"...Characterized by the property that the record of a limited number of events in the process enables is to predict the next event, and all subsequent events, with complete accuracy. Suppose, for instance, we have a process which consists of writing down the numbers zero, one, two, threem, four, and five. We perceive immediately that there is an order, that each figure is greater by one than its predecessor. We can move from understanding into prediction by predicting that the next number will be six. Here, however, we encounter a fundamental principle. Understanding only adds to prediction if the system that we understand remains stable.
"... In mathematical terms, a numerical process in time is a sequence, or rather a special case of a sequence, for sequences can also occur in space. What we mean by understainding is the discovery of a differnce or differenctial equation of finite degree which governs the sequence. A difference equation of the first degree is a stable relationship between any member of the sequence and the next number, as in the example above. In a difference equation of the second degree, the stable realtionship is between two successive numbers of a sequence and the one following. Suppose for instance, we write down the famous mathematical sequence 1, 1, 2, 3, 5, 8, 13, 21,.... A little observation reveals that each number is the sum of the two previous ones (this is know as the Fibonacci series). It is easy to predict the next number in the series will be 34, and a little simple arithmetic enables is to continue the series as far as we wish." 10
"...Consideration of the nature of conflict processes. Perhaps the most importatn class of these processes i what may be called reaction processes. There are processes inb which a movement on the past one party so changes the field of the other that it forces a movement of this part, which in turn changes the filed of the fist, forcing another move of the second, and so on. The economist is familiar with the theory of the price war. The politicial scientist meets the reaction process in the concept of the arms race, which is theoretically very similiar to the price war. We find the same processes going on, however, at all levels of relationships--between union and management, between husband and wife, betweem king and parliment, between president and congress, between administration and faculty, between teacher and student, and even in the animal kingdom, between predator and prey, parasite and host, eater and eaten." 11
"Birth: bi = Fb(Xi, X2,..., Xn)
Death: di = Fd(Xi, X2,..., Xn)
Equilibrium: bi = di
Suppose we have no species in an interacting system, where Xi is the population of the ith species at a given time, then suppose that bi is the number of births and di the number of deaths of the ith species at a given period. For the speices i, we can then postulate three equations which must be fulfilled in equilibrium: