D. C. Mikulecky

Professor of Physiology

Medical College of Virginia Commonwealth University

1. Emergence results from the complexity of nature and the limits of the machine metaphor

We have observed that the concept of complexity had to arise when the dominant formalism, the Newtonian Paradigm, began to be pushed to its limits. What happened was a series of surprises, all of which led to a need for the concept of complexity in order to explain what was happening. This process was repeated many times in many independent settings. Gradually, as different people experienced it, the field of complexity research was born. The appearance of seemingly new attributes of systems that were recognized as complex often was called emergence. Thus, in one sense, emergence is a result of the limits of a dominant formalism, and might even be associated with error of a certain kind. There is a value in seeing this since we can then distinguish between truly differing forms of emergence.

1.1     Emergence and complexity as new developments within the dominant formalism: chaotics

The Newtonian Paradigm centers on dynamics. Because of the way the mathematical basis for the formalism developed, it was dominated by linear dynamics, first in particle kinematics then in linear systems theory. As the mathematics of non-linearity was developed in the context of dynamics, new results were obtained that significantly altered our view of the world. The culmination of these was the discovery of chaotic dynamics. It was easy to see how these discoveries in the mathematical structure underlying the Newtonian Paradigm, which really were forerunners to the concepts of complexity and emergence, became central examples of those concepts. Once the identification was made, it had the added reinforcement of novelty, public awe, and widespread applications. Suddenly chaos appeared everywhere one looked and butterflies were making weather happen. As novel and exciting chaos is, it is neither an example of complexity nor of the strongest kind of systems emergence. It did give rise to another concept, the idea that emergence is aided or even stimulated as systems leave some stable domain and approach chaos. The "edge of chaos" became associated with novel behavior and emergence of new phenomena. Thus, the Newtonian Paradigm, for a moment, seemed to regain its claim to being generic and seemed to exhibit all that was necessary to absorb the newly recognized realm of complexity and emergence. This did not last long and soon chaotics was seen, by at least some, as a diversion. The reason is clear in the context of this discussion. Nothing chaotics revealed was outside the Newtonian Paradigm. It merely explored the limits of the non-linear dynamics that lies at the heart of the formalism. Complexity defies this formalism, for by its very nature, it can not be seen from within formalism. It requires that one view from outside! This brings us right back to our definition, and once more things are consistent. That leads us to the next form of emergence that arises from our surprise when the dominant formalism fails us.

1.2    Emergence as the failure of the dominant formalism.

Nature is complex and therefore it is replete with examples of things that do not form models when placed into a modeling relation with the Newtonian Paradigm. Here is another source of emergence. This is a temporary class of emergent phenomenon, since the eventual expansion of science beyond the Newtonian Paradigm will incorporate the explanation for these phenomena into the dominant set of formalisms.

.1.3    Emergence in nature

There are a number of natural phenomena which include aspects which would seem to warrant the description of being emergent. Two, in particular, are developmental biology and evolution. In each case, a system is able to change profoundly and to generate new properties and structures from existing ones. Neither of these is capable of being modeled by the Newtonian paradigm, so they also fit that category of emergent property. Once again, the lasting aspect of the emergent nature of these systems is in their own change, not in the need for new ways to describe them.

2.0    The claim for emergent properties in computer simulations

The use of genetic algorithms, Boolean networks, cellular automata, artificial neural networks, and other related approaches is merely an implementation of the Newtonian Paradigm made possible buy the huge increases in modern computing power. Some of these interesting and impressive systems behave in ways that, in limited ways, seem life-like. In this limited context, the systems do exhibit what might be called a form of emergence. This emergence is a manifestation of a form of surprise when the Newtonian paradigm is taken to new limits of complication. The confusion between complication and complexity is one which needs further elaboration and that will be forthcoming. Another forthcoming topic requiring far more elaboration is the difference between simulations and models.