Frankel, Edward

Edward Frankel
Professor of Mathematics
University of California, Berkeley

Book: Love & Math     Review by Alexandra Wolfe, Wall Street Journal

Most recent email: Wed, Nov 15, 2017 at 7:02 AM

Dear Edward,

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 67 notations –is a perfect place for the Langlands
programs. It’s the 64 doublings within the Wheat & Chessboard story all over
again with a few steps to spare. There’s plenty of room to build a case.

Each notation should be a domain for pure mathematics, number theory,
geometry and all the functions in-between.
I am slowly writing it up:

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:
I am slowly trying to interpret those numbers:
Here’s my little chart from 2014 inspired by your first note:
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 Camber
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. 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 in 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 with 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, and Phil Morrison’s Powers of Ten, and Cary Huang’s Scale of the Universe. We were following geometries. We were dividing by 2. Our goal was the Planck scale. Our model was a wholly-different-other.

At 45 steps within we were in the range of the size of a proton. Another 67 steps were 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.


Bruce Camber
an enthusiastic, new reader of “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+ and more.

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