On discovering the work of Kirsten Wickelgren

TO: Kirsten Wickelgren, Department of Mathematics,
Trinity College of Arts & Sciences, Duke University, Durham, NC USA
FM: Bruce E. Camber
RE: Your articles in ArXiv (29) especially Massey products (2016); your homepage(s), your other publications, and your CV. Even your Wikipedia entry is helpful.

Fourth email: 17 October 2025

FYI:

Third email: 24 March 2025 (updated)

Dear Prof. Dr. Kirsten Wickelgren:

I am not sure you would find this very germane, but I have been asking Grok about our speculative geometries within the octahedron. The feedback has been encouraging. Besides discovering the gaps, we have been pondering these four hexagonal plates that are intrinsic to the octahedron. In 2001 I asked John Conway (Princeton) about them. He had been unaware of those plates!

My intuition is that they are related to the four primary irrational numbers. On March 4, Grok concurred that there are excellent relations to the sphere for all four. And, within the octahedral setting, there are very interesting possible relations to the four hexagonal plates.

Do you have any interest in the relation between the four primary irrationals?

Thank you.

Sincerely,

Bruce

Second email: 5 July 2024

Dear Prof. Dr. Kirsten Wickelgren:

Over a year ago, I sent a note about an octahedral gap that appears to have been overlooked by our scholars. Although it’s a bit off your beaten path, I thought you might know of somebody who had done a study of it.

Today, I noticed in the logs that our page about your work had been visited a couple of times today so reviewed it and made a few updates. If you ever want anything added or deleted, please let me know and it will be accommodated. Thank you.

Warmly,

Bruce

PS. Also, if you know of any scholar who has done a base-2 expansion of the Planck natural units, I would be very, very grateful. Thanks again. -BEC

First email: Apr 21, 2023, 4:33 PM

Dear Prof. Dr. Kirsten Wickelgren:

Your CV includes the 2012 work on Grothendieck’s Anabelian Conjectures (The Harvard College Mathematics Review). Impressive. Your Wikipedia page is also most impressive. Of course, Duke is a great place to be!  And, you are to be a speaker in Paris at the GAP 2023 — Homotopy Algebras and Higher Structures. Congratulations on creating great foundations. 

Even though I am just a visitor to your work from among the great unwashed, given your history, I hope that I can ask a few basic questions:

1. Have you ever seen the five-tetrahedral gap (famously missed by Aristotle and documented by Lagarias and Zong, AMS-2015 Conant Award) over and under a five-octahedral gap? It’s a pretty object, but I don’t think there is anybody else who has written about it. Do you think it could be important?

2. Do you know if there are any scholars who have written about the nature of these gaps? How do such gaps manifest within space and time? These questions are part of my trek as an occasional high school geometry  teacher and my walk with the students inside a tetrahedral-octahedral complex. It is a sweet story. In just 45 base-2 steps we were within the fermions. With another 67 steps we were within the Planck scale. Going out larger, in 90 steps we were at the current time and estimated size of the universe. It is a challenging outline! Of course, your comments about it all would be highly valued. Thank you.

Most sincerely,

Bruce

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