Format: This visualization will be created on a canvas within your mind. I’ll be trying to create that visualization with mostly words alone so I’ll need your help to paint the picture. To help formulate that picture I will rather informally comment about the images that I see and I hope you can begin to see as well, possibly even better. The words to create our visualization will be within a block quote; my comments will be formatted just like this paragraph.
Notations #1-3: Picture a circle. It has just two vertices and it is defined by an equation that contains an irrational number called pi. When it is used to generate anything, it instantly becomes transcendental. The infinite becomes finite and you have a circle. In the first notation, each of the Planck base units double. However, these base units are defined by an array of formulas. Though some call these Planck units “a singularity,” it is truly a diversity of absolutes, constants (both physical and mathematical), transfinites, and universals. If it is called a singularity i a gross sense, it is unlike any other singularity heretofore defined. There is an infusion of numbers that have specificity and it is the first introduction of physicality, but this physicality is not like then physicality we know. When it first doubles, there is not much to it. Yet, by the third doubling, it begins to approximate our very first image that comes from a dynamic gif within Wikipedia under close-packing of equal spheres.
By the third notation there are 64 scaling vertices. We begin with a single circle that becomes a sphere. With eight scaling vertices there are four base spheres. With 64 scaling vertices, there are as many additional spheres as is required to do sphere stacking such that lattice is generated, and the first triangles emerge. It would require all nine spheres as pictured and the additional nine green spheres as demonstrated. That lattice generation to create the lines, triangles, tetrahedrons, and octahedrons is part of the opportunistic thrust of creation.
Comments: You know the old formula, π r2; however, it appears that not many have thought about it as a possible beginning point of creation. There are other possibilities and we will explore these as we progress. But π is simple-but-complex; analyzed now out well over a trillion places, it is never-ending and never-repeating. And, it certainly is deeply rooted within our common history. The recognition of the numbers defined by pipredates Pythagoras (ca. 570 to ca. 495 BCE). Within Wikipedia’s explanation of pi, there is a reference to the book, Pi Unleashed, by Jörg Arndt and Christoph Haenel (Springer-Verlag, 2006 ISBN 978-3-540-66572-4/ English translation by Catriona and David Lischka); they claim that the earliest written approximations of π come from Egypt (1850 BCE) and Babylon (1900–1600 BCE).
We will have to examine the nature of numbers and how numbers shape geometries. To do so, we’ll review the insights of the greatest mathematicians and philosophers throughout our history and then see what our current scholars say.
Tetrahedrons
Notation #4:What might happen with the 512 new scaling vertices? The tetrahedrons and octahedrons could readily begin to double. One might also conclude that the spheres continue to double as well. Given that the Planck Length doubles, these new objects are twice as large as the objects within notation #3. The build out might begin looking for something like those tetrahedrons and octahedrons scaling up three times within this first illustration. Inside each tetrahedron is a half-sized tetrahedron in each of the four corners and an octahedron in the middle.
Consider the image on the right. The purple number, 1, is the smallest tetrahedron. The green number, 2, is the next larger and the yellow, number 3, is the entire figure displayed here. Just under the 3 is the octahedron, in the middle, surrounded by tetrahedrons. The octahedron is comprised of a half-sized octahedron in each of the six corners and a tetrahedron in each of the eight faces. Also, within the octahedron are four hexagonal plates and everything shares a common center point.
Here is a single tetrahedron with a tetrahedron covering each of its four faces. Each tetrahedron picture here is no less complex than the one just above.
The model just above only has 33 vertices so quite literally this perfectly-fitting form could be about 20 times more complex assuming 512 vertices. Each face could share 15 vertices so you might picture this object with a similar object attached to each of the four faces. Each of these would require just additional 18 vertices each for a total of just 72 vertices for the addition of these four new tetrahedrons. Just to keep some focus on it all, we have used just 105 of the 512 new vertices.
The resulting object has no special distinction. Yet, with the addition of just two more tetrahedrons, it introduces a radical new idea, the beginning of spaces for quantum fluctuations.
Five tetrahedrons all sharing a common center point creates a gap of about 1.5 degrees. One face of the icosahedron is pictured here. Five tetrahedrons share a common edge in the center. All four faces are similarly flexible. Among the high school students, it is known as squishy geometry. Another word for it is quantum geometry.
Much more to come…on Saturday, May 13
Prime numbers: Another possible key to understand diversity. The hypothesis is that each prime introduces a new constant that continues to more deeply define everything. The prime numbers below 202 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, and 199.
One of my many articles-in-process, Measuring an Expanding Universe Using Planck Units, studies a groups of the Planck units doublings based on a prime number, particularly 31, 67, 107, 149, 173, and 199.
The number, 1, is not a prime number. It probably should be the listing of the Planck base units. Today it is assumed that these base units constitute 0, and 1 is for the first doubling. That assumption will be reviewed over and over again.
Here is a single tetrahedron with a tetrahedron covering each of its four faces. Each tetrahedron picture here is no less complex than the one just above.
Five tetrahedrons all sharing a common center point creates a gap of about 1.5 degrees. One face of the icosahedron is pictured here. Five tetrahedrons share a common edge in the center. All four faces are similarly flexible. Among the high school students, it is known as squishy geometry. Another word for it is quantum geometry.
Worldviews limit perspective 