Reflections on the finite and infinite

“We have already seen that the infinite is nowhere to be found in reality, no matter what experiences, observations, and knowledge are appealed to.
Can thought about things be so much different from things? Can thinking processes be so unlike the actual processes of things?”

– David Hilbert, On the infinite, 1905

Infinite to the Finite and then Finite to Infinite

By Bruce Camber, Sunday, February 18, 2018

81018 is Infinity-Unity-Null-Unity-Infinity.  This website is about the finite-infinite relation. Little understood, there are five primary transitions in our thinking that might help to open the discussion about the very nature of the finite-infinite relation.

These are:

1. What is finite?  The 202 notations using base-2 exponentiation from the Planck units  create a container universe whereby space and time are finite, derivative and discrete. There is no past. All notations are always active and interdependent, and function constantly to define the whole as well as to define itself uniquely. Between the CERN-scale of fermions and the Planck-scale, theorized as a domain for strings, there are 67 notations.  Like the Chessboard & Wheat story, each doubling provides more than enough space for complexification and a much deeper definition of strings (all strictly mathematical definitions of the infinitesimal).  More

2. Observations:  Natural inflation and Euler’s Equation. The notations define a natural inflation, a quiet expansion and an exponential universe whereby Euler’s equation is maximized; the Big Bang theory is minimized. An analysis of six groups of numbers somewhat evenly spaced across all the notations follows the logic in light of the classically defined cosmolical epochs.

3. What is infinite? In 1925, the great mathematician, David Hilbert wrote, “We have already seen that the infinite is nowhere to be found in reality, no matter what experiences, observations, and knowledge are appealed to.”  Most scholars would agree even today. 

Maybe they are mistaken.  There are many non-ending and non-repeating numbers such as pi, Euler’s equation (e), and all the other dimensionless constants. Aren’t these numbers evidence or a manifestation of the infinite within the finite?

Yes, I believe access to the infinite is found in the primary dimensionless constants where the number being generated does not end and does not repeat. There are 26-to-31 such numbers that have been associated by John Baez, Frank Wilczek, and others to be necessarily part of the primary definition of the Standard Model of Particle Physics. There are over another 300 such numbers defined by the National Institute for Standards and Technology (NIST).  All are dimensionless constants that seemingly never-end and never-repeat. And, then there is Simon Plouffe; he has identified, through algorithmic programming, 11.3 billion mathematical constants (as of August 2017) which includes pi, Euler’s number, and more.  This use of “never-ending, never-repeating” as the entry to the infinite will be challenged. If it can be defended, then there are more connections betweeen the finite and infinite than David Hilbert and most scholars had ever anticipated.  More

The single most used and best known dimensionless constant is pi. Pi is everyone’s pi and it is our single best connection to the infinite. More

4. Doublings. Base-2 is a simple doubling of the Planck base untis that can be observed from the lattice generation through cubic-closed packing of the spheres such that triangles, then the tetrahedron then the octahedron are generated, and the doubling begins automatically at each notation. There is also the thrust within Planck Charge as well as within ther emergence of numbers within each generation of a dimensionless constant. More

5. The infinite.  If the infinite cannot be known as absolute space and time, it should be known for those characteristics of the finite that are perfect and reflect aspects of perfection. Three aspects are selected.
•   Continuity.  First, there is the continuity of numbers within the dimensionless constants. Second, there is the logic of number theory and logic.
•   Symmetry.  First there this the symmetry of ther spheres, then there is symmetry within the tetrahedrons and octahedrons, and there are constantly evolving symmetries and complex symmetries.
•   Harmony.  When two symmetries actively interact in a moment of time, there is a moment of harmony. Musicians and audiences here that perfection often.

Other pages to consider:
As a homepage:
Overview: (this page)
Expanded Overview: and
General Discussions:

Many people have been asked to provide some feedback about some part of this work. Until we have heard, “That’s wrong,” we will continue working on this effort that began in a high school geometry class.