In such systems, the whole is more than the sum of the parts, not in an ultimate, metaphysical sense, but in the important pragmatic sense that, given the properties of the parts and the laws of their interaction, it is not a trivial matter to infer the properties of the whole. In the face of complexity, an in-principle reductionist may be at the same time a pragmatic holist.
Complexity as hierarchy
Hierarchy is one of the central structural schemes of complexity.
Structures of a complex system are made of interrelated substructures, each of which are also made of subsystems, etc. Until some elementary particle level is reached.
In most systems in nature, it is somewhat arbitrary as to where we leave off the partitioning, and what subsystems we take as elementary.
Different things might be considered elementary depending on what is being studied. Ex: cells, stars, atoms can all be used as elementary subsystems for biology, astronomy and chemistry.
Most physical and biological hierarchies are described in spatial terms. We detect the organelles in a cell in the way we detect the raisins in a cake — they are “visibly” differentiated substructures localized spatially in the larger structure. On the other hand, we propose to identify social hierarchies not by observing who lives close to whom but by observing who interacts with whom. These two points of view can be reconciled by defining hierarchy in terms of intensity of interaction, but observing that in most biological and physical systems relatively intense interaction implies relative spatial propinquity.
Complex systems and emergence through evolutionary processes
The “improbability” of evolution has nothing to do with this quantity of entropy, which is produced by every bacterial cell every generation. The irrelevance of quantity of information, in this sense, to speed of evolution can also be seen from the fact that exactly as much information is required to “copy” a cell through the reproductive process as to produce the first cell through evolution.
It is much easier to create complex hierarchies with Evolution, because subsystems are stable stepping stones from which new larger system can emerge. On the other hand, creating a very complex system from scratch is very unlikely.
Moreover, there is selectivity in the evolutionary process, mainly due to two causes:
- Building blocks are stable, and passively guide further evolution
- Reproduction is possible in many complex systems, allowing transmission of experience from past complex hierarchies.
The argument can be turned around by saying that predominance of hierarchies in complex systems is simply a result of properties of the evolutionary process.
Dynamic properties of hierarchically-organized systems
Some systems are decomposable. This means that it can be seen as a sum of independent subsystems made of elementary particles. This is often not very accurate and we can also use the theory of nearly decomposable systems, where subsystems interact weakly.
This is often useful for separating high-frequency dynamics (usually within the subsystems) of a hierarchy from its low-frequency dynamics (interactions between subsystems).
Relations between complex systems and their descriptions
For nearly decomposable systems, little information is lost by representing them as hierarchies.
If there are important systems in the world that are complex without being hierarchic, they may to a considerable extent escape our observation and our understanding. Analysis of their behavior would involve such detailed knowledge and calculation of the interactions of their elementary parts that it would be beyond our capacities of memory or computation.
Complex systems often admit simple descriptions (relative to the initial complexity). One of the main simplification mechanism is redundancy.
If genetic material is a program — viewed in its relation to the organism — it is a program with special and peculiar properties. First, it is a self-reproducing program ; we have already considered its possible copying mechanism. Second, it is a program that has developed by Darwinian evolution. On the basis of our watchmaker’s argument, we may assert that many of its ancestors were also viable programs — programs for the subassemblies.
How complex or simple a structure is depends critically upon the way in which we describe it. Most of the complex structures found in the world are enormously redundant, and we can use this redundancy to simplify their description. But to use it, to achieve the simplification, we must find the right representation. The notion of substituting a process description for a state description of nature has played a central role in the development of modern science. Dynamic laws, expressed in the form of systems of differential or difference equations, have in a large number of cases provided the clue for the simple description of the complex. In the preceding paragraphs I have tried to show that this characteristic of scientific inquiry is not accidental or superficial. The correlation between state description and process description is basic to the functioning of any adaptive organism, to its capacity for acting purposefully upon its environment. Our present-day understanding of genetic mechanisms suggests that even in describing itself the multi-cellular organism finds a process description — a genetically encoded program — to be the parsimonious and useful representation.