Zong, Chuanming

Chuanming Zong

Tianjin Center for Applied Mathematics (TCAM)
Tianjin, China

Articles: Mysteries in Packing Regular Tetrahedra (PDF)
• “The kissing number, blocking number and covering number of a convex body”, in Goodman, Pach, Pollack (eds.), Surveys on Discrete and Computational Geometry: Twenty Years Later (AMS-IMS-SIAM Joint Summer Research Conference, June 2006, Snowbird, Utah), Contemporary Mathematics, 453, Providence, RI: American Mathematical Society, pp. 529–548, doi:10.1090/conm/453/08812, 2008
ArXiv (19): On Lattice Coverings by Simplices, 2015 (PDF)
Award: 2015 AMS Levi L. Conant Prize
Books: Sphere packings, Springer, 1999
The Cube-A Window to Convex and Discrete Geometry, 2009
Mathematics Genealogy Project
Wikipedia: Keller’s conjecture, H. F. Blichfeldt, Kissing Number

References within this website to your work:
May 26, 2020: https://81018.com/duped/#R3-2
May 5, 2020: https://81018.com/duped/#Aristotle
_______________ https://81018.com/duped/#1b
April 2020: https://81018.com/fqxi-aristotle/
March 2020: https://81018.com/imperfection/
October 2018: https://81018.com/realization6/
January 2016: https://81018.com/number/#En7

Third email: Wednesday, May 28, 2020

Dear Prof. Dr. Chuanming Zong:

First, let me congratulate you on your new location. Wonderful. It appears that you are still within 100 miles of Beijing. That’s excellent.

I am still quoting you after all these years (see above). Because the citations were getting so numerous, I created references page for you and Prof. J. Lagarias. My page for you: https://81018.com/2020/05/28/zong/

In these days and times, my most important conclusion is here about all our work, collectively and individually: https://81018.com/duped/#R3-2 Of course, if you would like anything changed, deleted, or added, I will be glad to accommodate your request.  Thank you.

Warm regards,


Second email: Wednesday, January 8, 2014

Your paper is sensational.
It is exactly what I needed to be assured that Frank-Kaspers
and many others were not leading us astray. 

Your mathematics and analysis are spot on.

Let me share my reasons for my enthusiasm below this note to you. Thanks.


PS. Your work helps us with #2 and #4 below:

1.  The universe is mathematically very small.
Using  base-2 exponential notation from the Planck Length
to the Observable Universe, there are somewhere over 202.34
and under 205.11 notations, steps or doublings.  NASA’s Joe Kolecki
helped us with the first calculation and JP Luminet (Paris Observatory)
with the second. Our  work began in our high school geometry
classes when we started with a tetrahedron and divided the edges
by 2 finding the octahedron in the  middle  and four tetrahedrons
in each corner.  Then dividing the octahedron we found
the eight tetrahedron in each face and the six octahedron
in each corner.  We kept going inside until we found the Planck Length.
We then multiplied by 2 out to the Observable Universe.  Then it
was easy to standardize the measurements by just multiplying
the Planck Length by 2.  In 202 notations we go from the smallest to the largest possible measurements of a length.

2.  The very small scale universe is an amazingly complex place.
Assuming the Planck Length is a singularity of one vertex, we also
noted the expansion of vertices.  By the 60th notation, of course, there are
over a quintillion vertices and at 61st notation well over 3 quintillion more
vertices.  Yet, it must start most simply and here we believe the work
within cellular automaton and the principles of computational equivalence
could have a great impact. The mathematics of the most simple is being
done.  We also believe A.N. Whitehead’s point-free geometries should
have applicability. 

3.  This little universe is readily tiled by the simplest structures.

The universe can be simply and readily tiled with the four hexagonal plates
within the octahedron and by the tetrahedral-octahedral-tetrahedral chains.

4. And, the universe is delightfully imperfect.
In 1959, Frank/Kaspers discerned the 7.38 degree gap with a simple
construction of five tetrahedrons (seven vertices)  looking a lot like the Chrysler logo. We have several icosahedron models with its  20 tetrahedrons and call squishy geometry.  We also call it quantum geometry (in our high school). Perhaps here is the opening to randomness.

5. The Planck Length as the next big thing.
Within computational automata we might just find the early rules
that generate the infrastructures for things. The fermion and proton
do not show up until the 66th notation or doubling.

I could go on, but let’s see if these statements are interesting
to you in any sense of the word.  -BEC

 First email: Fri, Aug 30, 2013, 7:19 PM

Just a terrific job. A wonderful read.
Thank you.

Coming up on two years now, we still do not know what to do with a simple little construct: https://81018.com/2014/05/21/propaedeutics/

That five-tetrahedral construct plays a key role.

Your work gives me a wider and deeper perspective.




Georgi, Howard

GeorgiHoward Georgi

Mallinckrodt Professor of Physics
Harvard University
Leverett House, 28 DeWolfe St.
Cambridge, Massachusetts

Articles: Why Unify? (Nature, v.288, pages 649–651, 1980)
ArXiv (51): Unparticle Physics (May 2007) Wiki
Books: Lie Algebras In Particle Physics (Westview, 1999) (CRC Taylor & Francis, 2018) (PDF)
Wikipedia: Unparticle Physics

Most recent email: Tuesday, March 17, 2020 (Rewrite: 19 May 2016)

Dear Prof. Dr. Howard Georgi:

Your work on Unparticle Physics has finally come to my attention so my studies of your work are still quite young. I apologize in advance for my lack depth.

In and around 1979 John Wheeler sent me a copy of his booklet, The Frontiers of Time (PDF). Unfortunately, soon thereafter, I went back into a business that I had started nine years earlier.

I recently revisited Wheeler’s writings about quantum foam and simplicity. I would ask him today, “What about the Planck base units?” Might we consider Planck Time the first unit of time? Might we consider today, the Now, to be to be an endpoint that gives us the current estimated age of the universe between 13.81-to-14.1 billion years?

If we apply base-2 notation to that continuum, there are just 202 notations that encapsulate the universe. At one second (between Notation 143 and Notation 144) the Planck Length is within .001% of the distance light travels in a vacuum.

Throughout those 202 notations, there are many places to check the validity of the numbers, including the Planck Charge and Planck Mass doublings. There is a deep logic to it all. The first 64 notations are too small to be measured. The first doubling of the Planck Length that can be measured is within Notation-67. The first measurement of a unit of time that can be measured is the attosecond; it is within Notation-84.

Here is a domain, 1-64, for your unparticle physics, including Langlands programs, string theory, and loop quantum theory. If real, it has dimensionality and physicality that cannot be measured directly. Indirectly, it just may become part of the definition of dark energy and dark matter.

When we considered the look and feel of these unparticles, might an infinitesimal sphere at the Planck level be defined by the Fourier transform, Poincaré spheres, and cubic close packing of equal spheres? What are  our limitations within mathematics and physics?

All notations appear to be active, so time is surely redefined. It would appear that there is symmetry across all but the current notation.

I hope you will comment.  Thank you.

Most sincerely,


PS. Another recent attempt to describe all this ideation was for FQXi (Aguirre and Tegmark group):  https://81018.com/3u/

Long, long ago… I was a member of Harvard SDS ’64 (local high school student – recruited from an all-night teach-in at Memorial Hall), also a member of the Harvard Philomorphs with Arthur Loeb and Bucky Fuller, 1970-1973, and one of nine (1977) with Arthur McGill (HDS) on Austin Farrer’s Finite and Infinite.

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). Pacing throughout3, 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 Pace-Man is our affectionate name for Nima, 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

Conway, John Horton

John Horton Conway

Fine Hall, Princeton University
Princeton, New Jersey

Articles/books (PDF)- More
Twitter (he has had an account since 2013 but does not use it)

Another email: November 18, 2019

RE:  I remember well a day sometime just before September 2001

Dear Prof. Dr. John Conway:

Strange to think that our day of discussions has led to a base-2 model
of the universe, but it has.  I’ll write up that story soon.

This is the precursor: https://81018.com/bridge/

Best wishes,

First email: July 9, 2013 @ 4:45 PM

Dear Prof. Dr. John Conway:

You may not want me to reference your work because this article I am struggling to write just might be penultimate foolishness. Your quick comments will be appreciated.

Back now about ten years ago, you allowed an acquaintance and me to spend a day essentially following you around the campus. We chatted often and had a late lunch. My name is Bruce Camber and I had flown in from California. My work at the time was producing a television series, Small Business School, that aired on PBS stations around the USA and on the Voice of America around the world.

Long before — in 1972 — I had been a member of the Philomorphs with Arthur Loeb; and, Bucky’s Synergetics I & II were part of my early education. You may remember that I was particularly hung up on the nesting of simple platonic geometries, particularly the octahedron. David Bohm got me going in that direction.

Two years ago, my nephew asked if I would substitute for him within his five high school geometry classes, “Introduce the platonic solids!” I had been studying a little about Planck’s length and had the kids guess, “How many base-2 notations within would we have to go before we hit at the Planck limit?” We discovered just over 110. We then went out to the Observable Universe* in another 91+ steps, assuming a wide variegation of nested geometries all the way.

I thought it was a neat ordering system, but we couldn’t find it anywhere on the web, so we put it up. And now, we are puzzling over the first 65 notations (steps, doublings, layers, etc).

Here is the beginning of a speculative, entirely idiosyncratic article about that very simple work: https://81018.com/big-board/

I would be delighted to hear from you.


Bruce Camber
Small Business School
Private Business Channel, Inc.

* PS. In an email, I suggested to Luminet that the universe is probably more like the Pentakis Dodecahedron than a simple dodecahedron….