By Bruce Camber, 2018
A key problem within our lifetime is our understanding of the infinite.
We so little understand it. Infinity’s obtuseness has made for crazy religions, crazy science, and crazier people. It’s time to rethink our commonsense view adopted through Isaac Newton when in 1687 he published his Principia and threw the world a penultimate screwball – absolute space and time. Absolutes are by nature abstract. We’ve needed more common grounds especially now that some of the really-really smart ones are calling for space-and-time to be thrown out! No kidding. Here’s a link to a leading proponent (whose office is just down the hall from Einstein’s old office) in Princeton, New Jersey .
Now, I’ll gladly stand among the discounted people by suggesting that infinity is better redefined by three rather commonly used concepts:
This definition of infinity necessarily permeates, defines, and gives rise to all that is finite.
To introduce this point of view is the purpose of these writings.
I had formulated this notion of infinity sometime in 1971; but as a conceptual frame of reference, though pleasing, it was hardly scientific. It went nowhere. It was too general and not necessarily relevant to current scientific research. Of course, continuity was the cornerstone of logic and science, but so was discontinuity. The net-net is a null.
Symmetries were well-defined, but then there were quantum asymmetries. Harmony was illusive and seemed more experiential than experimental.
Something changed for me in December 2011. When set within our recently-developed chart, Big Board-little universe (December 2011) whereby “everything, everywhere for all time” was indexed, and with its simple geometries and even more simple doublings from the Planck Length, continuity-symmetry-and-harmony seemed to be more formidable.
First, the numbers did not defy simple logic. Though a challenge, the chart maps a quiet expansion, a perspective created by this analysis of six sets out of 202 sets of numbers.
Second, doubling is a natural process, readily and graphically demonstrated, and it all begins with dimensionless numbers. It doesn’t get any more simple than that.
Third, in this model there is an implicit value component to space-time and matter-energy. And, that’s substantial. In 1975, I began my doctoral studies at Boston University thinking that the essence of the infinite was continuity, symmetry and harmony, not absolute time. Though largely unconstructed, it assumed a special perfection that could only manifest in a momentary way within the finite. Though creating a seismic gap between my professors and me, I held firm yet eventually had to leave that work, unfinished, in 1980.
Can infinity be defined in terms of continuity, symmetry and harmony?
Continuity creates order.
It seems that I have always understood the infinite to be a perfection of some kind. So, the key question becomes, “What has perfect continuity?” My answer: non-ending, non-repeating numbers. Enigmatic, these numbers are always unique and always the same. Think of pi and its 22 trillion digits (as of 2017). Pi deserves all the attention that it gets.
I’ll argue that it is the most important of all the dimensionless constants; thinking about John Wheeler’s quantum foam , my guess is that it is the initial and a primary gateway between the finite and infinite.
One of our scholars asks, “How many of these dimensionless fundamental constants are there? This depends on your opinion on some new developments, but my best guess is 26” (ninth paragraph).  His discussion is in context with the Standard Model. 
Of course now, everybody is looking for the unifying “something” to simplify this model and it has engendered formal studies that are currently summed up as the Physics beyond the Standard Model.  It’s their bread-and-butter today, the mother’s milk of physics. 
The scholars of National Institute for Standards and Technology (NIST) have over 300 fundamental mathematical constants. Their work in 2010 is most comprehensive. 
More recently another scholar, Simon Plouffe, defined over 11.3 billion  mathematical constants (as of August 15, 2017). The results of his computation programs called the “Inverter” are now part of a website maintained within the On-Line Encyclopedia of Integer Sequences (OEIS). 
One might ask, “How many lines are there between the finite and infinite?” At the level of the Standard Model of Particle Physics, the smallest simple number appears to be around 26. To begin to see the fullness of how the infinite encapsulates the finite, we’ll study the 300+ ratios from NIST. Then to begin to understand how exquisitely intimate it all is, we’d take the next generation of numbers (all ratios) that Simon Plouffe  has generated.
That is a lot of mathematics to integrate into this study to say the least.
If the actual interface between the finite and infinite is pi, the next challenge is to create a pathway between pi and all those numbers. We have used this little dynamic gif found within Wikipedia section about cubic close-packing of equal spheres. It is one of several ways to go from the continuous to the discrete, from so-called quantum foam to tetrahedrons.
Prior discussions within this website have been rather limited:
- https://81018.com/number particularly those numbers scholars thought were keys for understanding our universe.
- https://81018st .com/a0 and https://81018.com/a1 attempt to look at those numbers in light first two notations within our chart of the universe.
- https://81018.com/2017/10/16/eight/#Symmetry  where the image, a dynamic gif, shows the transition from circles and spheres to triangles and tetrahedrons.
- https://81018.com/fabric/ is from my initial attempt to get inside Langlands programs. Though unsuccessful, it was the beginning of the notation-by-notation analysis.
As of today (May 25, 2018) the subject has been picked up in this homepage. Thank you.