TO: Yair Shenfeld, Brown University, Providence, RI USA
FM: Bruce E. Camber
RE: Your homepage(s), including at Brown, your CV, your many publications, especially your ArXiv files and your slides!
This page: https://81018.com/shenfeld/
Second email: November 8, 2023
Dear Prof. Dr. Yair Shenfeld:
I was an acquaintance of Philip Davis for many years. https://81018.com/philip_davis/ Recently I wrote about his sense of a fundamental starting point:
Philip Davis, once of NIST and Brown University, had been asking that question for generations. He assumes there is “something” more fundamental than particles and waves. In mathematics it includes equations, dimensionless constants, natural numbers, geometries, and so much more. The question persists, “What is the most simple building block that is within everything, everywhere for all time?”
Would you make any changes? Do you think it is a fair representation of his thinking?
Thank you.
Warmly,
https://81018.com/bec/
Austin, Boston, Winter Park
First email: September 7, 2022 at 7:38 PM
Dear Prof. Dr. Yair Shenfeld:
Might a most simple geometry be involved with the Brownian transport map? My intuition says, “Maybe. It’s worth checking out.”
1. Five tetrahedrons. Are you aware of the 7.35610+ degree gap created by five tetrahedrons sharing a common center point? Aristotle missed it. Mysteries in Packing Regular Tetrahedra is an unusual history (PDF), but it is usually forgotten and is relatively unrecognized even though in 2015 the AMS gave the Conant award to the authors.*
2. Five octahedrons. More recently in May 2022 we became aware of the same gap using five octahedrons: https://81018.com/2022/05/19/five/#Gap. This simple geometric figure consists of five octahedrons, all sharing a centerpoint (three sharing two faces with another octahedron and two sharing only one face). It is relatively unknown and undocumented.
3. A Stack. An interesting image is when the five-tetrahedrons are added on the top and bottom. That stack has 15 objects sharing the centerpoint. Interactive geometry software (IGS) with their dynamic geometry environments (DGEs) do not easily re-create this geometry. None of the kits like Zometool can. This simple geometry requires true physical models.
I took the picture of those pages in June but to date it appears that there is no scholarship about it. Have you seen any scholarly analysis of it? Do you think it is important? My intuition is telling me it is related to quantum fluctuations. If so, then it is huge and it will become a major part of scholarship. Thank you.
Bruce
* Key parts of this history came from an MIT professor of mathematics, Dirk Jan Struik from his work, Het Probleem ‘De impletione loci’ (Dutch), Nieuw Archief voor Wiskunde, Series 2, 15 (1925–1928), no. 3, 121–137 (translation)
https://81018.com/analysis/ reinforces the conclusion that “Worldviews limit perspective” and “A mathematically-integrated view of the Universe does not.” -BEC