Modularity, networks and growth of complexity

Herbert Simon and Albert Ando (Simon and Ando 1961) have developed the concept of near decomposability, which is based on the idea that systems of interactions can be separated into groups (modules) according to the strength of interactions. If there are groups of elements among which interactions are much stronger than among other elements, while they show less strong interactions with other groups of interactions, it is assumed that these intergroup interactions can be neglected.

The obvious danger in this assumption is that interactions between groups are neglectable, which may be correct in the short run or under normal conditions but may also be wrong under longer terms and more unusual conditions, which leads under positive feedback to the crossing of thresholds and phase transitions and then may be observed as increased stress, risk and ‘catastrophes’.

While the system can be applied to the analysis of systems it may, under conditions, also be turned around to the explanation of emergence and system change.

Simon-Ando decomposability implies that microstates may be aggregated into (different) macro-states that describe aggregate system behaviour respectively macro-state variables. This is relevant for the analysis of different views, explanations and approaches to the analysis of an issue such as it occurs in science in general and in social sciences in particular.

Decomposability, i.e. separable modularity of a system correlates with flexibility, adaptability and ease of change of a system such as an organization. Thus, decomposability, innovation and the inverse of risk correlate. Decomposability is related inversely with risk as non-decomposable systems are characterized by systemic interlinkages that are more difficult to account for and manage. Near decomposability (Simon ) involves the assumption that interlinkages among a systems (possibly developing) modules can be neglected for analytical and extrapolation purposes. If non-decomposable systems are taken to be decomposable or decomposed according to non-fitting schemes, risk increases relative to a better match between partial model and its extrapolation. It is a viable assumption that interpretation schemes associated with non-fitting problem decompositions based on erroneous models are at the root of individual organizations threatening business failure as well as the economic crisis currently affecting the world economy.