**Karen Keskulla Uhlenbeck (KKU)**, Institute for Advanced Study, Princeton, NJ

Abel Prize 2019 (Norway’s Nobel Prize for Mathematics)**ArXiv**: *Responses to `Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics’, by A. Jaffe and F. Quinn*, with Michael Atiyah, G. J. Chaitin, Benoit B. Mandelbrot, Edward Witten and others (1994)**Celebration**: September 16, 2022 IAS recognized the collected work of KKU**Homepage**(s): **IAS** MacTutor Texas *Celebratio Mathematica*, inSPIRE^{HEP}, **Twitter**, **Wikipedia**

YouTube: Abel Math Prize Winner Truth & Beauty

Within this website: This page

Most recent and fourth email: 6 July 2022 at 4:32 PM

Dear Prof. Dr. Karen Uhlenbeck:

Have you ever seen a group of five-octahedrons and the 7.35+ degree gap that is created? It is the same gap created by the five tetrahedrons so it can create a very interesting stack. What are its natural functions within geometry? Could part of an icosahedron made with tetrahedrons be substituted for the five tetrahedrons?

My first picture of a five-tetrahedron, five-octahedron, five-tetrahedron stack is here: https://81018.com/15-2/ My initial analysis: https://81018.com/geometries/

I do not believe this group has been seen heretofore. Is it of any value to you? Thanks.

Warmly,

Bruce

PS. I’ve added links to the IAS celebration of your 80th birthday. Very special. Also, there is now a link to *Celebratio Mathematica *within our online profile of you. -BEC

Third email: 20 April 2022 @ 8:09 PM

Dear Prof. Dr. Karen Uhlenbeck:

Sixteen years ago Edward Witten and Anton Kapustin published within ArXiv an ambitious projection for the future, *Electric-Magnetic Duality And The Geometric Langlands Program*.

There was some hope that a real bridge could be built between Langlands and string and M-theory.

But, first, we should be asking, “Is there a bridge to the Planck scale? Is there a bridge to pi? …to all the dimensionless constants?”

That Langlands and our strings have been floating for over 50 years should be a red light flashing and blaring, “You are on the wrong track!” So, I asked 12 questions.

Could you help me to sharpen these questions?

Thank you.

Most sincerely,

Bruce

Second email: Wednesday, April 14, 2021, 4:45 PM (Updated a little)

Dear Prof. Dr. Karen Uhlenbeck,

The transition from your mappings of a surface to the circle from bubbles may seem quite natural. Both Wheeler and Denis Weaire are with you, but the high school kids liked the idea of a sphere that could not be divided any further. Our spheres were more simple than the preon or instanton or … Up until recently we rather confidently thought our sphere was defined by Planck’s base units. Frank Wilczek, among others, gave us some assurance that Planck’s constant was properly defined. Today, that’s being challenged so we no longer harbor our earlier confidence.

We are more attracted to Kepler’s simplicity and the concept of cubic close packing of equal spheres. It was there that we learned how the tetrahedron and octahedron could be created by these scale-invariant, infinitesimal spheres.

That was a special day.

We were then attracted to combinatorial geometry and that is a possible direction for some of our students. We also decided that *quantum geometry* is another direction for others. “Be open to it all.” We actually created models with the tetrahedral gap for the dodecahedron (pentakis) and icosahedron and called it “squishy geometry” because there were so many gaps.

Of course, in our simplicity we thought of quantum fluctuations and even charted consciousness along that grid and allowed for “ontological fluctuations.” We are so idiosyncratic and quite desperate for help.

So, I said when I read your response, “I’ve got to do a little more homework right now… to see if there are connections to those 18 Uhlenbeck entries in ArXiv. I’ve got a long way to go but I am committed to work through all 18!

You are working on rarefied connections discerned over a lifetime of study. We are just trying to understand the most simple connections we can see.

If I get any clues to be able to communicate better to somebody as key to mathematics as you are, I’ll send it along otherwise I’ll not bother you again. Thanks again for the wake up!

Grace & peace,

Bruce *

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

Bruce E. Camber

First email: Tuesday, 13 April 2021 at 10:30 AM (Updated a little)

Dear Prof. Dr. Karen Uhlenbeck,

Can anything good come out of work within a high school? Certainly, it would be quite naive and filled with many gaps, but just maybe with a bit of coaching…

We were studying the tetrahedron — https://81018.com/tot/ — and the octahedron within it. We could not find any references to the four hexagonal plates within that octahedron. I had asked John Conway about them in and around May 2001. It was a busy day in Princeton and that discussion didn’t get enough attention.

December 19, 2011, New Orleans: It wasn’t until my few days with the kids in high school that we did a three-dimensional Zeno walk down inside the tetrahedron and octahedron. We didn’t know that we were blazing a new trail. Dividing the edges by 2, connecting the next vertices, down inside we went. It was like a rabbit hole, that became a wormhole, and then an infinitesimal, ever-smaller path within…

After getting comfortable with the concepts, we went all the way down into Planck’s scale and then out to the age of the universe following the doublings of Planck Time and Length. It mapped out: https://81018.com/chart/ There were just 202 base-2 notations from the start until Now!

Now that was five years ago (2016). Now what do we do? We were splashing pages all over the web so collected them in one place: https://81018.com The homepage is always our latest stab in the dark.

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 answer our plead for a little guidance from somebody with the fewest number of gaps in this walk between physics and math. Thank you, thank you.

Warmly,

Bruce

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

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**:

__________