Hierarchies, explicit and implicit

[Allan Randall (920714.1900)]

I'm one of the contractors who does work for Martin Taylor. I'm still
just becoming familiar with control theory, and the following is part
of my attempt to mesh what I've learned so far on this group with
my background in AI and neural nets.

Bill Powers (920713.1200) writes --
< In the PCT hierarchy as I have conceived it, new levels consist of new
< control systems; they aren't simply the same bottom-level systems looked at
< from farther and farther away. If a level of control is added, it is added
< EXPLICITLY, as input, comparison, and output functions physically distinct
< from the components of already-existing systems at lower levels.

   I think I see with your basic point here, but that big capitalised
"EXPLICIT" still bothers me somewhat, and I'd like to use it as a starting
point to express some of my concerns with the hierarchical control notion.
Could your argument be summarised as follows? There are two ways one can talk
about different "levels":
   (1) Conceptual: perceived levels.
   (2) Physical (architectural): perceiving levels.

   In (1) the "levels" are not actually in the control system under discussion,
but are in the type (2) perceiving levels in the mind of the scientist building
the model. The scientist is, hopefully, controlling for these perceptions to
square with reality (or to get him grant money, whatever). Type (1) perceived
levels are IMPLICIT in the control system under study, while type (2)

   Now I have two (possibly related) concerns with this breakdown. (Forgive
me if most of this is in AI/connectionist terms, rather than PCT, but I'm still
in the process of relating the two. Feel free to translate/refute any of this
stuff in terms of PCT).

   How do emergent properties (a la connectionism) fit into this scheme?
If the division into levels of control is required to be explicit, it must be
localised in a single ECS (that is, one ECS for each variable under control at
that level). That's one level of the hierarchy, right? To require this to be
"explicit" sounds a lot like the symbolic AI approach. In a distributed
connectionist system, a single node can participate in the (non-localised)
representation of more than one concept, depending on the global dynamical
activation of the network. A "higher level" does not necessarily exist
explicitly in the network. E.g.: the generalised concept of PERSON could be an
*implicit* emergent property at the same *explicit* (i.e. architectural)
level as the less general concepts of JOHN and MARY. The fact that it is at a
higher level can only be determined by studying its dynamical/informational
properties. Also, to get interesting distribution, as opposed to localised
classification, you need a recurrent network.
   Now if I extend this principle straightforwardly to networks of control,
then the "level" at which an ECS is controlling is a dynamical/informational
property of the net, and would not be explicit in the architecture. A
"high-level" ECS could provide its perceptual output to a lower level in
the "hierarchy," so the network would not be a strict hierarchy in its
architecture. A node that might be called "low-level" in one context, might be
controlling at a higher level in another context.
   Two questions: (1) Is this coherent within the framework of control
theory (PCT)? (2) Can such a system be said to be hierarchical, within the
paradigm of HPCT?

   More generally, how valid is it to make this distinction between
implicit and explicit hierarchy? It seems to me that the describability
of a system in terms of an implicit hierarchy does not necessarily mean that
the hierarchy is only in our heads and not a real property of the system.
A random system, for instance, cannot be any more compactly described with a
hierarchy than without. A more organised system, however, may be describable
with fewer bits of information using a language with a notion of hierarchy.
So isn't the hierarchy a real informational property of the system? Just where
is the dividing line between an explicit and implicit hierarchy? Can't
one always claim the hierarchy is not really a property of the system,

but rather of the language used to describe the system? Even then, can't
I claim the hierarchy isn't a property of the language, but of the
language used to describe the language? Etc, etc, etc...

   I guess talk of explicit hierarchies just strikes me as wrong. I've
always thought of "lower" levels as also controlling for things in
the "higher" levels. At least this has been my notion of "control"
before running across PCT. I do not know for sure how consistent this
is with the HPCT paradigm. I have a feeling you will say that such a system
would not be hierarchical?


Allan Randall randall@dciem.dciem.dnd.ca
NTT Systems, Inc.
Toronto, ON