TO: Francesca Vidotto, The Rotman Institute of Philosophy, Western University, London, Ontario, Canada
FM: Bruce E. Camber
RE: Your ArXiv (47) articles, particularly Philosophical Foundations of Loop Quantum Gravity w. Carlo Rovelli (2022); Time, space and matter in the primordial universe (2022); and even your homepages(s): CV-Bilboa, inSpireHEP, LinkedIN, Loopy Space-Bilboa, Selected Publications, Wikipedia, and Z/Twitter.
This page is: https://81018.com/vidotto/
Also: https://81018.com/questions-questions/#Vidotto, https://81018.com/lqg/
Second email: 7 October 2025
Dear Prof. Dr. Francesa Vidotto:
Can we do a toy model of the Hubble Tension? First, use a geometrical and mathematical calculation using base-2 exponentiation. Using perfectly embedded geometries of the tetrahedron and octahedron — https://81018.com/tot-2/ — we have just 202 sizes of geometries from Planck Length to the size of the universe. The same 202 notations in numbers from Planck Time to the Age of the Universe: https://81018.com/chart/ These were calculated in 2011 and 2014. We realized an expansion rate could be calculated by assuming one Planck Sphere per unit of Planck Time & Planck Length: https://81018.com/tredecillion/ A toy model, the number of infinitesimal spheres being generated was 1.85 × 10^43 spheres per second. In the popular jargon, that is 18.5 tredecillion Planck Spheres/second. Last week both Grok — https://81018.com/hubble-constant/ — and ChatGPT — https://81018.com/toy-model-derivation-of-the-hubble-constant/ — did a toy model calculation to see what such a rate would look like for the Hubble Constant. They both arrived at ≈ 71 km/s/Mpc which, of course, is close to the supernovae measurements (~73 km/s/Mpc) — https://81018.com/5-sigma/. We are tightening up those numbers with another interesting calculation, our expansion of the never-ending, never-repeating numbers of pi (π) with the intrinsic hexagonal plates of every octahedron with the four primary irrational numbers — https://81018.com/planck-polyhedral-core/
Now, is our km/s/Mpc calculation “just” coincidental? How would you go about instantiating meaning to it?
Thank you.
Most sincerely,
Bruce
First email: 11 January 2024
Dear Prof. Dr. Francesa Vidotto:
Very early in our work (2011), we exchanged emails with your colleague, Carlo Rovelli. By 2016 he had become very busy and we were studying so many scholars’ work, we started a reference page for whomever we contacted.* It has helped me tremendously, especially given how years pass so quickly.
We were too naive to address a question like, “How does gravity work on the quantum scale?” We were still struggling to grasp the essence of the Planck base units. We had mapped the universe with them by applying base-2 and found only 202 doublings before we were up to the current time, 13.8 billion years later. For those of us just starting to explore cosmology and astrophysics, those 202 notations were very approachable and comfortable. Of course, we asked, “What might the first notation look like?” Brown University professor Phil Davis convinced me that an infinitesimal sphere was the most likely prospect.
Frank Wilczek of MIT was among the first people to advise us. On a cold winter’s day (January 2013), I made my way to his office and he actually encouraged us! ”Keep studying the Planck Length!” We did. We learned a bit about natural units and dimensionless constants and tried to picture that unexplored infinitesimal domain of about 64 notations. It seemed like the Grand Canyon there were so many possibilities. Quantum fluctuations seemed to be first measured between Notations 65-67.
Freeman Dyson, an old acquaintance from my work at MIT in 1979, also encouraged us to learn more about dimensional analysis and scale invariance. We never imagined that this would be our path to do so.
The first second is within Notation-143. The first million years is within Notation-189.
Base-2 exponential notation is de facto the undeclared notation of big bang cosmology. Yet, a big bang is not needed. Hawking’s singularity seemed unnecessarily obtuse. Having everything-from-everywhere at that moment was just too much to absorb. And, with our natural inflation and emergence, it seems like the universe does just fine.
Would you encourage our explorations? Thank you.
Most sincerely,
Bruce
_________________
Bruce E. Camber
Austin, Boston
https://81018.com/bec/
* Unfortunately, many of our earliest emails were lost… –BEC
Embedded URLs: https://www.uwo.ca/philosophy/people/vidotto.html
https://daily.jstor.org/francesca-vidotto-the-quantum-properties-of-space-time/
@FrancesVidotto: https://twitter.com/FrancesVidotto
https://en.wikipedia.org/wiki/Francesca_Vidotto