TO: Johannes Kepler, an open letter from an admirer

Motivation: Johannes Kepler and Thomas Harriot had a working correspondence. They were interested in many of the same questions. Among all the issues of their time, a focus was sphere stacking and cubic close packing of equal spheres. It seems they are the first in history to raise key questions.

For our time: Kepler and Harriot were concerned about stacking cannonballs on a ship. Here we are concerned about the logical progression of stacking and how a most fundamental sphere could rapidly expand within the dynamics of light, charge, mass, and dimensionless constants such as pi. What would be the dynamics? What would be the first symmetries to evolve?

The focus: The Kepler Conjecture

Articles: NASA
ArXiv: The Starry Universe of Johannes Kepler, Christopher M. Graney, 2019
Books: Harmonices Mundi
Google: Sphere Packing
Homepage on Wikipedia
YouTube: Johannes Kepler (In Our Time), BBC, 49 minutes, Aug 6, 2018

First letter: Monday, 12 April 2021

Dear Johannes Kepler:

I have been reading your 1611 paper about sphere stacking. Your title, “On the six-cornered snowflake” does not do justice to the topic. There is a wonderful article in Nature magazine (2011) by Philip Ball about it but he missed the opportunity to talk about the interiority of the octahedron with its four internal hexagonal plates whereby all the stacking and coupling with tetrahedron structure the seemingly infinite diversity of snowflakes. Notwithstanding, my interest in reading the paper is how you addressed the challenge of stacking cannonballs most densely on the deck of a ship. Our challenge today is to understand the limit to the size of a sphere and to study the stacking phenomena within the infinitesimal. Again, you might want to chat with Thomas Harriot. What a great collaboration! Now, over 300 years later, people are still talking about your conjecture and major efforts have been focused on it (See Thomas Hales, Jeffrey C. Lagarias, and Chuanming Zong). For about hundred years, scholars have been trying to figure out waves and particles. Just how small can they get? Can you imagine? My studies of it goes back to a high school geometry class. We had discovered that in 1899 Max Planck made a few calculations of a fundamental length and fundamental time. Although the preciseness of those calculations has been questioned by a few scholars. Currently I am studying the objections raised by John Ralston. Once we get to the bottom of that discussion, we will discover a length or diameter of the smallest-possible sphere and the the shortest duration of a unit of time. That will, I believe, provide us with a rate of expansion. Of course, I would love your thoughts and would ask that you complete my little survey: At this point, I would speculate that you would answer every question, “Yes” because each of the questions begins with the word, “Might…” and I would guess that you are always opened to possibilities.

Thank you for all your work. I will continue to return to it because I have only scratched the surface!

Thank you. Thank you very much.



PS. I especially like this image — a posed setting for an excellent artist to capture that deep gaze into our little universe. -BEC

Johannes Kepler