Quantitative History

Quantitative history uses numerical data analysis as a primary source for the analysis and interpretation of historical events. Historians have made use of numerical data and simple statistics, but it has only been since the advent of computer-assisted data analysis, facilitating Fourier transforms of data series, quantitative modeling, filtering of stochastic drifts and other advances in the analysis of secular trends that quantitative history has come of age. However, this type of history is often ignored by historians who conceptualize history as a record of events and view the quantitative analysis of these events with skepticism and sometimes disdain. To better understand the idea of the quantitative history, let us elucidate some of its basic principles.

Cyclical theories of history Early theories of historical change were cyclical. This concept can be found among Greek and Roman historians of the classical era, such as Empedocles or Marcus Aurelius. In its classic formulation by Aristotle, ''the same things have always existed, passing through a cycle of changes.'' Giambattista Vico (1688-1744) elaborated this notion of history in his Scienza Nuova (1725), a favorite of Karl Marx and James Joyce, who used the Vico's New Science to structure his Finnegan's Wake. The pattern Vico perceived in history was cyclical, encompassing development and repetition. With respect to the cyclic nature of historical trends Russell (1971) maintains that every community is exposed to two opposite dangers: ossification and dissolution, elaborating on this postulate as follows:

''Civilizations start with a rigid belief system based on a dogma. If the dogma is relaxed, civilization may reach a point of balance between discipline and freedom, often its period of brilliant genius. This stage typically dissolves into anarchy. The anarchy leads to tyranny, justified by a new dogma.''

A single cycle of this pattern was elaborated within Spengler's (1920) theory of historical change, outlined in terms of growth, flourishing, and decline of civilizations. Similar approaches can be observed in the historical theories of Edward Gibbon (1776-1788) and the early writings of Arnold J. Toynbee (1889-1975). Toynbee is best known for his Study of History (1934-1961). In this 12-volume series, Toynbee analyzes the genesis, growth, and disintegration of 26 civilizations. His conclusion known as the Toynbee's hypothesis is that the failure of a civilization to survive was the result of its inability to respond to ideological challenges rather than to physical or environmental challenges.

The spiral model of history The prototypes of historical theories are the chaotic, cyclical, and linear theories of historical change. These basic forms exist in many modifications, e.g., Moyal’s (1949) use of Poisson distribution to model variations of the cyclical theory, logistic curve modification of the linear theory by the Club of Rome, or the convoluted spiral model of Marx and Hegel.

Marxist theory of societal development spans the history of humanity in a series of five stages:

Since the last stage of this model is seen as a return to the initial stage of primordial communism, albeit on a higher level of social development, this model is sometimes referred to as a spiral model. Accordingly, the communist society should return to the natural state of humankind, not perverted by the greed of capitalist society. Marx patterned this theory after the philosophy of Georg Hegel (1770-1831). In his lectures on the Philosophy of History, Hegel elaborated on the polarized tensions in reality (thesis and antithesis), as antecedents of transcendence, synthesis and emergence of new knowledge. Within the context of history, Hegel outlined the historical stages of humanity as a series of progressions from subjectivity to objectivity, partiality to unity, and bondage to freedom. The hope in this progression of events was shared by Hegel with the philosophers of the [[Enlightenment. However, this course of events is also subject to reversal, as observed with respect to the ''subjectivity-objectivity'' trend by Guy Debord (1995) in his société du spectacle, and in the other respects by Umberto Eco commenting

on the opening years of the 21^st century. Umberto Eco's observation is supported by Richard Barber in his The Holy Grail: Imagination and Beyond. According to Barber, The New York Times mentioned the Holy Grail 32 times in 1995-1996, but in 2001-2002 140 times. In the Times of London (1985-1986 and 2001-2002 time intervals) the frequency of mentioning of the Holy Grail increased from 14 to 171 and within the 1985-1986 and 2001-2002 time intervals this frequency increased from 56 to 133 in Le Figaro.

Chiliastic theories of history The linear theory of historical change is exemplified in writings of St. Augustine. In his De civitate Dei (413) Augustine introduced his theological perspective on history, resolutely linear, a tendency which can be traced to the Judeo-Christian scriptural tradition describing history as the sequence of events from the time of Creation to the End of the World. The linear movement of human history aims at the eventual separation of the Chosen, a small minority saved by God's unmerited grace, from the rest of the humanity.

The resurrected bodies of the Chosen will experience eternal bliss while most of the humanity will encounter the second death and will be subject to eternal torment by flames that will inflict pain without consuming the body. The people not chosen must suffer without end, for to suffer any less would be to undermine our confidence in the eternal blessedness of the Chosen and would also contradict the scriptures. (De civitate Dei, 21, 23).

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 on History, 1963, pp. 24-25).

Chaotic theories of history The chaotic concept of history is characteristic of contemporary historians. This view is exemplified by Geyl's assertion (in his Debates with Historians, 1955) that there is an

ingrained habit of the human mind to try to construct a vision of history in which chaos is reduced to order, characteristic of the discredited theories of historical change proposed during the nineteenth’s century.

In another words, reality exists independently of ideas concerning it, is basically random, and we construct our subjective realities by imposing meaning on flow of events that, in fact, are no more than stochastic drifts. The primary mover behind this type of reasoning was Karl Popper, a vocal critic of the logical positivism, who in his book (1957) The Poverty of Historicism rejected the concept of history that aims at discovery of historical trends. Popper's (1934) Logik der Forschung (logic of scientific discovery) was criticized as being only a restatement of Kantian synthetic a priori propositions and their quid facti verity and some assumptions in the The Poverty of Historicism as simple reversals of Kant's beliefs, similar to those by Marx of Hegel's. In the similar vein, Francis Fukuyama's (1992) The End of History' with the passage of time, seems less and less to be a viable theory of history.

Methodology There is a different time perspective associated with each of the basic models of historical change. Chaotic models of human history tend to be based on detailed considerations of historical events, with an associated attenuation of the time perspective. Cyclical models are frequently used for descriptions of historical events within the time span of two or more generation cohorts. The linear models often attempt holistic explanations of human history. Consideration of both the abstract visualization of historical change and the degree of its generalization suggests that these two parameters are related and play an important role in formulation of theories of history. Would it be possible to simulate these parameters and their corresponding theories of historical change?

Selecting among several suitable models, we opted for the method of Moving Averages and Fast Fourier Transforms. There are several advantages to these methods as compared to other methods of trend analysis. The advantage of moving averages is that no prior assumptions about the analyzed trend are necessary. The only parameter that has to be specified is the order of the moving average. Fast Fourier Transforms are superior to moving averages in cases when the magnitude of the order of the moving averages is too large relative to the length of the series.

We decided to simulate the theory described above on Quincy Wright's (1965) database, containing frequencies of wars from the 15^th to the 20^th century, by using the method of moving average and Fast Fourier Transforms. The method of moving average, used for analysis of secular trends, is similar to the low-pass filters used in signal processing. This convolutionary method averages the values adjacent to a central value of an interval, rolled over the entire span of the series. The main parameter of this method is called the order of the moving average, which can vary from 1 to n, where the n is the length of the series. The central value of the moving average can be any of the methods used for estimation of the central tendency of data; commonly used method is the algebraic mean. If the value of the order of the moving average is 1, the moving average does not abstract values of the series from the values adjacent to its central value, but merely reproduces the data series. This is analogous to observation and description of historical events with no attempt at their generalization. As the value of the order of the moving average increases, the values adjacent to the central value of the moving average are averaged over larger and larger intervals, simulating more and more general abstractions from the observed events.

Simulation of the chaotic theory of history Initially, we set the order parameter of moving averages to unity, so the data were reproduced, but not generalized. This model simulated descriptions of historical events with no attempts at abstraction of historical trends. When visualized, no compelling pattern was discernible, creating impression that observed events are chaotic and unrelated, suggesting that the prevailing trend among contemporary historians to describe historical even without attempts to discern their patterns may be related to a low level of abstraction.

Simulation of the linear model of historical change An increase of the order parameter to a value resulting in averaging of adjacent data points over a moving interval of 300 years would run into technical difficulties, so we had to resort to Fast Fourier Transforms for simulating generalizations of this magnitude. Smoothing the obtained monotonically ascending trend resulted in a linear, rapidly increasing trend. This linear component of the time series data for wars in Western civilization captures the progress of war making capabilities, along the timeline, as a linear increase in the ability to project power. With the passage of time, the severity of armed conflicts of Western Civilization steadily increased. Reminiscent of linear models of historical change, telescoping the time interval over which the cognitive generalizations are made to the whole history of mankind is characteristic of these theories, typical, among others, of St. Augustine and Immanuel Kant.

Simulation of the cyclical trends of historical change Generalizations over twenty year intervals were simulated by the 20^th order of the moving average. Era that started with Columbus sailing to America in 1492 and sometimes called the Century of Spain was punctuated by the Thirty Years' War (1618-1648) when the Protestant States of Europe (England, Scandinavian states, some German principalities and others) were at war with the Empire of Spain. In the series of wars between the Thirty Years' War and the Wars of the French Revolution and the Napoleonic Wars Britain's main adversaries were Spain and France. During the Napoleonic Wars (1789-1815) the principal adversary of Britain was France and it was the British-Russian alliance that defeated Napoleon. The British-Russian alliance which in its final phases also included the United States as a principal combatant also won the World Wars (1914-1918, 1939-1945). At this level of generalization, the cycles of war show average amplitude of about 50 years.

Assumptions of quantitative history Quantitative history was pioneered by Lewis F. Richardson, a student of Karl Pearson, who assimilated his mentor's maxim that ''beliefs ought to be tested by statistics''. Richardson's assumptions pertained to questions debated over centuries in the philosophy of history. His key assumptions were that

The past could serve to guide the future, for what has happened often is likely to happen again, as human affairs are partly free, and partly determined. The statistical methods allow one to find patterns, association, and sequences that regularly recur. Mathematical expressions of these regularities help to make the implicit assumptions explicit, their consequences deduced, absurd implications deleted, and disputable statements pinpointed. (Richardson, 1960, Wilkinson, 1980).

Methods of quantitative history Methods of quantitative history are those of statistics, reinforced by computer algorithms for data analysis and visualization. A landmark in the study of secular trends was the publication of Makridakis and Wheelwright's (1978) Interactive forecasting: univariate and multivariate methods. During the 1970's, 1980's and 1990's Robert B. Ammons edited a section in the Psychological Reports on Quantitative History and William B. Michael edited a section on innovative computer programs in the Educational and Psychological Measurement. Most of these programs, supplementing the standard statistical packages as SAS or SPSS, were collected in Silver and Hittner's (1998) Guidebook of statistical software for the social and behavioral sciences.

David McClelland (1917-1998).

Origins of quantitative history can be also traced to the work of David McClelland, who summarized findings of his numerous empirical studies about quantitative history in his books The Achieving Society (1961), and Power: the inner experience (1975). McClelland’s empirical methodology was coined within the theoretical framework of social theories of Talcott Parsons and Karl Marx and theories of history of Pitirim Sorokin and Arnold Toynbee with his empirical studies revolving around the measurement of the need for achievement, need of affiliation, and need for power. Using content analysis of historical documents, McClelland have described the role these theoretical constructs play in the formation, flourishing, and fall of societies and civilizations. Analyses of documents from early stages of a civilization typically show high levels of the need for achievement. With the passage of time, the need for achievement is replaced by the need for affiliation and the need for power. Changes in these motivational patterns are reflected by the increase in violence and the probability of war.

Stories expressing the dominant needs of a society may be found in magazines, books, and children's readers or portrayed in movies and theaters. If a story is popular, it may express not only the motivation of the writer, but can also reflect the needs that the readers, audience, and motivational currents within a society. Achievement motivation also finds its expression in art. Sculptures, paintings, and architecture may reflect these motivational traits. Straight lines are generally indicators of achievement motivation; convoluted lines indicate the lack of it. Thus, for instance, the Doric order marks the rise of classical Greece, the Ionic order it’s flourishing, and the Corinthian order its decline. These architectural changes paralleled changes in the general level of achievement motivation of classical Greece. Shortly after the invention of scuba diving apparatus, treasure hunters began to recover Greek amphorae from the ancient Greek ship sunk in the Mediterranean. Adorned by scenes from Greek mythology, amphorae served as containers for transport of grain. Analyzing paintings on the amphorae recovered from the sea floor, the level of achievement motivation encoded within the painting’s design was related to the distance of the location of their recovery from Athens. The result showed a significant relationship between the prosperity of Greece and the need for Achievement, reflected in paintings on her amphorae resting for centuries on the bottom of the Mediterranean.

Another landmark study, confirming validity of McClelland's theories, was the study of Bradburn and Berlew (1961) who analyzed achievement motives in British school readers (bottom) and showed a strong correlation of these themes, a generation later, (top) with the

Britain

's industrial growth.

Retrospect and prospectus Toward the end of his life, David McClelland contemplated the impact of his life-long work that aimed at quantification of history. McClelland writes that he tried to show historians how things could be done, but that in the intervening years, he did not notice a slightest inclination on the part of the historians to follow his example. History in general, and historians in particular, with few notable exceptions, do not describe historical events by using the methodology of quantitative analysis, but more likely find their truths among the ultima veritas inscriptions that can be found on barrels of medieval cannons. However, the number of the quantitative history entries on the Internet search engines is rapidly growing. Let us hope that McClelland's observation only affirms that he was well ahead of his time.

Isaac Asimov (1920-1992) at 20
Enhanced Reality Portrait.

Postscript Psychohistory is the name of a fictional science in Isaac Asimov's Foundation Trilogy (1951-1953), which combined history, psychology and mathematical statistics to create a (nearly) exact science of the behavior of very large populations of people, such as the Galactic Empire. Asimov used the analogy of a gas where the motion of a single molecule is very difficult to predict, but the mass action of the gas can be predicted to a high level of accuracy. Isaac Asimov's Foundation Trilogy in many respects resembles Gibbon’s History of the Decline and Fall of the Roman Empire. Asimov tells the story of Harry Sheldon’s group of social scientists who, using the quantitative methodology, was not only able to predict the decline and fall of the Galactic Empire, but also suggested how to shorten the subsequent period of the Dark Ages. Asimov’s trilogy captured the general optimism of his times and the imagination of many readers. Using quantitative methodology, physicists were able to describe the structure of our physical world. Toward the end of 1950s computer programs became available, and it seemed that the vision of the new social science, called by Auguste Comte the "social physics" would finally come of age.

On September 25, 1987, Asimov gave an interview to Terry Gross on her National Public Radio program, Fresh Air, excerpted as follows.

Gross: What did you have in mind when you coined the term and the concept of psychohistory?

Asimov: Well, I wanted to write a short story about the fall of the Galactic Empire. I had just finished reading the Decline and Fall of the Roman Empire for the second time, and I thought I might as well adapt it on a much larger scale to the Galactic Empire and get a story out of it. In order to keep the story going from story to story, I was essentially writing future history and so I assumed that the time would come when there would be a science in which things could be predicted on a probabilistic or statistical basis.

Gross: Do you think that would be good if there really was such a science?

Asimov: Well, I can't help but think it would be good. I think if we can somehow get across some of the problems that face us now, humanity has a glorious future and that if we could use the tenets of psychohistory to guide ourselves we might avoid a great many troubles.

Asimov’s writings also contain some interesting insights into problems inherent in time series analysis. In his story The Ugly Little Boy Asimov supported the plot by the concept of "being too close," which he illustrated on the example of trying to touch one's shoulder and elbow with the hand of the same arm. Although elbow is closer, one can touch the shoulder, but not the elbow. In his youth, the author of this website was impressed by that story to the point of translating it into an obscure East European language. The memory of a personal letter he received from Isaac Asimov at that occasion helped him to keep up his spirit when, while conducting research on quantitative history, he encountered seemingly insurmountable obstacles.

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Jean Fourier (1768-1830)	Quincy Wright (1890-1970)