edge in half and connecting those new vertices. We discovered the four half-sized tetrahedrons in each corner and the octahedron in the middle. Applying the same process with our octahedron, we discovered the six half-sized octahedrons in each corner and the eight tetrahedrons in each face, all sharing a common centerpoint. We also found the four hexagonal plates surrounding that centerpoint and quickly tiled the universe with them. We also found the plates of squares, triangles, and other configurations.
It was all quite fascinating, but our adventure was just starting.
We continued to divide the edges in half for both objects, going deeper and deeper inside. We had Zeno in mind. By the 45th step inside (of course, on paper only), we were in the range of the sizes measured within particle physics. We called it the CERN-scale. In another 67 steps within, we were down in the Planck scale. There were 112 steps from our little 2.5″ tetrahedron down to the all those dimensionless constants that make up the Planck base units.
We quickly learned that what we were doing was applying base-2 notation. We then learned about Kees Boeke’s base-10 work in 1957 (also in a high school). And, rather quickly, we thought about multiplying by 2.
That was the biggest surprise.
In just 90 steps or doublings going out, we were at the Hubble’s measurement of the approximate size of the universe. A NASA scientist helped us with that calculation. Many others did as well. But three years later, we finally added Planck Time to the scale and it blew us away. The two scaled so well together. But then, we commented, “Of course they do!”
In another year, we added Planck Charge and Planck Mass and that was totally challenging. We are still working on those numbers and have a long ways to go. But, in the process, we have talked with some of the finest people on the planet. Yet, we know what we have done is quite idiosyncratic and naive because nobody is critical, yet everybody is reluctant to engage such simplicity.
The implications are just too strange. 202.34 notations or doublings or steps and we have a very unique map of the universe. But, is it useful? Or, is it just a collection of useless numbers? What does a retired high school teacher do? What would you do with this odd-duck collection of simple math and simple logic? Just forget it?