[From Bill Powers (2010.07.09.0500 MDT)]
Martin Taylor 2010.07.09.00.10 –
BP: I’m going to focus on this post, being pressed for time,
MMT: Just as I was leaving for
Europe May 25, I wrote in response to a message from Bill [From Bill
Powers (2010.05.25.1035 MDT)]
“I think there will be merit in further discussion, based around
your: “As in all diagrams of hierarchical control, a copy of the
perception at the lower order is sent to the higher order of
control.” I don’t think this is necessary, and am prepared to
discuss why I don’t, but only after I either get a reasonable connection
in Europe or after I come back.”
That time has come.
BP: Good, I think this will clear up some problems.
…
MMT: Let us consider the
canonical “Keep the car in its lane” control structure. In its
simplest form, there is a control unit that controls a perception of
where the car is in its lane. The perceptual input function of this
control unit gets data only from the visual system. The output of the
“in-lane” control unit is provided as a reference value for a
“steering wheel orientation” control system, increasing (say)
that reference value if the car is visually too far left and decreasing
it if the car is visually too far right. The steering wheel control
system is pretty good at setting the orientation to near the provided
reference value, and its output influences the alignment of the car
wheels.
BP: First, you’re right in saying that the visual car-steering system
could use an unfedback command to the steering wheel positioning system.
Even though that system would not actually position the steering wheel
exactly where specified, the specifications could be adjusted (via an
integrating output function) as much as necessary to make the visual
appearance of the road ahead match the reference appearance in the visual
systems. To some extent that happens under any conditions, because no
control system is perfect. In fact my visual-motor models work that way,
with no contribution to the position perception from the force or
velocity control systems at lower levels. So we know that this
arrangement will work. Or course my models don’t get tired and
disturbances are limited to just a few kinds.
However, there are several reasons to doubt the open-loop output
hypothesis as a general feature of the hierarchy.
First, all the evidence says that the position of the steering wheel is
sensed, so at least we know first-hand that the sensory information is
available at higher levels. When the car’s front wheels encounter a bump,
or the camber of the road tilts the car to one side, there is a torque
applied to the front wheels to change their angle, and some of that
torque is reflected backward even through a power-steering unit to the
steering wheel. The driver calls this “road feel” and perceives
it as part of the general sense of the body’s dynamic relationship to the
car. Modern power-steering units, unlike the early ones, are designed to
allow enough road feel by limiting their loop gain, because cars with no
road feel proved hard to steer. I know that when the car tilts to the
right, I feel the forces disturbing the steering wheel, and can feel
myself resisting them. If I can consciously feel them, the perceptions
are probably getting to higher levels in some form.
Second, in the brain, at every level I have found out about, the sensory
pathways cross over from the input to the output side through
collaterals, as we would expect. But those fibers regularly bifurcate so
a copy of the same sensory signals is sent on upward to higher levels. It
was this repeated appearance of bifurcations of sensory signals that gave
me the idea initially of structuring the hierarchical model so each level
received copies of the sensory signals in lower levels, I think primarily
the next lower level but maybe not.
I remember the very moment when the big insight occured: I was describing
the general forms I was finding in my reading of neuroanatomy, and my
friend Kirk Sattley said, “It’s sort of like a ladder, isn’t
it?” I immediately saw the sensory signals going up the left-hand
rail of the ladder and the output signals going down the right-hand rail,
with the rungs carrying copies of the signals across from input to output
at many levels. We were in the kitchen of the apartment Mary and I lived
in for the first two years of our marriage, so this was between 1956 and
1958. I had been working at the VA Research Hospital with Clark and
MacFarland for about four years. The hierarchy was born at that
moment.
I won’t insist that every perception at every level has components coming
from every lower-level system used for controlling the higher
perceptions. We will eventually know the truth – well, I won’t but
someone will. But look at this the other way around, from the higher
system’s viewpoint.
At the relationship level, for example (which has been in the discussion
for some time now) the driver is controlling the relationship between the
steering-wheel angle and the position of the car in its lane. If the car
is too far left there is one sign of error requiring the torque applied
to the wheel to be clockwise. If too far right and the other sign of
error, counterclockwise. And we perceive this relationship. If it’s ever
disturbed, there is a big error signal until we learn how to reverse
something else.
I learned about this at the age of 16 when I worked for a summer on a hay
ranch in Jackson Hole, Wyoming, and drove a buck-rake. The buck-rake was
a converted pickup-truck chassis with the steering wheel, seat, and foot
controls turned around to face the rear, and a set of wooden teeth that
could be hydraulically raised and lowered extending out from the rear.
The task was to drive (in reverse gear) down windrows of hay scraped
together by another type of rake, zig-zagging to even the load and scoop
up a large load of hay, delivering it to a bulldozer with a pusher on it
to push it up a ramp and onto the top of a haystack under
construction.
[The ranch hands who invented, built, and named these contraptions
treated metal sort of like play-dough. When a crane boom being moved on a
flatbed trailer was too long to turn a sharp corner, I watched in
unbelief as Bob Tomingus got out his torch, cut the boom in two, and then
welded it back together after passing the corner. Took about an hour. He
case-hardened the welds by peeing on them – sorry, but that’s what he
did.]
The point is that the steering of the buck-rake was reversed: to turn
right you had to turn the steering wheel to the left. It took several
days before I could quit thinking consciously about which way I was
turning the steering wheel. I learned from that experience that
relationship perception was necessary, though I didn’t say it that way
for another 15 years or so.
The steering example is a good one for another reason. Any little error
of steering is, eventually, infinitely magnified, because the nature of
the physics is such that steering errors are integrated. This means that
if a higher level emits a signal to a lower control system saying it
should apply a certain torque to the wheel, or turn it to a certain
angle, and the wheel doesn’t happen to turn by exactly the specified
amount, there will be a little steering error and the higher, slower,
visual control system will have to do the error correcting itself. If
there is feedback from the wheel angle control system’s perceptual signal
to the higher system, then the higher system doesn’t have to wait until
there is a visual error to correct: the wheel angle error can be adjusted
by a quick change in the reference signal before any significant error
can develop.
The fourth reason and to me the best one is right up your alley:
evolution always prefers belt and suspenders (that is, braces, all you
Brits) to belt alone. If a perception is a function of many lower-level
perceptions, then the more of those lower-level perceptions that are
controlled, the less effect the environment can have on the higher-level
perceptions. Uncontrolled perceptions from below entering a perceptual
function are disturbances relative to the higher system. Controlled
perceptions are far less susceptible to arbitrary effects from the
environment.
It’s not necessary that every input to a higher-level input function be a
copy of a controlled lower-level perception. Control systems are quite
good at dealing with reasonable disturbances and we do it all the time.
But the more of the contributing perceptions that are controlled, the
better the higher-order control will be. That, I think, is where we will
find the most sections of the hierarchy where controlled lower
perceptions are inputs to higher perceptual input functions: when the
controlled lower perceptions are the same elements from which the higher
perception is constructed.
…
MMT: If in your version of HPCT
it is true that " in all diagrams of hierarchical control, a copy of
the perception at the lower order is sent to the higher order of
control", and by that you mean it is sent to the input of the
control unit that provided the reference value for the lower level, then
I break with your version of HPCT.
You would be correct in doing so because I have overstated the case. I
think I was so astonished by seeing the advantages of having lower-order
systems control the elements of higher-order perceptions that I forgot
the cases where this wouldn’t work – where a lower-order system is used
as output to control a higher-order system through effects on the
environment, and where the variables involved in producing those effects
are not elements of the higher-order controlled variable.
So, any suggestions as to how we ought to name these two types of control
hierarchy?
Best,
Bill P.