[Martin Taylor 2019.03.27.23.03]
···
This is getting almost as weird as the
curvature discussion. I don’t know who is on which side of Alice’s
Looking Glass any more. I asked why it is that whenever I say I
agree with you, you insist that I don’t, and you tun that around
into my getting upset when you say you don’t agree with me. Anyone
who read the thread so far will understand the difference between
those two concepts.
As for this "disturbance causes output" and Bill's message, Bill
mistakenly thought that by “disturbance” I meant "causes of
disturbance, which are permanently unknowable and irrelevant.
Can you seriously contend that when a disturbance changes the
variable you call the controlled environmental variable, the
output does not change to compensate? That seems to be what you
are insisting today. What you will insist tomorrow is anyone’s
guess, but I really wonder what kind of control would happen if
the output did not change to compensate for changes in the
disturbance.
Finally, about "information from the disturbance", you have never
understood that information analysis is a generalization of
variance analysis, which you have no qualms about using. For my
part, I have never understood what so horrifies you about that
simple mathematical fact. The point is and always was very simple.
The disturbance and the output are highly correlated negatively,
the disturbance and the perception have a very small correlation.
The reference and the perception are highly correlated. Those are
fine statements when the variables have a Gaussian probability
distribution, not when their distributions are far from Gaussian.
They don’t work very well, for example, when the disturbance or
the reference makes irregular step changes among a small number of
possibilities.
All of those statements have precise equivalent in
informational/uncertainty terms: The disturbance and the output
have low mutual uncertainty (high mutual information relative to
their individual uncertainties), the disturbance and the
perception have low mutual information, and the reference and
perception have low mutual uncertainty. When all the variables
have a Gaussian (Normal) distribution, the variance and
informational ways of reporting the relationships are exact
synonyms. Numerically they differ by a single fixed constant whose
value I am not bothering to look up right now. The
information.uncertainty statements remain valid no matter whatever
the distributions of the variables.
What's so hard about that? It seems to me preferable to use
statements and mathematics that remain valid over statements that
are their direct equivalents but that are restricted to one kind
of probability distribution.
But I don't suppose you have any better answer than you had at the
time, just to repeat over and over that “there is no information
from the disturbance in the output”, in the same way as in the
curvature discussion you insisted that because the velocity
formula was the same in two equations, the velocity value is also
identical in the two equations, when ANY velocity could be plugged
into one of the equations leaving the equation still true. You
never once made any apparent effort to show how your many critic
were wrong in their demonstrations and analyses. All you did was
repeat “I’m right and you are wrong, and moreover you don’t
understand PCT.”
Maths was never your strong point, which is no problem, until you
persist in asserting the truth of some idea that got into your
head based on a faulty mathematical analysis, long after the error
has been demonstrated to you in a variety of ways.
As I said up front, I have lost interest in this thread because of
the way meanings have been weirdly twisted and distorted into
unrecognizable forms recently. If you wish to comment seriously on
the relationship or lack thereof between PCT and Free
Energy/Predictive Coding, and I find your comment sensible, I may
contribute further to the thread, but I am not prepared to
continue trying to follow the tortuous and tortured ways you find
to prove that I disagree with you when I say that I agree with
what you write.
Martin
[Rick Marken 2019-03-27_15:19:12]
[Martin Taylor 2019 03 26.22 55]
MT: Second: What makes you think I control a perception of
my level of agreement with you?
RM: Because when I didn't agree with you you got very
upset; my lack of agreement was clearly a disturbance to a
perception you were controlling that could be called “Rick’s
level of agreement with me”.Â
MT: I don't. I do control for
supporting what I consider to be correctly stated,
RM: If that were true then you wouldn't care whether or
not I agreed with you.
MT: I have no idea why or when you got into your head the
idea that i think or ever thought that “the disturbance
causes the output”…
RM: From all the "information in the disturbance is the
basis of output" discussions on CSGNet. And just recently
you said that a change in the disturbance leads to a change
in output.
MT: So far as I can remember, the
first time I heard this idea “disturbance causes the
output” applied to me (and to Bruce Abbott) was when we
showed you the glaring error in your mathematical argument
in your curvature analysis.
RM: You'e been consistently arguing that the disturbance
causes output from the time you got on the net. I have
copied to the end of this message a post from Bill Powers to
you from 1996. It’s worth reading the whole thing since it
not only shows what Bill thought of your ideas about the
role of the disturbance relative to that of the output of a
control system but it also shows what Bill thought of your
style of argument.
Â
MT: Why did I call you "an enemy of
PCT"? By not withdrawing that curvature paper, you laid
open to a wider audience the suspicion that PCT research
is done by people not long out of mathematical
kindergarten, a situation not likely to induce people to
learn more about its power and beauty.
RM: Well, of course, I should have withdrawn my
published, peer reviewed paper when you told me too and when
I didn’t the only appropriate thing to do was to call me the
“enemy of PCT”.Â
Â
MT: By allowing the paper to stand
and neither withdrawing it before publication nor
retracting it afterwards, and even continuing later to
claim that the paper presented a PCT explanation of the
curvature power-law effect, you did act like an enemy of
PCT.
RM: Funny, I thought it was your mathematical
“explanation” (or justification) of the power law was
completely irrelevant to a PCT explanation of the power
law. Â
RM: But enough of this. Here's Bill's post. Knowing you,
I’m sure you will be able to spin it as the highest of
praise for your genius. God I wish he were still here.
Best
Rick
 =========
Date:Â Â Â Â Â Â Â Â Tue, 18 Jun
1996 01:01:43 -0600
Reply-To: "Control
Systems Group Network (CSGnet)"
             <CSGNET@POSTOFFICE.CSO.UIUC.EDU> Sender: "Control
Systems Group Network (CSGnet)"
             <CSGNET@POSTOFFICE.CSO.UIUC.EDU> From: "William T.
Powers" POWERS_W@FORTLEWIS.EDU
Subject:Â Â Â Â Â Re:
information blah blah perception blah blah disturbance
blah…To: Multiple
recipients of list CSGNET
             <CSGNET@POSTOFFICE.CSO.UIUC.EDU>
[From Bill Powers (960617.1500 MDT)]
Martin Taylor 960617 15:45 –
What was said in 1992 seems to be mostly a matter of
what you now think
were your most important points then, and thus what you
select from the
stream of communications to show that you were right
all along. One
great difficulty is that your arguments then did not
impress me any more
than they do now, yet you cite them as if they settled
the matter once
and for all -- and as if I had agreed that they did.
Let’s just look at
a few of them.
    In fact, [the discussion] arose out of my 921218
analysis of the
    informational basis of PCT:
    "The central theme of PCT is that a perception in
an ECS should be
    maintained as close as possible to a reference
value. In other
    words, the information provided by the perception,
given knowledge
    of the reference, should be as low as possible."
This is not and never was the central theme of PCT as I
see it. The
central theme of PCT is that organisms control their
perceptions by
acting on the environment. How well they control them
depends on the
parameters of the control system. There is no "should"
involved.
Organisms control as well as they control, neither
better nor worse.
I have no idea what you mean by saying "the information
provided by the
perception, given knowledge of the reference".
Information and knowledge
are not the same thing, and anyway what is there in a
control system
that can evaluate the information in a perception, with
or without
"knowledge" of the reference? You're talking
gobbledygook.
    Later, dogmatic assertions were made that there is
no information
    about the disturbance in the perceptual signal,
assertions that we
    proved false, using experimental simulations
agreed to be effective
    for the purpose.
They were not adequate for the purpose except in your
own mind. You and
Randall agreed they were effective; Rick and I did not.
In fact there is
no way to tell what the disturbing variable is from
knowledge of the
variables in the control loop (perception, reference,
error, output) or
from the forms of the functions in the loop
(perceptual, comparison,
output, feedback). The reason is very simple: exactly
the same
perturbation of the loop can arise from an infinity of
different
disturbing variables acting (singly or together)
through an infinity of
different disturbance functions.
In your first demonstration, you employed a
step-disturbance acting
through a unity disturbance function. This led to a
step-change in the
perceptual signal, which you then assumed represented
the true
disturbance. But it did not. The same step-change in
the perceptual
signal could have been created by an infinity of
different disturbances
acting through different disturbance functions. There
is no possibility
that one could work backward from knowledge of the
perceptual signal to
deduce the nature of an unknown disturbing variable or
variables acting
via unknown functions. There is simply no information
(in any sense of
the word) about the disturbing variables in the
perceptual signal.
Every now and then you seem to wake up and say "Oh, OF
COURSE there is
no information about the CAUSE of a perturbation in the
perceptual
signal. How could you ever have thought I would suggest
such a silly
thing? Please read what I say and you will not
attribute such foolish
ideas to me." And then you turn right back to the same
theme and claim,
as above, that there really is information in the
perceptual signal
about the disturbance, and that you proved it.
I can't account for this except by guessing that you
are shifting
meanings of "disturbance" between one set of statements
and the other.
One sense refers to the proximal perturbation of the
input to the
perceptual function that results from whatever distal
disturbing
variables happen to be acting. The other sense (which I
always mean by
"the disturbance") refers to the changes in the distal
disturbing
variables themselves. Your statement about information
in the perceptual
signal about "the disturbance" cannot apply to the
distal disturbing
variable. It applies trivially to the proximal
variable, because the
proximal variable is exactly what we mean by a CEV. To
say that the
perceptual signal contains information about the state
of the CEV is a
tautology, because that relationship defines the nature
of the
perceptual input function. As I tried to point out
four years ago, if y
is the sum of a, b, c ... d, then there is no way to
work backward from
knowledge of y to the state of a, b, c, and so on. You
could have
exactly the same value of y arising from an infinity of
combinations of
a, b .. d. A control system can control y if it can
vary one of the
variables on which y depends. To do so, it does not
need to know
anything about the states of the other variables on
which y depends.
Nothing. NADA.
    At least, they were agreed to be effective until
the results showed
    the dogma to be false. Then, and only then, were
irrelevant
    objections raised.
This somewhat scurrilous allegation rests on our
initial difference in
conceiving the conditions of the "challenge." Rick and
I were assuming
that you would be given only the state of the
perceptual signal. You
then proceeded to use your own assumptions about the
forms of all the
functions, including the disturbing function, and the
values of all the
variables and signals, including the reference signal,
to deduce the
only remaining unknown, the disturbing variable.
Rick sent you some lists of numbers on several
occasions, representing
the state of the perceptual signal in a working control
model, and
challenged you to deduce the behavior of the disturbing
variable from
knowledge of the behavior of the perceptual signal (I
see that he is
offering to do this again). If the perceptual signal
had contained
information about the disturbance, you should have been
able to use that
information to deduce the behavior of the disturbance.
Obviously, you
could not do this. Rick's challenge should have been
completely
sufficient to show you how we conceived of the
challenge in general.
What you did was to permit yourself to use all kinds of
knowledge that
Rick and I were ruling out. Our objections were quite
relevant to our
understanding of the phrase "information in the
perceptual signal about
the disturbance."
You citing you:
    The fact that the fixed functions were the output
function and the
    feedback function of the control loop is neither
here nor there.
    The fact that they don't vary as a function of the
waveform of the
    disturbance is what matters. The only varying item
used was the
    perceptual signal.
You citing me:
>>You forgot to mention the form of the input
function, the function
>>relating the disturbing variable to the
controlled variable, and the
>>setting of the reference signal, all of which
you must also know.
You now:
    And could you now, after three years of
consideration, tell me
    which of these varies in a manner coordinated with
variations in
    the disturbing influence on the CEV? If you can
correctly assert
    that any one of these contains information about
the fluctuations
    of the disturbance, then and only then can you
criticize the
    demonstration experiment and the derived
conclusion.
Wait a minute. You're saying that I can't criticize
your experiment and
its conclusion if I can't correctly assert that any
variable or function
in the control loop but the perceptual signal "varies
in a manner
coordinated with variations in the disturbing influence
on the CEV." If
I've untangled this set of nested negatives correctly,
you’re saying
that the perceptual signal _does_ vary in a
“coordinated” way (whatever
that means) with the disturbing influence.
But this is exactly what I am trying to tell you is
your primary
mistake. The perceptual signal does NOT vary in a way
that correlates
with any particular disturbing variable. At one moment
there might be a
single disturbing variable acting through a simple
linear function; at
the next there might be twelve disturbing variables
acting through a set
of functions ranging from square to square root to
exponential. The
control system will behave no differently in any case.
It simply senses
the controlled variable and acts according to
deviations of its
perception from the momentary setting of the reference
signal.
Furthermore, given complete knowledge of everything in
the control loop,
but not of the environment beyond the input quantities
themselves, you
could certainly deduce the state of a hypothetical
disturbing variable
based on assuming a hypothetical disturbance function.
But this would be
a complete fiction; it would not be a "reconstruction"
of the true
disturbing variable. Your chances of guessing correctly
what the actual
number of disturbances is, and what their individual
waveforms are, and
how each one is linked to have an effect on the
controlled variable, are
essentially zero. And the control system can't do this,
either.
    But (as I said those long years ago as well), is
it not absurd to
    ask the control system, which has but a single
scalar value for its
    perceptual signal, to _know_ (perceive,
understand,…) anything
    other than the value of the CEV. Is it not a red
herring to suggest
    that anything in the discussion hinges on this
absurdity?
I use "know" in a loose way, to be sure. I say that a
system “knows”
about something outside it if there is a variable
inside the system that
covaries with the external something. A photocell
“knows” about light
intensity, but not about color. In a simple control
system, the only
"knowledge" that exists is the perceptual signal. And
it is “knowledge”
only in the sense that it represents the value of a
function of some set
of input quantities.
Since this is the only knowledge that the system itself
has, it is
absurd to say (as you have said) that the system "uses
information" that
is "contained in" the perceptual signal. All the
control system needs is
the perceptual signal itself. It does not have to
perform any operations
to detect or manipulate measures of information. So who
is being absurd
here?
    You should be stating that "as the precision of
opposition to the
    disturbance increases, so the information about
the disturbance
    remaining in the perceptual signal decreases" and
then you would
    see it as a perfectly straightforward,
self-evident proposition, in
    place of a paradox contrary to reason.
But that is contrary to the idea that the control
system uses the
information in the perceptual signal to construct an
output that
precisely opposes the effects of the disturbance on the
input quantity.
The paradox lies in claiming that control -- the
precise opposition to
the effects of an unknown disturbing variable or
variables – relies on
information in the perceptual signal, and also to say
that the better
the control, the less information there is in the
perceptual signal. In
the limit, according to this way of looking at the
system, control would
be perfect if there were NO information in the
perceptual signal. But in
that case, what would be the basis for constructing the
output?
Well, let’s move on.
    Firstly, consider a predictable world. PCT is not
necessary,
    because the desired effects can be achieved by
executing a
    prespecified series of actions.
I thought this was silly in 1992 and I still do. If the
world is
predictable, this does not mean that any organism is
capable of
predicting it. Furthermore, as I pointed out back then,
even if the
world is predictable, a control system is still the
fastest and least
complex way to control it. Suppose the muscles were
calibrated perfectly
and the organism somehow could carry out the
calculations necessary to
generate the muscle tensions required to produce any
position of the
limbs. Yes, in principle one could do an open-loop
calculation involving
all the inverse kinematics and dynamics, but at what
cost? Probably a
large portion of the brain would have to be devoted to
performing this
calculation over and over in real time. But the same
result can be
achieved, for all practical purposes, using a few very
simple negative
feedback control systems which do only a few elementary
calculations. So
even in a perfectly predictable world, the control
system is still the
system of choice. To say that the world is predictable
is not to say
that it is simple or that a given organism is capable
of predicting it.
Your assumption is not tenable. Unfortunately, you
insist that it is
correct, and go on from there.
    At the other extreme, consider a random world, in
which the state
    at t+delta is unpredictable from the state at t.Â
PCT is not
    possible. There is no set of actions in the world
that will change
    the information at the sensors.
There is no information at the sensors. Information, as
you have said a
number of times, depends on the nature of the receiver.
It does not
exist independently in the environment. If the receiver
is monitoring
the mean noise level of the sensor signals, acting at
random can raise
or lower that noise level, since random acts imposed on
a random world
will add in quadrature to the net effect. Control would
still be
possible, if not very useful.
    Now consider a realistic (i.e. chaotic) world.
Fine. But you are assuming at this point that PCT would
not be necessary
in a predictable world, which is false. That vitiates
the strength of
this orderly argument. You are equating "predictable"
with “simple” or
"understandable." In fact, you are attributing
predictableness to the
environment, as if it were a property of the
environment and not a
function of the organism’s capacities to predict.
    At time t one looks at the state of the world, and
the
    probabilities of the various possible states at
t+delta are thereby
    made different from what they would have been had
you not looked at
    time t. If one makes an action A at time t, the
probability
    distributions of states at time t+delta are
different from what
    they would have been if action A had not occurred,
and moreover,
    that difference is reflected in the probabilities
of states of the
    sensor systems observing the state of the world.Â
Action A can
    inform the sensors. PCT is possible.
When you start talking like a quantum physicist you
lose me. This whole
way of dealing with phenomena strikes me as awkward and
ugly. And
anyway, I don't have to follow your arguments any
further, since you
have made a basic mistake in saying that in a
predictable world, PCT
would not be necessary.
    Things become more interesting when we go up a
level in the
    hierarchy. Now we have to consider the source of
information as
    being the error signals of the lower ECSs, given
that the higher
    level has no direct sensory access to the world
Not the error signals: the perceptual signals. These
are not the same
thing, even though you try to make them the same:
    Even though the higher ECSs may well take as
sensory input the
    perceptual signals of the lower ECSs, nevertheless
the information
    content (unpredictability) of those perceptual
signals is that of
    the error, since the higher ECSs have information
about their
    Actions (the references supplied to the lower
ECSs) just as the
    lower ones have information about their Actions in
the world.
This is patching up your argument as you go. The error
is the difference
between the reference signal and the perceptual signal.
If the higher
system is in the imagination mode, it is not receiving
the perceptual
signal. If it is in the action mode, it is not
receiving a copy of its
own output. When you try to design a system can can
operate in both
modes at once, you run into all sorts of problems. But
I don’t expect
that such niggling details will deflect you.
    (Unexpected events provide moments of high
information content, but
    they can't happen often, or we are back in the
uncontrollable
    world.)
So you are still assuming that disturbances have to be
predictable for
control to work?
    What does this mean? Firstly, the higher ECSs do
not need one or
    both of high speed or high precision. The lower
ECSs can take care
    of things at high information rates, leaving to
the higher ECSs
    precisely those things that are not predicted by
them–complexities
    of the world, and specifically things of a KIND
that they do not
    incorporate in their predictions. In other words,
the information
    argument does not specify what Bill's eleven
levels are, but it
    does make it clear why there should BE level of
the hierarchy that
    have quite different characteristics in their
perceptual input
    functions.
If information theory could really, out of its own
premises, come up
with these predictions, that would be impressive. But
it can’t because
it didn't. You're solving a problem to which you
already know the
answer, and throwing in all the assumptions needed to
make your
"prediction" come out right. Those assumptions are not
contained in
information theory. What does information theory have
to say about
“kinds” of perceptions? Nothing.
Another item
    In your comment, you take it to refer to how a
functioning ECS is
    to be designed, and that the perceptual bandwidth
should be low.
    If the perceptual bandwidth is low, then the ECS
will have
    difficulty matching the perceptual signal to the
reference signal,
    and thus the error signal will have high
information content.
First I have never said that the perceptual bandwidth
should be low.
They are what they are. And second, if the perceptual
bandwidth is low,
the ECS will have an easier time in matching the
perceptual signal to
the reference signal, and the error signal, in your
parlance, will have
a low information content. Your deduction here is
exactly the opposite
of what would happen. Of course if the reference signal
varied rapidly,
the error signal would also vary rapidly and contain
more information –
but why would a reference signal from a higher, slower
system vary more
rapidly than the perceptual signal of a lower, faster
system?
    Now it is true that if the perceptual signal has
lower bandwidth
    than the reference signal and the same resolution,
then the error
    signal will in part be predictable, thus having
lower information
    content than would appear on the surface. But I
had the
    presumption that we are always dealing with an
organism with high
    bandwidth perceptual pathways, so I forgot to
insert that caveat.
By your argument, a completely random error signal
would have the lowest
predictability of all, and thus contain the most
information. But so
what? The control system would not work with a random
error signal.
    Well, given last year's experience, I didn't
expect my information-
    theory posting to be understood, and I wasn't
disappointed in my
    expectation. Is it worth trying some more?
No, it is not. You don't have a clear and rigorous
argument that can be
built up from basic principles without any outside
assumptions to carry
you across the rough spots. If you knew what you were
talking about, you
would be able to explain it clearly.
Lastly:
    The situation is different if we take a
full-blooded outside view
    of the action of a CEV. It is from this kind of
view that we argue
    that the disturbance provides information that
passes through the
    perceptual signal to the output signal. From the
outside we can
    see the disturbing variable do whatever it does to
affect the CEV,
    and we can see the ECS modifying its output to
bring the perceptual
    signal back to its controlled value. From outside
we can see the
    reference signal of the ECS changing, and the
ouput changing to
    move the CEV so that the perceptual signal comes
to its new
    controlled value. From outside, the arguments
about there being no
    information from the disturbance in the perceptual
signal lose
    their force.
So from the outside view, it is the information from
the disturbance
that passes through the perceptual signal to the output
signal, with the
result of modifying the output to bring the perceptual
signal back to
its controlled value? This takes us back to the
original information-in-
perception argument. If the information in the
perception decreases as
the output comes to oppose the effects of the
disturbance more
precisely, how can it be the information passing
through the perception
to the output that is responsible for the increase in
precision? Does
precision improve as the amount of information on which
it is based
decreases? What you are saying may make perfect sense
to you, but to me
is is nonsense.
One more peanut:
    [Allan Randall 930325 12:40] to Rick Marken
    > >Are we also agreed that this disturbance,
while defined in this
    > >external point of view, is nonetheless
defined in terms of the
    > >CEV, which is defined according to the
internal point of view?
    >
    > Say what? Why not just say CEV(t) = d(t) +
o(t). If that’s what
    > the above sentence means then I agree with
it.
    The point is that the disturbance d(t), if
separated out from o(t),
    is not a meaningful quantity to the ECS. It is
meaningful only to
    the external observer. By drawing an arrow marked
d(t) you are
    talking about something the ECS has no direct
access to. From the
    perspective of the ECS, only the variation in the
CEV matters. It
    cannot separate out its own output from the
disturbance. On the
    other hand, this disturbance is defined in terms
of the CEV, since
    only things in the world that affect the CEV can
be said to be
    disturbance.
It is not the disturbance that is defined in terms of
the CEV, but the
effect of the disturbance. As you say, all that matters
is the value of
the CEV itself. Words like "meaningful" are just
noises. Talking about
the ECS "having access to" something is just a noise.
My whole point is
that the ECS does NOT have "access" to the disturbance
d(t). Nor does it
have "access" to the form of the function relating d(t)
to its effect on
the CEV. Nor is the linking function or the nature and
number of d(t)
variables necessarily the same from one moment to the
next.
The basic problem in the "information about
disturbance" argument is
that you keep forgetting that a given fluctuation of
the CEV can be
produced by many different independent variables in the
environment,
acting through many different paths, even from one
moment to the next.
All your arguments are based on the (often apparently
unconscious)
assumption that there is a _single_ disturbing variable
acting through a
_known and invariant_ disturbance function on the CEV.
When that
assumption is true, your conclusions follow trivially,
but you are
dealing only with a special case set up to MAKE your
arguments true. In
general, a control system _however intelligent and
complex_ cannot know
what is causing a CEV to vary at any given time. All it
can know – that
is, all that can be represented by its perceptual
signal – is the
current state of the CEV. And that is all that it needs
to know.
    If Signal X matches the disturbance, the
perceptual signal must be
    the route from which the mystery function M(r, p)
gets the
    information about the disturbance. Right?
    Now let the function M be indentical to O(R-P).Â
Signal X will then
    be the negative of the output signal, which is the
disturbance.
    The only question here is whether O(error) is a
function or a
    magical mystery tourgoodie. I prefer to think we
are dealing with
    physical systems, and that O is a function.
Therefore, information
    about the disturbance is in the perceptual signal,
and moreover, it
    is there in extractable form.
    QED.
See what I mean? This sloppy analysis omits two things:
the form of the
function through which even a single disturbance acts
on the CEV, and
the number of such functions with disturbing quantities
operating
simultaneously. What you have shown is that if you
assume a single
disturbance acting through a unity transfer function,
you can deduce its
value from knowledge of all other signals and functions
in the system.
Big surprise! But you have not shown that there is only
one disturbance,
or that the form of the disturbance function is a
simple multiplier of
1. You're in such a hurry to get to your triumphant
“QED” that you
overlook an elementary omission in setting up your
imaginary experiment.
Enough. I'm just not up to following through all these
arguments which
are made up on the spur of the moment to meet a
particular case and then
forgotten about when the same principle comes up in a
different context.
What I am hearing are arguments for the sake of
arguing, for the sake of
appearing to win an argument. I've been picking holes
in your arguments
for a good four years now, with no discernible effect.
I know when I am
trying to alter a controlled variable that is being
maintained by a
strong and active system, although I may be somewhat
slow to admit that
I can’t budge it.
This time I am going to stick to my oft-broken
resolution: no more
participation in this line of discussion.
Best,
Bill P.
–
Richard S. MarkenÂ
"Perfection
is achieved not when you have
nothing more to add, but when you
have
nothing left to take away.�
   Â
            --Antoine de
Saint-Exupery