Some of the more far-reaching implications of the Big Board-little universe model

Introduction.  The Big Board-little universe Project uses base-2 exponential notation from the singularity of the Planck base units going out to this present time, Right Now, to encapsulate everything, everywhere, throughout all time1. Though seemingly a bit of  an overstatement, the simple mathematics and logic appear to corroborate such a conclusion. The implications of this fledgling model seem rather far-reaching so five are presented for the discerning analysis and critical review of scholars and thinkers.

Some of the more far-reaching implications of the Big Board-little universe model:

  •  This model begs the question about the finite-infinite relation.  If space and time are derivative, finite, quantized and discrete, then what is infinite? Our working answer is continuity which creates order, symmetries which create relations, and harmonies (multiple symmetries working together) which create dynamics. These are the inherent qualities that define the infinite for science.2
  • There appears to be an ethical bias to the universe. Continuity-order, symmetry-relations, and harmony-dynamics also begin to define a valuation system whereby every notation at every moment has a perceived and dynamic value.3
  • Each notation defines an element of the current universe. Even though time is derivative, it still defines a duration within a single notation. Even though space is derivative, it still defines a length within which particular things have their beingness. In this model each notation has its own particular beingness. The entire universe actively appears to share this length (space) – time infrastructure within the small-scale universe.
  • The structure for homogeneity and isomorphism is defined within the small scale. It is also the bridge between the finite and infinite so renormalization works in quantum electrodynamics and universality works throughout physics on every scale.4
  • This model appears to trifurcate nature. These three seemingly natural domains of this model of the universe appear to be episodic:
    (1) The small scale from notation 1-to-67 could generally be described as ontology and each notation just might manifest again within the human scale and then again within the large scale.
    (2) Perhaps the human scale from notations 67 to 134 could be understood as the domain for epistemology. In some manner of speaking all 67 manifest in the notation for the current time.
    (3) The large scale from notation 134 to 201 is currently considered the domain for cosmology. It begins when the duration (or speed) is less than one second (see notations 142 to 143). Within notation 200 (possibly 201) is the current time.  Its duration is approximately 10.8 billion years.  The duration at notation 134 is within a thousandth of a second.

    Of course, each duration for each notation gets increasingly short as we approach the Planck Time. The duration at notation 67 is 10-to-the-negative-23 seconds (10-23).  Notation 67 is approximately the Planck Length multiple where fermions and protons appear.  There will be many adjustments of these numbers as others help to fine-tune the model.5

All people and things appear to be trifurcated.

One might hypothesize or hypostatize that from the small-scale universe we get our being. Systems are imputed between the 50th and 60th notation; and within systems, the human mind has also been imputed have notations within which to be.

From the human-scale we get our knowing.  Carl Jung called these archetypes.  A special vocabulary will emerge for this part of our self-definition.

Within the Now, this moment, today, there is an integration as a thing, an entity.  All human history, all civilization is within the 200th notation.  Just as an aside, if time travel were to become possible, it will be as an observer. Interactions would also require trifurcating, i.e. simultaneously entering the space and duration of the being and knowing of any given moment in time.

For more, consider these pages:

  1. The Big Board-little universe Project
  2. Top Ten Reasons Top Ten Reasons to give up those little worldviews for a much bigger and more inclusive UniverseView. These are the inherent qualities that define the infinite for science.
  3. Every moment has a perceived and dynamic value.
  4. An analysis of numbers
  5. A Simple View Of The Universe

Sheldon Glashow

On Fri, Oct 19, 2012 at 7:19 PM, Bruce Camber
Bruce Camber wrote:

Dear Prof. Dr. Glashow:

Just over 34 years ago I contacted you regarding a special project at MIT called, “An architecture for integrative systems.”  It was a display project in the main rotunda just off Massachusetts Avenue. It borrowed Erwin Schrodinger’s title from his much earlier work, “What is life?”  Seventy-seven leading, living scholars participated and you were one of them.

We are taking that old product and re-purposing it online within a very similar framework — Small Scale, Human Scale, Large Scale — however, we are using base-2 exponential notation from the Planck Length to the edges of the observable universe which gives us over 201 ordered steps in which to context information.  By assuming nested geometries at each doubling, it seems that we will have an inherent structure for analogous or metaphorical connection-making.

But before we go to far, I would like to re-engage you and ask for your advice:
1.   If the Planck Length is a dimensionful number representing a singularity or a point, can we multiply it by 2 and assume two points? ..multiply it again and assume 4, then 8, 16, 32 and on up to 1024 by the 10th doubling?
2.   Can we assume nested geometries throughout?
3.   We will use the same infrastructure as used by Wikipedia to build it out, so owner’s of information can readily edit and update content. Is there any particular recent work to which you would want us to take note?

Thank you.

Most sincerely,

Bruce Camber
Small Business School, a television series on PBS stations

PS.  A few simple web pages provide more background:
Our working model:

What Did We Ever Do Without Our Universe View?

1957: The Beginnings of a somewhat Integrated Universe View

In 1957 Kees Boeke’s book, Cosmic Vision, The Universe in 40 Jumps, was published; it was the first integrated view of the known universe. He could have but did not engage the Planck base units. He could have, but did not consider any geometric calculations. Yet, he did get the attention of prominent scientists including Nobel-laureate, Arthur Compton. Thereafter, the Eames film, the Phylis and Philip Morrison book, Powers of Ten, the IMAX (Smithsonian) movie (guide), and the Huang’s scale of the universe opened this conceptual door for anyone who chose to walk through it.  Anyone could begin to have an integrated view using base-10 notation of the entire universe. It was a fundamental paradigm shift; all the attention given to it has been justified.

Most of the world’s people live within what we might call, their OwnView.  Even though subjective and often quite naïve, the elitists and the solipsistic and narcissistic among us, lift up that view as the best view, the only view, and/or the right view.

If and when we start to grow up, spread our wings and begin to explore beyond our horizons, we develop an objective view of the world.  As we integrate more and more facets of our subjective and objective views, it begins to qualify as a WorldView (in the spirit of the old Weltanschauung).

In light of Boeke’s work, the next step for all of us is to bring whatever WorldView we have, and see how it fits and works within a view of the entire universe. Kees Boeke’s work is historically the very first UniverseView. Although Boeke only had 40 jumps and used base-10 exponential notation, it is still the first systematic view of the entire Universe.

2011:  A Second Universe View Emerges From Another High School

A high school geometry class just up river from the French Quarter of New Orleans developed what appears to be the second systematic UniverseView.  It is quite a bit more granular than Boeke’s work and it originated from the students’ work with simple embedded and nested geometries. Using base-2 exponential notation this  group emerged with about 202+ doublings, layers, notations, or steps from the Planck Length  to the Observable Universe.  Eventually beside each length, the calculations from the Planck Time out to the Age of the Universe were added.

This fully-integrated UniverseView first emerged in December 2011 and was officially dubbed, “Big Board – little universe.” One of the initial boards was over eight feet high and the second and third generations were around 60 inches high.  The entire universe, mathematically-and-geometrically related within 200 or so notations, seemed to bring the universe down to a manageable size!

Now, what do we do with it?

The first thought was that this UniverseView with its 200+ notations could be a good container for Science-Technology-Engineering-Mathematics (STEM) education.  It puts everything in the known universe within a simple ordering system.  Then, in January 2012, in the process of trying to find scholarly references to understand the foundations of their work, the students and their teachers discovered Kees Boeke.  In so many ways, it was a vindication — “Somebody had been here before us.”  Yet, even with all the fanfare around Boeke’s work, not too much was done to extract meaning from that model.

The base-2 model is quite different. It has simple geometries and a more granular mathematics.  The students and teachers thought this ordering system might help to answer those historic queries by Immanuel Kant about (1) who we are, (2) why we are, (3) where we are going, and (4)  the meaning and value of life.

Given this model has a starting point and an end point, the students and teachers opted to see the universe as finite.  Always encouraging students to go deeper in their understanding of mathematics, their teacher, Bruce Camber, commented To engage the Infinite it appears that we hold the objective and subjective in a creative balance and that balance is called geometry, calculus and algebra through which we can more fully discover relations.”

Boeke’s base-10 work has an important role in history.  It gave the human family a starting point to see an ordered universe.  The base-2 model takes the next step. Instead of just adding or subtracting zeroes, it adds 3.333 times more steps or doublings. It provides more data to explore the simplest continuities, relations and dynamics within and between each notation.  Base-2 is the heart and spirit of cellular division, chemical bonding, complexification (1 & 2), and bifurcation.

Perhaps it is here that the academic community might begin to create a truly relational, integrated and functional UniverseView. Surely it is here that we find the rough-and-tumble within science.

So, although base-2 UniverseView is the second UniverseView, it seems to hold some promise.  And though these are preliminary models,  just a crack in the doorway, what a sweet and simple opening it is.  Perhaps Kepler would be proud.

This high school group is now just starting to discover the work of  real-and-graciously-open scholars.  With the help of this larger academic community, our work just might  somehow capture the spirit of one of the world great physicists throughout history, John Wheeler, when he said, “Behind it all is surely an idea so simple, so beautiful, that when we grasp it — in a decade, a century, or a millennium — we will all say to each other, how could it have been otherwise? How could we have been so stupid for so long?” 


This Shifting Paradigm Changes Our Perception Of Everything

Editor’s note:  This page was first posted within Small Business School, a television series that aired for over 50 seasons on PBS-TV stations (1994-2012).  It is the author’s business website, so many of the links go to that Small Business School website.    Eventually all links will be redirected to pages within The Big Board – little universe Project.


Background: Our study of the Planck Length to the Observable Universe began formally on December 19, 2011. Though we thought about the matrix from the Planck Time to the Age of the Universe, it took until December 8, 2014 to add it the Planck Length chart. Logically, but non-intuitively, the two tracked well together. Based on that work, we started looking at our own foundations for understanding first principles, universals and constants.

First, our television series began in 1994 based on first principles (linked from here). These were a direct reflection of our faith and our belief that faith and science must cohere or one of them is wrong.

Second, we used those first principles in all that we have done. That’s how one knows the first principles work. Yet, eventually, those first principles inform in new ways. It is not automatic. It takes time. But, there is always a next step. We can always improve on the initial conditions.

Third, we all need to extend our principles globally, then extend them throughout the universe. That drove our work on the Big Board-little universe back which started in December 2011.And oddly enough, we can now see how such principles just might become the core of a new small business revolution.

Here is a paradigm shift that just might change our perceptions of everything.

1. The Universe appears to be finite. That’s huge. It has measurable smallest units for space and time. It has measurable units for the largest dimensions of space and time, the Observable Universe and the Age of the Universe, respectively.More

2. The Universe has an ethical bias. Yes, hard to believe, but it seems to be true. If so, the theological among us have some very real work to do because theology will be informed by science and science will actually be informed by theology. And, those within radical Islam will learn that they still have much to learn from their Allah and our science!

3. The Universe is smaller and more ordered than we think.In 202+ steps, you go from the smallest measurement to the very largest.Initially it sounded ridiculous and it seemed inconceivable, yet over time, it sinks in.

4. The Universe is more connected than we think. In fact, everything is related to everything, all within 202+ steps! Seems impossible; it’s not.

5. The Universe gets structure from space-and-time, but not its essence. The structures go back to basic geometries that have become exquisitely complex (Also, see reference #4). One might conclude that the essence of that structure comes from the Infinite through our constants and universals which appear to be best engaged through the Planck Units.

Now, with all these references, we now say, “Let’s get focused; there are great things to do to get us all on track for a brilliant future.”

Planck Time to the Age of The Universe alongside Planck Length to The Observable Universe

Early in December 2014 we started this page to follow-up that earlier work on just the Planck Length. We began that effort three years earlier (December 2011) in our local high school’s geometry classes. Because we will continue to find obvious errors (from simple mathematics to our interpretation) of the chart below, this page will be subject to frequent updates.

Background: We had been asking around the scholarly community, “Has anyone done a progression of the Planck Time to the Age of the Universe using base-2 exponential notation (a fancy way of saying, multiplying by 2)?” We did it from the Planck Length to the Observable Universe and had wanted to compare that progression to Planck Time.

Going from the smallest to the largest is a simple ordering logic. Using Max Planck’s smallest possible measurements to go to the known limits seems like an exercise high school students should do.

Here we introduce the simple math from the Planck Time to the Age of the Universe.

In July 2014, Prof. Dr. Gerard ‘t Hooft and Stefan Vandoren published a very helpful book, Time in Powers of Ten, a base-10 chart. We were looking for a base-2 chart which would be 3.333+ times more granular. We could not find it anywhere so this page is our working draft, our starting point.

Perhaps it goes without saying… as you read this note, I appeal to you to ask questions and make comments and suggestions. Thank you. –Bruce Camber

Planck Time is the smallest possible unit of measurement of time. The ratios of all 201+ multiples of the Planck Time to its respective multiple of Planck Length is consistent across the chart.  The original calculations were done by Max Planck in and around 1899. This chart of 201+ notations was done in December 2014. Any numbers smaller than the Planck Time are just numbers that cannot be meaningfully applied to anything.

Planck got his Nobel Prize in 1918 for his discovery of energy quanta. He was also a mentor and friend of Einstein (who received his Nobel Prize in 1921).

The Planck Length and Planck Time are actual values that can be multiplied by 2.
Of course, if one were to multiply each by 2 over and over again, you can assume that you would reach their outer limits. That process looks a bit tedious. After all, the Age of the Universe is somewhere over 13.8+ billion years and the Observable Universe is millions of light years from common sense. Yet, rather surprisingly, to complete that effort doesn’t require thousands of doublings. It is done in somewhere just over 201+ doublings.

That is so surprising, the doublings for both are charted below.

These doublings do kind-of, sort-of end up in sync. Where there is a problem, we assume it is within our simple math. Considering the duration and the length, and the nature of very large measurements, for all intents and purposes, they are synced mathematically. We’ve got a bit of work to do to sync them up intellectually!

Though these charts will be tweaked substantially, the best place to start is at the notations (or doublings) that define a day, a week and a year (in Planck Time units) to see how each corresponds with the distance light travels in Planck Length units, i.e. a light year, “light week,” and “light day.” These are our first baby steps of analysis. How many hundreds of steps are there to go to discern all the faces of its meaning? Who knows? From here, we will continue to look to see what meaning and relation evolves at a particular notation where one column appears to impart value to the other. Just on the surface, this chart seems to suggest that there are other possible views of the nature of space and time where order (sequence), continuity, symmetries, and relations seem to play a more fundamental role.

Science and our common sense worldview assume the primordial nature of space and time. As a result of our work with the Planck Units, we hold that conclusion up for further inspection. How do things appear as one begins to approach a synchronized Planck Length and Planck Time?

Planck Units: As we add more Planck Units to this chart, what else might we see? What might we learn? So, we will add mass, electric charge, and temperature to these listings. And then, we’ll add the derived Planck Units (12) and then ask, “Is there anything more we can do to establish a range from the smallest to the largest? What might a comparative analysis at each doubling reveal to us?” We don’t know, however, we are on a path to explore! We’ll report in right here.

At this point, we are attempting to learn enough to make a few somewhat educated guesses about the nature of things within these scales of the universe.

So, as a result of where we are today, I think it is okay to ask the question, “What would the universe look like if space and time were derivative of order-continuity and relation-symmetry, and of ratios where the subject-object are constantly in tension?”

This stream of consciousness continues at the very bottom of this chart.

Planck Time Doublings:
Primarily in Seconds
Planck Length Doublings:
Primarily in Meters

The Age of the Universe:
13.78 to 13.8 billion years

It appears that we currently live in the earliest part of 201 doubling.

Observable Universe: 8.8×10(26) m Planck Multiple: 8.31×1026 m

4.155×1026 m Future Universe

203 6.9309178×1017 seconds (21.9777+ billion years) 2.077×1026 m Future Universe
202 346,545,888,147,200,000 seconds (10.9888+ billion years) 1.03885326×1026 m Observable Universe
201 173,272,944,073,600,000 seconds (5.49444+ billion years) (1017) 5.19426632×1025 m
In this model: Time is discrete so to know how many years are to be aggregated (to see how close we are to the Age of the Universe), each notation must be added together. By the 200th notation, we would be one Planck Time unit shy of 10.9888 billion years. A possible conclusion could therefore be that we are within the 201st notations.
200 86,636,472,036,800,000 seconds (2.747+ billion years) 2.59713316×1025 m
199 43,318,236,018,400,000 seconds (1.3736+ billion years) 1.29856658×1025 m
198 21,659,118,009,200,000 seconds (686.806+ million years) 6.49283305×1024 m
197 10,829,559,004,600,000 seconds (342.4+ million years) (1016) 3.24641644×1024 m
196 5,414,779,502,320,000 seconds (171.2+ million years) 1.62320822×1024 m
195 2,707,389,751,160,000 seconds (85.6+ million years) 8.11604112×1023 m
194 1,353,694,875,580,000 seconds (42.8+ million years) (1015) 4.05802056×1023 m
193 676,847,437,792,000 seconds (21.4+ million years) 2.02901033×1023 m
192 338,423,718,896,000 seconds (10.724+ million years) 1.01450514×1023 m
191 169,211,859,448,000 seconds (5.3+ million years) (1014) 5.07252568×1022 m
190 84,605,929,724,000 seconds (2.6+ million years) 2.5362629×1022 m
189 42,302,964,862,000 seconds (1.3+ million years) 1.26813145×1022 m
188 21,151,482,431,000 seconds (640+ thousand years) 6.34065727×1021 m
187 10,575,741,215,500 seconds (320+ thousand years) (1013) 3.17032864×1021 m or 3 Zettameters or 310,000 ly
186 5,287,870,607,760 seconds (160+ thousand years) 1.58516432×1021 m or about 150,000 ly (1.5z)
185 2,643,935,303,880 seconds (83.7+ thousand years) 7.92582136×1020 m
184 1,321,967,651,940 seconds (41.8+ thousand years) (1012) 3.96291068×1020 m
183 660,983,825,972 seconds (20.9+ thousand years) 1.981455338×1020 m
182 330,491,912,986 seconds (or about 10,472.9 years) 9.90727664×1019 meters
181 165,245,956,493 seconds (1011) 4.95363832×1019 m
180 82,622,978,246.4 seconds 2.47681916×1019 m
179 41,311,489,123.2 seconds 1.23840958×1019 m
178 20,655,744,561.6 seconds 6.19204792×1018 m
177 10,327,872,280.8 seconds (1010) 3.09602396×1018 m
176 5,163,936,140.4 seconds 1.54801198×1018 m
175 2,581,968,070.2 seconds 7.74005992×1017 m
174 1,290,984,035.1 seconds (109) 3.87002996×1017 m
173 645,492,017.552 seconds 1.93501504×1017 m
172 322,746,008.776 seconds 9.67507488×1016 m
171 161,373,004.388 seconds (108) 4.83753744×1016 m
170 80,686,502.194 seconds 2.41876872×1016 m
169 40,343,251.097 sec (466 days)(Note: 31,536,000 s/year) 1.20938436×1016 m
Comments: A light year is about 9.4605284×1015 meters (Google) or 9,460,730,472,580,800 metres “exactly” (Wikipedia). Use the Gregorian calendar (circa 1582) where a year is 365.2425 and the speed of light is given as 299,792,458 metres/second, the calculation is 365.2425 times 86400 seconds/day (or 31556952 seconds/year) times 299,792,458 meters/second or 9.4605362+×1015 meters. Discrepancies would become quite large at the size of the Observable Universe and the Age of the Known Universe.Using Planck Units:
One Light Year 9.45994265715×1015m
168 20,171,625.5485 seconds (233.468 days) 6.0469218×1015 m [one light year (ly) is 9.4×1015 m]
167 10,085,812.7742 seconds (116.73 days) (107) 3.0234609×1015 m
166 5,042,906.38712 seconds (58.36+) 1.5117305×1015 m
165 2,521,453.19356 s (29.1835 days) 7.55865224×1014 m
164 1,260,726.59678 s (14.59+ days) (106) 3.77932612×1014 m
163 630,363.29839 s (7.29+ days) 1.88966306×1014 m (about 7-day light travel)
162 315,181.649195 seconds (3.64794 days) 9.44831528×1013 m
161 157,590.824 s (1.82 days) (105) 4.72415764×1013 m
160 78,795.4122988 s (.911984 days) 2.36207882×1013 m (or close to 24-hour light travel)
159 39,397.7061494 seconds 1.18103945×1013 m
158 19,698.8530747 seconds (104) 5.90519726×1012 m
157 9849.42653735 seconds 2.95259863×1012 m ()
156 4924.71326867 seconds(3600 s in hour) 1.47629931×1012 m
155 2462.35663434 seconds 738,149,657 kilometers 1011
154 1231.17831717 seconds (103) 369,074,829 kilometers 1011
153 615.589158584 seconds (10.259+ minutes) 184,537,414 kilometers 1011
152 307.794579292 seconds 92,268,707.1 kilometers (range of earth-to-sun)1010m
151 153.897289646 seconds (102) 46,134,353.6 kilometers 1010
150 76.948644823 s (16+ sec over 1 min) 23,067,176.8 kilometers 1010
Comments: A light minute is, of course, sixty times 299,792.458 km/second. Again, using simple mathematics, the distance light travels in one minute is 17,987,547.48 which is about 1000 kilometers off of 17,986,420.0329 km/second using the simple mathematics of this chart. This difference will be further analyzed.
149 38.4743224115 s (21.53 sec to 1 min) 11,533,588.4 kilometers 1010
148 19.2371612058 seconds 101 5,766,794.2 kilometers 109
147 9.61858060288 seconds 2,883,397.1 kilometers 109
146 4.80929030144 seconds 1,441,698.55 kilometers 109 m
145 2.40464515072 seconds 720,849.264 kilometers 108
144 1.20232257536 s (1s ≠ perfect tp multiple)
One Second:
360,424.632 kilometers 108 meters
Speed of light equals 299,792,458 m/s
Comments: Science knows experimentally that light travels 299,792.458 km/second (a light second). A Planck Time multiple, either 1.202 seconds or .6011 seconds, could be used as a standard unit of time that is based on a theoretical constant. We will explore further the calculations for a day, week, month and year based on such a system. We’ll also explore it in light of recent work to define the theoretical chronon.
A Light Second 299,792.458 km
143 6.0116128768×10−1 seconds 180,212.316 kilometers (111,979+ miles) 108 m
142 3.0058064384×10−1 seconds 90,106.158 kilometers 107 m
141 1.5029032192×10−1 seconds 45,053.079 kilometers 107
140 7.514516096×10−2 seconds 22,526.5398 kilometers 107
139 3.757258048 × 10−2 seconds 11,263.2699 kilometers or about 7000 miles
138 1.878629024 × 10−2 seconds 5631.63496 kilometers 106
137 9.39314512 × 10−3 seconds 2815.81748 kilometers 106

The transition from the Human-Scale to the Large-Scale Universe

136 4.69657256 × 10−3 seconds 1407.90874 kilometers (about 874 miles) 106 m
135 2.34828628 × 10−3 seconds 703.954368 kilometers 105
134 1.174143145978 × 10−3 seconds 351.977184 kilometers (218.7 miles) 105
133 5.8707157335 × 10−4 seconds 175.988592 kilometers (109.35 miles) 105
132 2.93535786675 × 10−4 seconds 87.994296 kilometers 104
131 1.46767893338 × 10−4 seconds 43.997148 kilometers 104
130 7.33839466688 × 10−5 seconds 21.998574 kilometers104
129 3.66919733344 × 10−5 seconds 10.999287 kilometers or within 6.83464 miles 104
128 1.83459866672× 10−5 seconds 5.49964348 kilometers 103
127 9.1729933336 × 10−6 seconds 2.74982174 kilometers 103
126 4.5864966668 × 10−6 seconds 1.37491087 kilometers 103
125 2.2932483334 × 10−6 seconds 687.455439 meters 102
124 1.1466241667 × 10−6 seconds 343.72772 meters or about 1128 feet 102
123 5.73312083348 × 10−7 seconds 171.86386 meters or about 563 feet 102
122 2.86656041674 × 10−7 seconds 85.9319296 meters 101
121 1.43328020837 × 10−7 s 42.9659648 meters 101
120 7.16640104186 × 10−8 sec 21.4829824 meters 101
119 3.58320052093 × 10−8 sec 10.7414912 meters or 35.24 feet or 1.074×101 m 101
118 1.79160026046 × 10−8 seconds 5.3707456 meters 100
117 8.95800130232 × 10−9 seconds 2.6853728 meters or 105.723 inches 100
116 4.47900065116 × 10−9 seconds 1.3426864 meters or 52.86 inches 100
115 2.23950032558 × 10−9 seconds 67.1343176 cm (19.68+ inches or 6.71×10-1
114 1.11975016279 × 10−9 seconds 33.5671588 centimeters or 3.356×10-1 m)
113 5.59875081396 × 10−10 seconds 16.7835794 centimeters or 1.6783×10-1
112 2.79937540698 × 10−10 seconds 8.39178968 cm (3.3+ inches or 8.39×10-2 m)
111 1.39968770349 × 10−10 seconds 4.19589484 centimeters 4.19589484×10-2 m
1109 .99843851744 × 10−11 seconds 2.09794742 centimeters or 2.0979×10-2 m
1098 3.49921925872 × 10−11 seconds 1.04897 centimeters or 1.04897375×10-2 m
108 1.74960962936 × 10−11 seconds 5.24486856 mm (about 1/4 inch) or 5.24×10-3 m
107 8.7480481468 × 10−12 seconds 2.62243428 millimeters or 2.62243428×10-3 m
106 4.3740240734 × 10−12 seconds 1.31121714 millimeters 1.31121714×10-3 m
105 2.1870120367 ×10−12 seconds .655608568 millimeters or 6.55608568×10-4 m
104 1.09350601835 ×10−12 seconds .327804284 millimeter or 3.27804284 x10-4 m
103 5.46753009176 ×10−13 seconds .163902142 millimeters or 1.63902142×10-4 m
102 2.73376504588 × 10−13 seconds 81.9510712 microns or 81.9510712 x10-5 m
101 1.36688252294 × 10−13 seconds 40.9755356 microns or 4.09755356 x10-5 m
100 6.83441261472 × 10−14 seconds 20.4877678 microns or 2.04877678×10-5 m
99 3.41720630736 × 10−14 seconds 10.2438839 microns or 1.02438839×10-5 m
98 1.70860315368 × 10−14 seconds 5.12194196 microns (.0002+ inches or 5.12×10-6 m)
97 8.5430157684 × 10−15 seconds 2.56097098 microns or 2.56097098×10-6 m
96 4.2715078842 × 10−15 seconds 1.28048549 microns or 1.2804854×10-6 m
95 2.1357539421 × 10−15 seconds 640.242744 nanometers 6.40242744×10-7m
94 1.06787697105 × 10−15 seconds 320.121372 nanometers 3.20121372×10-7 m
93 5.33938485524 × 10−16 seconds 160.060686 nanometers or 1.6×10-7 m
92 2.66969242762 × 10−16 seconds 80.0303432 nanometers or 8.0×10-8 m
91 1.33484621381 × 10−16 seconds 40.0151716 nanometers or 4.0×10-8 m
90 6.67423106904 × 10−17 seconds 20.0075858 nanometers or 2.0×10-8 m
89 3.33711553452 × 10−17 seconds 1.00037929×10-8 meters or 10 nanometers
88 1.66855776 × 10−17 seconds (smallest measurement – 2010) 5.00189644×10-9 meters
87 8.34278883632 × 10−18 seconds 2.50094822 nanometers or 2.50094822×10-9 m
86 4.17139441816 × 10−18 seconds 1.25474112 nanometers or 1.25×10-9 m
85 2.08569720908 × 10−18 seconds .625237056 nanometers or 6.25237056×10-10 m
84 1.04284860454 × 10−18 seconds .312618528 nanometers or 3.12×10-10 m
83 5.21424302272 × 10−19 seconds .156309264 nanometers or 1.563×10-10 m
82 2.60712151136 × 10−19 seconds 7.81546348×10-11 m
81 1.30356075568 × 10−19 seconds 3.90773174×10-11 m
80 6.5178037784 × 10−20 seconds 1.95386587×10-11 m
79 3.2589018892 × 10−20 seconds 9.76932936×10-12 m
78 1.6294509446 × 10−20 seconds 4.88466468×10-12 m
77 8.147254723 × 10−21 seconds 2.44233234×10-12 m
76 4.0736273615 × 10−21 seconds 1.22116617×10-12 m
75 2.03681368075 × 10−21 seconds 6.10583084×10-13 m
74 1.01840684038 × 10−21 seconds 3.05291542×10-13 m
73 5.09203420188 × 10−22 seconds 1.52645771×10-13 m
72 2.54601710094 × 10−22 seconds 7.63228856×10-14 m
71 1.27300855047 × 10−22 seconds 3.81614428×10-14 m
70 6.36504275236 × 10−23 seconds 1.90807214×10-14 m
69 3.18252137618 × 10−23 seconds 9.54036072×10-15 m
68 1.59126068809 × 10−23 seconds 4.77018036×10-15 m

Transition from the Small-Scale Universe to the Human-Scale Universe

67 7.95630344044 × 10−24 seconds 2.38509018×10-15 m
66 3.97815172022 × 10−24 seconds 1.19254509×10-15 m
65 1.98907586011 × 10−24 seconds 5.96272544×10-16 m
64 9.94537930056 × 10−25 seconds 2.98136272×10-16 m
63 4.97268965028 × 10−25 seconds 1.49068136×10-16 m
62 2.48634482514 × 10−25 seconds 7.45340678×10-17 m
61 1.24317241257 × 10−25 seconds 3.72670339×10-17 m
60 6.21586206284 × 10−26 seconds 1.86335169×10-17 m
59 3.10793103142 × 10−26 seconds 9.31675848×10-18 m
58 1.55396551571 × 10−26 seconds 4.65837924×10-18 m
57 7.76982757856 × 10−27 seconds 2.32918962×10-18 m
56 3.88491378928 × 10−27 seconds 1.16459481×10-18 m
55 1.94245689464 × 10−27 seconds 5.82297404×10-19 m
54 9.7122844732 × 10−28 seconds 2.91148702×10-19 m
53 4.8561422366 × 10−28 seconds 1.45574351×10-19 m
52 2.4280711183 × 10−28 seconds 7.27871756×10-20 m
51 1.21403555915 × 10−28 seconds 3.63935878×10-20 m
50 6.07017779576 × 10−29 seconds 1.81967939×10-20 m
49 3.03508889788 × 10−29 seconds 9.09839696×10-21 m
48 1.51754444894 × 10−29 seconds 4.54919848×10-21 m
47 7.58772224468 × 10−30 seconds 2.27459924×10-21 m
46 3.79386112234 × 10−30 seconds 1.13729962×10-21 m
45 1.89693056117 × 10−30 seconds 5.68649812×10-22 m
44 9.48465280584 × 10−31 seconds 2.84324906×10-22 m
43 4.74232640292 × 10−31 seconds 1.42162453×10-22 m
42 2.37116320146 × 10−31 seconds 7.10812264×10-23 m
41 1.18558160073 × 10−31 seconds 3.55406132×10-23 m
40 5.92790800364 × 10−32 seconds 1.7770306×10-23m
39 2.96395400182 × 10−32 seconds 8.88515328×10-24m
38 1.48197700091 × 10−32 seconds 4.44257664×10-24 m
37 7.40988500456 × 10−33 seconds 2.22128832×10-24m
36 3.70494250228 × 10−33 seconds 1.11064416×10-24m
35 1.85247125114 × 10−33 seconds 5.5532208×10-25m
34 9.26235625568 × 10−34 seconds 2.7766104×10-25m
33 4.63117812784× 10−34 seconds 1.3883052×10-25m
32 2.315589×10-34 seconds 6.94152599×10-26 meters
31 1.15779453196× 10−34 seconds 3.47076299×10-26m
30 5.78897265978 × 10−35 seconds 1.735381494×10-26 m
29 2.89448632989 × 10−35 seconds 8.67690749×10-27 m
28 1.44724316494 × 10−35 seconds 4.3384537×10-27 m
27 7.23621582472 × 10-36 seconds 2.16922687×10-27 m
26 3.61810791236 × 10−36 seconds 1.0846134×10-27 m
25 1.80905395618 × 10−36 seconds 5.42306718×10-28 m
24 9.045269781089 × 10−37 seconds 2.711533591×10-28 m
23 4.522263489044 × 10−37 seconds 1.35576679×10-28 m
22 2.26131744522 × 10−37 seconds 6.77883397×10-29 m
21 1.13065872261 × 10−37 seconds 3.38941698×10-29 meters
20 5.65329361306 × 10−38 seconds 1.69470849×10-29 meters
19 2.82646806528 ×10−38 seconds 8.47354247×10-30 meters
18 1.41323403264 ×10−38 seconds 4.2367712×10-30 m
17 7.0661701632 × 10−39 seconds 2.11838561×10-30 m
16 3.530850816 × 10−39 seconds 1.0591928×10-30 m
15 1.7665425408 × 10−39 seconds 5.29596404×10-31 m
14 8.832712704 × 10−40seconds 2.64798202×10-31 m
13 4.416356352 × 10−40 seconds 1.32399101×10-31 m
12 2.208178176 × 10−40 seconds 6.619955ƒx10-32 m
11 1.104089088 × 10−40 seconds 3.30997752×10-32 m
10 5.52044544 × 10−41 seconds 1.65498876×10-32 m
9 2.76022272 × 10−41 seconds 8.27494384×10-33 m
8 1.38011136 × 10−41 seconds 4.1374719232×10-33 m
7 6.9005568 × 10−42 seconds 2.0687359616×10-33 m
6 3.4502784 × 10−42 seconds 1.03436798×10-33 m
5 1.7251392 × 10−42 seconds 5.1718399×10-34 m
4 8.625696 × 10−43 seconds 2.58591995×10-34 m
3 4.312848 × 10−43 seconds 1.29295997×10-34 m
2 2.156424 × 10−43 s The second doubling 6.46479988×10-35 meters
1 1.078212 × 10−43 s The first doubling 3.23239994×10-35 m The first doubling, step, or layer.
5.39106(32)×10−44 seconds 1.616199(97)x10-35 meters

The Planck Time

The Planck Length

Endnotes:1. We are in the process of refining this chart and will be throughout 2015 and 2016.

2. Our very first calculation with the Planck Length column (December 2011), resulted in 209 doublings! We found several errors. Then , with help of a NASA astrophysicist, Joe Kolecki (now retired), we updated our postings with his calculation of 202.34. Then, a French Observatory astrophysicist, Jean-Pierre Luminet, calculated 205.1 doublings. We are very open to all ideas and efforts! We are studying the foundations of foundations. One might call it a hypostatic science based on the simplest mathematics, simple geometries and observations about the way the universe coheres.

One might say, “The Finite is finite, the Infinite is the Infinite, and the constants and universals describe the boundary conditions and transformations between each. One manifests a panoply of perfections; the other has only momentary instants of perfection.”

Open Questions: Is it possible that Planck Length starts first and Planck Time begins on Planck Length’s 2nd or 3rd notation? Could there be a two for one at the beginning and at the transitions? By using experimental speed of light per second, can we force the Planck units from that point? If the ratio of Length/time is consistent across the grid (and it is), how do we fine tune this chart?

What is a second?

What are Planck Units?

What is time?

What is a meter?

What is length?

What is space?

What happens just before the Planck time at 10-44 seconds? Theorists say that all of the four fundamental forces are presumed to have been unified into one force. All matter, energy, space and time “explode” from the original singularity.

3. Our online “Google” calculator often rounds up the last digit. It is usually beyond the eleventh postion to the right of the decimal point.

4. For more about this place and time, go to Hyperphysics (Georgia State):

5. A copy of this chart has also been published in the following locations:




d. ResearchGate Documents: 3052, 3054, 3056

Could The Planck Base Units Open A Secret Door To A New Universe Of Knowledge?

Five Planck Base Units Science is filled with mysterious numbers that defy logic and explanation. Among them are extremely small numbers that were introduced in 1899. Largely ignored for over 100 years, today these Planck Units have opened a rather magical pathway that has a little potential to become a new study within the sciences. Some might think it is a science of the mind. Though possibly true, it could be much more. (new window).

CurtisHere the old-fashioned thought experiment could become a new art form. A little high school, not far from the levee along the Mississippi River, a little up river from the French Quarter but downriver from the New Orleans airport, has big dreams and plenty of brains-and-brawn. Yet, never did they expect to be the place where base-2 exponential notation from the Planck Length to the Observable Universe and from the Planck Time to the Age of the Universe would be birthed. The fateful day was December 19, 2011, the last day of classes before their Christmas holiday recess and it begged the question, “Could this possibly be the beginnings of a very simple model for everything, everywhere, for all times?” More

For five groups of students who were studying the basic tenets of geometry, a strange thing happened. They saw the entire universe and parts of the unknown universe all at one time, all interrelated on one board, and organized by (1) a simple logic, (2) the Planck Length, (3) simple geometries and (4) simple mathematics (multiplying and dividing by 2). Just over 201 doublings captured our entire known universe. More

Just over 201 notations. What does it mean? What difference does it make? The first insight was that there is a deep-seated order in the universe. The order is imputed. It comes from logic and mathematics not from experimentation and measurement. Although it creates a special continuity from the smallest to the largest measurements of space and time, they can only say for sure, “Here it is,” then ask questions such as “What is wrong with this picture?” Very quickly, fifteen more key questions were raised. Third, also imputed are structural relations that create a diversity of symmetries that literally bind everything in the known universe. That’s quite an achievement unto itself, but it must be defended with facts that have some basis in reality.  More

Hardly intimidated, this group believes that the facts are, by and large, self evident and that there is so much more to discover and learn. More


Located in River Ridge (a hamlet just downriver from the airport), the Curtis School is well-known among the football quarters, not within  the studies of cosmology and astrophysics. Though there are rumblings and a very small scientific group moving away from the Big Bang Theory, this little  group within the school could land a tackle that suddenly causes this leading intellectual theory to stop in its tracks. If their map of the universe is truly a new domain of science, the human mind may end up taking its rightful place of importance within their grid that begins to redefine who we are and why. More…

That is enough, but there is more.To date, science has had very little to say about values and ethics, You can hear the pragmatists say, “Those are not measurable qualities.” And they would be right, yet here, if the inherent structure of science is order-continuity and relations-symmetry, extended logically, it could become a structure for value and even for a moment of perfection within what appears to be a finite universe. Two symmetries interacting over time, give us the first dynamical moments that have a harmony which unto itself is a compelling infrastructure for valuation and ethics. More…

Also, deep in the heart of this discussion is the place of the finite-and-infinite, and geometry-and-calculus. The old world of geometry gave us a special grounding. Structure was everything. Then, the newer world of calculus came in and slowly began to give us a new sense of change, openness, and a very long vision. People thought they could see forever. Professor Max Planck was 41 years old when he did those special calculations back in 1899. He was 60 years old when in 1918 he received his Nobel Prize for his work to define a quanta of energy. By 1944, now 87 years old, he penned these few special words that could set the stage for a science of the Mind. More

Throughout it all, his precious Planck Units had been virtually ignored. It wasn’t until 2001 before his earlier calculations, now over 100 years old, began to see the light of day. In a series of three articles in Physics Today. Prof. Dr. Frank Wilczek of MIT (Nobel laureate, 2004) acknowledged their presence and potential importance. Finally, the Planck numbers gained a little respect as the conceptual limits on the smallest side of every equation. It seemed to suggest a way to begin to see the universe as a finite place. Rather suddenly Planck’s work gained a solid foothold. Also, science had advanced far enough to begin to suggest that there are upper boundaries as well. For the first time in centuries, the finite was gaining ground; the infinite seemed more ephemeral. The kids had plenty of ideas and comments. “This is a great STEM tool. Science-Technology-Engineering-Mathematics all makes sense here.” Another said, “Let’s keep the small “I” of the infinite so all our atheist friends have something in which to believe so they don’t have to believe.” More

Our “Planck students” soon discovered that they were not alone in their sense that the universe could be reduced to simple, logical working principles. In 1957 in Holland a little-known high school teacher, Kees Boeke, wrote a very short book, Cosmic Vision, The Universe in 40 Jumps. In 1962 a film was made about it and then in 1965 a coffee table book was published. By 2001, the scholarly community had become Boeke.png
familiar with base-10 notation. The River Ridge group was just getting to know him. They quickly acknowledged that Boeke’s book was the very first universe view. But because he only found 40 of 62 base-10 notations, it was dubbed “universe-view light.”Yet, base-10 has an important place in this discovery process and work with it is still being done. In July 2014, Gerard ‘t Hooft and Stephan Vandoren published a book, Time in the Powers of TenOf course, base-2 is much more granular (3.3333 times) and mimics cellular reproduction on one hand and chemical bonding on the other. More importantly, this base-2 work is rooted within the Planck base units and basic geometries where space and time are seen working together throughout the 201+ notations that define our universe. More.

There are several next steps. A few students (and their teacher) speculate:
Let’s make a movie about it that focuses on our most speculative guesses.”
Let’s focus on that small-scale universe and try to figure it out. There are doctoral dissertations in there.
“Let’s get other schools involved and promote this simple model as a powerful STeEM (Science-Technology-[Education]-Engineering-Technology) tool. (A link will be forthcoming)*

Endnote: The following Max Planck quote is currently linked to the place where the source pages are housed in Berlin at a place called the Archiv zur Geschichte der Max-Planck-Gesellschaft: “All matter originates and exists only by virtue of a force which brings the particle of an atom to vibration and holds this most minute solar system of the atom together. We must assume behind this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter.” (opens in a new window)From “The Nature of Matter” within the Archiv zur Geschichte der Max-Planck-Gesellschaft, Abt. Va, Rep. 11 Planck, Nr. 1797, 1944


Center for Perfection StudiesThe Big Board–Little Universe Project 

What is finite? And, what is truly infinite?

“Finite or Infinite? Is That The Question?”    (link goes to Part II)

Some of our high school students think our scientific community makes the study of Science, Technology, Engineering and Mathematics (STEM) all too difficult to understand and overly complex by defying a certain commonsense logic. (Reference #1)

We have been studying simple math and simple geometries from the smallest possible measurement of a length to the largest (Reference #2). It appeared to some of the students, based on this work, that the universe is obviously finite. They have been told that intellectually and historically, it is an open question. For them, “Make a choice and see where it takes you.”

The students with strong faith statements said, “Only God is Infinite. All things within space and time are finite.” (Reference #3) When asked about all the universals-and-constants and space-and-time, the concurrence is that these are the access paths, interconnections and transformations between the Finite and the Infinite.

For the best of these students, asking the question, “What is the Infinite?” is like asking the question, “Who is God?” And, they have answers.

Of course, as a result of a little coaching, they say, “First, God is Perfect.” When asked, “What is perfection?” they echo their coach: “Perfection is order-continuity, relations-symmetry and dynamics-harmony, all rolled into one.” (Reference #4) That amounts to an understanding of the Infinite without importing all the related history and revelation from the various faith statements within our very short history throughout our little world. The Finite is another story. We turn to many people from Euclid to Einstein for inspiration to provide the academic and religious communities with our simple observations and assumptions.

Hardly postulates and axioms, our statements are a praxis in-search-of theoria:

If these statements are taken as a given, then what kind of universe and what kind of science do we have? Should we re-examine the use of infinity throughout the ages going back to the ancient Greeks? Should we reconsider the theory of indivisibles? And, perhaps we should even reconsider the very nature of the Big Bang and its theory.

Of course, that is our agenda (Reference #8),   our current focus for the immediate future.


1. One of two key general overview and working article,  Order in the Universe

2. One of the earliest reflections on all our efforts and work: Is it true that everything starts most simply?

3. Initially written in November 2012, just what is the nature of belief?

4. In light of those constants, universals and the finite-infinite relation, the nature of perfection seems to follow:

5. Examining basic structure in basic ways: Simple View of the Universe

6. Our first look at the progression of doublings.  This listing was written to accompany an article for Wikipedia: Written in March 2012 to support an article for Wikipedia

7. There are somewhere over 201 base-2 exponential notations (doublings, domains, layers or steps) within the Known Universe.

8. Another analysis of key points: There are 15 in this article.

Even between atheists and believers

Perhaps all it comes down to is an answer to the question, “Whose metaphor is more meaningful?” You will not find many atheists who deny science. They do not deny the constants and universals that are always in the back of the science textbooks.

There are three constants within the sciences that remain clear, in spite of quantum mechanics. The first is that there is order and continuity in the world. It is the basis of knowing. In every discipline there are multiple parameter sets where this is true. Beginning in mathematics, a rather pure form of thought, abstraction and representation, we then move into physics. It has multiple parameter sets as well. There is one for Newtonian mechanics, another for General Relativity and Special Relativity and yet another for quantum mechanics. Then chemistry and biology have their own parameter sets. All these parameters simply establish the boundary conditions of what is being measured within them.

Each has a formalized language. And, each has a metaphorical language that pushes into the edges of the unknown.

The sciences all embrace varying definitions of relations yet all of these definitions are understood by a symmetry function.

Specialized disciplines with each of the sciences hypothesize about the nature of the unknown, just beyond their limits of knowledge, and all these hypotheses are a study of the deepest dynamics of their discipline. The experience of insight, the “ah-ha” of the creative surge, is experienced as a concrescence of symmetries or harmony.

The atheists mostly object to the use of specialized language. They understand rules, mores, and societal law and order even though many are nihilistic, others narcissistic, and many both.

Yet, change will come. Some of these folks will begin to realize that time is not a fundamental frame of reference and that there are qualities of life that permeate everything in every way, and that these qualities empower order, relations, and dynamics, and that these three scientific functions with the faces of continuity, symmetry and harmony just might also be understood with very personal language. When and if they do, they are on their way to create a personal bridge to religion and some of the brave among them just may cross it.

Is There Order In The Universe?

UniverseTable Updated: November 30, 2015
Note: Links open a new tab or window. If any link goes back to Small Business School where it was first posted, use your back button to return here.  All postings are being consolidated within, the main website for secondary schools, and within, the main site for college, university and research-and-development.

Our high school geometry classes created a simple, mathematically and geometrically-ordered view of the known universe. We also found an inherent geometry for disorder.

Yes, rather unwittingly we backed into developing what we now call our Universe View. We used a very simple logic and math. First, we divided an object by 2 until we were down in the range of the smallest measurement of a length; then we multiplied the object by 2 until we were finally out around the largest-known measurement of a length.

Our work began in December 2011. That simple exercise resulted in measurements which opened paths to challenging facts, rather fun concepts, obviously wild-and-crazy ideas, and truly playful speculations.

Throughout this little article there are many references with links. However, there are just nine primary references to other pages. These links are also at the bottom of the page. Also, please be advised, that this project will always be a work in progress.

1. The Power of 2. There are 201+ base-2 exponential notations (that just means “doublings” or multiplying by 2) starting at the Planck Length, the smallest conceptual measurement of a length in the universe, out to the Observable Universe, the largest possible length. Within a few years we also did the simple multiplication of the Planck Time, side-by-side with the Planck Length, out to the Age of the Universe. Then on February 11, 2015 we posted our very first draft of a table of the basic five Planck Units (with a most-speculative guess regarding temperature).

The number of notations (also known as doublings, domains, clusters, groups, layers, sets or steps) is a fact established by simple mathematicsReference #1 (below) goes to the initial chart of 2011.  Yes, it is just simple mathematics. And, we were quickly informed that there was a precedence for it.

In 1957 a Dutch high school teacher, Kees Boeke, used base-10 (multiplying by 10). He found 40 of the 62 base-10 notations. Yet, we believe Boeke’s work is the very first mathematically-driven Universe View. We were unaware of Kees Boeke at that time our work began. Also, we started with (1) embedded geometries, (2)  the two measurements, Planck Length and Observable Universe, (3) a simple logic based on the concepts of continuity and symmetry, and (4) multiplying by 2 (base-2 exponential notation). It was not just a process of adding and subtracting zeros. Because base-2 is 3.3333+ times more granular than base-10, it is more informative and natural; the geometries create natural symmetries and levels of imperfection for symmetry-making and symmetry-breaking; and, it mirrors the processes in cellular division, the dipole nature of chemical bonding, combinatorics, group theory, and complexification (1 & 2).

2. Inherent Geometries. We were studying tetrahedrons and octahedrons, two of the most simple Platonic solids. We started our project by dividing each edge of a tetrahedron in half. We connected those six new vertices and discovered a half-sized tetrahedron in each of the four corners and an octahedron in the middle.

We did that same process with the octahedron and found six half-sized octahedrons in each of the six corners and a tetrahedron within each of the eight faces (link opens a new window). We did that process of going within about 118 times. On paper, in about 50 steps we were inside the atom; and, rather unexpectedly, within another 68 steps we were in the range of the Planck Length.

We then multiplied our two objects by 2 and within about 91 notations or steps, we were in the range of the Observable Universe. Then, to standardize our emerging model, we began at the Planck Length and multiplied it by 2 until we were at the edges of the known universe. We had some help to calculate the number of notations.  We settled for a range from 201 to 205.1  (Reference 2 – See point #4   within those 15 points).

Because we started with a geometry, we learned ways to tile the universe with that geometry. It is also quite simple. It puts everything within a mathematically-compact relation that over the years has had a wide range of names from the aether (or ether), continuum, firmament, grid, hypostases, matrix, plenum to vinculum. We call it, TOT tilings. The TOT begins with a ratio of two tetrahedrons to one octahedron.  That combination fills three-dimensional space perfectly. Also, there are two-dimensional tilings everywhere within and throughout the TOT tilings! There are many triangular tilings, square tilings, hexagonal tilings and combinations of the three. One of the most simple-yet-fascinating is created by that group of four hexagonal plates within every octahedron. Observing the models, one can readily see how each of those four plates extend as four hexagonal tilings of the universe.  Each is at a 60 degree angle to the other and each group of four shares a common center vertex.

It is all so fascinating, we are now exploring just how useful these models can become.

That tiling is a perfection, however, imperfections were readily discovered. Using just the tetrahedron, we found that not all constructions fit together perfectly. For example, the simple pentastar, a five-tetrahedral cluster, cannot perfectly tile space; it creates gaps.

Those gaps have now been thoroughly documented; yet to the best of our knowledge, Frank & Kaspers were the first to open this discussion in 1958Englishman F.C. Frank was knighted in 1977 for his lifetime of work.

Using simplicity as our guide, we concluded that here is one of the early beginnings of an imperfection.   This shape is created with just five tetrahedrons and seven vertices. We refer to this object as a pentastar.  It has a gap of about 7.36° (7° 21′) or less than 1.5° between each of the ten faces.

There is a quite fascinating warping and weaving between the perfect and imperfect.

By adding just one more tetrahedron to that pentastar cluster, a 2D perfection is created by the hexagonal base of six tetrahedrons.  Then, by adding more tetrahedrons it can become the 20 tetrahedral cluster known as the icosahedron, and then out to the 60 tetrahedral cluster, the Pentakis Dodecahedron.

We dubbed these imperfect figures, squishy geometry; the constructions have considerable play. Yet in more temperate moments, we call this category of figures that do not fit perfectly together, quantum geometry.  At that time, we did not know there is actually a disciple within geometry and theoretical physics defined as such.

3. Numbers and Potential Geometries Gone Wild. By the 10th doubling there are 1024 vertices. Assuming 1 for the Planck Length, there are then 2, 4, 8, 16, 32, 64, 128, 256, 512, and 1024. The simple aggregation of all notations up to 10th would be 2000+ vertices. Within just the 20th doubling (notation) there are over 1-million vertices, within just the 30th notation over 1-billion, the 40th notation over 1-trillion, and the 50th over a quadrillion vertices. By the 60th notation, a quintillion more vertices are created and that measurement is still below the range of our elementary or fundamental particles.

Imagining all the possible hidden complexities has become a major challenge!

Although this rapid expansion of vertices within each doubling is entirely provocative, it became even greater when we finally followed the insights of Freeman Dyson (Reference #3 – point #11). Dyson is Professor Emeritus, Mathematical Physics and Astrophysics at the Institute for Advanced Studies in Princeton, New Jersey. He said, “Since space has three dimensions, the number of points goes up by a factor eight, not two, when you double the scale.”  On the surface, it is straightforward, yet we are now trying to get the deepest understanding of scaling laws and dimensional analysis to most fully work with Dyson’s comment. Also, we believe that scaling symmetries are necessarily involved with the transitions from one doubling (domain, layer, notation or phase) to the next.

4. Driving Concepts. The simple mathematics provides a basic order and continuity that we have imposed on the universe. The simplest geometries provide a robust range of symmetries and relations. Add time and put these objects in motion, folding and enfolding within each other like a symphony, and we can begin to intuit very special dynamics and a range for harmony (Reference #4).  When those concepts were first written up back in the 1970s, it seemed to describe a perfected state within space and time, but it was too vague. It needed a domain or container within which to work and it seems that this just may be it (opens new window/tab).

5.  Initially called, Big Board-little universe and then, The Universe Table (Reference #5). By September 2013, a class of sixth grade students got involved and a core group of about 40 high school students continued to study this formulation. First, it seemed like an excellent way to visualize the entire universe in a systematic way and on a single piece of paper. Second, as a simple ordering tool, it placed most of the academic disciplines in the right sequence. Mathematics, logic, philosophy, theology and ethics seemed to apply to every notation. An interdisciplinary study called STEM for Science-Technology-Engineering-Mathematics seeks a deeper and more vibrant exploration of all four. This chart readily did that and more. Our chart was developing a special traction. It was working for us.

We then began observing some very simple correlations between notations and let our imaginations work a little overtime.

6. Keys to humanity are in the middle of the Known Universe. Within our range from 201+ to 205+ notations, human sperm is within notation 100, human hair within 101, the thickness of paper (upon which we record our history) 102, and the human egg 103 (Reference #6).

That seems like a concrescence of meaning.

We are just starting to parse the 201+ notations in thirds, fourths, fifths… using musical notation as the analogue and metaphor.

7. The first 60+ notations, doublings, or layers are unchartered. We asked, “What could possibly be there?” To get some ideas, we started going back throughout history and philosophy. We placed Plato’s Forms (Eidos) within the first ten notations. Aristotle’s Ousia (Essence or structure) became the next ten from 11 to 20. Substances were 20-30, Qualities from 30-40, Relations 40-50 and then Systems 50-60. Within Systems we projected a place for The Mind (Reference #7), from the most primitive to the most developed.

Within these first sixty notations, it seems we just might be seeing the basis for isotropy and homogeneity within our little universe. As the domains (doublings, layers, notations, steps) approach he Planck Units, the number of vertices become smaller, and the everything in the universe increasingly shares  some aspect of the systems, relations, qualities, substance and structures, and perhaps everything shares all aspects of the forms. Here is the pre-structure of structure.  Of course, we are just being speculative.

It’s great fun to be speculative, yet we will try not to be too reckless!

“It seems that the cellular automata (of the Wolfram code) belong right within the Forms.” Of course, that’s also a simple guess. We continued, “And within Systems, we have all those academic subjects that have never had a place on a scientific grid or scale of the universe.”

We dubbed this domain “the really-real Small-Scale Universe.”

8. Einstein-Rosen Bridges, Wormholes & Intergalactic Travel The imagination can readily get ahead of facts, yet bridges and tunnels appear everywhere in nature. So, when we partitioned our known universe in thirds, we discovered that elementary particles and atoms began to emerge in the transition area from the first-third, our Small-Scale Universe, to the second-third, our Human-Scale. Well then, what happens in the transition to the third-third, from the Human-Scale to the Large-Scale Universe?

We decided to be wildly speculative.

In the grand scheme of things, the transition from the second-third begins with notations 134 to 138. At Notation 134 you could up on the International Space Stations,  just 218 miles above the earth’s surface. At Notation 137, you would be about 1748 miles up and at Notation 138, about 3500 miles up.

What happens? “Einstein-Rosen!” was the charge. “It’s the beginning of wormholes!”

That raised a few eyebrows. After all, we surely need a shortcut to explore the Large-Scale Universe. So, now we are calling on our leading space entrepreneurs (Reference #8), especially Elon Musk of SpaceX, “Go out looking, but don’t go inside any of those wormholes yet. We all need to be thinking a bit more about their structure.” If we take it as a given that space is derivative of geometry (symmetries), and time derivative of number (continuities), we begin to see the universe quite differently.

Of course, we have far more questions than we have insights so we truly welcome yours.

9. A system for value, thinking, logic, reasoning and more. As you can see, our evolving Universe View was quickly becoming a structure for a rather idiosyncratic style of thinking, reasoning and logic (Reference #9).

The concept of a perfected moment in space-and-time was pushing us to think about order, relations and dynamics in new ways. Continuity, symmetry and harmony were becoming richer than space and time. This marks our first attempt to begin writing about this perception of our interior universe where our numerical-geometrical structure of the universe became its own inherent logic. It wasn’t long before we began thinking about how this structure could also be applied to thinking itself, then reasoning, and so much more. A mentor and friend from long ago, John N. Findlay, might call it an architecture for the thrust or zest for life.

This system seems to have within it many possibilities for seeing wholeness where today information and systems do not cohere, so we are glad to share these skeletal models (including the one just to the left) for your inspection. We hope you find it all as challenging as we have, and that you have enjoyed taking this rather quick tour through this work.

We are in the very early stages of this journey and we welcome your insights, your comments, and your questions. Thank you.

Endnotes, footnotes and references:

  1. The URL for the very first chart of our simple math:
    These pages were to support our attempt to publish a Wikipedia article about base-2 exponential notation from the Planck Length. That article was published in April 2012 but their specialists led by an MIT mathematician deemed it “original research” and it was removed early in May 2012. That was our truly first indication that our simple logic-math-and-geometry had been overlooked by the larger academic community.
  2. An analysis of 15 key points:
  3. Prof. Dr. Freeman Dyson, Professor Emeritus, Mathematical Physics and Astrophysics of the. Institute for Advanced Studies (IAS), Princeton, New Jersey since 1953., author (among hundreds of article and dozens of books)  of Interstellar Transport (Physics Today 1968), Disturbing the Universe (Harper & Row, 1979). This link opens within the IAS website.
  4. The first principles based on the concept of perfection:
  5. A ten-step tour of the Big Board-little universe and the Universe Table:
  6. Space Entrepreneurs to Star Wars VII:
  7.  An analysis of the work in progress:
  8. Belief systems:
  9. The circular chart just above.

More analysis: All these writings are in process. Here are our initial drafts:

There will come an invitation to participate, then perhaps a collaborative exploration of these questions:

NASA scientist’s report regarding his calculations

Some Thoughts about Measurement

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!!!

– Joe Kolecki, NASA scientist, retired

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