For one thing, complex systems do not easily lend themselves to analysis, the process of taking apart a system and examining its components individually. If taken apart, many complex systems lose precisely the character that makes them complex. The essence of these systems, then, seems to lie not in the nature of their components but in how the components interact—across different hierarchies, in synergistic and antagonistic manners. The agents within these systems are heterogeneous (think participants in a market economy or molecules within a cell), and their behavior is influenced by the type and quantity of other agents nearby. Such systems defy description with the traditional tool of theory builders: mathematics. Instead, they must be modeled by taking into account the rules of interaction, the natures of the agents, and the way the agents, rules, and ultimately whole systems came about. In his Signals and Boundaries: Building Blocks for Complex Adaptive Systems, John Holland proposes that computational modeling is the appropriate tool not only for describing but, fundamentally, for understanding such systems. In particular, he argues that this modeling approach is in no way inferior to a mathematical one. Rather, he advocates that the computational modeling of signal-boundary systems (which I will describe in more detail below) goes where mathematics cannot go while being no less rigorous, no less exact.
Boldly Going Beyond Mathematics
Science 14 December 2012:
Vol. 338 no. 6113 pp. 1421-1422
Signals and Boundaries: Building Blocks for Complex Adaptive Systems
John H. Holland
Via Complexity Digest, Eugene Ch'ng