In December 2011 a group of high school people went inside the tetrahedron, dividing by 2, and found the half-sized tetras in the four corners and an octahedron in the middle. We went inside that octahedron, dividing by 2, found the half-sized octas in each of the six corners and eight tetras in each face, all sharing a common center point. We kept going within all 19 objects. Within just a few steps we found our nematode friends. In another few steps the prochlorococc greeted us, “Set em up baby…”
In just 45 steps within we were zipping by the fermions and protons and just kept going! In the next 67 steps, you wouldn’t believe what we saw! We were at the door of a singularity that Max Planck gave us and all those secret codes, but it took 100 years and Frank Wilczek to begin to interpret them (2001, Physics Today, Scaling Mt. Planck I-III).
Just over 112 notations. What was that?
It didn’t take too long before we got the bright idea, “Let’s multiply by 2.” What an epiphany! In less than 90 steps we were out to the Age of the Universe and the Observable Universe. Looking at ourselves, we were lost within all this new information, so we decided to turn to the experts. Huh? We found Kees Boeke’s base-10 work from 1957 but he only had 40 quick jumps (Cosmic View) and missed so much of life! We found Stephen Hawking but he was in tight with big bang theory. Where are our experts?
What? Huh? Our knowledge of the universe is so incomplete, our sense of the universal is so limited, our understanding of the constants is so elementary, we are flying blind.
Now we are amateurs, but we really feel that biology and the search for life must begin with that initial creation, the first moment, when there was a profound integration, and come through it all right to the 200th notation to our present day. Let’s encapsulate the universe so we can truly address the “… transcendent qualities in the human consciousness, and sense of human need” (from your Ted Talk).
Are we crazy? Of course, we are, but hopefully delightfully so! Thanks.
Questions about the nature of mass and charge have been addressed by the most highly-respected scientists over the centuries. Both mass and charge are manifestations of fundamental faces of reality. Both have necessarily-related concepts. Mass has density, weight, force and the mass-energy equivalence . And charge has electric charge (Coulombs, ampere, time and force) and color charge (generating set of a group, symmetry groups, and Hamiltonian). All these concepts have been reviewed thousands-upon-thousands of times. However, to our knowledge, never have these concepts been reviewed within the framework of the first 65 or so notations of the Quiet Expansion model. Here, within each notation, we are using a most-simple mathematical formulation to ask the question, “What are these numbers saying about the nature of reality?”
A possible answer
It seems that the mathematics, particularly those ratios rendered within each doubling of the Planck base units, defines mass (weight, density, force, mass-energy equivalence) and charge (both electric and color) as a derivative of the other base units and all of the constants such as light, gravity, and the reduced Planck constant that define them.
To research what that means and to prepare to write this document, the very creative work of several PhD research physicists came to our attention. It is all truly amazing work. These are scholars who are attempting to push through some of the well-known problems with the Standard Model. Some have posited exciting new theories and ideas. We could easily get lost in that sea of ideation. We can’t. It is all very encouraging to feel their creativity, however, our model is based on simplicity — simple concepts and simple mathematics. So, we won’t stray too-too far from where we are as we attempt to impute meaning to our simple doublings of the five basic Planck units.
Notwithstanding, within the first 60 or so notations, mass, time, space, charge, and temperature take on a very different meaning. These five are so inextricably related, they can not be pulled apart and each truly exists in reality, but prior to the 65th notation can only be known by their ratios .These ratios are real, and a real definition of a very real reality. Each notation builds upon the prior notations. All notations continue their prior notation’s more fine doubling as well as what I’ll call their archetypal doubling; that is the doubling into the next notation. With each doubling our universe is increasingly networked and related. Within the gross doublings, these networks begin systematizing sets and groups, given the definitions within and between each notation, and begin to emerge as cells within the cells notation, as people within the “people” notations, as solar systems within the solar system notations, as galaxies within the galaxy notations, and so on.
“I have learned that many of the Greeks believe Pythagoras said all things are generated from number. The very assertion poses a difficulty: How can things which do not exist even be conceived to generate? But he did not say that all things come to be from number; rather, in accordance with number – on the grounds that order in the primary sense is in number and it is by participation in order that a first and a second and the rest sequentially are assigned to things which are counted.”
– Theano, On Piety (as reported by Thesleff, Stobaeus, and Heeren)
Please note: Links inside the body of the article most often open a new tab or window within a Wikipedia page. For those occasional inks that do not open new windows, please use the back-arrow key to return to the referring page. All links within the Endnotes will eventually go to source materials if posted on the web.
That little fact is as unknown as it is incredible (even as of January 2016 when this article was first posted).
In December 2011 we could find no references to the 201+ notations in books or on the web. We did find Kees Boeke’s 1957 work with base-10 notation. It was a step in the right direction, but it had no lower and upper boundary, no Planck numbers, and no geometry. It had just 40 steps amounting to adding zeroes.
We were looking for anything that could justify our “little” continuum. We didn’t know it at the time, and we later learned that we were looking for those deep relations and systems that give us homogeneity and isotropy, a cosmological constant, and an equation of state. Though we already had put everything, everywhere throughout all time in an ordered relation, we had no theoria, just the praxis of numbers. We tried to set a course to go in the direction of a theory that might bind it all together.
The first 60+ doublings constitute a range that scholars have been inclined to dismiss over the years as being too small; some say, “…meaninglessly small.” Yet, being naive, it seemed to us that the very simple and very small should be embraced, so we started thinking about the character of the first ten (10) doublings. Trying to understand how to “Keep It Simply Simple,” we were pleasantly surprised to discover that there was so much work actively being pursued by many, many others throughout academia and within many different disciplines to develop the logic of the most simple and the most small.
It is from within this struggle to understand how all these numbers relate, we began our rank ordering of all possible numbers. This exercise helps to focus our attention.
Planck Length and Planck Time. One might assume that we would put the five Planck base units among the most important numbers to construct the universe. As important as each is, it appears at this time that none of them will be among the Top 5. Although very special, the Planck numbers are determined by even more basic and more important concepts and numbers. At the very least, all those numbers will come first.
“#10” for us it is, “Continuity contains everything, everywhere, for all time, then goes beyond.” One of the key qualities to select our most important numbers is the condition of continuity and discontinuity starting with the simplest logic and simplest parts.
A Quick Review of the Top Ten Numbers in the Universe.
Because many scholars have addressed the question, we did a little survey.
Pi was somewhere on most everybody’s list among our sample.
Base-2 notation. Yes, our work with base-2 notation originated from within a high school. We have no published scholarly articles and there has been no critical review of our emerging model. Nevertheless, we forge ahead with our analysis of numbers and systems.
Not a very popular topic, one might ask, “How could it possibly be your second choice?” Even among the many histories of Kepler’s voluminous work, his conjecture is not prominent. To solve a practical problem — stack the most cannon balls on the deck of a ship — he calculated that the greatest percentage of the packing density to be about 74.04%. In 1998 Professor Thomas Hales (Carnegie Mellon) proved that conjecture to be true. By stacking cannon balls, all the scholarship that surrounds cubic close packing (ccp) enters the equation. The conjecture (and Hales 1998 proof) opens to a huge body of current academic work.5 There we found this animated illustration on the right within Wikipedia that demonstrates how the sphere becomes lines (lattice), triangles, and then a tetrahedron. With that second layer of green spheres emerges the tetrahedral-octahedral couplet.
This image file (right) is licensed under the Creative Commons Share-Alike 2.5 Generic license.
Revisions. As we find experts to guide us within those disciplines where pi has a fundamental role, undoubtedly sections of the article will be substantially re-written and expanded. Our goal has been to find the most logical path by which all of space and time becomes tiled and tessellated. Perhaps there is a new science of the extremely small and the interstitial that will begin to emerge. These just might be foundations of foundations, the hypostatic, the exquisitely small, the ideal.6 We plan to use all the research from Kepler to today, particularly the current ccp (hcp and fcp) research from within our universities, in hopes that we truly begin to understand the evolution of the most-simple structures.
The little known 7.356103 degree gap is our fourth most important number, the possible basis for diversity, creativity, openness, indeterminism, uniqueness and chaos.7 That Aristotle had it wrong gives the number some initial notoriety; however, it is easily observed with five regular tetrahedrons which would have eight vertices. It appears to be transcendental, non-repeating, and never ending. Where the tetrahedron with four vertices and the octahedron with six have been been whole, ordered, rational, and perfect, tessellating and tiling the entire universe, the potential for the indeterminate which has the potential to become the chaotic resides somewhere deep within the system. We believe that place just may be right here.
Within this infinitesimal space may well be the potential for creativity, free will, the unpredictable, and the chaotic. Here may well be the basis for broken symmetries. Of course, for many readers, this will be quite a stretch. That’s okay. For more, we’ll study chaotic maps and the classification of discontinuities.
Of all the many articles and websites about the golden ratio and sacred geometry, our focus is on its emergence within pi and within the platonic solids. Phi is a perfection. It is a mathematical constant, a bridge to infinity. We are still looking to see if and how phi could unfold within the tetrahedral-octahedral simplex. Could that answer be within Petrie polygons? The magic of the golden ratio does unfold with the dodecahedron, the icosahedron, and the regular pentagon. Within this listing, phi has bounced back and forth with the Pentastar gap. Which manifests first? Is it manifest if it is inherent?
Starting with this article, we have begun an active study of Phi and its relations to pi and the Platonic solids. Although there are many, many papers about phi, none are from our special perspective of 201+ notations.
We are the first to admit that we are way beyond our comfort zone, yet to analyze and interpret the processes involved within each of the doublings, each an exponential notation, requires tools. This Feigenbaum constant gives us a limiting ratio from each bifurcation interval to the next…. between every period doubling, of a one-parameter map. We are not yet sure how to apply it, but that is part of our challenge.
It gives us a number. It tells us something about how the universe is ordered. And, given its pi connection, we need to grasp its full dimensions as profoundly as we can. We have a long way to go.
We have been working on our little model since December 2011. Over the years we have engaged a few of the world’s finest scientists and mathematicians to help us discern the deeper meaning of the Planck Base Units, including the Planck Constant. We have studied constants from which the Planck numbers were derived, i.e. the gravitational constant (G), thereduced Planck constant (ħ), the speed of light in a vacuum (c), the Coulomb constant, (4πε0)−1 (sometimes ke or k) and the Boltzmann constant (kB sometimes k). This engagement continues. We have made a very special study of the Planck Base Units, particularly how these numbers work using base-2 exponential notation and with the Platonic solids. We had started with the Planck Length, then engaged Planck Time. Finally in February 2015, we did the extension of Planck Mass, Charge, and, with a major adjustment to accommodate simple logic, Temperature. We have a long, long way to go within this exploration. Essentially we have just started.9
Notwithstanding, there is a substantial amount of work that has been done within the academic and scientific communities with all the Planck numbers and those base numbers that were used to create the five Planck base units. Perhaps chemistry professor, C. Alden Mead of the University of Minnesota began the process in 1959 when he first tried publishing a paper using the Planck units with serious scientific intent. Physics professor Frank Wilczek of MIT was the first to write popular articles about the Planck units in 2001 in Physics Today (312, 321, 328). From that year, the number of articles began to increase dramatically and experimental work that make use of these numbers has increased as a result. https://bblu.org/2016/01/08/number/#7
In studying the functionality of these many numbers, especially those among the dimensionless constants, we believe this list will evolve and its ordering will change often. In searching the web for more information about about dimensionless constants, we came upon the curious work of Steve Waterman and an emeritus chemistry professor at McGill University in Montreal, Michael Anthony (Tony) Whitehead. I showed their work to a former NIST specialist and now emeritus mathematics professor at Brown University, Philip Davis. He said, “There are always people who wish to sum up or create the world using a few principles. But it turns out that the world is more complicated. At least that’s my opinion. P.J.Davis” Of course, he is right; Einstein did a good job with e=mc2. Because claiming to find all the physical constants derived by using pi, the isoperimetric quotient, close cubic packing and number density is not trivial10, we’ll be taking a second look. Perhaps they are onto something! We have brought their work out in the open to be re-examined and in so doing we will re-examine over 140 physical and mathematical constants. This work is also ongoing.
This number is important because it creates a boundary condition that is generally recognized for its accuracy throughout the scientific and academic communities. Though it may seem like an impossibly large number of years, it becomes quite approachable using base-2 exponential notation. Without it, there is no necessary order of the notations.
Although there are many different measurements of the age of the universe, for our discussions we will use 13.799±0.021 billion years. The highest estimate based on current research is around 13.82±0.021 years. Also, within this study there are some simple logic problems. In 2013, astrophysicists estimated the age of the oldest known star to be 14.46±0.8 billion years.
Notwithstanding, using base-2 exponential notation all these measurements come within the 201st notation. At the 143rd notation, time is just over one second. Within the next 57 doublings, we are out to the Age of the Universe. So, with the Planck Time as a starting point and the Age of the Universe (and our current time) as the upper boundary, we have a container within which to look for every possible kind of doubling, branching and bifurcation. We can study hierarchies of every kind, every set, group or system. Eventually we can engage holomorphic functions within our larger, ordered context, i.e. the seen-and-unseen universe.11https://bblu.org/2016/01/08/number/#8
2We are simple, often naive, mathematicians. We have backed into a rather unique model of the universe. To proceed further we will need to understand much more deeply a diverse array of relatively new concepts to us; we are up for the challenge. We have introduced just a few of those many concepts that attempts to define the very-very small and/or the transformations between the determinant and the indeterminant. There will be more!
3Of the Top Ten Reasons, the first three given are our first principles. We know it is an unusual view of life and our universe. The sixth reason advocates for a Quiet Expansion of our universe whereby all notations are as active right now as they were in the very earliest moments of the universe. When space and time become derivative, our focus radically changes. It opens a possible place for the Mind down within the small-scale universe. Our current guess is between the 50th and 60th notations. The archetypes of the constituents of our beingness are between notations 67 (fermions) to notation 101 (hair) to notation 116 (the size of a normal adult). Then, we live and have our sensibility within notation 201, the current time, today, the Now. So, this unusual view of the universe has each of us actively involved within all three sections of the universe: small scale, human scale, and large scale. To say that it challenges the imagination is a bit of understatement.
4Open Questions. There are many open questions throughout this document. It is in process and will surely be for the remainder of my life. All documents associated with this project may be updated at anytime. There should always be the initial date the document was made public and the most recent date it was significantly updated. Although the Feigenbaum constants are our seventh number selected (and there are more links and a little analysis there), we will attempt to find experts who can guide us in the best possible use of these two constants within our studies. Bifurcation, it seems, has an analogous construct to cellular division, to chemical-and-particle bonding, to cellular automaton (especially Rule 110,) and to the 80 categories of binary operations.
6 A hypostatic science. Our small-scale universe, defined as the first 1/3 of the total notations, ranges from notation 1 to just over 67. It is established only through simple logic and simple mathematics. Because it cannot be measured with standard measuring tools or processes, validating its reality requires a different approach. Because it cannot be measured with standard measuring tools or processes, validating its reality requires a different approach. Our first indication that it may be a reality is found between notations 143 and 144 at exactly one second where the speed of light “can be made” to correspond with the experimental measurement of the distance light travels in a second. Currently it appears to be one notation off which could be as brief as just one Planck Time unit.
One of our next tasks is to carry that out to a maximum number of decimal places for Planck Time and Planck Length, and then to study the correspondence to a Planck second, a Planck hour, a Planck Day-Week-Month, a Planck Light Year, and finally to the Age of the Universe and the Observable Universe.
Our goal is to determine if this is the foundational domain for the human scale and large-scale universe. We are calling this study a hypostatic science because it is a study of the foundations of foundations.
7From SUSY to Symmetry Breaking and Everything In Between. One of the great hopes of the Standard Model and many of the CERN physicists is that supersymmetries will be affirmed and multiverses will wait. Within the Big Board-little universe model, their wish comes true. Plus, they gain a reason for quantum indeterminacy and embark on a challenge to apply all their hard-earned data acquired to embrace the Standard Model to the most-simple, base-2 model.
8Cellular Automaton. Although the discipline is intimately part of computer science, its logic and functions are entirely analogous to mathematical logic, functions, and binary operations. We have just started our studies here with great expectations that some of this work uniquely applies to the first ten notations.
9The Planck Platform. All the numbers associated with the generation of the Planck Constant and the five Planck base units, plus the Planck units unto themselves are grouped together until we can begin to discern reasons to separate any one number to a notation other than notation 1.
11The first 67 notations. Given the work of CERN and our orbiting telescopes, we can see and define most everything within notations 67 to just over 201. The truly unseen-unseen universe, defined only by mathematics and simple logic, are: (1) the dimensionless constants, (2) that which we define as infinite, and (3) the first 60-to-67 notations. It is here we believe isotropy and homogeneity are defined and have their being. It is here we find the explanation for the most basic cosmological constant. It is here the Human Mind takes its place on this grid which claims to include “everything-everywhere-for-all-time.”
In December 2011 two teachers and about 80 high school students rather naïvely began to explore a geometric progression that first went down in size to the Planck Length then reversed to go back up all the way to the Observable Universe (most links open a tab or window and go to an in-depth Wikipedia page).
The first chart to be developed, pictured on the left, measures 60×11 inches. It is a view of the entire universe and has just over 200 base-2 exponential notations (dividing or multiplying by 2, over and over again). Thinking that this simple math was already part of academic work, they began asking friends and family, “What is right or wrong within our logic for this model?” A two-year search did not uncover any references to base-2 and the Planck Length.* In that time, asking around locally and then globally, many people were puzzled and asked, “Why haven’t we seen a base-2 scale of the universe before now?”
An Integrated Universe View
Dubbed Big Board – little universe, this project started as a curiosity; today, it is an on-going study to analyze and develop the logic and potential links from their simple mathematics to all the current mathematics that define the universe, all its parts, everything from everywhere, and from the beginning of time to this very moment in time. Their hope is that this simple logic has simple links to real realities. Their standing invitation is, Open To Everyone, to help. This chart follows the progressions from the smallest to the largest possible measurement of a length. Subsequent charts engage the other Planck base units. With more questions than answers, this group is trying to grasp the logic flows in light of current academic-scientific research. Progress is slow.
They ask, “Where are the informed critics to tell us where we are going wrong?” One rather brilliant, young physicist told them that the concept for this project is idiosyncratic. They quickly learned how right he was. Nobel laureates and scholars of the highest caliber were asked, “What is wrong with our picture? Where is our fallacy of misplaced concreteness?” The group is slowly analyzing the logic and developing their thoughts as web postings with the hope that somebody will say, “That’s wrong” and be able to tell them in what ways they have failed logically and mathematically.
If not wrong, the extension of their basic logic could begin to yield rather far-reaching results. For example, the Big Bang theory could get a special addendum, the first 67 notations. That would make it simple, symmetric (entirely relational), predictive, and totally other. The entire universe could get an infrastructure of geometries whereby many issues in physics, chemistry and biology could be redressed. The finite-infinite relation is opened for new inquiries. In this model of the universe, time-and-space are derivative of two quantitative qualities of infinity: continuity-and-symmetry. As a result, these derivative relations begin to have an inherent qualitative or value structure. If so, ethics and the studies of the Mind (the discernment of qualities) just might, for the first time in history, become part of a scientific-mathematical continuum. A trifurcated definition of the individual may emerge whereby people are simultaneously within the small scale, human scale, and large scale universe. Embracing a different sense of the nature of space and time by which both are localized by notation is surely enough; yet there will always be more. There are many working postings that have been written since their first chart; all of it needs constant updating. Many can be found through the top navigation bar option, INDEX.
Notes, lesson plans and posts (and all new posts) are being consolidated and linked from this homepage. Now called, The Big Board – little universe Project, it is a Science-Technology-Engineering-Mathematics (STEM) application. Secondary schools from around the world are being invited to join the exploration. Daily work on the topic is being researched, developed, and communicated through a sister website, http://81018.com.
The earliest postings and blogs were done by Bruce Camber within a section of his website — SmallBusinessSchool.org. That site supports a television series, Small Business School, that he and his wife, Hattie Bryant, started. It aired for 50 seasons on most PBS-TV stations throughout the USA and on thousands around the world via the Voice of America-TV affiliates.
Articles and blogs have been posted on WordPress, LinkedIn, Blogger, and Facebook (often those links open in new windows). An April 2012 article, formatted for and displayed within Wikipedia for a few weeks, was deleted on May 2, 2012 as “original research” by highly-specialized Wikipedia editors. Only then did this little group of teachers and students finally begin to believe that base-2 notation had not already been applied to the Planck base units. And, as they have grown in their analyses, it has become increasingly clear that this area of simple math and simple logic is a relatively new exploration and that notations 1-to-67 may be a key to unlock a new understanding of the nature of physical reality.
* Footnote: In 1957 Kees Boeke did a very limited base-10 progression of just 40 steps. It became quite popular. In July 2014, physicists, Gerard ‘t Hooft and Stefan Vandoren wrote a scholarly update using base-10. Notwithstanding, base-2 is 3.3333+ times more granular than base-10 plus it mimics cellular reproduction and other naturally bifurcating processes in mathematics, physics, chemistry, biology, topology, botany, architecture, cellular automaton and information theory; it has a geometry; it has the Planck base units, and, it has a simple logic and so much more.
Elitists of every kind are caught up in the fallacy of misplaced concreteness. The abstract thought they treat as real, is “I am more important than you and my insights about life are better than yours.” They hold that their beliefs, attitudes, and sense of self are a proper basis for making judgments about “really-real” realities. In spirit and in fact, we are all more alike than different and we all don’t know what we don’t know. Here is a simple example.
We are family whether we like it or not. Mathematics provides a simple logic.
Back in 1992, I had a special apron made to give as a Christmas gift for everyone in my immediate family and some of the extended family. As you can see, this apron (as pictured on the right) proclaims, “We are family! Everybody …includes you and me.”
Below that heading was a progression of our gene pool as we go back each generation. With a 20-year average spread for each generation, it didn’t take long to see how richly diverse we necessarily would become within 1000 years. Even with all the inter-marriage within relatively small villages and towns, diversity is quickly introduced with the unknowns.
The final conclusion was simply, “You’ve got the whole world in your genes.”
Let us see. Take a look at the picture on the right. Consider each of those four columns:
On far left are the years going back in time. It uses 30 years per generation. Many would argue that 20-year average might be more appropriate. It has only been in the last few generations that the average has climbed up over 20 years. In the USA in 2007, the average was 25.2 years (U.S. Census Bureau 2007, November 30, 2007).
The next column is the successive number of generations as we go back in time. Just imagine if everyone in your family throughout the last 400 years magically came alive and were present at your birth. How many people would be there to greet you? Most people do not have a clue.
In the fourth column there is a discussion. The challenge is to grasp the simple concept that you have the entire world in your genes… that everyone on earth is related.
The First Thousand Years
Your immediate family
There is your Mom’s side & your Dad’s side.
Just 20 years ago
Four grandparents – two more uniques
About 40 years ago
Eight great-grandparents; four more uniques
60± years ago
16 great-great grandparents; 8 more uniques
80± years ago
32 great, greats; 16 more possibilities
64 Great-Greats; up to 32 more possibilities
400 + years ago.You can easily calculate the year. In just just 20 big generations we all have over 1± million genetic strands and many, many unique family names.
In relatively short order we have more genetics — 8,334,272,992 — than the total world’s population today.
That is over 8 billion genetic recombinations within 33 generations. That is in as few as 700 years and perhaps as many as 1000 years. What happens with another 1000 years by going back another 1000 years is staggering.
As we go back our genetic richness increases greatly, yet the world’s population decreases. Similar to the idea that there are only six degrees of separation, here we learn there is hardly a degree of separation.
No wonder there are so many people descendant from that little group on the Mayflower! About 1000 years ago we would all have over 15 billion women within our genetic pool. Given that there are so many overlapping genetic pools, it is a powerful thought that we are all in some manner related.
Of course, we recognize that not too long ago there was not today’s mobility and we were marrying not-so-distant cousins, yet with the introduction of one wandering troubadour, genetic diversity is guaranteed.