Krus, D. J. & Blackman, H. S. (1980). Time-scale factor as related to theories of societal change. Psychological Reports,  46, 95-102.

Time-scale factor as related to theories of societal change

David J. Krus
Arizona State University

Harold S. Blackman
Idaho State University

Summary:--A computer model of theory building was used to simulate the length of historical period used for abstraction of apparent trends from empirical observations. Relationships between different types of abstracted trends and implicit assumptions of various of theories of historical change were discussed.

Theories of societal change are based on observations and analysis of structural relations and apparent trends in longitudinal observations of social events. The abstract forms of observed trends can be approximated by algebraic functions with corresponding geometrical representations, frequently by a line, parabola, spiral, or a sinusoid. Another possibility is that no pattern of historical change is discernible, corresponding to the geometric analogy of disjoint points or disjoint clusters or points.

The early theories of historical change were cyclical. This type of theory can be found among Greek and Roman historians of the classical era, as, e.g., Heraclitus, Empedocles, or Marcus Aurelius, describing history as following a path of perpetually recurring cycles.  In its classical formulation by Aristotle  (1927, p. 107) this type of theoretical stance maintains that 'chaos did not exist for an infinite time; but the same things have always existed, passing through a cycle of changes or obeying some other law.'

This notion of history was elaborated during the Italian Renaissance by Giambattista Vico. The pattern Vico perceived in history was a cyclical movement, encompassing both development, corso and repetition, ricorso (Vico, 1968). A single cycle of this pattern can be observed within Spengler's (1920) theory of historical change, typifying parabolic theories of growth, flourishing and decline of civilizations. Similar approaches can be observed inter alia in historical theories of Machiavelli, Gibbons, and in the early writings of Toynbee.

The linear theory of historical change is implicit in writings of St. Augustine. Facing the charges of his contemporaries that a decisive factor in the disintegration of Roman civilization was the spread of religious modes of thinking (a view implying a parabolic theory of societal development), St. Augustine postulated six linearly sequenced historical periods, a theological perspective spanning the time from creation to the end of the world (cf. Nash, 1969). The time dilation, characteristic of linear theories of societal development, may be also observed in writings of Immanuel Kant. Scanning the story of civilization from ancient Greece, through the Roman Empire and Middle Ages to the end of the First German Empire, he concluded that 'one will discover a regular progress in the constitution of states on our continent. This [idea of human history] gives us a consoling view of the future, in which there will be exhibited in the distance how the human race finally achieves the condition in which all the seeds planted in it by Nature can fully develop and in which the destiny of the race can be fulfilled here on earth' (Kant, 1963, pp. 24-25).

Another geometric function can be observed in Marxist theory of societal development (cf. Marx, 1932), spanning the history of mankind in a series of five stages: primitive communism, slavery, feudalism, capitalism, communism. Since the latest stage was convoluted as paralleling the stage of primitive communism, this model is sometimes referred to as a spiral model. Karl Marx patterned his theory of historical process after the philosophy of G. W. F. Hegel. In his lectures on the Philosophy of History, Hegel (1900) outlined the historical stages of mankind as a series of progressions from subjectivity to objectivity, from partiality to unity, from bondage to freedom, finally integrated into the unified system where the will of one is replaced by the will of all.

The view maintaining that history has no pattern or meaning can be called a chaotic model of history, typical of a group of contemporary historians and social scientists. A representative statement of this theoretical position can be taken from Geyl (1955, p. 156) who admits that there is 'an ingrained habit of the human mind to try to construct a vision of history in which chaos, or apparent chaos, is reduced to order.' However, Geyl dismisses that view as 'fashionable in the eighteenth and nineteenth centuries.'

It appears that three general types of theories of societal development can be observed: chaotic, cyclical and linear. These basic forms exist in frequent modifications, as e.g., clustered variation of the chaotic theory; sinusoid, irregular periodic, or Poisson variations of the cyclical theory; and step-wise, convoluted, spiral or logistic forms of the linear theory. A corollary to this observation is that the time perspective associated with each of the three basic models varies. The chaotic models of human history tend to be based on detailed considerations of historical events with associated attenuation of the time perspective. The cyclical models were frequently used for general descriptions of particular societies or civilizations. The salient property of the linear model is its utilization of holistic explanations of human history, often spanning agglomerations of societies and civilizations. In its extreme forms this viewpoint includes the theological Armageddon or, in secular versions, nuclear, overpopulation or other termination scenarios.

Joint consideration of the geometric form of a theory and the degree of historical generalization it encompasses suggests that these two parameters may be related and play an important role in the process of building theories of societal development.  The present communication describes the modeling of geometric forms of hypothetical theories of historical change as dependent on variations of temporal intervals, simulating the degree of cognitive generalization from empirical data.

Method

Conceptually, the cognitive process of abstraction from temporally subsequent events necessitates a series of inter-event comparisons, resulting in an estimate of general characteristics common to the series of scrutinized events. To model this process, a series of comparisons among elements of data arrays have to be made, resulting in a quantitative estimate of a typical value for a given interval. This procedure was repeatedly conceptualized within the theory of time-series analysis. Several suitable models are available; in the present analysis we have opted for the method of moving averages.

There are several advantages to this method as compared to other, more complex methods for trend analysis. The main advantage is that no prior assumption about the form of the expected trend is necessary. The only parameter is the order of the moving average. Its magnitude determines the length of the interval over which the successive estimates of the typical values of the series are made. The lower limiting value of this parameter is one, indicating that no generalization has been made. The size of the series is its upper limit of the order parameter, in which case the moving averages method returns a single value, the arithmetic mean of the series. Arithmetic mean, a basic method of data generalization, is thus a limiting instance of moving averages method when all data were used to make a single generalization. Intermediate values of the order parameter can be used for simulation of the various degrees of the cognitive process of generalization over varying segments of the series.

An optional parameter of the method of moving averages are the weights which can associated with the order of the moving average. Various weighting schemes can be employed, simulating the effect of value judgments on the outcome of the cognitive generalization process. In the present experiment, no weighting scheme was used, simulating the absence of value judgments assigned to observed events.

Results

Quincy Wright's list of hostilities spanning five centuries as analyzed with the value of the order parameter of the moving averages preset to unity and plotted as a X Y scatter-plot is presented in Fig. 1. No compelling pattern is discernible in this plot. It appears that a low level of historical generalization may be related to formal representation of observed events in a series of chaotic or clustered chaotic events.

Fig. 1.   Frequency of wars with order parameter of the moving average
preset to a one year interval.

 A generalization over a 20-yr. interval, was simulated by moving average with order of twenty and plotted in Fig. 2 with obtained points connected by a curve. This plot suggests a cyclical nature of human conflicts and is in congruence with Richardson's (1960, p. 200) observation that 'the generation who had not fought in the earlier war but who were brought up on tales about its romance, heroism, and about the wickedness of the enemy, became influential from 30 to 60 yr. after the war ended,' resulting in an increased probability of a retaliatory conflict.

 
Fig. 2.   Frequency of wars with order parameter of the moving average
 preset to a twenty years interval.

 Presetting the order of the moving average to 100, a  hundred years generalization showed in Figure 3, suggested the presence of 80- to 120-yr. cycle, described by Denton and Phillips (1968, p. 194) as caused by 'an action-reaction process in political philosophy, taken in the broad sense to include the general attitude of the elites toward the 'correct' society.'

Fig. 3.   Frequency of wars with order parameter of the moving average
preset to a one hundred years interval.

Increase of the order parameter to a 300-yr. interval and smoothing the obtained monotonically ascending trend resulted in a trend showed in Fig.  4. Reminiscent of linear models of historical change, telescoping the time interval over which the cognitive generalizations are made to whole history of mankind as in the case of social theories of St. Augustine and Immanuel Kant.

Fig. 4. Frequency of wars with order parameter of the moving average
preset to a three hundred years interval    .

Discussion

The obtained results suggest that without appropriate quantitative qualifications, the form of heuristically formulated theories of societal development may be dependent on the time scale implied by the theory.  This relativity of postulated forms of historical change is also supported by results of related simulation experiments (cf. Armstrong & Soelberg, 1968; Krus & Weiss, 1976) suggesting the possibility of obtaining meaningful formal structures by optimal weighting of random data elements in the least squares sense.

 Discussed topics bear relevance to the philosophy of social sciences in general and to the philosophy of history in particular. Observed relativity of obtained formal structures supports the notion that replacement of speculative analysis with quantitative methodology does not per se guarantee unequivocality of results. Perhaps regaining the sense of historical perspective cum quantitative scrutiny could provide for viable alternatives to the Faustian bargain made by societies accepting a political judgment in the absence of a scientific one.

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