Finite-Infinite Bridge: A Nexus of Transformation

Author: Bruce Camber  Initiated:  December 2014. An emerging document, last update: May 2020

The Finite-Infinite Bridge: In 1687 Isaac Newton was confused about the nature of infinity. And, his confusion became our confusion; and, it has become the world’s confusion. To create parameters within which to work without referring to infinity, Newton made space and time absolute. It was a mistake. More…  More recent [1][2][3]

Infinity to this day remains a problem for many in the academic community because it is too often interlaced with theological and religious language. The God wars between the arrogant among religious thinkers have caused many intellectuals to avoid those discussions altogether. It’s understandable, so most secular thinkers avoid religion.

Notwithstanding, since The Clark-Leibniz Correspondence (1715-1716) the debates about the finite-infinite relation have become increasingly heated.

A possible resolution to that conundrum is to use those terms that describe the universals and constants that originate in mathematics and science. Those terms should capture facets, a certain essence, that is part of both the finite and the infinite. Mathematics has had its own very special approach and together, I believe the bridge between the finite and infinite will be understood as a transformation center or nexus. More…

On one side we have an array of infinitesimal numbers, well-below the thresholds of measurement, that appear to be “out on the bridge.” Also, many of the dimensionless constants appear to cross the bridge, the foremost example being pi (π). Also, within mathematical logic there is a classification system called Ramsey’s theorem for pairs, where young mathematicians are attempting to bridge the finite and infinite.

This introductory page will remain active and open for updates, as will the following:

Our On-going Finite-Infinite Studies

1.  Index
2.  History Lessons
3.  Constants and Universals and Reality
4.  Finite-Infinite Intro
5. Finite-Infinite I
6. Finite-Infinite II
7.  Current homepage
8. The first five notations: A0, A1, A2, A3, A4 and A5.

Notes from Wikipedia on Infinity:

  • Our redefinition of the infinite: A qualitative expression of continuity (order), symmetry  (relations),  and harmony (dynamics) while the finite is the quantitative expression of continuity (order), symmetry  (relations),  and harmony (dynamics).
  • David Hilbert, 1926, On the Infinite
  • 1888 Richard Dedekind re-defined the term “infinity” and Georg Cantor used that definition to create the first set theory
  • Bernard Bolzano, The Paradoxes of the Infinite, 1851
  • In 1655, John Wallis first used the notation ( lemniscate) for such a number in his De sectionibus conicis,[21]
  • To Leibniz, both infinitesimals and infinite quantities were ideal entities, not of the same nature as appreciable quantities, but enjoying the same properties in accordance with the Law of Continuity.
  • The first published proposal that the universe is infinite came from Thomas Digges in 1576.[47]
  • Gauss said scientific theories involve infinities as idealizations (and in order to make for easy applications of those theories, when in fact all physically real entities are finite).
  • Zeno’s paradoxes, the first alert, in 450 B.C.E. Today, we have Planck’s base units. The Planck base units are empirical and are validated by the speed of light.