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.”
Steve Curtis is a mathematics teacher at the Curtis School. He is also a football coach (defensive backs).
This project officially began on December 19, 2011 in Steve’s classroom with his three geometry classes and two ACT preparation classes. The class learned about base-2 exponential notation by observing nested geometries using the tetrahedron and octahedron.
The process. These classes went deeper and deeper inside each object by dividing each edge in half and by connecting the new vertices to create a smaller set of nesting tetrahedrons and octahedrons. By about the 45th step within — on paper — the size of the tetrahedron and octahedron was about the size of a fermion. Within about 67 more steps, that size was approaching the Planck Length. At that time there were about 112 steps within from the size of our original plastic models.
We then went out into the universe by multiplying each edge by 2. Somewhere between 90 and 98 steps, we were in the area of the Observable Universe. It wasn’t until we followed Planck Time to the Age of the Universe did we finally settle on just over a total of 202 notations.
This project has been under the watchful eye of Steve Curtis right from its beginning.
Simple facts, figures, and logic in search of a theory. The chart with five columns for each of the base Planck units and 204 notations down, 1020 boxes, provides real data to examine the logic flows both across and up-and-down. The goal of this article is to examine no less than 10 boxes. Looking across would be 50 boxes; adding two or three boxes up and down would total over 150 boxes. Ten percent should be enough to learn if a simple logic actually flows through the numbers. If it does… well, perhaps we have a new science in the making.
201+ Notations Begin With The Planck Length. The simple mathematical progression that rendered the 201+ base-2 exponential notations was the result of following embedded geometries going smaller and smaller until in the range of the Planck Length. Going in the other direction, larger and larger, was achieved by multiplying by 2 until in the range of the Observable Universe. The total, just over 201 doublings, could not be found within the writings of the academic community. The base-10 work done back in the 1957 by Kees Boeke and his high school classes in Holland was abundantly indexed; there were no references to a base-2 progression from the Planck Length to the Observable Universe, especially as a result of following embedded geometries within the tetrahedron and the primary octahedron within that tetrahedron.
Planck Time to the Age of the Universe is applied. There is general scientific concurrence regarding the estimates of the age of the universe. That figure provides a better framework for the doublings of Planck Time, from the beginning of time to this moment, right now, our current time, which always defines the endpoint. Planck Time and Planck Length track together in informative ways. For example, the notation that defines one second is between 142nd notation (.6011 seconds) and the 143rd (1.2023 seconds). The doublings of the Planck Length are 180,212.316 kilometers at Notation 142 and 360,424.632 kilometers at Notation 143. As one might have expected, the speed of light is confirmed in between the two at 299,792,458 meters for one second. At this point in time the other three Planck base units have become quite large, larger than any common number within human experience.
This Quiet Expansion begins at the first doubling. Quite literally, there is no room for sound until out to the 108th doubling (the beginning of sound waves) and on out to the 119th (the full spectrum of sound ranges from Notation 108 to Notation 119). There is something quite helpful within a visceral sense of the number and parameter. Examining groups of numbers associated with a common human experience is more than helpful; it provides the infrastructure of logic. Yet, there is no point where simple logic flows across all five Planck units. Yet, as demonstrated, it is quite informative when even two such numbers correspond.
For example, one of the very smallest notations with an experiential human equation is Notation 93 where observable light begins to manifest. Notation 101 is within the range of the thickness of human hair. This, of course, is where a large group within Planck Length and Planck Time correspond. This is the human scale universe. And, within that group there is one place where length and temperature correspond.
Planck Length and Planck Temperature. First, it was a leap of faith to hold to our working premise, “Everything starts simply” and to place the extremely hot Planck Temperature at the top of the chart. That put a very common number between Notation 103 and 104 where the temperature has cooled to 98.6 degrees Fahrenheit. Here we find among many other common things, the human egg cell. At Notation 105 the temperature has risen to 894 Kelvin or a very hot 1149.53° Fahrenheit and at Notation 102 it has dropped to a very cool –58° Fahrenehit.
Planck Mass. The very smallest notation with a common figure is the 31st doubling (Notation 31) where we find 103 pounds (46.74 kilograms). For many people, it is a key weight threshold signifying our coming of age, quickly approaching being an adult. Within this doubling the other four figures are so small, it causes one to ponder. So much seems to be happening with each of these doubling, that 103 pounds encourages some speculation. How about this? Perhaps the 103 pounds is the sum total weight of this notation! At the top end of this column are the outrageously large numbers that come very close to estimates by some of the more speculative within the scientific community, especially if each number in this column is the sum total weight of that notation. In some peculiar ways, this just may be a measurable concept.
The Human Scale Universe. Within the human and large scale universe, there are many familiar things within the Planck Length notations, yet the other Planck figures remain largely remote.
Planck Time. Although we cannot meaningfully perceive much smaller than a tenth of a second (Notation 140), in 2010 machines at the Max Born Institute in Berlin measured down to 100 attoseconds (Notation 87). Perhaps each notation with the Planck Time column describes a range in which relations are defined. Some elements of that statement may be measurable.
What Is Is? If looked to discern any special logic, one’s conclusion might be that each notation, with its vast array of vertices and multiples of the Planck base units, define the terms and conditions by which that notation-qua-notation is. That is, these numbers define the “isness” of the notation.
So, let us look in depth at one second between Notation 143 and 144. The total mass ranges from 2.4268×1034 kilograms to 4.8537×1034 kg. It defines a range, “no greater than twice that amount, and not less than half that amount.” In a similar manner, the total energy has a range, 2.0913×1025 coulombs but not greater than twice this amount and no less than half that amount. The total of heat within the notation, a huge stretch of the imagination, is 2.4578×1014 K to 4.9156×1014 K. Though an unimaginable amount of heat to be spread out throughout this single Notation 142, it just may be a measurable concept.
Planck Charge. Let’s look at which notations Planck Charge becomes a common number. For example, a lightning bolt is typically around 15 C, large bolts up to 350 C. That is quite visceral, yet on the chart it is in the range of Notations 63 to 67, the run up to the transfer from the small-scale to the human scale universe. If it represents the sum total charges within each notation, it certainly provides us with something to ponder.
These five Planck base units create very large continuity equations. Though imputed, remember that this schema is also based on the simplest geometries. Taking the entire chart and the weight of its simple logic, it suggests that the symmetries of these imputed geometries and these continuity functions are infinite, and that length (space), time, mass, charge and temperature are finite. These 201+ notations seem to define a finite universe and each notation defines a range in which particular subjects and objects are bounded by their Planck base units doubling, thereby each notation has a certain functional uniformity which provides a range within which particular groups or sets of things work.
Questions are asked, “Is this model the abiding, on-going, current structure of things as they are? How?”
201+ notations, divided by three, renders a small-scale, human scale, and large scale universe. The application of scaling laws and dimensional analysis to the first 60 notations resulted in learning about the power of base-8 expansion. By the 20th notation there are plenty of vertices with which to build structures; that is 1,152,921,504,606,846,976 or 1.152 quintillion vertices. By the 60th notation, add 36 more places (zeros). That is a robust infrastructure with 1152921504606846976000000000000000000000000000000000000 vertices (perhaps point-free vertices).
There is what would appear to be an infinite number of possible constructions. Add in the 131 better-known dimensionless constants and the fundamental physical constants, there should be enough variables to accommodate the Standard Model in physics as well as the science that has resulted from the standard model in cosmology. Please note that at the 60th notation, the size of the Planck Length doubling is not yet large enough to accommodate a fermion. From the 1st doubling to at least the 60th doubling, all the “structure” may best be described as hypostatic, which means in this instance, the essence or underlying reality.
Humanity doesn’t physically appear within the Planck Time column until well into the 201st notation. There has been a dispersion of length (space) mass, charge and temperature throughout an ever-expanding universe. Obviously there is a lot of science to learn between Notation 101 to Notation 202, and it will all be in relation to the deeper dynamics between Notation 1 and 101.
Reflections and Projections. Our base-2 chart of the Planck Base Units was first published in February 2015. This is its first review. It is an introduction that requires many more years of work and analysis. It frames a detective story whose final chapter could be written in many different ways. To expand the grounds of the analysis will require going deeply inside the simple geometries within the first 60 notations to discern how these geometries extend undetected, but measurably present throughout the entire universe. The assumed universals — order and continuity, multiple grids of relations with symmetries as well as asymmetries, and dynamics that seem to conjure up transformative instants of harmony, degrees of perfection and the darkest forms of chaos within degrees of imperfection — will be studied in light of duality,finite andinfinite sets,group theory, and set theory. That study will focus on the correlations with advanced combinatorics,matroids,amplituhedrons, and the Buckingham pi theorem.
Much more editing and perhaps a little more writing to come.
Working notes: When this page is ready to be declared “a working first-draft,” I will post an index of related articles; and as a working first draft, this post will be the first in that list. -BEC
Editorial note: Our world seems increasingly crazy. This model just might help to open new insights that might mitigate some forms of that craziness. So though still quite rough, it’s being brought into the light of the public rather early. Also, by working on it in public, perhaps others will have comments and suggestions to shape its potential.
Perhaps a few more questions and comments would help.
What is it about a circle and sphere that pi is always-always- always true?
How does a number become a constant, irrational and transcendental all at the same time?
Let us compare pi to other unique numbers that have a special role among all numbers. These are e,0, 1, and I. They are all magical, but π stands out. So, let’s ask, “What are the shared qualities of these numbers?” Let’s study them to see if we can find any necessary relations.
We have the ratio between a circle and a line. Perhaps this is the fundamental transformation between the finite and infinite? Are circles and spheres always implicating or imputing the infinite?
That is a big question and enough to ponder for awhile.
Notwithstanding, there are many more questions to ask.
Some speculations: Pi may be the key to unlock the small-scale universe within the big Board-little universe
1. To get to the application of pi within the Planck Units, we’ll need to emerge from the singularity of the Planck Units. Is the radian a key to understanding this process? First, a radius is extended from the singularity. A radius extends into the preconditions for space and time, a now emergent small-scale universe. It makes that first arc equal to its own length. It does it again and again and again and again and again (six radians) and then makes that last leap, 2 pi, to complete the circle. Is this a reasonable scenario? Why? Why not?
2. We need to run through dozens of scenarios, often, and slowly and carefully. What scenarios are perfect and obvious?
For further discussion:
1. Is the Small-scale Universe the basis for the homogeneity and isotropy of space and time?
2. Does everything in the universe share some part of the Small-Scale universe?
3. How is Planck Temperature calculated? Does it begin with the other Planck Units and expand from that figure at the first notation?
Note: All of human history has occurred in the last doubling. Yet, all doublings remain active and current and dynamic. Continuity trumps time. Symmetries trump space.
What does sleep have to do with anything? If all time is current, within the moment, we particularize by the day and uniquely within a given waking day. Sleep seems to bring us into the infinite. Dreams seem to be the helter-skelter bridge between the finite and infinite. It seems that these naïve thoughts are worth exploring further.
Back in December 2011, Bruce Camber and five high-school geometry classes in New Orleans involved themselves in an interesting little thought journey. When I was contacted by them, they were deeply into the process to discover that the number 2202.34 represents the ratio between the Hubble radius of the observable universe (according to the results in March 2012) and the Planck length (a number from modern quantum physics).
Here is how they did it:
1. The Hubble radius [astronomical measurement] is taken to be 1.31 x 1026 m and the Planck length [calculated] is 1.62 x 10-35 m. The Hubble radius comes from a recent estimate of the age of the universe published in Discover Magazine. The Planck length L may be calculated from: L = (hG/(2πc3))1/2 where h is Planck’s constant, G is Newton’s gravitational constant, and c is the speed of light, all in appropriate units of measure.
2. The ratio between the two distances is then found to be: 1.31 x 1026 m / 1.62 x 10-35 m = 202.34
This calculation arises from a related classroom activity, begun by Mr. Camber with those five geometry classes. The ratio is shown as a power of 2 (it could as well have been shown as a power of 10, or of any other number) in answer to the original class question, “How many times does one have to double the smallest known distance (the Planck length) to acquire the largest known distance (the present-day Hubble radius of the universe). I was consulted by Mr. Camber and assisted and advised him and his classes to produce the result shown above.
The significance of this result is that it displays the most extreme distance ratio imaginable in terms of a surprisingly finite number (202.34) of doublings. In a sense, it takes two quantities, neither of which can be adequately pictured in the mind, and shows them in ratio as a number that can be more easily pictured. I thought the exercise interesting and worth the effort and was happy to be called upon to contribute.
3. One additional note, the standard meter (1m) when compared to the Planck length corresponds to a ratio of 2115.57. We note that 2115 corresponds to 0.67m, and 2116 corresponds to 1.35m. In other words, the standard meter is not an even power-of-2 multiple of the Planck length. Mr. Camber and his classes have therefore suggested that a possible redefinition of the standard meter might be made by choosing one of these possibilities (i.e., 2115 or 2116 times the Planck length) and used to replace the present-day standard. The present day standard is based on the wavelength of a particular atomic emission line. This new standard would be based on a purely theoretical concept.
Bravo to Mr. Camber and his classes for some very nice (and out-of-the-box) original thinking!!!