What is finite? And, what is truly infinite?
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.”
The students with strong faith statements said, “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 within our very short history throughout our little world. The Finite is another story. We turn to many people from Euclid to Einstein 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. However, even here 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 primary vertices (measurement determined by an increment of the Planck Length) within just the 60th base-2 exponential notation and then another two million-trillion within just the 61st notation (Reference #6). That uses the simple math of base-2 exponential notation. After the third and fourth notation, it could be argued that entire objects double in which case base-4 and base-6 could be used to calculate the expansion of what might be called secondary vertices. We are currently trying to discern how these expansions would work with those shared vertices that are not a double of the Planck Length. To say that it gets a bit confusing quickly is an understatement. Notwithstanding, here we find over 60 virtually unexplored domains from the Planck Length to particle physics.
- A range of notations. There are somewhere over 201 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-strongest-most interrelated 3D tiling is a tetrahedral-octahedral-tetrahedral (“octet”) ball, clusters and lines that define the 201+ layers. Also, within the octahedron are 2D tilings, three plates of triangles, four plates of squares, and four hexagonal plates at 60 degree angles around the center point. And that is just the tilings created within each octet. Other types of 2D tilings can be discerned by using squares or triangles from the abutting tetrahedrons and octahedrons. This study is within its most early stage; much more is coming about 2D tilings and their interactions with the octet 3D tilings. Also, we have much more to learn from people like Roger Penrose and John Conway. And, just perhaps, they might learn something from the students, i.e. an answer to the question, “What are the simplest first principles and starting points to build anything, anywhere for all times?”
- 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.
1. One of two key general overview and working article, Order in the Universe
2. One of the earliest reflections on all our efforts and work: Is it true that everything starts most simply?
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: Simple View of the Universe http://smallbusinessschool.org/page2546.html#TetraInside
6. Our first look at the progression of doublings. This listing was written to accompany an article for Wikipedia: Written in March 2012 to support an article for Wikipedia
Even between atheists and believers
Perhaps all it comes down to is an answer to the question, “Whose metaphor is more meaningful?” You will not find many atheists who deny science. They do not deny the constants and universals that are always in the back of the science textbooks.
There are three constants within the sciences that remain clear, in spite of quantum mechanics. The first is that there is order and continuity in the world. It is the basis of knowing. In every discipline there are multiple parameter sets where this is true. Beginning in mathematics, a rather pure form of thought, abstraction and representation, we then move into physics. It has multiple parameter sets as well. There is one for Newtonian mechanics, another for General Relativity and Special Relativity and yet another for quantum mechanics. Then chemistry and biology have their own parameter sets. All these parameters simply establish the boundary conditions of what is being measured within them.
Each has a formalized language. And, each has a metaphorical language that pushes into the edges of the unknown.
The sciences all embrace varying definitions of relations yet all of these definitions are understood by a symmetry function.
Specialized disciplines with each of the sciences hypothesize about the nature of the unknown, just beyond their limits of knowledge, and all these hypotheses are a study of the deepest dynamics of their discipline. The experience of insight, the “ah-ha” of the creative surge, is experienced as a concrescence of symmetries or harmony.
The atheists mostly object to the use of specialized language. They understand rules, mores, and societal law and order even though many are nihilistic, others narcissistic, and many both.
Yet, change will come. Some of these folks will begin to realize that time is not a fundamental frame of reference and that there are qualities of life that permeate everything in every way, and that these qualities empower order, relations, and dynamics, and that these three scientific functions with the faces of continuity, symmetry and harmony just might also be understood with very personal language. When and if they do, they are on their way to create a personal bridge to religion and some of the brave among them just may cross it.