Donald C. Mikulecky

The emergence of complexity: science coming of age or science growing old?

The emergence of a new field of science called complexity theory has made an impact on the community of scientists as well as the general public. This brief tutorial takes a very special view of this. The thesis is that complexity science has grown out of a general lack of satisfaction with traditional scientific practices and their failure to find a way of capturing anything but a shadow of complex reality. In spite of the many impressive advances from science and technology, it is clear that the picture delivered of the world is that of a surrogate world populated by machines and mechanisms. The nature of the real world demands more than traditional science can deliver. Yet traditional science has constraints and bounds on its universe of discourse. Complexity science, as presented here, demands that the barriers and constraints be removed in order to gain a more complete view of nature. This tutorial presents a summary of what is entailed by this new methodology.

Network thermodynamics and complexity: a transition to relational systems theory.

Most systems of interest in todays world are highly structured and highly interactive. They cannot be reduced to simple components without losing a great deal of their system identity. Network thermodynamics is a marriage of classical and non-equilibrium thermodynamics along with network theory and kinetics to provide a practical framework for handling these systems. The ultimate result of any network thermodynamic model is still a set of state vector equations. But these equations are built in a new informative way so that information about the organization of the system is identifiable in the structure of the equations. The domain of network thermodynamics is all of physical systems theory. By using the powerful circuit simulator, the Simulation Program with Integrated Circuit Emphasis (SPICE), as a general systems simulator, any highly non-linear stiff system can be simulated. Furthermore, the theoretical findings of network thermodynamics are important new contributions. The contribution of a metric structure to thermodynamics compliments and goes beyond other recent work in this area. The application of topological reasoning through Tellegens theorem shows that a mathematical structure exists into which all physical systems can be represented canonically. The old results in non-equilibrium thermodynamics due to Onsager can be reinterpreted and extended using these new, more holistic concepts about systems. Some examples are given. These are but a few of the many applications of network thermodynamics that have been proven to extend our capacity for handling the highly interactive, non-linear systems that populate both biology and chemistry. The presentation is carried out in the context of the recent growth of the field of complexity science. In particular, the context used for this discussion derives from the work of the mathematical biologist, Robert Rosen.

COMPLEXITY SCIENCE AS AN ASPECT OF THE COMPLEXITY OF SCIENCE

1. INTRODUCTIONHow can we treat science as an object of scientific inquiry? The centralproblem arises with that question. Science has tried to rid itself of circu-larity and in so doing has become a very limited method for examining thecomplex world it tries to have us understand. Self reference is at the centerof so many of the interesting thing we want to understand including andespecially life itself. The existence of this self referential character is theessence of what we have come to call “complexity”. The works of RobertRosen [1, 2, 3] spell this out in great detail. This series of investigationsbegan over a half century ago yet still remains virtually unrecognized by thevast majority of those who call themselves “scientists”. That fact alone canbe a springboard to launch a study of science as an object, which is whatthis study is all about. I have reviewed the technical aspects of Rosen’swork elsewhere [4] and will consider the broader philosophical implicationshere.Using the ideas Rosen developed, we can begin with the following work-ing definition of complexity:Complexity is the property of a real world system that is manifestin the inability of any one formalism being adequate to capture allits properties. It requires that we find distinctly different ways ofinteracting with systems. Distinctly different in the sense that whenwe make successful models, the formal systems needed to describeeach distinct aspect are NOT derivable from each other.Rosen created a dichotomy between complex system and simple systems,or mechanisms. The essence of that dichotomy is summarized in Table 1.

Methods of mathematical modelling

Nonequilibrium thermodynamics and kinetics as presented in chapter 1 are adequate and sufficient for the analysis of systems or processes in the steady state. On the other hand, they only provide necessary tools for the analysis of a system on its way to a steady state, but not the actual means of performing the analysis. To carry out such an analysis one must invoke mathematical modelling. Moreover, even in the steady state modelling proves to be a valuable means of exploring the behavior of complex systems. Thus mathematical modelling is an important subject in bioelectrochemistry and hence is dealt with in this chapter. Furthermore, this chapter includes a number of carefully-chosen worked examples. These examples are not only illustrative and designed to cover most features of modelling, but they are also biologically realistic, and in an important sense extend the treatment given in chapter 1. In addition, they present novel aspects of bioelectrochemistry which are difficult to display without the aid of simulation.