Part of the Big Board – little universe project.
Order Relation Dynamics
|Functions Continuity Symmetry Harmony||
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A WORK IN PROGRESS.
© 2014 Bruce Camber
Planck Time to the Age of the Universe
PLEASE NOTE: This page was started early in December 2014. There are many simple errors within the chart below, so this page will be subject to frequent updates.
Are there any comparison between the progressions from the Planck Time and the Planck Length using base-2 exponential notation through the successive doublings out to their given limits, i.e. the Age of the Universe and the Observable Universe respectively? At this point in time, I do not think there are, so we are making our first working draft attempt to do it here.
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
The Planck Time, like the Planck Length, is an actual value. It can be multiplied by 2. Of course, if one were to multiply it by 2 over and over again, you can assume that you would reach those outer limits. That process looks a bit tedious. After all, the Age of the Universe is somewhere over 13.78 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 between 202 to 206 doublings. That is so surprising, the doublings for both are charted below.
These doublings do kind-of, sort-of end up somewhat in synch. Considering the duration and the length, and the nature of very large measurements, for all intents and purposes, they are synched! Though these charts will be tweaked substantially, the best confirmation is at the notations (or doublings) that define a day in Planck Time units correspond closely to distance light travels in a day in Planck Length units. And, the doublings within the Planck Time column for the definition of a week correspond closely with the distance light travels in a week within the Planck Length column. And, finally, the doublings in the Planck Time column that define a year correspond closely with the distance light travels within a year in the Planck Length column. These are the 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
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 the Planck Length and Planck Time in synch? 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?
At this point, we are attempting to learn enough to make a few somewhat intelligent guesses.
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?"
By the way, on May 10, 2010, the very smallest unit of measured time was experimentally demonstrated; the result was 1.2 × 10−17 seconds. That is a long way from 10−44 seconds! For more background, see: http://phys.org/news192909576.html
This stream of consciousness continues at the very bottom of this chart.
Planck Time Doublings: Primarily in Seconds
Planck Length Doublings: Primarily in Meters
The Age of the Universe: 13.78 to 13.8 billion years
8.310×1026 m or Future Universe
It appears that we are in the earliest part of 202 doubling:1019
4.155×1026 m or Near Future Universe
6.9309178×1018 seconds (21.9777+ billion years)18
2.077×1026 m or in the range of the Observable Universe
346,545,888,147,200,000 seconds (10.9888+ billion years)
1.03885326×1026 m approaching the Observable Universe
173,272,944,073,600,000 seconds (5.49444+ billion years)
86,636,472,036,800,000 seconds (2.747+ billion years)
43,318,236,018,400,000 seconds (1.3736+ billion years)
21,659,118,009,200,000 seconds (686.806+ million years) 17
10,829,559,004,600,000 seconds (342.4+ million years)
5,414,779,502,320,000 seconds (171.2+ million years)
2,707,389,751,160,000 seconds (85.6+ million years)
1,353,694,875,580,000 seconds (42.8+ million years)
676,847,437,792,000 seconds (21.4+ million years)
338,423,718,896,000 seconds (10.724+ million years)
169,211,859,448,000 seconds (5.3+ million years) 15
84,605,929,724,000 seconds (2.6+ million years) 14
42,302,964,862,000 seconds (1.3+ million years) 14
21,151,482,431,000 seconds (640+ thousand years) 14
10,575,741,215,500 seconds (320+ thousand years) 14
5,287,870,607,760 seconds (160+ thousand years) 13
2,643,935,303,880 seconds (83.7+ thousand years) 13
1,321,967,651,940 seconds (41.8+ thousand years) 13
660,983,825,972 seconds (20.9+ thousand years) 12
330,491,912,986 seconds (or about 10,472.9 years) 12
1.26813145 x1022 m
3.17032864×1021 m or 3 Zettameters or 310,000 ly
1.58516432×1021 m or about 150,000 ly (1.5z)
165,245,956,493 seconds 12
82,622,978,246.4 seconds 11
41,311,489,123.2 seconds 11
20,655,744,561.6 seconds 11
10,327,872,280.8 seconds 11
5,163,936,140.4 seconds 10
2,581,968,070.2 seconds 10
1,290,984,035.1 seconds 10
645,492,017.552 seconds 9
322,746,008.776 seconds 9
1.93501504 x1017 m
161,373,004.388 seconds 9
80,686,502.194 seconds 8
40,343,251.097 sec 8(466 days)(Note: 31,536,000 s/year)
20,171,625.5485 seconds (233.468 days)8
10,085,812.7742 seconds (116.73 days)8
5,042,906.38712 seconds (58.36+)107
2,521,453.19356 s (29.1835 days)
1,260,726.59678 s (14.59+ days) 107
630,363.29839 s (7.29+ days) 106
315,181.649195 seconds (3.64794 days) 106
6.0469218×1015 m [one light year (ly) is 9.4×1015 m]
1.88966306×1014 m (about 7-day light travel)
157,590.824598 s (1.82 days)106
78,795.4122988 s (.911984 days) 105
39,397.7061494 seconds 105
19,698.8530747 seconds 105
9849.42653735 seconds 104
4924.71326867 seconds(3600 s in hour)104
2462.35663434 seconds 104
615.589158584 seconds (10.259+ minutes)103
307.794579292 seconds 103
2.36207882×1013 m (or close to 24-hour light travel)
738,149,657 kilometers 1011
369,074,829 kilometers 1011
184,537,414 kilometers 1011
92,268,707.1 kilometers (range of earth-to-sun)1010m
153.897289646 seconds 103
76.948644823 s (16+ sec over 1 min) 102
38.4743224115 s (21.53 sec to 1 min) 102
4.80929030144 seconds 10?
2.40464515072 seconds 10?
1.20232257536 s (1s ≠ perfect tp multiple) 10?
46,134,353.6 kilometers 1010
23,067,176.8 kilometers 1010
11,533,588.4 kilometers 1010
5,766,794.2 kilometers 109
2,883,397.1 kilometers 109
1,441,698.55 kilometers 109 m
720,849.264 kilometers 108
360,424.632 kilometers108 m
180,212.316 kilometers (111,979+ miles)108 m
90,106.158 kilometers 107 m
3.757258048 × 10−2 seconds
1.878629024 × 10−2 seconds
9.39314512 × 10−3 seconds
4.69657256 × 10−3 seconds
2.34828628 × 10−3 seconds
1.174143145978 × 10−3 seconds
5.8707157335 × 10−4 seconds
2.93535786675 × 10−4 seconds
45,053.079 kilometers 107
22,526.5398 kilometers 107
11,263.2699 kilometers or about 7000 miles
5631.63496 kilometers 106
2815.81748 kilometers 106
1407.90874 kilometers (about 874 miles )106m
703.954368 kilometers 105
351.977184 kilometers (218.7 miles 105
175.988592 kilometers (109.35 miles )105
87.994296 kilometers 104
1.46767893338 × 10−4 s
7.33839466688 × 10−5s
3.66919733344 × 10−5 s
1.83459866672× 10−5 s
9.1729933336 × 10−6 s
4.5864966668 × 10−6 s
2.2932483334 × 10−6 s
1.1466241667 × 10−6 s
5.73312083348 × 10−7 s
2.86656041674 × 10−7 s
43.997148 kilometers 104
10.999287 kilometers or within 6.83464 miles104
5.49964348 kilometers 103
2.74982174 kilometers 103
1.37491087 kilometers 103
687.455439 meters 102
343.72772 meters or about 1128 feet 102
171.86386 meters or about 563 feet 102
85.9319296 meters 101
1.43328020837 × 10−7 s
7.16640104186 × 10−8 s
3.58320052093 × 10−8 s
1.79160026046 × 10−8 seconds
8.95800130232 × 10−9 seconds
4.47900065116 × 10−9 seconds
2.23950032558 × 10−9 seconds
1.11975016279 × 10−9 seconds
5.59875081396 × 10−10 seconds
2.79937540698 × 10−10 seconds
42.9659648 meters 101
21.4829824 meters 101
10.7414912 meters or 35.24 feet or 1.074×101 m100
5.3707456 meters 100
2.6853728 meters or 105.723 inches 100
1.3426864 meters or 52.86 inches 100
67.1343176 cm (19.68+ inches or 6.71×10-1
33.5671588 centimeters or 3.356×10-1 m
16.7835794 centimeters or 1.6783×10-1
8.39178968 cm (3.3+ inches or 8.39×10-2 m
1.39968770349 × 10−10 seconds
6.99843851744 × 10−11 seconds
3.49921925872 × 10−11 seconds
1.74960962936 × 10−11 seconds
8.7480481468 × 10−12 seconds
4.3740240734 × 10−12 seconds
2.1870120367 ×10−12 seconds
1.09350601835 ×10−12 seconds
5.46753009176 ×10−13 seconds
2.73376504588 × 10−13 seconds
4.19589484 centimeters 4.19589484×10-2 m
2.09794742 centimeters or 2.0979×10-2 m
1.04897 centimeters or 1.04897375×10-2 m
5.24486856 mm (about 1/4 inch) or 5.24×10-3 m
2.62243428 millimeters or 2.62243428×10-3 m
1.31121714 millimeters 1.31121714×10-3 m
.655608568 millimeters or 6.55608568×10-4 m
.327804284 millimeter or 3.27804284 x10-4 m
.163902142 millimeters or 1.63902142×10-4 m
81.9510712 microns or 81.9510712 x10-5 m
1.36688252294 × 10−13 seconds
6.83441261472 × 10−14 seconds
3.41720630736 × 10−14 seconds
1.70860315368 × 10−14 seconds
8.5430157684 × 10−15 seconds
4.2715078842 × 10−15 seconds
2.1357539421 × 10−15 seconds
1.06787697105 × 10−15 seconds
5.33938485524 × 10−16 seconds
2.66969242762 × 10−16 seconds
40.9755356 microns or 4.09755356 x10-5 m
20.4877678 microns or 2.04877678×10-5 m
10.2438839 microns or 1.02438839×10-5 m
5.12194196 microns (.0002+ inches or 5.12×10-6 m
2.56097098 microns or 2.56097098×10-6 m
1.28048549 microns or 1.2804854×10-6 m
640.242744 nanometers 6.40242744×10-7 m
320.121372 nanometers 3.20121372×10-7 m
160.060686 nanometers or 1.60×10-7 m
80.0303432 nanometers or 8.00×10-8 m
1.33484621381 × 10−16 seconds
6.67423106904 × 10−17 seconds
3.33711553452 × 10−17 seconds
1.66855776726 × 10−17 seconds (smallest measurement – 2010)
8.34278883632 × 10−18 seconds
4.17139441816 × 10−18 seconds
2.08569720908 × 10−18 seconds
1.04284860454 × 10−18 seconds
5.21424302272 × 10−19 seconds
2.60712151136 × 10−19 seconds
40.0151716 nanometers or 4.00×10-8 m
20.0075858 nanometers or 2.00×10-8 m
1.00037929×10-8 meters or 10 nanometers
2.50094822 nanometers or 2.50094822×10-9 m
1.25474112 nanometers or 1.25×10-9 m
.625237056 nanometers or 6.25237056×10-10 m
.312618528 nanometers or 3.12×10-10 m
.156309264 nanometers or 1.563×10-10 m
1.30356075568 × 10−19 seconds
6.5178037784 × 10−20 seconds
3.2589018892 × 10−20 seconds
1.6294509446 × 10−20 seconds
8.147254723 × 10−21 seconds
4.0736273615 × 10−21 seconds
2.03681368075 × 10−21 seconds
1.01840684038 × 10−21 seconds
5.09203420188 × 10−22 seconds
2.54601710094 × 10−22 seconds
1.27300855047 × 10−22 seconds
6.36504275236 × 10−23 seconds
3.18252137618 × 10−23 seconds
1.59126068809 × 10−23 seconds
7.95630344044 × 10−24 seconds
3.97815172022 × 10−24 seconds
1.98907586011 × 10−24 seconds
9.94537930056 × 10−25 seconds
4.97268965028 × 10−25 seconds
2.48634482514 × 10−25 seconds
1.24317241257 × 10−25 seconds
6.21586206284 × 10−26 seconds
3.10793103142 × 10−26 seconds
1.55396551571 × 10−26 seconds
7.76982757856 × 10−27 seconds
3.88491378928 × 10−27 seconds
1.94245689464 × 10−27 seconds
9.7122844732 × 10−28 seconds
4.8561422366 × 10−28 seconds
2.4280711183 × 10−28 seconds
1.21403555915 × 10−28 seconds
6.07017779576 × 10−29 seconds
3.03508889788 × 10−29 seconds
1.51754444894 × 10−29 seconds
7.58772224468 × 10−30 seconds
3.79386112234 × 10−30 seconds
1.89693056117 × 10−30 seconds
9.48465280584 × 10−31 seconds
4.74232640292 × 10−31 seconds
2.37116320146 × 10−31 seconds
1.18558160073 × 10−31 seconds
5.92790800364 × 10−32 seconds
2.96395400182 × 10−32 seconds
1.48197700091 × 10−32 seconds
7.40988500456 × 10−33 seconds
3.70494250228 × 10−33 seconds
1.85247125114 × 10−33 seconds
9.26235625568 × 10−34 seconds
4.63117812784× 10−34 seconds
1.15779453196× 10−34 seconds
5.78897265978 × 10−35 seconds
2.89448632989 × 10−35 seconds
1.44724316494 × 10−35 seconds
7.23621582472 × 10-36 seconds
3.61810791236 × 10−36 seconds
1.80905395618 × 10−36 seconds
9.045269781089 × 10−37 seconds
4.522263489044 × 10−37 seconds
2.26131744522 × 10−37 seconds
1.13065872261 × 10−37 seconds
5.65329361306 × 10−38 seconds
2.82646806528 ×10−38 seconds
1.41323403264 ×10−38 seconds
7.0661701632 × 10−39 seconds
3.530850816 × 10−39 seconds
1.7665425408 × 10−39 seconds
8.832712704 × 10−40 seconds
4.416356352 × 10−40 seconds
2.208178176 × 10−40 seconds
1.104089088 × 10−40 seconds
5.52044544 × 10−41 seconds
2.76022272 × 10−41 seconds
1.38011136 × 10−41 seconds
6.9005568 × 10−42 seconds
3.4502784 × 10−42 seconds
1.7251392 × 10−42 seconds
8.625696 × 10−43 seconds
4.312848 × 10−43 seconds
2.156424 × 10−43 s The second doubling
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
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."
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:
d. ResearchGate Documents: 3052, 3054, 3056
Key references are below.
Thank you for your lecture, A New Kind of Science. Although over ten years ago, I have learned and have been challenged.
Intellectually, you are quite compelling.
Yet, a few facts and a few ideas may need to be further examined:
- The universe is mathematically very small.
Using base-2 exponential notation from the Planck Length to the Observable Universe, there are just 202.34 (NASA, Kolecki) to 205.11 (Paris, Luminet) notations, steps or doublings. This work (the mathematics) actually began in 2011 in a high school geometry class when we started with a tetrahedron and divided the edges by 2 finding the octahedron in the center and four tetrahedra in each corner. Then dividing the octahedron we found the eight tetrahedron in each face and the six octahedron in each corner. We kept going within until we found the Planck Length. It was easy to decide to multiply by 2 out to the Observable Universe. Then it was easy to standardize the measurements by just multiplying the Planck Length by 2.
- The small-scale universe is an amazingly complex place.
Assuming the Planck Length is a singularity of one vertex, we also noted the expansion of vertices. By the 60th notation, of course, there are over a quintillion vertices and at 61st notation well over 3 quintillion vertices. Yet, it must start most simply and here the principles of computational equivalence have a possible impact. AN Whitehead’s point-free geometries could also have applicability.
- This little universe is readily tiled by the simplest structures.
The universe can be simply and readily tiled with the four hexagonal plates within the octahedron and by the tetrahedral-octahedral-tetrahedral chains.
- Yet, the universe is delightfully imperfect.
In 1959, Frank/Kaspers discerned the 7.38 degree gap with a simple construction of five tetrahedrons looking a lot like the Chrysler logo. The icosahedron with 20 tetrahedrons is squishy. We call it quantum geometry in our high school. It is the opening to randomness.
- The Planck Length could become the next big thing.
The behavior may not be so complicated on the surface, but far more complicated just below it.
Computers generate rules and this might be what nature is using.
I could go on, but let’s see if these statements are at all helpful. Our work began in December 2011 within a high school, however, it relies on several assumptions — order (continuity), relations (symmetry), and dynamics (harmony) — that have been waiting to be engaged since 1972. I’ll insert a few references below.
Many thanks again for your cellular automaton lecture.
References to pages within our blogs and websites:
First principles: http://bigboardlittleuniverse.wordpress.com/2013/03/29/first-principles/
Earlier edition: http://smallbusinessschool.org/page869.html
Next Big Thing: http://tinyurl.com/PlanckLength
One of our student’s related science fair project: http://walktheplanck.wordpress.com/2013/12/03/p1/
References to your work:
UCSD Institute of Neural Computation, 2003 H. Paul Rockwood Memorial lecture 4/30/2003
How does structure take shape in the universe?
What are the fundamental problems to this approach?
What does it mean to be a universal system?
Rule 30 and 110 and computational equivalence
The film, Gravity, didn’t even attempt to give us a cosmological view.
Our most-visible space entrepreneurs — Richard Branson, Elon Musk, Paul Allen, and Jeff Bezos — are working hard and investing heavily to open new ways to outer space. NASA and a few professors like Carl Sagan once owned the domain. Certainly it has included some of our best science fiction writers. The blockbuster producers of major motion pictures like Star Wars, Star Trek, 2001, A Space Odyssey, Gravity, ET, Contact, and Close Encounters, teased the imaginations of the public, but did very little to teach.
Interstellar was to change the SciFi metaphor. They surely tried. They had the best of the best to help shape their narratives, including Cal Tech’s gravitational-black hole expert, Kip Thorne (author, The Science of Interstellar). But what can we expect when the working concepts of today’s scientific elite still do not include an integrated Universe View?
The Narratives: Next up. Just think what might happen if Star WarsVII incorporated iconic storylines where our four space entrepreneurs (pictured above) had a role. Just think what would happen if the best of future science fiction movies built upon each other’s themes and developed a meta-reality which clearly beckoned us all into the future.
New concepts and ideas can be communicated in the drama of a major theatrical production. These four people could make a huge difference. Educate the public? No, these folks could mesmerize the world.
Let us look at four very simple facts that sound more like science fiction, but these alone truly engender the imagination to see things in new ways:
1. 205.1+ base-2 exponential notations. That takes us from the smallest possible measurement of a length to the largest; that is from the Planck Length to the Observable Universe. That seems unbelievable, but it is true. Simple math. Add some simple geometries and magic happens. Within our most speculative visions, we ask, “Why not try to apply the work with amplituhedrons (new window) and the Langlands program (new window) as a partial definition for the transformations between notations (layers, domains, doublings, or steps)?” There is a certain magic that happens when you envision the universe in 205+ steps. Perhaps it will only be a metaphor or possibly a new intellectual art form. It may be, as the intellectual elites might say, “Not Even Wrong,” but what fun the rest of us can have learning a little about an ordered universe and about the limitations of thought!
2. There is no concurrence about the first 60 notations. These notations are not acknowledged by the general scientific community, so none per se have been knowingly used experimentally! So, be speculative. Use this domain with its no less than a quintillion vertices to construct primal machines. Be bold. Develop a simple logic to control gravity. Extend it to create enormous reserves of a most basic energy that gives rise to quantum fluctuations. Develop logical-albeit-quite-imaginative constructs that educate and challenge us to understand “Beam me up, Scotty!” Have fun and put down that gun (symbolic or otherwise).
3. Work the ratios between all 205.1+ notations and the natural groupings and sets. That range is naturally divided in half, and then by thirds, fourths, fifths and so on.
Consider the halfway point. Within the 101st notation is the human hair, within the 102nd notation is the width of the piece of paper, within the 103rd notation is the egg (and the sperm is at 100). Yes, there is a concrescence for life in this middle of this definition of the universe. From here we go on out to discover the remaining 101 to 103+ exponential notations to the Known or Observable Universe.
4. Consider the potential magic within the thirds. Physical things emerge between notations 67 and 80. That includes all the particles, all the atoms and all the elements of the periodic table. That is the transition from the small scale to the human scale.
Now, consider the transition from the human scale to the large scale. It is highly speculative yet entirely within the scope of a vivid imagination to expect that the Einstein-Rosen tunnels and bridges, commonly known as wormholes (possibly good for inter-galactic travel, just might begin to emerge between notations 136 and 138. That’s in the range of the two-thirds transition. And, that would put them in the range of 874 to 3500 miles above the earth. The International Space Station is anywhere from 230 to 286 miles above the earth and geosynchronous satellites are around 35,786 kilometers or 22,236 miles above the earth’s equator.
A Dream: Develop a cooperative production studio area that incorporates a space elevator that becomes a major edutainment sector whereby the public can actually begin to participate in the most extraordinary educational scenes of major science fiction productions. Surely, the drama of a meteor shower might be part of it taking scenes directly out of Gravity.
Editor’s Notes: Most of the links stay within the domain of the primary URL displayed above. Some links go to a Wikipedia reference and open in a new window or tab. Also, many of these short articles have been duplicated on other sites. The three primary sites are Small Business School, where the very first reflections about the Big Board-little universe and its Universe Table were first posted in January 2012. You will also find these postings in several inter-related WordPress pages and within LinkedIn pages. The related Facebook and Blogger pages will be included eventually.
Endnotes, footnotes and references:
This article is really by a rather large group of high school students with some help from Bruce Camber who helps our in their geometry classes on occasion.
We were studying symmetries and Plato’s solids when we rather circuitously developed a model of the universe from the smallest-to-the-largest possible measurements of a length. We had divided each edge of a tetrahedron in half and connected the new vertices. We kept on dividing by 2 until we were at the Planck length. Then we multiplied by 2 until we were at the Observable Universe. We wondered why we had not seen this particular scale of the universe anywhere on the web (of course, Kees Boeke’s 1957 work on base-10 is well-known, but we had not learned about it yet). So, we wondered, “Could this be an outline to begin doing the smallest-and-the-biggest, yet possibly-the-most-simple, scientific experiments?” We cautiously thought, “Maybe it is.”
Yes, this journey began by looking inside our clear plastic models of the tetrahedron and octahedron. We wanted to see what was perfectly inside. That was easy. We then asked, “How many steps within would it take to get to the Planck Length?” The Planck Length was a topic in our physics classes. When we found just 50 steps to the diameter of the proton and another 68 steps to the vicinity of the Planck Length, we were surprised. We were expecting many, many more steps.
Within a couple of days, we began multiplying each edge by 2. Our goal was to get out into the range of the Observable Universe. It appeared that we were getting into the general vicinity in just 91 steps.
What? …so few steps? We were dumbfounded but undeterred. To make our emerging chart of the universe consistent, we decided to start at the Planck Length and just multiply by 2 and assume those simple geometries as a given. But, we weren’t sure we could multiply the Planck Length by 2, so we turned to experts on the Planck Length. One of them said our work was idiosyncratic and would go no further. Another cautioned us to work within group theory but encouraged our work. Frank Wilczek, one of the world’s experts on the Planck Length and an MIT Nobel Laureate, also encouraged our explorations and use of the Planck Length.
Further checking the web to see if we were making stupid logic errors, we quickly found the base-10 work of Kees Boeke, a high school teacher from Holland. Back in 1957 he published a little picture book, Cosmic Vision, that became quite popular within academic circles. Many people have subsequently refined his work. In the ’60s Charles & Ray Eames made a movie about it and Phil & Phyllis Morrison of MIT did an expanded picture book. And, then in 1997 the Smithsonian’s IMAX Theater did an expanded version of the movie with Morgan Freeman. More recently Cary Huang did a lovely online, Flash-based, version dubbed, The Scale of the Universe. All very good, but for us it just doesn’t go far enough in either direction. Certainly it is not granular enough, and it has no inherent geometries. It amounts to what one might call, “exponential notation light”. As Phil Morrison once said, “Just add zeros!” “It’s exponential notation for dummies.” To which our students add, “It’s exponential notation for Dummies.”
The Planck Length was first defined in 1899 by Max Planck. Though little used, it is generally accepted to be the smallest meaningful measurement of a length; and because it is based on three constants including the speed of light in a vacuum and the gravitational constant, most scholars believe Planck was right.
Though the Observable Universe is a difficult figure to discern, there have been many published guesses over the years. But to give us some confidence that we were on the right track, we turned to a NASA scientist and a French astrophysicist. In this early search, we could not find anybody using base-2 exponential notation to extrapolate a view of the universe.
Although our intention was not to create a so-called perfect sequence or scale of lengths from smallest to the largest, we backed into using base-2 exponential notation because it was simple and we were studying embedded-and-nested geometries. So, we could readily number and spatialize each sequence of the scale. It seemed like a logical way to create ordered sets, groups and real relations between everything.
Yet, we were quickly approaching our limits of knowledge. Questions abound. What happens in the first 66 notations? Could this be an area for pure math and geometries? Might the first 20 or 30 notations be a domain for cellular automaton? Could the Mind be located somewhere just before the proton? What happens between each doubling? What are the boundary conditions? What is the relation between number and space? Currently we do not know any answers to those questions. Although somebody else might know, we have begun trying to discern a path to discover answers. We began to apply what we knew about the scientific method. How will we identify the types and functions of the constants and variables all along the scale? How will we define the independent and dependent variables? Are there control and moderating variables? What would we use for a control group? Can we begin to make a few hypotheses to test?
We are still crawling, trying to find our walking legs. We often find ourselves in a fog of unknowns, but we did come up with a few ideas to create an experiment.
Could this be a simple experiment?
Our first hypothesis is that there will be significant transitions points along the scale. A most simple projection would be to look for significance within the midpoint (dividing in the entire scale by 2, 1:2). We also hypothesize that there will be something significant at the thirds (dividing the entire scale by 3, 1:3), as well as by fourths, fifths, sixth, sevenths, eights, ninths and tenths. We are currently on that path of discovery.
It was easy and straightforward to find a range that we could call the midpoint. It was also easy to discover that these notations are where life begins. Yes, the sperm and egg are within that range. Life appears to be the concrescence of the two extremes. That was a very simple experiment and our hypothesis seems to be validated. It is a significant transition.
Next, by dividing by 3, we have begun looking at notations 67 to 69 and 134 to 137. Being relatively inexperienced at understanding such small measurements, we made many initial mistakes. Today, we believe at notation 65 we are close to the size of a proton, (rp = 0.84184(67) fm).3 Here is the basic building block of the visible universe between notation 65 at 5.96272544×10-16 meters and notation 66 at 1.19254509×10-15 meters.
Though this scale amounts to a view of the known universe, on a serious note, we will call it a Universe View. On a whimsical note, we call it the Big Board-little universe. It feels unique. We have not seen it within our studies. It gives us perspective. It puts everything in a nice grid. It appears to open new areas to study.
Another simple hypothesis emerged. We thought, “People with a universe view would be more optimistic, more insightful, and more productive than people who rely on their own views or even a worldview.” It became a project for the National Science Fair.4 We developed a ten-step tour of this Universe View, then asked people if they felt more optimistic, insightful, and productive as a result. Our results were not conclusive, however, we have not given up on developing a cleaner methodology and a better control group.
1. It is a helpful ordering tool. It puts everything in a necessary sequence and a place on a somewhat granular scale.
2. It has inherent geometries. Seen or unseen, we believe these geometries are inherent throughout the known universe and we believe there should be testable hypotheses that we can discern. Perhaps, we are talking about Alfred North Whitehead’s point-free geometries. Our life is filled with things we do not see, but assume there is a structure for it. It could be a memory of times gone by, a creative insight of a possible solution to a problem, or a recurring dream of things to come.
3. Geometry tiles the known universe, first with the four hexagonal plates within the octahedron and then with tetrahedral-octahedral chains and clusters. This remains to be studied, but it certainly suggests that from the Planck Length to the Observable Universe in just under 206 notations, steps, layers, doublings, or sections, everything is necessarily related to everything. The geometer John Conway (Princeton emeritus) with Yang Jiao and Salvatore Torquato recently expounded on this basic configuration.6
4. The known universe has deep-seated symmetries that create a diversity of relations. BUT, we know because of Max Planck’s work to define quantum mechanics, there are also asymmetries, indeterminacy and chaos. We readily find the geometric imperfection and logical opening, first from within the work of Frank-Kaspers and now within the work of many others (just below).7
5. A speculative summary. Historically space and time have been the container within which everything takes place. As much as Einstein tried to dislodge Sir Isaac’s commonsense worldview, nothing has really taken its place. We started with simple geometries and mapped the known universe including a very, very small universe that is ignored by most. In our work, number and geometry pervade everything. We can see the Frank Wilczek’s Grid emerging from the Planck Length; there is order and continuity within a deep substructure. As we move up through the notations, we can see and feel relations and symmetries building. Yet, we can also feel and see asymmetries and discontinuities taking shape. I believe ultimately we will see how space becomes derivative of geometry and time derivative of number. We just might be able to move on from Newton’s commonsense and develop a simple-but-compelling universe view, whereby order, relations, and dynamics are known through continuities and discontinuities, symmetries and asymmetries, and harmony and discordance.
3 Davide Castelvecchi, “What Do You Mean, The Universe Is Flat?, Part 1,” Scientific American, July 25, 2011
7 Frank/Kaspers to P. K. Doye on polytetrahedral structure to J.C. Lagarias and C. Zong on tetrahedral packing which is Footnote 19 within an article at this URL: http://doublings.wordpress.com/2013/07/09/1/#Footnote19
Touch down on ten different parts of the two charts and get a little overview of both (is back under construction).
– The Universe Uses Very Big and Extremely Small Numbers (Make friends with numbers and geometries).
Notes about Look-Feel and Navigation: If the line just above extends out of the white background, please open your window larger (perhaps full screen). Also, within the tour, if you click on the last sentence in each description, you should go to the next page.
More related pages:
There are over 202.34 and as many as 205.11 notations. This table focuses on the Human Scale and notations 67 to 134-138. The Small Scale (1 to 67-69) and Large Scale (134-138 to 205) will follow after updates, verifications, and the footnotes have been completed for this first table.
This chart is 60″ x 12″ and it was the original depiction of the 202.34-to-205.11 notations.
An analyze and opinions about the Universe Table and the Big Board – little universe
The simplest parameters of science and mathematics opened the way for this entire inquiry.
The question was asked on December 19, 2011, “Why isn’t this stuff on the web someplace?” It seemed like somewhere in our midst was a fundamental logic flaw. Very cautiously, this page was put up on the web over on the Small Business School website so family and friends could be asked to read this introduction and caution us or encourage us along the way.
To invite critical review and collaboration, this article was submitted and then publicly posted within Wikipedia back in April 2012 yet it was deleted in the first week of May. That original iteration was again published within Small Business School.
Joe Kolecki was the first person outside our little group of students to help. He provided us with this calculation in May 2012. Soon thereafter, the Argonne National Laboratory and Nikon Small World helped a little, too.
This page provides all the numerations from the first Planck Length through all 202.34 doublings.
The background story about how this perception emerged and when it was introduced in high school geometry classes on that last day before the Christmas holidays, Monday, December 19, 2011.
Universals and constants can be applied to every belief system. If the belief system is unable to accommodate both, then it is incomplete.
The conceptual foundations for this work start with the thrust or energy to make things better or more perfect.
May we turn to you for insight? That big chart on the left measures 62″ x 14″ so it can be a bit awkward to use at your desk. We wanted to present the data in a more simple format (to be printed on 8.5×11 inch paper or displayed on a smartphone) so we created the chart on the right. We are calling it, the Universe Table. This is a long-term project, so we would like to ask a few questions to help us prioritize and focus on important things to do.
The large-scale universe seems so much more approachable. On the Big-Board-little universe chart every notation is listed. Within the Universe Table all the notations within the Human Scale are listed, but those within the small-scale are in groups of ten notations and within the large-scale they are also in groups of ten, each corresponding to one of the images from Andrew Colvin.
Your Views, Worldviews, Universe View. All views are important. Yet, some views are more optimistic, some are more creative, and some more productive. Our hypothesis is that those who balance their views with a strong worldview and a truly integrated universe view will be the most optimistic, creative and productive.
It is going to take us a long time to figure that out, so we need to get started. We are asking our guests — “Would you please take a very quick, very simple survey, then go on the tour. On the right, you will see a green arrow. Just click on it to begin.
Both charts represent the same thing — the visible universe. The very smallest measurement is the Planck Length. The largest is the Observable Universe. From the smallest to the largest, there are less than 206 notations or steps. Click on each image to see the full-sized rendering.
Feb. 4, 2014:
Bruce Camber sends the following email to Alan Dershowitz about Natural Law
January 2014, after 50 years of teaching at Harvard Law School, Dershowtiz has stepped down to give his many unfinished projects his undivided attention.
Rights from Wrongs: A Secular Theory of the Origins of Rights, Alan Dershowitz, Basic Books, 2005, page 31
Dear Prof. Dr. Dershowitz:
Congratulations on a most-provocative, productive career; and, just think, you are just getting started!
I awoke this morning thinking about you and natural law. Now, that’s a first and it did seem a bit peculiar. I thought, “Maybe it’s an inspired moment.” So, at about 4:30 AM, I went to my computer and started reading about your disdain for natural law: “Human beings have no singular nature… We are creatures of accidental forces who have no preordained destiny or purpose” (Rights from Wrongs: A Secular Theory of the Origins of Rights, Basic Books, 2005, page 31). It is entirely obvious that you have very little patience for those who advocate natural law.
Given that you have spent so much time arguing the case against natural law, it may appear silly to learn that a group of high school geometry students may have found a basis for natural law. Though unusual, it is not frivolous. I would not waste your time or mine. It is instead based on simple logic and simple mathematics; and thus, it is simple enough to be compelling.
Base-2 exponential notation is a odd combination of words that simply mean, multiply by 2, then continue by multiplying each result by 2.
The Planck Length — http://en.wikipedia.org/wiki/Planck_length — uncovered in 1899, is the smallest possible measurement of a length.
There are an increasing number of measurements for the Observable Universe – http://en.wikipedia.org/wiki/Observable_universe — which, of course, is the largest measurement of an actual length. There are limits.
If we assume the Planck Length as calculated by Max Planck in 1899 and 1900 is correct, then multiply it by 2, there are only 202.34-to-205.11 notations (doubling, steps, or layers) from the smallest to the largest. The range is given because there is a variance in the calculations regarding the age of the universe.
It is not easy to conceive of so few notations from the smallest to the largest so I’ll provide a link to the actual calculations so you can see that progression. http://doublings.wordpress.com/2013/04/17/60/
Basic geometries begin with the second doubling. It is not a gimmick, but a way of ordering the known universe that is efficient, relational, holistic, instructive, and simple.
And, because it starts with an inherent geometry that expands rapidly (cellular automaton), it has an implicit structure (form/function) that evolves within every notation. Here, time appears to be derivative of number and space derivative of geometry.
Bottom line, this construct first pushes out an inherent continuity/order, symmetry/relations, and harmony/dynamics that is wonderfully complex, ordered and dynamic. It also allows the freedom of its inverse. The pentastar1 (five tetrahedrons, seven vertices) and the icosahedron (20 tetrahedrons, 12 external vertices, one internal) actually create a basis for imperfection, or degrees of freedom, or within science, quantum mechanics. Taken together, it seems we have the foundations or the beginnings of a natural law.
It lets group theory, set theory, and systems theory evolve in natural ways from the Planck Length to the Observable Universe. By the 60th notation there are over a quintillion vertices for constructions. Fermions and protons do not show up until the 65th. Here is a chart and a quick tour if you are interested: https://utable.wordpress.com/2013/07/19/intro/
I thought you might find this work to be of interest. Thanks.
A little recent history: http://bigboardlittleuniverse.wordpress.com/2013/03/18/history/
1 This simple little configuration is actually quite imperfect. Aristotle thought it was perfect yet it appears that a couple of chemists, Frank & Kaspers, in 1959 discerned the basic asymmetries. To make it simple, look at the Chrysler logo. That is a pentastar and notice the gap. That is the asymmetry or imperfection.