Martin R. Bridson, Mathematics Institute, Andrew Wiles Building

Oxford University, Oxford, England

Clay Mathematics Institute, Peterborough, New Hampshire

ArXiv (81): *On the profinite rigidity of triangle groups* (April 2020), *The homology of groups*… (2019), *Subgroup separability in residually free groups* (2007), and others

Book: *Metric Spaces of Non-positive Curvature*, published by Springer-Verlag, 1999

CV (PDF)

Google Scholar

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Wikipedia

YouTube: International Centre for Theoretical Sciences, Part II

Third email: July 12, 2021 at 6 PM RE: Lighting fires

Dear Prof. Dr. Martin Bridson:

My last note in July 2020 has been summarized as a web page: https://81018.com/conference/

Also, my notes to you and my references to your work are here: https://81018.com/bridson/

Again I make a case to use base-2 to parse time from the most infinitesimal scale (conceptually defined by calculations like those of Max Planck and George Johnston Stoney) to the current time. We know there are 202 notations. We know that quantum fluctuations and the wave-particle duality begin after Notation-64 (between Notations 65-and-67). First, what is going on between Notation 1-and-64? Is it a domain for M-theory, Langlands programs, and all the infinitesimal, mathematically-defined, theoretical particles? …what else? …geometric group theory?

If the first manifestation within space and time is a sphere, the Lagarias-Chong work has value to begin to discern how this universe took shape. Packing densities are a fact, a detail. The dynamics of cubic close packing of equal spheres and the generation of the five platonic solids is key. The dynamics of the sphere with the Fourier and integral transforms is key. The grasp of autonomic forms is a key.

With the advent of tools for relatively large virtual meetings, theoretically a subject could be announced and “flash mob” spontaneous emerge within virtual meetings that focus on key open questions. If 100 are invited, would five show up? Might that group make decisions or stimulate new insights? Why not try?

Just a few questions for a Monday late afternoon here in Nashville. Thank you.

Warmly,

Bruce

Second email: Jun 1, 9:27 AMUpdated/resent:July 20, 2020

RE: Continuity-symmetry-harmony becomes a sphere becomes geometry becomes finite

Dear Prof. Dr. Martin Bridson:

Again, I thank you for your support of the work by Jeffrey Lagarias and Chuanming Chong. I believe their work has been under-valued within academic studies. I am not referring to their interests in packing densities; that has been addressed by many since Kepler. The more important question, it seems, is the very nature of the infinitesimal scale and that 7.35+ degree gap that is created by the geometry of five tetrahedrons sharing a common edge.

Does this gap have anything to do with quantum fluctuations? Is this the geometric gap that Aristotle did not see and scholars missed for over 1800 years? Does it hold key insights about the indeterminate and the nature of chaos, unpredictability, undecidability and uncomputability?

Beyond the origin of fluctuations, could these geometries within the infinitesimal between the Planck scale and particle-and-wave duality, also create the conditions for the unique identity of everything-everywhere, including consciousness and creativity?

To create space for such an analysis is a straight-forward exercise if we assume that Planck Time and Planck Length are the first units of time. If we apply base-2 or simple doublings of these numbers, we create a modest but fascinating grid from the first moment of time to this very day. There are 202 notations and the first 64 notations are below our current thresholds of measurement. Yet, logically and mathematically, those 64 notations have potential to provide new insights and answers to persistent questions.

Perhaps a seminar of leading scholars addressing this configuration and the question about the relation of geometries to fluctuations would gather some attention and may render fascinating results that could substantially impact both mathematics and physics.

**I’ve begun mapping an overview of such a seminar**. Even today, David J. Gross, Stephen Weinberg, Lee Glashow, Anthony Zichichi and a few others of their caliber and age might like to attend and/or contribute.

Thanks again for taking time with me.

Most sincerely,

Bruce

`First email: May 31, 2020 at 5:28 PM`

Dear Prof. Dr. Martin Bridson:

In 2012 Jeffrey Lagarias and Chuanming Zong wrote, *Mysteries in Packing Regular Tetrahedra* (PDF). In April 2015 his Clay Fellow Senior Talk, *Packing Space with Regular Tetrahedra*, was a natural sequel.* *There are elements of those analyses that need a deeper review; i.e. what is that gap created by the five tetrahedrons? Where does it first manifest? Does it have anything to do with quantum fluctuations within the Planck scale?”

Perhaps CMI might entertain such a sequel. I have written to Brendan Hassett, Clifford Taubes, Simon Donaldson and Arthur Jaffe to suggest further examinations of this gap. I also believe that Robert Langlands and Edward Witten would have insights.

Might these questions be worth pursuing? Thank you.

Most sincerely,

Bruce

PS. A link to that 2015 Clay ICERM lecture is here.