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Mario Castagnino and Rafael Ferraro explain the differentiation between curved space-time, and the measurement of it by a clock. Whilst the physical parameters recorded by the clock are recorded as natural time, there is said to exist an infinite number of such parameters, all of which are defined as observer-dependent.

It is well known that there is a small confusion between a physical observer’s system and a geometrical coordinate system (or chart) in several papers. Of course they are two different concepts, e.g., in classical physics, an observer’s system is a rigid frame and a clock, where we can use all kinds of charts, for instance, Cartesian or polar coordinates. In curved space-time we cannot use a rigid frame and the natural generalization of the observer’s system will be a timelike fluid of observers, each one endowed with a clock, i.e., a set of timelike paths, each one with a different parameter, the “time” measured by the clock. This time is not necessarily the proper time; it is only an arbitrary continuous function of space-time. Of course we can describe this fluid of observers with any chart we like. We will find that physics is, in fact, observer dependent, but it is of course, chart independent. We shall restrict ourselves to irrotational fluid; thus we can define a set of orthogonal timelike hypersurfaces to the fluid paths, and we can define a parameter T, on each surface, such that the equations T = const would define the orthogonal hypersurfaces. We shall call this parameter a “natural time.” Of course, there exists an infinite set of natural times. We can pass from one to another via a continuous function T -> T’ = T'( T). We shall see that physics is independent of the natural time we use; it is only dependent on the chosen observer’s fluid. Of course, in general, natural time is different from proper time. We can label each fluid world line by three real parameters x1, x2 , x3 ,* and we can call x0 to the natural time T induced by the fluid of observers. Then x0, x1, x2, x3 is a chart and every event of space-time has its coordinates x0, x1, x2, x3 – namely, the space coordinates of the fluid world line, where the event happens, plus the natural time measured by the clock of this world line when the event happens. We shall call this chart an adapted chart (Castagnino and Ferraro 1988, 52-53).

Castagnino, Mario, and Ferraro, Rafael. 1988. “Toward a complete theory for unconventional vacua,” In Claudio Teitelboim (ed.) Quantum mechanics of fundamental systems 1, 51-62. New York: Springer Science+Business Media.

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Julia Kristeva illustrates how women are often correlated with a cyclical, natural, maternal temporality, excluded from the linear, historical, progressive temporality that is associated with men. Kristeva further notes first-wave feminism’s attempts to insert women, otherwise deemed to be bound to a natural temporality, into the linear time of social projects and histories.

As for time, female subjectivity would seem to provide a specific measure that essentially retains repetition and eternity from among the multiple modalities of time known through the history of civilizations. On the one hand, there are cycles, gestation, the eternal recurrence of a biological rhythm which conforms to that of nature and imposes a temporality whose stereotyping may shock, but whose regularity and unison with what is experienced as extrasubjective time, cosmic time, occasion vertiginous visions and unnameable jouissance

Temporality…traditionally linked to female subjectivity insofar as the latter is thought of as necessarily maternal should not make us forget that this repetition and this eternity are found to be the fundamental, if not the sole, conceptions of time in numerous civilizations and experiences, particularly mystical ones. The fact that certain currents of modern feminism recognize themselves here does not render them fundamentally incompatible with “masculine” values.

In return, female subjectivity as it gives itself up to intuition becomes a problem with respect to a certain conception of time: time as project, teleology, linear and prospective unfolding; time as departure, progression, and arrival – in other words, the time of history. It has already been abundantly demonstrated that this kind of temporality is inherent in the logical and ontological values of any given civilization, that this temporality renders explicit a rupture, an expectation, or an anguish which other temporalities work to conceal…

In its beginnings, the women’s movement, as the struggle of suffragists and of existential feminists, aspired to gain a place in linear time as the time of project and history. In this sense, the movement, while immediately universalist, is also deeply rooted in the sociopolitical life of nations. The political demands of women; the struggles for equal pay for equal work, for taking power in social institutions on an equal footing with men; the rejection, when necessary, of the attributes traditionally considered feminine or maternal insofar as they are deemed compatible with insertion in that history – all are part of the logic of identification with certain values: not with the ideological (these are  combated, and rightly so, as reactionary) but, rather, with the logical and ontological values of a rationality dominant in the nation-state (Kristeva 1981, 16-19).

Kristeva, Julia. 1981. ‘Women’s Time.’ Translated by Alice Jardine and Harry Blake. Signs 7(1): 13-35.

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Jose Arguelles characterises human life as occurring within an artificial time that is separated from the natural rhythms of the biosphere’s (planet’s/universe’s) time. The clock is portrayed as an artefact of artificial time. Contrarily, the Law of Time is said to show that energy, combined with real time, equals art. Time, governing energy, is here positioned as inherent to naturally artistic creation.

From my experiment in time, seeing and studying the human as part of the larger self-evolving fabric of the biosphere, I came to the conclusion that the human is living in a time apart from the rest of the biosphere – an artificial time whose climax and termination is inevitable, for nothing artificial can withstand the force of truth. If the human is living in artificial time, the clock is an artifact whose system of measure has nothing to do with natural cycles but is a totally abstract standard, then there must be something called natural time. I will go even farther and state that not only is there natural time, but that there is a law governing natural time, and that is the Law of Time. Just as Newton only discovered gravity some 300 years ago, though gravity has always existed, so the Law of Time has always been in operation, even though it was just recently discovered…

The Law of Time is formulated very simply, and in some people’s way of thinking, rather unscientifically as T(E) = Art, “energy factored by time equals art.” All phenomena in the material world represent some state of energy, and every state of energy is governed by time, the resultant product of which is always something beautiful or elegant. Have you ever seen an ugly sunset? A hideous flower? Even if you examine a scorpion with some objectivity you will be amazed at the flawless and elegant manner in which its parts are organized. Yes, all of nature is organized by time to produce in you the sensation of beauty. And time itself, well, believe it or not, time is a frequency, and a frequency is not measurable by a clock. The Law of Time states that time is the universal frequency of synchronization. It is the nature of time to synchronize and to maintain all things in a condition of synchronization. Synchronicity, then, is the experience of real time. When we say that time is a frequency, we can be more precise and say that time is a universal constant expressible by the mathematical ratio 13:20. That is, the 13:20 ratio is the frequency of synchronization (Arguelles 2002, 3-4).

Arguelles, Jose. 2002. Time and the technosphere: The law of time in human affairs. Rochester: Bear & Company.

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Mark Smith observes that with the proliferation of clocks and watches during periods of American slavery, plantation owners forced slaves to move from a temporality which naturally revolved around the sun and stars, to an existence governed by the clock. Whilst natural time and clock time are not entirely divorced for Smith, a distinct transition between them is apparent.

Nor should we be misled, as Michael O’Malley has wisely counseled, into thinking that a naturally derived understanding of time (time defined by sun, moon, wind, and a host of other naturally occurring phenomena) necessarily precludes a commitment to clock time. Not only is the dichotomy false, not only is nature itself sometimes as frenetic as the clock (as humans find when planting and harvesting, for instance), but there is evidence suggesting that natural time and clock time are in many respects complementary. Both are largely cyclical in their movements, and the regular, perpetual movements of the clock are to some extent mirrored in the rhythms of the seasons or sun. Naturally derived, task-oriented, and clock-regulated forms of time measurement, in short, coexist in any society, the most modern included…

Under modernity, the clock becomes a fetish: the clock is time itself, and clock time develops an apparent autonomy and hegemony. The dictates and needs of the capitalist mode of production ensure that the clock is used to control workers, measure labor, increase efficiency, and heighten personal time discipline in order to coordinate workers and society generally. Given these imperatives, clock and watch ownership under capitalism tends to increase considerably. Conversely, in pre-modern societies, clock time is usually bound to religion and has little secular significance or function…

Before anyone, whether master, industrialist, or worker, could reduce time to money, however, they had to dilute, or at least modify, age-old Christian imperatives stressing that all time was God’s time. According to Jacques Le Goff, this process began in the Middle Ages, when “[a]mong the principal criticisms levelled against the merchants was the charge that their profit implied a mortgage on time, which was supposed to belong to God alone.” But God was not the only impediment to secular commercial time. According to Le Goff, “Like the peasant, the merchant was at first subjected by his professional activity to the dominion of meteorological time, to the cycle of seasons and the unpredictability of storms and natural cataclysms.” To rationalize time, European merchants used God’s time by recruiting the aural power of his church clocks to coordinate city life and the times of markets. “The same process for the rationalization of time,” Le Goff points out, “was responsible also for its secularization.” Once this rationalization was under way, mercantile activity, while “distinct and, at particular points, contingently similar,” to God’s time, became regulated by the clock. And it was the dual forces of God’s temporal imperatives and merchants’ commercial time that provided the historical basis for the rise of clock consciousness among workers and managers in the eighteenth and nineteenth centuries.

Slaves remembered the clock and watch and testified that they had come to accept, albeit grudgingly, timed agricultural labor under slavery. Although they originally came from societies where natural time was predominant and that same reliance on natural time remained important to them, southern slaves, like nineteenth-century urban-industrial workers, found their reliance on sun and stars as exclusive arbiters of time attacked and, ultimately, undermined (Smith 1996, 1435-37 & 1461).

Smith, Mark. 1996. “Old south time in comparative perspective. American historical review 101(5): 1432–69.

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Edward Evans-Pritchard describes how an African community, the Nuer, experience time in a manner that is intimately connected to natural events. This is distinguished by Evans-Pritchard from the abstract form of time that is said to be constructed by the mechanics of his own culture.

Though I have spoken of time and units of time the Nuer have no expression equivalent to ‘time’ in our language, and they cannot, therefore, as we can, speak of time as though it were something actual, which passes, can be wasted, can be saved, and so forth. I do not think that they ever experience the same feeling of fighting against time or of having to co-ordinate activities with an abstract passage of time, because their points of reference are mainly the activities themselves, which are generally of a leisurely character. Events follow a logical order, but they are not controlled by an abstract system, there being no autonomous points of reference to which activities have to conform with precision. Nuer are fortunate.

Also they have very limited means of reckoning the relative duration of periods of time intervening between events, since they have few, and not well-defined or systematized, units of time. Having no hours or other small units of time they cannot measure the periods which intervene between positions of the sun or daily activities. It is true that the year is divided into twelve lunar units, but Nuer do not reckon in them as fractions of a unit. They may be able to state in what month an event occurred, but it is with great difficulty that they reckon the relation between events in abstract numerical symbols. They think much more easily in terms of activities and of successions of activities and in terms of social structure and of structural differences than in pure units of time.

We may conclude that the Nuer system of time-reckoning within the annual cycle and parts of the cycle is a series of conceptualizations of natural changes, and that the selection of points of reference is determined by the significance which these natural changes have for human activities (Evans-Pritchard 1940, 103-04).

Evans-Pritchard, Evan. 1940. The Nuer. Oxford: Oxford University Press.

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Jonathan Kramer explores the position that a real, musical time, exists. In comparing the clocked measurements of the durations of musical notes, with how long such notes seem to a listener, a consideration is developed of which constitutes the real time of music.

Many writers on music acknowledge, directly or indirectly, that music provides more than one kind of time experience, more than one temporality…Some writers address implicitly, some explicitly (and some not at all), which of music’s temporalities is/are “real” and which are, in some sense, virtual or illusory or transitory or imaginary…

I will take up questions of time taken vs. time evoked in a musical performance, real time as a performer’s or a computer’s reaction without delay to a musical stimulus, real time as objectively measurable (clock time) vs. real time as the essence of subjectively perceived music, and the relationship among the composer’s, the performer’s, and listener’s real time.

The distinction – between musical time that is real and musical time that somehow is not – is meaningful not only on the abstract philosophical level addressed by my questions above. Even in the pared down context of a simple sequence of durations, the question fo what time is real is complex…We now understand that the durations implied in musical notation do not generally correspond to the “actual” durations performed, yet our perception of these durations corresponds more closely to the notation than to their clock-time measurement. Consider, for example, this series of durations, which has been studied by Henkjan Honing and Peter Desain.

Honing and Desain have found that, in an expressive performance at a certain tempo, the duration of note A is 0.34 seconds and the duration of note B is 0.35 seconds. Note B – a sixteenth note, presumably representing a quarter of a beat – is performed slightly longer than note A – an eighth note of a triplet, presumably representing a third of a beat. Yet listeners do not perceive B as longer than A. Quite the contrary: they invariably hear A as longer than B, because of the rhythmic and metric context.

So: which is the “real” time? The objectively measured time, which tells us that B is longer than A, or the musical time as interpreted by performers, which tells us that A is longer than B? The answer depends on just what we mean by “real.” Is real musical time an objective time, out there in the world, or is real musical time the way listeners perceive musical events in relation to one another? Scientists may be more comfortable calling clock time “real,” but performing musicians may well feel the opposite. The musical time they feel and project, and that they hope listeners sense, is for them the essential musical reality. Musicians tend to disparage or dismiss outright objective time…

So, which is the real time? The lengths of sections as measured by the clock, or their apparent lengths as felt by listeners? (Kramer 2016, 161-62).

Kramer, Jonathan. 2016. Postmodern music, postmodern listening. New York and London: Bloomsbury.

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Espen Hammer argues that human practices and actions shift time from being a natural phenomenon, to that which bears the intelligibility of social composition. This effect is said to be more apparent in contemporary eras than it was in pre-modern cultures, which Hammer attributes to the dominance of clock-time.

I started out by trying to establish that, for human agents, temporality necessarily has a social (and therefore also historical) dimension. In human practices and actions, natural time is humanized, thereby becoming a form of intelligibility that weaves together past, present, and future, and narratives bring structure and representational unity not only to actions but to events as well. Time is anthropologically temporalized in many ways: there are the daily biological rhythms; there is the cycle of life through adolescence and maturity to old age and death; and there is the transindividual time of periods and historical epochs. In all three contexts the modal shape of our lives and the meaning we are able to experience will inevitably have a temporal dimension.

I then drew on this account in order to make at least conceivable the idea of a specifically modern form of temporality. I argued that modernity generates conceptions of human time as increasingly quantifiable, a linear series of “nows,” where the future, with its goals to be actualized, attains priority over the past and its accumulated space of experience. The notion of lived time experienced (in line with the ideologies of progress) as a continuous rupture with the past was then analyzed in terms of notions such as modernization and purposive-rational action, requiring temporal organization to be calculative and forward-looking. The dominant temporal configuration in modernity is clock-time, the empty ticking away of transitory units of time that irreversibly and irretrievably distance us from the past. Modern time thus generates the dual problem of meaning and transience that I argue occupy the thinkers I deal with later in the book. For one thing, as the present is increasingly disconnected from structures of collective historical understanding and geared towards a linear progression towards an unknown future, it becomes incapable of securing a sense of stable meaning. Indeed, as the narratives that both individually and collectively relate actions and evaluations to a fabric of collective meaning unravel in the face of progress, the modern self tends to experience a sense of fragmentation, melancholy, and boredom. For another, as modern time is a time of perpetual transition, of the ever-new of the mere passing of homogeneous moments, the sense of transitoriness, I submitted, is stronger and existentially more devastating than that which, in pre-modern societies, gave rise to various types of metaphysics of counter-worldly immutability. In the accelerating world of modernity, there is never enough time (Hammer 2011, 237-38).

Hammer, Espen. 2011. Philosophy and temporality from Kant to critical theory. New York: Cambridge University Press.

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Akhil Gupta notes that industrial, capitalist time, is often conceptually separated from the rhythm of natural time. It is added by Gupta that typically capitalist time is characterised as abstract, linear, and associated with Western development and progress, contradistinguished from the cyclical, less-distanced from nature, sense of the time of non-Western cultures.

Whereas time in industrial capitalism becomes abstract, homogeneous, empty, linear, and progressive, shorn of “nature’s rhythms,” and unconnected to the task at hand, historical and cultural Others construe time as concrete, cyclical, closely connected to nature, and experience it in the context of specific tasks…

It would, of course, be foolish to deny that the far-reaching changes that accompanied the industrial revolution permanently and irreversibly altered western notions of time. It is also true that dominant representations of time in the West emphasize its linear, continuous, unidirectional, and progressive character, its preciousness, and its interchangeability with money. What I wish to question is whether the changes that occurred in conceptions of time are best understood as the move from cyclicality to linearity, from task-orientation rooted in concrete activity to an abstract passage disconnected from the flow of everyday life, and from a close synchrony with the rhythms of nature to an alienated homogeneity imposed by work-discipline. Rather than accepting this narrative as a plausible reconstruction of the western past and a powerful prediction about the “Third World” today, rather than acquiescing to the dominant portrayals of the difference between Self and Other that circulate widely in the western world, we need to ask why discursively available representations of time in the West remain oblivious, despite easily observable evidence to the contrary, to features of cyclicality, concreteness, rhythms, and yes, even rebirth. The political importance of this silence lies in the fact that it allows the western narrative of progress to go unchallenged, and enables the continued management and surveillance of the “Third World” in the guise of “development”…

Another major contrast often drawn between industrial and nonindustrial societies is that in the former time is homogeneous, empty, and regular whereas in the latter it is rhythmic and irregular. The (often unstated) basis for this difference can be traced to their respective relationship to nature. Whereas agricultural, pastoral, and hunting-gathering societies are closely at- tuned to the “rhythms of nature,” in industrial societies these bonds are severed. For example, much has been made in pop sociology of the fact that electric lights, three work shifts, all-night radio and television broadcasting, and twenty-four-hour restaurants, grocery stores, and laundromats-what might be called the “Denny’s revolution”-are slowly blurring any meaningful distinction between night and day. Once again, as with the case of cyclical time, we find a troubling set of essentialist dichotomies being constructed in which agricultural (and more generally, nonindustrial) societies are identified with “nature” while industrial societies are identified with technology (Gupta 1992, 195-96, 199-200).

Gupta, Akhil. 1992. “The reincarnation of souls and the rebirth of commodities: Representations of time in “East” and “West.”” Cultural Critique 22: 187-211.

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Eduardo Mendieta observes an historical differentiation between natural time, historical time, and social time. These differences are said to be reducing, however, as the rate at which historical events develop is accelerated. Furthermore, despite an opposition between natural and social constitutions, social time is regulating shorter temporalities for naturally occurring rhythms.

The symbolic deconstruction of time, partly a result of the information revolution discussed above, has lead to a rethinking of the differences among natural, historical, and social time. Social time is the time in which and at which societies experience their lifeworld. Or rather, just as Henri Lefebvre spoke of the “social production of space,” we must also speak of the “social production of time.” This socially produced time is social time; it is the time that punctuates the rhythms of social existence. This is the time that ticks at the sounds of seconds, minutes, hours, days, months. This is the time that keeps track of workdays, academic calendars, and leisure time. This time, however, is timed by clocks and timetables that have been arranged in terms of assumptions, beliefs, and ideologies about how much time constitutes a workday, a work week, how long should persons work in their lifetime, and so on. Like maps, clocks clock only what they have been arranged to clock. The rhythms of social existence, however, intersect with historical and natural time. Historical time has to do with the time in which historical events, forces, processes, and transformations take place. Historical time is the time in which societies and civilizations live and mark their transformations. Historical time, one may say, is punctuated by political revolutions, wars, elections, and technological revolutions that may have accelerated the rhythms of social time. Finally, natural time is the time of nature, of tectonic plates, of seas, of weather patterns, of draughts and floods, of freezing or melting polar ice caps, and other such forces that are punctuated in millennia, in cycles whose regularity or patterns are not discernable because their time span is beyond human time.

What is distinctive about the global condition, at the phenomenological level, is that these three times have began to merge, or seem to have collapsed into each other. Social time has accelerated to such an extent that it has caught up with historical time. Revolutions are lived within decades. Major social transformations occur where entire societies are uprooted and restructured in the blink of the eye. What took centuries, now takes decades, and sometimes a score of years. History is being televised at any given moment, even as its revisionism is aired and posted that same evening. By the same token, historical time seems to have caught up to natural time: The El Niño weather pattern is now part of pedestrian speak. The greenhouse effect is melting the ice caps, and sea levels are rising, regions are turning into desserts, while desserts are turning into irrigated gardens. The cumulative effect is that time has to be symbolically reconstituted. The self-assurance of Cartesian and Newtonian thought that operated on the dependability and seeming immutability of natural and world historical time have to be traded for a type of thinking that will set out from the social productivity of temporality (Mendieta 2007, 21-22).

Mendieta, Eduardo. 2007. Global fragments: Latinamericans, globalizations, and critical theory. Albany: State University of New York Press.

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Robert Kastenbaum characterises statistical, behaviour analysis, as a form of psychology which neglects the phenomenological reality of natural time. Such methods, Kastenbaum asserts, construct the appearance of the time of an individual, and of a population, when actually the focus is on time-bereft, quantitative outcomes.

There is probably a connection between the psychologists’ perceived irrelevance of death and two other variables: (a) the psychologist’s separation from phenomenological and natural time; and (b) the preference for aggregated rather than individual (nomothetic) types of quantitative analysis. Experimental psychology is strong on establishing its own designer time frameworks-reinforcement schedules are one familiar example. Statistical psychology is strong on analyzing data on the basis of techniques and assumptions that have an underlying spatial or other atemporal foundation. This tendency expressed itself in the early days of statistical treatment of behavioral data when research designs were borrowed from agricultural experimentation. (The “hort” in cohort bears witness to its horticultural roots.) Investigators became adept at studying the effects of treatment A, treatment B, and control conditions on “crops” of rats or undergraduates who had been assigned to these various conditions, much like sweet peas to Mendellian garden patches. The results are analyzed by aggregated clumps (Group A, Group B, Group C). We are not really much interested in what happened to this particular sweet pea. Furthermore, natural time (in this case, the growing season) is replaced by quantitative outcome. True, there is the appearance that time has really been taken into consideration. But the statistical analysis merely compares two sets of numbers based upon aggregated performance. The growing season might have been a month or an hour. The process might have been linear or geometric, smooth or discontinuous. We’ll never know.

Natural time is seldom treated as natural time in psychological research. It is replaced by outcome measures that are indifferent to the actual temporal course. Similarly, the typical research program concentrates upon aggregated numbers. Individuals disappear as individuals almost as soon as they are fed into the computers. Combined, the tendency to dispose of both the individual and of natural time comprises a splendid way to make death appear irrelevant. Without individuals and the actual passage of time, how is this unpleasant topic to intrude itself? Furthermore, the already mentioned dislike of introspective studies has pretty much taken care of phenomenological time as well. Psychologists may not have any extraordinary ways to maintain social stability and continuity, but they can create little time and death-free worlds in their studies and theoretical models (Kastenbaum 2000, 15-16).

Kastenbaum, Robert. 2000. The psychology of death: Third edition. New York: Springer Publishing Company.