System Stability: A Proxy for "Graceful Degradation"

Within the military sector the notion of graceful degradation is universally accepted. Military systems e.g., weapons, force mixes, communication links, air defense systems and even a system of strategies and tactics should, it is agreed, gracefully degrade e.g., under hostile conditions, or random failures, or variations in mission, or changesmodifications in personnel and equipment - rather than collapse like a house of cards. Unfortunately, there is no agreement as to how one defines graceful degradation, or how it is measured. Furthermore, and perhaps most unsettling, the attributes of optimality and graceful degradation may - if the hypothesis of this article holds - actually be in opposition. To illustrate this phenomenon, consider the simple block world problem depicted in Figure 1. The stack of blocks on the left side of Figure 1 is unequivocally optimal in the sense of being the taller of the two stacks. However, while the stack on the right side of the figure is shorter, less impressive in appearance, and sub-optimal it is also clearly far more stable. Given the choice between attempting to stand on either of the two stacks, most people would select the suboptimal stack. Clearly, something more than the height of the stack is important - something difficult to put into words or formulas. In this article I explore the very real possibility that optimal solutions may be invariably unstable - wherein stability is defined as the measure of both the speed and ease by which a given solution de-evolves degrades to some minimally acceptable level. In the case of the block world illustration given earlier, it should be apparent that the optimal stack is likely to collapse easier and faster than the shorter stack.