**CENTER FOR PERFECTION STUDIES: CONTINUITY•SYMMETRY•HARMONY• USA•GOALS**•March 2019

**HOMEPAGES**: ASSUMPTIONS|DARK|EMERGENCE|INFINITY|Inflation|INTRO|REVIEW|Scholars|START

# On Bridging the Finite-Infinite

###### by Bruce Camber

**THE SPHERE STARTS WITH PI:** Although we can see and hold circles and spheres in our hands, there is something about pi (π) that is not finite. There is something about the “never-ending, never-repeating numbers” that do not describe what we understand to be finite *per se*. Yes, the formula for pi is a ratio that never changes, yet is constantly changes, never repeats itself, and never ends. Is it telling us that such a key *dimensionless* constant is always dynamic, in a constant relation? Ergo, is it infinite, too?

I think it is. This ratio, a dynamic relation, is what we might consider to be “really-real.” It fundamentally tells us something about the nature of the universe.

Some scholars calculate that there are 26 such constants (which includes pi) required to define the *Standard Model for Physics*. Others say 31. And, the folks at NIST say there are over 300 dimensionless constants that help to define physical reality.

Those four concepts, *dimensionles*s, *never-ending*, *never-repeating*, and *constant* either describe a bridge between the finite and infinite, or describe a quality of the infinite that resides within the finite but is not finite. I know it sounds entirely oxymoronic yet please keep an open mind to the concept. That sphere also inculcates the ideals of continuity, symmetry and harmony. Being the best representation of all these concepts and inherent equations gives it a primordial status.

**KEY QUESTION**: Given its nature described above and its ubiquity within our essential mathematics and physics, might we assume the sphere is the first expression of space-time, mass-energy *at the Planck scale*?

If an affirmative response is take as a given, how might it all work?

**The Sphere at the Planck Scale**. Within this infinitesimally small domain, the sphere has been known as a *plancksphere.* Going back to 1955, John Wheeler called it quantum foam. Perhaps you can imagine it as an extrusion within the finite-infinite relation as a constant stream of spheres, creating, filling and generating all of space-time.

Apply cubic-close packing and form-and-structure become emergent. Cubic-close packing is an inherent doubling function whereby geometric structures, particularly the tetrahedron and octahedron, emerge. The thrust, now a constant, endless flow, may well come from Planck Charge, light, and the never-ending, never-repeating numbers of pi and other dimensionless constants. It is instructive to follow any one of the numbers on our horizontally-scrolled chart where that logic flow can be analyzed.

**CONCLUSIONS**: Here is a new domain for logic, mathematics and a hypostatic science.

**1. The 64th Doubling**: Below current thresholds of measurement, an active registration of just 9.945379×10^{-25 }seconds and happening within a space of 2.981362×10^{-16 }meters, yet compared to the very first doubling at notation #1, the 64th is well-beyond ginormous. The complexity that can be logically and mathematically and geometrically developed can readily open up the particle zoo and every facet of it by the 67th notation.

It would see that spheres are being churned out somewhere in the neighborhood of 536×10^{42} units per second and aggregating (networking) with all prior notations.

2. **Prime numbers**. The eighteen (18) prime numbers from the first notation to the 64th are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, and 61. Are there 18 mathematical systems that can be readily shown to develop upon each other (with base-2 as the common denominator holding it all together)? What about the 26-to-31 dimensionless constants prior to the emergence of the Standard Model of Physics? My simple guess is that it will give us a level of complexity that reflects our current understanding and the sophistication of the tools we use to measure things. Causal Dynamical Triangulations (CDT), Regge calculus, fractal structure, and the flavors of the simplex will all find an appropriate place.

3. **The Dynamics of the Sphere**. To date our only images to summarize the potential dynamics of the sphere are here: *Let’s start at the very beginning until our universe is filled with sphere*s. Almost certainly, there will be more as we further study E8 Lie geometries and begin to engage ever-so-illusive amplituhedron with a string to “…a planar N = 4 supersymmetric Yang–Mills theory.” A scholar like Nima Arkani-Hamed declares that it’s “…equal to the perturbative topological B-model string theory in twistor space (an ever-so-positive Grassmannian).” Though a steep learning curve for most of us, the simplicity of our overall construct will make this classic Arkani-Hamed comment and the general subject much more approachable and understandable.

4. **All time is the Now**. All notations are active (dynamic) and evolving (changing). Past, present and future are understood to be perceptions or a sense of time that is encapsulated between and within sleep and sleep might be considered a recompile much like the system of a computing machine.

**Infinity**. **Re-open the door to redefine the concept of infinity**. We’ve all got to lighten up a little. It is obvious nobody is making real progress within the old-time debates, but some progress just might be made both within mathematics, physics and logic. *And* *more*…

**Everything you think, say or do immediately effects the fabric of the universe.**

The study of string theory will initially evolve around the work of Ed Witten at the Institute of Advanced Studies in Princeton. The study of quantum fluctuations and emergence will initially evolve from out of the work being done by many different groups including Steven Weinberg and his group at the University of Texas-Austin. To engage these studies from such an idiosyncratic construct will never be easy. Yet, it gets even more stretched and difficult with the following assertions: Obviously, within this 202^{nd} notation, there is a perception of past-present-and-future, a sense of time. This notation is 10.9 billion years and only about 2.84 billion years of it have emerged. *More*…

**Summary**. It is such a different model, it is hard to engage. It took me the better part of four years to realize in what ways this nascent model could become more than a STEM tool.

**My Themata**:

1. The primary search for unity begins with pi, the sphere, and the dynamics of the inside and outside of the sphere.

2. The relation is primarily real (vis-a-vis Leibniz-Newton).

3. Everything starts simple before it becomes complex. The need for “renormalization” tells us that we have not found a baseline for simplicity.

4. The faces of infinity are continuity/order, symmetry/relations, and harmony/dynamics.

5. There is a finite-infinite transformation that we begin to know through pi with its never-ending, never-repeating, always the same and then through the other dimensionless constants.

6. The sphere (Wheeler’s quantum foam or Plancksphere) manifests as space-time and mass-energy.

## __________

## Summaries

*Homepages from 2016*to April 2022

**Endnotes, footnotes, references and resources**

**Causal Dynamical Triangulations (CDT), Regge calculus, fractal structure, 2-D spacetime, and the flavors of the simplex**

## Challenge us. Coach us. We need all the help we can get.

Which concept is strongest? Which is weakest?