Properties and behaviours at the systemic aggregate level are derived as statistical averages from probability distributions describing the likelihoods of the various states available to the components.

The relative freedom and political stability of seventeenth- and eighteenth-century Britain produced an intellectual milieu amenable to advances in the natural sciences and philosophy. The major theme of British psychological thought was empirical, emphasizing knowledge acquired through sensation. The mechanism of this acquisition process was association. Founded by Hobbes but fully articulated by Locke, British empiricism retained the necessity of the mind construct while underlining the importance of sensations. Berkeley, Hume, and Hartley evolved skeptical positions concerning the reality of matter and mind that could have left the British movement in the same sterile position as French sensationalism. In addition, James Mill, although he was somewhat salvaged by the utilitarian influence, reduced associations to mental compounding. However, the Scottish common sense writers succeeded in restoring empiricism to a more flexible and open-ended position that recognized complex and integrative psychological phenomena. Thus, the later empiricism of John Stuart Mill, while adhering to scientific inductive methods, adopted a broadly based model of psychology that viewed mental operations and physiological processes as complementary and necessary dimensions of psychological inquiry. By the nineteenth century British philosophy was providing strong support for the study of psychology.

We discuss forecasting of the transitions accompanying the intermittent dynamics of complex systems. Co-evolutionary dynamics is particularly challenging.

Assume we are able to obtain the joint probability for a set of time series representing a complex system. Based on the joint probabilities, information theory can help to analyse the nature of the interdependence in the system. It is particularly important to be able to distinguish between different types of emergent behaviour, such as synergy or redundancy.

The Romans adaptation of Greek philosophy was illustrated by the Stoics and Epicureans. The Stoics held that humanity is determined by the fates of nature, while the Epicureans believed that happiness came from seeking pleasure and avoiding pain. Plato was revived by Plotinus and dominated Roman philosophy during the early years of Christianity. Both the missionary zeal of early Christians and the tranquility of Roman administration rapidly spread Christianity. The teachings of Jesus were bolstered by defenders, who gave Christianity form and content. St. Augustine successfully reinterpreted Platonic thought within Christian theology, and the consequent influence on psychology continued well beyond. With the fall of the Western empire, intellectual life came to a virtual halt, and only the monastic movement preserved remnants of Greek and Roman civilization. The papacy assumed a leading role in spiritual direction and civil administration. The power shift to the East saw the Byzantine Empire assume a distinctive Greek character. The rise of Islam threatened the survival of Christianity in the Middle East and in North Africa. But, at the same time, much of the Greek heritage of scholarship was preserved and extended in the great academic centers of medieval Islam.

The next chapters are dedicated to mathematical approaches of central relevance to the analysis and modelling of emergent behaviour amongst many interacting components.

German science and culture of the seventeenth and eighteenth centuries benefited from the enlightened patronage of the Prussian King Frederick the Great. Moreover, the universities of Germany prospered and became centers of excellence in the West, especially in science. Advances in psychology by German philosophers focused primarily on mental activity. Discarding the environmental determinacy of British empiricism, Leibniz defended the active agency of the mind in molding sensory data to provide experience. The active principle of his monadology lent itself to a dynamic view of harmony between independent physical and psychic processes. The rationalism of Wolff was fully elaborated by Kant, who described pure reason as the formation of perceptions innately through time and space, and asserted an elaborate structure of the mind in terms of categories that order the environment. From these formulations, German psychology received a variety of models suggested by Herbart, Beneke, and Lotze. Collectively, the German tradition is diverse but united by the belief in the activity of the mind and its control of environmental influences.

The ascendancy of French political power supported literary success and scientific achievement. Investigators such as Lagrange, Laplace, and Lavoisier gave mathematical and empirical support to modern chemistry, physics, and biology. In parallel, philosophical discourses on psychology led to a reinterpretation of Descartes’ formulation to focus on sensation. Condillac, Bonnet, and La Mettrie argued for the equation of mental operations and sensory input, with the result that they reduced psychology to sensation. Helvétius and Cabanis attempted to back off from such extremism by asserting the mediating role of a central ego, although both remained committed to sensory physiology. Biran and Comte recognized the consequences of reducing psychology to mere sensory physiology, but each worked out separate solutions. Biran rejected sensationalism as inadequate, suggesting an individual psychology based on consciousness and the will. In contrast Comte ultimately accepted sensationalism and dismissed psychology. For him, the individual person should properly be studied by physiology; the individual behaving in a group is the province of sociology. Comte, however, advocated a spirit of objective observation that was eventually useful to psychology. Thus, the successors to Descartes in France left psychology in a somewhat tenuous position, removed from recognition as a formal discipline.

In agent-based modelling the dynamics of the components, i.e. the agents, is defined in terms of rules for the agents’ response to their surroundings.

We consider dynamics represented by successive stochastic moves. Assuming we know the transition probabilities for going from one configuration to the next, we will discuss ways to determine the probabilities of the individual configurations.

Functional psychology was less a system than an attitude that valued the utility of psychological inquiry. Assuming a philosophical underpinning from the pragmatism of William James and Charles Sanders Peirce, functional psychology fit well into the pioneering spirit of America. From its beginning, functional psychology had a clear emphasis on applying psychology to individual and social improvement, as was evident from the works of Münsterberg, McDougall, and Hall. The tradition of British natural science and evolutionary theory was integrated into psychology in the views on adaptation championed by the Chicago functionalists, such as Dewey, Angell, and Carr. Mental testing and the study of human capacity constituted important areas of investigation among the Columbia functionalists, represented by Cattell, Thorndike, and Woodworth. Although its reaction to structural psychology kept functional psychology from developing a systematic alternative model of psychological inquiry, this phase of American psychology resulted in two critical benefits. First, functionalism firmly entrenched the new science of psychology in America and imposed on it a particular American orientation toward applied psychology. Second, functional psychology provided a necessary transition from the restricted context of structural psychology to more viable models of psychology, permitting the science to progress.