Thomas Kuhn held that science goes through periodic revolutionary periods followed by long periods of normal growth. His critics, on the other hand, claim that whether any particular scientific activity is. "normal" or "revolutionary" is a matter of the way it is described and not a quality intrinsic to the activity itself. It is my contention that both are correct. It is a property of complexity that dramatic change can come about as the direct result of normal change, and that this kind of change can be described as an emergent property of the interaction of a critical number of "normal" activities. As a result, the close examination of individual actions during a period of extraordinary change may reveal that they Do not differ significantly from the same kinds of activities during less climactic periods. Sudden and dramatic change similar to these have been studied extensively in physical systems. Such changes, as laser activity, or the effect of Curie temperature in ferromagnetic materials, have been examined from three different aspects, phase transitions, group renormalization, and catastrophe theory. Despite differences, all three approaches attempt to explain dramatic changes which are not caused or triggered by external causes, but which are instead, emergent qualities that some normal interactions exhibit when they reach a critical, or threshold level.

Phase transition is a method of describing the sudden and abrupt change a-I the emergence of a higher level of activity Upon the attainment of threshold condition. Boiling water, for example when it is heated evenly from the bottom first begins; to form random bubbles of steam, and then, when it reaches a critical temperature, it begins to roll. Laser activity is another example. Laser materials, as they are "pumped" with electromagnetic energy, begin to emit light. Under ordinary circumstances the light has. a random energy distribution but, when the threshold level is reaches lt suddenly switches to a condition of coherence, with a single, or narrow band of frequencies, a single polarization, and in a single direction. The object of phase transition studies has been to develop mathematical models of this kind of activity. these models, however have been descriptive rather than explanatory.

Kenneth Wilson received the Nobel Prize in physics for his. approach to an allied problem. This deals with the fact that physical systems exist simultaneously at many different scales of length. Physicists normally deal with only one scale at a time, abstracting out others. For example, an ocean has currents that persist for thousands of millimeter, tides of global extent, and waves that range in size from a few millimeter-; to several meters. From the smallest structure to the largest comprises some 17 orders of magnitude. Yet, considering the interactions between two molecules of water, it makes no difference whether they are in a tea cup or in the middle of the pacific ocean. There are conditions, however, under which there occurs a total interaction encompassing all levels. These happen when a "threshold " condition occurs, such as for example, in water at a pressure of 17 atmospheres. Once that point is reached (when a threshold condition is reached, a step change take-_ place) water cannot be made to boil until it reaches. a temperature of 647 degrees Kelvin. As it approaches this point, the water develops fluctuations at all possible scales and at precisely that point the fluctuations become infinite.

As Wilson described it, Renormalization group is not a theory, but a general method of constructing theories. It is developed around a similarity in the critical behavior of a large number of materials called "(critical-point universality). According to this hypotheses, only two quantities determine the critical behavior of most systems, the dimensionality of space and the dimensionality of the order parameter. An example of an order parameter would be an isotropic ferromagnet where the spins can be aligned in any direction in three dimensions. Such a system would have a dimensionality of 3. What interests us in this thesis is that it represents another approach to the problem of sudden and drastic change. ln Renormalization group the system is seen as a neural net that is a network: of nodes developed after the design in animal nervous system, where the state of any given node is determined by the states of the nodes it is in communication with (its neighborhood). As the critical point is reached instead of states changing individually, complete neighborhoods begin to flip as though they were reacting to those neighborhoods they are in contact with until at the critical point the entire mass switches at one time

. Catastrophe theory, developed by Rene Thoms, and discussed by Colin Renfrew, is a method of utilizing topological language to show how discontinuities in a system can be produced by gradual and continuous; change in the control variables. It deals primarily with systems whose equilibrium states are obtained hy maximizing or minimizing a cost function, a situation which has correlations in many human systems. The attainment of critical conditions determines the advent of the step change (called a catastrophe cusp).

My point is that revolutionary change does not necessarily have to be produced by a change in applied forces, it can occur as a normal reaction to gradual change as lt approaches a critical point. If we describe this in terms of complexity theory, then only the language is different. In this case we consider the constraints on the system as a new level that has emerged from the lower, or active level. As an emergent system lt is determined not by the forces acting from the outside. but serves to insulate the lower lever systems from the outside environment.

This can be seen particularly in human social systems. Social systems are developed to respond to pragmatic world-three models of environmental forces which, being part of the autonomous world-three, are not directly available to the human mind. As with all pragmatic world-three structures, it is at best a gross approximation. The failure of the social system to meet the requirements of the real environment is seldom blamed on the model, which is. inevitably faulty. It is normally blamed on the social system. The social system, on the other hand, has probably been determined through a process of maximization and minimization and might very well represent an optimum response to the model.

What this means is that the existence of variety In the social system can mean that a new and novel Interpretation of the model can cause a major reordering of the system. ln the case of science, it is a matter of the occurrence of a theory which when tested against the physical world. Presents. a solution to real problems that requires a reordering of the paradigm. In this case their will be a sudden and revolutionary change and each individual element of that change will, lf it is examined alone, appear to be simply a maximization according to new Information and not some special kind of revolutionary change.