Feedback is too slow

[FROM Dennis Delprato (930113)]

Allegations that movements occur too rapidly for feedback
to play a role represent one of the major arguments against
feedback control theories. The central-peripheral issue
goes back to the 19th century, and peripheral control was
tied to "response-produced feedback" -- usually as a
stimulus (!) for the next response. Thus, control theory
as we know it never really came up. Nonetheless,
feedback control theory of the modern type (I acknowledge
the major contributions of K. U. Smith and W. T. Powers
for this) has been saddled with the near-ancient arguments
used against its very distant relative.

From S. W. Keele (Attention and Human Performance, Pacific

Palisades, CA: Goodyear Publishing Co., 1973), it appears that
data interpreted in support of the allegation go as far back
as Woodworth (1899, The accuracy of voluntary movement,
Psychol. Rev.). Lashley (1917, The accuracy of movement in
the absence of excitation from the moving organ, Amer. J.
Physiol., v 43, 169-194) also cites Woodworth (1899). In this
1917 paper (well in advance of his much-cited 1951 "The Problem of
Serial Order" chapter) Lashley brings up the musician.

I found it interesting to be reminded of just how influential the
set construct was. This is especially the case insofar as the
set construct is simply an earlier version of today's notions
of cognitive control, motor programs, schema, et al. The latter
tell us not a bit more than did the idea of set or determining
tendency. Such is progress.

As far as feedback control theoretical arguments against the
feedback is too slow position, I have been able to find this
addressed by T. J. Smith and K. U. Smith. This is in a
preprint of a chapter entitled "Feedback-Control Mechanisms
of Human Behavior" prepared for the Handbook of Human Factors/
Ergonomics. I received the preprint approx. 1987; thus, the
book must be published by now. In the preprint, the authors
address our topic in Section 8.6.3.3 (Control Theories of
Fast Movement Coordinations).

They point out that it is virtually impossible to test the
alternative to feedback control -- central brain programming--
and that feedback control has been much evaluated, including
with musicians. They find that feedback delay has major
debilitating effects on performance to the point that
the highly - skilled musicians they used invariably refused
to continue with the process after brief exposues fearing
permanent impairments. One of their main reactions to the
argument of feedback being too slow to play a role in
skilled movements is that if this is the case, delay and
other distortations of feedback (e.g., displaced visual
feedback) should not impair performance. But data from a
wide variety of performances (musical, drawing, writing, and
many more) clearly show increased impairments with increases
in experimentally-manipulated distortations and delays of feedback.

They also bring up considerations that, to me, require
elaboration to be convincing: what they call predictive control
and body movement tracking.

[From Bill Powers (2010.02.11.1830 MST)]

Thanks to Henry Yin, I now know where the "feedback is too slow"
rumor got started. Just Google on that phrase. It was Karl Lashley,
"The problem of serial order." Lashley started campaigning against
the idea that feedback was necessary ("proprioceptive information")
as early as 1917. The whole idea of central pattern generators and
open-loop planning of movements grew out of this. The investment in a
non-feedback model, in other words, is close to a century old and
absolutely enormous, and it was encouraged by major figures in this
field. The citations of Lashley's rumor run just about right up to
present time. I don't know how to use that Google citation index
service, but it would be interesting to see the influence of this one paper.

Best,

Bill P.

LashleyFeedback4.jpg

LashleyFeedback1.jpg

LashleyFeedback2.jpg

LashleyFeedback3.jpg

[From Richard Kennaway (2010.02.12.1004 GMT)]

[From Bill Powers (2010.02.11.1830 MST)]

Thanks to Henry Yin, I now know where the "feedback is too slow"
rumor got started. Just Google on that phrase. It was Karl Lashley,
"The problem of serial order." Lashley started campaigning against
the idea that feedback was necessary ("proprioceptive information")
as early as 1917. The whole idea of central pattern generators and
open-loop planning of movements grew out of this. The investment in a
non-feedback model, in other words, is close to a century old and
absolutely enormous, and it was encouraged by major figures in this
field. The citations of Lashley's rumor run just about right up to
present time. I don't know how to use that Google citation index
service, but it would be interesting to see the influence of this one paper.

On the other hand, none of the demos in LCS III involve sequence control or sequential actions, and I don't recall any other PCT demos that do. So it would be easy for a critic to say, "that's all very well, but how do you explain sequential action?". Googling on things written about "The problem of serial order" suggests that some demos in this area would be useful.

Walking would be one example. My walking robot simulations have built into them the sequential action of picking up some of their legs, swinging them forward or back, and putting them down, but I'm not sure if this bears on the hypothetical objection above.

···

--
Richard Kennaway, jrk@cmp.uea.ac.uk, http://www.cmp.uea.ac.uk/~jrk/
School of Computing Sciences,
University of East Anglia, Norwich NR4 7TJ, U.K.

[From Bill Powers (2010.01.12.1250 MST)]

Richard Kennaway (2010.02.12.1004 GMT) –

JRK: On the other hand, none of
the demos in LCS III involve sequence control or sequential actions, and
I don’t recall any other PCT demos that do. So it would be easy for
a critic to say, “that’s all very well, but how do you explain
sequential action?”. Googling on things written about
“The problem of serial order” suggests that some demos in this
area would be useful.

Walking would be one example. My walking robot simulations have
built into them the sequential action of picking up some of their legs,
swinging them forward or back, and putting them down, but I’m not sure if
this bears on the hypothetical objection above.

Sequential action, as you imply, would be achieved by controlling for a
specific sequence of perceptions. As each perception is achieved, the
next reference signal is sent and the previous one is turned off. But the
fast rate at which some sequences can be executed suggests something more
complex.
Lashley cited fast piano playing as his evidence that sequences are
accomplished open-loop. He said that pianists can create sequences of
keystrokes as fast as 16 per second, which is much too fast to allow
waiting for feedback. However pianists (and their audiences) can clearly
perceive sequence errors at least that fast, because a note struck out of
sequence, as the saying goes, really “stands out.” There is an
almost instantaneous error signal, especially in the performer who knows
exactly what note was intended next. As with typing errors, however, a
mistake perceived in a fast sequence is not always identified correctly
as to which key was struck in error.
We know that sequence errors can’t be corrected that fast. This implies
that the output of a sequence controller is an open-loop sequence of
reference signals issued at the speed at which the notes are to occur,
and the perception is a sequence that is compared with the reference
sequence continuously but can be corrected only once in a while.
However, controlling a sequence is a bit odd since the elements can’t be
changed after they have happened, and changing a sequence by any means
available only makes it more erroneous. If there is an error, nothing can
be done about it after the fact without creating even more error, so
professional pianists (as is true of other intrumentalists) are
instructed continue to play and ignore the error, and are specifically
cautioned not to stop the sequence, go back, and replay it from an
earlier step. Even in solo performances doing that would create an even
more jarring break in the sequence, and of course in ensemble
performances it would put the errant musician out of sync with the other
performers and destroy the entire effect.
In fact, we can perceive sequences, and we have reference sequences with
which to compare the perceived one, and have various strategies for
correcting the errors as soon as physically possible. The tendency to
stop and repeat the sequence from a point before the error is hard to
overcome in cases where it is inadvisable; otherwise, that is generally
what we do. I do it all the time while typing. I can type extremely fast
as long as I am not required to hit the right keys. My average typing
speed, however, is nothing to brag about.
The speed with which we can control sequences depends in part on the
level to which the reference signals are issued. If the reference signals
specify a heard note, it’s hard to keep up with fast changes in reference
signals, because the pitch control system has to convert errors into
adjustments of reference configurations for the fingers. If, however,
finger configurations are specified, the speed of matching perception to
reference is far greater. Executing finger movements without listening is
fast but tends to make the result sound mechanical.
Of course it’s still impossible to make one finger strike 16 notes in one
second, but in a trill of 16th notes the repetition rate for one finger
is only 8 per second, and in an arpeggio that uses all 5 fingers it is
only a little over 3 per second and half of that if both hands are
involved.
Art Tatum, it was said, could run an arpeggio the full length of the
keyboard at a rate of 90 strokes per second. I think that’s an
exaggeration but not by an order of magnitude. He could play
“stride” left hands at a rate of around two or three per
second, a “stride” consisting of a bass note followed by a
left-hand chord in the middle range of pitch. As any pianist would
realize, enormous strength and endurance are required to move the
mass of the hand accurately and repeatedly back and forth that fast,
reforming the entire hand configuration and aiming the contact points
within a fraction of the width of a key. It’s even more remarkable when
you reflect that during any given performance, Tatum was probably
drunk.
Lashley spoke only about executing strings of outputs. He thought that
involved planning a starting point, and end point, and sequence of points
in between, and then executing the sequence with no feedback. The idea of
specifying a position and then letting a lower-order system achieve that
position while the next position for a different finger is being
specified never, of course, occurred to Lashley, though all he really
missed was the role of feedback. Also, it didn’t occur to Lashley that
the brain is a highly parallel processor, not a single CPU frantically
trying to time-share its attention and services among a dozen different
tasks. You can play ten successive notes at high speed if you use 10
control systems each controlling one finger. Just stagger the starting
times by 100 millisecond intervals. I can tap the fingers and thumb of
one hand on the table at 10 or so taps per second – but only in order
from little finger to thumb. I just listen to the rattling sound and
adjust the speed up and down to keep it uniform.
My impression is that when feedback came on the scene and Lashley
realized how fast pianists could press successive keys, he decided that,
thank goodness, he didn’t have to learn that new fangled cybernetics
stuff with all the equations and jargon. A lot of relieved psychologists
jumped on that bandwagon. The flag was unfurled, argent with the banner
“FEEDBACK * IS * TOO * SLOW” on a fess sable with three
bezants between three fleur-de-lys gules
. Good old Google.

Best,

Bill P.

[From Avery Andrews 2010.02.13 11:46 Eastern Oz DST]

The problems of controlling sequence errors reminds me of a phenomenon I noticed with my young children, that if they made a speech error, they would often abort the entire communication, and to all the way back to re-securing the communication channel:

C: hey Dad, you know what?
D: what.
C: well yesterday when ... yadda yadda SPEECH ERROR CRASH
     PAUSE
C: hey Dad, you know what?
D: what.
C: well yesterday when ...

So the idea that how to manage perception of error with sequence control is a learned skill has some legs for language, too, I think (for language, there are rather complex 'repair strategies', just ignoring them tends to not be a good option). The default would appear to be just to back up and do the sequence again (a complexity being that
a language can't be learned as a list of possible sequences, but only as a (almost always recursive) method
for producing or recognzing them).

Except that for lin

···

-----Original Message-----
From: Control Systems Group Network (CSGnet) on behalf of Bill Powers
Sent: Sat 13/02/2010 8:12 AM
To: CSGNET@LISTSERV.ILLINOIS.EDU
Subject: Re: Feedback is too slow

[From Bill Powers (2010.01.12.1250 MST)]

Richard Kennaway (2010.02.12.1004 GMT) --

JRK: On the other hand, none of the demos in LCS III involve
sequence control or sequential actions, and I don't recall any other
PCT demos that do. So it would be easy for a critic to say, "that's
all very well, but how do you explain sequential action?". Googling
on things written about "The problem of serial order" suggests that
some demos in this area would be useful.

Walking would be one example. My walking robot simulations have
built into them the sequential action of picking up some of their
legs, swinging them forward or back, and putting them down, but I'm
not sure if this bears on the hypothetical objection above.

Sequential action, as you imply, would be achieved by controlling for
a specific sequence of perceptions. As each perception is achieved,
the next reference signal is sent and the previous one is turned off.
But the fast rate at which some sequences can be executed suggests
something more complex.

Lashley cited fast piano playing as his evidence that sequences are
accomplished open-loop. He said that pianists can create sequences of
keystrokes as fast as 16 per second, which is much too fast to allow
waiting for feedback. However pianists (and their audiences) can
clearly perceive sequence errors at least that fast, because a note
struck out of sequence, as the saying goes, really "stands out."
There is an almost instantaneous error signal, especially in the
performer who knows exactly what note was intended next. As with
typing errors, however, a mistake perceived in a fast sequence is not
always identified correctly as to which key was struck in error.

We know that sequence errors can't be corrected that fast. This
implies that the output of a sequence controller is an open-loop
sequence of reference signals issued at the speed at which the notes
are to occur, and the perception is a sequence that is compared with
the reference sequence continuously but can be corrected only once in a while.

However, controlling a sequence is a bit odd since the elements can't
be changed after they have happened, and changing a sequence by any
means available only makes it more erroneous. If there is an error,
nothing can be done about it after the fact without creating even
more error, so professional pianists (as is true of other
intrumentalists) are instructed continue to play and ignore the
error, and are specifically cautioned not to stop the sequence, go
back, and replay it from an earlier step. Even in solo performances
doing that would create an even more jarring break in the sequence,
and of course in ensemble performances it would put the errant
musician out of sync with the other performers and destroy the entire effect.

In fact, we can perceive sequences, and we have reference sequences
with which to compare the perceived one, and have various strategies
for correcting the errors as soon as physically possible. The
tendency to stop and repeat the sequence from a point before the
error is hard to overcome in cases where it is inadvisable;
otherwise, that is generally what we do. I do it all the time while
typing. I can type extremely fast as long as I am not required to hit
the right keys. My average typing speed, however, is nothing to brag about.

The speed with which we can control sequences depends in part on the
level to which the reference signals are issued. If the reference
signals specify a heard note, it's hard to keep up with fast changes
in reference signals, because the pitch control system has to convert
errors into adjustments of reference configurations for the fingers.
If, however, finger configurations are specified, the speed of
matching perception to reference is far greater. Executing finger
movements without listening is fast but tends to make the result
sound mechanical.

Of course it's still impossible to make one finger strike 16 notes in
one second, but in a trill of 16th notes the repetition rate for one
finger is only 8 per second, and in an arpeggio that uses all 5
fingers it is only a little over 3 per second and half of that if
both hands are involved.

Art Tatum, it was said, could run an arpeggio the full length of the
keyboard at a rate of 90 strokes per second. I think that's an
exaggeration but not by an order of magnitude. He could play "stride"
left hands at a rate of around two or three per second, a "stride"
consisting of a bass note followed by a left-hand chord in the middle
range of pitch. As any pianist would realize, enormous strength and
endurance are required to move the mass of the hand accurately and
repeatedly back and forth that fast, reforming the entire hand
configuration and aiming the contact points within a fraction of the
width of a key. It's even more remarkable when you reflect that
during any given performance, Tatum was probably drunk.

Lashley spoke only about executing strings of outputs. He thought
that involved planning a starting point, and end point, and sequence
of points in between, and then executing the sequence with no
feedback. The idea of specifying a position and then letting a
lower-order system achieve that position while the next position for
a different finger is being specified never, of course, occurred to
Lashley, though all he really missed was the role of feedback. Also,
it didn't occur to Lashley that the brain is a highly parallel
processor, not a single CPU frantically trying to time-share its
attention and services among a dozen different tasks. You can play
ten successive notes at high speed if you use 10 control systems each
controlling one finger. Just stagger the starting times by 100
millisecond intervals. I can tap the fingers and thumb of one hand on
the table at 10 or so taps per second -- but only in order from
little finger to thumb. I just listen to the rattling sound and
adjust the speed up and down to keep it uniform.

My impression is that when feedback came on the scene and Lashley
realized how fast pianists could press successive keys, he decided
that, thank goodness, he didn't have to learn that new fangled
cybernetics stuff with all the equations and jargon. A lot of
relieved psychologists jumped on that bandwagon. The flag was
unfurled, argent with the banner "FEEDBACK * IS * TOO * SLOW" on a
fess sable with three bezants between three fleur-de-lys gules. Good
old Google.

Best,

Bill P.

[From Rick Marken (2010.02.13.1120)]

Bill Powers (2010.01.12.1250 MST)--

Lashley cited fast piano playing as his evidence that sequences are
accomplished open-loop. He said that pianists can create sequences of
keystrokes as fast as 16 per second, which is much too fast to allow waiting
for feedback.

According to my data (see
http://www.mindreadings.com/ControlDemo/HP.html) that is way to fast
for sequence control; at best, sequence control is possible only when
the elements are occurring no faster than about 2 per second. I think
controlling a pianist controlling notes that are occurring 16/sec is
not controlling sequence but, rather, lower level perceptions like
transition (apparent motion) or configuration (temporal shape of the
notes). I think it might be hard to distinguish the difference between
sequence and lower level control, other than by timing. But I just
thought of an example of the difference between sequence and
(possibly) configuration control in terms of my own experience.

When I first was learning to play the guitar I was taught something
called Scruggs picking (a banjo pick for guitar; the guy who taught it
to me was also a banjo player). I had to learn it as a sequence of
finger plucks and strings to pluck, something like: thumb (1st
string), middle(2nd), thumb (5th), first (4th). It was very difficult
to learn to produce this sequence (perception); and I had to do it
quite slowly at first; about 2 picks per second at best. But now I can
do it quite swiftly (maybe 8 picks per second on a good day) and I
don't think I am doing this by control of sequence; I'm not even aware
of the sequence anymore; it's just a pattern of picks; a
configuration, maybe. The fact that it's not a sequence I'm
controlling is suggested to me by the fact that 1) I can control for
this sequence at a far faster rate than I can control for a sequence
of sizes in my hierarchy demo and 2) I now have to stop and think
about what the sequence actually is in order to teach it to someone
else; indeed, I just tried it (slowly!) on the guitar and found that
my description above is wrong. So I can produce the sequence or
outputs needed to produce the perception I control; but the perception
I control is not a sequence.

So an important contribution that PCT makes to the question of how
"fast" feedback must be (in terms of transport lag and integration
time) in order to control the perception is that it depends on the
type (level) of perception being controlled. The higher level level
of the perception controlled, the slower the feedback must be in order
for control to occur. So the the ability to control sequences doesn't
mean that feedback is too slow; it depends on what kind of perception
is actually referred to by the term "sequence". If it's actually a
sequence that is being controlled, then the feedback must be slow or
the sequence cannot by controlled; if the sequence that is controlled
is actually a configuration of elements that occur in a particular
sequence, then the perception can be controlled when the feedback is
much faster (short transport lag and/or fast integration time).

I've rushed through this a bit but I think there is a germ of truth in
this. What do you think?

Best

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

[From Bill Powers (2010.02.14. 0828 MAST)]

Avery Andrews 2010.02.13 11:46 Eastern Oz DST --

AA: The problems of controlling sequence errors reminds me of a phenomenon I noticed with my young children, that if they made a speech error, they would often abort the entire communication, and to all the way back to re-securing the communication channel:

C: hey Dad, you know what?
D: what.
C: well yesterday when ... yadda yadda SPEECH ERROR CRASH
     PAUSE
C: hey Dad, you know what?
D: what.
C: well yesterday when ...

BP: Love it. The default does seem to be hitting the reset button and starting over, wherever "over" begins.

AA: The default would appear to be just to back up and do the sequence again (a complexity being that a language can't be learned as a list of possible sequences, but only as a (almost always recursive) method for producing or recognzing them).

BP: Maybe the language part per se can't be learned that way, but to communicate you have to be able to speak or write words in some particular sequence. So the sequence has be be generated as an appropriate ordering of reference signals.

All this is making me more suspicious that there's missing or misdefined level in here somewhere. I think of the sequence level as concerned with serial ordering, not with the mechanisms of producing a timed sequence. The sequence that goes

ABC .... D .........................E ....FG..H

is the same sequence with any other spacing, as long as the order of the letters is the same. Note that written words have no specified temporal spacing except for what punctuation suggests. Spoken language does: "Come.... here .... right .... NOW!"

The idea of a "central pattern generator" has been lurking in the background for quite a while. Bob Clark tried to formulate a level which he called "temporal patterns," but couldn't figure out how it would fit in. I think he had the right idea, though -- the timing is more important that the specific sequence in the sort of case he was thinking about, and timing errors would have to be corrected even if the ordering of the elements were correct. We need recognizeable timed patterns for things like dancing or walking or singing songs or drumming. Maybe this is what should go in place of the current "events" level. This is where the sentence would actually get said, as opposed to the sequence level at which the words would be selected in the right order but with no particular rhythm.

Hope all is well with you, Ave. I miss your dad. And your aunt.

Best,

Bill P.

[From Bill Powers (2010.02.14.1120 MST)]

Rick Marken (2010.02.13.1120) --

So an important contribution that PCT makes to the question of how
"fast" feedback must be (in terms of transport lag and integration
time) in order to control the perception is that it depends on the
type (level) of perception being controlled. The higher level level
of the perception controlled, the slower the feedback must be in order
for control to occur. So the the ability to control sequences doesn't
mean that feedback is too slow; it depends on what kind of perception
is actually referred to by the term "sequence". If it's actually a
sequence that is being controlled, then the feedback must be slow or
the sequence cannot by controlled; if the sequence that is controlled
is actually a configuration of elements that occur in a particular
sequence, then the perception can be controlled when the feedback is
much faster (short transport lag and/or fast integration time).

We're thinking along the same lines. I don't think it's a configuration simply because configurations are static patterns. But there is a temporal pattern there that's not just the ordering of elements. What do you think of sticking it in at the 5th level that I've been calling "events"? The pattern generator idea, where the pattern is accomplished by using transitions, configurations, and so on, timed to occur with a specific temporal pattern. That's more general than "events," but includes them. An event is just one iteration of a temporal pattern.

Best,

Bill P.

[From Rick Marken (2010.02.14.1230)]

Bill Powers (2010.02.14.1120 MST)]

We're thinking along the same lines. I don't think it's a configuration
simply because configurations are static patterns. But there is a temporal
pattern there that's not just the ordering of elements. What do you think of
sticking it in at the 5th level that I've been calling "events"? The pattern
generator idea, where the pattern is accomplished by using transitions,
configurations, and so on, timed to occur with a specific temporal pattern.
That's more general than "events," but includes them. An event is just one
iteration of a temporal pattern.

Sure, that's fine with me. I just use terms like "configuration" and
"transition" in order to discuss it in terms of the hypothetical
hierarchy described in B:CP. My main point is just that the
perception being controlled by the behaving system is not necessarily
the same as the one that may appear to an observer to be the one
controlled. It may look to an observer like a sequence is being
controlled when a musician plays a sequence of notes; that may be what
was controlled when the musician was first learning the riff but what
is actually controlled when the riff is learned may be what you call
an event. The same is true with what appears to be control of
"if-then" contingencies (programs). Many behaviors, like pressing a
lever, can be described in "if-then" terms: if the lever is up then
press down; if the lever is down then release. One way to tell that
that pressing a lever does not involve control of a program (if-then)
perception is to look at the speed of control. An organism can press a
lever at a much faster rate than it can control a program (at least
according to what little research I've done on it). I think that a
properly refined version of the timing approach that I use in my
"Hierarchy of perception and control" demo might be a good way to map
out _relative_ levels of perceptual control without worrying about
what the type of perception should be called at each level.

Best

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

[Rupert Young (2014.04.22 18.00)]

I’ve heard people on here talk about others making this claim as an argument against PCT, and I would like to investigate this further.

Can someone point me to some references of those who have made this claim, and also any refutations that have been made in support of PCT?

Regards,

Rupert

[From Adam Matic 2014.06.26.1300]

I think these might be what you’re looking for (MS Word files attached).

DEVIL’S.BIB.docx (165 KB)

DISPUTE.PCT.docx (37.3 KB)

···

On Tue, Apr 22, 2014 at 2:23 PM, rupert@moonsit.co.uk rupert@moonsit.co.uk wrote:

[Rupert Young (2014.04.22 18.00)]

I’ve heard people on here talk about others making this claim as an argument against PCT, and I would like to investigate this further.

Can someone point me to some references of those who have made this claim, and also any refutations that have been made in support of PCT?

Regards,

Rupert

I am loving this, and Bill’s acute use of language and clear frustration with the science that is out there.

So much for considering Ashby and Powers idea to be similar eh Boris?

Here’s another gaggle of myths, this time from W. Ross Ashby, in _An Introduction to Cybernetics (New York: Wiley, 1966 (third printing, copyright 1963).

The basic formulation of s.11/4 assumed that the process of regulation went through its successive stages in the following order:

1.A particular disturbance threatens at D;

2.it acts on R, which transforms it to a response;

3.the two values, of D and R, act on T simultaneously to produce T’s outcome;

4.the outcome is a state of E, or affects E." (p. 221)

E is an essential variable that is to be stabilized by the action of a regulator R, acting through an environmental function T which is fixed. Regulation is achieved when the effect of D on T is precisely cancelled by the response of the regulator R to D, also acting on T. It is assumed that E depends on T and T alone, so there are no disturbances acting directly on E that can’t be sensed by the regulator.

If R and T are precisely calibrated and act with infinite precision, then perfect regulation is possible but not otherwise. Ashby tended to overlook the question of precision, largely because in examples he tended to use small integers or decimal fractions accurate to one decimal place to represent the variables. As a result he greatly overestimated the capacities of compensating systems, and therefore, by comparison, greatly underestimated the capacities of control systems.

Regulation by error. A wellknown regulator that cannot react directly to the original disturbance D is the thermostat controlled water bath, which is unable to say “I see someone coming with a cold flask that is to be immersed in me I must act now.” On the contrary, the regulator gets no information about the disturbance until the temperature of the water (E) actually begins to drop. And the same limitation applies to the other possible disturbances, such as the approach of a patch of sunlight that will warm it, or the leaving open of a door that will bring a draught to cool it." (p. 222).

Note the implication that a compensating regulator might exist which, on seeing someone approach with a flask, could deduce that it contains cold water and is about to be immersed in the bath. Note also the unspoken assumption that merely from qualitative knowledge about a flask of cold water, a patch of sunlight, or a potential draught through an open door, the regulator could be prepared to act quantitatively: to add heat to the bath that would exactly compensate for the cooling from the water in the flask or the evaporation due to the draught, or cooling just sufficient to prevent any rise in the temperature of the bath. From qualitative knowledge of the disturbance, the regulator somehow achieves exact quantitative compensation for the quantitative effects of the disturbance. If, of course, such a thing were possible, the compensator would be much superior to any form of feedback controller. But such a thing is not remotely possible.

After doing through a series of diagrams, Ashby finally diagrams the true errordriven control system:

… we have the basic form of the simple ‘errorcontrolled servomechanism’ or ‘closedloop regulator,’ with its wellknown feedback from E to R." (p. 223)

The diagram is D > T > E

^ |

R <

Now we get to a whole fountain of misinformation about control systems, a series of deductions that is just close enough to reality to be convincing, and just far enough from it to be utter nonsense.

A fundamental property of the errorcontrolled regulator is that it cannot be perfect in the sense of S.11/3" (p.223)

He then goes through a “formal proof” using the Law of Requisite Variety to conclude

It is easily shown that with these conditions E’s variety will be as large as D’s i.e., R can achieve no regulation, no matter how R is constructed (i.e., no matter what transformation is used to turn E’s value into an Rvalue)."

If the formal proof is not required, a simpler line of reasoning can show why this must be so. As we saw, R gets its information through T and E. Suppose that R is regulating successfully, then this would imply that the variety of E is reduced below that of D perhaps even to zero. This very reduction makes the channel

D > T > E

to have a lessened capacity; if E should be held quite constant then the channel is quite blocked. So the more successful R is in keeping E constant, the more does R block the channel by which it is receiving its necessary information. Clearly, any success by R can at best be partial." (p. 223224)

This argument has apparently convinced many cyberneticists and others that the Law of Requisite Variety is more general than the principles of control, and in fact shows that control systems are poor second cousins to compensators when it comes to the ability to maintain essential variables constant against disturbance.

In fact this argument shows how utterly useless the Law of Requisite Variety is for reaching any correct conclusion about control systems.

Having swept through this dizzying exercise in proving a falsehood, Ashby then grudgingly allows feedback control to creep humbly back into the picture:

Fortunately, in many cases complete regulation is not necessary. So far, we have rather assumed that the states of the essential variables E were sharply divided into “normal” … and “lethal”, so occurrence of the “undesirable” states was wholly incompatible with regulation. It often happens, however, that the system shows continuity, so that the states of the essential variables lie a long a scale of undesirability. Thus a land animal can pass through many degrees of dehydration before dying of thirst; and a suitable reverse from half way along the scale may justly be called “regulatory” if it saves the animal’s life, though it may not have saved the animal from discomfort. "

Note the gratuitous “half way along the scale.”

Thus the presence of continuity makes possible a regulation that, though not perfect, is of the greatest practical importance. Small errors are allowed to occur; then, by giving their information to R, they make possible a regulation against great errors. This is the basic theory, in terms of communication, of the simple feedback regulator." (p. 224)

The argument then veers off into “Markovian machines” and Markovian stochastic regulation. This is billed as the most important and farreaching application of the errorcontrolled regulator.

Note how the argument relies on qualitative statements to reach quantitative conclusions. It is perfectly true that if a compensating regulator affects T equally and oppositely to the effect of D, E will not be affected at all. But by that same argument, to the extent that R does not have perfect information about D (and about the nature of the connection from D to T and from R to T), T will not be affected equally and oppositely, and thus to the extent of the imperfection, E will not be perfectly regulated. Furthermore, if there is any disturbance at all that is NOT detected by R (for example, a disturbance that acts directly on E), the effects of that disturbance will not be compensated at all. If R does not compensate for all nonlinearities and timefunctions in the connection from D to T, compensation will not occur. When the processes involved are thought of as real physical processes in a real environment, the idealized assumptions behind the compensatory regulator are easily seen to be unrealistic they predict regulation that is far, far better than any that could actually be achieved in this way.

Note also how the qualitative concept that errorregulated control must be imperfect is used to imply that it must be more imperfect than compensatory regulation. This non sequitur has appeared in the literature over and over ever since Ashby. In his earlier book Ashby was still toying with true feedback control and continuous systems; the appendix is heaped with rather aimless mathematics that is oriented in that direction. But in this second book, Ashby shows that he never understood how an “errorcontrolled” regulator works. He didn’t know that the “imperfection” inherent in such systems can be reduced to levels of error far smaller than the errorreductions that any real compensating system could achieve smaller by orders of magnitude, in many cases, particularly cases involving human behavioral systems.

Ashby’s entire line of reasoning about feedback control in An introduction to cybernetics is spurious. Yet Ashby has been revered in cybernetics and associated fields for 40 years as a deep thinker and a pioneer. His Law of Requisite Variety has nothing at all useful to say about control systems and in fact led Ashby to a completely false conclusion about them yet it is still cited as a piece of fundamental thinking. Whether Ashby originated these misconceptions or simply picked them up from others I don’t know. One thing is certain: he did not get them from an understanding of the principles of control.

···

On Tue, Apr 22, 2014 at 2:23 PM, rupert@moonsit.co.uk rupert@moonsit.co.uk wrote:

[Rupert Young (2014.04.22 18.00)]

I’ve heard people on here talk about others making this claim as an argument against PCT, and I would like to investigate this further.

Can someone point me to some references of those who have made this claim, and also any refutations that have been made in support of PCT?

Regards,

Rupert

I love this from Bill too…

I have 200 pounds of ice cubes, and you have 50 gallons of boiling water.Desired: a nice tub of water for a bath. I get to throw in the ice cubes (youcan see exactly how may I throw in); you get to pour in the boiling water. Asyou see me disturbing the bath with ice-cubes,you estimate how much boiling water to pour in to arrive at a bath of the righttemperature. When I have exhausted my ice cubes, you finish the process byadding more boiling water in the amount you think is necessary.

``

As an alternative, I will let you see a thermometer in the tub, but willnot let you see how many ice cubes I am throwing in. You must base youradditions of boiling water entirely on the thermometer reading.

``

Whichever method of filling the tub you elect, when the process is finishedyou must then step into the tub and immediately sit down in it.

``

Which method would you choose: compensating for known disturbances, orbasing your action on perception of the state of the essential variable withoutknowing what the disturbances are?

`

`

``

···

On Tue, Apr 22, 2014 at 2:23 PM, rupert@moonsit.co.uk rupert@moonsit.co.uk wrote:

[Rupert Young (2014.04.22 18.00)]

I’ve heard people on here talk about others making this claim as an argument against PCT, and I would like to investigate this further.

Can someone point me to some references of those who have made this claim, and also any refutations that have been made in support of PCT?

Regards,

Rupert

Thanks Warren. Some day I'd like to publish a children's PCT book based on
Bill's wonderful little games...like the leading questions in Chapter 2 of
B:CP.

Once, when we were working on MSOB, I caught an error (rare, but huge fun)
that took his marching soldiers right off the edge of the world. We roared
laughing when he read it again.

Alice

···

I love this from Bill too...

I have 200 pounds of ice cubes, and you have 50 gallons of boiling
water.Desired: a nice tub of water for a bath. I get to throw in the ice
cubes (youcan see exactly how may I throw in); you get to pour in the
boiling water. Asyou see me disturbing the bath with ice-cubes,you
estimate
how much boiling water to pour in to arrive at a bath of the
righttemperature. When I have exhausted my ice cubes, you finish the
process byadding more boiling water in the amount you think is necessary.

As an alternative, I will let you see a thermometer in the tub, but
willnot
let you see how many ice cubes I am throwing in. You must base
youradditions of boiling water entirely on the thermometer reading.

Whichever method of filling the tub you elect, when the process is
finishedyou must then step into the tub and immediately sit down in it.

Which method would you choose: compensating for known disturbances,
orbasing your action on perception of the state of the essential variable
withoutknowing what the disturbances are?

On Saturday, April 26, 2014, Warren Mansell <wmansell@gmail.com> wrote:

I am loving this, and Bill's acute use of language and clear frustration
with the science that is out there.

So much for considering Ashby and Powers idea to be similar eh Boris?

Here's another gaggle of myths, this time from W. Ross Ashby, in _An
Introduction to Cybernetics (New York: Wiley, 1966 (third printing,
copyright 1963).

The basic formulation of s.11/4 assumed that the process of regulation
went through its successive stages in the following order:

  1.A particular disturbance threatens at D;
  2.it acts on R, which transforms it to a response;
  3.the two values, of D and R, act on T _simultaneously_ to produce T's
outcome;
  4.the outcome is a state of E, or affects E." (p. 221)

E is an essential variable that is to be stabilized by the action of a
regulator R, acting through an environmental function T which is fixed.
Regulation is achieved when the effect of D on T is precisely cancelled
by
the response of the regulator R to D, also acting on T. It is assumed
that
E depends on T and T alone, so there are no disturbances acting directly
on
E that can't be sensed by the regulator.

If R and T are precisely calibrated and act with infinite precision,
then
perfect regulation is possible but not otherwise. Ashby tended to
overlook
the question of precision, largely because in examples he tended to use
small integers or decimal fractions accurate to one decimal place to
represent the variables. As a result he greatly overestimated the
capacities of compensating systems, and therefore, by comparison,
greatly
underestimated the capacities of control systems.

_Regulation by error._ A wellknown regulator that cannot react directly
to
the original disturbance D is the thermostat controlled water bath,
which
is unable to say "I see someone coming with a cold flask that is to be
immersed in me I must act now." On the contrary, the regulator gets no
information about the disturbance until the temperature of the water (E)
actually begins to drop. And the same limitation applies to the other
possible disturbances, such as the approach of a patch of sunlight that
will warm it, or the leaving open of a door that will bring a draught to
cool it." (p. 222).

Note the implication that a compensating regulator might exist which, on
seeing someone approach with a flask, could deduce that it contains cold
water and is about to be immersed in the bath. Note also the unspoken
assumption that merely from qualitative knowledge about a flask of cold
water, a patch of sunlight, or a potential draught through an open door,
the regulator could be prepared to act quantitatively: to add heat to
the
bath that would exactly compensate for the cooling from the water in the
flask or the evaporation due to the draught, or cooling just sufficient
to
prevent any rise in the temperature of the bath. From qualitative
knowledge
of the disturbance, the regulator somehow achieves exact quantitative
compensation for the quantitative effects of the disturbance. If, of
course, such a thing were possible, the compensator would be much
superior
to any form of feedback controller. But such a thing is not remotely
possible.

After doing through a series of diagrams, Ashby finally diagrams the
true
errordriven control system:

... we have the basic form of the simple 'errorcontrolled
servomechanism'
or 'closedloop regulator,' with its wellknown feedback from E to R." (p.
223)

The diagram is D > T > E
                             ^ |
                             > >
                             R <

Now we get to a whole fountain of misinformation about control systems,
a
series of deductions that is just close enough to reality to be
convincing,
and just far enough from it to be utter nonsense.

A fundamental property of the errorcontrolled regulator is that _it
cannot
be perfect_ in the sense of S.11/3" (p.223)

He then goes through a "formal proof" using the Law of Requisite Variety
to conclude

It is easily shown that with these conditions _E's variety will be as
large as D's_ i.e., R can achieve no regulation, no matter how R is
constructed (i.e., no matter what transformation is used to turn E's
value
into an Rvalue)."

If the formal proof is not required, a simpler line of reasoning can
show
why this must be so. As we saw, R gets its information through T and E.
Suppose that R is regulating successfully, then this would imply that
the
variety of E is reduced below that of D perhaps even to zero. This very
reduction makes the channel

               D > T > E

to have a lessened capacity; _if E should be held quite constant then
the
channel is quite blocked_. So the more successful R is in keeping E
constant, the more does R block the channel by which it is receiving its
necessary information. Clearly, any success by R can at best be
partial."
(p. 223224)

This argument has apparently convinced many cyberneticists and others
that
the Law of Requisite Variety is more general than the principles of
control, and in fact shows that control systems are poor second cousins
to
compensators when it comes to the ability to maintain essential
variables
constant against disturbance.

In fact this argument shows how utterly useless the Law of Requisite
Variety is for reaching any correct conclusion about control systems.

Having swept through this dizzying exercise in proving a falsehood,
Ashby
then grudgingly allows feedback control to creep humbly back into the
picture:

Fortunately, in many cases complete regulation is not necessary. So far,
we have rather assumed that the states of the essential variables E were
sharply divided into "normal" ... and "lethal", so occurrence of the
"undesirable" states was wholly incompatible with regulation. It often
happens, however, that the system shows continuity, so that the states
of
the essential variables lie a long a scale of undesirability. Thus a
land
animal can pass through many degrees of dehydration before dying of
thirst;
and a suitable reverse from half way along the scale may justly be
called
"regulatory" if it saves the animal's life, though it may not have saved
the animal from discomfort. "

Note the gratuitous "half way along the scale."

Thus the presence of continuity makes possible a regulation that, though
not perfect, is of the greatest practical importance. Small errors are
allowed to occur; then, by giving their information to R, they make
possible a regulation against great errors. This is the basic theory, in
terms of communication, of the simple feedback regulator." (p. 224)

The argument then veers off into "Markovian machines" and Markovian
stochastic regulation. This is billed as the most important and
farreaching application of the errorcontrolled regulator.

Note how the argument relies on qualitative statements to reach
quantitative conclusions. It is perfectly true that if a compensating
regulator affects T equally and oppositely to the effect of D, E will
not
be affected at all. But by that same argument, to the extent that R does
not have perfect information about D (and about the nature of the
connection from D to T and from R to T), T will not be affected equally
and
oppositely, and thus to the extent of the imperfection, E will not be
perfectly regulated. Furthermore, if there is any disturbance at all
that
is NOT detected by R (for example, a disturbance that acts directly on
E),
the effects of that disturbance will not be compensated at all. If R
does
not compensate for all nonlinearities and timefunctions in the
connection
from D to T, compensation will not occur. When the processes involved
are
thought of as real physical processes in a real environment, the
idealized
assumptions behind the compensatory regulator are easily seen to be
unrealistic they predict regulation that is far, far better than any
that
could actually be achieved in this way.

Note also how the qualitative concept that errorregulated control must
be
imperfect is used to imply that it must be _more imperfect than
compensatory regulation_. This non sequitur has appeared in the
literature
over and over ever since Ashby. In his earlier book Ashby was still
toying
with true feedback control and continuous systems; the appendix is
heaped
with rather aimless mathematics that is oriented in that direction. But
in
this second book, Ashby shows that he never understood how an
"errorcontrolled" regulator works. He didn't know that the
"imperfection"
inherent in such systems can be reduced to levels of error far smaller
than
the errorreductions that any real compensating system could achieve
smaller by orders of magnitude, in many cases, particularly cases
involving human behavioral systems.

Ashby's entire line of reasoning about feedback control in _An
introduction to cybernetics_ is spurious. Yet Ashby has been revered in
cybernetics and associated fields for 40 years as a deep thinker and a
pioneer. His Law of Requisite Variety has nothing at all useful to say
about control systems and in fact led Ashby to a completely false
conclusion about them yet it is still cited as a piece of fundamental
thinking. Whether Ashby originated these misconceptions or simply picked
them up from others I don't know. One thing is certain: he did not get
them
from an understanding of the principles of control.

On Saturday, April 26, 2014, Adam Matic >> <adam.matic@gmail.com<javascript:_e(%7B%7D,'cvml','adam.matic@gmail.com');>> >> wrote:

[From Adam Matic 2014.06.26.1300]

I think these might be what you're looking for (MS Word files
attached).

On Tue, Apr 22, 2014 at 2:23 PM, rupert@moonsit.co.uk < >>> rupert@moonsit.co.uk> wrote:

  [Rupert Young (2014.04.22 18.00)]

I've heard people on here talk about others making this claim as an
argument against PCT, and I would like to investigate this further.

Can someone point me to some references of those who have made this
claim, and also any refutations that have been made in support of PCT?

Regards,
Rupert

--
Dr Warren Mansell
Reader in Psychology
Cognitive Behavioural Therapist & Chartered Clinical Psychologist
School of Psychological Sciences
Coupland I
University of Manchester
Oxford Road
Manchester M13 9PL
Email:
warren.mansell@manchester.ac.uk<javascript:_e(%7B%7D,'cvml','warren.mansell@manchester.ac.uk');>

Tel: +44 (0) 161 275 8589

Website: http://www.psych-sci.manchester.ac.uk/staff/131406

See teamstrial.net for further information on our trial of CBT for
Bipolar Disorders in NW England

The highly acclaimed therapy manual on A Transdiagnostic Approach to CBT
using Method of
Levels<http://www.amazon.co.uk/Transdiagnostic-Approach-Method-Levels-Therapy/dp/0415507642/ref=sr_1_1?ie=UTF8&qid=1351756948&sr=8-1>is
available now.

Check www.pctweb.org for further information on Perceptual Control
Theory

--
Dr Warren Mansell
Reader in Psychology
Cognitive Behavioural Therapist & Chartered Clinical Psychologist
School of Psychological Sciences
Coupland I
University of Manchester
Oxford Road
Manchester M13 9PL
Email: warren.mansell@manchester.ac.uk

Tel: +44 (0) 161 275 8589

Website: http://www.psych-sci.manchester.ac.uk/staff/131406

See teamstrial.net for further information on our trial of CBT for Bipolar
Disorders in NW England

The highly acclaimed therapy manual on A Transdiagnostic Approach to CBT
using Method of
Levels<http://www.amazon.co.uk/Transdiagnostic-Approach-Method-Levels-Therapy/dp/0415507642/ref=sr_1_1?ie=UTF8&qid=1351756948&sr=8-1>is
available now.

Check www.pctweb.org for further information on Perceptual Control Theory

[Rupert Young (2014.05.20 19.00)]
Thanks. Very interesting to see that PCT is consistent with standard control theory, but standard control theory has been has been misapplied to behavioural systems.

Is DISPUTE.PCT available on the internet to reference, and where are figures 5 & 6?

Regards,
Rupert

···

On 26/04/2014 11:57, Adam Matic wrote:

[From Adam Matic 2014.06.26.1300]
I think these might be what you're looking for (MS Word files attached).

On Tue, Apr 22, 2014 at 2:23 PM, <mailto:rupert@moonsit.co.uk>rupert@moonsit.co.uk <<mailto:rupert@moonsit.co.uk>rupert@moonsit.co.uk> wrote:

[Rupert Young (2014.04.22 18.00)]

I've heard people on here talk about others making this claim as an argument against PCT, and I would like to investigate this further.

Can someone point me to some references of those who have made this claim, and also any refutations that have been made in support of PCT?

Regards,
Rupert

[From Dag Forssell (2014 05 20 12:20 PST)]

Is DISPUTE.PCT available on the internet to
reference, and where are figures 5 & 6?

Check out

ftp.pctresources.com/CSGnet_Threads/

User name pctstudent password
re5earch!

Best, Dag

[From Rupert Young (2014.05.21 11.00)]

Thanks. What about the figures?

I'd like to cite this paper but don't think I can do it unless it is public. Can it be made available on one of the PCT sites, or can I put it on mine?

Regards,
Rupert

···

On 20/05/2014 20:19, Dag Forssell wrote:

[From Dag Forssell (2014 05 20 12:20 PST)]

Is DISPUTE.PCT available on the internet to reference, and where are figures 5 & 6?

Check out <ftp://ftp.pctresources.com/CSGnet_Threads/> ftp.pctresources.com/CSGnet_Threads/

User name pctstudent password re5earch!

Best, Dag

Hi Rupert, I have this one public but not the Dispute document.
http://www.pctweb.org/devilbib.htm

···

On Wed, May 21, 2014 at 10:51 AM, Rupert Young rupert@moonsit.co.uk wrote:

[From Rupert Young (2014.05.21 11.00)]

  Thanks. What about the figures?



  I'd like to cite this paper but don't think I can do it unless it

is public. Can it be made available on one of the PCT sites, or
can I put it on mine?

Regards,
Rupert

On 20/05/2014 20:19, Dag Forssell wrote:

[From Dag Forssell (2014 05 20 12:20 PST)]

      Is DISPUTE.PCT available on the

internet to
reference, and where are figures 5 & 6?

  Check out

    ftp.pctresources.com/CSGnet_Threads/



  User name         pctstudent   password  

re5earch!

    Best, Dag


Dr Warren Mansell
Reader in Psychology
Cognitive Behavioural Therapist & Chartered Clinical Psychologist
School of Psychological Sciences

Coupland I
University of Manchester
Oxford Road
Manchester M13 9PL
Email: warren.mansell@manchester.ac.uk

Tel: +44 (0) 161 275 8589

Website: http://www.psych-sci.manchester.ac.uk/staff/131406

See teamstrial.net for further information on our trial of CBT for Bipolar Disorders in NW England

The highly acclaimed therapy manual on A Transdiagnostic Approach to CBT using Method of Levels is available now.

Check www.pctweb.org for further information on Perceptual Control Theory

Hi Warren,

Thanks. Could we get the dispute one on there as well?
Regards,
Rupert Young
Mobile: +447795 480387
Moon's Information Technology Limited

Hi Rupert, I have this one public but not the Dispute document.

<http://www.pctweb.org/devilbib.htm>http://www.pctweb.org/devilbib.htm

[From Rupert Young (2014.05.21 11.00)]

Thanks. What about the figures?

I'd like to cite this paper but don't think I can do it unless it is public. Can it be made available on one of the PCT sites, or can I put it on mine?
Regards,

Rupert

···

On 21/05/2014 13:27, Warren Mansell wrote:

On Wed, May 21, 2014 at 10:51 AM, Rupert Young <<mailto:rupert@moonsit.co.uk>rupert@moonsit.co.uk> wrote:

On 20/05/2014 20:19, Dag Forssell wrote:

[From Dag Forssell (2014 05 20 12:20 PST)]

Is DISPUTE.PCT available on the internet to reference, and where are figures 5 & 6?

Check out <ftp://ftp.pctresources.com/CSGnet_Threads/> ftp.pctresources.com/CSGnet_Threads/

User name pctstudent password re5earch!

Best, Dag

--
Dr Warren Mansell
Reader in Psychology
Cognitive Behavioural Therapist & Chartered Clinical Psychologist
School of Psychological Sciences
Coupland I
University of Manchester
Oxford Road
Manchester M13 9PL
Email: <mailto:warren.mansell@manchester.ac.uk>warren.mansell@manchester.ac.uk

Tel: +44 (0) 161 275 8589

Website: <http://www.psych-sci.manchester.ac.uk/staff/131406>http://www.psych-sci.manchester.ac.uk/staff/131406

See <http://teamstrial.net>teamstrial.net for further information on our trial of CBT for Bipolar Disorders in NW England

The highly acclaimed therapy manual on <http://www.amazon.co.uk/Transdiagnostic-Approach-Method-Levels-Therapy/dp/0415507642/ref=sr_1_1?ie=UTF8&qid=1351756948&sr=8-1>A Transdiagnostic Approach to CBT using Method of Levels is available now.

Check <http://www.pctweb.org>www.pctweb.org for further information on Perceptual Control Theory

Would love to… Dag, was this a manuscript you were thinking of reformatting?

Warren

···

Hi Warren,

  Thanks. Could we get the dispute one on there as well?

  On 21/05/2014 13:27, Warren Mansell wrote:
Regards,
Rupert Young
Mobile: +447795 480387
Moon's Information Technology Limited
    Hi Rupert, I have this one public but not the

Dispute document.
http://www.pctweb.org/devilbib.htm

      On Wed, May 21, 2014 at 10:51 AM,

Rupert Young rupert@moonsit.co.uk
wrote:

[From Rupert Young (2014.05.21 11.00)]

            Thanks. What about the figures?



            I'd like to cite this paper but don't think I can do it

unless it is public. Can it be made available on one of
the PCT sites, or can I put it on mine?

Regards,
Rupert
                On 20/05/2014 20:19, Dag Forssell

wrote:

                  [From Dag

Forssell (2014 05 20 12:20 PST)]

                    Is DISPUTE.PCT available on the

internet to reference, and where are figures 5
& 6?

                Check out
                  ftp.pctresources.com/CSGnet_Threads/



                User name                       pctstudent   password  

re5earch!

                  Best, Dag


Dr Warren Mansell

      Reader in Psychology

      Cognitive Behavioural Therapist & Chartered Clinical

Psychologist

      School of Psychological Sciences

      Coupland I

      University of Manchester

      Oxford Road

      Manchester M13 9PL

      Email: warren.mansell@manchester.ac.uk

       

      Tel: +44 (0) 161 275 8589

       

      Website: [http://www.psych-sci.manchester.ac.uk/staff/131406](http://www.psych-sci.manchester.ac.uk/staff/131406)


        See [teamstrial.net](http://teamstrial.net) for further information

on our trial of CBT for Bipolar Disorders in NW England

        The highly acclaimed therapy manual on [              A Transdiagnostic Approach to CBT using

Method of Levels](http://www.amazon.co.uk/Transdiagnostic-Approach-Method-Levels-Therapy/dp/0415507642/ref=sr_1_1?ie=UTF8&qid=1351756948&sr=8-1) is available now.

        Check [www.pctweb.org](http://www.pctweb.org)
        for further information on Perceptual Control Theory