As our colleague in Neuroscience, John Donoghue, points out, learning to type is a matter of going from an isolated execution of individual letters, gradually to a single, smooth, integrated execution of entire words. Of course there are critical issues of feedback, timing, and control. Indeed, so much more seems to be involved than in a typical perceptual task. Yet the arguments for hierarchy and incremental learning are the same. This complexity relates to the number of samples or trials needed to achieve any given level of precision.
Complexity sets the speed limit for learning.
I have argued that hierarchy decomposes the learning task into manageable, low-complexity increments. E. The answer is that the complexities in a hierarchical representation are multiplicative, not additive. The richness of a category emerges, one step at a time with each embedded composition, as the number of the instantiations of constituents are multiplied by the number of meaningful arrangements of the constituents into a composite. It is true, then, that hierarchical systems can represent rich categories. But not all categories can be represented hierarchically.