Leading Questions - Chapter 1

I am resolved to work my way through B:CP for a second time.
The first time was in 1975 and I didn't exactly work my way
through it back then.

I propose to go through B:CP a chapter at a time, answering
the leading questions at the end of each chapter. Y'all can
comment if you like or simply ignore my postings.

Here goes with Chapter 1.

1. A man exercising raises a dumbbell slowly at arm's length.
In what direction do his muscle forces act on the dumbbell?
(Upward) Now he begins slowly to lower the dumbbell. In what
direction do his muscles forces now act on the dumbbell?

His muscle forces still act in an upward direction; however,
with less force.

2. A woman is pulling a reluctant little boy by the hand
toward a schoolroom door. In what direction do the boy's
walking movements carry his body? (Forward) In what
direction would the leg-muscle forces end to move the boy's
body? Do movements depend only on muscle forces?

The leg-muscle forces would tend to move the boy's body
backward. Movements can be effected (and affected) by
forces other than muscle forces. The rolling, pitching
deck of a ship at sea comes immediately to mind (but then
I spent 20 years in the Navy--on destroyers--so that's to
be expected). On a side note, I wouldn't refer to the
boy's "walking movements" as such; the imagine conjured
up in my mind is of a boy being dragged. What you call
his "walking movements" I would refer to as his "balancing
movements" (i.e., some mix of pulling back and trying to
remain upright--or at least not fall).

3. A man stands before a large screen tracking a moving
spot of light by keeping his finger on it. The effective
stimulus is the distance of the spot from the finger. The
response to a given stimulus is expressible as the position
and velocity of the finger relative to the spot. Is the
stimulus measure independent of the response measure? Is
any independent measure possible? Is there any response
that does not entail a change in the stimulus?

I don't know what "independent" means in this context so
I'll have to answer the questions as best I can.

Given that the stimulus has been defined as the distance
between the spot and the finger, and the response has been
defined as the position and velocity of the finger relative
to the spot, it seems to me that to measure the distance
between the spot and the finger you must know also the
position of the finger to determine the distance between
the two. However, you need only to know their positions
relative to one another and not in relation to any other
reference point.

The "kicker" in this is that the response includes the
velocity of the finger (which I take as referring to the
speed with which it is moving--again, relative to the spot).
This would imply that the velocity of the finger in relation
to the spot is the net of any speed of movement in the spot,
so again, you can't get at one without getting at the other.

As for independent measures, I imagine I could measure the
speed and direction of finger movement with respect to the
corner of the screen on which the spot is moving and that
would be independent of what the spot is doing but I don't
know that that would tell me much. Ditto for the movement
of the spot itself.

The only response I can think of that doesn't require a change
in the stimulus is if the spot were to remain stationary. The
finger would remain on top of the spot and neither would move.
The reference condition, that is, the condition requiring no
action, would be realized.

4. Behaviorists say that in apparent goal-seeking behavior,
the goal is reached because stimuli at each stage of the process
evoke the next response leading toward the goal. If a man is
operating remote guidance controls to steer a car through a maze
toward a goal, what will his response be if the car spontaneously
moves along the correct path at all times? What would happen if
the man did produce any steering movements?

Presumably, if the man noticed the car was doing what was wanted,
without (or despite) any effort on his part, he would "back off"
and let the car run the course on its own. If he did attempt to
steer the car, his actions--by way of the remote control device--
would constitute "disturbances" (which the car could presumably
counter because it apparently has a built-in control system all
its own).

As a side note, I find the situation in this last question really
interesting. I wonder how long it would take the man to realize
that all he was doing was "disturbing" the fine job the car was
doing on its own. (I wonder, also, what would happen if manager
was substituted for man and employee for toy car. Hmm.)

Anyway, there are my answers to the Leading Questions at the end
of Chapter 1 in B:CP.

Anyone care to respond?

···

--

Regards,

Fred Nickols
Distance Consulting
http://home.att.net/~nickols/distance.htm
nickols@worldnet.att.net
(609) 490-0095

[From Bill Powers 981226.0648 MST)]

I am resolved to work my way through B:CP for a second time.

Brave soul.

1. A man exercising raises a dumbbell slowly at arm's length.
In what direction do his muscle forces act on the dumbbell?
(Upward) Now he begins slowly to lower the dumbbell. In what
direction do his muscles forces now act on the dumbbell?

His muscle forces still act in an upward direction; however,
with less force.

No, with the same force, if the arm is moving at a uniform speed (not
accelerating). FYI, the changes in force occur only where the dumbbell
reverses direction, and then only for as long as it takes for the velocity
reversal to be complete. See Newton's laws of motion.

2. A woman is pulling a reluctant little boy by the hand
toward a schoolroom door. In what direction do the boy's
walking movements carry his body? (Forward) In what
direction would the leg-muscle forces end to move the boy's
body? Do movements depend only on muscle forces?

The leg-muscle forces would tend to move the boy's body
backward. Movements can be effected (and affected) by
forces other than muscle forces. The rolling, pitching
deck of a ship at sea comes immediately to mind (but then
I spent 20 years in the Navy--on destroyers--so that's to
be expected). On a side note, I wouldn't refer to the
boy's "walking movements" as such; the imagine conjured
up in my mind is of a boy being dragged. What you call
his "walking movements" I would refer to as his "balancing
movements" (i.e., some mix of pulling back and trying to
remain upright--or at least not fall).

I agree.

3. A man stands before a large screen tracking a moving
spot of light by keeping his finger on it. The effective
stimulus is the distance of the spot from the finger. The
response to a given stimulus is expressible as the position
and velocity of the finger relative to the spot. Is the
stimulus measure independent of the response measure?

....

As for independent measures, I imagine I could measure the
speed and direction of finger movement with respect to the
corner of the screen on which the spot is moving and that
would be independent of what the spot is doing but I don't
know that that would tell me much. Ditto for the movement
of the spot itself.

The position and velocity are independent of each other -- that is, for any
given positions of finger and spot, there could any _rate of change_ of
distance between finger and spot. This one was sort of a hint about how you
can set up control equations. The velocity of arm movement can be
proportional to the distance between finger and spot, while the distance
between finger and spot depends on the _time integral_ of finger velocity.

4. Behaviorists say that in apparent goal-seeking behavior,
the goal is reached because stimuli at each stage of the process
evoke the next response leading toward the goal. If a man is
operating remote guidance controls to steer a car through a maze
toward a goal, what will his response be if the car spontaneously
moves along the correct path at all times? What would happen if
the man did produce any steering movements?

Presumably, if the man noticed the car was doing what was wanted,
without (or despite) any effort on his part, he would "back off"
and let the car run the course on its own. If he did attempt to
steer the car, his actions--by way of the remote control device--
would constitute "disturbances" (which the car could presumably
counter because it apparently has a built-in control system all
its own).

As a side note, I find the situation in this last question really
interesting. I wonder how long it would take the man to realize
that all he was doing was "disturbing" the fine job the car was
doing on its own. (I wonder, also, what would happen if manager
was substituted for man and employee for toy car. Hmm.)

Right on. You got the point exactly.

Best,

Bill P.

[Fred Nickols (981227.0955 EST)]--

Bill Powers 981226.0648 MST)]

From me earlier...

1. A man exercising raises a dumbbell slowly at arm's length.
In what direction do his muscle forces act on the dumbbell?
(Upward) Now he begins slowly to lower the dumbbell. In what
direction do his muscles forces now act on the dumbbell?

His muscle forces still act in an upward direction; however,
with less force.

Bill...

No, with the same force, if the arm is moving at a uniform speed (not
accelerating). FYI, the changes in force occur only where the dumbbell
reverses direction, and then only for as long as it takes for the velocity
reversal to be complete. See Newton's laws of motion.

Okay; I think I get it. Whether lifting upward or lowering,
the weight of the barbell and the pull of gravity are the same.
So if the speed up and the speed down are the same, equal muscle
forces are in play. If I let it down faster than I lifted it
then I'm using less muscle force on the way down (or someone
substituted a heavier barbell at the top of the lift :slight_smile: ).

Thanks for the lesson.

Bill, in response to my response to question 4
about the man tracking the spot on a screen...

The position and velocity are independent of each other -- that
is, for any given positions of finger and spot, there could any

_rate of change_ of distance between finger and spot. This one

was sort of a hint about how you can set up control equations.
The velocity of arm movement can be proportional to the distance
between finger and spot, while the distance between finger and
spot depends on the _time integral_ of finger velocity.

Huh? The position of what and the velocity of what are independent
of each other? I think I get the last part.

Let me try to restate that.

The velocity of arm movement can be proportional to the distance
between finger and spot I take to mean that the arm might move
faster the farther away the finger is from the spot and slower
as the finger gets closer to the spot. That affects the rate of
change at which the distance between finger and spot might be
closing (or opening, if the tracker is a perverse cuss). What
does "time integral" of finger velocity mean (rate of closing
the distance or what?)?

···

--

Regards,

Fred Nickols
Distance Consulting
http://home.att.net/~nickols/distance.htm
nickols@worldnet.att.net
(609) 490-0095

[From Bill Powers (981227.1302 MST)]

Fred Nickols (981227.0955 EST)-

Okay; I think I get it. Whether lifting upward or lowering,
the weight of the barbell and the pull of gravity are the same.
So if the speed up and the speed down are the same, equal muscle
forces are in play.

What counts is that the speed be _constant_ (no acceleration). To keep the
speed constant, the applied force must be equal to the force caused by
gravity, so there is no NET force applied to the dumbbell. It doesn't
matter what the constant speed is, great or small.

Bill, in response to my response to question 4
about the man tracking the spot on a screen...

Huh? The position of what and the velocity of what are independent
of each other? I think I get the last part.

The position of the finger relative to the spot is independent of the
velocity of the finger relative to the spot's velocity.

Let me try to restate that.

The velocity of arm movement can be proportional to the distance
between finger and spot I take to mean that the arm might move
faster the farther away the finger is from the spot and slower
as the finger gets closer to the spot.

Right.

That affects the rate of
change at which the distance between finger and spot might be
closing (or opening, if the tracker is a perverse cuss).

Right.

What
does "time integral" of finger velocity mean (rate of closing
the distance or what?)?

"Time integral" means the sum of velocities measured at successive moments
of time, each velocity multiplied by the time between measurements.
Velocity times time is distance. If we designate the interval between
measurements as "dt", the velocity at a given time t by v(t), and the
distance moved during the interval by d(t) then

d(t) = v(t)*dt (distance = velocity times time)

Assuming that the velocity is changing with every new interval, we can sum
up the total distance moved (D) by adding up all the little d(t)s.

D = d(t1) + d(t2) + ... d(tn)

D = v(t1)*dt + v(t2)*dt + ... v(tn)*dt

That last expression is the "time integral" of velocity when we let the
time interval dt go towards zero, so many, many tiny distances are being
added up, the velocity hardly changing between one dt and the next. Thus
the time integral of a varying finger velocity, calculated over some total
interval of time, is just the total distance moved by the finger.

Best,

Bill P.