Introduction. The Big Board-little universe Project uses base-2 exponential notation from the singularity of the Planck base units going out to this present time, Right Now, to encapsulate everything, everywhere, throughout all time1. Though seemingly a bit of an overstatement, the simple mathematics and logic appear to corroborate such a conclusion. The implications of this fledgling model seem rather far-reaching so five are presented for the discerning analysis and critical review of scholars and thinkers.
Some of the more far-reaching implications of the Big Board-little universe model:
This model begs the question about the finite-infinite relation. If space and time are derivative, finite, quantized and discrete, then what is infinite? Our working answer is continuity which creates order, symmetries which create relations, and harmonies (multiple symmetries working together) which create dynamics. These are the inherent qualities that define the infinite for science.2
There appears to be an ethical bias to the universe. Continuity-order, symmetry-relations, and harmony-dynamics also begin to define a valuation system whereby every notation at every moment has a perceived and dynamic value.3
Each notation defines an element of the current universe. Even though time is derivative, it still defines a duration within a single notation. Even though space is derivative, it still defines a length within which particular things have their beingness. In this model each notation has its own particular beingness. The entire universe actively appears to share this length (space) – time infrastructure within the small-scale universe.
The structure for homogeneity and isomorphism is defined within the small scale. It is also the bridge between the finite and infinite so renormalization works in quantum electrodynamics and universality works throughout physics on every scale.4
This model appears to trifurcate nature. These three seemingly natural domains of this model of the universe appear to be episodic:
(1) The small scale from notation 1-to-67 could generally be described as ontology and each notation just might manifest again within the human scale and then again within the large scale.
(2) Perhaps the human scale from notations 67 to 134 could be understood as the domain for epistemology. In some manner of speaking all 67 manifest in the notation for the current time.
(3) The large scale from notation 134 to 201 is currently considered the domain for cosmology. It begins when the duration (or speed) is less than one second (see notations 142 to 143). Within notation 200 (possibly 201) is the current time. Its duration is approximately 10.8 billion years. The duration at notation 134 is within a thousandth of a second.
Of course, each duration for each notation gets increasingly short as we approach the Planck Time. The duration at notation 67 is 10-to-the-negative-23 seconds (10-23). Notation 67 is approximately the Planck Length multiple where fermions and protons appear. There will be many adjustments of these numbers as others help to fine-tune the model.5
All people and things appear to be trifurcated.
One might hypothesize or hypostatize that from the small-scale universe we get our being. Systems are imputed between the 50th and 60th notation; and within systems, the human mind has also been imputed have notations within which to be.
From the human-scale we get our knowing. Carl Jung called these archetypes. A special vocabulary will emerge for this part of our self-definition.
Within the Now, this moment, today, there is an integration as a thing, an entity. All human history, all civilization is within the 200th notation. Just as an aside, if time travel were to become possible, it will be as an observer. Interactions would also require trifurcating, i.e. simultaneously entering the space and duration of the being and knowing of any given moment in time.
Yes, today is Thursday, November 26, 2015. Paris is healing. Al-Raqqah is burning. And, without question, we all need a new model of who we are and why we are. There is simply too much darkness within this world and within our views of the universe.
Many people are aware that we have been on a speculative journey 1 that began in 2011 in a high school. Our journey is based on an idiosyncratic way of looking at our universe.2 Everything, everywhere, throughout all time is contained within just over 201 base-2 exponential notations from the Planck Base Units out to their largest possible measurements, always “this given moment” or the Now. Although our charts are simple, logical, and comprehensive, and all the numbers show us an exquisitely interconnected universe, they challenge some of our commonsense worldviews.
It is not easy to change one’s conceptual frame of reference. Oftentimes I feel a little slow because it becomes so difficult to put one-and-one and two-and-two together. But, we are motivated to break through the bottleneck of questions that have remained unanswered over our lifetime and throughout the centuries. We are pushed to ask, “What are we missing?” Taunting myself, I say, “Go over this one more time; you really are missing something here.”
Dark Matter and Dark Energy are in that camp for me. Yet, recently a faint light has come on. A new book by physicist, Lisa Randall, had become a subject of a discussion over lunch. The subjects of cosmology have always been way out there for me. Since childhood, especially on the occasion of a dark, clear Maine night, I have had a visceral reaction to it all. Spooked, jammed and suffocated by the vastness of the seemingly infinite universe, truly impossible to take it in, I learned to avoid cosmology and astronomy.
Dark Matter 3, 4 (links that go to Wikipedia open new tabs or windows). I had begun thinking that Dark Matter was a misnomer. Within the Big Board – little universe model, it is not dark per se, especially if part of the first 60 notations where there is an absence of light. Within our isotropic and homogeneous universe, space-time-charge-mass-and-temperature have a tightly-woven fabric, tiled and tessellated defined by base-2 exponential notation and the Planck Base Units.
Though associated with analyses of structures on the order of galactic scale, Dark Matter may best be seen within the context of all 201+ base-2 notations, yet especially the first 60 or so notations.
Everything, everywhere, throughout all time. That is the simple mathematical model we call the Big Board-little universe. We can see that space and time are contained. We can see a very simple beginningand we see-experience-feel the current time. We have our seeing-experiencing-feeling moments within the current time which is within the 201st notation. We have the physical definition of parts, for now I call these our physical archetypes between the 67th and 116th notations within the Human-Scale Universe. Our most essential being, the archetypes of our archetypes, are within the small-scale universe. Everything-everywhere-throughout-time has some kind of presence with the small-scale, human-scale, and large-scale universe.
There will be many challenges ahead to texture, define and defend such statements especially given that Dark Matter now constitutes only as much as 26% of the universe.5 Out of our naïveté, it just may be that our simple model, this Big Board – little universe, gives Dark Matter a space and time, mass and charge, and a reason for being, and for being where it is.
I believe our little chart is like a gold and diamond mine because the key figures of the universe are all there just waiting to be examined. These figures have been given a cursory review. It is now time for the professionals to go in and take a hard look. I believe we can find configurations within those first 60 notations that can give rise to the observations and research throughout the entire history of cosmology and astronomy.
Most speculative: The small-scale universe is the human-scale universe is the large-scale-universe. It is discrete, quantized and derivative of continuities and symmetries and even an overarching harmony of the universe. Within this speculative journey we are defined by every notation. Our particularity and humanity come out within the 101 to 116th of the Planck Length but we are fully at the 201+ notation within “the moment” or “the now.”
A special challenge will be to come up with a better name than Dark Matter. Although the inherent continuity equation for those 201+ notations has classic characteristics generally used to describe God, here we will rely strictly on the simple logic and mathematics, the Planck Base Units, and basic geometries to create the parameters for our naming convention.
Dark Energy. Though this conceptual frame of reference is related to the expansion of the universe, and dark energy weighs in at 68.3% of the total energy in today’s observable universe, we would postulate that it, too, is related through the Planck Base Units and the systemic expansions within the first 60 steps of the Big Board – little universe model. Light (a light second) does not appear until the 143 notation; that requires another 80 or so steps or notations or doublings from those first 60.
Obviously, for me, concepts need time to incubate.
First, as uneven as we are, I hope we are getting closer to justifying to the academic communities to come in to take a look at the inherent structures of the first 60 notations. To begin examining how those first 60 notations came to be and why they have been ignored, we have begun to focus on all the research and all the data from cubic-close packing (ccp), face-centered cubic (fcc), hexagonal close-packed (hcp), root system (A3) and Lie theory. It seems that all these applications and functions apply to the first 60 notations. And, inside those first 60 steps come all the dimensionless constants and soon thereafter, all the physical constants, and soon thereafter, the fermions and every expression of physicality.
The most simple engaging the most simple: Here may be the beginning of value structure.4 If so, it necessarily resides deep within the fabric of the universe, the very being of being. Could these very first doublings be the essential tension of creation?
NOTE: The TOT as a tiling would be the largest-but simplest possible system that spatially connects everything in the universe. Yet, even with just octahedrons and tetrahedrons, it is also exquisitely complex; we’ll see the beginnings of that complexity with the many variations of R2 tilings (two dimensional) within this initial R3 tiling (three dimensional).6 Thus, the TOT would also be expanding every moment of every day opening new lines instantaneously. One might say that the TOT line is the deepest infrastructure of form and function. Perhaps some might think it is a bit of a miracle that something so simple might give such order to our universe.
The purpose of this article is to begin to introduce why we believe that this could be so.
Notwithstanding, we acknowledge at the outset that our work is incomplete. By definition tilings are perfect and the TOT tiling is the most simple. In our application these tilings logically extend from the within the first doubling to the second doubling to all 201+ doublings necessarily connecting all the vertices within the universe.
We Can Only Speculate. We can only intuit the form-functions of this tiling as it expands. And, yes, within the first 60 or so notations, it seems that it would extend equally in all directions. With no less than two million-trillion vertices (quintillion), using our simple math of multiplying by 2, we will see how that looks and begin to re-examine our logic. Again, this tiling is the most simple perfection. And although we assume the universe is isotropic and homogeneous, there is, nevertheless, a center of this TOT ball, Notations 1, 2 and 3.8
That center even when surrounded by no less than 60 layers of notations is still smaller than a fermion or proton. This model uniquely opens up a very small-scale universe which for so many historic reasons has been ignored, considered much too small to matter.
Nevertheless, it seems to follow logically that this TOT tiling is in fact the reason the universe is isotropic and homogeneous.9
A SECOND GROUP OF TILINGS. Within the octahedron are four hexagonal plates, each at a 60 degree angle to another. Each of these plates creates an R2 tiling within the TOTs that is carried across and throughout the entire TOT structure.
These same four plates (R2 tilings) can also be seen as triangle. There ares six plates of squares. One might assume that all these plates begin to extend from within the first ten notations from the Planck Length, and then, in theory, extend throughout our expanding universe.
Only by looking at our clear plastic models could we actually see these different R2 tilings.
We have just started this study and we are getting help from other school teachers.
We were challenged by Edkins work to see if we could find her plates within our octahedral-tetrahedral models. We believe we can find most of her tilings within the models.
Within the Wikipedia article on Tessellation (link opens a new window), there is an image of the 184.108.40.206 semi-regular tessellation. We stopped to see if we could find it within our R3 TOT configuration. It took just a few minutes, yet we readily found it! One of our next pieces of work will be to highlight each of these plates within photographs of our largest possible aggregation of nesting tetrahedrons and octahedrons.
Here the square base of the octahedrons couple within the R3 plate to create the first manifestation of the cube or hexahedron. We will also begin looking at the very nature of set theory, category theory, exponential objects, topos theory, Lie theory, complexification and more.12
Obviously there are several R2 tilings within our R3 tiling. How do these interact? What kinds of relations are created and what is the functional nature of each? We do not know, but we will be exploring for answers.
A THIRD TILING BY THE EXPERTS. Turning to today’s scholars who work on such formulations as mathematical jigsaw puzzles, I found the work of an old acquaintance, John Conway. In 2011 with Professors Yang Jiao and Salvatore Torquato (all of Princeton University), they defined a new family of three-dimensional tilings using just the tetrahedrons and octahedrons.13
We are studying the Conway-Jiao-Tarquato (CJT) tiling. It is not simple. Notwithstanding, conceptually it provides a second R3 tiling of the universe, another way of looking at octahedrons and tetrahedrons. Here are professional geometers and we are still attempting to discern if and how their work fits into the 201+ base-2 notations. And, we are still not clear how the CJT work intersects with all of the R2 tilings, especially the four hexagonal plates within each octahedron.
AS ABOVE, SO BELOW
It takes on a new meaning within this domain of the very-very-very small. Fine structures and hyperfine structures? Finite and infinite? Delimited infinitesimals? There are many facets — analogies and metaphors — from the edge of research in physics, chemistry, biology and astrophysics that can be applied to these mathematical and geometric models.
From where do these expressions of order derive? “From the smallest scale universe…” seems like a truism.
Perhaps this entire domain of science-mathematics-and-philosophy should be known as hypostatic science (rather loosely interpreted as “that which stands under the foundations of the foundations”).
Notes & Work Areas:
Endnotes, Footnotes, and other References
1. This article is linked from many places throughout all the articles and documents. It is a working document and still subject to updates.
2. In 2006 I wrote to Dr. Francis Collins, once director of the National Genome Research Institute and now the National Institutes of Health. His publisher sent me a review copy of his book, The Language of God, and we spent several hours discussing it with her. The genome, the double helix and RNA/DNA have structure in common and it all looks a lot like a TOT line. Collins, a gracious and polite man, did not know what to say about the more basic construction.
Also, on a somewhat personal note, although we call it a TOT line it is hardly a line by the common definitions in mathematics; it’s more like Boston’s MBTA Orange Line. Now here is a real diversion. Thinking about Charlie on the MTA in the Boston Transit (a small scale of the London Underground or NYC Transit), this line actually goes places and has wonderful dimensionality, yet in this song, it is a metaphorical black hole. Now, the MBTA Orange Line is relatively short. It goes from Oak Grove in Malden, Massachusetts to Forest Hills in Jamaica Plain, a part of Boston where I was born.
6. As of this writing, there does not appear to be any references anywhere within academia or on the web regarding the concept of counting the number of vertices over all 201+ notations. Using the simplest math, multiplying by 2 (base-2), there is a rapid expansion of vertices. Yet, it can also be argued that vertices could also expand using base-4, base-6, and base-8. That possible dynamic is very much part of our current discussions and analysis. It is all quite speculative and possibly just an overactive imagination.
8. If the Planck Length is a vertex from which all vertices originate, and all vertices of the Universe in some manner extend from it, the dynamics of the notations leading up to particle physics (aka Particle Zoo) become exquisitely important. Questions are abundant: How many vertices in the known universe? What is the count at each notation? Do these vertices extend beyond particle physics to the Observable Universe? In what ways are the structures of the elementary particles analogous? In what ways are the periodic table of elements analogous? What is the relation between particle physics and these first 60 or so notations? Obviously, we will be returning to each of these questions often.
10. The two small images in the right column are of a very simple four-layer tetrahedron. The Planck Length is the vertex in the center. The first doubling creates a dynamic line that can also be seen as a circle and sphere. The next doubling creates the first tetrahedron and the third doubling, and octahedron and another tetrahedron, the first octahedral-tetrahedral cluster also known as an octet. The fourth doubling may be sixteen vertices; it may be many more. When we are able to understand and engage the Freeman Dyson logic, the number of vertices may expand much more rapidly. Again considering the two images of a tetrahedron in the right column and its four layers, today we would believe that it amounts to three doublings of the Planck Length. When we begin to grasp a more firm logic for this early expansion, we will introducing an image with ten layers to see what can be discerned.
11. I went searching on the web for images of tetrahedrons and tessellations or tilings of hexagons. Among the thousands of possibilities were these very clean images from Jo Edkins for teachers. Jo is from the original Cambridge in England and loves geometry. She has encouraged us in our work and, of course, we thank her and her family’s wonderful creativity and generosity of spirit. http://gwydir.demon.co.uk/jo/tess/bighex.htm
12. Virtually every mathematical formula that appeared to be an abstraction without application may well now be found within this Universe Table, especially within the very small-scale universe. We will begin our analysis of set theory, category theory, exponential objects, topos theory, and Lie theory to show how this may well be so.
14 Our example of a TOT line was introduced on the web in 2006. In July 2014, this configuration was issued a patent (USPTO) (new window). That model is affectionately known within our studies as a TOT Line.
Please note: Many pages within The Big Board-little universe Project were originally posted on the web within the Small Business School website. Some links still go back to the original site. If so, please your back button to return to this page. Thank you.
All three major domains of human activity — Science, Business & Religion — are fraught with travail and have been blemished with the worst of human behavior. Notwithstanding, there is a deep ethical bias within science which is also an essential infrastructure of business, and it is the heart of good religion.
The circular color chart opens the door on the story. This chart seems to represent all the energies, negative and positive, within our finite universe, including our finite world, and our finite life. Using Cartesian coordinates as the container, here the x-axis (horizontal axis) is the totality of time. The vertical y-axis becomes the totality of space. This work emerged from our earlier discussions about foundations.
These thrusts -the energy and purpose – are the most basic forms/functions of life. Though part of our business formulations for many years, this circular image marks the first time it has been used as a comprehensive valuation structure and the basis for modelling the universe (a very large file, may open slowly).
Above the x-axis are all the constants and universals that define who we are, our life, the arts, sciences, business and religion. Below that x-axis — domains that involve so much of human activity — is the antithesis of Order/Continuity, Relations/Symmetry, and Dynamics/Harmony.
Thus, we have the beginnings of business (and economics), ethics and morality.
Any assertion that counters life’s evolving perfections is not religion (at best, it’s a cult*); it is also not business (it’s exploitation or a bad company); certainly it is not good government; and most often, it is not even good science.