Engquist, Björn

Björn Engquist

The University of Texas at Austin
201 E. 24th Street, 1 University Station, Austin, Texas 78712-1229

ArXivNumerical methods for multiscale inverse problems (January 2014)
YouTube: Basis in Information Theory

References within this website:
This page is https://81018.com/2019/04/18/engquist/

First email: 18 April 2019

Dear Prof. Dr. Björn Engquist:

Not being a scholar or expert, I am still fascinated with your work to define the development of absorbing boundary conditions.

We began our work in a high school geometry class where we were observing how an octahedron is in the center of a tetrahedron with half-sized tetrahedrons in each corner. Within the octahedron, there is a half-sized octahedron in each of the six corners and a tetrahedron in each of the eight faces all sharing the centerpoint.

We decided to do a Zeno-like progression and applied base-2 going back deeper and deeper inside. In 45 steps we were in the range of particle physics, and in another 67 steps we were in the range of Planck’s base units.

We then decided to multiply by 2 and in 90 steps we were in the range of the age and size of the universe.

For high school people, it was great fun. We encapsulated the universe in 202 steps. We only then found Kees Boeke’s work and began thinking of the differences between base-10 and base-2.

I suspect that you are one of the few people on earth who has thought very deeply about computational multi-scale methods. Might you advise us? Are we being illogical? Are we doing something wrong? Thank you.

Most sincerely,

Links above:

Current research:

Nima Arkani-Hamed says, “Spacetime is doomed.”

From an October 2017 homepage:

Nima Arkani-Hamed1 of the Institute for Advanced Studies in Princeton, with a sweeping naturalness, proclaims “Spacetime is doomed2 (go to 5:45 minutes of 1.22.44). A little yo-yo like3, his really-real reality is within his ever-so-illusive amplituhedron4 with a string to a planar N.5 He declares that it’s equal to the perturbative topological B-model string theory in twistor space6 (an ever-so-positive Grassmannian7)   (related ArXiv article).

To which I reply, “Yes, of course. We knew that.”

1 The first link goes to our correspondence (mostly emails) to Nima Arkani-Hamed. He has also received a few tweets as well.

2 Spacetime is doomed is a YouTube video. If you go to 5:45 minutes of his 1 hour 22 minute lecture, you will hear that indeed, spacetime is doomed. The entire lecture is his focus on this concept.

3 Yo-Yo-Man is our affectionate name for Nima.  Although Tommy Smothers claimed the name for antics with a yo-yo and there is a wonderful cellist by the name of Yo Yo Ma, Nima got the nickname from his pacing back and forth when he gives a lecture.

4 The amplituhedron has a special place within our work.  It was one of many basic structures and by no means is the most basic.  The transformations between circles and spheres to lines and tetrahedra and then octahedra are.

We knew that:

5  The N=4 supersymmetric Yang–Mills theory within Wikipedia is entirely readable, but not easily understood.

6 Twistor space

7 Grassmannian

Torquato, Salvatore

Salvatore Torquato

Lewis Bernard Professor of Natural Sciences
Princeton Institute for the Science and Technology of Materials
Princeton, New Jersey

Articles: ArXiv (149): The structure factor of primes (2018), Hyperuniform States of Matter (2018)
Google Scholar
Group Homepage
YouTube: Hyperuniformity in many-particle systems and its generalizations

First email: Mar 10, 2014, 8:54 PM
1. Thank you: http://www.pnas.org/content/108/27/11009.abstract?sid=a37de813-198f-4f81-9641-ad2025190fd7
2. Beautiful: http://chemlabs.princeton.edu/torquato/research/maximally-dense-packings/
3. Hypostatic Jammed Packings (2006): http://pi.math.cornell.edu/~connelly/Hypostatic.pdf

Dear Prof. Dr. Salvatore Torquato:

Thank you, thank you, thank you for your work (referenced just above).

Back in 2002 I spent a very pleasant day with John Conway but he did accuse me of being hung up on the relation between the tetrahedron and octahedron. For more I’ll copy in part of the story below. Though I am late to discover your July 5, 2011 paper, I was so glad to discover it today. It adds fuel to the fire and opened the door to your work.

I am so glad to meet you through your writings. I have already inserted references to your work in two articles (referenced below).

After spending a bit more time with your writing, may I call you?

Thank you.



PS. I’ve been working with clear plastic models — made the molds and made thousands of octahedrons and tetrahedrons — to delve into the issues of fragmentation and wholeness. David Bohm’s book by that title, has a prominent place in my library.

Our references about which you might be interested:

Here is what I said about John Conway:

“An earlier history began with the study of perfected states in space time.
Sometime around 2002, at Princeton with geometer, John Conway, the discussion focused on the work of David Bohm, once a physicist from Birbeck College, University of London. “What is a point? What is a line? What is a plane vis-a-vis the triangle? What is a tetrahedron?” Bohm’s book, Fragmentation & Wholeness, raised key questions about the nature of structure and thought. It occurred to me that I did not know what was perfectly and most simply enclosed by the tetrahedron. What were its most simple number of internal parts? Of course, John Conway, was amused by my simplicity. We talked about the four tetrahedrons and the octahedron in the center.

“I said, ‘We all should know these things as easily as we know 2 times 2. The kids should be playing with tetrahedrons and octahedrons, not just blocks.’

“What is most simply and perfectly enclosed within the octahedron?” There are six octahedrons in each corner and the eight tetrahedrons within each face. Known by many, it was not in our geometry textbook. Professor Conway asked, “Now, why are you so hung up on the octahedron?” Of course, I was at the beginning of this discovery process, talking to a person who had studied and developed conceptual richness throughout his lifetime. I was taking baby steps, and was still surprised and delighted to find so much within both objects. Also, at that time I had asked thousands of professionals — teachers, including geometry teachers, architects, biologists, and chemists — and no one knew the answer that John Conway so easily articulated. It was not long thereafter that we began discovering communities of people in virtually every academic discipline who easily knew that answer and were shaping new discussions about facets of geometry we never imagined existed.

“Of course, I blamed myself for getting hung up on the two most simple structures… “You’re just too simple and easily get hung up on simple things.”