The Finite and the Infinite

Most recent update: Sunday, 8 October 2017   Prior homepage  Next homepage   On Time

Stephen Hawking and Max Tegmark
Stephen Hawking – Max Tegmark

The relation between the Finite and the Infinite is rather hotly debated, mostly between people who equate the infinite with God and those who have no place for any kind of god. Yet, the infinite also creates conundrums within science. In 2014, MIT physicist, Max Tegmark advocated, “I’m betting that we also need to let go of it.” He wants to retire what he and others call an incorrect assumption – infinity. His friend, Stephen Hawking, opened that door with his 1983 No Boundary Proposal that holds that the universe has no beginning or end.1

“Not so fast y’all” as it is said along the banks of the Mississippi River in New Orleans. With these two thought leaders, Hawking and Tegmark, it should be acknowledged that both are being speculative and that their concepts are brilliantly incomplete.

In the Big Board-little universe model using base-2 notation from the Planck Time to the Age of the universe, the entire physical universe is contained within just over 200 notations that are highly-integrated and totally-predictive. Notations are also known as clusters, doublings, groups, sets or steps. Within the first second of the universe, there is more than enough “natural inflation” from the Planck Charge to get “things” going. As a result of studying and working with this model since December 2011, there are many-many facets to explore, however one of the most important is that this model logically suggests that time is derivative and that the finite and the infinite are perhaps best understood in terms of continuity, symmetry and harmony.

Continuity. Though an unusual way to define infinity, even with quantum indeterminacy, continuity throughout the universe is the bedrock of science, logic, and rational thought. Numbers clarify this continuity. If we were to carry our measurements out a billion places, the universe and its systems around us would still replicate day after day with utmost precision.

Within this model, continuity is more fundamental than time; it begets time. It is the initial condition of order.  More…


The complexity of a single molecule


Symmetry. The second face of the infinite is symmetry. Though so much of life is asymmetrical, the deepest examination of any physical thing begins to reveal deeper symmetries. Numbered relations define those symmetries, relations are created, and the universe appears to be tiled and tessellated deeply within every notation throughout the model. Here symmetry is more fundamental than space; it begets space.  More…

Harmony. Speculating, it is hypostatized that two symmetries begin interacting within a notation and then across notations, dynamics are created, and though not quite perfect, the interaction of the symmetries perfects the moment for the observer or for the notations involved. Therefore, we have moments of perfection within our experiences of the universe. More…

Our studies. At this point in our studies, there is not much more we can say about how the infinite defines the model and what the model says about the very nature of the infinite. These three insights, although reflective of the model, in part come out of a study of a moment of perfection in 1972,3 then from studies of the book, Finite and Infinite: A Philosophical Essay (Austin Farrer, Oxford, Dacre Press, Westminster, 1943), and from an application to a business model.4    More…

These three qualities became the bedrock for our model of the universe and for discussions about the shared nature of the finite and infinite.

What difference does it make? First, it is a clear contrast to the nihilism of big bang cosmology. Building in strength and popularity over the past 30 years, that nihilism has had a lot to do the fraying of our little world. So much is out of control and spinning apart. Money is not the issue. What we believe and how we believe is. Hope is. Charity is. Integrity is.

What is 5000 to 13.8 billion years?

The finite and infinite relation has been the focus of humanity for as long as we have been recording our ever-so-short history. In light of 13.8+ billion years, five thousand years of records is, of course, quite short. We’ve just begun to make sense of it all.

Today in history. The finite is usually associated with physical, limited things. The infinite is often capitalized and associated with godly things, the eternal and everlasting. To our knowledge, Max Tegmark is the first theoretical physicist who has suggested that the concept of the infinite be abandoned. His rationale is that it gets in the way. He cannot make it work for the science he wants to create. Within these many articles, we hope to convince him, Hawking, Guth and so many others to re-engage our simple definition of the infinite. It does not require a religion or religious beliefs. Notwithstanding, it also does not necessarily fly in the face of those who believe in a much more robustly-defined Infinite.

We can all begin to tolerate each other.

This is our simple introduction to a very large topic and we will return to this page often to expand its range and its depth.

1 A general introduction: See the prior homepage. Also, this Wikipedia article about the 1983 Hartle-Hawking State (wave function) provides even more information.
2 This construct was introduced within these pages at the end of the year, December 2015.
3 This construct goes back to work in 1972 at both Synectics Education Systems in Cambridge, Massachusetts and the Harvard Philomorphs with Arthur Loeb and Buckminster Fuller.
4 The original construct was used as the foundation of a business model for a weekly television series, Small Business School, that Bruce Camber and Hattie Bryant started in 1994. It aired on PBS-TV stations throughout the USA and on the Voice of America around the world for over 50 seasons (2012).


Related homepages:

Key references: Communications

Focusing on Max Tegmark’s infinity and mathematics


Max Tegmark, Professor of Physics, MIT Kavli Institute
Cambridge, Massachusetts

Article: What scientific idea is ready for retirement?  “Infinity!”
ArXiv (11): The Mathematical Universe PDF
Book: Our Mathematical Universe, Knopf (2014)
Facebook inSPIREHEP PhD Reddit Twitter Website Wiki YouTube

Links above go to a few of Tegmark’s pages on the web.
Links below go to references with this website

__2021: Redefine Space, Time, And Infinity!
__2018: Open Letter to Max, Arkani-Hamed and Neil Turok, What is a concept?
__With Hawking on the infinite, October 16, 2016
__Time Is Always Right Now, This Moment… October 2, 2016
• ArticlesJuly 2015  The very first reference to Max Tegmark was in December 2012 (that reference is just below). Found in many posts throughout the site, here it is again under the title, “A Simple View of the Universe: Is a simple mathematical and geometrical view of the Universe meaningful or useful?”
December 2012: In 2001 Frank Wilczek (MIT) wrote, Scaling Mt. Planck (Physics Today). In 2006 Wilczek with Max Tegmark (MIT), Anthony Aguirre (UC Santa Clara), Martin J. Rees (Cambridge) focus on 31 key dimensionless constants (ArXiv).
All emails from January 2012 to January 2022: Tegmark is a very busy person and has never responded to these emails. His system did send an automated response to a LinkedIn request in 2014. Because it was automated and has an important link, it’s inserted below.

Oops. I forgot my last comment in that last email… sorry. I’ll try harder.

Most recent email: 12 May 2022 at 2:48 PM

Dear Prof. Dr. Max Tegmark:

On the homepage today, first paragraph, with Eugene Wigner, we are building on your Mathematical Universe. More references and links to your pages will be forthcoming. I thought you would want to know. Thanks for all that you do to stimulate discussions about first principles and initial conditions.



Tenth email: 23 January 2022 at 5 PM

Of course the hadron didn’t cut it.
Composites aren’t fundamental.
None of the subs are.
It’s got to be more like a perfect 23 January 2022 at 5 PM

Aren’t spin dynamics manifestations of sphere dynamics?

Compared to the Planck base units or Stoney base units, all the subs and hypotheticals are rather large and clunky.

Of course, historically these “Planck Particles” have been considered tiny blackholes while others insist such entities simply do not exist.

My shot at it: Of course, we’ve got to work on that definition of the finite-infinite relation: Hilbert needs to be placed on hold for a bit. Why not? 



Ninth email: Saturday, July 17, 2021 at 7 PM

Dear Max:

Picking up on your theme that we need to redefine spacetime and infinity, perhaps you would like to get involved with these explorations:

  • The first second is still alive, well and moving outward 13.8 billion years later!
  • Or, today’s expansion of the universe is also the first moment of the universe.
  • Blackholes aren’t just sucking everything in; they (Type B) are also pushing it out at levels (sizes) that our measuring devices will never pick up.


PS. I think the current homepage is worth a quick read:
Also, I know you get too much email so I will not send another email to you without an invitation to do so. -BEC

Eighth email: Tuesday, 1 September 2020

Dear Prof. Dr. Max Tegmark:

On the homepage today is this paragraph:

DEEPER DYNAMICS. Max Tegmark of MIT wants to retire infinity. We want to expand our understanding of infinity. Our key question is to discern how that finite-infinite relation gives rise to infinitesimal spheres, sphere stacking, and cubic-close packing of equal spheres, and how it is that this special mix renders basic geometries, emergence,  and a natural inflation.

My record of my emails to you is here: To come up with such an idiosyncratic point of view, here my presuppositions that fall outside the mainstream: I hope you and your family are well and doing fine.




Seventh email: 28 March 2020

Dear Prof. Dr. Max Tegmark:

Along with Nima and Neil, you three constitute a force in physics and are three of my favorites among the legions of the brilliant. Today’s homepage — — has links to you three, plus to one of my very favorite pages:

Our idiosyncratic model of the universe is different:
1. The infinite-finite relation is unique — the infinite is the qualitative expression of continuity (order), symmetry (relations), and harmony (dynamics) while the finite is the quantitative expression of continuity, symmetry, and harmony. For me, any other definition of the infinite has too much historicity that is limited within time.
2.  The initial perfections of the qualitative is challenged by the geometric gap of the five tetrahedral configuration. It becomes the grounds for quantum fluctuations which becomes systemic before Notation-64 where particles and waves begin to manifest.

The fact that the speed of light is confirmed within .01% of laboratory-defined speed at the one second mark between Notation-143 and Notation-144 and then again with a light year between Notation-168-and-169 is sweet.

When it comes to testing new ideas, we are all fools albeit some of us more foolish than others given those quantum leaps and impatience with incrementalism.

I wish you well. We all must try to stay healthy in these very odd times.

Most sincerely,

Sixth email: Thu, Jun 1, 2017 at 5:39 PM

Subject: Fwd: Do our simple mathematics at all jive? I hope so.

Hi Max –

Whenever I quote somebody’s work, I send a copy of that reference.

We all should know your work and your thinking. To that end, we have
a Max Tegmark page within our website (Editor’s note: This page!)

We live in such crazy times and I believe a lot of it has to do with Stephen Hawking’s dystopian, nihilistic bang. Also, to address your desire to throw out infinity, I have offered a redefinition (only highlighted here within this document).

Our naive model has a simple logic, a most-simple start, and simple mathematics. It is all-inclusive yet particularized. And, it also has a simple logical start for infinity, indeterminacy, fluctuations, incompleteness, and imperfections.

So I ask myself, “Why not try to integrate it with the Standard Model of Physics, with quantum gravity, and with the ΛCDM model?” Would you advise us? Thank you.

Most sincerely,
Bruce (as the Editor) answers his own note on 27 March 2020:
“Advice…? So, you want advice? Here’s my advice as a question: What, are you crazy?”

Fifth email Email: Sunday, 2 October 2016

Max –

Is this a fair summary?  Today, it is our homepage:



PS. We are the simple people — simple model, simple logic, simple math, filling in the continuum from the Planck scale to the CERN-Atlas scale, and then beyond.

Fourth email: 4 August 2016

Hi Max,

Your endearing smile and wonderful openness should have the world on your doorstep.  Congratulations on all that you do.

Of course, the big bang is one of those answers that only a fool would dare question. So, here I stand among the fools. We’re just high school folks; we claim no special status, so maybe we can be excused for being nicely idiosyncratic and naive!

I think you might enjoy seeing the numbers all filled in from the Planck base units to the Age of the Universe using base-2 notation.  Boeke’s Cosmic View looks a little timid by comparison. Even ‘t Hooft’s Time in the Powers of Ten misses too much. If you have a moment — it is looking for a special critique.

Is it solipsistic poppycock? That chart is big; it is horizontally-scrolled, starts with the five Planck base units (and some simple geometries), and it is  carried out the 202 notations to the Age of the Universe.  You can follow the changes of each base unit in contrast to the others. There are over 1000 simple-simple-simple calculations. But, simple is good.  It tells a bold and dramatic story but it may have more to do with fantasy than reality… but I don’t think so. I respect you too much to waste your time that way.

Is it possible that the universe started with those infinitesimally small numbers and grew quietly and rather prodigiously and all rather quickly?  Of the 200+ notations, the first second is between 143 and 144.  The first light year is between 168 and 169.  And the first million years between 188 and 189.

That small scale universe, 1-67, could be a new science and math.  Maybe Langlands is on the right path after all.  Below I’ll post some of the other work-in-progress asking for critical review! Thank you.

Most sincerely,

* * * * *

Third email: 22 September 2015 

I am now a groupie of sorts. Too old and too naive to be deeply informed.

You encourage me with your great spirit while I’ve begun working through your “Dimensionless constants, cosmology and other dark matters.”

From the perplexing place we were within my first note, to the questioning within the third, would you tell us why our basic concept is wrong headed and “to take a break.”
A Simple View of the Universe:

On Developing A Rationale For A Working Model Of The Universe Based On A Quiet Expansion:

Your website is sensational!  Thank you for all that you do to stimulate scholarship and creative thinking!


An automated response: September 22, 2014:

Thanks for your LinkedIn invitation, which I’m going to accept shortly! Although there’s essentially no information on my LinkedIn page, I have an active public Facebook page where you can connect and discuss with me and others intrigued by science and life’s big questions. I very much hope you’ll join me there! Just surf over to the link below and click “like”:
You’ll also find movies, articles and an FAQ for my book at
Second email: May 9, 2013


Max –

I was 20 when you came into this world, I suspect you came in feet first.  So much standing comedy in all that you are and do. It is entirely refreshing. I am enjoying your pages-and-writing immensely.

I am on a search for simple wisdom. I’m a simple person.

But, I do have a seriously silly question for you. It started when I was asked to substitute for my nephew a couple of years ago. He was to have a second child and I got his five geometry classes for a few days. I wanted to stand them on their head a little, so they actually made models of the “Big Five.” They took a tetrahedron, divided the edges in half, connected the new vertices, and bingo, there is a tetrahedron in each corner and an octahedron in the middle. Then, the same with the octahedron, with six baby octahedrons in the corners and eight tetrahedrons in the faces, all sharing a centerpoint.” That’s a goldmine and you kids have got to go in there and start digging!”

That was the beginning of my regression. The next time, Stevie wanted to take his bride on a fifth-anniversary cruise and left me with those buggers on the last day of class before the Christmas recess, Monday, December 19, 2011.

Enter “The Big Board – little universe.”

“Come one, come all, see the universe and everything in it from the smallest to the largest measurement in about 202 steps!”

We used the Planck Length and started multiplying by 2.  Within a relatively short time, we had the entire universe looking like a Planck Factory. Everything had a place. Geometry was pervasive. Here was the homunculus of all homunculi. One part Plato, add a little relativistic aether, and mix well into the first sixty steps — nobody seems to have explored 2-to-60, possibly 64 (just before getting hit with any sensibility and a neutrino and quark).

Absolutely crazy?!? Worth exploring further??? Or, shall I tell the kids to come out of that cave?




Bruce  Camber  (part of my life as a television producer)
Small Business School

First email: January 12, 2012


Dear Max,

Please, help me to debunk this crazy Alice-in-Wonderland hole that I’ve dropped into….

I am a television producer.  But recently,  I was asked to substitute for a high school geometry teacher, a nephew. He asked me to introduce the kids to Plato’s five. It would be my second time with them, so I had to expand my own horizon a bit for my visit on December 19, 2011.

The first time I had them, back in March 2011, they made icosahedrons out of 20 tetrahedrons. I called it squishy geometry and said that it probably fits into quantum geometries or imperfect geometry somewhere and somehow, but I couldn’t find any online references to it. This link goes to pictures of those icosahedrons.

Then Shechtman comes along with his quasicrystals and five-fold symmetries… I got to thinking about the nesting of tetrahedrons and octahedrons within the icosahedron and wrote up that little note to him (link above).

I thought, “…speculative, fanciful thinking, probably just nonsense.”

Yet, just after that first encounter, I became impatient with my little paper model of a dodecahedron. I took the same pentagonal groups of five tetrahedrons, and attached twelve of them together. I filled it with PlayDoh, then tried to discern what was inside.

A smaller icoshedron was in the center of the thing.  Fascinating for me. No study of it online yet.  I found a name – hexacontagon — but none in the shape of this particular pseudo-dodecahedron.

I’ve been looking inside those five-tetrahedral structures for awhile. A week before that class, I asked, “How far within, how many steps by dividing by 2, would I have to go to get to the range of Planck’s length?” I assumed thousands.  Nope. Just 118 steps! There I was, dividing one meter by 2 and then by 2 again u.s.w until 1.6×10−35 or Planck’s length. Then I thought about the large scale universe and in 91 steps I was out in the range of 1027 meters and the edge of the observable universe.

I hadn’t seen such an application of scientific notation so I made it up and produced a colorful chart for the class:

Where did I go wrong? Is there anything here?