This is illustrated by the complex system consisting of a set of particles in three dimensions interacting with a long range force such as gravity or electrostatic charge. Consider Figure 3.9 which shows a general domain D in a complex system. We define the volume of this domain by the information in it. Mathematically, is the computational complexity needed to simulate D in isolation. The domain D is not in general isolated and is connected to the rest of the complex system.
Information flows in D and again in a geometric system.
If we view the complex system as a graph, is related to the number of links of the graph inside D and is related to the number of links cut by the surface of D . We define the system dimension to preserve the surface versus volume interpretation of Equation 3.15 compared to Equation 3.14 . In particular for the long range force problem, one finds independent of . Here there is no connection between the different members in the spatial domain. Applying this to parallel computing, we see that if or is spatially disconnected, then it can be parallelized very straightforwardly.