Another fascinating tome edited by Robert Rosen: Theoretical Biology and Complexity. This time it is a book of essays divided into three sections, each by a different author but all originally from the same department of Physiology and Biophysics at Dalhousie University in Halifax Novia Scotia, Canada. These are:
1. The Dynamics and Energetics of Complex Real Systems, by I.W. Richardson.
This first chapter makes use of the conventional understanding of complexity as interpreted by thinking of complexity as simply many interacting objects, particles, forces. This just means that simple things stay simple because there is only one force driving it. Complexity then arises from the interplay of many such forces. This article uses the usual Newtonian approach of phase space and particle space. A kind of hierarchical structure. As usual there are particles and forces pushing them around based on conservative potentials. These potentials are either scalar or vector potentials with scalar ones related to energy and vector ones to momentum. There are also certain material properties, fluxes, fields and continuity equations. It's basically a kind of unified Newtonian paradigm with some additional aspects such as information and how it relates to energy. This article does a good job of unifying, ordinarily, disparate subjects as seen in many a mechanics/fluid/continuum dynamics text. However, it doesn't really do anything different from what is already understood. No new questions are asked, no new structures are created.
2. Categorical System Theory, by A.H. Louie
On the other hand here we have a new way of studying natural systems using category theory, first invented in pure mathematics as a way of studying the relationships between mathematical structures, e.g. groups, topological spaces, rings, etc. Category theory, its basic tenets, is introduced, e.g. morphisms, functors, natural transformations etc explaining how we may form maps connecting say sets with other sets and mappings with other mappings. This leads onto defining equivalence relations and how these may be used to study how given formal systems may be used to relate to each other, e.g. a meter (as one system) being used to observe another (the system being measured). This was first delineated by Rosen in his first major work: "Fundamentals of Measurement and Representation of Natural Systems" (FM). The main difference is that this whole set of ideas is put into a more rigorous mathematical frame by using categories. Gradually, this leads onto both continuous and discrete dynamical systems and how to define them using category theory, including bifurcation. Finally the modelling relation is discussed in this context and followed by biological implication such as aging and growth as well as how to define an organism. This is a wholly new way of looking at mathematical biology first initiated by Rosen and put into this framework by his student Louie. Unless you are already quite familiar with category theory and some abstract algebra then this second section will be difficult to follow. For a far fuller and simpler explanation of what is going on a read the book by Rosen FM, mentioned above. Rosen's book is also much more engaging whereas Louie's is more pragmatic and pure mathematical.
3. Organism as Causal Systems Which are not Mechanisms: an essay into the nature of complexity, R. Rosen
In this third and last essay Robert Rosen summarises much of his best known work including (M,R) systems. He starts off by discussing the state of the art in biology up to 1985 which emphasises molecular biology and the standard doctrine that is accepted now in this science. Then he starts to criticise this conventional view and introduces Rashevsky's relational biology. This is followed by his own study in the area, specifically metabolism-repair, (M,R) systems. Such systems throw away the material and keep the organisation. This is a radical departure from the norm and a very refreshing change. There follows a brief introduction to the modelling relation, the causal categories of Aristotle and then a study of the essence of the Newtonian paradigm elucidated in a simple but enlightening way where the various categories of causation in this approach are laid bare. Finally truly complex systems are introduced which essentially have very little to do with the usual version of this idea as promoted in section 1. above. This idea goes way beyond state spaces and the usual reductionism of the Newtonian paradigm. Complex systems essentially becomes systems which may be approximated to some degree by say mechanical approaches but only in a limited way. They possess many such mechanical models but none of these models can capture all of these systems. Complex systems also possess the extra category of causation left out of the Newtonian paradigm which only works with the material, efficient and formal causes. This extra category is final causation usually interpreted as teleological in nature (future effects working into the past). This is found to be wrong and in fact final causation is a kind of predictive, anticipatory model existing within another model. This anticipatory model informs the original one thereby acting to predict the future rather than the future acting back into the past.
These essays are very good for those wishing to polish up on previously studied areas but of little use to someone new to the subject. It is possible to learn something of these ideas, especially the first essay, but strong familiarity with category theory is a good idea. An excellent summary of old and new ideas in the subject.
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