The Planck Length is the smallest. The largest length is the Observable Universe.
Here are two simple charts with simple mathematics (doublings or base-2) that render a simple model that opens many questions.
The Planck Length is not a point because it has length. Points do not have length. And, if you were to multiply that length over and over again by 2, anywhere over 202.34 times, you will go out to the largest possible length, the Observable Universe. Called exponential notation, it is a very simple scale of the universe.
First, these ordered relations by numbers and geometries for so few notations are already helping students to understand the relations between disciplines. Looking up or looking within, there is a sense of real order where there was chaos.
This project is Science, Technology, Engineering, Mathematics (STEM).
We will be referring back to these two measurements throughout the next eight pages of this short tour to discern some of the other surprises as well as many of the other questions that are raised. On each page there are the arrows and a line. Below the lines there are references, links and informal discussions. Please come back to those sections after you have gone through all ten pages. So, let’s continue on and look a little further >>>
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 should paste in. Also, 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More notes about the how these charts came to be: The simple math The simple conceptual starting points An article (unpublished) to attempt to analyze this simple model.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.
Key Surprises: First, just the very small number of notations was a surprise. When we started at one meter and got down to the size of a proton in about 50 steps (at that time, we were dividing each notation in half), it seemed hard to believe. Then, when we got in the range of the Planck Length in another 66 steps, it was puzzling. When we went to the large scale and found only another 90 or so notations, we were flummoxed.
Consider notations 100 to 103. That range is right in the middle of the universe of sizes. ….in the middle! And, it is all so very, very human. How can it be that humanity is in the middle of this universe by length?
The universe divided in thirds. The old logic of the Small Scale, the Human Scale, and the Large Scale universe is in play, yet here the start points are quite different than the historical use of those terms. Here the very logical range for each is defined by simple math. What does it mean to look at the totality of the universe and it in thirds.
The simple geometries. If the Planck Length is defined as a single vertex at notation 1, by step 60, it becomes a major structural enterprise. The proton-fermion-electron appear to manifest at step 66. This small scale universe of geometry and numbers is unexplored. Perhaps it is the first step for a science and basic logic for perfected states within this continuum.