Lagarias, Jeffrey C.

Jeffrey C. Lagarias

University of Michigan
Ann Arbor, Michigan

Google Scholar
Homepage (2)
Video: Clay Fellow Senior Talk – Packing Space with Regular Tetrahedra

Pages within this website:
(Lagarias and Zong)
Geometric gap

Most recent email: 27 March 2020

Dear Prof. Dr. Jeffrey Lagarias,

I thank you again and again for your scholarly work. I endorse your work!

Yet, given our work is so idiosyncratic, you probably would prefer that I didn’t.

Notwithstanding, I am glad for Mysteries in Packing Regular Tetrahedra.”
Each day, I wonder what 1800 years of being wrong did to our scholarship.

Best wishes,


The two references below are here:

10 Geometric gap: 0.12838822+ radians and 7.35610317245345+° degrees. Even today, March 2020, this gap is little studied and less known. Our first encounter with it was in 2016 upon writing the article, “Which numbers are the most important and why?”  At that time, it seemed like Chrysler Corporation had branded that geometry as the pentastar. And though it is a five-tetrahedral representation, they never looked uniquely at the gap of  7.35610317245345+° also defined by  0.12838822+ radians. Two chemists (Frank & Kasper) came closest to opening the discussion in the 1950s. Two academics (Lagarias and Zong) did a preliminary analysis that was a tremendous help; the relation of this gap to the deeper geometries of life remains as a challenge. Our modest start is here:


The guess is that little gap
just above is
the beginning
of quantum


11Aristotle’s failure is our failure. Perhaps the gravity and nature of this error is only now beginning to be understood. We all make mistakes. When we are challenged, we defend our concepts as best we can, and then adapt. We change or our associates change.

Some people become larger than life within their own time. Three examples are Aristotle, Newton and Hawking. All three were wrong about one key impression about the nature of  life, yet their egos and their position and their person were so illuminated, it became increasingly difficult to challenge their assumptions.

Aristotle’s geometric gap, Newton’s absolute space and time, and Hawking’s infinitely hot big bang have each mislead scholarship and we all lost the scent and direction of the chase with its resultant discovery and creativity. Throughout our ever-so youthful human history, such people can readily continue to mislead us. We have to be vigilant to review and re-review all the concepts we hold dear and begin to adjust them appropriately.

First email: Saturday, 31 August 2013 at 8:19:21 PM

Jeffrey C. Lagarias, Professor of Mathematics, University
Chuanming Zong, Professor of Mathematics, Peking University

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: The five tetrahedral construct plays a key role.

Your work gives me a wider and deeper perspective.



Bruce E. Camber

PS. Long ago I studied with David Bohm, Phil Morrison, and so many others like them, but to make a living, I became a television producer!  We had the longest-running television series on PBS stations in the USA and the Voice of America around the world about best business practices.

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 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 somewhere under 205.11 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


Feldbrugge, Job

Job Leon Feldbrugge

Perimeter Institute for Theoretical Physics
Waterloo, Ontario, Canada

Google Scholar
Homepage (Perimeter Institute)
Thesis: PhD thesis (PDF)

Places within this website with references to you:
Get a Grip – Get the Universe
If Turok Tells Us That Hawking Is Wrong,  The Big Bang Apple Is Falling
Job Feldbrugge:  Breaking out of Ruts of Misunderstanding

Most recent email: Friday, March 26, 2020 at 11 AM

Congratulations on your PhD. No small achievement especially with Turok observing.

No page will ever be static on the website until I die
(and then who knows what will happen!).

That’s all to say, has
been updated and a new page for you has begun:

Just a few minutes ago, I found your 505 page doctoral thesis and started to read it (PDF). Of course, I had questions:
• Though you tell us a little, I would want to hear more about your minimal assumptions, especially about the very nature of space and time.
• What is assumed about space and time within the topology of a real manifold AND by looking at the critical points of a real function? I think, “Perhaps the singularity and unitarity are further away than you currently intuit.” So, I went looking throughout the thesis for your analysis of the Planck scale and found on page 142 (5.2.4 Recovering unitarity), particularly where you say, “…we should recover local quantum field theory, along with unitarity of scattering amplitudes in the quantum field theory sense.”  Really?
• References: Picard-Lefschetz theory, catastrophe theory, infinite dimensional measure theory, and weak-value theory… page 177,  Putting everything together, we find the causal propagator to create a perturbed three-sphere of radius R in reduced Planck units “from nothing”…

And, of course, who am I to be reading your thesis and certainly the question should be asked, “Is it of any consequence?”  I don’t want to waste your time so, let me stop here and thank you, and again offer my sincere congratulations.

Stay well. Be bold. Have integrity!


Second email:  Tue, Sep 26, 2017, 1:13 PM

Dear Job,

I really  think you and your colleagues are the hope of the world.

Your integrity matters most so I’ve placed my letter to you on my homepage: which will be when a new page takes over.

If you have any objections, I will remove it immediately.

First email: Monday, September 25, 2017

Dear Job:

There are two pages where I prominently cite your work with Neil Turok and Jean-Luc Lehners. Because the television series, The Big Bang Theory, is in its final season, there will be an increased number of discussions around the globe about the theory. And, of course, because your Neil Turok has had such a deep history with Hawking, a major focus will be on your collective work.

In your work, you all say, “perpetual bangs.” I think you should be saying, “perpetual starts” and leave the “bang” out of it.

Guth, Linde, and so many others of equal caliber have lamented the “bang” tag that Fred Hoyle gave it in 1949. I believe that a “quiet expansion” encapsulates the action a little more succinctly.3 When sound waves become possible, they have too much catching up to do to make a difference! Of course, I could be wrong on those two pages (as well as any number of others) on so many levels.

If you have any suggestions to improve the two pages referenced above, I would be delighted. If it is all just too pedestrian for you all, I will expect this email to be ignored.

My studies within cosmology are still in their earliest stages. I have a lot to learn.  However, my work in ontology goes back to the early 1970s. I’ll be contacting many scientists from major universities who use the words, “According to the big bang theory…” because it is an indication that their starting points may well be incorrect.

I think our biggest problems stem from another Lucasian Professor, Hawking’s predecessor, Isaac Newton and his absolute space-time.

Arkani-Hamed4 wants to throw them all out and Tegmark5 wants to retire “infinity.” As smart as those two are, I think they are both mistaken. Space-time and infinity can be defined more succinctly.

Thank you and your team for all the work you are doing with Picard-Lefschetz theory and the rather slippery concept of a singularity.

Most sincerely,

Bruce E. Camber


Lidström, Suzy

Suzy Lidström

IOP: Life, the Universe, and everything—42 fundamental questions, Physica Scripta, 2016
IOP: Consciousness as the collective excitation of a brainwide web – understanding consciousness from below quantum fields to above neuronal networks
Google Scholar (20 articles on Muon research and other matters)
ArXiv: Light, the universe and everything 12 Herculean tasks for quantum cowboys
_______ and black diamond skiers, J.Mod.Opt. 65 (2017) no.11, 1261-1308) Feb. 2017
_______ The sounds of science: a symphony for many instruments and voices (PDF) 2019
_______ See: 6. What is consciousness, and do we have free will? with Roland E. Allen


Physica Scripta, editor


Second email: 26 March 2020 at 5:30 PM

Dear Dr. Suzy Lidström:

I have three documents opened on my desktop:

  1. Life, the Universe, and everything — 42 fundamental questions
  2. Light, the universe and everything 12 Herculean tasks…
  3. Consciousness as the collective excitation of a brainwide web

The two articles that include “the universe and everything” beg for bold thinking. The Consciousness article, like all 20 references, suggests we have a long way to go before we know what we are trying to model.

In our naive-and-entirely-idiosyncratic model of the universe, everything, everywhere, for all time is necessarily pulled into a base-2 grid that begins with the Planck base units and captures the universe in 202 notations. I think that chart is rather magical. There are real clues within those first 64 notations.  Clearly we are in a never-never land of the infinitesimally small, way smaller than particles and waves, and probably into the land of strings and Langlands programs. The upper end of those notations would necessarily involve loop quantum gravity.

Because this work began as recently as December 2011 in high school geometry classes, it has not had any serious review by the scholarly community. To attempt to get some critical feedback I have written a fair number of letters and most recently I have submitted a short article for the FQXi people:

By the way, that particular submission did not go through the HTML to PDF conversion very well. Many links were lost and images abused. A bit better version is here:

I have developed a summary page of your work so I can have a quick review before going further:

Would you have any advice for us?

Stay well!  I hope to hear from you.



First email: Dec 8, 2018, 4:30 PM

Dear Prof. Dr. Suzy Lidström:

Congratulations on all that you do. You have an extraordinary scope and depth, perhaps best encapsulated within your five years as the Editor-in-chief of Physica Scripta.

I initially found you through the PQE Colloquium, “Light, the universe, and everything…” and particularly through your work with Roland Allen. I reference you in my note to him.

I know how idiosyncratic our work is. The concept of a base-2 model of the universe is too simple and obvious, and out of the mainstream! Given you are are who you are, I would enjoy your comments.

Again, congratulations on all that you’ve done. Most impressive!



Bousso, Raphael

Raphael Bousso

University of California at Berkeley
66 LeConte Hall MC 730
Berkeley, CA, 94720-7300

Everything would just come out of math and pi and twos. And we came in and said, ‘Look, it’s not going to happen, and there’s a reason it’s not going to happen. We’re thinking about this in totally the wrong way.’” – Is Nature Unnatural? by Natalie Wolchover, Quanta Magazine, May 24, 2013  (also published in Scientific American, June 2013)

ArXiv: Joseph Polchinski: A Biographical Memoir
Bousso Group, Interests, Members

FQXi   1999-INI

First email: 25 March 2020 @5:43 PM

Dear Prof. Dr. Raphael Bousso:

What a fine read, your tribute to Joe Polchinski. Thank you.

Might you be able to reconstruct a comment you made to Natalie Wolchover when you said, “…everything would just come out of math and pi and twos. And we came in and said, ‘Look, it’s not going to happen, and there’s a reason it’s not going to happen. We’re thinking about this in totally the wrong way.’ “ It prompted these questions:

  • Do you know anybody who has thought about starting the universe from Planck Time and his base units? If not, you are meeting one such knucklehead with this note.
  • Has anybody thought to apply base-2 exponential notation?
  • Has anybody thought that the first manifestation of Planck units could be a sphere?
  • Has anybody thought about sphere stacking beyond the density math questions?

Now you know why I was taken back with your quote. Could it possibly be that simple?

You may find our current homepage to be a short summary of our idiosyncratic work:


Most sincerely,



Visser, Matt

Matt Visser

MattVisserVictoria University of Wellington, New Zealand

ArXiv: What is “fundamental”?
•  The utterly prosaic connection between physics and mathematics
•  Which number system is “best” for describing empirical reality?
Books: Lorentzian wormholes: from Einstein to Hawking
CV (through to February 2011)
Google Scholar

First email: 25 March 2020

Dear Prof. Dr. Matt Visser:

In looking at who else quoted Wigner’s Unreasonable Effectiveness,
I discovered your work in ArXiv, among all the other papers, particularly
The utterly prosaic connection between physics and mathematics.
BTW, that’s quite a nice ArXiv collection! You do not hold back!

Then, I found you again within the wormholes discussions and
dropped a reference to you (so to be sure to dig deeper into it).
One of our most fundamental questions is always about the
very nature of space and time. Though Nima Arkani-Hamed says
“It’s doomed,” it certainly needs to be better defined.

I have also enjoyed your spirited engagement of the question,
What is fundamental?” and in light of it, I wonder if you
might comment on that homepage where I make reference to you.

I know how naive and overly simple that model is.
It seems, however, nobody thought applying base-2
to the Planck base units (emerging within 202 notations)
could be meaningful.
It is a quick read and I would so thoroughly enjoy
hearing your comments. Thanks.


PS. A couple of years ago my wife and I did a driving tour
of New Zealand. What a joyous special home you have.
When we were in Wellington, we took the cable car up to
your Wellington Botanical Gardens and walked back down
through your campus. Just lovely. -BEC


Communications in late March, 2020

March 24, 2020
Francisco S. N. Lobo, Instituto de Astrofisica e Ciencias do Espaco, University of Lisbon (FQXi)
Fotini Markopoulou, Empathic Technologies
Frank Wilczek, MIT  (FQXi)

March 25, 2020
Raphael Bousso, University of California at Berkeley
Basil Hiley, University of London, Birbeck College
Jürgen Mlynek, Humboldt University in Berlin and Helmholtz Association
Matt Visser, Victoria University of Wellington  (FQXi)

March 26, 2020
Suzy Lidström, Department of Physics and Astronomy, Texas A&M University

March 27, 2020
Job Feldbrugge, Perimeter
• Jean-Luc Lehners, Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)
Neil Turok, Perimeter

March 28, 2020
Max Tegmark, MIT
David Gross, Kavli Institute for Theoretical Physics, University of California, Santa Barbara

March 30, 2020
Steven Weinberg, University of Texas – Austin

March 31, 2020
Rudolph Schild, Harvard-Smithsonian Astrophysics
•  Helen Quinn, Stanford Linear Accelerator
•  Jeffrey Lagarias, University of Michigan

April 2, 2020
Alan Guth, MIT
Daniel Shechtman, Technion, Israel

The next group would include:

April 4, 2020
• Lawrence Summers, Harvard

April 5, 2020
Martin Rees
Sabine Hossenfelder
Edward (Rocky) Kolb, Kavli Institute, University of Chicago

April 7, 2020 (maybe):
Joseph Silk
Paul Steinhardt, Princeton
Lisa Randall, Harvard
Brian Josephson, Cambridge

Among the next ten to be added in early April.
• Roland E Allen, Texas A&M, Life, the Universe, and everything-42 fundamental questions:  (PDF) (ArXiv)

Markopoulou, Fotini

Fotini Markopoulou

Perimeter Institute, Waterloo, Ontario, Canada
Empathic Technologies, Doppel, New Wing, Somerset House, Victoria Embankment, London, United Kingdom

Articles: Collaborators in creation, Aeon, Feb. 2020
ArXiv: The Internal Description of a Causal Set: What the Universe Looks Like from the Inside (1999)
Planck-scale models of the Universe
YouTube: Why is the Universe So Beautiful? (Oct 29, 2019)

First email: 24 March 2020

RE: Our many levels of stress

A part of our personal stress, national stress, and global stress
is all the unknowns. Within our sciences, would you concur that
one of our most fundamental questions (that is an unknown) is the
very nature of space and time. Though Nima Arkani-Hamed says
its doomed, it certainly needs to be redefined.

Might you comment on our naive model based on applying
base-2 to the Planck base units to emerge within 202 notations It is a quick read and I would
so thoroughly enjoy hearing your comments. Thanks.