# Redefining points, point particles, and vertices

A word of caution. This website’s construct of the universe is different. With this page, it is gets more so. In December 2011 when we began this trek, the first 64 notations were a mystery to us. We wondered, “How do we understand something that is below the thresholds of measurement even though each notation has very specific values for length, time, mass and charge?” Long-long ago I remember not liking the definitions for points and vertices in our geometry textbooks. That goes back to 1961 in my high school geometry days; I felt those definitions were too limited and often circular.[1] Now, 61 years later, insights have opened to redefine both as well as many other terms used within this range known as the infinitesimal, our Notation-1 to Notation-64 out of a total of 202 notations. -BEC

Point particles also redefined. That definition has been very much in process.[2] It is hardly settled science. So, within these web pages a point particle is an infinitesimal, primordial sphere that emerges within Notation-1 and continues to emerge to this day and moment. It is only known logically and mathematically and are called hypostatic particles.[3] Around Notation-64, we are able to detect and measure aspects of quantum fluctuations. It is hypothesized that these spheres represent at least 64 different vertices, all functioning like those represented by points within classic geometry. These vertices first have all the functionalities of an infinitesimal sphere, and then those functionalities that are already well-defined within Langlands programs and string and M-theories. Other working theories that define some aspect of the infinitesimal will eventually be included.

When better understood, some of these vertices may also begin to look like known characteristics of hypothetical particles.

In the first instance, these infinitesimal spheres through the Fourier Transform are either gravitationally or electromagnetically active (attractorsrepellers) and then each builds from there.

So, yes, within this redefinitions of points, point particles and vertices, we’ve hypothesized that each becomes part of the functionality of everything finite, everything within the 202 base-2 notations from the Planck Time to the Age of the Universe Right Now. Again, there are no less than 64 doublings from the Planck scale to quantum fluctuations, so an entire science of the functionality of points/point particles/vertices at each notation may begin to be identified, especially within those studies that have not found a means to connect to the grid.

Within our 2013 Universe Table chart, we hypothesized that from Notation-1 to Notations-10 are forms and the mathematics of Langlands programs. Vertices look like automorphic forms. Hypothesized from Notation-11 to Notation-20 are structures and the mathematics of string theory and M-theory and the vertices look like the mathematics of strings.

Hypothesized from Notation-21 to Notation-30 are archetypal substances well prior to the Periodic Table of Elements which is well prior to the Standard Model for Particle Physics. Hypothesized from Notation-31 to Notation-40 are archetypal qualities. The closest we’ve come to a chart of qualities is here. Hypothesized from Notation 41 to Notation-50 are archetypal relations. And, hypothesized from Notation 51 to Notation-60 are archetypal systems.

More to come…

_____

[1] Laurie E. Bass, Randall I. Charles, Art Johnson, and Dan Kennedy, Geometry, Prentice Hall Mathematics, 2004, page 11: “Point: You can think of a point as a location. A point has no size. It is represented by a small dot and is named by a capital letter. A geometric figure is a set of points. Space is defined as the set of all points.” page 11

“Vertex: A vertex is a point where three or more edges intersect.” page 512.

Endnote: This definition of a vertex is unsatisfactory. When just fourteen-and-fifteen years old, I asked questions, “How do those point cohere? Who ties the knot or anchors or glues them together? What is going on between the two or more lines? Is there any energy along the line or within the enclosed space?” There were no answers at that time and there are still no answers today.

[2] Point Particle, Wikipedia, retrieved on April 22, 20: “Its defining feature is that it lacks spatial extension; being dimensionless, it does not take up space.”[Reference]

Endnote: In our redefinition of a point particle, each has unique spatial extension. Though generated by dimensionless numbers, each has specific quantities of length, time, mass and energy, yet all these quantities are below the thresholds of any possible direct measurement. Within this website, these are called hypostatic particles. The [Reference] just above for within Wikipedia goes to F. E. Udwadia, R. E. Kalaba (2007), Analytical Dynamics: A New Approach. Cambridge University Press. ISBN 978-0-521-04833-0

[3] Hypostatic particles. Hypostatic jammed packings of frictionless nonspherical particles, Kyle VanderWerf, Weiwei Jin, Mark D. Shattuck, and Corey S. O’Hern, Physical Review E 97, 012909, 2018

_____

References & Resources

Historic or traditional point particle defined:
1. Point Particle Model (PPM) and Superstring theory
2. Wikipedia. Because the first 64 notations are not recognized, Findzus E. Udwadia (USC) and Robert E. Kalaba (authors of Analytical Dynamics: A New Approach, (2007) said that the defining feature of the point particle is the lack spatial extension. Being dimensionless, they assumed that it does not take up space. They needed the 202 base-2 notations and to have recognized the 64 notations well prior to particle physics and beyond the thresholds of measurement.
3. Learning Constrained Dynamics with Gauss’ Principle adhering Gaussian Processes

_____

Email Social media, the press, television and the political class often miss the universal face of truth and justice which these emails attempt to convey. -BEC

_____

IM

@deseretmagazine and @DNewsOpinion Our problem will always be incomplete worldviews that compete for mindshare when every worldview is too small. We need a highly-integrated view of the universe to context concepts and ideas. Here’s a start: https://81018.com/

We need an inherent ethics: https://81018.com/ethics/

12:38 PM · Apr 12, 2022 @QuantaMagazine Thanks, QM. Deep within pi (π) is continuity which yields to symmetries which yield to harmonies and all things qualitative and infinite. Bring in the Planck or Stoney scale for the start of time, and in 202 notations (doublings) you have the universe!

_____

_____

Keys