2013: From extremely small to extremely large numbers

What have we learned in 2013?!?

First, we stretched well beyond our comfort zones.
We started with the two key numbers, Planck Length – 1.61619926×10-35 meters
or .000 000 000 000 000 000 000 000 000 000 000 016 161 992 6 meters
and the size of the observable universe: 8.79829142×1026 meters 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 lense 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. If we were to 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.

Notes about the how these charts came to be:
1. Articles authored by Prof. Dr. Frank Wilczek:
• Scaling Mt. Planck
• C. Alden Mead’s letter and Wilczek’s response in Physics Today
• Wilczek’s August 2013 Lecture notes on units and magnitude
•  If you like that paper, also read this one.
2. This giant puzzle called the universe:
• The simple conceptual starting points.
• Analyze this simple model (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.
3. Wikipedia on the Planck length. Wikipedia on the Observable Universe

Vertices as building blocks. If we take it as a given that that the Planck Length 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.

Letters to experts:
Ed Frenkel, author of Love & Math

1. Social media begins at Step 119, which is within the size of a home. It also involves several steps for the actual transmission of information within wires, to satellites, and stored within computer hardware. All of those details are not as important as what I have posted.
2. We all live, work, and enjoy life usually within a 100 mile radius of our home. That involves steps 120 to 133. What happens outside of those steps is not important to me.
3. To me, my friends are the most important people on earth.
4. If we give Barack Obama (United States), Vladimir Putin (Russia), and Xi Jinping (China) time together, they will work out their differences and focus on ways to help the world.
5. I would like to travel to Washington, DC, Moscow, and Beijing to learn, first-hand, how these governments work.
6. No nation should consider itself to be the best; we all need to strive to get along with everyone.
7. The Big Board-little universe was driven by geometry first and base-2 exponential notation second,
which is fascinating. That the entire universe has the possibility of having that deep-seated geometry in 202-to-205 steps is especially intriguing.
8. Given that each notation is related by geometries and numbers, the parameters of continuity and symmetry take on new meaning.
9. The Big Board-little universe makes astrophysics and cosmology more approachable.
10. The transition from one notation to the next must involve and creatively use all the universals and constants that we currently understand. This opens another possible world for exploration and speculation.

Rolf Dieter-Heurer, CERN Director General. He employs over 10,000 scientists and asks, “Are scientists getting it wrong?

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