[From Bill Powers (2002.02.21.1641 MST)]
Bill Curry (2002.02.21.1220 EST)--
I find it curious that the sexual sensation control system can be happily
perking
along (presumably at zero error with zero sensation), and upon
stimulation, shift
to a reference for high stimulation and shed other important control
processes.
Me, too. But it does seem to work that way, doesn't it? I once proposed a
"universal error curve" in an attempt to deal with this general problem.
The general problem is that when errors get _very_ large, people don't (I'm
guessing) just continue producing more and more output. Instead, they
"give up." What is a _very large_ error? Well, consider a dog chasing a
car. If the car is going 10 mph, the dog can pretty well keep up with it.
At 15 mph, it may start lagging behind a little, with a discernible error.
But what if the car goes past at 75 mph? The dog might make a slight effort
to chase it, but the positional error or the speed error will be way
outside the range that any dog could possible correct. So does the dog
chase on down the road after the car at maximum speed, getting farther and
farther behind, miles and miles behind, for the next hour? No, it simply
turns and trots back home as if it didn't care about cars at all.
This can be handled as higher-level control, of course. A higher system
concerned with not wasting energy, or with controlling successfully, or
whatever else you want to propose, vetoes reference signals sent to lower
systems if this control system imagines that they will (or perceives that
they do) accomplish nothing but creation of huge errors and physical
exhaustion. The reference signals that would cause such results are
inhibited, or perhaps the systems that sent them are turned off at the
output function.
That's a straightforward proposal, but it does clutter up the model with a
lot of extra higher-level control systems that do nothing but inhibit
reference signals when errors get too large. It would be nicer if there
were a simpler (and dumber) way to account for the giving-up phenomenon.
This is where the universal error curve comes in.
Suppose that as the difference between a perceptual signal (any perceptual
signal) and a reference signal increases from zero, the error signal rises
at first (as we always assume in the simple basic control model). Beyond a
certain magnitude of difference, the error signal begins to fall below the
strictly linear representation of error. At some still larger discrepancy,
say when the car is going 30 mph and the dog is going all-out at 25 mph, a
further increase in the discrepancy does not increase the error signal at
all, and then for still greater discrepancies, the error signal begins to
_decrease_.
It's that final decrease that leads to the giving-up phenomenon. The sign
of the feedback loop is negative for small errors. The loop gain for
changes goes to zero where the error signal levels out, and then becomes
positive, creating positive feedback for further increases.
The result will be that resistance to a small disturbance will be normal,
but as the disturbance continues to get larger, the resistance to the added
amounts of disturbance will become weaker, until for the largest
disturbances the resistance will collapse to zero. You can see that if at
any level an increase of disturbance causes a _decrease_ in the opposing
action, that will allow the error to be come even larger, which will lead
to greater error, which will decrease the action more, and this
regenerative process must lead to a total collapse in the opposition. When
opposition ceases, we call that "giving up." There is a much larger error
than usual, and no output action at all.
How does HPCT explain the concept of priority in this context? When
the rat switches [or is switched] to controlling a variable creating sexual
sensations, what mechanism preempts the other control processes?
"Priority" implies (among other things) an ordering in time, I think -- a
sequence. If you want to enter a house, you need to open the door and step
over the threshold. But if you try to do these things at the same time, you
will be in conflict, pushing at the door at the same time you try to unlock
it. By generating the associated reference signals in a specific sequence
-- unlock, then enter -- you prevent the conflict.
Prioritizing also arises in straightforward conflicts. If we want to do two
things at the same time, and they are mutually exclusive, a higher-order
system can raise the loop gain in one of the two systems and/or decrease
the gain in the other, so one system will prevail over the other one. Then,
if the winning system is the sort that doesn't need continuous effort to
keep its error small, the other system will be allowed to correct its
error. Here the sequencing isn't explicit, but the effect is the same: the
system that is given the higher loop gain gets to correct its error first,
and then quite naturally other other system acts when the first system's
error, and action drops to zero (or gets small enough). This doesn't work,
of course, if the first system requires continuous action to keep its error
from getting large again. In that case, its action would continue to
overwhelm any attempt by the other system to act.
Some people think that prioritizing is a simple intellectual act that we
can do just by stopping and thinking for five minutes. The problem is that
we have many goals and they are all important to us, although for different
higher-level and lower-level reasons. We can't just decide offhandto give
one goal priority over another, because when we try to turn off the other
goal, even temporarily, we will be disturbing all the higher systems in
which that goal plays a part. And those higher systems, whether we are
conscious of them or not, will automatically oppose the changes.
In fact, the need to prioritize always implies that there is some kind of
conflict. So if we can develop an effective way of helping people resolve
conflicts, we will bypass the need for prioritizing, which to my mind is a
questionable way of resolving conflicts.
Oh, one more thing. It's possible that certain phenomena, such as sneezes
and sexual arousal, _do_ involve positive feedback.
Best,
Bill P.
