By Bruce Camber, 6 April 2018
What is finite and 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 and Euler’s equation (e), and then possibly all the other dimensionless constants. 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 (never-ending) and a deep uniqueness (never-repeating)? By definition isn’t never-ending and never-repeating part of our understanding of what is infinite?
Definitions. Take as a given that access to the infinite is found in the most well-known dimensionless constants where the number being generated does not end and does not repeat. Although that has been proven with pi, we recognize it is very difficult to prove and may well be the only one that has been proven per se.
Standard Models. There are 26 dimensionless constants used by John Baez, and 31 by Frank Wilczek (and-others) as a necessary part of the definition of the Standard Model of Particle Physics. There are over 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 scholars ever anticipated. More…