**Edward Vladimirovich Frenkel**

Professor of Mathematics

University of California, Berkeley

(an expert on the Langlands programs)

Berkeley, California

**ArXiv**: https://arxiv.org/find/math/1/au:+Frenkel_E/0/1/0/all/0/1**Book: Love & Math ** A review by Alexandra Wolfe, Wall Street Journal

**CV**: https://math.berkeley.edu/sites/default/files/faculty/files/frenkel-biblio_0.

**Homepage:**http://www.edwardfrenkel.com

**Wikipedia**: https://en.wikipedia.org/wiki/Edward_Frenkel

**YouTube**: https://www.youtube.com/channel/UCpF6IVIBI-UpR2taxmogj0A

References to Edward Frenkel's work within these web pages:

- From the simplicity of pi to the complexity of E8 (April 2019)
- Reformulating Space, Time, and Infinity (December 2018)
- Fabric of the Universe (December 2017)
- Defining Forms from Plato to Langlands (November 2017)
- Before we can understand the complex (November 2017)
- This reference page: https://81018.com/2013/10/13/frenkel/

Most recent email: 6 April 2019

Dear Prof. Dr. Edward Frenkel:

Of three related articles, today’s has a reference to your work

and a link to our page about your work within our website which is:

https://81018.com/2013/10/13/frenkel/

These are the three related articles

https://81018.com/e8/ (Today, April 6. https://81018.com/e8/#EF )

https://81018.com/maybe/ (Wednesday, April 3)

https://81018.com/standard_model/ (Tuesday, April 2)

At some point in time, the evidence will become

compelling enough, our scholarly community will have to address it;

and at that time, perhaps Wheeler’s comments will become true:

“Behind it all is surely an idea so simple, so beautiful, that

when we grasp it — in a decade, a century, or a millennium —

we will all say to each other, how could it have been otherwise?”

Thanks.

Best wishes always,

Bruce

Second email: Wed, Nov 15, 2017 at 7:02 AM with small updates.

Dear Prof. Dr. Edward Frenkel,

Thank you for your acknowledgement back in October 2013.

Today, I am digging around through your ArXiv contributions.

Your work is consistently informative and inspirational. Thanks again.

Not being a mathematician or scholar, it has taken me a little time to realize that the domain we outlined with our base-2 notation from the Planck scale to the CERN-scale — that’s 64 notations — just might be a perfect place for the Langlands programs. It’s the same 64 doublings within the *Wheat & Chessboard* story. There’s plenty of room to build your case.

Each notation should be a domain for pure mathematics, number theory, geometry and all the functions in-between. I tried writing it up: https://81018.com/exponential-universe/

From notations 67 to 201, I would guess that all the infrastructure from each notation gets carried forward and all notations are active all the time. There is no past. We are within notation 202 today.

Just a bit idiosyncratic and probably a whole lot crazy, our chart of numbers is here: https://81018.com/chart/ I am slowly trying to interpret those numbers: https://81018.com/planck_universe/

Here’s my little chart from 2014 inspired by your first note: https://81018.com/chart2/ The first 60 notations are in groups of ten and are just wistful speculations.

I know that you have no time, but I also thought it was impolite of me to not respond to your note from four years ago. I just didn’t want to waste your time. Thanks.

Most sincerely,

Bruce

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

Bruce Camber

http://81018.com

Austin, Texas

PS. I have copied Prof. Dr. Robert Langlands. I had sent him a note to introduce this naive (high school) work not too long ago. Although he may not remember it, this copy might help to open a discussion. I am sure, like you, he is overwhelmed with email from all the idiosyncratic folks who have studied “not-quite enough” mathematics and physics to be helpful. And, of course, within such a small world, there are a lot of us! -B

First email: Sun, Oct 13, 2013 at 4:24 PM

Dear Prof. Dr. Edward Frenkel:

I was substituting for my nephew — “Teach them a little about the five platonic solids” — when we were observing how the tetrahedrons and octahedrons can endlessly enfold within each other and the question was asked, “How far within can we go?”

We divided each of the edges in half, connected the new vertices, and had the four half-sized tetrahedrons and an octahedron within the parent tetrahedron, and six octahedrons and eight tetrahedrons in the parent octahedron. We talked about tiling the universe, and then we did the simple math back to the Planck Length.

At that time we were not familiar with Kees Boeke’s work from 1957, or with Phil Morrison’s *Powers of Ten*, or Cary Huang’s *Scale of the Universe*. We were following geometries. We were dividing by 2. Our goal was the Planck scale.

At the 45th step within we were in the range of the size of a proton. In another 67 steps we were in the range of the Planck Length. “*Wow. That was interesting*,” I observed. We then started on the path out to the edges of the Observable Universe. Another 90-or-so steps, we were there.

So, what is this thing we just created? We went to the web and found very little. Our simple geometry and simple multiplication and division was just too simple. Or, is it?

I told the kids, now over 120 of them, we’ll find out! But, we are still searching!

Why is this little effort of so little interest to the professional mathematicians? It is a wonderful ordering system for information. Its inherent geometries — those five platonic solids — are just fascinating to see them embed so easily and readily within each other.

Of course, there is so much more to come, but perhaps our simple questions are quite enough for now.

Thank you.

Warmly,

Bruce Camber

an enthusiastic, new reader of your book, *Love & Math*

PS. The book will go to the school’s library when I finish and any math student will get extra credit for reading it, possibly upping their grade from a D to a C- for some! Hopefully the book will push it to an A+ for more.