[From Bill Powers (2004.05.14.0301 MST)]
Bruce Abbott (2004.05.13.2155 EST)--
Thanks but -- I already got one. It isn't called "hen bit" by any chance,
is it?
No, "bindweed," out here at least.
On another matter, Martin Taylor may have said something like this
already, but I thought it might be worth pointing out that strange
attractors and the like don't actually attract anything. The topography
in phase space is not a description of a mechanism, but a description of
the possible behaviors of a mechanism, a set of possible trajectories the
system will follow from different starting points.
Yes, I understand this. The HPCT model defines a multidimensional phase
space just as Martin describes it, except for the idea that the system is
made of nonlinear oscillators, which may or may not be an essential part of
the concept of chaos. To say "nonlinear phase space" is only to say that
not only the dimensions, but the derivatives, are numerous.
However, there is one essential difference between the concept of phase
spaces and the way I envision the operation of a control hierarchy. It is
how one pictures the error signals in a properly working system. As I see
the system, the error signals are normally kept very small. The system does
not work by gradually bringing perceptual signals closer and closer to
their respective reference levels along trajectories in phase space, but by
acting as required to keep the perceptions ever from becoming very
different from their reference conditions. In the language of chaos theory,
the perceptions remain very close to their attractors at all times. Only
when very large and sudden disturbances occur do the perceptions ever get
very far from their reference levels and then follow trajectories over
significant distances back to the attractor.. The coordinates of attractors
at one level, of course, are adjusted by the outputs of systems at the next
level.
Maintaining this condition of low error requires continuous and complex
behavior. That is what we observe from outside the system. These behavior
patterns reflect the interactions among controlled variables, disturbances
of various kinds that are being kept from having significant effects, and
natural laws that determine how some variables must change to have specific
effects on other variables. For example, to walk from point A to point B
requires controlling a path, which requires controlling velocities and
accelerations in a specific way.The journey from A to B is a controlled
entity in itself. It's not just a dynamic "trajectory" dictated by balances
of inertial and applied forces, but a series of positions that is always
kept in the intended state by variations in leg movements. We move from A
to B because the reference signal for position is changed to define an
arbitrary series of positions along a path from A to B at any point of
which the changes could cease.
This is in contrast to the conception in which we are at point A, set a
reference condition for being at point B, and then allow the dynamics of
control interacting with the natural world determine a trajectory between A
and B. That happens only in cases of "ballistic" behavior where the
transition takes place at the maximum possible speed. In all other cases,
the path is determined not by physical dynamics but by the manner in which
the reference signal for current position is changed smoothly from one
value to another.
So this means that I see behavior differently from this desciption that you
take as a premise for drawing further conclusions::
If the brain's pattern of neural activity can be summarized by a given
topography and decisions viewed as a point in phase space moving into one
or another attractor basins,
I see behavior as involving a collection of attractor basins being moved in
system space, while perceptions follow them around with a lag that is
normally very small both in time and in phase space. The attractor basins
at one level of organization are moved around by the actions of
higher-level systems keeping their own perceptions centered in their own
attractor basins. Only when there is some very large and rapid perturbation
(or some perceptual problem) do we see, on a time-scale appropriate the the
level of organization being discussed, a set of perceptions moving along
trajectories back toward the origins of their respective basins along paths
determined only by system dynamics.
This is simply a different mode of description of how a hierarchy of
control systems operates. I say that higher systems alter the settings of
lower-order reference signals; a chaos theorist says that the higher system
alters the coordinates of an attractor basin (or would say this if it
occurred to him). The attractor basin exists only because there is a
control system operating to push the perception toward a condition of zero
error through a feedback loop involving certain dynamics. But we do not see
those dynamics under most circumstances; we see controlled and arbitrary
paths of change, which we should not mistake for the dynamics of an
attractor basin, or of a control system.
Best,
Bill P.