Finite or Infinite? Is That The Question?

Some of our high school students think our scientific community makes the study of Science, Technology, Engineering and Mathematics (STEM) all too difficult to understand and overly complex by defying a certain commonsense logic. (Reference #1)

We have been studying simple math and simple geometries from the smallest possible measurement of a length to the largest (Reference #2). It appeared to some of the students, based on this work, that the universe is obviously finite. They have been told that intellectually and historically, it is an open question. For them, “Make a choice and see where it takes you.”

These students also conclude, “Only God is Infinite. All things within space and time are finite.” (Reference #3) When asked about all the universals-and-constants and space-and-time, the concurrence is that these are the access paths, interconnections and transformations between the Finite and the Infinite.

For the best of these students, asking the question, “What is the Infinite?” is like asking the question, “Who is God?” And, they have answers.

Of course, as a result of a little coaching, they say, “First, God is Perfect.” When asked, “What is perfection?” they echo their coach: “Perfection is order-continuity, relations-symmetry and dynamics-harmony, all rolled into one.” (Reference #4) That amounts to an understanding of the Infinite without importing all the related history and revelation from the various faith statements with our very short history throughout our little world. The Finite is another story. We turn to Euclid for inspiration to provide the academic and religious communities with our simple observations and assumptions.

Hardly postulates and axioms, our statements are a praxis in-search-of theoria:

• Interior geometries. There are basic geometries within basic geometries. Two of the most simple platonic solids are the tetrahedron and octahedron. The simple interior structures can become exceedingly complex. (Reference #5)
• A domain that remains largely unexplored. We assume that among its many possible descriptions, the Planck Length could be taken to be a vertex. If so, there are over a million-trillion vertices within just the 60th base-2 exponential notation and then another two million-trillion with the 61st notation. (Reference #6) There are over 60 virtually unexplored domains from the Planck Length to particle physics.
• A range of notations. There are around 205.11 base-2 exponential notations (doublings, domains, layers or steps) within the Known Universe. (Reference #7)
• There are imperfect geometries. These appear to begin within the five tetrahedral “pentastar’ cluster and these are extended within the icosahedron and the Pentakis dodecahedron. It appears that this imperfection was first recorded within history in 1958 (Frank & Kaspers).
• The universe can be perfectly tiled. The simplest 3D tiling is with tetrahedral-octahedral-tetrahedral chains and clusters within those 205.11 layers. Also, within the octahedron are four hexagonal plates at 60 degree angles around the center point. These each extend as planes with abutting octahedrons for 2D tiling. This is the simple beginning of possible ways to tile the universe. For more, we turn to Penrose, Conway, and many others.
• In theory, the Planck Length is indivisible. It is, however, a specific length. If that conclusion is taken as a given, the Planck Length could be considered the indivisible unit in the historic Theory of Indivisibles and the start of the Finite and the transformation between the Finite and Infinite.

If these statements are taken as a given, then what kind of universe and what kind of science do we have? Should we re-examine the use of infinity throughout the ages going back to the ancient Greeks? Should we reconsider the theory of indivisibles? And, perhaps we should even reconsider the very nature of the Big Bang and its theory.

Of course, that is our agenda (Reference #8), our current focus for the immediate future.

References:

1. An associated article within LinkedIn titled, Order in the Universe

2. One of the earliest reflections on this work: https://bigboardlittleuniverse.wordpress.com/

3. Initially written in November 2012, this article was first posted on March 2013 within WordPress: https://bigboardlittleuniverse.wordpress.com/2013/03/21/belief/

4. In light of those constants, universals and the finite-infinite relation, the nature of perfection seems to follow: http://smallbusinessschool.org/page1695.html

5. Examining basic structure in basic ways: http://smallbusinessschool.org/page2546.html#TetraInside

6. A new domain to explore with exponential numbers of vertices: http://doublings.wordpress.com/2013/04/17/60/

7. There are around 205.11 base-2 exponential notations (doublings, domains, layers or steps) within the Known Universe

8. An analysis of 15 key points: http://doublings.wordpress.com/2014/05/08/15/

The TinyURL for this page is: http://tinyurl.com/finitePlanck

 

Every view is important. Yet, some views are more optimistic, creative and productive.

	Welcome, welcome, welcome. Thank you for joining us here. We are on an adventure and we need a little help and guidance. Back on December 19, 2011, our high school geometry class was introduced to the big chart on the left. It is a very simple view of the entire universe and everything within it, from the smallest possible measurement to the largest, all based on multiplying by 2 and very simple geometries. We were studying embedded geometries and asked, “How far within can we go?” The result, the chart, was helpful for many reasons, but we couldn’t find it anywhere on the web. We asked, “Are we off on the wrong foot?” We dubbed it the Big Board-little universe and began asking the experts about it. Equally perplexed, some encouraged us. We are now turning to family, friends, and neighbors for help. That big chart on the right measures 62″ x 14″ so it can be a bit awkward to use at your desk. We wanted to present the data in a more simple format to be printed on 8.5×11 inch paper or displayed on a smartphone so we created the chart just below. We dubbed it, the Universe Table. Though it is very much under construction, we’ve decided it will always be under construction. This is a long-term project, so we would like to ask a few questions to help us prioritize and focus on important things to do. Your Views, Worldviews, Universe View. All views are important. Yet, some views are more optimistic, some are more creative, and some more productive. Our hypothesis is that those who balance their views with a strong worldview and a truly integrated universe view will be the most optimistic, creative and productive. It is going to take us a long time to figure that out, so we need to get started so we are asking our guests — “Would you please take a very quick, very simple survey, then go on the tour. On the right, you will see a green arrow. Just click on it to begin. Both charts represent the same thing — the visible universe. The very smallest measurement is the Planck Length. The largest is the Observable Universe. From the smallest to the largest, there are less than 206 notations or steps. Click on each image to see the full-sized rendering. If you ready to take a tour, click here or on the right pink arrow.
_____________________________________________________________________________________________ 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 came back here after completing the survey, please click on the pink arrow on the right to go on the 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