Please note: Many of the links within this article have been updated. If some links continue to go dead pages, please advise me. Many linked references open a new window and go to Wikipedia. Thank you. -BEC
Quick Answer: Yes. The entire Universe and everything within it is mathematically notated and necessarily interrelated, all within just 202 doublings from the smallest measurement of space and time, the Planck Length and the Planck Time respectively, to the largest, the Observable Universe and the Age of the Universe.
Key Question: Have you seen an exquisitely detailed view of the entire universe all on a single chart? In these 202 steps (or sets, notations, layers, groups, clusters or doublings), it goes from the smallest logical measurement of a length (the base unit called Planck Length) to its currently-known largest value, the approximate size of the universe. It all started in a high school geometry class so it is relatively straightforward and easy to understand, yet it opens some mystery as well. It is difficult to figure out how to interpret and work with the first 65 steps. These are extremely small and, to date, have not been addressed as such by the academic community. Yet, these steps may open a way to understand our universe and ourselves in new ways.
Let’s take a look, here within a new window.
At the very top of the chart there are two rows of the most basic three-dimensional figures. The top five are named by Plato and his school so we simply refer to them as the five Platonic solids. It seems curious that only a very select group of people ever look inside these figures. If children did, this simple view of our universe would be second nature. Take any of those figures and divide each edge in half and connect those vertices (opens in new window). Each little circle is a vertex. Keep doing it. In just 101 steps, you will be approaching what most scientists believe is the smallest possible measurement in this universe (the Planck Length). Max Planck laid the foundations for quantum theory and received a Nobel prize in 1918. He was one of the first to recognize Einstein’s gifts and became his mentor and friend. He formulated his initial measurements in 1899 and 1900. These most basic measurements have been around for awhile and today are generally considered to be among the fundamental constants of our universe. To make things a little easier we should start at the bottom of the left-three columns of the chart at the Planck Length, 1.616199(97)x10-35 meters. Others use the simple figure, 1.616×10-35 meters.
The next step, multiplying each result by 2, is an application of base-2 exponential notation. Now, let’s move up the chart. At step 101 at the top of those columns on the left, we emerge with the width of a fine human hair. Multiply that by two and you are at the width of a typical piece of paper; that is step 102 on the right.
Now go down those three columns on the right side of the chart. Continue to multiply by two. In just over 101 steps you will have gone out past the Sun, then exited the Solar System and then the Milky Way, and quickly pushed out to be in the range of the edges of the observable universe.
We wanted to give this chart a playful name so it is called, Big Board – little universe.
Big Board – little universe: From the Planck Length to the Edges of the Observable Universe.
Yes, this project began in December 2011 in River Ridge, Louisiana just a few miles up river from New Orleans (NOLA) and just downriver from the NOLA airport. Within a few hundred feet of the river is the Curtis School. Though well-known for football, their academics are very good. In the geometry classes they had been studying the platonic solids. Strange things can happen when one is invited to be a resource teacher, essentially just an assistant for the students and their teacher, Steve Curtis, who is part of our extended family.
December 19, 2011 was the last day before the Christmas break. What a day to be a substitute! One quickly asks, “How do you keep their attention? What could catch their imagination?” For example, “How could one make that simple dodecahedron (pictured) a bit more interesting?”
These students had already done model building with tetrahedrons and octahedrons so they could begin to explore the inside structures of the basic five.
Up until that point, the dodecahedron had not part of that effort. To make it simple, we asked, “Why not make each face of that dodecahedron out of five tetrahedrons (pictured)?”
That makes the familiar strange. Instead of a simple dodecahedron, this one had 60 external faces
Indeed. That object is known as the Pentakis Dodecahedron. We filled the inside cavity (pictured) with Play Doh. In a few days, that unusual object was removed and the obvious pieces were carved out . It was in this process when the key evocative question was asked, “How many steps within would we have to go to get to the Planck length?” We assumed thousands and found just over 100. Flummoxed! “Why haven’t we done this before? Could it be that it’s just too simple?”
It was a straightforward task to do the simple base-2 math to create the first draft of what would become a rather big board. On December 17, the first draft was printed at Office Max in Harahan, Louisiana. Their widest paper for this kind of thing was 24 inches. “Let’s do it.” The resulting chart measured ten feet long. It didn’t take long to agree that it was too big and awkward so on the next day, two smaller charts, 12″ by 60″ were printed.
We put the two small charts on the left and right side of the class and then cut that ten-foot board in half and put the top section in the front and the bottom in the back. The setting was magical.
Now, there is a huge history of work about which we were not aware that used base-10 exponential notation. Kees Boeke, a high school teacher, started that work in 1957 in Holland and it had become a staple of the classroom to study orders of magnitude. Although our “big board” is quite analogous to Boeke’s work, it has a very different sense of itself. Instead of multiplying and dividing by simply adding or subtracting a zero (0), we begin with exacting measurements given to us from Max Planck. Second, we have all of our geometries with us. So, our chart is much more visceral; it has 3.3333+ times more notations. It emulates natural cellular growth and chemical bonding. Now, that was enough to get us going, yet we knew along the way we would find many other foundational reasons.
Not too much later, we decided to start at the Planck length and just multiply by two. It worked out better and kind-of-sort-of confirmed our earlier work. That became our next version 2.0.0.1 which you see here.
What does it mean and what can be done with the data?Our universe view initially had 202.34 to 205.11 steps. Using just the doublings of the Planck Units, there are between 201 and 202. Notwithstanding, this chart is a simple tool to help order information. When we began finding simple math errors within Version 1, we turned to the professionals. A leading astrophysicist said, “There are 205.11 notations.” Then on May 2, 2012, a retired NASA physicist, Joe Kolecki, made the calculation based on the results of the Baryon Oscillation Spectroscopic Survey (BOSS). He reported 202.34 notations. We trusted them both so we used that range. Then, in December 2014 we emerged with our own figure based simply on the doublings of the Planck Time and the 13.78 billion years, estimated age of the universe Yes, we found over 201 and somewhere around 202 doublings.
The Planck Length, the first step and the next 60 steps. We have thought and thought about the Planck length. It is an elusive concept defined by three fundamental physical constants: the speed of light in a vacuum, Planck’s constant, and the gravitational constant. Yet, what is it? What is happening at that infinitesimal level. For over 100 years, people have attempted to define it more richly than 1.616×10−35 meters, so we knew that our simple answer would be challenging us to go further for a long, long time.
It’s a puzzle with many puzzle pieces with no images or colors on them. Do you have any clues? It’s January 12, 2012. Our most current work is our home page. So come back and visit and see where we are in this grand process of exploration. Perhaps you have some ideas for us. Please don’t hesitate to contact us. We need all the help we can find! Thank you. -BEC