Tour #2 Step 3: Extremely-Small and Extremely-Large Numbers

Big Board - little universe

Big Board – little universe

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? Green Arrow

Pink Arrow

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Notes about Look-and-feel and Navigation: If a little thumbnail of any picture is displayed, simply refresh your browser and the full-size version hopefully will paste in. Also, if any of the letters from right column, particularly the Archives and Meta listings, are bleeding through the image of the Universe Table, please open your window larger (possibly to full screen). Usually if you click on the last sentence in each description you will go to the next page.

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.

TOUR #1. NEEDS EDITING. BENEFITS STATEMENT
REGARDING PRODUCTIVITY, INSIGHT AND OPTIMISM.
The universe is mathematically very small:
http://doublings.wordpress.com/2013/07/09/1/

TOUR #2. The very small scale universe is amazingly complex.
Assuming the Planck Length is a singularity of one vertex, consider
the expansion of vertices. By the 60th notation, of course, there are
over a quintillion vertices and at 61st notation well over 2 quintillion more
vertices. Yet, it must start most simply and here we believe the work
within cellular automaton and the principles of computational equivalence
could have a great impact. It’s mathematics of the most simple. We also
believe A.N. Whithead’s point-free geometries should have applicability.
Key references for more: http://doublings.wordpress.com/2013/04/17/60/

TOUR #3. This little universe is readily tiled by the simplest structure.
The universe can be simply and readily tiled with the four hexagonal plates
within the octahedron and by the tetrahedral-octahedral-tetrahedral chains.
Key references for more: http://bigboardlittleuniverse.wordpress.com/2013/03/29/first/

TOUR #4. And, the universe is delightfully imperfect.
In 1959, Frank/Kaspers discerned the 7.38 degree gap with a simple
construction of five tetrahedrons (seven vertices) looking a lot like the Chrysler
logo. As I said in the restaurant, we have several icosahedron models with its
20 tetrahedrons and call squishy geometry. We also call it quantum geometry
(just in our high school) and we guess, “Perhaps here is the opening to randomness.”
Key references for more: YET TO BE WRITTEN

Future tours: The Planck Length as the next big thing.
Within computational automata we might just find the early rules
that generate the infrastructures for things. Given your fermions and proton
do not show up until the 66th notation or doubling, what are we to do with those
first 65?

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