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UPDATE: Speed of Light, Planck Units, and Base-2 Exponential Notation

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Note:  This article was first published in March 2015.  This version has been updated (2016).

Précis. By using Planck Length-and-Time and the simplest mathematics (multiplication by 2), a speed of light can be determined within all 202 base-2 notations from Planck Time to the Age of the Universe. At one light second, it is off by 1% from the experimental data.

Planck Numbers. These most-fascinating, magical numbers have been questioned since their introduction in 1899 by Max Planck. The place of the Planck Base Units did not become a focus of the scientific community until Frank Wilczek (MIT, Nobel laureate, 2004) wrote a series of articles, Scaling Mt. Planck (Physics Today) back in 2001 and 2002 [1].

Yet, even today, these numbers are still questioned by many.

Looking for some boundary conditions within which to work, a New Orleans high school geometry class used the Planck Base Units as a starting point to construct their model of the universe. Their primary operating assumption was that continuity and symmetry are the foundational concepts for universal constructions. As a geometry class they were looking to see how they could tile-and-tessellate the universe. This group found a bit of a correspondence between data derived from experimentation and data derived purely by mathematical theory using Planck Length and Planck Time.

Their first chart with Planck Time. This chart carried over an error (a notation was skipped between Notations 39 and 40) within the listing of the Planck Length.  That error did not exist in the December 2012 chart of just the Planck Length.  As of February 3, 2016, documents from March 2015 forward are being updated.

By the 142nd doubling the Planck Time is correctly posted as .6011 seconds. At the 143rd doubling, it is 1.2023 seconds. In between the two is a single second. In the corresponding column, the Planck length incorrectly reported within the 142nd doubling to be 180,212.316 kilometers and by the 143rd  to be 360,414.632 km. Using the wrong length figure to do the calculation resulted in a number very close to the distance light travels in a second. In actuality, instead of 299,773.654587, that figure without any adjustments would be…

Back to the drawing boards.

There are three facts of mathematics that were particularly noted in the process of developing this base-2 chart of the basic Planck Units to their largest known values, particularly the Age of the Universe and the Observable Universe.

Fact 1: The universe can be contained within 201 to 202 doublings of the Planck Length and the Planck Time [4].  An initial fact of applied Planck mathematics is that the entire known universe can be ordered in 201 to 202 necessarily-related groups by using base-2 exponential notation. The chart is simple to calculate; it was a project that started in a high school geometry class. Unlike Kees Boeke’s base-10 work in 1957 (also in a high school), this chart begins with the Planck Units and gets its order through the Planck Units and the base-2 progression as well as the observed-and-imputed, simple, embedded geometries [5] which adds another dimension of order, i.e. symmetry.

Fact 2: Between notations notation 142 and 143 is a light second.

Experimentally defined over the years [6], here if we were to use the Planck Length as the determinant, light would be quite slow between the 142 and 143 notation. There will be three charts studied.  As noted above, the original with the mistake will be preserved within the Small Business School website.  The page with the correction from February 3, 2016 will be preserved as the “initial correction.”  Additional charts will be constructed whereby a simple logic is imputed whereby adjustments are made to the model so experimentally-defined data is introduced. The small-scale and human-scale notations are in some manner of speaking archetypal.  At one second we are looking at the raw universe just one second old. If the entire universe is dynamically adjusting itself, nothing is static, all notations are dynamic and active, we can begin to hypothesize at which notation the light makes its appearance and at which notations light begins to speed up.

Fact 3:  Either the Known Universe may not be as old as it has been calculated to be and it is not as large as it is thought to be, or it is much older than it is calculated to be, and/or one (or more) of the initial Planck calculations is off,  and/or there is more to learn about the nature of light. There are many more “and/or” scenarios that we can intuit.

Around notation 202 is the estimated Age of the Universe [8].

Though as noted earlier, the Planck Base Units were virtually ignored until MIT professor Frank Wilczek began his earnest study of them in Physics Today (June 2001) [9].  C. Alden Mead, who upon reading the Wilczek article commented in the “Letters” section about his work back in 1959 that argued for the use of the Planck Length. Wilczek acknowledged that Mead had been the first pioneer to advocate for the use of the Planck Length [10] as part of experimental data.

It also seems that this approach of the New Orleans high school geometry class is a first.   Senior editors of Wikipedia told them that they could not publish an article on their site because it was “original research.” Though they readily admit that this work is rather idiosyncratic, they have persevered since December 2011. Using base-2 exponential notation first they found no less than 201 doublings or groups. By dividing the entire scale in half, they found themselves in the middle of the Human Scale universe. By dividing in thirds, there was a natural division between the small-scale, human-scale, and large-scale universe. Within each scale and within each group, they know that there is much more to be uncovered. They have just started to open this door and are working to discover more.[11]

In 2002, Wilczek reflects, “It therefore comes to seem that Planck’s magic mountain, born in fantasy and numerology, may well correspond to physical reality.” [12]   Here the students and their teacher conclude, “The space-time continuum is really real even when using discrete steps.”

References:

[10] http://ctpweb.lns.mit.edu/…/Alden-Repsonse323.pdf From American Institute of Physics, New York, NY, PHYSICS TODAY, S-0031-9228-0111-220-2, 2001 p15

Pi equals 3.1415926535897932384626433832795028…

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Pi-unrolled-720.gif

An arc of a circle with the same length as the radius of that circle corresponds to an angle of 1 radian.

A full circle corresponds to an angle of 2π radians.

3.14159265358979323846264338327950288419716939937510

  1. Pi is a constant.
  2. Pi is an irrational number.
  3. Pi is a transcendental number.
  4. Pi is a non-repeating number – no pattern has been identified using computer analysis within over twelve trillion places.
  5. Pi ( π ) is the exact ratio of the circumference of a circle to its diameter.   It is that simple.

Thank you, Wikipedia, for the graphics (above) that demonstrate this simple definition.  There are over 45 Wikipedia articles about pi.

So, what do you make of it?  What is going on?

Perhaps a few more questions and comments would help.

  1. What is it about a circle and sphere that pi is always-always- always true?
  2. How does a number become a constant, irrational and transcendental all at the same time?
  3. Let us compare pi to other unique numbers that have a special role among all numbers.  These are e, 0, 1, and I. They are all magical, but π stands out. So, let’s ask, “What are the shared qualities of these numbers?” Let’s study them to see if we can find any necessary relations.
  4. We have the ratio between a circle and a line. Perhaps this is the fundamental transformation between the finite and infinite? Are circles and spheres always implicating or imputing the infinite?

That is a big question and enough to ponder for awhile.

Notwithstanding, there are many more questions to ask.

Some speculations: Pi may be the key to unlock the small-scale universe within the big Board-little universe
1.   To get to the application of pi  within the Planck Units, we’ll need to emerge from the singularity of the Planck Units.  Is the radian a key to understanding this process?  First, a radius is extended from the singularity.  A radius extends into the preconditions for space and time, a now emergent small-scale universe. It makes that first arc equal to its own length.  It does it again and again and again and again and again (six radians) and then makes that last leap, 2 pi, to complete the circle. Is this a reasonable scenario? Why? Why not?

2. We need to run through dozens of scenarios, often, and slowly and carefully.  What scenarios are perfect and obvious?

3. We are at the singularity of the Planck Units.  We are establishing the foundations for the physical world.  If all things start simply, this must be the place to start.  It doesn’t get more simple and more mysterious. Nothing is a mistake, everything comes from a perfection to a space-time moment, so what could possibly happen?

What happens within the first six doublings?    (to be continued)

For further discussion:
1.  Is the Small-scale Universe the basis for the homogeneity and isotropy of space and time?
2.  Does everything in the universe share some part of the Small-Scale universe?
3.  How is Planck Temperature calculated?  Does it begin with the other Planck Units and expand from that figure at the first notation?

Note:  All of human history has occurred in the last doubling.  Yet, all doublings remain active and current and dynamic.  Continuity trumps time. Symmetries trump space.

What does sleep have to do with anything?  If all time is current, within the moment, we particularize by the day and uniquely within a given waking day.  Sleep seems to bring us into the infinite.  Dreams seem to be the helter-skelter bridge between the finite and infinite.  It seems that these naïve thoughts are worth exploring further.

This Shifting Paradigm Changes Our Perception Of Everything

Bruce CamberLeave a comment

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

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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
204

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
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): http://hyperphysics.phy-astr.gsu.edu/hbase/astro/planck.html

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

a. http://walktheplanck.wordpress.com/2014/12/09/base/

b. http://utable.wordpress.com/2014/12/12/planck/

c. http://SmallBusinessSchool.org/page3053.html

d. ResearchGate Documents: 3052, 3054, 3056

Frank Wilczek

EditorLeave a comment

First email to 2004 Nobel laureate, MIT physics professor, Frank Wilczek

On Fri, Dec 14, 2012 at 5:40 PM
Bruce Camber wrote:

Dear Prof. Dr. Frank Wilczek:

Back ten days ago, we sent this note through your resources page
within your your website — http://frankwilczek.com/resources.html
It is from five high school geometry classes.

We have a model of the universe and we are not sure what to do with it.

We started with one meter and divided it in half as if it
were an edge of a tetrahedron, and then we continued dividing
in half until we got down in the area of the Planck Length. Later,
we started at the Planck Length and used base-2 exponential notation
to go out the 202+ steps to the edges of the observable universe.
We used Plato’s five basics as an inherent continuity equation and
symmetry function.

It seems too easy, perhaps a bit of poppycock, but we don’t know
why. The question now is how to continue to develop it. Is it a useful
ordering system (STEM project)? Or, could it possibly be more?
We don’t know. After all we are just five high school geometry classes.

Is it just a bit of silliness? Or, might it be useful? We, the kids and
teachers, are anxious to know. We will be having a major discussion about it
next week with all five classes. Thanks. -Bruce

Bruce Camber

Note: We first found you here:
Physics Today, Alden Response PDF
http://frankwilczek.com/resources.html

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

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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…

NewOrleans

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 Ten. Of 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.”  From “The Nature of Matter” within the Archiv zur Geschichte der Max-Planck-Gesellschaft, Abt. Va, Rep. 11 Planck, Nr. 1797, 1944

Just what’s happening here?

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For over 100 years, the Planck Length was virtually ignored.  That length was so small, it seemed meaningless.¹  Nothing and nobody could measure it.  It was just a ratio of known constants.  Yet, it created a conceptual limit of a length which gave a New Orleans high school geometry class a goal or a boundary beyond which they did not have to go.  Recent measurements from the Hubble telescope provided the upper limit so this class could define the number of base-2 exponential notations from the smallest measurement of a length to the Observable Universe, the largest.

Within that continuum everything can be placed in a mathematical and geometric order.  Everything.  That is, everything in the known universe. The most remarkable discovery was that it took no more than 205.1 base-2 exponential notations.  It would be our very first view of an ordered universe. And, it readily absorbed all of our worldviews.

That was December 19, 2011.  Formally dubbed, “The Big Board – little universe,” we then asked, “What does it mean?  How do we use it?”  When we engaged the experts, they appeared a bit puzzled and seemed to be asking, “Why haven’t we seen this chart before?” Those who knew Kees Boeke’s 1957 book, Cosmic Vision,  asked, “How is it different from Boeke’s work using base-10 exponential notation?”   That was a challenge. Our best answers to date – it’s more granular, it mimics chemical bonding and cellular reproduction; it’s based on cascading, embedded, and combinatorial geometries – were not good enough.  In April 2012 even the Wikipedia  experts  (Steven Johnson,  MIT) protested.  He classified our analysis as  “original research” and within a very short time our Wikipedia article was taken down.  Others called it idiosyncratic (John Baez, UC-Riverside), but they did not tell us what was wrong with our analysis.

“Let’s just make as many observations as we can to see what can we learn?”  A NASA senior scientist and a French astrophysicist helped us with our calculations.  Their results gave us a range; the low was 202.34 notations and the high, 205.11.  We could identify many things between the 66th notation and the 199th notation.  But, there were blanks everywhere so we got busy speculating about them. The biggest group of empty notations was from 2 to about 65. We asked, “Conceptually, what could be there?”  Max Planck may have given us a clue when in 1944, in a speech in Florence, Italy; he said, “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.” (The Nature of Matter, Archiv zur Geschichte der Max-Planck-Gesellschaft, Abt. Va, Rep. 11 Planck, Nr. 1797, 1944)  Matrix is a good word. Throughout history others have described it as the aether, continuum, firmament, grid, hypostases, plenum and vinculum.

We made two columns and within the top notations, 100-to-103, we found humanity.  That seemed politically incorrect until we discovered the cosmological principle that the universe is isotropic and homogeneous.  So, if it is true for us, it would also have to be true for “everybody” anywhere in the universe.

This is high school.  We had been following embedded geometries, particularly the tetrahedron and octahedron.  We observed a tetrahedral-octahedral-tetrahedral chain.  In no more than 206 layers everything in the universe is bound together.  We learned about tilings and could see that the four hexagonal plates we discovered within the octahedron also created tiles in every possible direction.

“What is this all about?  Just what’s happening here?”

We knew we were imposing a certain continuity and order with our mathematics (base-2 exponential notation), and we were also conveying certain simple symmetries and relations with our geometries.  That wrapped our work within a conceptual framework that was quite the opposite of the chaotic world of quantum mechanics.  Our picture of the known universe was increasingly intimate and warm; it was highly-ordered and had immediate value. And the more we looked at it, the more it seemed that all of science and life had an inherent valuation structure.   Here numbers became the container for time, and geometries the container for space.  How each was derived became our penultimate challenge. Ostensibly we had backed into a model of the universe and somehow we began to believe that if we could stick with it long enough, it just might ultimately give us some answers to the age-old question, “What is life?”

We had strayed quite far from those tedious chapters in our high school geometry textbook.  Yet, we also quickly discovered how little we knew about basic structure when we attempted to guess about the transitions from one notation to the next.  We asked, “How can we get from the most-simply defined structure, a sphere, to a sphere with a tetrahedron within it?”  We needed more perspective.

“Who is doing this kind of work?”  We began our very initial study of the Langlands Program and amplituhedrons. Then, we walked back through history, all the way to the ancient Greeks and we found strange and curious things all along the way. There were the circles of Metatron that seemed to generate the five platonic solids. “How does that work? Are there experts who use it?  How?”  We still do not have a clue.  All the discussions about infinitesimals seemed to come to a crescendo with the twenty-year, rancorous debate between Thomas Hobbes and John Wallis.  It was here that we  began to understand how geometry lost ground to calculus and algorithms.

The Big Board-little universe was awkward to use.  It was five feet tall and a foot wide.  Using the Periodic Table as a model, an 8½-by-11 chart was created and quickly dubbed, The Universe Table.  It would be our Universe View into which we could hopefully incorporate any worldview.  It was an excellent ordering and valuation system.

Frank_WilczekThough the Planck Length became a natural unit of measurement, a limit based on known universal constants, it wasn’t until Frank Wilczek of MIT opened the discussion did things really begin to change. In an obscure 1965 paper by C. Aldon Mead, his use of the Planck Length was pivotal. In 2001 Wilczek’s analysis of Mead’s work and their ensuing dialogue was published in Physics Today. Wilczek, well on his way to obtaining a Nobel Prize, then began writing several provocative articles, Scaling Mt. Planck.  Even his books were helpful. In January 2013 he personally encouraged us on our journey.

In 1899 Max Planck began his quest to define natural units.  At that time he took some of the constants of science and he started figuring out natural limits based on them. There are now hundreds that have been defined. Each is a ratio and each can be related to our little chart and big board.  The very nature of a ratio seems to be a special clue. It holds a dynamic tension and suggests that the relation is primary and all else is derivative.

We have a lot of work in front of us!  And, we are up for the challenge.

Who would disagree with the observation that our world has deep and seemingly unsolvable problems?  The human future has become so problematical and complex, proposals for redirecting human energies toward basic, realizable, and global values appear simplistic.  Nevertheless, the need for such a vision is obvious. Rational people know that there is something profoundly missing. So, what is it? Is it ethics, morality, common sense, patience, virtues like charity, hope and love?  We have hundreds of thousands of books, organizations and thoughtful people who extol all of these and more.  The lists are robust.  The work is compelling, but obviously none of it is quite compelling enough.

First, it has to be simple.  Our chart is simple.

Second, it has to open up to enormous complexities. Using simple math, by the tenth notation there are 1024 vertices. We dubbed it the Forms or Eidos after Plato. The 20th notation would add a million vertices; we called it Structure. The 30th adds a billion new vertices. We ask, “Why not Substances?” The 40th adds a trillion so we think Qualities. The 50th adds a quadrillion vertices. We speculate Relations. By the 60th notation there are no less than a total of 2 quintillion vertices with which to create complexity. We speculate Systems and within Systems there could be The Mind. As if a quintillion vertices is not enough, the great physicist,  Freeman Dyson, advises us that really we should be multiplying by 8, not by 2, so potential complexity could be exponentially greater.

Three, it should be elegant.  There is nothing more elegant than complex symmetries interacting dynamically that create special harmonies.  We can feel it. And, we believe the Langlands program and amplituhedrons will help us to further open that discussion.

What is life?  Let us see if we can answer very basic questions about the essence of life for a sixth grade advanced-placement science class and for very-average, high-school students.  These are our students.  The dialogue is real.  The container for these questions and answers is base-2 exponential notation from the Planck Length to the Observable Universe.  To the best of our knowledge, December 19, 2011 was the first time base 2 exponential notation was used in a classroom as the parameter set to define the universe.  Though our study at that time was geometry, this work was then generalized to all the scientific disciplines, and more recently it was generalized to business and religion.  So, as of today, readers will see, and possibly learn, the following:

1.  See the totality of the finite, highly-ordered, profoundly inter-related, very-small universe where humanity is quite literally back in the middle of it all.

2.   Engage in speculations about the Infinite and infinity whereby the Creative and the Good take a prominent place within the universal constructs of Science.

3.   Extend the scale of the universe by redefining the Small Scale and engaging in speculations about the deep symmetries of nature, giving the Mind its key role within Systems, and demonstrating the very nature of homogeneity and isotropy.

4.   Adopt an integrated universe view based on Planck Length and Planck Time such that Science, Technology, Engineering and Mathematics are demythologized,  new domains for research are opened, and philosophies and religions are empowered to be remythologized within the constraints of universals and constants.

People ask, “Aren’t you getting ahead of yourself?  Isn’t this a bit ambitious?”  The concepts of space and time raise age-old questions about who we are, where we have come from, and where we are going.  With our little formulation, still in its infancy, we are being challenged to see life more fully and more deeply.  And so we reply, “What’s wrong with that?”

###

1  http://www.phys.unsw.edu.au/einsteinlight/jw/module6_Planck.htm   Physics professor, Joe Wolfe (Australia), says, “Nothing fundamentally changes at the Planck scale, and there’s nothing special about the physics there, it’s just that there’s no point trying to deal with things that small.  Part of why nobody bothers is that the smallest particle, the electron, is about 1020 times larger (that’s the difference between a single hair and a large galaxy).

Is There Order In The Universe?

Bruce CamberLeave a comment

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 http://bblu.org, the main website for secondary schools, and within http://81018.com, 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 mathematics.  Reference #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 1958.  Englishman 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: http://smallbusinessschool.org/page2851.html
    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: http://smallbusinessschool.org/page3006.html
  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: http://smallbusinessschool.org/page869.html
  5. A ten-step tour of the Big Board-little universe and the Universe Table: http://smallbusinessschool.org/page2990.html
  6. Space Entrepreneurs to Star Wars VII: http://smallbusinessschool.org/page3007.html
  7.  An analysis of the work in progress:   http://smallbusinessschool.org/page3000.html
  8. Belief systems: http://smallbusinessschool.org/page1887.html
  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:

15 Key Questions About Our Universe And Us

Bruce CamberLeave a comment

Prepared by Bruce Camber for five classes of high school geometry students and a sixth-grade class of scientific savants. There are no less than 15 concepts reviewed here. All have been explored within a high school yet have been virtually ignored by the larger academic community. It begs the questions, “Are any of these concepts important? Which should we keep studying and which should be deleted?” And, of course, if we delete any, we need to know why.

TetrahedronStudents have been known to ask a rather key question, i.e., “Can’t you make it easier to understand?”

So, in light of the universal pursuit for simplicity, beauty and wholeness, our geometry classes just may have stumbled onto a path where we begin to see all the forces of nature come together in a somewhat simple, beautiful, yet entirely idiosyncratic model. It feels a bit like Alice-in-Wonderland — the entire known universe in 201+ notations or doublings — all tied together with an inherent geometry, an ever-so-simple complexity. The students ask, “Can this somehow be embedded within every thing everywhere?”

#1 Key Question: Is there a deep-seated order within the universe?

Geometry 101: From the Planck Length to the Observable Universe
December 19, 2011: Defining our Parameters and Boundaries

octahedronOver 120 high school students and about twenty 6th graders have divided each of the edges  of a tetrahedron in half.  They connected the new vertices to discover four half-sized tetrahedrons in each of the corners and an octahedron in the middle. They did the same with that octahedron and observed the six half-sized octahedrons in each of the corners and eight tetrahedrons, one in each face. We continued this process mathematically about 116 times until we were in the range of the Planck length. We eventually learned that this process is known as base-2 exponential notation. When we discovered-then-compared our work to that of Kees Boeke (Cosmic View, Holland, 1957), we thought base-2 was much more informative, granular, and natural (as in biological reproduction and chemical bonding) than Boeke’s base-10. Plus, our work began with an inherent geometry, not just a process of adding and subtracting zeros.  More… (opens in new tab/window).

 

#2 What are the smallest and largest possible measurements of a length?

Doublings and Measurement
December 2011: Getting More Results

We had taken those same tetrahedrons with their embedded octahedrons and multiplied them by 2. Within about 90 steps (doublings), we thought we were in the range of the recently-reported findings from Hubble Space Telescope and the Sloan Digital Sky Survey (SDSS III), Baryon Oscillation Spectroscopic Survey (BOSS) measurements (opens in new tab/window) to bring us out to the edges of the observable or known universe. It appeared to us that this perfect conceptual progression of embedded tetrahedrons and octahedrons could readily go from the smallest possible measurement to the largest in less than 209 notations. We decided at the very least it was an excellent way to organize the data in the entire universe.

More questions:  What are the most-simple parameters with which to engage the universe?  Do the geometries (relation/symmetry), base-2 (operations of multiplication or division), and sequence (order/continuity) provide an operational formula for expansion of the operand?

#3  Do these charts in any way reflect the realities within our universe?

 Big Board – little universe and our first Universe Table
2011 -2012SDSS-III-BOSS

We had also develop a big board (1′ by 5 ‘) upon which to display this progression so we could begin inserting and updating examples from the real world within each notation (domain, doubling, or step). To simplify the look and feel of those listings, we also made a much smaller table (8.5″ x 11″) in September 2012.   The very first, very rough board (December 2011): http://smallbusinessschool.org/page2790.html and within a blog (May 2012): http://doublings.wordpress.com/  Then, we developed the Universe Table based on the board: http://utable.wordpress.com/2013/11/01/1/

Another question: What are the necessary relations between adjacent notations?

#4 How do we prioritize data (calculations), information and insight?  What is wisdom?BigBoard8.5.jpg

202.34 to 205.11: From Joe Kolecki to Jean-Pierre Luminet
May 2012: Getting Some Professional Insight and Confirmation

We consulted with Joe Kolecki, a retired NASA scientist involved with the education of school children. He did a calculation for us and found about 202.34 notations from the smallest to the largest (based on the age of the universe).

We had also consulted with Jean-Pierre Luminet, a French astrophysicist and research director for the CNRS (Centre National de la Recherche Scientifique) of the observatory of Paris-Meudon. He calculated 205.11 notations: http://doublings.wordpress.com/2013/07/09/1/#Footnotes See footnote 5 on this page within doublings.wordpress.com.

The nagging question: What are the necessary relations between adjacent notations (or doublings, layers or steps)?

#5 How does each notation build off the prior notation? Is it geometrical?
An Encounter with Wikipedia
April-May 2012: Grasping the New Realities

We wrote it up for Wikipedia to have a place to collaborate and build out the document with other schools and even universities. But, in May 2012, their review group told us that it was original research. Though there was a clear analogue to base-10 notation from Kees Boeke from 1957, an MIT professor, Steven G. Johnson (he reviews entries for Wikipedia) said that it was “original” research. We begrudgingly accepted his critique:
http://bigboardlittleuniverse.wordpress.com/2013/02/26/1/
The simple math: http://doublings.wordpress.com/2013/04/17/60/

#6 What is perfect and what is imperfect?

Pentastar, Icosahedron, Pentakis Dodecahedron

December 2011 to December 2012: One Year of Insights

We then observed some curious things. First, geometries can get messy very quickly. We were using the five Platonic solids. Starting with the tetrahedron, we quickly discovered that these objects rarely fit perfectly together. The pentastar, five tetrahedrons clustered tightly together, do not perfectly tile space, but leave a gap. This gap has been thoroughly documented yet to the best of our knowledge it was first written up by two mineralogists, Frank & Kaspers, in 1958. In its simplicity, we concluded that this was the beginning of imperfections and it extended out to the 20 tetrahedron cluster also known as the icosahedron, and then out to the 60 tetrahedron cluster (just the outer shell), which is called a Pentakis Dodecahedron. We dubbed these figures, “squishy geometry” because you could actual squish the tetrahedrons together. In a more temperate moment, we dubbed this category of figures a bit more appropriately, “quantum geometry.”

#7   What is the Planck Length? Is it a legitimate concept?

Frank Wilczek, Encouragement from an Authority, December 2012

We consulted Prof. Dr. Frank Wilczek (MIT) regarding his many articles in “Physics Today” about the Planck Length. He assured us that it was a good concept and that the Planck Length could be multiplied by 2. We titled our next entry, “Everything Starts Most Simply. Therefore, Might It Follow That The Planck Length Becomes The Next Big Thing? The current state of affairs in the physics of CERN Labs is anything but simple. We figure if we built things up simply, we might gain a few new insights on the nature of things.

#8  Is life a ratio?  Does it begin with Pi and the circumference of a circle?

Steve Waterman’s polyhedra and mathematics
March 2014: Discovering Others Searching the Boundaries

In December 2013, I sent a note around to an online group of mathematicians, mainly geometers; and of those who responded, Steve Waterman had done some truly original, rather-daunting, work that had certain similarities to Max Planck’s work a century earlier. It was not until a lengthy discussion in April 2014 that I began to understand the simplicity and uniqueness of his extensive work. He had emerged with many, if not most, of the 300+ NIST constants, the gold standard of the sciences. He had used constants in a similar way that Max Planck used the speed of light and the gravitational constant to begin his quest for the Planck Length. Waterman provokes the ratios of known constants to come ever so close to the NIST measurements. His math implies an inherent universal wholeness and he does it with a series of “what if” questions. It took me awhile to grasp his fascinating, far-reaching results:
http://watermanpolyhedron.com/abequalsc2.html
http://www.watermanpolyhedron.com/smallFOUR.html

#9 Is there anybody doing mathematics in any way related to these notations?

 Edward Frenkel and his book, “Love & Math: The Heart of Hidden Reality”

In October 2013, Edward Frenkel’s book, “Love & Math: The Heart of Hidden Reality” became part of our picture. Perhaps this remarkable mathematician can shed light on those areas where we all are weakest. We let him know we had his book and would be reading it to answer simple questions, “Why doesn’t anybody care about this construction? What are we missing? Why are people so sure that the fermion and its extended family represent the smallest-possible measurement of a length, especially in the face of the Planck Length? Why shouldn’t we attempt to think of the Mind and mathematics as representations of those steps between the Planck Length and those within the particle families?”

Through Frenkel’s work we have begun to discover the Langlands Program and its progenitors (i.e. Frobenius) and the current work in areas like sheaves, the categorifications of numbers, and the correlation functions. We have begun to learn about the work of other remarkable mathematicians like Grothendieck, Drinfield, Witten, Kapustin, and so many more.

The most important first-impression was that we could begin to discern the transformations from one notation to the next and possibly even discern the very nature of a vertex.

#10   What is a vertex? Are there primary vertices that establish the Planck Unit measurements and secondary scaling vertices?

Over a Quintillion key vertices within just the 60th notation using base-2 exponentiation

Throughout these past 2+ years, we have discerned other simple-yet-interesting mathematical facts.  First, we decided that we should not refer to the Planck Length as a point because it is a rather exact length, so we are giving each vertex a special status and believe we might learn more by understanding Alfred North Whitehead’s concept of pointfree geometries introduced within his book, “Process and Reality.”

Within just the 10th doubling there are 1024 vertices. The simple aggregation of all notations up to 10 would be 2046 vertices. Within just the 20th doubling (notation) alone there are over 1 million vertices. In just 30th notation alone, another one billion-plus vertices are created. Within the 40th notation another trillion-plus vertices. With just the 50th notation, you’ll find over a quadrillion vertices. By the 60th notation, a quintillion more vertices are created. Imagine all the possible hidden complexity!

The expansion of vertices within each doubling has been a challenge for our imaginations and conceptual limitations. Yet, it could be an even greater challenge and far more complex if we were to follow Freeman Dyson’s suggestion. Using base-4 notation for the expansion of the tetrahedrons and base-6 notation for the expansion of the octahedrons, at the 60th notation, there would be a subtotal of 1.329228×1036 for the tetrahedrons and 4.8873678×1046 vertices from the octahedrons. Using simple addition that would be:

488,736,780,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

+                    1,329,228,000,000,000,000,000,000,000,000,000,000,000,000

488,736,780,001,329,228,000,000,000,000,000,000,000,000,000,000,000,000

The base-2 exponentiation is the “simple math” starting point. It is a simple focus on the process called doubling and only accounts for number of times the original Planck Length has been doubled for each notation. If the focus is on objects, after the fourth doubling, there are four expansions to track, base-1 for the sole octahedron within the tetrahedron, base-4 for the tetrahedrons within the tetrahedrons, and base-6 for the octahedrons within the octahedron and base-8 for the tetrahedrons within the octahedron.  Addressing that schema and the results are:

Base-8 tetrahedrons:   1.5324955×1054 units

Base-6 octahedrons in the octahedron:  4.8873678×1046

#11 What are scaling laws and dimensional analysis?

Freeman Dyson

Mon, Oct 22, 2012

Freeman Dyson, in an email to me (for which he gave me permission to share), suggested the following: “Since space has three dimensions, the number of points goes up by a factor eight (scaling laws and dimensional analysis), not two, when you double the scale.” Of course, we felt we had more than enough vertices with which to contend, so we just multiplied by 2, using the simple analogue from biology or chemistry. Yet, we readily acknowledge that his advice could readily open even more doors for new explorations, so this question is raised and another dimension of our work has been set out before us by a sage of our time!

#12 Key Question: Is the inherent structure of the first 60 notations shared by everything in the universe?

January 2013 to today

#12a   January 2013:  Speculations about the first 60 notations

With our simple logic, it seems that with the diversity of particles and the uniqueness of identity, that the structure could continue to expand right up to the 201+ notations.

However, below that emergence of measurable particles, and their aggregate structures, a simple logic would tell us that there is a cutoff point as you go toward the Planck Length where a deep-seated Form (perhaps notations 3-to-10) and Structure (perhaps notations 11-20) might somehow be shared by every thing in the known universe. With vertices rapidly increasing with every doubling, options begin to manifest for types of Substances (possibly notations 21-to-30), then types of Qualities (perhaps notations 31-to-40), then types of Relations (possibly 41 to 50), and finally types of Systems (possibly 51-to-60). What does that mean? How are we to interpret it? It is on our list to continue to ponder.

#12b   February 2013   Literature survey

We’ve thought about this very, very small reality from the first notation to the 60th. Perhaps it is what Frank Wilczek (MIT) calls the Grid and Roger Penrose (Oxford) calls Conformal Cyclic Cosmology. We just call it the Small-Scale Universe. Actually, in deference to one of my early mentors, we call it the “really-real” Small-Scale Universe. And, because we started with simple geometries, our imaginative notions of this part of our universe appear to be historically explored yet relatively unexplored as a current scientific framework. First, we turned to our six sections: Forms (Eidos), Structures (Ousia), Substances, Qualities, Relations, and Systems (The Mind).

Also, picking up on a suggestion by Philip Davis (NIST, Brown), that the sphere is more fundamental than the tetrahedron, we start with a one-dimensional length, the Planck Length. When it doubles, it becomes a two-dimensional sphere. When it doubles again (4), it becomes a three-dimensional sphere with a tetrahedron within it. When it doubles again (8), we see the octahedron within the tetrahedron. When it doubles again (16), we begin to see the four hexagonal plates within the octahedron. We are projecting all these forms-structures, substances-qualities, relations-and-systems are complexifications of the first two vertices within the first doubling. We further project that there is a transitional area between each of the three scales, Small-Scale Universe, Human-Scale Universe, and Large-Scale Universe and each would include somewhere between 67-to-69 notations.

#12c.     Discovering Quanta Magazine

       May 2014

Amplituhedrons, Euler, and geometries mixing within necessary relations with geometries

We discovered the writings of Natalie Wolchover within Quanta Magazine, quantum geometries, and on the work of Andrew Hodges (Oxford), Jacob Bourjaily (Harvard) and Jeremy England (MIT). We believe these young academics are opening important doors so our simple work that began in and around December 2011 has a larger, current scientific context, not just simple mathematics. Within the excitement and continuing evolution of the Langlands programs, we perceive it all in light of defining a science of transformations between notations. We are now pursuing all the primary references for people working within quantum geometries.

The simplest, smallest, largest experiment, albeit a  thought experiment based on logic, the simplest mathematics (base-2 notation and platonic geometry), and the base Planck Units, quickly opened doors to look at this data in a radically new way. It will slowly become the basis for many new science fair projects.  The question is asked, “Could This Be The Smallest-Biggest-Simplest Scientific Experiment?” http://walktheplanck.wordpress.com/2014/03/03/domain/

#13a  October 2013 to February 2014: A National Science Fair Project

Some students wanted to take the project further. Here was an initial entry of one of our brighter students:

http://walktheplanck.wordpress.com/2013/12/03/welcome/

#13b January 2012: Is there a concrescence in the middle?

IUniverse Tables the ratio, 1:2, somehow special? Approximately between 101 and 103, clustered in the middle by the width of a hair, are paper upon which we document our history and the human egg. Perfectly human representations in the middle of this scale became a source for some reflections.

http://walktheplanck.wordpress.com/2013/12/03/c/

#13c   October 2013: Considering the Thirds, 1:3

Between Notation 66-to-67 and from 132-to-134:

The significance of the first third, particularly the transformation from the small scale to the human scale, was obvious — particles and atoms. The last third, the human scale to the large scale, we played with ideas, then made an hypothesis. In a most speculative gesture, turning to the Einstein-Rosen bridges and tunnels, we posited that range as a place to begin looking for wormholes.

http://walktheplanck.wordpress.com/2013/12/03/j/

We are now studying the fourths, fifths, sixths and sevenths… wondering in what ways are there parallels to music. How do things combine, mix, and move together to create a specific thing or a new thing? We began studying the notational ranges defined by simple mathematics and music to see what we could see.

Notational range for The Fourths: 50.6 – 51.3, 101.17 – 102.6, and 151.7 – 153.8 and finally 202.34 – 205.11 Notational range for The Fifths: 40.47 – 41.2, 80.94 – 82.4, 121.41-123.6, 161.86 – 164.8… Notational range for The Sixths: 33.72 – 34.35, 67.44 – 68.70, 101.17 -102.6, 134.89 – 136.95, 168.61 – 171.30… Notational range for The Sevenths: 28.62 – 29.30, 57.24 – 58.60, 86.46 – 87.90, 114.48 – 117.20…

To date, our very cursory, initial observations have not opened up more wild-and-crazy speculations! However, the obvious parallel to music has us thinking about the nature of chord, half notes and ratios (July 2014).

#14 Who are we and where did we come from?
1971-1973: Synectics, Polymorphs, Colloquiums, and more
Continuity-Order, Symmetry-Relations, Harmony-Dynamics

We are products of our experience. In 1971, when I (Bruce Camber) was just 24 years old, though active in the radical-liberal political community, my longstanding intellectual curiosity was the nature of creativity, the processes for problem-solving, the nature of a paradigm, and the stuff of scientific revolutions. At a think tank in Cambridge, I focused on interiority, analogies, empathy, and processes to open pathways to a deeper sense of knowing and insight. Within a Harvard study group, the Philomorphs, I studied basic geometric structures with Arthur Loeb. At Boston University, I was deeply involved with the weekly sessions of the Boston Studies in the Philosophy of Science with Robert S. Cohen, chairman of the Physics Department. It was within this mix, that the form-and-function of a momentary perfected state in space and time was engaged (continuity-order, symmetry-relations, harmony-dynamics). For many years, that formulation drove my studies to the point of ignoring all else. Now, years later, that work continues.

#15 Where are we going?  What is the meaning and value of life?

This Day and beyond   The Derivative Nature of Space and Time

Some of us have come to believe that space is derivative of geometry and time derivative of number… and all things as things are unique ratios between the two. Of course, we continue to ask ourselves, “So? What does that mean and what do we do with it?” And, as you might suspect, we have far more questions than we have insights. We are way out on the edges looking for new meaning in this universe. The inquiring minds of our most inquisitive students, want to go further,”Maybe we can find a path to a multiverse! “

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Let’s develop a community of people and schools who are working on this simple structure.  Please let us know if you are interested. Please share your helpful comments.

Extremely-Small and Extremely-Large Numbers

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Let us start with the two key numbers:
1. The Planck Length: 1.61619926×10-35 meters which is 0.0000000000000000000000000000000000161619926 meters

2. The Observable Universe: 8.79829142×1026meters or 879,829,142,000,000,000,000,000,000 meters

There are many numbers in between the two. Each “0” represents a major base-10 transformation; and within each base-10, there are three or four base-2 notations. Though some say that the Planck Length is a special type of singularity, it has a specific length. Yet, that length is so small, for about 100 years, it was virtually ignored by the entire scientific community. Perhaps a better way of looking at the Planck Length is through the lenses of geometry. If we make it one of Alfred North Whitehead’s point-free vertices of a specific length, each time we multiply by two we grow the size as well as the number of vertices.

The Numbers of Vertices at Key Notations Between 1 and 65. When you assume that the Planck Length is a vertex, unusual concepts flow. First, consider the generation of vertices just by multiplying by 2, then each result by two, over and over again. By the tenth doubling there are 1024 vertices. By the 20th doubling, over a million more are added. On the 30th, another billion+ are added. Then, comes another trillion+ at the 40th, a quadrillion+ at the 50th notation and a quintillion+ at the 60th. At the 61st there are another 2+ quintillion vertices added. These vast arrays and systems of vertices cannot be observed.

This is the domain of postulations and hypostatizations. Consider this concept: going within from about the 65th notation, the domains begin to be shared. More and more is shared by everything as the Planck Length approaches. Each notation organizes uniquely, yet within groups. And these natural groupings reflect all the diversity within all the notations 65 and higher. It seems that the mathematics of cellular automaton may figure into the first 20 or 30 notations. We start with the most basic Forms, then Structures, which become the pre-structure for Substances, archetypes for Qualities, then Relations, then the Mind. We turn to systems theory, group theory, and set theory to discern the order of things.

Perhaps there are five hot spots for immediate research:
* Notations 1-20 and the foundations of cellular automaton and fractal geometries by using the functions created by more than one million vertices
* Notations 50-60 and the foundations of the Mind, logic, psychology, memory, thought, epistemology and learning with over 500 trillion vertices at the 59th notation and then another quintillion+ vertices within the 60th notation.
* Notations 60-80, the emergence of the particles and atoms and the most basic structures of all physical matter
* Notations 100-103, the emergence of the human life and most all life as we know it
* Notations 135-138, the transition to the Large-Scale Universe with the possibilities of uncovering pathways to the Einstein-Rosen bridges and tunnels also known as wormholes.
Key references for more: The numbers

Facts & Guesses. The Facts are what is measurable and what fits within each domain. The Guesses are about what goes on with those domains (aka steps, notations, layers or doublings) especially those that remain blank. Is there a pattern, especially a cyclic pattern that manifests in another notation? We followed Max Planck where he took the constants of nature, starting with the speed of light to calculate the smallest number. We took the age of the universe, with some help from scientists, to learn the largest calculation of a length, the Observable Universe. Making sense of these numbers is another story. So, over the forthcoming weeks, months and years, we will be looking even deeper. Would you help us now and take the little survey?

More notes about the how these charts came to be:
1Three downloads authored by Prof. Dr. Frank Wilczek: Scaling Mt. Planck (from Columbia University), C. Alden Mead’s letter and Wilczek’s response in Physics Today, and Wilczek’s August 2013 Lecture notes on units and magnitude (If you like this paper, also read this one).

The simple conceptual starting points
An article (unpublished) to attempt to analyze this simple model. There are pictures of a tetrahedron and octahedron.
A background story: It started in a high school geometry class on December 19, 2011.
The sequel: Almost two years later, a student stimulates the creation of this little tour.

Wikipedia on the Planck length
Wikipedia on the Observable Universe

Take it as a given that it is also a vertex. By the second doubling, there are four vertices, just enough for a tetrahedron. By the tenth doubling there are 1024 vertices. The number doubles each notation. By the 20th doubling, over a million more are added. On the 30th, another billion+ are added. Then, comes a trillion+ at the 40th, a quadrillion+ at the 50th notation and a quintillion+ at the 60th. At the 61st there are another 2+ quintillion vertices. What does it mean?

The simplest geometries yield a deep-seated order and symmetries throughout the universe. Those same simple geometries also appear to provide the basis for asymmetry and the foundations of quantum fluctuations and perhaps even human will.

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