The course of Nature cannot be limited by time, which must proceed in a continual succession. ~ James Hutton
A jumble of ongoing incoherency provides no basis for stability. Without continuity, there could be no consistency or predictability.
Without continuity, each instant is an isolated event, each thought fleeting and unrelated, each precept without relevance, each person a stranger, every event unexpected. ~ American psychologist Anthony Greene
Continuity is incremental moment-by-moment manifestation: the current instant entangled with the moment before. A vector of time is the perceived medium for continuity. Disorientation would be de rigueur if time did not seem to flow continuously.
In life forms, continuity comes from remembering a past, and its temporally vectored converse: the future, toward which organisms feel compelled to survive. Continuity offers opportunities for comprehension, problem-solving, goals, and planning.
Despite its necessity, continuity is an illusion, in that only the present instant exists. Sense of continuity comes from memory recall, which a problematic device. The mind tailors memories to suit the situation, not for veracity. As such, memory is frequently a shimmering mirage, even as it is commonly taken as gospel.
The seeming stability of the outside world reassures us of continuity, but, as perception is entirely within, that assurance of continuity is unassured. Nevertheless, we commonly take continuity for granted and count upon it, even as our life experiences repeatedly point out the hazard of doing so.
Continuity is the temporal aspect of consistency. There is a spatial aspect as well. The harmony of consistency is attained by keeping the locations of objects in space in memory.
Topographic memory is vital to creating a comprehensible world. We have all experienced distress at not knowing the current location of a desired object. Life would be inoperable if such were an environmental norm.
Categorization plays an essential role in achieving a sense of continuity. All objects decay in time, foods especially quickly. Categorization affords recognizing the same object in different states. Learning about processes and phase transitions is only possible via categorization.