
TO: John Lane Bell, University of Western Ontario (emeritus), London, Ontario Canada
FM: Bruce E. Camber
RE: Your ArXiv especially Cover Schemes, Frame-Valued Sets and Their Potential Uses in Spacetime Physics (2003); Reference by D Perlis: Taking physical infinity seriously(2016); Michael O’Connor, An Introduction to Smooth Infinitesimal Analysis (2008); Homepage(s): Wikipedia, Youtube: Lecture at Ecole Normale Superieure, May 2007
A sample of articles:
- The Continuous, the Discrete, and the Infinitesimal in Philosophy and Mathematics, Springer, 2019
- Oppositions and Paradoxes: Philosophical Perplexities in Science and Mathematics. Broadview Press, 2016
- Intuitionistic Set Theory. College Publications, 2013.
- Set Theory: Boolean-Valued Models and Independence Proofs. Oxford University Press 2011
- The Axiom of Choice. College Publications, 2009.
- The Continuous and the Infinitesimal in Mathematics and Philosophy, Polimetrica, 2005
- (With D. DeVidi and G. Solomon) Logical Options: An Introduction to Classical and Alternative Logics. Broadview Press, 2001.
- The Art of the Intelligible: An Elementary Survey of Mathematics in its Conceptual Development. Kluwer, 1999.
- A Primer of Infinitesimal Analysis. Cambridge University Press, 1998. Second Edition, 2008.
- Toposes & Local Set Theories: An Introduction. Clarendon Press, Oxford, 1988.[2] Reprinted by Dover, 2008.
A sampling of books:
- Higher-Order Logic and Type Theory, Cambridge Elements, Cambridge University Press, 2022
- The Continuous, the Discrete, and the Infinitesimal in Philosophy and Mathematics (New and Revised Edition of 8), Springer, 2019.
- Oppositions and Paradoxes: Philosophical Perplexities in Science and Mathematics, Broadview Press, 2016.
- Intuitionistic Set Theory. College Publications, 2014.
- Perpetual Motion: The Making of a Mathematical Logician. Llumina Press, 2010.
- The Axiom of Choice. Front Matter. College Publications, 2009.
- The Continuous and the Infinitesimal in Mathematics and Philosophy. Polimetrica, 2005.
- The Art of the Intelligible: An Elementary Survey of Mathematics in its Conceptual Development. Kluwer, 1999.
- A Primer of Infinitesimal Analysis. Cambridge University Press, 1998. Second Edition, 2008. Review by W.A. J. Luxemburg.
- Toposes & Local Set Theories: An Introduction. Clarendon Press, Oxford, 1988. Reprinted by Dover, 2008. Reviews (?) thereof.
- Boolean-Valued Models and Independence Proofs in Set Theory. Clarendon Press, Oxford, 1977. 2nd edition, 1985. 3rd edition, 2005. Paperback edition, 2011.
- Appearing within this website: Intuition https://81018.com/intuition/
This page is: https://81018.com/2022/06/20/bell/
Fourth email: 16 October 2025
Dear Professor Emeritus Dr. John Lane Bell:
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
PS. Our study of your work is here: https://81018.com/2022/06/20/bell/
_______________
Bruce Camber
- https://81018.com/
- https://81018.com/assume/
- https://81018.com/deepseek
- https://81018.com/hubble-derivation/
- https://81018.com/planck-polyhedral-core/
- Lagrangian: https://81018.com/lagrangian/
- https://81018.com/testable/
- https://81018.com/testable-ai/
Third email: 13 March 2024
Questions: Is basic continuity an artifact of pi (π)? … symmetry and harmony (Fourier) as well? We’ve been ignoring our most basic-and-simple math and geometry. Now observations do not match theory: JWST galaxies within 300 million years? Big bang theory is in the way. We have not been clear about absolute space and time (1687 – Newton) versus the Now. And, Aristotle missed most basic gaps in geometry.
Dear Prof. Dr. John Lane Bell:
You might appreciate a different path around pi (π): https://81018.com/2024-piday
Within the Critique on that page, there are links to four related pages. We’ve been wrong too long. Perhaps “more simple” is better.
Thanks.
Warmly,
Bruce
PS. I been following you and many of your colleagues for years! -BEC
Second email: 21 June 2022 at 1:16 PM
Dear Prof. Dr. John Lane Bell:
In 2011 we followed Zeno down into a tetrahedron (and its octahedron) by dividing the edges by 2 and connecting the new vertices. It creates a rather unique path down into particle physics in about 45 steps and down to the Planck base units in another 67 steps.
That’s simple geometry. When we multiplied by 2, we found just 90 additional steps to the approximate age and size of the universe. No mystery. Boeke did a base-10 version in 1957 with his high school class.
We thought it was a great little STEM tool: 202 notations to see the universe as an integrated whole. Naiveté can be invigorating at first, then it becomes confusing within its own idiosyncrasies:
1. It was more simple than big bang phenomenology.
2. It had 67 notations that had never been explored per se. Here the infinitesimal is truly outlined.
Is our logic so naive, it would be too much trouble to just slap it down? You’ve only got a couple of years on me. At this stage in our life, you can be brutal!
Thanks so much.
Warmly,
Bruce
PS. Embedded links above:
1. STEM: https://81018.com/stem/
2. 202 Notations: https://81018.com/chart/
Other references:
1. Our page about your work: https://81018.com/2022/06/20/bell/
2. Tetrahedron: https://81018.com/tot-2/
3. Boeke: https://81018.com/Boeke/
Thanks. -BEC
First email: Monday, September 4, 2017, 2:27 PM
https://plato.stanford.edu/entries/continuity/
http://publish.uwo.ca/~jbell/
Dear Prof. Dr. John Lane Bell:
I thank you again and again for your body of work and the work of your doctoral students (now professors) who studied with you.
Our work is focused on base-2 notation from the Planck units, out to Observable Universe and the Age of the Universe in 202 notations: http://81018.com. Chart of numbers: http://81018.com/chart
We are entirely idiosyncratic, often naive, yet hopefully open to learning as much as we can about why we are wrong, and, if by chance, why we are right.
Thanks again for all your work so germane to our discussions.
Warmly,
Bruce
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