After reading On Intelligence in 2005, Hawkins convinced me that time and hierarchy are crucial to understanding cognition. Whether his company's particular implementation is the right technological path is an open question, but I think in terms of identifying the important theoretical concepts, he's dead on.
So what is a hierarchy?
In The Sciences of the Artificial, Herbert Simon says:
By a hierarchical system, or hierarchy, I mean a system that is composed of interrelated subsystems, each of the latter being, in turn, hierarchic in structure until we reach some lowest level of elementary subsystem. (emphasis mine)
I didn't find this definition very satisfying, though it's all right.
Wikipedia does a nice job, I think:
A hierarchy is an arrangement of objects, people, elements, values, grades, orders, classes, etc., in a ranked or graduated series.
Items in a hierarchy are typically thought of as being "above," "below," or "at the same level as" one another.
Not bad, though I'd truncate it down to simply:
A system of ranked elements.
Rank, it seems to me, is the most important aspect of hierarchy, and this simple working definition seems to capture nicely the essentials of hierarchy.
So why is hierarchy important to understanding cognition?
Well for starters, because the world is hierarchical. The universe is composed of galaxies, which are composed of subsystems, including solar systems. All matter is composed of atoms and molecules, which are composed of subatomic particles. And multicellular organisms, including ourselves, are composed of subsystems (nervous, circulatory, etc.) that are composed of organs composed of cells composed of molecules and so on.
And that's just spatially. Temporally, our lives are composed of stages (early childhood, adolescence, the college years, etc.), which are hierarchically divided down to individual moments.
Our neocortex is hierarchically-arranged, and I believe its architecture has evolved specifically to exploit and encode the hierarchical nature of the world around us. In The Quest for Consciousness, Christof Koch refers to the neocortex as "quasi-hierarchical," by which he means that it is not a strict hierarchy. Some cortical areas don't report directly to the area just above them. Many connections skip levels, like a private reporting not only to his sargeant, but to the general as well.
I don't really like the term "quasi-hierarchy" much, though. The neocortex is no less hierarchical because of this arrangement. If a system is composed of elements which are all the same rank, it's not a hierarchy. If there is any difference in the ranking of elements in a system, then it's a hierarchy. I'd prefer qualifiers like "strict" and "flexible" to describe the extent to which the relationship between elements in a hierarchy is between adjacent levels.
And I'll leave you to ponder this adapted diagram of the organization of the macaque monkey's visual from Felleman and Van Essen (1991). The information flows from bottom to top. The bottom part is information coming from the eyes, and the hippocampus sits on top. Our visual processing system is very probably arranged in the same way.