**Natalie M. Paquette**, Institute for Advanced Studies, Princeton, New Jersey

Articles: String Theoretic Illuminations of Moonshine, Wednesday, January 15, 2020

• A View from the Bridge, Inference (magazine), 2018

ArXiv

Homepage: Also at IAS

inSPIRE^{HEP}

YouTube: The Unreasonable Effectiveness of Physics in Mathematics, Stanford, 2017

Within this website: https://81018.com/15-2/

Second email: Friday, July 8, 2022 at 5:43 PM

Dear Prof. Dr. Natalie Paquette:

I share your appreciation of Eugene Wigner‘s *Unreasonable Effectiveness*… along with Tegmark and so many others. Quick question: Have you ever seen the five-octahedral gap? It is a little like the five-tetrahedral gap that Aristotle failed to observe. You may have seen reports. It was replicated by many for over 1800 years, and little discussed for another 500 years. In none of these studies, especially the Lagarias-Zong article (PDF), it doesn’t mention octahedra.

I am not finding any specific references to the five-octahedral gap anywhere! Perhaps it goes by another name. It has the same 7.35610+ degree gap created by five tetrahedrons. Taken together, I believe the gaps are significant and attractive! Here is my best image of the gaps to date!

Of course, the twenty-tetrahedral icosahedron also has significant gaps. Any five tetrahedrons of the twenty fit nicely on top or under the five-octahedral gap. It is a very different gap, yet makes for a most-fascinating stack (infinitesimal spindle) and complexity. It is a challenge.

Currently, I envision this tetrahedral-octahedral generation as part of the dynamics of the first ten base-2 notations (within the 202 that encapsulate the universe — everything-everywhere-for-all-time). Perhaps here may be a hypergeometric* as well as* *hypogeometric* series and a very different start of automorphic forms… all conjectures and very simple geometries. Thank you.

Warmly,

Bruce

First email: Tuesday, April 13, 2021 at 5:08 PM

Dear Prof. Dr. Natalie Paquette:

We are so far removed from your flux vacua and F24 SCFT, I can only hope that you have a moment for a few naive questions?

Our work started within the unique naïveté of a high school geometry class. We were studying the tetrahedron — https://81018.com/tot/ — and the octahedron within it. We could not find references to the four hexagonal plates within that octahedron so on a visit with John Conway, I asked a few questions. It was a busy day in Princeton and that discussion didn’t get enough attention.

December 19, 2011, New Orleans: I had a few days with the kids in a high school where we did a three-dimensional Zeno walk down inside the tetrahedron and octahedron. We didn’t know we were blazing a new trail. Getting infinitesimally ever-so-much-smaller, we went all the way down to Planck’s scale and then out to the age of the universe following the doublings of Planck Time and Length. It mapped out nicely: https://81018.com/chart/ There were just 202 base-2 notations from the first moment to Now!

What do we do it? We had posted pages all over the web so in 2016 I started collecting them in one place: https://81018.com

The homepage is usually our latest query. If you do not have time to go to those pages, might you consider the questions just below that are on the homepage today? Your answers would be very helpful as we try to continue our walk between physics and math. Thank you, thank you.

Most sincerely,

Bruce

************************

Bruce E. Camber

http://81018.com

Questions:

1. Might there be fundamental units of length and time, as well as mass and charge (similar to, but more accurate than, the Planck base units), that are among the parameters that define the first moment or instant of the universe?**Answer**: Yes | No | Maybe**Comment**:

____________

2. Might an infinitesimal sphere be a first manifestation of such base units?**Answer**: Yes | No | Maybe**Comment**:^{____________}

3. Might sphere stacking and cubic-close-packing of equal spheres be among the first functional activities to define the universe?**Answer**: Yes | No | Maybe**Comment**:_{____________}

4. Might the rate by which spheres emerge be determined by a fundamental unit of time which would be one sphere per unit of a fundamental length? For example, we used Planck Time. That computes to 539.116 tredecillion spheres per second given the value of Planck Time is 5.39116(13)×10^{-44} seconds.**Answer**: Yes | No | Maybe**Comment**:^{____________}

5. Might base-2 notation be applied to create an ordering schema for these spheres? If that fundamental unit of time were Planck Time, approximately 436,117,076,900,000,000 seconds would pass to get to the current time which would be within the 202nd doubling (base-2).**Answer**: Yes | No | Maybe**Comment:**^{____________}

6. Might there be a range of perfection from the earliest notations and prior to any kind of quantum fluctuation, be it ontological or physical?**Answer**: Yes | No | Maybe**Comment**:

____________

7. Might these spheres:

___(a) be defined by continuity-symmetry-harmony (which redefines infinity)?

___**Answer**: Yes | No | Maybe **Comment**:

___(b) …become the basis to define the aether?

___**Answer**: Yes | No | Maybe **Comment**:

___(c) …be the reason for homogeneity and isotropy?

___**Answer**: Yes | No | Maybe **Comment**:

___(d) …and, be the essence of dark matter and dark energy?

___**Answer**: Yes | No | Maybe **Comment**:

____________

8. Might you be open to receive another eight questions about foundational concepts no sooner than eight months from today?**Answer**: Yes | No | Maybe**Comment**:

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# String Theoretic Illuminations of Moonshine

Natalie Paquette, Wednesday, January 15, 2020

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