POSTED FIRST ON APRIL 14, 2013
Sometimes the most simple concepts elude us.
Would you agree that two of the most simple parameters of science and mathematics are (1) smallest-to-largest and (2) multiplying-and-dividing by-2? Then, why, as a well-educated general public, do we not know the smallest and largest lengths of measurement?
We will assume that Max Planck was right in 1900 when he calculated the Planck Length. Certainly it is well-worth the time to study its derivation; however, for this discussion, take it as a given that the Planck length is the smallest unit of measurement of length.
The number is 1.61619926 × 10-35 meters.
The largest measurement of length is an on-going research effort; and although there are many different conclusions, there is a general direction and concurrence within the scientific community. Among the more recent calculations, we turned to the Sloan Digital Sky Surveys (SDSS-III), particularly her Baryon Oscillation Spectroscopic Survey (BOSS) measurements from March 2012 to establish a working range from the smallest-to-the-largest lengths. We are simply taking it as a given that the SDSS BOSS measurement is close enough. They have confirmed earlier statements, i.e. “The universe is 13.75 billion years old.” Others are as high as 13.798.
You would think it is a rather straightforward conversion, yet, even those calculations (convert years to a length) are diverse.
With their Scale of the Universe Cary & Michael Huang suggest 9.3×1026 meters (93 trillion light years). Paul Halpern, physics professor and author of the book, Edge of the Universe: Voyage to the Cosmic Horizon and Beyond, told me (email) that a better figure is 4.3×1026 m.
Yet, that end figure is not as important as the starting figure, it just helps to know when we are getting close to it.
To create a simple relation between everything in the universe, take the Planck Length and multiply it by two, then continue multiplying each result by 2 until we are out to that largest measurement. It is a natural progression much like the unfolding of life within cellular division.
So, based on their calculations, how many times will we multiply by 2 to go from the smallest to the largest measurement lengths in the universe?
That process is called base-2 exponential notation and the answers are quite surprising:
- NASA physicist, Joe Kolecki, calculated 202.34 notations or doublings. So, let us start with his figure.
- Others calculate it a bit differently. Halpern’s calculations give us about 204+ notations.
- Jean-Pierre Luminet of the Observatoire de Paris suggests around 205.11 notations.
Notwithstanding, that range, 202.34 to 206, is a very small number of doublings (notations, layers or steps) from the smallest to the largest measurement of a unit of length.
It is a cause for wonder. At the 202nd doubling of the Planck Length, the measurement is 1.03885326×1026 meters. At the 203rd doubling it is 2.07770658×1026 meters. And, at the 204th it is 4.15541315×1026 meters and the 205th doubled to 8.31082608×1026 meters. Within respectable universities they have used a number as high as 2×1028 meters!
202.34 to 206 doublings from the smallest measurement of a length to the largest. It is quite fascinating to find the thickness of a human hair (around 40 microns) at notation 101, the thickness of paper at 102, and diameter of an egg cell at 103.
Step back and look at the board. Here we have the universe, all of it, within a natural ordering sequence and we can begin to see relations between everything. A high school geometry class explored this simple model in December 2011 and we have been trying to understand why we have not found it anywhere in the academic community. It seems to be an oversight. We were studying nested geometries, starting with the tetrahedron, discovering the octahedron and four tetrahedrons inside it. Then the students discovered the half-sized objects inside the octahedron — six octahedrons and eight tetrahedrons. It was this progression that opened the smallest-largest question.
The purpose of the many discussions within these pages of the Big Board – little universe is to encourage students to explore each notation to see what is unique within it, to grasp the parameters and boundary conditions that could define each notation, to consider possible transformations between notations, to see how the constants and universals work within each notation, to grasp as many new concepts, ideas and insights as possible, and then to attempt to relate those insights to its smaller notation and then to its larger notation.
That is a lot of work.
So first, we will use it as a simple way to order information. Then, we will see if each notation opens new areas for speculations and analysis — the first sixty steps have never been critically explored. If just the simplest geometry of tetrahedrons and octahedrons is used, we have a simple structure for coherence throughout the universe in less than 206 notations. If we systematically add and analyze layers of complexity, more areas are opened to explore.
That is why these pages are here. Let’s explore the universe in the simplest ways possible, then ask, “What difference does it make?”
Editor’s Note: This page was last updated on May 12, 2013.