Kairos and Chronos are the two words for time used by the ancient Greeks, Chronos as a sequential passage from past to future, Kairos as the "opportune moment"--perhaps something as brief and fleeting as what we colloquially call a "moment" but perhaps also something as expansive as the right season to sow or the right reason to reap. We've come to reduce time to only the former, dismissing the latter as a mere epiphenomenon fetishized by scientifically illiterate idealists, a notion regrettably reinforced by the naive denial of Einstein's rigorous confluence of space and time by many thinkers (though contrary to popular belief, not Bergson, whose qualms, justified or not, were about semantic ambiguities), but a pragmatic understanding of these concepts as two attributes by which we can understand time through different topologies with differing pragmatic, historical and technological bases can show why one should not treat these two conceptualizations of time as mutually exclusive.
I am not an anthropologist or a historian, and this is not supposed to be an accurate description of history. This is a parable loosely based on a handful of reasonable approximations meant to demonstrate how our own ideas of time are at the root a matter of function:
While there's always been some understanding of time as a linear passage from past to future, differences in material and social affordances dictate the actionable significance of seeing time this way. Before the advent of writing and civilization, the scope of both history and the forseeable future must have been fundamentally limited: specific memories died with the passing away of those who held them, and that meant that with each generation that passed away, any record of that record could only be carried on through hearsay. This of course has two serious limitations without the advent of writing: a tribe can only accumulate so much stored history because of limits to memory, and any memory passed on verbally would be inevitably distorted like a game of telephone.
Being costly and fragile, any kind of memory passed down orally would exist insofar as it serves some kind of function, and to accomplish this feat would require passing down knowledge in a way that converges on something that maintains a kind of stability sufficent for such a function. Such stability would require that there be some kind of error correcitng code: a set of grammmatical rules could recognize and correct any sufficiently small distortion of the original message. In the absence of writing, such a grammar would exist as a body of behavioral regularities and constraints actively learned and passed on through the repeated deliberate practice of ritual. These rituals may nonetheless change in many ways, but so long as some kernel that maintains is fucntionality is preserved, the ritual continues to live on as a single memory that is accessed and utilized in the same manner as the recall mechanisms of our own individual nervous systems.
Even in the absence of the written word, however, humans have always been biologically capable of creating physical artifacts, and these too would play a role in ritual: a tribe could, for example, warn future generations of areas that are prone to infrequent but catastrophic events by providing physical markers whose tacit interpretation is preserved through inherited rituals built around them. In both the case of oral tradition and such markers, however, there is a fundamental limitation: there are limits to how much one can memorize, and by extension limits on rituals. The past, therefore, does not accumulate: it remains fixed and eternal and constitutes what we know today as myth. Time, prior to certain fundamental technological breakthroughs, is cleaved into two areas: the eternal and unchanging past of myth, and a neighborhood of time around the present moment through which its living inhabitants travel.
In the neighborhood of the present, there is an obvious passage of time: after all, pedants who angst about whether it's an illusion still make plans for the future. But for somebody who actively lives time in a way where the past before their living ancestors exists only statically, any sequential idea of past and future exists only within a trajectory that spans only a few generations. Any such idea of time as a linear and cumulative sequence of events is therefore only a local property of their own iteration of a larger cycle, and it is this cycle that lives on indefinitely. This clevage between past and present-neighborhood applies not only to their own lifespan, but also in varying degrees to any number of cycles that exist at smaller scales: plans may be made for the immediate hunt, or the next cycle of animal migration, or the cold winter; in each case, memories exist in varying detail and with varying organizations to aid in the execution of the present enactment, and they will just as quickly be forgotten unless they adopt some kind of relevance beyond the matter at hand and consequently become part of the skeleton of some encompassing narrative.
Every such narrative, and in fact every narrative, is a topology defined on time: a terrain that by and large, though never entirely, constrains and affords the ways in which events relate to one another. Every topology on time has some kind of material and practical basis, whether that be the rhythm of a percussive instrument, the seasonal cycles of agriculture, the completion of a complex task, or the preservation of a ritual.
Kairos is the concept of understanding time through such topologies, the "opportune moment" it denotes referring to the understanding of the present not as a single infinitesmal point but a neighborhood that defines one's power of action. Chronos, by contrast, refers to an understanding of time not based in action and proximity but in linear order. This concept of time, in the absence of the right technology, was deeply local and cursory; with the written word, that changed. Writing was what allowed the past to be something not fixed but cumulative: as long as literacy was preserved through generations, an indefinite amount of past events could be stored and accessed at will, gradually transforming the past from mythology to history.
More and more of time therefore became understandable as something strictly ordered and therefore a progression rather than mere cycles, but the idea of time as a totally ordered continuum of points required yet another technological revolution.
Even with the advent of calendars and written history, most day to day operations still revolved around a present defined acting within the relevant moment: farmers got up at dawn and finished working at dusk. Society was also, prior to the industrial revolution, almost entirely autarkic: markets were the icing on the cake, with most goods and tasks taken care of by the community with minimal specialization. Working according to this kind of system, there was simply no need for there to be any real precision for time: as long as you got the day's work done the best you could, that was that. Peasants might give a large chunk of their output to a lord who would make sure they're not being short-changed, but this did not necessitate any kind of fine-grained accounting for time.
Calendars became gradually less sloppy through advances in astronomy that more precisely tracked and predicted celestial movements, and between this and other scientific advances the mechanical clock, precise under its own stored power, became a standard of time for scientists even if not for the average person. The emergence of industry, however, created a type of work that required the maximization of profits through optimized efficiency and precise accounting, and while there were still limits to what could be done with this mode of production, its ubiquity was achieved through an exponentially growing positive feedback loop of standardization, urbanization, and profit sparked by the invention of the steam engine. The more painstaking irreducible craftsmanship could be taken out of the equation by standardizing parts, the more could be rapidly produced through the raw energy of burning fossil fuels, the more factories could effortlessly outcompete artisinal goods, the more artisans flocked to the cities to work at factories in exchange for money that could buy these cheaper goods, the more industry could even further expand both its market and its operations.
Currency had always existed before, but as it ate away at autarky it became the ultimate replaceable part. The new way of working for an exponentially growing number of people was therefore no longer one based on loose approximations that work well enough, but on showing up at the exact minute work began and earning a precise amount of money for each minute worked. The mechanical clock therefore became increasingly the way in which everyone related to time on a practical level. The steam engine of course not only powered factories but also railroads, the means by which large amounts of goods and people could be transported across long distances. The need to coordinate such transportation added yet another restriction to time: mechanical clocks alone are not enough, they must also be coordinated with each other; prior to this, each town might have its own chronological time that works well enough, but train schedules necessitated that every city belong to a specific time zone and base its time of day precisely on its time zone.
This was the key challenge that led to the deep understanding of the relationship between time and space we have today. Despite the best of efforts, perfectly synchronized clocks would inevitably fall subtly out of sync, creating barriers to how precisely anything could be coordinated. The question of what went wrong was only solved when Einstein, in his theory of relativity, demonstrated that bodies move through time at varying speeds depending on their own spatial speed, an effect known as time dilation. With this achievement, humanity's construction and understanding of Chronos was perfected. At no point here should "construction" be misunderstood as a way of challenging the objectivity of Einstein's theory: relativity is objectively true insofar that it really does work in a way that is impossible to deny.
The way in which the theory of relativity solved the problem of synchronization by accounting for time dilation is not just a mere tweak but a revolution in how one understands chronological time. Any illusion that clocks may have engendered of time and space being passive backdrops against which change happens was completely abolished, instead affirming that there is always, no matter how small or subtle, a relationship between a body's motion and its own passage through time. The geometric subtleties of relativity are a revelation of the fact that even a purely chronological notion of time is ultimately not an extensional backdrop but an intensional structure defined by differences in the mass and speed of physical bodies.
However, although it overturned the fundamentally extensional view from Newton's laws of motion, it also had to piggyback off of it by preserving a mechanistic notion of processes: a trajectory, understood as nothing more than a mapping between a single point defining the location of an atomically defined body and an independently defined time, was overhauled into an understanding that decrowned time's status as an independent variable and wove it into a set of relationships between the mass, speed, acceleration, and gravity of multiple bodies but maintained the same simplistic idea that a trajectory is ultimately decomposable into points in time that carry all relevant information.
None of this is a discredit to physics: physics is by and large the study of trajectories defined in this manner, as it studies fundamental laws of motion that everything else must obey. It is a kernel of our physical reality and any extant physical process must obey the laws of physics. Physics, in fact, could not have been any other way, as trajectories must be defined in this manner if one is to use clocks, since to use clocks as an instrument requires accepting their totally-ordering topology on time. At the same time, this does not mean that this is the only valid or "true" topology on time and that any other conceptualization of time is "psychological" (i.e. an account of figments of someone's imagination): every topology on time is defined not by some disembodied notion of "perception" but by actual change.
And change is something that has many different definitions: the "time" used by physicists being only one very specific kind of change; that of physical bodies distilled into a bare bones idea of movement through physical space. But if one wants to talk about history, biology, memory, or any number of more complex and nebulous things, it is absurd to think that their logic can be in any way reconstructed from these procrustean building blocks any more than one could derive the theory of relativity by simply adding some extra props to Newton's fundammentally Euclidean theater. Just like relativity could only be derived by identifying fundamental relationships within the fabric of space and time that define movement within it, the same goes for any other process in that one must look at the actual relationships that define that process in order to understand how its parts change vis a vis one another.
One cannot define, historically, the exact second that a war began, and one might not even define the beginning of a war with the day war was declared depending on what they identify as some point of no return based on other things that happened before or after, so to try to define history in a completely linear form is simply absurd: this is not mere "approximation" of some underlying physical world where every quantum of physical time is pregnant with variables and transition rules—this is looking at the relationships that exist rather than overlooking them in favor of pretenses rooted in ersatz Platonism. The study of memory provides an even better example: that memory is not temporally precise like a video camera is not some simple "psychological" mismatch from reality; memory, being a medium that both guides and follows behavior on multiple scales, has dynamics and consequences that are very real beyond some "content" that may or may not contradict what a video camera would find; to see memory as mere illusion would be to discount the fact that actors must ultimately synthesize the significance of events and that this cannot be accomplished by any recording device whatsoever. A topology of time for understanding this is not mere "psychological time" but a study of actual intersubjective enactments that exist regardless of what scientific cheauvinists think.
Chronos, in this sense, should not be seen as the one true way to understand time: every topology on time is a material intersubjective substrate by which processes relate to change. Chronos is not a topology on time so much as it is time conceptualized as a progression, with varying topologies being chronological to different degrees insofar that they unambiguously order events. The theory of relativity, in turn, is a kernel common to all topologies of time discovered through a process that took us from our relationship to the movements of the stars all the way to a a set of mathematical invariants, defined with regards to a constructed total ordering on events, that demonstrate the way in which change is not accidental but essential to time even when one strips away all possible confounding baggage.
While the theory of relativity may only be articulated with a purely chronological vocabulary, it is nonetheless a kernel common to all understandings of time insofar that it is a kernel of the purely chronological notion of time and this chronological notion of time is itself a kernel of the idea of time (being a kernel is always a transitive property); it therefore sets immutable conditions on chronological time that would have to ultimately be respected by any topology of time. To speak of something in terms of another topology is not to reject relativity or to speak of a "merely" subjective "perception" of time, but to highlight different ways in which trajectories are defined and relate to one another. Contrary to Einstein's rebuttal against Bergson that there is no philosophical notion of time but only a physical one, the theory of relativity affirms that time always exists not as some metaphysical backdrop but as a latent medium of relationships co-extensive with the very idea of change. As such, physics can never be a stage against which all change is defined but only a specific manifestation of this truth embodied in the elegant geometry that demonstrates how time would remain relational even if we reduced all of reality to inert corpuscles.