Tour #2: Step 1. The Universe Is Very Small

Big Board - little universe

Just 202 to 206 exponential notations for the entire known Universe?

“No way! Impossible. That’s just impossible.”

We, too, couldn’t believe it at first. We triple-checked our simple math,” then added, “And, the first 101 notations only bring us up to the width of a human hair at the very top of this chart.” The response, “What? That’s only 101 to 105 steps to the edge of the universe? …from the width of a hair? That’s very hard to believe.”

But, the numbers are the numbers. And, it opens a very different view of our universe. It’s more simple and more mysterious than most of us think.

The total grains of wheat: 18,446,744,073,709,551,615

The total grains of wheat: 18,446,744,073,709,551,615

The first 64 notations open our very small universe for exploration. Fermions and protons of theoretical physics emerge at notation 66.

At the very bottom on the left is the Planck Length. It is a specific length. It is not a point. It can be multiplied by 2.

Remember the old fable about a farmer and the king and the grain of wheat on the first block and what happens when you multiply it by 2, and each result by 2? It is the “Wheat and Chessboard puzzle.” When based on the Planck Length, what happens in those 64 steps is a bit of a mystery. But there is a lot of work — logic, research and mathematics — that could be immediately applied. We can actually begin to make a few guesses about what happens in first 64 notations (layers, steps, or doublings). But, we’ll hold that for later.

This Big Board on the left divides the known Universe into two sections. The next division would be into three sections. These would be:

The Small Scale Universe: Notations 1 to 67-68-and-69

The Human-Scale Universe: Notations 67-68-69 to 134-to-138

The Large-Scale Universe: Notations 134-138 to 202-to-306

These three scales are an excellent place to begin. Most of us would say that we spend our life within just 68 notations. The goal of this project is to have you engage as many notations as possible!

Simple is simple and small is small. One of our sixth-grade science classes understood the basic construct for the Big Board – little universe. Most of the class picked it up quickly yet with some amazement. They had to examine the numbers to believe it. And, once they saw how numbers grow exponentially, they also began to see how the interior constructions of the tetrahedron and octahedron began to pull it all together. These children wanted more. We hope you want to see more, too.

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) that seem to 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, let’s look even deeper.

Green ArrowPage 1 of 3.

Pink Arrow

______________________________________________________________________________________

Notes about Look-and-feel and Navigation: If any of the letters from right column, the Archives and Meta 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:

First, there are three 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

Tour #2: Step 2. The Universe Is Simple.

From the Planck Length to the Observable Universe

From the Planck Length to the Observable Universe

How simple is it? Multiplying by 2. Mathematically, that’s elementary. The result, somewhere over 200 base-2 notations from the smallest to the largest measurements of a length, is a simple view of the universe. The diameter of the human egg is at notation 103. The human sperm is a bit smaller within notation 100. From conception to birth, life begins within the mid-range of the universe; it seems sweetly logical and simple. The Big Board and Universe Table also seem like a reasonable, efficient and simple way to order all the information in the universe.

Divide by three. That results in two additional key notations that define the beginning and end of the Human Scale, the mid-range of this known universe.

The Transition between the Small Scale and Human Scale. This simple view gives two more areas to study the order of the universe. Besides the explosion of life in the mid-range, there is quantum tunneling for the explosion of particles and atoms in the transition from the small scale to the human scale (notations 66 to 69).

The Transition between the Human Scale and Large Scale Is Speculative.     Although scientists have been writing about Einstein-Rosen bridges and tunnels, since the 1920s, nobody has actually seen one. Today we know them as wormholes.

Wormholes. Nobody has made a prediction as to where these tunnels are located. With the simple view of the Big Board – little universe, one could make a projection that these wormholes are located between 136 (874 miles above earth) and 138 (3496 miles above earth), the transition from the human scale to the large scale universe.

First use of the word, wormhole: “…topologists would call (it) “a handle” of the multiply-connected space, and what physicists might perhaps be excused for more vividly terming a wormhole.” — John Wheeler in Annals of Physics, 1959

Page 2 of 3Green Arrow

Pink Arrow

_______________________________________________________________________________________________________________________

Notes about Look-and-feel and Navigation: If any of the letters from right column, the Archives and Meta 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.

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

________________________________________________________________________________________

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?

Tour #2: Summary Review, Speculative Possibilities, Onward and Upward

UT

Welcome back. Hopefully you have had a week to think about the first tour. We’ll review it, then we’ll go further in depth. This information is a new frame of reference. It gives us the simplest possible model of the known universe in an ordered relation. It has surprised many.

This is a new tool to engage the universe and to envision the unexplored.
Base-2 exponential notation is just a group of fancy words for multiplying by 2. You learned how to do that very well throughout elementary school. Yet, for the first time you are applying it to everything in the universe from the smallest to the largest measurements of a length.

It is as simple as simple can be, yet it’s new. It’s different. It’s accurate and it is deeply informative. Yet, from the first tour, there was push back, “The universe is so vast, so beyond human conception, something must be wrong with your math.”

It begged the question and incredulity, “You mean just by multiplying by 2, we reach the edges of the observable universe in just 205+ doublings?” It becomes even more of a stretch when you see that going from the Planck Length to the human egg takes 103 of those steps. Yes, from the diameter of a human egg, multiplied by 2, and each result by 2 over and over again, just 103 times, puts us out to the Observable Universe. The initial response, “That’s impossible.”

Nobody expected to find just 202.34 to 205.11 notations, or doublings, layers or steps. People stopped right there. They just couldn’t believe it. “Then, there is something wrong with your logic.” Yet, the math is the math and it does compute. The logic is the simple logic and it also computes.

So, we say, “Please live with it for awhile. Let it play with your imagination. See the universe in an ordered relation by size. It is novel and there is something special going on here with numbers and geometries. There so many questions that can be asked about each of the 205+ base-2 exponential notations. Seeing the universe from the smallest to the largest by length is worth exploring further.”

Let us explore a bit more deeply. There are many, many unknowns. You will find mostly guesses from notations 1 to 65. There are many other blanks in the 70s and from 170 to 202. The goal is to have an entry for every notation because each notation builds on the prior notation. Perhaps with some reflections we might emerge with rational explanations to understand the relations and dynamics of each and between each.

Big Board - little universe

Green Arrow

Pink Arrow

ArrowPinkRight

_____________________________________________________________________________________________

Notes about Look-and-Feel and Navigation: Links from the headers below the line go to the Index page. If any of the letters from right column, particularly the words, Archives and Meta, are bleeding through the image of the Universe Table, please open your window larger (possibly to full screen). If the header for this page is in more than two lines, you also need to open your window a little larger. If you’ve came back here after completing the survey to study further, you can click on the pink arrow on the right to review the second tour of the Big Board-little universe.

Footnotes: On every page there are references and more notes about the how these charts came to be.
The very-simple, philosophical foundations started with concepts of perfection and perfected states within space-time
The simple conceptual starting points
An article (unpublished) to attempt to analyze this simple model that seems to suggest that time is derivative of numbers and space is derivative of geometries. 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

This project began when we looked inside a tetrahedron and octahedron (two of the most basic geometric figures).1 Think of the embedded Russian (matryoshka) dolls. Usually there are no more than ten. Yet, here inside each tetrahedron there are four half-size tetrahedrons and an octahedron. Inside the octahedron are six half-sized octahedrons and eight tetrahedrons all sharing a common centerpoint and many common edges. It would seem that one could just kept going forever. Yet eventually you will reach the Planck length and can go no further. To standardize our study, we started at the Planck Length and multiplied it by 2 until we were at the Observable Universe. We were surprised to discover only 202-to-206 notations (or steps or layers or doublings) to go from the smallest to the largest measurements of a length.

1 All tetrahedrons and octahedrons have that interior perfection described just above. It appears that these basic objects transform dynamically in ways that capture basic processes within nature. Over the years we will be doing the work to explore these transformations, however, there is a website to learn more about such transformations today: http://loki3.com/poly/transforms.html

The simple math from the Planck Length to the Observable Universe

Welcome to a most simple view of the entire universe and everything within it. Each step is necessarily related through the simplest math and geometries.

Big Board - little universe

Introduction. Within the next ten pages, you will see our universe as we did in our high school geometry classes back on December 19, 2011.

On the left is a small image of what we dubbed, the Big Board-little universe. We then wanted to present the data in an even more simple format. So, on the right is an image of what we call, the Universe Table. That’s still being developed and has not yet been used in a class.

This is an introduction… just an initial tour. Because you can come back any time, we would like to challenge you to go through all ten pages in ten minutes so you get the big picture. Of course, you can take as long as you want. Please set your own pace.

Thank you for taking time with those survey questions. Now, on the bottom right of each page, you will see a green arrow. When you are ready to move on, just click on it. In the bottom left corner of each page, there is a pink arrow. If for any reason you need to go back a page, click on it.

Both charts represent the same thing — the visible universe. The very smallest measurement is the Planck Length. The largest is the Observable Universe. This link will take you to next page.

UT
Pink ArrowGreen Arrow

__________________________________________________________________________________________________________

Notes about Look-and-feel and Navigation: If any of the letters from right column, particularly the words, Archives and Meta, are bleeding through the image of the Universe Table, please open your window larger (possibly to full screen). If the header for this page is in more than two line, you also need to open your window a little larger. To go to the next page, you can click on the green arrow yet usually if you click on the last sentence in each description you will go to the next page as well.

More notes about the how these charts came to be:
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

This project began when we looked inside a tetrahedron and octahedron (two of the most basic geometric figures). Think of the embedded Russian (matryoshka) dolls. Usually there are no more than ten. Yet, here inside each tetrahedron there are four half-size tetrahedrons and an octahedron. Inside the octahedron are six half-sized octahedrons and eight tetrahedrons all sharing a common centerpoint and many common edges. It would seem that one could just kept going forever. Yet eventually you will reach the Planck length and can go no further. To standardize our study, we started at the Planck Length and multiplied it by 2 until we were at the Observable Universe. We were surprised to discover only 202-to-206 notations (or steps or layers or doublings) to go from the smallest to the largest measurements of a length.