Despite the elusive, back-and-forth nature of our conversations--all of the random tangents, anecdotes, and arbitrarily examples seemed somehow to push toward the same direction. I've come to recognize Time as a duality of sorts; simultaneously absolute and relative. How can it carry both connotations in a singular, consistent definition? Perhaps it embodies more than one.
Therefore, we ought to sort out what we mean when we seek to describe or characterize Time--considering the context, intention, and semantics that will correlate to the discussion. If we separate Actual Time (or Space-Time; that is, the absolute, unyielding, immeasurable processes of time) with Perceived Time (Time as we colloquially know it--practically measurable in terms of minutes, days, months, years, etc), it renders an indescribably more sensible means of discourse.
To elaborate, I would go on to suggest that Actual Time embodies the absoluteness of the Universe--it refers to the unending, perpetual processes that constitute all that reality is, even outside of our ability to measure it. It does not relate to specific integers, nor is it subject to our manipulation... it simply refers to the natural change that is incurred in objects or energies simply by existing.
Perceived Time, on the other hand, holds a more obvious and approachable connotation. In a contemporary sense, it corresponds largely to the lunar calender and rotation of the earth as we have observed it--though past civilizations have offered countless alternatives. It is highly critical to the functioning of modern societies, so much so that it's coordinated at an international level. In addition to daily/weekly measurements (that behave cyclicly), larger-scale increments likewise exist to map occurrences into chronology--and these are easily portrayed as being subject to a 'Time-line' or (mathematically speaking), a line segment.
"If we assume that the world has no beginning in time, then up to every given moment an eternity has elapsed, and there has passed away in that world an infinite series of successive states of things. Now the infinity of a series consists in the fact that it can never be completed through successive synthesis. It thus follows that it is impossible for an infinite world-series to have passed away, and that a beginning of the world is therefore a necessary condition of the world's existence."
~Immanuel Kant
