TO: Noam Elkies, Harvard University, Cambridge, Massachusetts
FM: Bruce E. Camber
RE: Your articles such as Skilled at the Chessboard, Keyboard and Blackboard, Dylan McClain, NYT (2010); your many arXiv (48) articles, especially Equations for a K3 Lehmer map (2021); your books such as Arithmetic Geometry, Number Theory, and Computation, eds. Jennifer S. Balakrishnan, Noam Elkies, Brendan Hassett, Bjorn Poonen, Andrew V. Sutherland, John Voight, conference proceedings (2021); even your homepage(s) in ads, dblp, Harvard-Radcliffe, LifeWiki, and the Prabook; your many publications, even your mentions in Twitter (Pickover, Eric Weinstein) and Wikipedia; and your YouTube videos especially K3 surfaces and elliptic fibrations in number theory (2018)
This page: https://81018.com/elkies/
Second email: 16 December 2025
RE: Questions about the infinity and the infinitesimal
Dear Prof. Dr. Noam Elkies:
1. Can we further define infinity by the nature of pi (π)’s continuity-symmetry-harmony?
2. Could an infinitesimal sphere, defined by the Planck units (or the best approximation today), be the first moment of space-time and the first manifestation of irrational numbers? If so, might a cosmological constant be calculated at one sphere per Planck length-and-time or 18.5×1043Planck Spheres per second? And if so, with such spheres, possibly acting like Einstein’s ether, can we calculate there are 202 base-2 notations that encapsulate the universe, all things and for all space-and-time?
3. Might the internal structures of the octahedron, particularly the four hexagonal plates (dynamically demonstrated) be basic to number theory, basic to the stability of spheres, be basic to every moment of space-time and its first manifestation as irrational numbers, an infinitesimal sphere defined by the Planck units or their best approximation today. On a visit with John Conway, he was intrigued.
4. Might the gap created within the five-fold symmetries of sphere-stacking, be our engine of differentiation? Might the most-common 7.356° natural gap, take us from geometries to physics?
Thank you.
Most sincerely,
Bruce
First email: July 7, 2022
Dear Prof. Dr. Noam Elkies:
Your history is breathtaking. I would be honored to have you read about our intellectual conundrum.
We have been working with the Platonic geometries in our high school and cannot find any references online to a very simple geometric figure of five octahedrons, all sharing a centerpoint, and three sharing two faces with another octahedron, and two sharing only one face. It is a very interesting image when the five-tetrahedrons are added on the top and bottom. That stack has 15 objects sharing the centerpoint. I took the picture below just a few weeks ago but, to date, it appears that there is no scholarly writings about it.
Have you seen such an analysis? If not, do you think it is important? Thank you.
Warmly,
Bruce
PS The URL: https://81018.com/15-2/
Preliminary analysis: https://81018.com/geometries/
Thanks. -BEC
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Bruce E. Camber
https://81018.com
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Note: non-symplectic automorphisms, p-adic lifting, elliptic fibrations and the Kneser neighbor method for integer lattices