Upon following the work of George F. R. Ellis…

George F. R. Ellis, FRS, Professor Emeritus, Applied Mathematics 
University of Cape Town, South Africa

Articles: The physics of infinity, Nature Physics, V. 14, Issue 8, p.770-772, 2018
________ Physics on Edge, Inference (International Review of Science), V3, #2________ Physicist George Ellis Knocks PhysicistsJohn Horgan, Scientific American, July 2014
ArXiv: Stephen William Hawking: A Biographical Memoir (PDF), February 2020
_____ Emergence of time (PDF), Nov. 2019
_____ Theoretical Cosmology (with Alan A. Coley), (PDF), Sept 2019 
_____ Causal Structures in Cosmology (PDF) Dec. 2016)
_____ 100 Years of General Relativity (PDF) Sept. 2015) (video)
_____ The arrow of time and the nature of spacetime (PDF), March 2013
_____ A Note on Infinities in Eternal Inflation (PDF), January 2010
Books: The Large Scale Structure of Space-Time (PDF, with Stephen Hawking), CUP, 1973
______ The Universe Around Us: An Integrative View of Science & Cosmology 2002-07-29
Conference: Time in Cosmology    FRS
Homepage(s): Google Scholar,   inSPIREHEP, Wikipedia  
Video: http://videolectures.net/george_ellis/  https://www.whyarewehere.tv/people/george-ellis/
YouTubePhilosophy of Cosmology, 2020; George Ellis, Ard Louis, Top-Down Causation, 2017

Within this website: (1) https://81018.com/validate/#1f and https://81018.com/validate/#References;
(2) https://81018.com/2016/06/30/perimeter/, and (3) https://81018.com/conference

Most recent email: 27 July 2022 at 5:01 PM

Reference: The physics of infinity, Nature Physics, V. 14, Issue 8, p.770-772, 2018

Dear Prof. Dr. George Ellis:

Given your wisdom, might you tender a slightly different notion of infinity. I describe it as one of three facets of pi that are not finite or quantitative so we assume (hypothesize and/or hypostatize) these facets define the infinite and the qualitative.

Continuity is our first facet of infinity. It is the very nature of order. Within the finite it looks like a string of numbers and feels like time. Pi qualifies; it’s an equation that has never-ending results that are always the same and always changing.

Symmetry is the second facet of infinity. It looks like geometries and is the very nature of a relation. Within the finite it feels like space. Pi qualifies; it’s a symmetry that generates symmetries. It’s an equation that generates equations.

Harmony is the third facet of infinity. It is the very nature of dynamics; and within the finite, it is always cyclical (periodicity) and experienced as space-time moments. Pi’s numbers, geometries, and equations (Fourier transform and others) are here within an eternal dance and there’s a domain of perfection which may be experienced as a moment of perfection.

All other definitions of the infinite are put on hold. Most are personal definitions that come from personal experiences and family history. That is one’s own business, not ours. If those beliefs help you through life, that is great. Our goal here is to engage those principles and functions that give rise to mathematics, physics, and eventually all the other sciences.

What do you think? …gobbledegook? …worthwhile? Thanks.

With warmest regards,


Eleventh email: 30 January 2022 at 12:06 PM

Dear Prof. Dr. George Ellis:

Oh, just to capture a sacred moment where time does not flow! 

I hope you are well-and-fine and that your life is good.

I have made a little reference to you, a footnote within an article that I am currently shaping to become a homepage: “Prove it to me!” Numbers-Geometry-Equations The link is here: https://81018.com/validate/#1f Also, there is a reference here: https://81018.com/validate/#References My “big page” about your work is here: https://81018.com/2016/01/11/ellis/ (this page)

Best wishes always,


PS. Just in case you do not go to links within emails, here is one of those references:

[1] VSL. There is a wide range of leading scholars who have been writing about VSL for many years. Perhaps the most foundational is by Robert Dicke in 1957. John Moffatt (1992), Andreas Albrecht (Wikipedia)George Ellis (Wikipedia) (2007), and João Magueijo (Wikipedia) (1998) kept it alive. The chart of 202 notations, particularly line 10, is quite possibly the first actual mathematical approach to validating a VSL.

• Ellis, George F RNote on Varying Speed of Light Cosmologies (PDF),  in General Relativity and Gravitation39 (4): 511–520. 2007
• Magueijo, JoãoNew varying speed of light theories (PDF), Reports on Progress in Physics, 2003, 66 (11): 2025–2068. arXiv:astro-ph/0305457
• Moffatt, John W, J. Magueijo), “Comments on “Note on varying speed of light theories”,” 2008
• Yves-Henri Sanejouand, Empirical evidences in favor of a varying-speed-of-light,” ArXivABSIOP, 2009

Tenth email: July 28, 2020 at 4:56 PM

Dear Prof. Dr. George Ellis:

I’ve tried to clean-up this page with all my references to your work and to some of my notes to you over the years:  https://81018.com/2016/01/11/ellis/

Also, our first reference to you on this site is here (top of page). The actual, long-term URL for that page is: https://81018.com/conference/  Along with 18 others I have also sent you my notes inviting a critical review of the base-2 chart of 202 notations from the Planck scale, especially Planck Time, to our current time.

One of the first principles of this website is that infinity is continuity/order, symmetry/relations and harmony/dynamics and that space/time matter/energy are all finite and derivative. I think Tegmark and Hilbert and so many others have just made it too big of an issue. Our working definition allows the ancient philosophies to breathe a little.

Also, my clean-up of your page was to prioritize my reading and study so I can readily answer my eight questions on that top-level page from your perspective. After I finish, I’ll send you a copy of it to see how close I have come.

As well, I should add that I think Frank Wilczek was simply saying that the Planck base units were largely ignored by scholarship until his three articles in Physics Today. Barrow’s Natural Units Before Planck (1983) is a favorite. Dirac had his large numbers. Planck had his infinitesimals.

The infinitesimals open clear questions about infinity and within this base-2 model, one face is quantitative and the other qualitative.

Best wishes always,


Ninth Email: May 22, 2020, 11:06 PM

Dear Prof. Dr. George Ellis:

The most recent homepage has a section about Hawking which starts off with your 1973 co-authored work. I thought you might find it of some interest: https://81018.com/duped/#HawkingThat article is entitled, Duped by Aristotle, Newton & Hawking. Thank you.
Most sincerely,Bruce

Seventh and Eighth emails: September 17 & 21, 2019

RE: Foundational Issues Relating Spacetime, Matter, and Quantum Mechanics (PDF), Journal of Physics: Conference Series, 2019 GFR Ellis – When I sent birthday greetings to Freeman Dyson, he responded “Nunc Dimittis is a better text for a 95-year old.” Yes, and perhaps Max Planck was right, “A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather… science advances one funeral at a time.” ( Max Planck, Scientific autobiography, 1950, p. 33).

I wish you well,

Bruce Camber

On Tue, Sep 17, 2019 at 3:36 PM Bruce Camber wrote:

Dear Prof. Dr. George Ellis:

Can’t we just start with the Planck base units? Can we assume with the dimensionless constants, Planck Charge, and light (c), that there is a very infinitesimal thrust that generates a simple sphere, and then another, and another until there is sphere stacking and a doubling, then another and another: https://81018.com/chart/ http://81018.com https://81018.com/2016/01/11/ellis/

If that is the simple start, time is derivative.



Sixth Email: Saturday, February 2, 2019

Dear Prof. Dr. George Ellis:

When we followed Zeno’s logic back to the Planck scale, ostensibly going deeper and deeper inside a tetrahedral-octahedral construct, we were challenged, “What if we multiply by 2?” We had to go down inside 112 notations to get to the Planck scale. When we went out, multiplying by 2, larger and larger, there were just 90 doublings to the Age of the Universe, the Now.

We asked further, “Is our chart logical? Is it a valid STEM tool?”

We have not been advised by any scholar to date as to why this basic logic is off. Might you? Our chart is here: https://81018.com/chart/ Our most recent overview: https://81018.com/boundary/

I thank you for your extraordinary career and for being a Platonist!

Most sincerely,


Fifth email: August 3, 2018, 4:18 PM

Dear Prof. Dr. George Ellis:

There is a huge space between the Planck scale and CERN Labs smallest measurements. It is “huge” because it is the size of the Planck scale doubled no less than 64 times. It may be infinitesimally small; it is mathematically huge and entirely open-ended. Of course, there is a mathematics of infinity. And, there is a physics of space-time (where infinity shares that space) and possibly a “physics” of the transformation (where a certain expression of finiteness is shared with infinity), but the physics of infinity per se?

Thinking of David Hilbert’s now famous paper, On the infinite, delivered, June 4, 1925, perhaps a most simple question to ask could be, “Where do the never-ending, never-repeating dimensionless constants like pi reside?” Surely if it is truly never-ending, never repeating, it exists within infinity and that actual ratio exists in the finite. If Hilbert were alive today, I’d like to ask him that question.

Regarding your article, The physics of infinity, I’ve only been able to read the first page here: https://www.nature.com/articles/s41567-018-0238-1.epdf

I have also engaged your May 11, 2017 article (PDF), The Standard Cosmological Model.


  1. Is it possible that Newton’s absolute space and time is throwing us off?
  2. Is it possible that space and time are finite and derivative?
  3. Is it possible that our weak understanding of infinity is holding us back? What if the dimensionless constants, every ratio, has a place within both the finite and infinite?

Naive, possible silly questions…

Most sincerely,


PS. The Epochs, 9/43 page of your article, The Standard Cosmological Model (PDF) commemorating the legacy of Fr. George Lemaître, Specola Vaticana, Castel Gandolfo, is especially helpful. Do you support an infinitely hot beginning per Hawking, Guth et al, or Lemaître’s cold start?

Thank you, thank you. You are the first person I have found to say this: “We probably don’t exist in small universe but case is not entirely closed.” And you explain: “If we did it would be only case we could see all matter in the universe, could actually predict the future from visible initial data, and see our own galaxy at different times in its history.”

Yes, yes, let’s explore this further!  -BEC

Fourth Email: Tuesday, April 18, 2017

Dear Prof. Dr. George Ellis, FRS:

Just an update…  we are still at it, working with the numbers generated from applying base-2 notation from the Planck units to the Age of the Universe.  Our latest chart is here: https://81018.,com/chart/  It is horizontally scrolled so we can more easily follow the progression of a particular Planck unit. The natural inflation of the numbers is sometimes counter-intuitive, but we attribute that to our learning curve and naïveté.

You have your own page within our new website! I’ll insert a link to it below. Essentially it is to document our letters to you and provide key references to your work for our students and web visitors.

I hope the page meets with your approval.  Thank you.

Most sincerely,


Third email: 5 October 2016 

Thank you for your work on The Universe Around Us: An Integrative View of Science & Cosmology.

In December 2011 we “fell into” an integrated view of the universe that started with the Planck base units and went to the Age of the Universe in just over 200 base-2 notations.

It appears to be the first time that little continuity equation with all its numbers was actually written out and posted on the web. It certainly is simple. It is mathematically integrated. It appears to be an alternative to the big bang (and the big bang’s nihilism).

It seems that most of the people at the Perimeter Institute conference, Time in Cosmology, accept the place of the big bang.

To help our students and to attempt to context that diverse dialogue, I have created a few links to the conference and to your work. There currently are three key pages. First, there is a brief overview of the conference on our homepage today (fourth section down). It will be there for a few days to come: http://81018.com. Thereafter: https://81018.com/2016/10/02/2october2016/
There is also this page on the conference:

Our general overview page of your work is this page; the URL is:

If there is anything you would like to have added, deleted or changed, please just say the word! Thanks.

Now, thinking about time and the large-scale universe, perhaps another conference could be entertained, Time in the small-scale and human scale universe. In less than a second, the universe within this base-2 model has already expanded well into the large-scale universe. Of the 200 notations, the first second from Planck Time is within notations 143-144. The first day (86400 seconds) is between notations 160 and 161. A light year is between notation 168 and 169. That’s all cosmology.

If we engage the numbers generated using base-2 from the Planck base units, it appears to expand rather quietly right out beyond the need for a big bang.


* * * *
Bruce E. Camber

PS. Yes, I know how naive and idiosyncratic our work is. The simplicity of the logic and math, however, has caught our attention. The numbers seem to speak louder than words. Although temperature is a problem, I think in time we’ll be able to adjust that line of figures with some kind of “reasonable” rationale, perhaps even a different algorithm. -BEC


Second email: August 4, 2016 

Dear Prof. George Ellis:

I am working through your 2009 ICG Portsmouth Powerpoint presentation at the Unity of the Universe meeting, “Critical Tests of the Standard Model of Cosmology
.”  Thank you.

Since this report below (January 2016), the following key documents have emerged.

  1. A horizontally-scrolled base-2 chart from Planck Scale: http://81018.com
  2. Big bang questions for academia: https://81018.com/2016/06/01/quiet/
  3. Questions for the public:  https://81018.com/bigbang/
  4. Planck Epoch: https://81018.com/Planck/

Also being tweaked:
  1. Unification: https://81018.com/Unification/
  2. Inflation: https://81018.com/Inflation/
  3. Electroweak: https://81018.com/Electroweak/
  4. Human will: https://81018.com/uniqueness/

Your comments are invited on any one posting, yet the small-scale domain from the Planck base units to the particle zoo is of keen interest to me.  Could pure math and geometry beget those numbers? I think so; and if so, we have as new view of reality within which to get to work.

Thank you.

Warm regards,


First email: January 11, 2016

Reference: https://www.quantamagazine.org/20151216-physicists-and-philosophers-debate-the-boundaries-of-science/

Dear Prof. Dr. George Ellis:

In reflecting on reports from your conference in December (2015) at the LMU in Munich, I ask a rather unusual question, “Could a new construct possibly come out of  a high school? Could the naive possibly have the simple mathematics for a model of the universe that includes everything, everywhere and for all times?  Yes, ours is a very simple model in search of a theory.

Our small-but-growing group of high school teachers and students used base-2 exponential notation, the Planck base units, simple geometries, and the simple numbers and concepts to map our universe.  We’ve been at it since December 2011.

At the time we did not know about Kees Boeke and his base-10 scale of the universe. We were studying a tetrahedron with its embedded octahedron.  We were observing the parts-whole relations — the four half-sized tetrahedrons and an octahedron within each tetrahedron  and the six half-sized octahedrons and eight tetrahedrons within each octahedron. We observed the four hexagonal plates within each octahedron and could see many different tessellations of our universe.

Chasing those geometries, going within about 45 times, we were in the range of the fermion. Another 67 times we were in the range of the Planck Length.  To get consistent we then started at the Planck base units and went out to the Age of the Universe in just 202 notations. It gave us an ordered universe, nevertheless, the authorities responded, “So what?” or “See Boeke’s work” or something like, “Cute.” The first 67 notations were so impossibly small, our “small-scale universe” was discounted by most “real” scientists and mathematicians.

So to attempt to explain its potential importance as an alternative model, at the end of the year I wrote up a David Letterman-like Top Ten. Ours is titled, The Top Ten Reasons to give up those little worldviews for a much bigger and more inclusive UniverseView.  That wasn’t enough, so I immediately began prioritizing the numbers that were important to us. Though way-way beyond our pay grade, we are trying to make sense of many new concepts all at the same time.  We ask, “What does Kepler’s conjecture have to do with anything?”  Right now I am in the process of abusing Mitchell Feigenbaum’s constants.

I’ll continue to stutter around, unfortunately skimming and bouncing over details on what skiers call Black Diamond slopes (way beyond my capacities). We’ll continue to take quite a few tumbles and hard falls. It is a heck of a way to attempt to make sense of things that we have never ever observed in the past.  It’s a very steep learning curve!

Your comments would be most welcomed.

Most sincerely,


Pages which reference the work of G. F. W. Ellis