202 11 Stages of Cognitive Development A problem commonly used to illustrate the difference between the Piagetan concrete opera- tional and formal stages is that of figuring out the rules for making pendulums swing quickly versus slowly [P58]. If you ask a child in the formal stage to solve this problem, she may pro- ceed to do a number of experiments, e.g. build a long string with a light weight, a long string with a heavy weight, a short string with a light weight and a short string with a heavy weight. Through these experiments she may determine that a short string leads to a fast swing, a long string leads to a slow swing, and the weight doesn’t matter at all. The role of experiments like this, which test “extreme cases,” is to make cognition easier. The formal-stage mind tries to map a concrete situation onto a maximally simple and manipulable set of abstract propositions, and then reason based on these. Doing this, however, requires an automated and instinctive understanding of the reasoning process itself. The above-described experiments are good ones for solving the pendulum problem because they provide data that is very easy to reason about. From the perspective of uncertain inference systems, this is the key characteristic of the formal stage: formal cognition approaches problems in a way explicitly calculated to yield tractable inferences. Note that this is quite different from saying that formal cognition involves abstractions and advanced logic. In an uncertain logic-based AGI system, even infantile cognition may involve these — the difference lies in the level of inference control, which in the infantile stage is simplistic and hard-wired, but in the formal stage is based on an understanding of what sorts of inputs lead to tractable inference in a given context. 11.4.4 The Reflexive Stage In the reflexive stage (Figure 11.8), an intelligent agent is broadly capable of selfmodifying its internal structures and dynamics. As an example in the human d