Cynthia M. Friend, T.W. Richards Prof. of Chemistry & Prof. of Materials Science, Harvard

Homepage(s): Harvard IMASC EFRC Director

First email: 29 February 2024   (Updated)

Dear Prof. Dr. Cynthia Friend:

Congratulations on all your work and so much success.

At Princeton in 2001 with surreal geometer, John Conway, we discussed the interior part of the tetrahedron and octahedron. He was pleased to see a model so clearly delineating the four hexagonal plates that crisscross within every octahedron and was grateful when I gifted him with that simple model (I had many manufactured: https://81018.com/octahedron-game/). Even today, people are surprised to learn of those parts-whole relations (i.e. six smaller octahedrons, one in each corner, and eight tetrahedrons, one in each face). And, to think, this scale-invariant object and emerges from a sphere.  They are also generally surprised to learn about the geometric gaps. We should know these gaps very well, especially the National Ignition Facility.

In 2011 we followed the combinatorics of these simple geometries back 45 steps to the particle scale and then another 67 steps to the Planck scale. Quite an adventure. Yet, more surprising were the 90 steps out to the age and size of the universe (assuming Planck Time to the chronon and a total of 202 active domains, notations or steps).

These are just a few of the basics that might change the paradigm. Could you be interested to learn a little more? Thank you.

Warm regards,

Bruce

PS. That part of my work with geometries began with Arthur Loeb in his Sever Hall attic studio! -BEC