Measuring An Expanding Universe Using Planck Units


Notations 31, 67, 101, 137, 167 & 199

Is it logical? Does it open a totally-predictive, integrated Universe View?

by Bruce E. Camber  First posted: August 2017 Updated: December 2017  Index of Notations

Notes: By using just six sets of figures out of the 202, we explore the logic of the base-2 model of the universe from the Planck units (and the beginning of time) to the Age of the Universe (and this day). Although challenging, it appears that the continuity and relationality of the numbers maintain a simple logic. I hope this article opens a door for much deeper explorations. Also, there is a related article that explores the inherent thrust of the universe. Here is our ever-so-slowly, but-evolving notation by notation analysis. -BEC

Open invitation: We are asking experts, scholarly specialists, to help with this work. Either it is right or it is wrong. If it is wrong, we will learn a lot about discontinuities within mathematics and about the principle of continuity itself. And, yes, given that you are on this page and you are reading these lines, you are also invited to participate. Bruce (comments)

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A novel approach to measure the universe is with the Planck base units and the power of 2 (doublings) also known as base-2 exponentiation. It renders very particularized results from the first moment of creation to the Age of the Universe. To open a discussion about this approach, a sampling of just six sets of numbers from the complete chart of 202 notations is provided. Each sampling was selected in part based on observing the emergence of a number that can be readily engaged from within our common experience. Also, each is a prime number, a basic building block for the emergence of new functions and groups of functions.

The first general observation is that these numbers are a natural inflation. The simple logic involved in defining every notation by starting with Planck Length, Planck Time, Planck Mass and Planck Charge renders a model of our universe that was never infinitely hot and infinitely dense as defined by the big bang theory. In this model, time is not an absolute frame of reference, but derivative, discrete, finite, and quantized. This model of the universe uses simple mathematics, it is highly integrated, and it is based on simple logic. Notwithstanding, the primary question is, “Does it capture our realities in a fundamentally new way?” To date, with our rather simple skills, we believe it just might be doing that so we invite you to explore it with us to either discount it or affirm it. Thank you.

Six Sets of Numbers: 3167101137167199

(Covers about 1.3727 billion years out of the total 13.8± years of the universe)

Planck:Time (Seconds)Length (Meters)Mass (Kilograms)Charge (Coulombs)
31:1.157794×10-34 s3.470762×10-26 m46.79kg (103 lbs)4.0278116×10-9 C
67:7.95630×10-24 s2.38509×10-15 m3.211962×1012 kg276.78910 C
101:1.366×10-13 s40.975 microns5.5181×1021 kg4.755×1012 C
137:9.3931×10-3 s2815.8174 km3.7920×1032 kg3.2677×1023 C
167:10,085,812.77 s30.234609×1015 km4.071×1041 kg3.508×1032 C
199:4.331×1016 s1.298×1024 km1.748×1051 kg1.506×1042 C
*Please note: Notations 107, 149 and 173 were part of the first listing. These were replaced with Notations 101, 137 and 167 so the intervals between numbers are a bit more uniform. As a result, a study of each number has commenced.

Setting the Stage: Notation #0

Planck Numbers, All Transformations Between the Finite And Infinite
Although Max Planck began developing these numbers in 1899 and first published them in 1906 (within his book, Theory of heat radiation), nobody paid much attention to what we now know as the Planck units. Even Planck ignored his work.

More Research Projects:
Enter Frank Wilczek, MIT, Nobel laureate 2004. In 2001 Frank Wilczek (MIT) began publishing three articles, Scaling Mt. Planck (312, 321, 328) for Physics Today. Although other scholars had engaged one or more of the Planck numbers, Wilczek, in our private conversations, took some credit for lifting the Planck units up-and-out of the category of numerology and to have opened the path for others to use and cite the Planck base units.
There were a few scholars who had even earlier intuitions about the significance of these numbers and dared to write about it. To understand that history, there are many stories that need to be reviewed. For example, in 1959 C. Alden Mead (UMinn) began his struggle to publish his work about the Planck Length. Though finally published in 1964, the article, Possible Connection Between Gravitation and Fundamental Length (Phys. Rev. 135, B849, 10 August 1964), was ignored by the scholarly community. At that time, the Planck Length commanded almost no respect as a fundamental unit of length.
The Finite and the Infinite. This is a study of the finite, yet the infinite has a substantial, abiding, and fundamental role. Within these studies the infinite is defined as (1) continuity, that which creates order, (2) symmetry, that which creates relations, and (3) harmony, a basis for all dynamics. These three postulations about form and function assume a panoply of necessary-and-abiding transformations. We choose to avoid all religious and theological language and to leave such extensions to each reader.
More Research Projects: Even today, support for the Planck base units is far from unanimous. Among our many research projects, a study will focus on those who are not ready to recognize that these Planck units are in any way fundamental units for science.
Studying and interpreting Max Planck’s 1899 logic to extract each of these base units is also part of our ever-so-slowly emerging secondary school program called Big Board-little universe and the programs of this website, our Quiet Expansion and our Simple, Mathematically-Integrated Chart Of Our Universe. Planck’s logic to select each facet of reality, define each quantitatively, and to define their relations, equivalencies, and ratios will eventually be examined.

Planck Length:Planck Length
Planck Time:PlanckTime
Planck Mass:PlanckMass
Planck Charge:Planck Charge

Scientists/scholars/experts. Now at work to analyze these numbers as best they can, within the framework of big bang cosmology, it is difficult to go deep and to be rigorous.

Dimensionless constants. What are these dimensionless constants that are never-ending and never-repeating numbers? If Pi is the mother lode, what follows? Is Euler’s number, e, next? Why? Do all equations that use pi, like the fine-structure constant, qualify? Does any equation that uses the reduced Planck constant (ħ) also qualify as a bridge between the finite and the infinite? Are these keys to understand the simple and most basic formulas that define our reality?
Prime: Each of these six selected notations is also a prime number. Mathematics recognizes the special role of prime numbers. Our never-ending, never-repeating numbers set within a prime number may open another door for discovery. Given our working assumption that everything starts simply, how does any group of equations start simply? What are the mechanisms for the simple-to-complex transformations, (1) within a given notation, then (2) between successive notations, and then (3) with other groups of notations? And then, by adding those never-never numbers (all ratios), does that create yet a fourth facet that defines finite-infinite transformation dynamics as well as space-time dynamics within every aspect of mathematics, logic and science?

Note: All notations are always active. No notation is in the past. There is only the present moment. Every thought, word, and deed impacts the flavors, textures and substance of the universe. Our universe is totally alive and interconnected and dynamically evolving.

Readily engaged from within our common experience

Notation #31: 46.79 kilograms (about 103 lbs.)

Overview: Our first group, after 31 doublings of the Planck base units, we discover that mass has become a rather common number. Length and time are still so small as to be non-intuitive. But the mass, a weight of 46.79 kilograms or about 103 pounds, is quite visceral for most of us. So, within this infinitesimal space within an equally infinitesimal duration of time, the universe is 103 pounds with a relatively modest charge.
Scaling Vertices: By the 31st notation the scaling vertices, line 9 within our horizontally-scrolled chart, have dramatically expanded to 1,237,940,039,285,380,274,899,124,224 or 1.23794×1027 vertices.
One might guess that even “pointfree” vertices could somehow constitute 103 pounds! Yet, at this notation the space per meter cubed is so infinitesimal, even 103 pounds is a stretch. In this model, called construction vertices, these pointfree vertices are defined within the study of mereology or gunk theory, extended within the manifold studies of topology including systems theory and ontology.
In prior articles we have considered the role of geometry and the evolution of ideal structures beginning with the circle, the sphere, cubic close packing, and the emergence of a line, triangle, then tetrahedron, its octahedron, and the four hexagonal plates that create structure within every octahedron. By the 31st notation, the potential complexity of structure is already overwhelming our imaginations.
Eleven Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31. By the 31st notation, there could be as many as eleven different mathematical systems at work. We postulate that within each prime there is that possibility. This idea was first introduced in our article (January 2016) about numbers. It is also the implied focus of line 11 within the horizontally-scrolled chart.

31st doubling of Planck Mass: 46.79 kilograms or about 103 pounds begs the question, how can numbers have mass? What is mass? What is gravity? What is charge? How are the three interacting within this notation at that time and within our current time? How has that definition of mass changed over the years as all the notations have come to be?
31st doubling of Planck Time: 1.157794×10-34 seconds. This notation is within a range used by the big bang theory to define the Grand Unification Epoch, 10−36 to 10−34 seconds which includes Notations 25-to-34, and the Inflationary Epoch, 10−33 seconds to 10−32 seconds which includes Notations 35-to-40. Each notation is postulated to continue to be the part of those keys that actually unlock both the unifying and the inflationary processes. There is always a process whereby there is holding together and a process of separation-and-particularization (of what those within big bang theory postulate as a singularity). Within this model, this singularity is more like a convention center because there is such a convergence of formulas, particularly ratios.

31st doubling of Planck Length: 3.470762×10-26 meters We have been told many times that this length is too small to be meaningful. Our answer, “May be so, but may be not.”

31st doubling of Planck charge: 4.0278116×10-9 Coulombs (nanocoulomb). Though small, it is known that the charge of one electron is about 1.6021766208(98)×10−19 Coulombs.

The big bang theory’s Grand Unification and Inflation Epochs: Although we currently accept the range given by the big bang theory for their Grand Unification Epoch and Inflationary Epoch, within this Quiet Expansion model, this notation, and all those notations before and after, are part of an active, on-going definition of the universe. There are unification processes holding all those equations in place from the finite-infinite transformation point as well as inflationary thrusts, the doublings, that continue throughout all notations.

Planck scales. Within our current conception of time, this expansion appears to be instantaneous. It is not. It also appears to be silent so we named it a Quiet Expansion. It is the opposite of the big bang theory and what Alan Guth posits (Inflation, June 1993, National Academy of Sciences) as inflation. He uses scalar field theory to justify his concepts of inflation; of course, scalar field theory is not necessarily tied to Guth’s inflation and its principles may be used by other conceptual frameworks.

[Endnote: The “Inflaton” discussed in his book, The Inflationary Universe: The Quest for a New Theory of Cosmic Origins. Basic Books. pp. 233–234. ISBN 0201328402]

Within the Quiet Expansion model, every formula involved at this 31st notation along with the prime numbers involved will be thoroughly analyzed for the logic that generates the next level of activity within our charts.

Open Questions: Who are world’s experts in understanding prime numbers?

What do prime numbers do? Does each open the possibility to begin a new mathematical system, building on all others within the doubling complex, but introducing a new function heretofore not defined?

Speculative projections based on simple facts. Between 2-to-202 there are 46 prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, and 199.

The next prime, 211, is beyond this definition and moment in time. Out of the 46 available prime numbers, the six numbers selected for this study are in bold type above.

Every prime number has its own flavor and personality. There are over 101 different types identified by Wikipedia editors. Are there mathematical experts within the studies of the functionality of prime who could help guide our thinking? Is it possible that each prime introduces a new mathematical set? Is this set properly described by set theory? Is each notation, within itself, defined by set theory and each transformation to the next notation defined by group theory?

To begin the process of answering these questions. We’ve made guesses regarding the ordering of the emergence of numbers, forms and functions within each prime. This listing comes from line 11 of the chart and an article about numbers.
2 • Euclidean geometries, starting with pi and cubic-close packing of equal spheres and lattice generation
3 • Bifurcation theory, including the Feigenbaum constant, and the various manifestations of the theory
5 • Golden ratio (Phi), the Fibonacci sequence and the nature of addition; five-fold symmetries, indeterminacy, the imperfect, fluctuation theory, and ratio analysis
7 • Computer automata theory with John Conway and Stephen Wolfram (this may be a special application of bifurcation theory)
11 • Group theory and projective geometry
13 • Algebraic geometries
17 • Langlands groups, Langlands correspondence, Langlands program, Langlands conjectures
19 • Zermelo–Fraenkel set theory (ZFC) and quantum gravity
23 • S-matrix theory, unitarity equations, Hermitian analyticity, connectedness
29 • Mandelbrot set, Julia set, Möbius transformations, Kleinian group

– – – – – – – – – – An early draft of a working project – – – – – – – – –

Not quite from our common experience, but from the heart of today’s research

Notation #67: 2.38509×10-15 meters

Overview: The 67th notation is one-third of the total notations. In the earliest stages of developing this model, the range of notations, 1-to-67, was called the small-scale universe. The next set of 67 notations, 67 to 134, were referred to as the human-scale universe, and notations 134 to 202 were considered the large-scale universe. Of course, this identification system will be subject to continued review!
67th Planck Length doubling: 2.38509×10-15 meters. This multiple of the Planck Length is now within the area of measurement by CERN’s Large Hadron Collider. Going within to a smaller scale, the next step or notation is, of course, fifty percent smaller. The next notation is fifty percent smaller.
67th Planck Mass doubling: 3.211962×1012 kilograms. The mass for such a small space (3.211962×1012 kg) is beyond imagination. The mass of the earth is 6×1024 kilograms. In 1971 a team at Harvard, Baym, Pethick & Sutherland calculated densities could approach 4.3×1014kg/m3 before nuclear pasta and saturation densities are reached. Subsequently that figure has been further calculated to be ≃2.3×1017kg/m3 (nuclear saturation density). Although stretching beyond our comfort zones, we are eager to learn something as simple as the proper computations for meters-cubed (m3) so we ask, “In the progression of doublings, is it assumed to be m3 or should we be using another calculus within these mathematical transformations before we approach what is known as neutron drip densities, nuclear pasta and Coulomb crystals?”
67th Planck Charge doubling: 276.7891 Coulombs. Equivalent to the discharge of a few average lightning bolts, in the International System of Units ( SI ), the coulomb (C) is the preferred unit of electric charge quantity.
67th Planck Time doubling: 7.95630×10-24 seconds. Within the big bang theory, the Quark Epoch begins at 10−31 and runs down to 10−12 seconds. Within our Quiet Expansion model, this epoch would begin within Notation 41 and extend through Notation 107.  At Notation 67, clearly halfway through the Quark Epoch, we propose that it be called the Quark Processes.

Plank Temperature

More Prime Numbers. From notation 31 to 67 there are multiple primes, all of which might initiate a special mathematics: 41, 43, 47, 53, 59, 61, and 67.  That is seven additional primes beyond 31.  One might conclude there are many opportunities to develop the mathematics of the Standard Model of Particle Physics.
From the Planck Temperature scale: Within our charts, the Planck Temperature is placed within the 203rd notation and divided by 2 over and over and over again. By the 67th notation it is approaching absolute zero at 3.25288×10-7 Kelvin. This is Zeno’s paradox all over again.

These numbers may appear to be difficult to interpret. Yet, there are many experts within every field who will see patterns, uniqueness, and new functions at each notation.

The big bang theory’s epochs…. According to the big bang theory, the Quark Epoch begins at about Notation 41 and ends with Notation 41 at about 10−12 seconds and might go up to Notation 136 where we project the Quark-Gluon Processes could begin because the Planck Temperature is now at 1.9201×1012 Kelvin. The Planck Time multiple is 4.6965×10-3 seconds.

An Open Question: What is the logical sequence, from the most simple to the most complex, and which would be required before another begins? Are there logicians and mathematicians, true scholars, who would be open to working with us, the neophytes? Remember this project originated from within a high school geometry class.
Cycles, frequency and periodicity: The first prime numbers might tell a special story. Staying within the 202 notations, consider multiplying-by-2 the primes up to 101. Does this open a potential for many systems within systems within this model?

– – – Please remember that this is a working first draft – – –

Between human sperm (#100) and egg (#103): The widths of a range of paper and hair

Notation #101: 40.975 microns (4.0975×10-5)m

Overview: This notation defines key assets within our common experience; it also defies simple logic. Notwithstanding, it doers not yet defy possibility. Science knows of configurations described within the 101st notation however much a stretch beyond commonsense.
The Planck Length multiple gives us the smallest of the cells, the sperm cell (50 micrometers) and the largest cell, the human egg (1000 micrometers). Between the two is a wide range of all other cells and other things like a range for the thickness of hair and the thickness of paper. Here we are approximately halfway between the Planck Length and the size of the known universe. Although this doubling of the Planck Length is a size that defines our common experience, the other doublings of the Planck units are not as straightforward.
101st Planck Time doubling: 1.366×10-13 second is between a picosecond at 10-12 and a femtosecond (fs) at one quadrillionth of one second or 10-15 seconds. We are well within the measurable units of time. This cycle time is in the range of ultraviolet light and femtosecond lasers. At 140 fs electrons are localized onto individual atoms (bromine).
101st Planck Length doubling: 40.975.microns There is the exact doubling of the Planck Length and there is also a range establish by the notations that precede and follow. That is 20.487.microns at the 100th notation and 81.95 microns at the 102nd notation. So, the true range of this notation would be from about 30.5 microns (.03 mm) to 61.3 microns (.061 mm) and would include many common objects vital to our life.
The conundrum. When we began our work on this scale of the universe, the Planck Length was the only facet that was followed. It took us three years to learn about Planck and his base units, and to gain the confidence that it was okay to multiply each unit by 2. When we finally began to add Planck Time and began to contemplate the simple logic, Notation #1 was the starting point of time and notation #202 held the current time and time increasingly appeared discrete, quantized, and derivative. So, at that point we began thinking about the necessary relations to time and how it would always be localized by notation. That pushed our thinking and we began our earnest study of cosmology, the big bang theory, quantum gravity, and the work of Carlo Rovelli, Richard Muller, and Neil Turok. True scholars, they were having difficulties with the nature of time as well.
101st Planck Mass doubling: 5.5181×1021kilograms Compare this mass to earth, 5.972 × 1024 kg, or the moon, 7.34767309×1022 kg, and we have a sense of how exquisitely dense and entirely inexplicable this mass appears to be. However, there are additional calculations to be made to consider the three dimensions of this mass or m3 as well as its application to the range from 30.5 microns (.03 mm) to 61.3 microns (.061 mm).
101st Planck Charge doubling: 4.755×1012 Coulombs We are not sure yet how to interpret the exact doubling of the Planck Charge, and the coulombs number and range. We are attempting to find scholars to help us. To say the least, there is no simple or easy logic for these numbers; this notation is as profound and unique a challenge as the notations 31 and 67.
From our Planck Temperature scale: 55.884 Kelvin

  • The human body temperature is 98.6 degrees Fahrenheit. That is equal to 310.15 Kelvin between notations 103 and 104.
  • The Sun’s temperature, 5778 K, is between notations 107 and 108.

The big bang theory’s Epochs. The Hadron Epoch theoretically begins at Notation 104 from 10−6 seconds to 10−1 seconds and goes up to Notation 141 and then begins the Lepton Epoch. The big bang treats these epochs as things of the distant past. We call these epochs, processes, and postulate each is an intimate and basic part of the operational universe and today these processes would now be concentrated within Notations 66 and 67.
Open Questions: Are there any Planck multiples that contradict any element of today’s science? Half way through our set of six, it appears that this natural inflation of these numbers creates a picture of the universe that is more predictive and particularized than any theory given today and there is nothing that stands outside the known mathematical and logic boundaries within science today.

Please note: The data about 107th notation at 2.6224 millimeters is now maintained on its own page.

Readily engaged from within our common experience

Notation #137: 9.3931×10-3 seconds

Overview: Now time is easily measured by our instrumentation; human competition, races of every kind, are won or lost within 9.3931×10-3 seconds or 9 milliseconds. Even the multiple of the Planck Length is well known and understood. Although the Planck Mass multiple seems counter-intuitive, we will quickly realize that all these numbers are actually working well together and are in concert.
137th doubling of the Planck Time: 9.3931×10-3 seconds or 9.3931 milliseconds The first second actually emerges between notations 143 and 144. We will be testing to see what it would mean if within this notation the average interaction were to be 9.39 milliseconds.
137th doubling of the Planck Length: 2815.8174 km (or 1749.67 miles) Although the transition to the large scale universe begins within notation 134 (351.977 km or about 218.7 miles), it is only meaningful when one projects it straight up overhead and into the thermosphere and just shy of the International Space Station’s perigee with earth (401.1 km or 249.2 miles). Just two doublings later, from 703.95 in #135, and 1407.908 in #136, brings us from Low Earth orbit (LEO), 160-to-2,000 km into Medium Earth orbit (MEO) from 2,000 km (1,240 miles). Geosynchronous orbit is the next step at 35,786 kilometers (22,236 mi).
137th doubling of the Planck Mass: 3.7920×1032 kilograms: As earlier observed, the sun is 1.989×1030 kilograms, so even at 2815 kilometers, the universe within this notation is in the density range of a neutron star. Though difficult to conceive, these figures do not defy known science.
137th doubling of the Planck Charge: 3.2677×1023 Coulombs: The coulombs scale has grown quite formidable, and we are trying to find scholars to help us interpret the meaning of that number and its correlation to 175 MeV per particle. It is a calculation from the big bang theory and if we can approximate it with our numbers from this quiet expansion model, that would turn some heads.

From our Planck Temperature scale: 3.8403×1012 Kelvin The Electroweak Epoch (now renamed Electroweak Processes) requires an estimated temperature of 2×1012 Kelvin to create the Quark-Gluon Plasma (QGP). This process could begin as early as notations 136 and 137 and it requires 175 MeV per particle while the universe grows through and then beyond one-hundredth of second from its primary start.
Although the Planck Temperature is not one of the basic four Planck units, its derivation resulted in an extremely hot temperature that became the basis of big bang cosmology. Big bang cosmologists had to ignore the four base units to make Planck temperature their focal point from which their theory would evolve. The best among the physicists entertain starting like we have from the very simple and we hope they become part of our coterie of insiders.
With our inherent logic that everything starts simply and small, the Planck Temperature, 1.416.808×1032 Kelvin was placed within Notation 203 at the top of the scale. It is line 7 within our horizontally-scrolled chart. At Notation 1 it has dropped very close to absolute zero at 4.4084×10-27 (K).

Certainly Kelvin is an unusual temperature scale. In this chart, going up the scale, with every new notation, it gets hotter, yet the mass and length also become proportionately larger. Between Notations 85 and 86 the Planck temperature goes from 1.74638 K to .8731907 K. 1 Kelvin is -457.87° F and -272.15° C. Also, superconducting temperatures range from -220 degrees Fahrenheit or -140 degrees Celsius at normal pressures, and -164 F and -109 C at high pressures.

The universe is less than one-hundredth of a second from its start. As we have observed, within this model, each notation is alive and well and still part of the sustaining infrastructure of the universe.

Of course, there will be much more analysis forthcoming. To continue this analysis we will be asking pointed questions of experts within mathematics departments of universities and colleges around the world.

We will dig deeper into our first three notational groups, the foundations of our foundations. As we develop this analysis of the remaining three notational groups, we constantly examine the logic in light of the big bang theory. It is all still very basic information and to say that we have substantial work to do is a bit of understatement. Notwithstanding, we are gaining a little confidence that these numbers are telling a plausible story that has a bit more logic than the stories told about inflation, super luminal speeds, and theinflaton. Much more to come
Attempting to grasp the Large-Scale Universe

Notation #167: The universe is 116.73 days old

Planck:Time (Seconds)Length (Meters)Mass (Kilograms)Charge (Coulombs)
167:10,085,812.77 s30.234609×1015km4.071×1041 kg3.508×1032 C

Overview: This notation is now defining our universe within 10,085,812.77 seconds or 116.73 days of activity. Just under a third of the year, this is a pivotal transition point. The universe is beginning to emerge out of a density range that appears to include today’s neutron star.

Editor’s note: We are still very much struggling within these numbers.

167th doubling of the Planck Time: 10,085,812.77 seconds Planck Time has now doubled 167 times. A quick conversion to days brings us close to the distance light travels in a year. Yes, the light year is between notations 168 and 169.

167th doubling of the Planck Length: 30.234609×1015 kilometers The Planck Length doubling is now 3.0234609×1015 meters or 3,023,460,900,000 kilometers or 3.0234 trillion kilometers (1,878,691,504,115.963 miles). The diameter of our sun is 9.461×1012 kilometers or just 1.392 million kilometers. The Solar System is possibly as small as 4.503 billion kilometers across, but some argue over 23 billion kilometers. A light year is 9,500,000,000,000 kilometers (9.5 trillion). Proxima Centauri, the closest star to our own, is only 40 trillion kilometers (4.3 light-years) from our sun. And, it appears that the entire Milky Way galaxy is estimated to be 1 quadrillion kilometers across.

167th doubling of the Planck Mass: 4.071×1041 kilograms The Planck mass multiple is off the charts at 4.071×1041 kilograms. We have begun to compare and contrast it to OJ 287, a BL Lac object located 3.5 billion light-years away with a mass of 18 billion times the mass of our sun (1.989×1030 kilograms).

167th doubling of the Planck Charge: 3.508×1032 Coulombs This simple calculation is for the total charge in the universe within the 167 notation.

167th doubling of the Planck Temperature: 4.123×1021 Kelvin. Within the big bang theory, the projected temperature is 109 Kelvin. One might assume that is is per meters cubed. We will take the calculation for size, 30.234609×1015 kilometers, and figure out what the temperature range could be with a goal to determine when the photon epoch and nucleosynthesis processes begin.

Please note: The study of Notation #173 is now on its own page.

How old and how large is our Universe now?

Notation #199: 1.3727 billion years

Overview: There are just three more doublings until we reach the current time. The 200th notation adds 1.37 billion years to bring us to total of 2.7 billion years. The 201st notation will add 5.4 billion years, and the 202nd notation will eventually add 10.8 billion more years. At this notation, our little universe has only been working for just 43.318 quintillion seconds. In light of this model, it does not seem so very long.

199th doubling of the Planck Time: 43,318,236,018,400,000 seconds (1.3727 billion years), the sum total for the entire universe

199th doubling of the Planck Length: 1.298×1024 kilometers, the sum total for the entire universe
From within Wikipedia, the best guess for the size of the universe is 8.8×1023 kilometers so this chart is within a seemingly reasonable proximity. By the 202 notation that figure will have increased to 1.038×1026 kilometers. It seems that all the numbers from the Planck Length, a logical natural inflation, holds a stronger hand and a more disciplined approach to reach its conclusions.

199th doubling of the Planck Mass: 1.748×1051kilograms, the sum total for the entire universe within Notation 199
Again consulting with the Wikipedia editors, their guess for the total mass of the universe is 1.46×1053 kilograms. At the 202nd notation the mass within our chart of numbers is 1.399×1052 kilograms. Although off by more than a mile, certainly these numbers are in the same family as those within Wikipedia and ArXiv.

199th doubling of the Planck Charge: 1.506×1042 Coulombs, the sum total charge for the entire universe within Notation 199

One possible conclusion: These numbers all seem to be working very well together. Even the temporary placement of Planck Temperature seems to have a coherency within the set of six notations. As we have asked since December 2011 and we will continue asking around, “What are we doing wrong?” The most substantial challenge to our imaginations is the density-mass numbers within the human-scale notations. The coulombs numbers throughout the human scale and large scale also challenge the imagination, so these elements within each notation will continue to be our primary analysis.


The next steps: An analysis of cycles, frequency and periodicity

The first prime numbers might give us new insights into systems theory, bifurcation theory, and numbers. Of course, staying within the 202 notations, the priority for this analysis will be determined by the following prime numbers (bold): 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, and 61.

Our focus will be on those numbers in bold and then those which are doublings of prime numbers:

•  1:2 and 1:4 and 1:8  (2-4-8-16-32-64-128) This notation, 128, contains many common elements of life. The Planck Length multiple is 5.499 km or 3.42 miles. That would be the size of the universe at just .0000183 seconds, readily measurable with today’s instrumentation. The mass is extraordinarily dense (7.406±×1029kg), considerably larger than the Earth’s mass (5.97×1024 kg) yet smaller than the sun (1.988±×1030 kg). So, among the next notations to be studied, notation 128 will be among them.

•   1:3 and 1:6 and 1:9  (3-6-12-24-48-96192) These two analyses will build up and around 67 and 101 for notation 96 and 169 and 199 for notation 192.

•    1:5 (5-10-20-40-80160) Things the size of buckyballs or fullerenes are at notation 80. The first day, the distance light travels within 86400 seconds is between notations 160 and 161. Each of these analyses will build upon and improve upon the closest prior analyses.

•   1:7  (7-14-28-56-112) At notation 112, everything and anything that is around 8.3917 cm or 3.3 inches.

•   1:11 (11-22-44-88176) Things the size of a virus are at Notation 88 and almost 500 years at Notation 176.

•   1:13  (13-26-52-104) At notation 104, the size of this “.” A dot!

•   1:23  (23-46-92184) Nanowires (92) and 41,891 years, a young universe (184)

•   1:29  (29-58-116) All things around 1.34 meters or 53 inches is Notation 116.

Then, the following notations that are in bold type will be engaged: 31-62-124, 41-82164, 43-86-172, 47-94188, 53-106, 59-118, and 61-122. The following notations will also be engaged yet each of these doublings are into the large-scale universe (where our challenges to the imagination seem to be fewer): 67-134-202, 71-142, 73-146, 79-158, 83-166, 89-178, and 97-194. Of course, Notation 101 is part of this article, and 202 will have been analyzed a little earlier.

  • What could be happening as number-form-function aggregate?
  • In how many different ways could these numbers be interpreted?

First, there is the simple doubling of the Planck Units and the study of inflation. Then, there is the scaling exponentiation of the construction vertices. There are the emergent geometries. And perhaps, there is this periodicity which just might also be doubled in the mix of processes, forms and functions.

What do you see?

Thank you.


Endnote on August 3, 2017: Three primes have been moved to their own page and are no longer part of this study. An attempt is being made to bring the jumps a bit closer together so the range is between 30 and 36 notations. The range had been from 24 to 42 notations.

Notations 107, 149 and 173 were part of the first listing and are now being replaced with Notations 101, 137 and 167.

Two additional key articles also currently under construction:
• The Thrust of the Universe: What is it?  Resource pages
• Visualizing the Universe


Figure 1: Four views of the numbers, key charts from 2011 to today

Four Charts1a. December 2011 Chart of the Planck Length to the Observable Universe
1b. 2012 Chart of the Human Scale Universe
1c. 2015 Vertically-scrolled Chart of the Universe from Notation 1 to 202
1d. 2016 Horizontally-scrolled Chart of the Universe from Notation 1 to 202


People ask, “Why haven’t we seen this model until now?

Planck Units: The four Planck base units are “…properties of nature and not from any human construct.” Yet, these Planck numbers did not command basic respect across the entire scientific community. Not until Wilczek’s (MIT, Nobel laureate, 2004) wrote a series of three articles for Physics Today (Scaling Mt. Planck, I, II, III), did these Planck units begin to move beyond numerology into wide-scale acceptability.

By that time, the big bang theory had gained the high ground. Nobody thought to follow simple nested or combinatorial geometries back to the Planck Length. Nobody thought to multiply the Planck units by 2. It took a huge amount of naïveté and almost no knowledge of cosmological models to bias our exploratory instincts. It also required discounting our commonsense view of time promulgated by Isaac Newton that space and time are absolute. In so doing, a more relational model, as suggested in 1715 by Leibniz, was entertained and the raw numbers emerged. Totally predictive, it should be as relatively straight-forward process to affirm or discount this model.