Yes, 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 its very nature:
1. What is finite? The 202 doublings from the Planck units to the Observable Universe create a container universe whereby space and time are observed to be derivative, finite and discrete. We have a sense of time; yet, nothing is truly past. All notations are always active and interdependent, and function constantly to define the whole as well as to define itself uniquely. From the CERN-scale of particles (and all the other particles of the Standard Model) to the Planck-scale, there are as many as 67 notations. Considered a domain for strings, the claim by many scholars is that it is too small for anything else.
But, just consider 64 of those doublings. We know what defines the Planck units. What more might be defined within each of those 64 doublings (domains or notations)?
Let us return to the Chessboard & Wheat story.
Each doubling provides more than enough space for complexification and a very gradual, systemic definition of strings. At first, this progression is mathematically-defined, just numbers, with no apparent physicality that can be measured, each doubling builds on the prior, from the most-simple to the complex. And yes, all 64 are obviously infinitesimal.
2. Observations of a natural inflation. These doublings define a natural inflation and quiet expansion; it directly challenges the Big Bang theory. An analysis of six groups of numbers somewhat evenly spaced across all the notations begins to follow the logic/research that define their cosmological epochs. More…
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.” Even today, many scholars would agree, but perhaps Hilbert and those scholars are mistaken. Consider the non-ending and non-repeating numbers such as pi, Euler’s equation (e), and possibly all the other dimensionless constants. If something is never-ending and never-repeating, how can it be finite? If we take these numbers as they are, in the most simple analysis, aren’t these evidence or a manifestation of the infinite within the finite? Isn’t this a deep continuity?
All are dimensionless constants. Never-ending and never-repeating. If you can, try to empathize with those words, never-ending and never-repeating. How could that ever be finite? Our historic problem is that we try to impute too much into the infinite. We tend to drag all of history with us with all the suspicions and problems.
Yes, I believe access to actually begin to understand the infinite is to be found in the primary dimensionless constants where the number being generated does not end and does not repeat. As a necessary part of the definition of the Standard Model of Particle Physics, there are as many as 26 such numbers given by John Baez and 31 by Frank Wilczek (and others). There are over 300 such numbers defined by the National Institute for Standards and Technology (NIST). 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 scholars ever anticipated. More…
The most-used and best-known dimensionless constant is pi. Pi is everyone’s pi, our single best connection to the infinite. And, every equation that uses pi qualifies! More…
4. Doublings. The simple doubling of the Planck base units appear to generate lattice through the cubic-closed packing of the spheres such that triangles, then the tetrahedron, then the octahedron, are manifest. Perhaps part of the thrust of Planck Charge is the emergence of numbers within every dimensionless constant. With tetrahedrons and octahedrons all space and time can hereinafter be tiled and tessellated (100% filled). More…
5. Faces of the infinite. If not absolute space and time, within these studies, the infinite may be known for three characteristics within dimensionless constants and basic symmetries that define the finite:
• Continuity. There is the continuity of numbers, first within the dimensionless constants, never-ending, never repeating, and then in creating the perfections that are simple geometries. Here is the logic of number theory and logic itself.
• Symmetry. The symmetry of the spheres, then the symmetry within the tetrahedrons and octahedrons, constantly evolve from simple to complex symmetries.
• Harmony. When two symmetries actively interact in a moment of time, there is a moment of harmony. Musicians and audiences often hear that perfection. Perfections are places and times when the infinite intersects with the finite.
These facets of the infinite are keys to more fully understand the finite and vice versa.
Our scholars struggle in a different way:
• A chart, The Quantum Structure of Space and Time, editor David Gross, Solvay 23, 2005
• A chart, Dimensionless constants, cosmology and other dark matters Wilczek-Aguirre-Reese-Tegmark article, 2006
These two charts are over ten years old, yet still summarize current scholarship.
Related pages. First, the URL for this page is https://81018.com/finite-to-infinite/
Results related page: https://81018.com/relations/
A study group based on this page: https://81018.com/s3a/
This discussion began as a 2016 homepage: https://81018.com/2016/10/16/infinite/
The next step is to attempt to bring the dimensionless constants, the simplest geometries, and all those ratios together within a transformation nexus.
Scholars: Many people have been asked to provide some feedback about our work. Until we have heard, “That’s wrong,” we will continue to try to learn as much as possible from current scholarship. Because there are so many fundamental intellectual problems that scholars have been struggling with for over 50 years (Big Bang Theory), over 100 years (Planck units, special & general relativity), over 300 years (nature of space and time), over 2300 years (the nature of bounds and the boundless, i.e. Euclid’s elements), and over 30,000 years (nature of infinity), we will ask, “In what ways might our insights address those historic problems?” knowing that this effort began in a high school geometry class. Thank you.