| Notations 1 to 6 of 204
Small-scale Universe 1-67
| Of the 200+ base-2 notations from the Planck base units to this day, 67± notations are within the small scale. The background story.
|Base-2 Vertices (×2)
|Scaling Vertices (×8)
|Speed of light (m/sec)
||Form 1: Sphere
||Form 2: Spheres
||Form 3: Stack
||Form 4: Pointfree
|The big bang theory in light of a quiet expansion of 201+ notations.
Three questions open up a more simple mathematical model of the universe:
1. Can this model, a Quiet Expansion (QE), actually defuse the big bang? The math within the QE model could redefine the first four “epochs”(and most-key elements) of the big bang theory (bbt). If it is defused and becomes an historic statement, From Lemaître to Hawking, science can move on within somewhat-prescribed boundary conditions and known parameters. The first four epochs of the big bang theory can readily be subjected to redefinition. These “epochs” amount to less than a trillionth-of-a-trillionth a second.
2. Are ethics and values built into the fabric of the universe? The QE model establishes a simple continuity equation from the first moment in time through the Age of the Universe (this day and this moment). These simple mathematical constructions quickly evolve as geometrical constructions and symmetry groups. Mathematically the constructions become quite dynamic and some harmonic. Continuity, symmetry and harmony are the foundations for a natural value equation deep-seated within the universe. Most every flavor of ethics, morals, and values can be appreciated for what they do and don’t do, and for why they are.
3. How can we more fully understand the finite-infinite relation? This finite-infinite relation is perhaps best described as a study of perfection and moments of perfection and that the geometries and mathematics of imperfection are also better defined and understood as a result and known today as quantum mechanics.Consider the four epochs in question:Planck Epoch or a Planck Moment: The finite-infinite relation most intimately defines the first notation and is necessarily within all notations building from the first. An infinitesimal duration, it is the beginning that creates space and time and then extends within space and time much like the birthing process. As of today, the Planck base units are our simplest-deepest-best description of this moment.
Grand Unification and the Electroweak Epochs or Processes: Based on the fact that entities and things require a necessary amount of space that only becomes available from the 67th notation and above, the first 60 to 66 notations are foundational to all notations. Using the analogy of the birthing process, all the forms-and-functions, then processes-and-procedures, and then relations-and-systems prior to the actual birthing event, are the first 60 or so notations. Here that finite-infinite relation creates the foundational order, the most basic relations, and many dynamical systems prior to the uniqueness of every reasonable analogue to the birthing event.
The Grand Unification processes continue beyond the 67th notation as specific Unification processes. The electroweak processes now begin to manifest and the measurements given by the big bang theorists can be tweaked and integrated within the Quiet Expansion model.
Inflationary Epoch or Processes: Just as there are still many many questions about cellular division, there are even more open questions within this model. However, the force, the infinitesimal amount of energy, available to this process are working ratios of the Planck base units whereby order, relations, and dynamics evolve with a perfect continuity, perfect symmetry, and a deep harmony within every sphere and basic structure. This concept was initially put forth as a philosophical orientation to life, and then it was explored in a post about numbers called,
On Constructing the Universe From Scratch (see pages 5 and 6).
Background Introduction: This is page 1 of 37. Here, side-by-side, all 37 pages can be horizontally-scrolled as a single page. It is the entire model of the universe called, Big Board – little universe. The vertically-scrolled chart was completed in February 2015. The first chart was done in December 2011. Here we continue the process of encapsulating everything, everywhere in the universe, throughout all time. Though this chart suggests that space-time-mass-energy-temperature are necessarily and inextricably related, the challenge of this model is to demonstrate how this is so. This work is quite at odds with the big bang theory (bbt), yet we believe every formula and relation defined throughout the bbt history can also be found within our emerging model and view of the universe. To broaden its perspective, we will also attempt to examine as many transitions as possible between the finite-infinite, especially the role of pi, projective geometries, bifurcation theory, the dimensionless constants, and number theory.
Key concept: Planck Temperature has been moved to the top of the chart. One of the working assumptions of the project is that everything starts most simply and complexity comes later, and that space-and-time are finite, discrete, derivative and quantized. Of course, this logic will be further discussed.
Key questions: What mathematics are at work? The simple answer is, “All mathematics are at work here. No formula is exempt. And, eventually every formula will be in some way tied back to this model.” Notwithstanding, here is our first, introductory post about numbers.
Speed of Light: A simple calculation is to divide the Planck Length by Planck Time. Using just the units displayed above, the result is 299,777,406.78 m/sec. Using 3.23239/1.078212 the result is 2.99791692172 or 299,791,692.172 m/sec. These simple results, first posted on May 3, 2016, will be tweaked. Of course, the result of experimental measurement is 299,792,458 meters/second in a vacuum. Within notation 3, it is 1.29295 divided by 4.312848 which equals 299,790,300.98. There is much more to come!
Entitive Manifestations: Though not an active row until July 4, 2016, the nature of thingness has been part of our mindscape for many, many years going back to Martin Heidegger’s key question, What is a thing? Our first charts of the Big Board-little universe all focused on things determined by the multiple of the Planck Length. All the data from those earlier charts will now be integrated within our horizontally-scrolled chart.
Help wanted: For every notation, we would like to have an expert and a team. Within this group of notations, we especially seek help from people who can help us re-enact Max Planck’s thinking and the veracity of each formulation of the Planck base units.
Can you help us?
Key words, primary concepts, and links to references for these ten notations:
1. Geometries: Projective, Euclidean, differential (Riemannian, Lie groups, etc), discrete and combinatorial, algebraic and transformational…
2. The Pre-Measureable Structure of Matter: Might we conclude that this Small-Scale Universe is the structure that holds things together? Is it a re-definition of the ether? Is it MIT Frank Wilczek’s grid?
3. Renormalization(Scale Invariance https://en.wikipedia.org/wiki/Scale_invariance), Universality, isotropy, homogeneity: Is it possible that everything-everywhere in the universe shares the first 67 notations, and uniquely evolves with those characteristics given within the 67th to 134th notations, and then begins to manifest in each of the large-scale notations, unfolding uniquely in the 201st as “the given within the current moment”?
Editor’s note: Can you help upgrade that last sentence? I’ll be profoundly grateful. -BEC
Finite-Infinite: Studied throughout the history of humanity, this model provides a basis for a thorough reexamination of the concepts, mathematics and principles that operate between the two. Already there are several posts that open these reflections: (1) What is finite? And, what is truly infinite? and (2) Finite-Infinite reflections.
1. The areas above and below the numbers and discussions could also be used for graphics that are related to these notations. Perhaps a color background could reflect its temperature in its part of the universe.
2. Perhaps the area above the “Big Board-little universe” title (underlined) can be used for related graphics and color.
3. This “one page” board ideally would be a wiki page where schools and universities and the public could collaborate, update and add data.
4. Base-2 notation from the five Planck Base Units to their maximums is still early-stage work. We’ll be adding dimensionless constants. Could this table be a spreadsheet? April 27, 2016: More updating to come.
Process: Examples of Horizontal Scrolling Horizontal Scrolling Example #1, #2, #3 and #4 (pop up windows).
|7 to 12
Notice the Scaling Vertices are already over 8 Million at the 12th notation
|Discussion: This fledgling model of the universe, to gain a little respect, will be required to incorporate the extensive work that has gone into the parametrization of ΛCDM (Lambda cold dark matter) or Lambda-CDM model. To begin that process, people have been challenged to find those formulas embedded within this model.
Speed of Light: These simple calculations are listed to challenge us to think of the processes and relations between numbers. This ratio, the notational multiples of the Planck Length to Planck Time, is very basic. Again, the experimental measurement is 299,792,458 meters/second in a vacuum. Within notation 7, the simple result of the numbers are given above. 299,791,784.89 m/s. Then variations are still difficult to discern. We will attempt to find the resolution of Planck Length and Planck Time carried out ten decimal places each and do recalculations.
Tweet and Retweet
“Light: The ratio between Planck Time/Planck Length along all 201+ base-2 exponentiations from the Planck base units.”
“Let there be light! https://bbludata.wordpress.com/1-204/ Observe the 10th row. Planck Length/Planck Time ratio along 201+ notations!”
“Help interpret the math?!? https://bbludata.wordpress.com/1-204/ Background: In early May, some among us began asking the question, “Could the Big Bang theory implode?” Others made projects, “Perhaps we might start a movement to blow up the big bang. It’s inherent nihilism is making a mess of this little world.” May 2016
Key observation: These five Planck base units are intimately woven. There are hundreds of calculations to test between them.
Prediction: All the dimensionless constants will all be discerned among those calculations! The fabric of life is just beginning to be woven. The numbers are so small, meaning has yet to be imputed to them. Here it seems that we are in the domain of ontology and ontological designing, pointfree or incidence geometries, and systems philosophy.
Key Questions: Do these notations give the ontological studies a possible domain within which to work? Is there also a place within these notations for the mind? (This discussion/observations/questions/inquiry was begun on May 6, 2016. It is “to be continued” UNTIL all 204 notations have been addressed.)
Key words: (primary concepts and links to references for these six notations) What about the placement of the Planck temperature? Do the calculations of Max Planck warrant that it be placed with the others at bottom of the chart?
Open: Your questions and comments are always welcomed.
Help wanted: For every notation, we would like to have an expert and a team. Within this group of notations, we seek help from those people expert in combinatorics, cellular automaton, cubic close packing, bifurcation theory (with Mitchell Feigenbaum’s constants), the Langlands program, mereotopology and point-free geometry (A.N. Whitehead, Harvard, 1929), the 80-known binary operations, and scalar field theory. Can you help us?
|13 to 18
The number of Scaling Vertices could now support any and all geometries.
|Discussion: Since the first Big Board-little universe in December 2011, there have been many other charts and posts to begin to discern the meaning and value of these all these numbers. One of the simplest charts was entitled, Universe Table, The Human Scale. In this chart the Small Scale and Large Scale are compressed so most of the entries represent as many as ten notations. Within the small scale, the first group of ten are labelled “Forms” after Plato’s work in the Timeaus. The next group of ten are labelled “Ousia” after Aristotle’s work on the nature of structure.
Within another posting about numbers, the place of Pi and bifurcation theory are raised. It is within the first ten notations, this work may well be applied and developed. It could also include combinatorics, cellular automaton, cubic close packing, bifurcation theory, the Langlands program, mereotopology and point-free geometry (A.N. Whitehead, Harvard, 1929), the 80-known binary operations, and scalar field theory.
Cellular Automaton. Work being done within computer science, its logic and functions, are entirely analogous to mathematical logic, functions, and binary operations. Our studies, particularly of Steve Wolfram’s New Kind of Science, is being pursued with great expectations that some of this work uniquely applies to the first ten-to-twenty notations.
Key questions about order, relations and dynamics: At last count, Pi has been computed out to over 12.1 trillion digits that form no discernible pattern and appear to be non-ending. It seems that pi holds part of the secret about the random, chaotic, statistical nature of things within quantum mechanics. The other is in the gap between the five tetrahedral cluster which is called a pentastar until a better name is posted.
Key words: Primary concepts and links to references for these six notationsOne of the supporting posts for these initial 67 notations asks the question, “Are the first 67 notations key missing links?”>Are the first 67 notations key missing links?”
Help: Complete numbers of scaling vertices: 4398046511104, 35184372088832, 281474976710656; 2,251,799,813,685,248 (2.2 quadrillion)
Open: Updated, May 7, 2016, Much more work to come.
|19 to 24
By the 20th notation there are over a quintillion Scaling Vertices.
|Discussion: A simple logic suggests that base-8 expansion, scaling vertices, build upon the prior notation. Nothing goes away. It is hypostatized or imputed to be the very structure of the universe that everything shares. The time within each notation could be understood to be the speed by which interactions take place. It is a duration that is infrastructure, not past-present-or-future. Within this definition, these would be pointfree vertices.
Key questions about order, relations and dynamics: What is sleep? Where is sleep? Why do living things sleep? The suspicion is that sleep is within the small-scale universe. Sleep does not activate any brain neurons (4 microns to 100 microns or notations 97 to 102), atoms or particles. More to come. This is a placeholder and today is May 8, 2016.
Key words, primary concepts, and links to references for these ten notations: Can we begin to explore the finite-infinite relation before we get too far away from notation #1. Can we assume that the simple mathematical continuity established by base-2 is meaningful? Is it a deep part of the structure of the universe? Much more work to come.
Notation, Exponentiation, Vertex Counts for B2 and Scaling Vertices: From notations 19 to 24 the actual number of vertices is stored in its own page which can be accessed by clicking here
| 25 to 30
By the 30th notation the universe weighs about 50 pounds (23.7 kilograms)!
|Discussion: The speed of light calculations are still very early-stage work. The experimental measurement is 299,792,458 meters/second in a vacuum. Within notations 25-30, simple results are given (above). To obtain more precise information, the next step will be to carry each out ten decimal places, and if that begins to suggest something, we will go out 100 places, and keep doing recalculations. Perhaps we just might find some clues along the way, i.e. begin to see some patterns, would tell us something all the dimensionless constants within those calculations.
Key words: Finite-infinite: Leibniz–Clarke correspondence: In the debate between Sir Isaac Newton (through Samuel Clarke), we side with the relational view of Leibniz. The Infinite appears to defined by continuity, symmetry and harmony, the perfections of order, relations, and dynamics. Of course, continuity equations are established between the Planck base units and their respective numbers at the Age of the Universe today and the Observable Universe today. We have imputed geometries from the first notations. For more, see the posting, Numbers: On Constructing the Universe From Scratch. These geometries create simple symmetries, broken symmetries, and a multiplicity of symmetry groups. At some point within the small scale universe, the symmetry have enough space and time to interact and cause dynamical moments. Within our Universe Table and UniverseView, Systems begins at notation 50.
Notation, Exponentiation, Vertex Counts for B2 and Scaling Vertices: From notations 25 to 30 the actual number of vertices is stored in its own page which can be accessed by clicking here
|31 to 36
By the 36th notation the universe weighs 3297.4238 pounds (1495.6 kg)!
|An Introductory Discussion About Mass: The mass of the universe has gone from the very small side of exponential notation to start the rapid climb up the very large side of exponential notation scale. To see how rapid it rises, we’ll use the whole numbers in kilograms within the next set of six notations (and occasionally also in pounds) so you can see how quickly it gets out of reach. For example, the weight of the earth is 5.972×1024. Within which notation would you guess that much weight could be found on the scale?
Notice within notation 30, it is 23.37 kg. Notation 31 is 46.79 kilograms or about 103 pounds. Here is a pure form of mass, all those vertices aggregating as forms (structure) and function. It is an ideal substance. By notation 36, it is 1,495.68628 kilograms or over 3297 pounds. That’s about the weight of an SUV. The “Spirit of Liberty” Bell stands 6 feet tall and weighs 3,200 pounds.
By Notation 111, the universe is still a long way to becoming a second old (not until Notation 143), and it is already the mass (weight-density-force) of the earth.
Much more to come.
Key questions about mass, order, relations and dynamics: Only the Human Scale version of the Universe Table or Universe Chart is done. The small scale and large scale are summarized in blocks of no more than ten notations. The first ten are Forms or the Eidos echoing Plato. The next ten are Structure or Ousia, echoing Aristotle. Synthesizing the two, the next ten notations have been labelled Substances knowing full well that it would be another 40 to 50 notations before anything that could be defined as entitve or physical would emerge (Notations 65-69).
So mathematically there are at least 60 notations to begin to define with pure math, geometry, logic, and patience. To date, there is one posting that touches on it: On Constructing the Universe From Scratch. It is from here that we will pick up again to postulate in what ways each notation is also an archetype, clusters, containers, domains, groups, layers, and sets. We will be more closely examining the ratios at each step and doubling.
Key words, primary concepts, and links to references for this group of notations: We are consulting wiith a journal, Multiscale Modeling and Simulations (MMS), an interdisciplinary journal of the Society for Industrial and Applied Mathematics (SCIAM) that focuses on the fundamental modeling and computational principles underlying various multiscale methods.
Notation, Exponentiation, Vertex Counts for B2 and Scaling Vertices: From notations 31 to 36 the actual number of vertices is stored in its own page which can be accessed by clicking here
| 37 to 42 of 200+
Now there are over one trillion simple base-2 vertices.
|Continued Discussion About Mass: The visual doubling within just these six notation goes from heavy to very heavy quickly. Measurements given are in kilograms (pounds):
47,861.96096 (105,517.56 lbs)
95,723.92192 (211,035.123 lbs.) On the scale of a blue whale!
Key questions about order, relations and dynamics: The outline for this chart was completed in April 2016. In the summer of 2016, many of these numbers are being examined for the first time. Although a simple model, it is aggregating a lot of data and guesses and conjectures are being made as to what it all means.
You help to make sense of it is most welcomed.
Key words, primary concepts, and links to references for these six notations: What is mass in this exquisitely small domain? We can only begin to guess, then make some conjectures and possibly postulate what it means.
Notation, Exponentiation, Vertex Counts for B2 and Scaling Vertices: From notations 37 to 42 the actual number of vertices is stored in its own page which can be accessed by clicking here
| 43 to 48
The time and length are still so small and short, for most of us, it is still less than meaningful.
|More Examination of Increases in Mass: Along the Mass/Kilogram lines, the sizes are now growing quite large:
Notation 43: 191,447.84 kilograms (km) or 422,070 pounds
Notation 44: 382,895.68
Notation 45: 765,791.37
Notation 46: 1,531,582.75
Notation 47: 3,063,165.50
Notation 48: 6,126,331 (13,506,247 pounds or about 6753 US tons like large metal cruise ships or bulk cargo-carrying ships).
Key questions about order, relations and dynamics:
The leading theory about the structure of the universe is founded within the big bang theory. It is not simple. It is not elegant. It does not respect the Planck base units. It has no causal efficacy. It is very poor theory upon which to base our sciences and our understanding of the universe.In stark contrast, this chart evolves from most minute quantities of the most basic constituents of reality. It builds incrementally. And as we will see, the it builds a universe cluster by cluster, domain by domain, one doubling at a time, with natural groups, layers and sets.
Notation, Exponentiation, Vertex Counts for B2 and Scaling Vertices: From notations 43 to 48 the actual number of vertices is stored in its own page which can be accessed by clicking here
Our guess is that within this domain, groups and sets become systems.
|Notations 50 to 60: Reader warning – very rough draft! There are several fascinating articles about consciousness and the brain-mind relation  . We know that we live within the 201 notation, 13.8 billion years from the first seconds of creation. Yet, we also know that there are multiples of the Planck length were things like particles and sub-particles could or should manifest and that these particles and sub-particles can be measured and their qualities understood. It would seem that each notation in which an entity can be first measured, and where there are the necessary relations above it and below it to create the groups and sets that make an entity manifest uniquely. These notations are a long way from current time. So, although specific notations are where entities manifest, everything must “transcend time” to be integrated as a whole within the 201 notation. Or, time is discrete, and all notations are always available to us. Each space/time (length) ratio exists uniquely, and long after it is first manifest for the first time, it continues to manifest dependent on all manifestations throughout the subsequent notations and on all prior notations.
In this context, the mind is hypostatized (imputed) to manifest within the “Systems” group which is also hypostatized to be between the 50th to 60th notations. In that context, we are now re-reading papers like  Mathematical Foundations of Consciousness, Willard L. Miranker and Gregg J. Zuckerman, Department of Computer Science and Mathematics, Yale University, 23 Oct 2008 and  The Simplest Mathematical Model of Consciousness, Roderick Wallace, New York State Psychiatric Institute, September 2, 2014.
Continued Discussion about Mass and kilograms::
53. 196,042,592.09216 is over 432,199,933 pounds
Key questions about order, relations and dynamics:
Even at the 54th notation, the other Planck base unit multiples are still infinitesimally small. We still have much to learn before we can begin postulating something special about each unit and their functions within each
container, cluster, domain, doubling, group, layer, notation, set and/or step.
Notations, Exponentiations, Vertex Counts for B2 and Scaling Vertices: From notations 49 to 54 the actual number of vertices is stored in its own page which can be accessed by clicking here.
Thoughts On The Variable Speed of Light Calculations: Using Notation #53 as our example, six decimals divided by six decimals equals 299,773,565.1. By using the seventh decimal within time, the new calculation is 299,773,552.76. Using #54, with seven decimals, it is 299,772,934.98. With six it is 299,772,947.33. And with five, matching the value within the space unit, is: 299,773,070.79. That could explain some of the variances, however, it does not explain the variances between notations.
Throughout the 54 notations, the highest calculation as 299,982,157 (#16) and the lowest (#3) is 299,790,300. The speed of light in a vacuum is 299,792,458. We might argue for a variable speed of light. At some point, we will average all speeds. From a cursory glance at the data, it appears that the figure will be higher than the experimental value measured in the laboratory. We might also discover that the range is always within 10% of our statistical average. Of course, we will be studying these variations and their calculations more closely.
At the 58th notation under charge (Coulombs) the value is just over 1.
|Planck Charge: Notice the Planck Charge multiple has now grown to a whole number. The transition to 1 coulomb is between notations 58 and 59. At a temperature of 6.3532×10-10 Kelvin, the Mass is still superconducting and will be up to about 203 Kelvin (or -70º C or -94.27º F) which manifests between notation 106 and 107. Now we will watch the rapid rise of the coulombs value. What does it mean?
Continued Mass Analysis: Within notation 55, mass is now 1.7 billion pounds (1,728,799,734.88 lbs).
55. 784,170,368.36864 kilograms
What about light?: 299,773,462.143 by 7 of 5 || 299,774,511.57 by 5 on 5
299,772,424.8 by 7 on 5 || 299,772,710.3 by 5 on 5
We will continue computing the light until the entire chart is completed. Then we will average the 201 notations and highlight the smallest and largest values after checking the math! Perhaps the figures will speak to somebody in some special way.
On working with the postulations of the big bang theorists:
All the Planck base unit values are keys to interpreting the epochs within the big bang theory.
Although technically the Planck Epoch should be just the first notation (#1) we will initially be giving it the first six notations. The Grand Unification Epoch we will float from Notations 7 to 60. The Inflationary Epoch will be renamed. The Electroweak Epoch may also be downgraded from an epoch to a transition. The Quark Epoch may begin with Notation 61. It is up for grabs. Much more analysis is required. We will be using the temperature requirements of the big bang theorists to determine some of their placements. Yet, to be sure we are all on the same page, the universe is still so young, we have no instrumentation to measure such a short duration. Our first measurement of a duration will not happen until Notation 84.
Notation, Exponentiation, Vertex Counts for B2 and Scaling Vertices: From notations 55 to 60 the actual number of vertices is stored in its own page which can be accessed by clicking here.
Finally at the 66th notation the space is large enough for the elements of particle physics.
|The Quark Epoch: Here the big bang theory outline for reality begins to work within this simple model using base-2 exponential notation and the Planck base units as the starting point. The post is titled, “How did the universe begin? And, what does it mean? Could a Quiet Expansion defuse the Big Bang?”
Who can validate or invalidate this simple model? Your suggestions are invited.
Notation, Exponentiation, Vertex Counts for B2 and Scaling Vertices: From notations 61 to 66 the actual number of vertices is stored in its own page which can be accessed by clicking here
Transitions from the Small Scale to the Human Scale
|Re-examining the big bang theory bbt in light of this quiet expansion of 201+ notations:: In this transition from the small-scale to human-scale universe, it is important to take stock of where we are in the universe. First, the 67th notation marks “one-third of 201.”
Though called the human-scale, Notation 67 to 134 are still very much a part of the infinitesimally small universe. At notation 134, the time duration is still 1.1741×10-3 seconds (one thousandth of a second). The first second of the universe is between notations 143 and 144.
Within the bbt, however, theorists are gaining some confidence because they can now confirm their concepts through experimentation and measurements. Most of the problems they will now encounter are due to the assumptions made to justify the four prior periods. Their contortions diminish the theory. They only have highly-theoretical data to justify the first four epochs of their theory. Up to about this point there has been no observational data from cosmology, astrophysics, particle physics, and theoretical physics to support their claims.
We are not yet aware of any problems the quiet expansion creates for this group at this point in the cosmic picture.
Within the QE Planck length scale, the fermion and proton could emerge within the 67th notation. Yet, according to big bang theorists, the Quark Epoch goes from about Notation 40 to Notation 100, the Hadron Epoch from 100 to 150, and the Lepton and the Photon Epochs from about 140 to 150.
As we move up the scale to 150, we can speculate about how each notation continues to evolve based on what is happening in the larger notations “above” it.
Key questions about order, relations and dynamics: cluster, domain, doubling, group, layer, notation, set and/or step…more to come
Link to Vertex Counts for B2 and Scaling: From notations 67 to 72 the actual number of vertices can be accessed by clicking here, the beginning of the Human Scale and end of the small-scale universe.
Notes and references: More to come.