[From Bill Powers (2006.08.17.1655 MDT)]
I've been reflecting about the nature of HPCT, specifically, the hierarchy.
What if it's not a "hierarchy"? What if it's flat? What if it's better
represented perhaps by a set of concentric circles? Could I still have the
same set of dependencies in a flat, concentric-ring representation? Might
the output of inner-circle control systems have the same relationship to
"outer" as to "upper"?
The idea of the hierarchy came about pretty early, from considering the spinal reflexes, which are organized as control loops. Those loops are built in; there's no way for the brain to operate the muscles except through them. When you trace out the circuits (as shown in B:CP), it's clear that the spinal motor cells are comparators, and that the so-called command signals reaching the motor cells from higher up are reference signals. I don't think there can be any doubt about that, and neither did people like Houk in the 1950s.
It slowly grew on me that the whole central nervous system could be organized that way. At the level of spinal reflexes there are at least 800 control systems, and probably quite a few more than that because different branches of a muscle can be separately energized. This meant that you could trace input from that level and outputs to that level, so the spinal systems became just like an environment of the rest of the brain, and you could then start over to define a second level of control, and so on for however many levels there really are. From then on the job became one of trying to see if there was any observable evidence for such levels, and what sorts of control systems might exist at each level. That was a slow process! Five levels in 1960, nine in 1973, eleven sometime in the 1980s, and none added since then.
There are circumstantial reasons for believing this organization. One is developmental. If the brain's organization matures from the bottom up, each new level could become organized and operate by itself, either with inherited values of reference signals or simply absent reference signals, equivalent to a value of zero. Each new level then becomes the world which new levels control. There is never any need for a higher system to supercede, replace, override, or "subsume" lower systems (the Brooks architecture). New levels can be added without requiring changes in the existing levels (though such changes would undoubtedly occur). The point is that adding levels doesn't call for total reorganization of everything below them.
Another reason is evolutionary. At earlier stages during evolution, it stands to reason that each level we now find in a human brain, or think we find, was the highest existing level. So we should be able to find organisms with only the intensity level, or with only the intensity and sensation levels, and so on. I never got past the stage of idle speculation about that, but it's interesting to look at other organisms with this in mind. The hierarchy organization makes it possible for viable organisms to exist with any number of levels from one upward.
Finally, neurophysiologists long ago realized that there is more than one level of reflexes; there are spinal reflexes, brainstem reflexes, and midbrain reflexes -- and possibly still more. Each level necessarily works through the systems that make up the lower reflexes. Not much circuit analysis has taken place; mostly neurologists chase impulses around, whereas what we need is for neural functions to be analyzed -- how one set of signals consisting of trains of impulses get turned into new signals. I see studies of that kind only rarely in Science and Nature, but even then nothing like what we need.
Martin Taylor has taken care of the geometric aspects of your question. As he says, it's not the geometry that matters, but the connectivity.
Besgt,
Bill P.