Martínez / Nagel

Servet Martínez, Universidad de Chile
Werner Nagel, Institut for Stochastik, Friedrich-Schiller-University Jena

RE: STIT Tessellations – Ergodic Limit Theorems and Bounds for the Speed of Convergence

Dear Prof. Dr. Servet Martínez and Prof. Dr. Werner Nagel,

Back now, almost 17 years ago, I was visiting and talking with John Conway in his Fine Hall, Princeton office, about tessellating the universe with tetrahedrons and octahedrons. I was particularly wondering why it was that the scholarly community was so little concerned about these two very basic objects. I was still learning so much from the two of them.

In 2011 my nephew asked for my help with his high school geometry class. We were observing the nested geometries of those two simple Platonic solids: and decided to do a Zeno: How far within can we go?

Within about 45 base-2 notations, we were at the CERN-scale of the LHC. Within another 67 notations we were back within the Planck base units.  It didn’t take too long before we multiplied our original objects by 2.  In just 90 jumps we were out to the Observable Universe and the Age of the Universe.

That little piece of work became our STEM tool and chart.

It has taken awhile — we are a little slow — but now we are asking, “Are these first 67 notations where is all begins?”  Your article has opened up an entirely new field of inquiry for us: STIT tessellations.  I am especially enjoying the dynamic and dimensional thrust of your work and wanted to thank you.

Thank you!

Most sincerely,

Bruce Camber