Institute for Advanced Study (IAS)
Princeton, New Jersey
First email: Wednesday, 26 April 2017 RE: Idiosyncratic concepts can emerge from a high school geometry class
Dear Prof. Dr. Steve Adler:
I was reading the 2008 compilations and commentaries on ArXiv
— https://arxiv.org/pdf/hep-ph/0505177.pdf — and thought you
just might be bold enough to tell us where we have gone so wrong.
In December 2011 with my favorite geometry classes, we followed
Zeno inside the tetrahedron to find the octahedron and four half-
sized tetrahedrons (by dividing all the edges by 2 then connecting
up those new vertices). We continued with our simple progression.
Besides ending up with an enormous number of parts, within 43
steps we were near the limits of CERN-labs measurements,
somewhere around the size of the Fermion. We continued our
base-2 divisions, on paper and in theory back to the Planck units
in just 67 additional steps. The next day we multiplied our original
We had tiled and tessellated the universe with octahedral-tetrahedral
clusters and had a terrific chart of everything, everywhere throughout
Of course, it was a bit of silliness. Or is it?
We weren’t sure. For three years we search around for something
like it and only found Kees Boeke’s work from 1957. My old friend,
Phil Morrison (MIT) loved Boeke’s work. Without any clear criticisms,
high school people.
Are the first 67 notations the matrix or Frank Wilczek’s grid? Is this
the domain of pointfree geometries?
I would be perfectly delighted to hear from you no matter how harsh
your criticisms. Thank you.