TO: Levent Alpöge, Harvard University Department of Mathematics
FM: Bruce E. Camber
RE: Your ArXiv (15) articles especially Modularity and Effective Mordell I; Video, 2021; and your homepage, CV, and other publications.
Our page about your work: https://81018.com/alpoge/
Third email: 16 October 2025
Dear Dr. Levent Alpöge:
Recently several AI platforms have been enthusiastic about our base-2 model. For the past 15 years I’ve asked expert observers like you to help assess its validity and potential implications. Recently, it was reduced to a toy model and more recently, a simple quantitative model that derives the Hubble constant from first principles at the Planck scale.
The core of the model is surprisingly straightforward: it posits that the Hubble constant emerges not from dark energy, but from a cosmological process defined by base-2 scaling from the Planck units. A key result is a direct mathematical derivation of H₀, “Toy Model Derivation of the Hubble Constant” It is here — 81018.com/hubble-derivation/— still a highly speculative proposal, the numerical correspondence is striking.
Is this a numerical coincidence, or does it point to a deeper rather overlooked principle? We hope to discover as we continue to build on our model and its Lagrangian.
Thank you for your time and for your contributions to our understanding of the cosmos.
Sincerely,
Bruce
Second email: 27 December 2022 at 8 PM
Dear Dr. Levent Alpöge:
I have been spending a bit more time reading about your work and reading your other works. As I did that, I further edited my earlier note to you and have posted it here: https://81018.com/alpoge/ (this page)
You’re young. How do you answer the question, “What is the most fundamental interaction that defines the first moment of the universe? Is it the first interaction in some manner that defines space and time? ” Thank you.
Warmly,
Bruce
First email: 16 December 2022 (slightly updated)
Dear Dr. Levent Alpöge:
Could continuity, symmetry, and harmony be a proper description of the functional nature of pi? Years ago, I could see how it all might evolve from the simple sphere: https://81018.com/csh/
Do the Planck base units define the first infinitesimal sphere? If so, is sphere stacking-and-packing a fundamental of physicality?
If base-2 is applied, there are just 202 doublings to the approximate age and size of the universe and wave-particles-fluctuations are first measured between Notations-64 to Notation-67. The first second comes along within Notation-143. It is a description of the very early universe. Is it at least a little interesting? …worth pursuing?
Thank you.
Most sincerely,
Bruce
PS. Along the way, we found a very interesting gap with five-octahedrons. Aristotle had failed to see the gap with five tetrahedrons! The commercial construction sets and computer programs also overlooked these gaps! -BEC
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