TO: Jan Ambjørn, emeritus, The Niels Bohr Institute (NBI), Copenhagen University, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark. Also: Institute for Theoretical Physics, Utrecht University, Minnaert Building, Leuvenlaan 4, NL-3584 CE Utrecht, The Netherlands
FM: Bruce E. Camber
RE: Out of over 220 ArXiv, I have focused on Causal Dynamical Triangulations: Gateway to Nonperturbative Quantum Gravity, J. Ambjørn, R. Loll, 2024 and Is the present acceleration of the Universe caused by merging with other universes?, J. Ambjørn and Y. Watabiki, Journal of Cosmology and Astroparticle Physics, Volume 2023, December 2023; Elementary Quantum Geometry, 2022; A model for emergence of space and time, J. Ambjorn, Y. Watabiki, 2015; Reconstructing the universe, 2005, The Universe from Scratch, (PDF), 2005; and of your books I have focused on The Geometry of Dynamical Triangulations, Springer 1997. Then of your homepage(s), DBpedia (More), Google Scholar, inSPIREHEP, Radboud (RU), Worldcat, Wikipedia, and YouTube: With Stephen Wolfram, August 2021
This page: https://81018.com/ambjorn/ Also: https://81018.com/reformat/#CDT
Sixth email: 20 February 2026
Dear Prof. Dr. Jan Ambjørn:
Because there was activity on our page about your work (this page) on our website (web analysis tool), I reviewed it. I re-read my four uninvited emails to you, and I thought about your work. First, let me apologize for another interruption. Second, there is no need to respond. Third, I just wanted to bring your attention to the involvement of six AI tools that provide a synthetic peer review of the work described in those emails.
They concur and encourage: https://81018.com/2026-state-of-the-universe-d/
I believe it is all coming along — rather slowly. Thank you.
Yours sincerely,
Bruce
Fifth email: 7 October 2025
Dear Prof. Dr. Jan Ambjørn:
What if our starting points have been confusing us? What if big bang scholarship has hard-wired us to think of photons and the particle zoo and we are stuck? It took a naive high school geometry class and their equally naive teachers to come up with a totally naive point of view.
Let’s 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 that number of infinitesimal spheres being generated — 1.85 × 1043 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? Where do we go from here?
Thank you.
Most sincerely,
Bruce
Fourth email: 12 March 2024 @ 1 PM (updated)
Dear Prof. Dr. Jan Ambjørn:
Has any scholar told us about the origins of the concept of continuity? … or symmetry? Some might answer, “…from spheres,” and be also thinking about the Fourier Transform and its harmony and spin states. Then perhaps we also begin thinking about dimensionless constants (like pi or π) and natural units and ask, from where do the Planck base units emerge? And, if they emerge as a simple sphere, from where do those infinitesimal spheres emerge? Infinity?
Perhaps. Might we take the continuity-symmetry-harmony of the sphere to be a good redefinition of infinity? Is it possible that there is one such sphere generated for every unit of Planck Length and Planck Time? Does cubic-closed packing of equal infinitesimal spheres (automatic stacking and packing), create tetrahedrons and octahedrons? It’s actually simple. The kids seemed to follow it without a problem. I think it’s important that they can go home and explain our universe to their folks. Why not?
This is my fourth email to you; the first was in November 2016, the second in 2021, and the third in 2022.
Again, let me thank you for all your work on Causal Dynamical Triangulations over the years (Where have they gone?). Given we started from within tetrahedrons and octahedrons and the 202 notations from the smallest to the largest scales within physics, and we are all about causal dynamic triangulations, perhaps we could say that we are CDT-light!
Best wishes, and with a smile,
Bruce
Third email: 5 February 2022 @ 5:30 PM. (updated)
Dear Prof. Dr. Jan Ambjørn:
In my first note to you in 2016, I never properly introduced myself. I apologize. High school teachers can be, unwittingly, as presumptuous as Nobel laureates. Of course, each of us is so tied up within our own work, we become oblivious to others.
In 2011 in our geometry class we did a base-2 progression to the Planck scale. From the classroom it only required us to divide by two 112 times (smaller and smaller steps within). We also went out, multiplying by two (or doubling), and we found only 90 steps going out. The universe was encapsulated within202 notations from the first instant to this day, from the smallest to the largest.
We then asked about Planck’s base units. What could be smaller? What would something look like if the first instance of space-time was defined by the basic four units? ZMight it be an infinitesimal sphere? We consulted with old friends (Freeman Dyson), with folks like Frank Wilczek at MIT, and specialists at NIST, Codata, Durham University Institute for Particle Physics Phenomenology and so many others.
Because I am older now and my memory is not as good as it could be, I have reference pages to the work of key scholars with my little notes and questions. My page for you is here: https://81018.com/Ambjørn/ Although our models for the emergence of space-time may appear very different, there will come a day that they’ll be reconciled! Thank you for all that you do.
Most sincerely,
Bruce
Second email: 13 July 2021 at 12:23 PM
Dear Prof. Dr. Jan Ambjørn:
Thank you for your work to develop Causal Dynamical Triangulations (CDT)
where Wikipedia cites you as the prime mover for its development.
The Planck scale is difficult for most of us.
1. Did Max do a reasonable job defining the base units?
John Ralston (Kansas) believes Planck’s Constant throws it all off.
Reference: Quantum Theory without Planck’s Constant, (PDF), Mar 2012
2. Do the Planck base units define (or metaphorically define) the first instant of the universe?
Thanks.
Warmly,
Bruce
First email: November 19, 2016, 10:20 PM (lightly updated)
References:
The Universe from Scratch, 2005. https://arxiv.org/pdf/hep-th/0509010v3.pdf
The Geometry of Dynamical Triangulations (Springer 1997)
ArXiv (113)
A model for emergence of space and time, 2015 https://arxiv.org/abs/1505.04353
Dear Professor Dr. Jan Ambjørn:
Thank you for all your work. Very, very helpful. I first found you within ArXiv. Though I am well along in years (69 years old), you have embraced topics which I find most fascinating, so, you have a new student (de facto)!
I will attempt to digest your writings to give me insight in order to write a sequel to my post yesterday: “Simple Math-Geometry-And-Logic Render A Simple Model Of The Universe” https://81018.com/math/
Of course, I would be honored with even your cursory look and comments.
Most sincerely,
Bruce
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