behaviorism versus/and PCT

CSGnet Archive CSG1997
1

[Hans Blom, 970911]

(Rick Marken (970910.0800))

The basic conclusion of behaviorism is that behavior is output
controlled by the environment; the basic conclusion of PCT is that
behavior is input controlled by the organism. I can't see how these
two points of view can be made to "fit" together. And why try?

I, however, _can_ see how these two points of view can be made to
"fit" together. And I'll try -- again -- to get it across.

Draw the PCT control loop, which we accept as our most basic truth
:wink:

    r ------
------->|+ | r-p
    p | C |---->----
    --->|- | |
    > ------ |
    > >
  ----- -----
  >Fi | |Fo |
  ----- ----- organism
    > > a = Fo (r-p) --------
    > ------- | world
    --<--| W +|<------

···

   -|<------ d

         -------

C is the comparator, Fi and Fo the input and output functions, W the
outside world, and d the disturbance. Now let's do some computations.
The only thing we can (at best!) observe about some organism is its
actions a, i.e. how the organism acts on the world W. All else is
inference. So let's compute a.

The output of block W can be written as

  W (Fo (r-p) +d)

and the perception p can thus be written as

p = Fi W (Fo (r-p) + d)

where now p occurs both in the left- and in the right-hand side of
the equation. An explicit solution for p is

     Fi W (Fo r + d) Fi W Fo Fi W
p = --------------- = ----------- r + ----------- d
      1 + Fi W Fo 1 + Fi W Fo 1 + Fi W Fo

Thus p, that which we perceive, is the inextricable sum of a
component due to internal reference r and a component due to external
disturbances d.

How about the action a? In the diagram, the action is written as

  a = Fo (r-p)

but using the above explicit formula for p, we can rewrite it into

                     Fo Fi W Fo
  a = Fo (r-p) = ----------- r - ----------- d
                 1 + Fi W Fo 1 + Fi W Fo

which demonstrates that the action a, too, is the sum of a component
due to the internal reference r and a component due to external
disturbances d. It may strike you as strange, but a closed-loop
system can be rewritten as a completely equivalent open-loop one!

How can this model help us in understanding the basic conclusion of
behaviorism, that behavior is output controlled by the environment?
The conclusion is correct only if Fi, W, Fo, and particularly r are
constant. In that case, the above formula reduces to

  a = K1 + K2 d

which tells us that any variation of a is due to a variation in d:
stimulus (delta-d) causes response (delta-a).

How can we understand the basic conclusion of PCT that behavior is
input controlled by the organism? Well, from the (comparator in the)
circuit diagram above, I guess. But I also hazard the guess that some
(only some?) people erroneously understand the main message of PCT in
a different way: that our actions a are caused by our will -- the
internal reference r. That may be true as well, although it is not
the message of PCT. If Fi, W, and Fo are constant and the disturbance
d can be neglected (i.e. in tightly controlled experiments or in
tightly controlled "real life", where we take care that d = 0), the
above formula reduces to

  a = C1 r

which tells us that (changes in) our actions are solely due to
(changes in) our internal goals r.

The above discussion -- although not the formula! -- is a severe
simplification. It assumes two things. First, that the world does not
change its characteristics, i.e. that the environment function W is
constant. And second, that no learning takes place in the organism,
i.e. that Fi and Fo are constant. If either happens, the analysis
becomes far more complex -- although the "open-loop" formula above
retains its validity. In particular, we might expect some
relationship between Fi and Fo on the one hand, and W on the other
hand, when learning takes place. But that's an entirely different
discussion...

And why try?

Well, my basic position is that most other people are not crazy, and
that what they report must make (some) sense. Understanding is, for
me, establishing a meaningful relationship between what others
believe and my own (idiosyncratic and changing) beliefs.

Greetings,

Hans

2

[From Bill Powers (970911.0541 MDT)]

Hans Blom, 970911--

    Fi W (Fo r + d) Fi W Fo Fi W
p = --------------- = ----------- r + ----------- d
     1 + Fi W Fo 1 + Fi W Fo 1 + Fi W Fo

Thus p, that which we perceive, is the inextricable sum of a
component due to internal reference r and a component due to external
disturbances d.

                    Fo Fi W Fo
a = Fo (r-p) = ----------- r - ----------- d
                1 + Fi W Fo 1 + Fi W Fo

which demonstrates that the action a, too, is the sum of a component
due to the internal reference r and a component due to external
disturbances d.

Your conclusions are qualitatively true but quantitatively false. Let Fo =
1000, and Fi and W = 1. We then get, to a close approximation,

p = 0.999 r + d/1000

and

a = r - d

The greater the loop gain (here concentrated in the output function), the
smaller the effect of the disturbance compared with its effect without
feedback, and the more closely the perception matches the reference signal
and is determined by it.

The action of the system is jointly determined by the reference signal and
the disturbance. With the reference signal constant, changes in action are
nearly equal and opposite to changes in the disturbance, which accounts for
the greatly reduced effect of the disturbance on the perception.

Best,

Bill P.

3

[From Rick Marken (970911.0750)]

Me:

>The basic conclusion of behaviorism is that behavior is output
>controlled by the environment; the basic conclusion of PCT is that
>behavior is input controlled by the organism. I can't see how these
>two points of view can be made to "fit" together. And why try?

Hans Blom (970911) --

I, however, _can_ see how these two points of view can be made to
"fit" together. And I'll try -- again -- to get it across
...
                    Fo Fi W Fo
a = Fo (r-p) = ----------- r - ----------- d
                1 + Fi W Fo 1 + Fi W Fo
...

The correct analysis can be found in my "Blind men..." paper
(http://home.earthlink.net/~rmarken/blind.html). It shows why
the behavior of a control system will look like S-R, control by
consequences or planned output to those who are unaware of (blind
to) the fact that they are watching the behavior of a control
system. The paper shows that there is only one "fit" between PCT
and behaviorism: behaviorism fits into PCT as an understandable
illusion.

I have found, by the way, that a paradoxical property of the
"Blind men..." paper is that it's simple message is invisible
to conventional psychologists who, as expected, approach it
wearing blindfolds;-)

Well, my basic position is that most other people are not crazy,
and that what they report must make (some) sense.

Behaviorists are not crazy; what they report not only makes sense
but it is what one would expect from observers who are not aware
of the fact that they are observing the behavior of input control
systems (again, that's the message of the "Blind men.." paper); it's
just that what they report happens to be wrong. Behaviorists are
sane and intelligent. They just don't seem to be willing to accept
the fact that they have made a fundamental error by seeing
behavior as caused output instead of controlled input.

The correct word to describe behaviorists is "stubborn", not
"insane".

Best

Rick

···

--
Richard S. Marken Phone or Fax: 310 474-0313
Life Learning Associates e-mail: rmarken@earthlink.net
http://home.earthlink.net/~rmarken

4

[From Bruce Gregory (970911.1110 EDT)]

Rick Marken (970911.0750)

Behaviorists are not crazy; what they report not only makes sense
but it is what one would expect from observers who are not aware
of the fact that they are observing the behavior of input control
systems (again, that's the message of the "Blind men.." paper);

You _can_ believe that the changing temperature in the room
causes the furnace to turn on and off. But that would be
wrong....

Bruce

5

[From Bruce Abbott (970911.1305)]

Bruce Gregory (970911.1110 EDT) --

Rick Marken (970911.0750)

Behaviorists are not crazy; what they report not only makes sense
but it is what one would expect from observers who are not aware
of the fact that they are observing the behavior of input control
systems (again, that's the message of the "Blind men.." paper);

You _can_ believe that the changing temperature in the room
causes the furnace to turn on and off. But that would be
wrong....

So if the thermostat is set to, say, 70 degrees, and the room temperature
drops from this level to, say, 65 degrees, it would be wrong to say that the
drop in temperature causes the furnace to come on? Really?

Regards,

Bruce

6

[From Rick Marken (970911.1230)]

Bruce Abbott (970911.1305)--

So if the thermostat is set to, say, 70 degrees, and the room
temperature drops from this level to, say, 65 degrees, it would
be wrong to say that the drop in temperature causes the furnace
to come on? Really?

Really!

You know, I get the feeling that you haven't been doing
my PCT demos. Of particular relevance here is the one
called "S-R vs control", which is at

http://home.earthlink.net/~rmarken/ControlDemo/Cause.html

This demo shows that a controlled variable (room temperature
in your example above) is _not_ the cause of control actions
(the furnace going on and off). Try it. Maybe then you'll be
less amazed at the way I don't love you all the time;-)

Best

Rick

···

--
Richard S. Marken Phone or Fax: 310 474-0313
Life Learning Associates e-mail: rmarken@earthlink.net
http://home.earthlink.net/~rmarken

7

[From Bruce Abbott (970911.1855 EST)]

Rick Marken (970911.1230) --

Bruce Abbott (970911.1305)

So if the thermostat is set to, say, 70 degrees, and the room
temperature drops from this level to, say, 65 degrees, it would
be wrong to say that the drop in temperature causes the furnace
to come on? Really?

Really!

. . . a controlled variable (room temperature
in your example above) is _not_ the cause of control actions
(the furnace going on and off). Try it. Maybe then you'll be
less amazed at the way I don't love you all the time;-)

You could knock me over with a feather. All this time I've thought that a
sufficient drop in room temperature relative to the thermostat's setpoint
leads to closure of the thermostat's contacts, thus switching on the
furnace, and that the raising of the room's temperature as a result of the
heating action of the furnace causes the contacts to pull with increasing
force against the magnetic attraction that is holding them together, until
sufficient force develops to pull the contacts apart (at the setpoint
temperature), thus turning the furnace off. It ain't so?

P.S. You should love me unconditionally -- I'm a regular Teddy bear.

Love,

Bruce

8

[Hans Blom, 970915]

(Bill Powers (970911.0541 MDT))

    Fi W (Fo r + d) Fi W Fo Fi W
p = --------------- = ----------- r + ----------- d
     1 + Fi W Fo 1 + Fi W Fo 1 + Fi W Fo

                    Fo Fi W Fo
a = Fo (r-p) = ----------- r - ----------- d
                1 + Fi W Fo 1 + Fi W Fo

which demonstrates that the action a, too, is the sum of a
component due to the internal reference r and a component due
to external disturbances d.

Your conclusions are qualitatively true but quantitatively false.

I generally prefer the general law ("qualitatively true") over its
specialization in a certain case.

Let Fo = 1000, and Fi and W = 1. We then get, to a close
approximation,

p = 0.999 r + d/1000

and

a = r - d

The special case is here that a (very!) good control system is in
place. A loop gain of 1000 hardly ever occurs in practice; I've only
encountered such high loop gains in simulations ;-). And _if_ a "loop
gain" of this magnitude occurs in practice, it is normally due to
integrative -- and not proportional -- action. Which, in turn, means
that not the disturbance but only its time-average (its low frequency
components) is controlled away.

Quantitatively you are correct. Realistic you are not...

The more general formulas above show other cases as well, besides a
high gain control loop. For instance, in case of general paralysis
(Fo = 0) we will not expect any actions (a = 0). More important is,
if one considers learning, that in the case of a high gain control
system (p = 0.999 r + 0.001 d) there is hardly any perception of the
disturbance. This is different from the situation where the loop gain
is still small, i.e. before effective learning has taken place, when
much of the disturbance can still be perceived. Tautologically
speaking, it is only when we can perceive a disturbance that we can
perceive it, i.e. make sense of it. Control too well and you cannot
learn...

The action of the system is jointly determined by the reference
signal and the disturbance. With the reference signal constant,
changes in action are nearly equal and opposite to changes in the
disturbance, which accounts for the greatly reduced effect of the
disturbance on the perception.

Right. And for exactly this reason one can say that the stimulus
(change in disturbance) causes the response (change in action). But
only in a high-gain controller that has finished (most of) its
learning. Not in a system that is still in its intial stages of
learning.

Greetings,

Hans

9

[From Bill Powers (970917.1502 MDT)]

Hans Blom, 970915--

Your conclusions are qualitatively true but quantitatively false.

I generally prefer the general law ("qualitatively true") over its
specialization in a certain case.

Let Fo = 1000, and Fi and W = 1. We then get, to a close
approximation,

p = 0.999 r + d/1000

and

a = r - d

The special case is here that a (very!) good control system is in
place. A loop gain of 1000 hardly ever occurs in practice; I've only
encountered such high loop gains in simulations ;-).

Then you have a limited experience with both artificial and living control
systems. I have seen an artificial control system with a loop gain of 1e9.
A typical operational amplifier used in a control loop (by me and many
others) has a loop gain of 1e5 to 1e7. The loop gain in a Honeywell
strip-chart recorder's pen-positioning control system is about 1e5. The
loop gain of my car's cruise control appears to be about 50. The loop gain
in the analog X-Y recorder I used to have was about 1e7. The loop gain in a
commercial auto-tracker for small telescopes is apparently about 1e6.

In our tracking experiments, the steady-state loop gain is somewhat hard to
measure because when the gain is high enough performance becomes quite
insensitive to large changes in loop gain. I have seen numbers between 100
and 300 at low frequencies.

And _if_ a "loop
gain" of this magnitude occurs in practice, it is normally due to
integrative -- and not proportional -- action. Which, in turn, means
that not the disturbance but only its time-average (its low frequency
components) is controlled away.

Most real control systems use a leaky-integrator type of output function,
when the environmental response is proportional. The ideal overall loop
response in any case is best approximated as an exponential rise to a final
value. which makes the whole system look like a leaky integrator. This type
of output function can be represented as a steady-state gain and a time
constant. All real control systems have an upper frequency limit of good
control. The "corner frequency" (where the error is about 1.4 times the
low-frequency error) varies considerably over different types of systems.
The automatic gain control of a radar system might have a time constant of
one microsecond; the time constant of my car's cruise control is about one
second. Human control systems in tracking tasks have a corner frequency of
about 2.5 Hz, corresponding to a time constant of something like 0.3
seconds. These are all closed-loop time constants, which are the open-loop
time constant divided by the gain.

Best,

Bill P.