Dimensionless constants: Either Finite, Infinite, or A Bridge Between Them

The Finite and the Infinite

By Bruce Camber (Initiated: 6 April 2018) Updated: April 30, 2019

In some geographies your life could be threaten based on beliefs about the finite and infinite. People do outrageous things because of what they believe. They are so profoundly convinced about the truth of their beliefs, if disputed or not readily affirmed, they become hostile.

In the academic world the power of belief is also very strong.

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.

Perhaps Hilbert’s Logic Is Incomplete. 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 mathematically proven with pi, we recognize it is very difficult to prove; and, pi may well be the only one that is ever proven per se.

Standard Models. Scholars use different criteria to grasp the essentials of the Standard Model for Particle Physics. Michael Duff would have us focus on 19 dimensionless parameters; John Baez has 26; and Frank Wilczek, Max Tegmark, Martin Rees and Anthony Aguirre have 31. These constants are a necessary part of the definition. There are over 300 such numbers identified by the National Institute for Standards and Technology (NIST), all 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 between the finite and infinite than David Hilbert and scholars had ever anticipated. More…