A progress report about a high school geometry project that became our first simple-but-coherent view of the known universe. Your comments are encouraged and welcomed.
We unwittingly backed into developing what 
we now call our Universe View. We used a very basic logic and math. First, we divided an object by 2 until we got into the range of the smallest measurement of a length, then we multiplied that object by 2 until we got out around the largest measurement of a length.
we now call our Universe View. We used a very basic logic and math. First, we divided an object by 2 until we got into the range of the smallest measurement of a length, then we multiplied that object by 2 until we got out around the largest measurement of a length.
Our work began in December 2011. That simple exercise resulted in some stunning measurements which over the past two years have opened paths to some rather fun concepts, wild-and-crazy ideas, and playful speculations.
We would like to share them with you to get your feedback. Please note that those numbers in parentheses that follow are references to other pages that are all linked at the bottom of this page. Also, please be advised, that this project will always be a work in progress.
1. The Power of 2. There are at most 205.11 base-2 exponential notations starting at the Planck Length (the smallest measurement of a length in the universe) to the Observable Universe (the largest). That is a fact (1) and it is just simple mathematics. Although a Dutch high school teacher used base-10 in 1957 and found about 40 notations, our work began with an inherent geometry; it was not just a process of adding and subtracting zeros. Plus, base-2 is so much more informative, granular, and natural; it mirrors the processes in biological reproduction and chemical bonding.
2. Inherent Geometry. 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 the 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. We did that process of going within about 109 times. On paper, in about 40 steps we were inside the atom; and, within another 69 steps we were in the range of the Planck Length.
We then multiplied our two objects by 2 and within about 86 steps or notations or layers, 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 universe. We had some help to calculate those 205.11 notations (2 - See point #4).
Because we started with a geometry, we were able to tile the universe with that geometry. It is simple. It puts everything within a meaningful relation. That is helpful. Yet, now we are exploring just how useful this emerging model could become.
3. Numbers and Potential Geometries Gone Wild. By the 10th doubling there are 1024 vertices. That is 1 for the Planck Length, then 2, 4, 8, 16, 32, 64, 128, 256, 512, and 1024. The simple aggregation of all notations up to 10th would be 2046 vertices. Within just the 20th doubling (notation) there are over 1-million vertices, by 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 is beyond our capacity!
The expansion of vertices within each doubling has been a challenge. Yet, it could be even greater and more complex if we were to follow the suggestion of Freeman Dyson (2 - See point #11) where he said,“Since space has three dimensions, the number of points goes up by a factor eight, not two, when you double the scale.”
4. Driving Concepts. The simple mathematics provides a basic order and continuity that we have imposed on the universe. The simplest geometries provide a startling 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 a very special dynamics and an occasional harmony. (3) When it was first written up back in the 1970s, it seemed to describe the concept of a perfected state within space and time, but it was still too vague. It needed a a domain or container within which to work and it seems that this may be it. (4)
5. Big Board-little universe and the Universe Table. 
By September 2013, a class of sixth grade students got involved and a core group of about 40 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.
By September 2013, a class of sixth grade students got involved and a core group of about 40 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.
That was all very helpful, but then, we began observing some relations and let our imaginations work a little overtime.
6. Humanity takes its place in the middle of these models of the Known Universe. At notation 100 is the human sperm, at 101 is human hair, a 102 is the thickness of paper upon which we record our history, and at 103 is the human egg.
That looks like a concresence of meaning.
7. The first 60+ notations, doublings, or layers are unchartered. We asked, "What could possibly be there?" So, we started going back throughout history and philosophy. We placed Plato's Forms (Eidos) within the first ten notations. Aristotle's Ousia or Structure became the next ten from 11 to 20. Substances were 20-30, Qualities from 30-40, Relations from 40-50 and Systems 50-60. Within Systems we projected a place for The Mind.
It was great fun to be speculative! "Cellular automaton belong right within the Forms." Of course, that's just 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 TravelThe imagination can readily get ahead of facts, yet bridges and tunnels appear everywhere in nature. So, when we first took our known universe in a partition of 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, 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 136, 137 and 138. At Notation 136 you could be 874 miles above earth. At Notation 137, you would be about 1748 miles up and at Notation 138, just 3500 miles up.
"Einstein-Rosen!" was the charge. "It's the beginning of wormholes!" That put a smile on most faces. We surely need a shortcut to explore the Large-Scale Universe. So, now we are calling on the space cadets (6), especially Elon Musk of SpaceX, "Go out looking, but don't go inside any of those wormholes yet. We all need to be thinking about their structure."
9. A system for value, thinking, logic, reasoning and more. As you can see, our evolving Universe View began to be perceived as a structure for thinking, reasoning and logic. This article marks our first attempt to begin writing about this perception of our interior universe. And as a result, it has started to become apparent that this assumed numerical-geometrical structure of the universe had its own inherent logic and that this structure could also be applied to thinking, 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 happy to share our little skeletal models (including the one just below) for your inspection. We hope you find it all as challenging as we have, and that you have enjoyed taking this tour through our work.
More References:
- The simple math: http://doublings.wordpress.com/2013/04/17/60/
- An analysis of 15 key points: http://doublings.wordpress.com/2014/05/08/15/
- The first principles based on the concept of perfection
- A ten-step tour of the Big Board-little universe and the Universe Table
- Universe Table, An Ongoing Work: http://utable.wordpress.com/2013/11/01/1/
- Space Cadets to Star Wars VII: http://utable.wordpress.com/2014/06/03/starwars/
- An analysis of the work in progress
- Belief systems: http://bigboardlittleuniverse.wordpress.com/2013/03/21/belief/
