[From Bill Powers (2003.12.22.1311 MST)]
Bruce Gregory (2003.12.22.1421) --
Let me start by quoting Bill's recent post:
"Remember that in PCT all action is driven by error signals. No
exceptions.
The amount of action indicates the size of the error signal, with the
most
energetic actions being the result of the largest error signals."
When I apply this theory to my bicycle riding (I try to get in an hour
every day) I arrive at the conclusion that I must be constantly
experiencing error while I ride and the faster I pedal, the larger the
error I must be experiencing.
Yes, this is correct. I might guess that the controlled variable is your
speed, in this case. If you set the reference speed low, only a small error
is required to produce a leisurely pedaling action. As you raise the
reference level, the pedaling action increases and the speed increases, but
for this to happen, the error must also increase. Thus the perceived speed
doesn't increase quite as fast as the reference signal does.
Suppose that when you intend to ride at 10 mph, the error is 0.1 mph so you
actually ride at 9.9 mph. The output gain appears to be 9.9 mph/0.1 mph or
99 mph per unit error. Assuming a linear system, what will the error be
when you want to be riding at 20 mph? How fast will you actually be riding?
In BGCT there is no direct coupling between action and error signals. I
pedal faster because I set the reference level for pedaling higher. I
normally experience very little error, no matter how fast I am
pedaling. This helps explain why I enjoy cycling rather than making
great efforts to avoid doing it. because of the constant error I
experience.
I anxiously await your slings and arrows!
No slings and arrows. I agree that you may normally experience very little
speed error when pedaling. When you double your speed, you still experience
very little speed error, because although the error is twice as large,
twice as much as very little is still very little.
My theory requires that physiological preparedness for action is generated
as a result of outputs to lower-level systems. A very small error, in a
system with high output gain, can produce a very large output. Under the
conditions of our example, an error of only 0.2 mph can generate a
physiological state producing energy at the rate needed to sustain riding
at 19.8 mph, which is probably a considerable amount. If you were cruising
along at 5 mph, you would not want to have your heart rate so high, or your
breathing so rapid and deep, or your circulating glucose at such a high
concentration as when you're sustaining a speed of 20 mph. So it's a good
thing your brain is able to adjust the reference levels for activity of
your biochemical systems at the same time it adjusts the reference levels
for motor activities.
Perhaps you were imagining that strenuous or rapid action would require
large errors as a percentage of the reference signal. As you can see, a
high-gain output function makes large error signals unnecessary. When you
notice the pedestrian, I assume there is an error in your system for
avoiding collisions, and the error results in your turning the steering
wheel or slowing down. If the pedestrian is far away, the error remains
almost, but not quite, at zero and the action is slow and moderate. If the
pedestrian appears only 50 feet ahead, the error becomes far larger --
perhaps as much as 10% of the reference signal -- and a very rapid action
takes place with enough force to make sure the car turns or stops in time
to avoid the collision. The reference degree of physical preparedness in
the two cases would roughly correspond to the speed and strength of the
output action, and therefore the intensity of the feeling state would also
vary in the same way. So you might be a little annoyed at seeing the
pedestrian in your path two blocks away, but scared out of your wits at
seeing the pedestrian about to be hit by your car, 50 feet away.
Does this seem reasonable?
Best,
Bill P.