TO: Martin Bojowald, Penn State, Eberly College of Science, University Park, PA
FM: Bruce E. Camber
RE: Your fundamental work: Loop Quantum Cosmology as well as your homepage(s): ArXiv (177): Absence of Singularity in Loop Quantum Cosmology, 2001; Physical Review Letters: Physical Implications of Fundamental Period of Time, 2020; Wikipedia
Within this website: Scroll through several pages.
URL for our page about your work: https://81018.com/bojowald/
Third email: 18 September 2025
Dear Prof. Dr. Martin Bojowald:
Attached is “a crisp mathematical structure.” It was uncovered in 1998 yet only became dynamic in July 2025. Today it seems to provide a framework for the four primary irrational numbers. Perhaps the best possible description is a mechanism to bridge the finite-infinite. Two files introduce and demonstrate the concepts:
https://81018.com/originals/
https://81018.com/planck-polyhedral-core/
Your comments would be appreciated. Thank you.
Most sincerely,
Bruce
Second email: 15 March 2025
Dear Prof. Dr. Martin Bojowald,
The header of your Mathematical Structures group reads: “Physics often advances when crisp mathematical structures are uncovered in a framework developed to describe observed phenomena.”
I don’t think there could be more crisp mathematical structures than the four primary irrational numbers, Pi (π), Phi (φ), the Square root of 2 (√2), and Euler’s number (e). I have turned to asking Grok about them: https://81018.com/irrationals/
Might the four hexagonal plates of the octahedron be an appropriate representation of that geometry?
I have discussed it in the last four homepages:
• Pi Day 2025: https://81018.com/pi-day-2025/
• Today’s homepage: https://81018.com/incommensurable/
• Breakthrough: https://81018.com/breakthrough/ https://81018.com/breakthrough-indeed/
Thank you.
Most sincerely,
Bruce
PS. If you have any updates-changes-deletions within our page about your work, just say the word. That page is: https://81018.com/bojowald/
An evolving page: https://81018.com/penn-state/ -BEC
First email: May 17, 2023, 6:41 PM (edited)
Dear Prof. Dr. Martin Bojowald,
I recognized your name cited within several pages of our website!
I had been pleased to read your 2001 work within ArXiv —Absence of Singularity in Loop Quantum Cosmology, and your more recent work in Physical Review of Letters — Physical Implications of a Fundamental Period of Time, 2020. It is also good to read about your work, Physics (APS) —The Period of the Universe’s Clock, 2020. I was getting so many references, I had to send this note of thanks. It was also my way to re-affirm those references in my mind.
My work is idiosyncratic and plebeian. It started in a high school when we ducked inside the tetrahedron that we were studying in geometry. We kept going more deeply within by dividing edges in half and connecting the new vertices. There were 45 steps to particle physics and 67 steps more to the Planck Length — https://81018.com/big-board/ That was done in New Orleans back in 2011.
We were having fun exploring the edges of our understanding and knowledge. We wrote it up as a STEM tool: https://81018.com/stem/. But it was more. First, it was simple. And, it was the most comprehensive view of the universe we had ever seen and we created it! I am working on the last page linked above — https://81018.com/the-firsts/ –and I have already cited your articles in the references and resources.
I thought you’d find it interesting especially in light of the deep questions being raised by the results of the JWST about our currently-accepted cosmological point of view.
Thanks.
Warmly,
Bruce
PS. There are so many links above, you may not find the reference to the 10-33 strong upper bound. It’ll not be easy for me to interpret your work, but I’ll try and be talking most appreciatively about it! -BEC
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