[From Bill Powers (990811.1923 MDT)]
Bruce Gregory (990811.1430 EDT)--
As far as I can tell once a control hierarchy starts controlling an
input it cannot stop. Clearly this arrangement is not optimized for
survival! Some mechanism must exist that allows a system to stop
controlling one input and start controlling another (assuming both
cannot be controlled simultaneously). Like you, I am puzzled by what
this mechanism might be. My conjectures so far have encountered lukewarm
(at best!) receptions.
Remember that we're working within the framework of a defined model,
meaning that if we want to change something in the "official" model we have
to justify and defend the change. This doesn't mean that changes are not
allowed; just that we don't want to make it too easy to mess around with
the basic structure, especially when we're just conjecturing.
Changes begin with noticing a problem and suggesting that the model can't
handle it as it stands. One way to criticize a suggested need for change is
to show that the model, without introducing anything new, can already
handle the problem. That's what we have done, so far, with the problem you
bring up (not for the first time on CSGnet).
The argument starts like this. If a given neural signal represents, say, a
position to the right of some zero-point, it can't also represent a
position to the left of that point, because a neural signal can't change
sign. If 100 impulses per second represents 10 centimeters to the right of
the zero point, then we can't say that 10 centimeters to the left is
represented by -100 impulses per second, because negative frequencies of
occurrance don't exist.
What this boils down to is that all neural control systems must be one-way
control systems. Let's consider the case in which the reference signal is
excitatory (+) and the perceptual signal is inhibitory (-), as these
signals enter a neural comparator. Clearly, a positive reference signal
must be matched by a positive perceptual signal that has an inhibitory
effect at the comparator, if control is to succeed. But what happens if the
reference signal is made smaller and smaller until it becomes zero? It can
still be matched by a perceptual signal that gets smaller and smaller, but
we have to be careful as zero is approached: a disturbance that makes the
perceptual signal a little larger, thus decreasing the error and the
action, can't make the error signal any smaller than zero. So there's a
region of reference signals near zero where there is a smaller and smaller
range of control against disturbances that tend to increase the perceptual
signal. And carrying this to the extreme, if the reference signal becomes
exactly zero, there is no control at all: the control system is effectively
turned off.
Think about it. The reference signal is zero, and the perceptual signal is
inhibitory. The inhibitory input can only make the output of the neural
comparator _decrease_. But if the reference signal is zero, there is no
output and the error signal is already zero; it can't decrease any further
no matter how much perceptual signal there is. The conclusion? A higher
control system can turn off a neural control system of this kind just by
setting its reference signal to zero.
If the signs of the inputs to the comparator are reversed, so the
perceptual signal is excitatory and the reference signal is inhibitory, the
same line of reasoning shows us that the control system can be turned off
by a higher system's setting the inhibitory reference signal to a value
higher than the highest value the perceptual signal can attain.
If all neural control systems are one-way, it follows that two-way control
must involve at least two control systems working in opposite directions,
each containing only positive neural signals, but the signals having
opposite significance in terms of external variables. Clearly, in order to
turn off a two-way control system, higher systems must set _both_ reference
signals to the values that turn off the respective control systems.
This is a way in which higher systems can turn off one lower control system
and turn on another one in its place. This way uses no connections that are
not already part of the "official" model -- that is, higher systems affect
lower ones _only_ through variations in reference signals.
Of course if we allow non-official connections, there are other ways to
turn whole control systems on and off. A higher system can simply gate the
entire output function of a lower system _off_. This requires that an
output signal from a higher system _not_ enter the comparator, but act on
the output function directly, and in an on-off rather than continuous way.
We could restore the continuity of control if we allowed a higher system to
vary the gain in the output function; turning off the control system them
amounts merely to setting its loop gain to zero. I actually think this
might prove to be a valuable addition to the official model.
There's only one problem: I can't demonstrate that this arrangement exists.
Maybe if I worked at it I could, but the fact is that I haven't done the
work, and I can't show anyone that this new arrangement would actually
explain something about observed behavior that we can't explain with the
model as it stands. Sure, I have a pretty good idea about what kinds of
experiments I'd try, and how I'd modify the model to test the new concept.
But I haven't done it, so the proposal stays in the "to do" stack.
If I won't let myself make any claims about these non-official
"improvements" to the model, I hope nobody will be surprised if I also
reject such claims offered by anyone else who hasn't done the work, either.
Conjectures are the easy part.
Best,
Bill P.