Abstract. A very simple ordering system that encapsulates everything, everywhere throughout the universe and throughout all time since the very beginning until the present moment is based on multiplication by 2 or base-2 exponential notation. Since December 2011, a small group of high school students and a few of their teachers have been trying to figure out what to do with their simple mathematical model. Findings to date are presented with the hope that the academic-scientific community can tell them how best to proceed.
Introduction. Since December 2011, a few high school teachers and their students have been puzzled by their very simple view of the entire universe. It seemed so simple and so elegant, it was easy to quote an American theoretical physicist, John Archibald Wheeler (1911-2008), “Behind it all is surely an idea so simple, so beautiful, that when we grasp it— in a decade, a century, or a millennium — we will all say to each other, how could it have been otherwise?”
Cf. the Ref .
Behind Wheeler’s question is a shared intuition that somehow simplicity and beauty are fundamental to science and life. We cannot imagine how there could possibly be a more simple model of the universe, i.e. one that begins at the Planck base units and within 202 notations dynamically encapsulates and appears to order everything, everywhere, throughout all time within a basic quadrant, all by multiplying-by-2 the smallest units of the most basic constituents of life (the Planck base units of length and time) until we are out to the very largest possible measurements of each.
History does not escape this model. It is all there from the beginning of time to the fullness of this moment, the Now. Even the elusive neutrino does not escape this model! And, the unrecognized substrate that gives rise to the simple neutrino is postulated.
Asking for Help. An entire small-scale universe, so robust as to be beyond imagination, is outlined, first within a chart of the Planck base units that extends out to their natural current limits, Cf. the Ref. . Then, there is an initial analysis of those numbers, Cf. the Ref. .
The earliest introduction to our work was posted in January 2012, Cf. the Refs. [4a] and [4b], and then, on about a monthly basis, we have posted our simple progress, Cf. the Ref . That chart and the rationale are our de facto pleading to engage the scientific – academic community to analyze, dissect and trisect this work, “What is wrong with this model?”
“Not encyclopedic, but new research.” An astute Wikipedia editor from MIT deleted our first attempt to write an article about our work about base-2 exponential notation from the Planck Length to Observable Universe, Cf. the Ref. . It was deemed to be original research, not encyclopedic work and it had no primary academic references. So, it began to strike us that our work on December 19, 2011 was somehow original. We were so sure that statement could not be true, it took over a year to begin to realize that it just may be true… that base-2 notation from the smallest to the largest possible measurements of a length had been an academic blind spot.
The first 60-to-67 notations. Though the substrate appears to be the mystery, we have spent a fair amount of time guessing about its most general nature. In our very first chart of the “Big Board – little universe” a number of guesses were made about the first 60+ notations. A year later more guesses were made within a new version of the chart that we dubbed “Universe Table”
Cf. the Ref. , and then “Universe View.”
Simple logic and a little intuition can be powerful tools.
Given the entire universe has been notated using simple mathematics (multiplying by 2) , basic concepts (Planck units), and imputed structural geometries, there is a skeletal outline to begin to ask, “What’s there?”, and to ask others to think about it. It seems to be a natural home for all the abstractions that academia loves but has no ordered system within which to give them some kind of universal-but-particular structure. Here consider the enigmatic mix of concepts within philosophy, theology, and psychology. Within this model each should find a place within those first 64 notations.
Perhaps periodicity is a product of essential symmetries within the universe. Every student knows in some manner of speaking, frequencies and numbers jive. There is an inherent dance within the universe. Frequencies, forms, and waves dance with numbers, points and particles. It’s the old subject-object issue all over again.
Prior to Marconi’s work within radio, nobody could image how sound could be broadcast. Then came television and we all became quasi-scientists. One of our more speculative postulations is that the essential modulating and computing functions of the human brain originate from within notations 50 to 60. This simple model opens up the back end of the very small as well as the top end to include all 201+ notations to postulate how these small-scale forms become human-scale archetypes that manifest within our epoch within our large-scale universe.
Of course, entirely speculative, but it all has a thread of simple logic which makes it cohesive. It is a bunch of numbers looking for a theory. Perhaps it might qualify as a pathway, perhaps a door, to a theory of everything. Why not? Yes, we ask, “Why not?”
Next Steps. As part of an ongoing discussion over the past couple of years about basic structures, distinguished mathematician, Prof. Dr. Philip Davis (emeritus Brown University and NIST), insisted that the sphere is more simple than the tetrahedron and, of course, he is correct. A sphere can be created with just two vertices and it takes four vertices to create a tetrahedron, the next most simple three-dimensional form.
Continuing within our most speculative framework, it might be that the sphere and vertices fundamentally define the small-scale universe in a system of forms that give rise to a substrate of archetypes of structure, substance, qualities, relations, and systems.
To open that exploration is to understand the role of Pi (π) and the dimensionless constants as gateways to the infinite, as well as those universals — order-and-continuities, relations-and-symmetries and dynamics-and-harmonies — that seem to be better options to define the infinite than space and time.
One of the first articles that I am requesting select mathematicians to analyze thoroughly was little read and highly criticized when it was first released by its authors. For some, it will be nonsense. Yet, it involves some serious mathematics and even more serious conclusions. Ref.  is more than bold and has engendered strong responses. What matters, however, is the cogency of the mathematics. So some of the finest, young and old mathematicians from around the world are being asked to examine the article, its mathematics, and conclusions. If it begins to stand the weight of such examination, and it is determined that Pi π is within the heart of all the dimensionless constants as well as the other physical constants, our simple small-scale substrate will have all the structure it needs to build out the rest of the universe.
Conclusions. It has taken us awhile to regain the confidence to write another article. We know this area of research is near and dear to many, many exquisitely trained scientists, logicians, philosophers and mathematicians. We are just high school folks. How could we possibly have stumbled onto a pathway that could lead to a theory of everything? Perhaps the only answer is, “It takes a certain naïveté to open a new door. We can only hope that it is to a more gentle and beautiful view of life and all of reality.”
Acknowledgements. My wife, Hattie Bryant, has been a loyal believer with a pragmatic skepticism that keeps me on my toes. Though it has taken years to get to this point, she has hung in there. How could one ask for anything more? There have also been many other people on this path, many-too-many to mention, for whom I will be eternally grateful. They know who they are, and I thank you.
- J.A. Wheeler, How Come the Quantum? Annals of the New York Academy
of Sciences, 480 (“New Techniques and Ideas in Quantum Measurement
Theory”), pp. 304-316 (1986),doi: 10.1111/j.1749-6632.1986.tb12434.x
- B. Camber, Five Base Planck Units, (2015, 2016)
- B. Camber, On Developing A Rationale For A Working Model Of The Universe
Based On A Quiet Expansionhttps://81018.com/2015/09/15/rationale/
- B. Camber, “Big Board – little universe:
B. Camber, The original Wikipedia article (March 2012)
B. Camber, An exploration of 101 steps from the smallest Planck length
to the human scale, and then 101 more
steps out to somewhere near the edge of the observable universe”
- B. Camber, “Is There Order In The Universe?
- B. Camber, “The Planck Length, Base-2 Exponential Notation, and Nesting Geometries.”
- B. Camber, “Universe Table – Human Scale”.
- S. Waterman and M. A. Whitehead, “A Review of a Self-Consistent Field
Approach To the Physical Constants: All Physical Constants are a Function of Pi”. In
Cascades Festschrift in Honour of Professor Emeritus M. A. (Tony)
Whitehead, The Richard Hart Symposium, McGill 27th-29th, June 2010,
Cascades (2011), pp. 172-184,
More Resources on this website to carry on this discussion: