Center for Perfection StudiesThe Big Board–Little Universe Project 

What is finite? And, what is truly infinite?

“Finite or Infinite? Is That The Question?”    (link goes to Part II)

Some of our high school students think our scientific community makes the study of Science, Technology, Engineering and Mathematics (STEM) all too difficult to understand and overly complex by defying a certain commonsense logic. (Reference #1)

We have been studying simple math and simple geometries from the smallest possible measurement of a length to the largest (Reference #2). It appeared to some of the students, based on this work, that the universe is obviously finite. They have been told that intellectually and historically, it is an open question. For them, “Make a choice and see where it takes you.”

The students with strong faith statements said, “Only God is Infinite. All things within space and time are finite.” (Reference #3) When asked about all the universals-and-constants and space-and-time, the concurrence is that these are the access paths, interconnections and transformations between the Finite and the Infinite.

For the best of these students, asking the question, “What is the Infinite?” is like asking the question, “Who is God?” And, they have answers.

Of course, as a result of a little coaching, they say, “First, God is Perfect.” When asked, “What is perfection?” they echo their coach: “Perfection is order-continuity, relations-symmetry and dynamics-harmony, all rolled into one.” (Reference #4) That amounts to an understanding of the Infinite without importing all the related history and revelation from the various faith statements within our very short history throughout our little world. The Finite is another story. We turn to many people from Euclid to Einstein for inspiration to provide the academic and religious communities with our simple observations and assumptions.

Hardly postulates and axioms, our statements are a praxis in-search-of theoria:

If these statements are taken as a given, then what kind of universe and what kind of science do we have? Should we re-examine the use of infinity throughout the ages going back to the ancient Greeks? Should we reconsider the theory of indivisibles? And, perhaps we should even reconsider the very nature of the Big Bang and its theory.

Of course, that is our agenda (Reference #8),   our current focus for the immediate future.


1. One of two key general overview and working article,  Order in the Universe

2. One of the earliest reflections on all our efforts and work: Is it true that everything starts most simply?

3. Initially written in November 2012, just what is the nature of belief?

4. In light of those constants, universals and the finite-infinite relation, the nature of perfection seems to follow:

5. Examining basic structure in basic ways: Simple View of the Universe

6. Our first look at the progression of doublings.  This listing was written to accompany an article for Wikipedia: Written in March 2012 to support an article for Wikipedia

7. There are somewhere over 201 base-2 exponential notations (doublings, domains, layers or steps) within the Known Universe.

8. Another analysis of key points: There are 15 in this article.

Even between atheists and believers

Perhaps all it comes down to is an answer to the question, “Whose metaphor is more meaningful?” You will not find many atheists who deny science. They do not deny the constants and universals that are always in the back of the science textbooks.

There are three constants within the sciences that remain clear, in spite of quantum mechanics. The first is that there is order and continuity in the world. It is the basis of knowing. In every discipline there are multiple parameter sets where this is true. Beginning in mathematics, a rather pure form of thought, abstraction and representation, we then move into physics. It has multiple parameter sets as well. There is one for Newtonian mechanics, another for General Relativity and Special Relativity and yet another for quantum mechanics. Then chemistry and biology have their own parameter sets. All these parameters simply establish the boundary conditions of what is being measured within them.

Each has a formalized language. And, each has a metaphorical language that pushes into the edges of the unknown.

The sciences all embrace varying definitions of relations yet all of these definitions are understood by a symmetry function.

Specialized disciplines with each of the sciences hypothesize about the nature of the unknown, just beyond their limits of knowledge, and all these hypotheses are a study of the deepest dynamics of their discipline. The experience of insight, the “ah-ha” of the creative surge, is experienced as a concrescence of symmetries or harmony.

The atheists mostly object to the use of specialized language. They understand rules, mores, and societal law and order even though many are nihilistic, others narcissistic, and many both.

Yet, change will come. Some of these folks will begin to realize that time is not a fundamental frame of reference and that there are qualities of life that permeate everything in every way, and that these qualities empower order, relations, and dynamics, and that these three scientific functions with the faces of continuity, symmetry and harmony just might also be understood with very personal language. When and if they do, they are on their way to create a personal bridge to religion and some of the brave among them just may cross it.

Did A Quiet Expansion Precede The Big Bang?

A question about the question: It is difficult to know; however, a better question might be,
“Do the dynamics of a quiet expansion deflate the Big Bang?”

Last update: February 16, 2015 (also, small corrections since then)
Sequel: June 5, 2016, This Quiet Expansion Challenges the Big Bang

September 2014: If you think about it, most of the world’s people have never heard of the Big Bang theory (Reference 1 – the cosmological model, not the TV series). Of those who know something about it, a few of us are somewhat dubious, “How can the entire physical universe have originated from a single point about 13.8 billion years ago?” It seems incomplete, like there are major missing parts of the story.

To open a dialogue about this pivotal scientific theory is the reason for these reflections. And, if we are successful, all of us will have re-engaged our ninth grade geometry classes and we will begin to ask a series of “what if” questions about the origins of this universe.

Big Board – little Universe. Some of you are aware of our work within several high school geometry classes (Reference 2) to develop a model called the Big Board-little universe (Reference 3). Possibly you even know a little about the 201+ base-2 exponential notations from the Planck Length to the Observable Universe. It is a study that informally began on December 19, 2011, so most of us have only begun to explore the inner workings of each of the 201+ notations.

Because we believe all things start most simply, the first 60+ notations are potential keys for understanding a rather different model of our universe. These notations (also referred to as clusters, containers, domains, doublings, groups, layers, sets, and steps) have not yet been studied per se within our academic communities (Also, see reference 4). The best guess at this time is that the range of our elementary or fundamental particles begins somewhere between the 60th and the 67th notations.

The simple mathematics (Reference 5) and the simple geometries are a given; the interpretation is wide open.

This little article is an attempt to engage people who are open to new ideas to look at those first 60+ notations. What kinds of what-if questions could we ask? Can we speculate about how geometries could grow from a singularity to a bewildering complex infrastructure within and throughout those first 60+ domains, doublings, layers, notations, and/or steps? What if in these very first steps, there is an ultra-fine structure of our universe that begets the structure of physicality? What would a complexification of geometries give us? Might we call it a quiet expansion? Though we have always been open to suggestions, questions and criticisms, we are now also asking for your insight and help.
Updates of both models are being prepared whereby those first 60+ notations of the Big Board-little universe begin to get some projections to study and debate. Also, another version of the Universe Table (Reference 6) is in preparation to emphasize every notation from 1 to 65. Also, at the time this article was introduced, we initiated a chart of base-2 exponential notations of time from the Planck Time to the Age of the Observable Universe side-by-side with our chart for the Planck Length to the Observable Universe. And, to make this study a bit more robust, we also projected a time to add the other three basic Planck Units — mass, electric charge and temperature. (Note: The very-first rough draft of that work was completed in February 2015.)

Big Bang Up. Most people start time with the Big Bang. Is there a possibility that there are events between Planck Time and the bang (or whatever sounds there were when things became physical somewhere between notations #66 to 67)?

In their 2014 book, Time in Powers of Ten, Natural Phenomena and Their Timescales, Gerard ‘tHooft and Stefan Vandoren of Utrecht University (Reference 7), use base-10 notation and assume there is nothing in the gap between the known time intervals of within theoretical physics and Planck Time.

We are doing a little fact check to see if the authors give those notations from Planck Time any causal qualities. It appears that they were not concerned about those base-10 notations until we pointed them out to them.

The first time period of interest to us is the first 20± base-10 notations which would be the first 67 base-2 notations. What happens between the Planck Units and the emergence of the elementary particles? These are real durations in time. A lot can happen.

We will be exploring this small-scale universe in much greater detail. By the 60th doubling there are quintillions-upon-quintillions of vertices with which to create many possible models. Also, in light of the work to justify the Big Bang theory, there is an abundance of information from all the years of research since the concept was first proposed in 1927 by Georges Lemaître.

Steven Weinberg, the author of The First Three Minutes (Reference 8), begins his journey through the origin of the universe at 1/100th of a second. Our hypothesis is that we can mathematically go back to a much, much smaller duration. We believe that we should start at the Planck Time and multiply it by 2. And, just as the fermion within notation 66 would be the size of a small galaxy compared to the Planck Length, 1/100 of a second between notations 137 and 138 represents an even greater gap of the ignored and unknown. We suspect starting one’s analysis so late misses key critical interactions and correlations (Reference 8b).

We’ve just started to see what the numbers can tell us.

A lot of pre-structuring of the universe could be quietly happening within such a duration (1/100th of a second). Using our most metaphorical, speculative thinking, one could imagine that the actual event within those first sixty notations was a gentle, symphonic unfolding, fully homogeneous and isotropic.* Although we should embrace all the key elements of today’s big bang theory, we should also be constantly asking, “What kinds of geometries would be required within each of the first 60 notations to render these effects?”

Perhaps the universe and our future belong to the geometers.

So, this article is to empower all of us to find the best geometers around the world to engage the Big Board-little universe model within what we call “the really-real small scale universe.” Of course, some of the work has already been done within the study of spheres, tilings, and combinatorial geometries.

If you would like to comment politely, please drop me a quick note (

Thank you.

Bruce Camber

* homogeneous Having the same property in one region as in every other region
isotropic Having the same property in all directions.


Endnotes and References:

1 A Wikipedia summary of the basic Big Bang theory. As you will see within this Wikipedia article, the basic theory has been highly formulated with a fair amount of scientific evidence. If our rather-naïve, quaint-little challenge to that model is ever to catch some traction, it will have to account for the results of every accepted scientific measurement about the Big Bang theory that has been thoroughly replicated.

2 Is There Order In The Universe? There are nine references within this article and each opens to a page that has been written since the first class on December 19, 2011.

3 This image of the Big Board-little universe is Version 2.0001.

4 This article is our very first attempt to provide a somewhat academic analysis of the work done to date. It was rejected by several academic journals so it was first released within WordPress, then the LinkedIn blog pages, and finally re-released right here.

5 The debate within Wikipedia about the importance of base-2 exponential notation resulted in their rejection of the original article. It was judged to be “original research.” We thought that judgment was just a little silly. The concepts were all out there; these articles were just to organize that data.

6 A WordPress blog page for our emerging UniverseView.

7 This article about the book, Time in Powers of Ten by Gerard t’Hooft and Stefan Vandoren, is the most comprehensive that I could find at this time. If you happened to find a better review, please advise us.

8 An online version of the entire book, The First Three Minutes by Steven Weinberg. There are many reviews, yet this one provides a little counterweight. Weinberg also wrote the forward to Time in Powers of Ten. Gerard t’Hooft (1997) and Steven Weinberg (1979) are Nobel laureates.

A chart showing the correlations between Planck Time and Planck Length at the 136th and 137th notations is here.

9 A WordPress article about very small and very big numbers. There is our initial discussion about the first 65 notations.