# Fixed intermediate reference value

**URL:** <http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446>\
**Category:** CSG1999\
**Created:** [December 11, 1999, 7:14pm UTC](http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446 "1999-12-11T19:14:25Z")\
**Posts on this page:** 20\
**Page:** 1

<div class="post-metadata">

**Author:** ![Martin\_Taylor](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/b19c9b/32.png) [@Martin\_Taylor](http://discourse.iapct.org/u/Martin_Taylor)\
**Post date:** [December 11, 1999, 7:14pm UTC](http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446/1 "1999-12-11T19:14:25Z")

</div>

[Martin Taylor 991211 11:37]

> [From Rick Marken (991210.0900)]

> It is true that a fixed reference will create no problem if the  
> system with the fixed reference is not used by any higher level  
> system as the means of controlling its perception. And it is,  
> indeed, possible to remove the problem by reorganization.

Actually, it is true that a fixed intermediate reference value will create  
no problem that perception \_is\_ used by higher level systems, if the  
higher perceptions are based on more than that single intermediate  
perception. Consider:

high level perceptions: a = x + y + z, b = x - y + 3z  
mid-level perceptions x, y, z.

Now set reference values for a = 3, b = 3

One way for the high-level perceptions to satisfy their reference values  
is for x, y, and z all to come to the value 1.

Now set a reference for the x-control system so that x is forced to be 2.  
According to Rick, this means that a and b cannot be controlled so as to  
regain their reference values of 3 each. But in fact they can. All that  
is necessary is for y and z each to take on the value 0.5. There is no  
loss of higher-level control.

Higher-level control is lost only when the fixing of an intermediate  
reference level means that there are fewer remaining intermediate  
degrees of freedom than are necessary to avoid conflict among the  
higher-level control systems. Without analyzing the details of the  
published spreadsheet, Rick's claim (that the high-level variables  
can't be controlled if an intermediate one is fixed) suggests that  
there really are 6 degrees of freedom at each level. If you fix one  
reference value in the middle level, this would allow the 6 high-level  
systems only 5 remaining degrees of freedom for control. If those  
high-level systems had been linear control systems, this would immediately  
mean that they were inevitably in a conflict situation.

However, as I show below, the published spreadsheet does not behave  
like this, and in fact all six third-level variables do retain control  
even when the reference level "F7" is fixed at 50.

Conflict occurs when N analogue control systems have at some point in their  
control loops fewer than N degrees of freedom (the famous 2 systems setting  
the same perception to 2 different reference values is a special case of  
this more general statement). But conflict is NOT assured when N \_logical\_  
(category-perceiving) control systems attempt to control through fewer  
than N degrees of freedom at lower levels, because there exist regions  
in which intermediate analogue perceptual values are compatible with  
different higher logical-valued references.

To see this, let's recast the example above, leaving "z" out of the  
higher-level perceptual signals.

(1) Analogue high-level perceptions: a = x + y, b = x - y  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Reference values: a = 3, b = 3

Both a and b can be brought to their reference values if x = 3, y = 0.

Now fix the reference value for x to be 2, as before. When you  
do this, a and b find themselves in conflict, since a is at its reference  
value only if y is 1, and b is at its reference value only if y is -1.

(2) Categorical (logical) high-level perceptions: a = (x+y)\>2, b = (x-y)\<4  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Reference values: true, true.

As before, these can be satisfied by x = 3, y = 0, when x+y=3 and  
x-y=3 (and by a wide range of other values for x and y).

Now fix the reference value for x to be 2, as above. This time there is  
no conflict between a and b. Both achieve their reference values when  
y = 1, and x+y = 3, x-y = 1 (and for a range of y values either side of 1).

Conflict need not happen between higher-level categorical control units  
when the reference value for an intermediate-level analogue control unit  
is fixed. But it may happen (not, however, with a and b defined as above,  
since there is a range of values of y that satisfies both inequalities  
no matter what value x is fixed at, and vice-versa).

> **···**
>
> -----------
> 
> Rick's spreadsheet provides a more complicated example. Rick said  
> (Rick Marken 991208.2130)
> 
> > I understand "keeping a commitment" to mean keeping a perceptual  
> > variable in some agreed to state. A child who is keeping a  
> > commitment to be quiet in class, say, is maintaining a perception  
> > of his own noise level in an agreed to state of "quiet". A child  
> > who keeps such a commitment is doing the equivalent of setting  
> > the reference value for one of the intermediate level perceptual  
> > variables in my spreadsheet hierarchy to a constant.
> > 
> > For example, change the reference value in cell F7 to a constant,  
> > like 50. This control system, at level two of the hierarchy model,  
> > is now \_commited\_ to keeping the perception it is controlling  
> > at 50; and you will see that the system will be able to do  
> > this successfully; the perceptual variable (in cell F8) is  
> > brought to and maintained at 50, protected from disturbance.  
> > The system keeps its commitment.
> > 
> > But you will also find that some of the level three systems  
> > (the ones in rows 3 through 5) can no longer keep the perceptual  
> > variables they control (the values in row 4) matching the  
> > references for these perceptions (the values in row 5).
> 
> I wonder if Rick (or anyone that subsequently argued the point) ever  
> actually tried this experiment? I did, and I find Rick's statement  
> to be false. The level 3 systems in Rick's spreadsheet as published  
> do keep their perceptual variables matching the references for these  
> perceptions.
> 
> I set the reference value in F7 to 50 (wildly different from its  
> prior value of around -41). I then watched the hierarchy try to come  
> to terms with this fixed setting. It takes a long time (several thousand  
> iterations because of the large slowing factors), but eventually  
> everything stabilizes with all the level 3 control perceptions matching  
> their reference values.
> 
> What the spreadsheet \_actually\_ demonstrates is that if the higher-level  
> variables are logical ones, then control can be maintained \_despite\_  
> fixing an intermediate level reference value.
> 
> Analyzing the nature of the logical variables used by Rick shows why this  
> is possible. The six level 3 perceptual functions D3-I3 are:
> 
> D3. if ((0.2\*D8) \> E8), reference value = true  
> E3. if ((0.5\*E8) \> F8), reference value = true
> 
> (in other words, if F7 is set to 50, and F8 therefore is near 50, the  
> E3 perception must be over 100, and the D3 perception over 500 (or possibly  
> even more, depending on where E3 actually settles).
> 
> F3. if ((0.1\*F8) \> G8), reference value false (i.e. G8 \> 5)  
> G3. if ((0.3\*G8) \> H8), reference value true (i.e. H8 \< 0.3\*G8, which is  
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;always satisfied by H8 \< 1.5)  
> H3. if ((0.4\*H8) \> I8), reference value false (i.e. I8 \> H8)  
> I3. if ((2\*I8) \> 0), reference value false (i.e. I8 \< 0).
> 
> It's clear that all these conditions can be satisfied by some set of  
> values for D, E, G, H, and I8 no matter what the value of F8. One such  
> is what the spreadsheet found: 508.95 101.31 (50.00) 24.23 -55.18 -14.89.  
> -------------
> 
> Summary:
> 
> If the higher level perceptions are analogue, they will be able  
> to maintain control if and only if there are enough intermediate  
> degrees of freedom remaining after some have been removed by the external  
> forcing of some intermediate reference values.
> 
> If the higher-level perceptions are categorical (logical) they will always  
> be able to maintain control under conditions that would allow analogue  
> perceptions to be controlled, but additionally they may be able to maintain  
> control even when there are fewer intermediate degrees of freedom than  
> controlled logical perceptions. Whether the logical units can in practice  
> maintain control will depend both on the reference value set by external  
> intervention and by the relationships among the logical variables  
> controlled.
> 
> I leave it to the reader to assess the relevance of this to the issue of  
> "commitment."
> 
> Martin

---

<div class="post-metadata">

**Author:** ![R\_Marken](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/r/8797f3/32.png) [@R\_Marken](http://discourse.iapct.org/u/R_Marken)\
**Post date:** [December 12, 1999, 12:30am UTC](http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446/2 "1999-12-12T00:30:43Z")

</div>

[From Rick Marken (991211.1630)]

Martin Taylor (991211 11:37) --

> I set the reference value in F7 to 50... I then watched the  
> hierarchy try to come to terms with this fixed setting. It  
> takes a long time (several thousand iterations because of  
> the large slowing factors), but eventually everything  
> stabilizes with all the level 3 control perceptions matching  
> their reference values.

True. Because of the nature of the equations that define  
the level three controlled perceptions (in cells D4 to I4)  
the spreadsheet can (after some time) compensate for a  
fixed reference value in cell F7.

Try setting cell I7 to 20. That should do it.

The problem created by fixed intermediate reference values  
has nothing to do with the type of perception controlled.  
It has to do with whether or not there is a solution to  
the set of simultaneous equations that define a perceptual  
level in the hierarchy.

Best

Rick

> **···**
>
> --  
> Richard S. Marken Phone or Fax: 310 474-0313  
> Life Learning Associates e-mail: rmarken@earthlink.net  
> [http://home.earthlink.net/~rmarken/](http://home.earthlink.net/~rmarken/)

---

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**Author:** ![Martin\_Taylor](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/b19c9b/32.png) [@Martin\_Taylor](http://discourse.iapct.org/u/Martin_Taylor)\
**Post date:** [December 12, 1999, 5:59am UTC](http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446/3 "1999-12-12T05:59:04Z")

</div>

[Martin Taylor 991212 0:03]

> [From Rick Marken (991211.1630)]
> 
> Martin Taylor (991211 11:37) --
> 
> \> I set the reference value in F7 to 50... I then watched the  
> \> hierarchy try to come to terms with this fixed setting. It  
> \> takes a long time (several thousand iterations because of  
> \> the large slowing factors), but eventually everything  
> \> stabilizes with all the level 3 control perceptions matching  
> \> their reference values.
> 
> True. Because of the nature of the equations that define  
> the level three controlled perceptions (in cells D4 to I4)  
> the spreadsheet can (after some time) compensate for a  
> fixed reference value in cell F7.

So I find, by actual experiment. But you've been basing a heavy argument  
on the assertion that if you fix \_any\_ intermediate reference value  
(in a living control system, as simulated by the spreadsheet), higher  
level control will be impossible. It sounded as though you had demonstrated  
this for your spreadsheet, and I was really quite surprised to find that  
it was untrue even for the spreadsheet itself.

> Try setting cell I7 to 20. That should do it.

Of course, since the reference I3 for the third level prception I4 is  
that I8 (the perception for which I7 is the reference) should be negative.  
To set I7 positive guarantees that I4 cannot match its reference. On the  
other hand, you can fix I7 so that control IS possible while I7 is fixed.  
Just set it to -15, and perception I4 is \_guaranteed\_ to match its  
reference I3 without affecting the ability of the other third level  
control units to control their perceptions.

That's hardly an instructive example.

> The problem created by fixed intermediate reference values  
> has nothing to do with the type of perception controlled.  
> It has to do with whether or not there is a solution to  
> the set of simultaneous equations that define a perceptual  
> level in the hierarchy.

Well, yes and no to that. Yes, it has to do with whether there is a  
solution to the set of simultaneous equations. But no--it's wrong to say  
that the problem has nothing to do with the type of perception controlled.

Why is it wrong? Because, as I pointed out (and as one can show in the  
spreadsheet at levels 1 and 2) if the higher-level perceptions are  
\_analogue\_ there must be at least as many degrees of freedom for control  
at the lower level as there are perceptions to be controlled at the  
higher. But, as I also demonstrated, this is NOT a necessary condition  
if the higher level perceptions are categorical/logical.

Control is possible if and only if the simultaneous equations have a  
solution. But the likelihood that a solution can be found is near zero  
for analogue systems if there are fewer low-level degrees of freedom  
than upper-level perceptions to be controlled, whereas it is considerably  
above zero for categorical/logical upper-level perceptions.

> **···**
>
> -------------------  
> Just for fun, I tried a little more drastic fooling with the spreadsheet  
> (after fixing the formula for cell I7, which originally was set =I5,  
> whereas all the other row-7 reference values were set like H7 =H5-G5.  
> I set I7 =I5-H5 in conformity with all the others).
> 
> What I did was to fix THREE of the six second-level references (D7,  
> F7, and H7). At first I fixed them at an integer near where they had  
> settled when all the third level perceptions were near their reference  
> values. I knew those values were compatible with a solution to the  
> simultaneous equations, but the question was whether control would  
> be retained against the external disturbance. It was.
> 
> Next I changed these three fixed reference values to other fixed values  
> which caused some of the third level perceptions to fail to match their  
> reference values. But the third level control systems still worked fine,  
> making their perceptions regain their reference values quite quickly.
> 
> Since I couldn't make the hierarchy fail to control by changing  
> the values of the fixed intermediate references, I tried to see whether  
> the third-level control units could control to other (true/false)  
> reference values while the three mid-level references remained fixed.  
> They could, at least for the three or four that I tried manipulating.
> 
> So, six logical perceptions could easily control through six analogue  
> second-level control units of which THREE had their reference values  
> externally fixed.
> 
> It's not a good demonstration of the assertion (Rick Marken 991208.2130):  
> that the spreadsheet would demonstrate that if you fixed any single  
> intermediate reference level...
> 
> > ... you will also find that some of the level three systems  
> > (the ones in rows 3 through 5) can no longer keep the perceptual  
> > variables they control (the values in row 4) matching the  
> > references for these perceptions (the values in row 5).
> 
> Nor is it a persuasive demonstration that a child would be unable to  
> control its higher-level perceptions if it committed to holding some  
> mid-level perception at a prespecified value.
> 
> Martin

---

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**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [December 12, 1999, 3:04pm UTC](http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446/4 "1999-12-12T15:04:42Z")

</div>

[From Bill Powers (991212.0746 MDT)]

Martin Taylor 991212 0:03 (replying to Marken):

> Of course, since the reference I3 for the third level prception I4 is  
> that I8 (the perception for which I7 is the reference) should be negative.  
> To set I7 positive guarantees that I4 cannot match its reference. On the  
> other hand, you can fix I7 so that control IS possible while I7 is fixed.  
> Just set it to -15, and perception I4 is \_guaranteed\_ to match its  
> reference I3 without affecting the ability of the other third level  
> control units to control their perceptions.
> 
> That's hardly an instructive example.

I think it is very instructive, and supports my (and Rick's) position  
exactly. If you're going to set goals for another person according to your  
own preferences, and enforce them, then to avoid creating conflict inside  
the other person (and ultimately with you) you will have to know his  
internal goal structure well enough to predict what will and will not  
result in conflict. And as in the case of the simple spreadsheet, you will  
find that if you want to set goals for I7 that do not create impossible  
demands on I4, you are restricted to a certain range of values of I7, here  
negative values. If your own wishes make you want the spreadsheet program  
to seek positive values of I7, you are going to create a conflict in that  
simulation as long as you insist on \_that\_ value for \_that\_ variable. If  
the simulation were smarter, it would adjust something else to nullify the  
effect of your forcing the positive value, so that nothing that mattered  
greatly to it would stay disturbed. That reorganization could include  
getting rid of you.

You can see all the subsystems in the spreadsheet program, and choose the  
goals you want it to achieve from those that can be achieved without  
internal conflict. That is very different from the case of the human being  
in the situation in question, where very little is known about the internal  
goal structure of the child, and your concern is with what you want, not  
what the child wants.

Best,

Bill P.

---

<div class="post-metadata">

**Author:** ![R\_Marken](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/r/8797f3/32.png) [@R\_Marken](http://discourse.iapct.org/u/R_Marken)\
**Post date:** [December 13, 1999, 9:05am UTC](http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446/5 "1999-12-13T09:05:04Z")

</div>

[From Rick Marken (991213.0900)]

Martin Taylor (991213 11:30) --

> Rick's argument (I can't say about yours) was that if you fix  
> ANY intermediate reference value in any hierarchic control system  
> (including the spreadsheet), higher-level control is immediately  
> lost.

No. The point of the demonstration was to show that setting  
arbitrarily selected goals for another person is \_likely\_ to  
result in internal conflict, destroying that person's ability to  
control perceptions that he could previously control. Actually,  
Bill Powers (991212.0746 MDT) stated the point of the demonstration  
rather clearly:

> If you're going to set goals for another person according  
> to your own preferences, and enforce them, then to avoid  
> creating conflict inside the other person (and ultimately  
> with you) you will have to know his internal goal structure  
> well enough to predict what will and will not result in conflict.

I think this is a the fundamental lesson of PCT for applied  
psychologists.

Martin:

> For anyone to continue to use the spreadsheet as a demonstration  
> that fixing any intermediate reference necessarily causes loss  
> of high-level control is, to use an unwarrantedly polite turn  
> of phrase, a little mind-boggling.

I agree. They should use it to demonstrate the point Bill and  
I are trying to make (see above).

Best

Rick

> **···**
>
> --  
> Richard S. Marken Phone or Fax: 310 474-0313  
> Life Learning Associates mailto: rmarken@earthlink.net  
> [http://home.earthlink.net/~rmarken](http://home.earthlink.net/~rmarken)

---

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**Author:** ![Martin\_Taylor](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/b19c9b/32.png) [@Martin\_Taylor](http://discourse.iapct.org/u/Martin_Taylor)\
**Post date:** [December 13, 1999, 4:42pm UTC](http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446/6 "1999-12-13T16:42:43Z")

</div>

[Martin Taylor 991213 11:30]

> [From Bill Powers (991212.0746 MDT)]
> 
> Martin Taylor 991212 0:03 (replying to Marken):
> 
> \>Of course, since the reference I3 for the third level prception I4 is  
> \>that I8 (the perception for which I7 is the reference) should be negative.  
> \>To set I7 positive guarantees that I4 cannot match its reference. On the  
> \>other hand, you can fix I7 so that control IS possible while I7 is fixed.  
> \>Just set it to -15, and perception I4 is \_guaranteed\_ to match its  
> \>reference I3 without affecting the ability of the other third level  
> \>control units to control their perceptions.  
> \>  
> \>That's hardly an instructive example.
> 
> I think it is very instructive, and supports my (and Rick's) position  
> exactly.

If so, it's a trivially simple position, which is most unlike you. And  
it's a position that has very little relevance to any biological  
control system.

The position you argue to be instructive is that if one has a higher  
level perception that can be affected only by altering the reference  
value of exactly one specific lower level control unit, and the reference  
input to the lower level unit is then disconnected by an external agency,  
the higher-level unit loses control.

Isn't it a bit trivial to base a whole argument on the denial of "the  
same result by many means" mantra of PCT, or on the notion that if you  
disconnect the output of a control unit, it fails to control?

Here's the picture of what you are arguing to be instructive...

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Able to control at level2 Unable to control at level 2  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\> \>  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-------o------- --------o---------  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\> \> \> \>  
level 2 PIF out PIF out level 2  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\> / | /  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;^ \_\_\_\<\_/ ^ X  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\> \> \>  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\> \> \> --------\<--------external  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\> \> \> \> forcing  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;+---\>---o-------- +----\>---o--------  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\> \> \> \>  
level 1 PIF out PIF out level 1  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\> \> \> \>  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;====^================V=== ===^=================V===  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\> \> \> \>  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;+--------\<------- +----------\<------  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\> \>  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\>disturbance |disturbance

Who would deny that the right hand setup prevents level 2 control?  
Who, other than yourself, would call "instructive" this inability of the  
right-hand system? Those for whom it might be instructive are hardly  
likely to be found on CSGnet, are they? Most readers of CSGnet realize  
that a feedback loop is essential for control.

Even if the instance is not "instructive", is it usefully illustrative  
of any real biological systems? Only if you can find a special case in  
which some high-level controlled perception can be affected \_only\_ by  
controlling a single specific lower-level perception \_and\_ in which the  
reference value for that perception can be accessed by an external agent  
to the extent that the upper-level control loses all influence on it.

I think such a situation likely to be extremely rare in the biological  
world, if it exists at all. But that's only my opinion, and irrelevant  
to the question of how instructive it is to know that a control unit  
whose output is disconnected has a problem controlling.

> **···**
>
> -----------------
> 
> Anyway, Rick's argument wasn't that if you disconnect the output of a  
> control unit, it loses control, and it wasn't that the spreadsheet has  
> been deliberately contrived so that there exists in it a connection  
> like the one illustrated above.
> 
> Rick's argument (I can't say about yours) was that if you fix  
> ANY intermediate reference value in any hierarchic control system  
> (including the spreadsheet), higher-level control is immediately  
> lost.
> 
> I showed this to be false even for a purely analogue hierarchy in which  
> there are enough intermediate degrees of freedom, and in a hierarchy  
> with categorical/logical perceptions under even less restrictive  
> conditions.
> 
> The spreadsheet shows that it is quite possible to fix the reference  
> values of as many as half (three) of the intermediate units, while  
> maintaining good control of the high-level units. The reason this is  
> so is that the high-level units control categorical/logical perceptions.  
> In a 6-6-6 spreadsheet in which all the levels controlled \_analogue\_  
> perceptions, high-level control would not be possible if even one of the  
> intermediatelevels had a fixed reference value.
> 
> For anyone to continue to use the spreadsheet as a demonstration that  
> fixing any intermediate reference necessarily causes loss of high-level  
> control is, to use an unwarrantedly polite turn of phrase, a little  
> mind-boggling.
> 
> Martin

---

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**Author:** ![Bruce\_Gregory](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/4bbf92/32.png) [@Bruce\_Gregory](http://discourse.iapct.org/u/Bruce_Gregory)\
**Post date:** [December 13, 1999, 5:28pm UTC](http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446/7 "1999-12-13T17:28:39Z")

</div>

[From Bruce Gregory (991213.1217 EST)]

"When I use a model," Humpty Dumpty said, in a rather scornful tone, "it  
means just what I choose it to mean - nothing more nor less." -- Lewis  
Carroll, \_CSG in Wonderland\_

---

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**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [December 13, 1999, 9:15pm UTC](http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446/8 "1999-12-13T21:15:14Z")

</div>

[From Bill Powers (991213.1411 MDT)]

Martin Taylor 991213 11:30--

> If so, it's a trivially simple position, which is most unlike you. And  
> it's a position that has very little relevance to any biological  
> control system.
> 
> The position you argue to be instructive is that if one has a higher  
> level perception that can be affected only by altering the reference  
> value of exactly one specific lower level control unit, and the reference  
> input to the lower level unit is then disconnected by an external agency,  
> the higher-level unit loses control.

No, that is not my point, although it is the basis for the point I am  
trying to make. My point is that another person is unlikely to know the  
effects of arbitrarily fixing a reference signal in someone else's  
hierarchy, assuming that is somehow possible to do. The effects of  
succeeding at this, I agree, are trivially obvious to one who understands  
the principles of hierarchical control. But that obviousness only makes my  
argument stronger.

Best,

Bill P.

---

<div class="post-metadata">

**Author:** ![Bruce\_Gregory](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/4bbf92/32.png) [@Bruce\_Gregory](http://discourse.iapct.org/u/Bruce_Gregory)\
**Post date:** [December 13, 1999, 10:02pm UTC](http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446/9 "1999-12-13T22:02:14Z")

</div>

[From Bruce Gregory (991213.1702 EST)]

Bill Powers (991213.1411 MDT)

> No, that is not my point, although it is the basis for the point I am  
> trying to make. My point is that another person is unlikely  
> to know the  
> effects of arbitrarily fixing a reference signal in someone else's  
> hierarchy, assuming that is somehow possible to do.

While it's true that telling you to hold your racket in a certain way  
when hitting a backhand stroke may lead to unexpected consequences in  
your hierarchy of control, its a chance I'd be willing to take, were I  
your tennis coach.

Bruce Gregory

---

<div class="post-metadata">

**Author:** ![Martin\_Taylor](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/b19c9b/32.png) [@Martin\_Taylor](http://discourse.iapct.org/u/Martin_Taylor)\
**Post date:** [December 14, 1999, 5:22am UTC](http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446/10 "1999-12-14T05:22:27Z")

</div>

[Martin Taylor 991213 17:32]

> [From Bill Powers (991213.1411 MDT)]

> My point is that another person is unlikely to know the  
> effects of arbitrarily fixing a reference signal in someone else's  
> hierarchy, assuming that is somehow possible to do. The effects of  
> succeeding at this, I agree, are trivially obvious to one who understands  
> the principles of hierarchical control. But that obviousness only makes my  
> argument stronger.

I guess we can all more or less agree on that as a matter of principle.

But there is a difference between "know the effects" and "expect the  
effects" based on experience with other people who appear to be like  
the one in question. Nobody can \_know\_ the effects of arbitrarily fixing  
a reference value--or even know whether the reference value being fixed  
corresponds to a perception being controlled. But anyone with much  
experience interacting with people can judge the effects of many kinds  
of attempts to set reference levels. It's the basis on which social  
structures are built.

> **···**
>
> ----------------
> 
> Which leads to the larger discussion: The term "reorganization" has been  
> used in a disparaging sense, as in "sure, if you force a person to  
> reorganize, they will--but why would you want to make them do that?"
> 
> I see reorganization in a more positive light. It is the mechanism  
> whereby people learn to get what they want in the environment in which  
> they find themselves. Purely physical feedback paths may be available to  
> allow them to influence perceptions they want to control. But in social  
> situations, other people usually form part of the useful feedback paths.  
> One gets what one wants more by influencing other people do do something  
> helpful than by ignoring them or using one's force or threat of force  
> to coerce them.
> 
> What that means is that if one is in a situation with coercive boundaries,  
> one is likely to reorganize so as not to test those boundaries, because  
> beating one's head against a metaphoric brick wall is unlikely to get  
> what one wants--unless one wants a headache. It's not a negative thing  
> to have negative feedback! Control works when one uses feedback paths  
> which influence the desired perceptions in the way one wants, not when  
> one's actions move one's perceptions even further from their reference  
> values (which usually happens when one tests a coercive boundary).
> 
> The \_potential\_ existence of coercion is everywhere in social situations.  
> We seldom experience it as such, because we have learned that being nice  
> to people is often (but not always) a way to get them to be nice to us.  
> If we try to get a shopkeeper to give us goods by threatening to shoot  
> them (coercion), we find ourselves coerced by the police, and probably  
> don't get to keep the goods. But if we are nice to the shopkeeper, and give  
> money in return for the goods, we probably get what we want, and so does  
> the shopkeeper. Coercion is in the background, but is not part of the  
> control loops in action, since we (and the shopkeeper) early in life  
> reorganized so that it isn't.
> 
> Bottom line: most of us have used our (random) reorganization to get  
> us into a state where more often than not we act towards other people  
> in ways that get us what we want. We act so as to set reference values  
> in their hierarchies so that they come to perceive that we are pleased  
> with their actions. (According to the Layered Protocol Theory, that's  
> how dialogue works, too).
> 
> We don't "know" that setting any particular reference value will  
> not have disastrous consequences, but most of the time the consequences  
> are in the desired direction--the feedback loop that goes through  
> the other person usually has a negative loop gain.
> 
> Back to your point: "that another person is unlikely to know the  
> effects of arbitrarily fixing a reference signal in someone else's  
> hierarchy, assuming that is somehow possible to do." Your point is  
> technically accurate, but is in practice misleading because we and  
> the people with whom we interact have reorganized to make it so.
> 
> Martin

---

<div class="post-metadata">

**Author:** ![Martin\_Taylor](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/b19c9b/32.png) [@Martin\_Taylor](http://discourse.iapct.org/u/Martin_Taylor)\
**Post date:** [December 14, 1999, 5:48am UTC](http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446/11 "1999-12-14T05:48:49Z")

</div>

[Martin Taylor 991214 0:34]

> [From Rick Marken (991213.0900)]
> 
> Martin Taylor (991213 11:30) --
> 
> \> Rick's argument (I can't say about yours) was that if you fix  
> \> ANY intermediate reference value in any hierarchic control system  
> \> (including the spreadsheet), higher-level control is immediately  
> \> lost.
> 
> No. The point of the demonstration was to show that setting  
> arbitrarily selected goals for another person is \_likely\_ to  
> result in internal conflict, destroying that person's ability to  
> control perceptions that he could previously control.

...  
Well, at least that's a pullback from your earlier position (991208.2130)

> I am saying that getting a child to keep a commitment  
> is likely to result in loss of control of \_some\_ perception that  
> was being controlled by varying the reference for the perception  
> to which the child is commited. The words may be convoluted but  
> you can understand it, I think, using my spreadsheet hierarchy  
> model.  
> ...  
> For example, change the reference value in cell F7 to a constant,  
> like 50. ...  
> ...you will also find that some of the level three systems  
> (the ones in rows 3 through 5) can no longer keep the perceptual  
> variables they control (the values in row 4) matching the  
> references for these perceptions (the values in row 5). So the  
> commitment to a particular reference for a perceptual variable  
> in a system at level two in the hierarchy destroys the ability  
> of some level three systems (the ones that control their  
> perceptions by varying the reference for the now committed  
> level two system) to control.

Now back to the 991213 message...

> Martin:
> 
> \> For anyone to continue to use the spreadsheet as a demonstration  
> \> that fixing any intermediate reference necessarily causes loss  
> \> of high-level control is, to use an unwarrantedly polite turn  
> \> of phrase, a little mind-boggling.
> 
> I agree. They should use it to demonstrate the point Bill and  
> I are trying to make (see above).

Well, if the "above" is the point, perhaps you ought to design a  
spreadsheet that does not demonstrate the opposite. The one you have  
illustrates the proposition that you can set 50% of the intermediate  
goals in the hierarchy quite arbitrarily without the slightest effect  
(apparently) on the ability of the higher levels to control their  
perceptions (except in the single case in which the higher level unit  
is cut off from influencing any input to its perceptual input function).

If people "should" use the existing spreadsheet to demonstrate the  
point you want to make, perhaps you should instruct us how. The only  
instruction given so far (fix F7 at some number, say 50) demonstrates  
the opposite of your point.

Try again.

Martin

---

<div class="post-metadata">

**Author:** ![R\_Marken](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/r/8797f3/32.png) [@R\_Marken](http://discourse.iapct.org/u/R_Marken)\
**Post date:** [December 14, 1999, 7:39am UTC](http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446/12 "1999-12-14T07:39:35Z")

</div>

[From Rick Marken (991214.0740)]

Martin Taylor (991214 0:34) --

> If people "should" use the existing spreadsheet to demonstrate  
> the point you want to make, perhaps you should instruct us how.

Gee, why does this get people so upset?

I tried demonstrating a point using an existing tool (the  
spreadsheet model). I think I did a pretty good job. But  
if you don't, why not present a better demo instead of  
yelling at me?

Best

Rick

> **···**
>
> --  
> Richard S. Marken Phone or Fax: 310 474-0313  
> Life Learning Associates mailto: rmarken@earthlink.net  
> [http://home.earthlink.net/~rmarken](http://home.earthlink.net/~rmarken)

---

<div class="post-metadata">

**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [December 14, 1999, 3:42pm UTC](http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446/13 "1999-12-14T15:42:15Z")

</div>

[From Bill Powers (991214.0841 MDT)]

Martin Taylor 991213 17:32--

> Back to your point: "that another person is unlikely to know the  
> effects of arbitrarily fixing a reference signal in someone else's  
> hierarchy, assuming that is somehow possible to do." Your point is  
> technically accurate, but is in practice misleading because we and  
> the people with whom we interact have reorganized to make it so.

Bruce Abbott has offered a very useful suggestion, which I will take with  
respect to this argument, too. I admit that I have lost this argument.

Best,

Bill P.

---

<div class="post-metadata">

**Author:** ![Martin\_Taylor](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/b19c9b/32.png) [@Martin\_Taylor](http://discourse.iapct.org/u/Martin_Taylor)\
**Post date:** [December 16, 1999, 5:52am UTC](http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446/14 "1999-12-16T05:52:43Z")

</div>

[Martin Taylor 991216 0:43]

> [From Rick Marken (991214.0740)]
> 
> Martin Taylor (991214 0:34) --
> 
> \> If people "should" use the existing spreadsheet to demonstrate  
> \> the point you want to make, perhaps you should instruct us how.
> 
> Gee, why does this get people so upset?
> 
> I tried demonstrating a point using an existing tool (the  
> spreadsheet model). I think I did a pretty good job. But  
> if you don't, why not present a better demo instead of  
> yelling at me?

Is it "yelling" to repeat the simple fact that your spreadsheet does NOT  
demonstrate the point you claimed it did. At least it does not do so  
when used as we were instructed to use it to demonstrate the point.

Since the spreadsheet, used as directed, demonstrates exactly the  
opposite of the point you wanted to demonstrate, I fail to see how  
you can claim you did a "pretty good job" using the existing tool.

I have no interest myself in demonstrating your point, but I do  
think that the academic value of the discussion in which it was  
introduced would be raised if you would either retract it or  
actually demonstrate it, rather than demonstrating the opposite  
and then claiming to have made your point by the demonstration.

All I asked, and ask on behalf of clarity of the discussion, is: if the  
spreadsheet can actually be used to demonstrate your point instead of its  
opposite, show us how. If not, stop saying you have used it to demonstrate  
your point.

Martin

---

<div class="post-metadata">

**Author:** ![R\_Marken](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/r/8797f3/32.png) [@R\_Marken](http://discourse.iapct.org/u/R_Marken)\
**Post date:** [December 16, 1999, 7:36am UTC](http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446/15 "1999-12-16T07:36:25Z")

</div>

[From Rick Marken (991216.0730)]

Martin Taylor (991216 0:43) --

> Is it "yelling" to repeat the simple fact that your  
> spreadsheet does NOT demonstrate the point you claimed it did.

Yes. It's not yelling when you explain what point you think  
I was trying to make and why it doesn't make that point.

> Since the spreadsheet, used as directed, demonstrates exactly the  
> opposite of the point you wanted to demonstrate, I fail to see how  
> you can claim you did a "pretty good job" using the existing tool.

You're right. It does a pretty good job of demonstrating my  
point (that forcing a hierarchical control system to control a  
perception at some arbitrarily selected fixed level is likely to  
destroy the system's ability to control other perceptions)  
\_to me\_ (and to some others). It apparently does not demonstrate  
my point -- indeed, it seems to demonstrate the opposite of my  
point -- to you.

Best

Rick

> **···**
>
> --  
> Richard S. Marken Phone or Fax: 310 474-0313  
> Life Learning Associates mailto: rmarken@earthlink.net  
> [http://home.earthlink.net/~rmarken](http://home.earthlink.net/~rmarken)

---

<div class="post-metadata">

**Author:** ![bnhpct](http://discourse.iapct.org/user_avatar/discourse.iapct.org/bnhpct/32/34_2.png) [@bnhpct](http://discourse.iapct.org/u/bnhpct)\
**Post date:** [December 16, 1999, 3:30pm UTC](http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446/16 "1999-12-16T15:30:37Z")

</div>

[From Bruce Nevin (991216.1030 EST)]

The difficulty with extrapolating from a simple simulation to a situation  
that is complex to model is somewhat like the difficulty with extrapolating  
from population statistics to individuals or to a disparate population.

&nbsp;&nbsp;Bruce Nevin

---

<div class="post-metadata">

**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [December 16, 1999, 3:31pm UTC](http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446/17 "1999-12-16T15:31:52Z")

</div>

[From Bill Powers (991216.0824 MDT)]

Martin Taylor 991216 0:43 --

> Is it "yelling" to repeat the simple fact that your spreadsheet does NOT  
> demonstrate the point you claimed it did. At least it does not do so  
> when used as we were instructed to use it to demonstrate the point.

I know I'm being lazy, but could you repeat for us, but perhaps in  
different words, exactly what's wrong with the way Rick's spreadsheet  
works? All I remember at the moment is that you found it incapable of  
controlling a higher (logical) perception if a lower variable were fixed at  
a negative value, although it could succeed if the variable were kept  
positive (or perhaps it was the other way around). This, of course, make  
the point Rick was making, which was that you have to know a lot about the  
control hierarchy if you want to cause a reference signal to become fixed  
in another person without causing conflict. You are now talking as if his  
spreadsheet, contrary to what he said, allows you to fix any reference  
signal at any arbitrary value without interrupting its ability to control  
at higher levels.

When three levels, three systems per level, and three environmental  
variables, it's hard for me to understand how that could be.

Best,

Bill P.

> **···**
>
> > Since the spreadsheet, used as directed, demonstrates exactly the  
> > opposite of the point you wanted to demonstrate, I fail to see how  
> > you can claim you did a "pretty good job" using the existing tool.
> > 
> > I have no interest myself in demonstrating your point, but I do  
> > think that the academic value of the discussion in which it was  
> > introduced would be raised if you would either retract it or  
> > actually demonstrate it, rather than demonstrating the opposite  
> > and then claiming to have made your point by the demonstration.
> > 
> > All I asked, and ask on behalf of clarity of the discussion, is: if the  
> > spreadsheet can actually be used to demonstrate your point instead of its  
> > opposite, show us how. If not, stop saying you have used it to demonstrate  
> > your point.
> > 
> > Martin

---

<div class="post-metadata">

**Author:** ![Martin\_Taylor](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/b19c9b/32.png) [@Martin\_Taylor](http://discourse.iapct.org/u/Martin_Taylor)\
**Post date:** [December 19, 1999, 5:11am UTC](http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446/18 "1999-12-19T05:11:14Z")

</div>

[Martin Taylor 991218 13:55]

> [From Rick Marken (991216.0730)]

> \> Since the spreadsheet, used as directed, demonstrates exactly the  
> \> opposite of the point you wanted to demonstrate, I fail to see how  
> \> you can claim you did a "pretty good job" using the existing tool.
> 
> You're right. It does a pretty good job of demonstrating my  
> point (that forcing a hierarchical control system to control a  
> perception at some arbitrarily selected fixed level is likely to  
> destroy the system's ability to control other perceptions)  
> \_to me\_ (and to some others).

Interesting that it demonstrated this fact by showing that if you fix  
three of the six intermediate level perceptions at arbitrary fixed levels  
there is no impairment of the system's ability to control any of the other  
perceptions.

> It apparently does not demonstrate  
> my point -- indeed, it seems to demonstrate the opposite of my  
> point -- to you.

And to anyone who actually uses the spreadsheet to see whether "forcing  
a hierarchical control system to control a perception at some arbitrarily  
selected fixed level is likely to destroy the system's ability to control  
other perceptions."

Anyone who tries it will find that doing so does NOT destroy the system's  
ability to control other perceptions--except in the single case where the  
arbitrarily fixed intermediate perception is the ONLY input to a higher  
level one (column I in the spreadsheet).

I find it fascinating to watch how simple assertion, repeated many times,  
is taken to be better evidence than observation of experimental results.

There's no need for anyone to take your or my word for what happens when  
you try different things with the spreadsheet. Almost everyone can run  
Excel, and see for themselves. That's what I did, largely because I  
initially believed it did what you said it would do. It was only when I  
found that it didn't do what you said (lose control at the higher levels  
when F7 was set to 50) that I started testing how far one could go in  
fixing intermediate levels while still allowing the higher-level units  
to retain perfect control.

And at the same time I showed mathematically how it was possible for  
this to happen if the higher-level systems controlled categorical/logical  
perceptions, but not if they controlled analogue perceptions and there  
were fewer un-fixed intermediate units than high-level units.

Since then, the only evidence you have come up with to show that "forcing  
a hierarchic control system to control a perception at some arbitrary  
selected fixed level is likely to destroy the system's ability to  
control other perceptions" is the sheer number of your assertions that  
it is so.

Not good, Rick. You can do much better (and often do). Leave this one, or  
produce a more convincing demonstration.

Martin

---

<div class="post-metadata">

**Author:** ![Martin\_Taylor](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/b19c9b/32.png) [@Martin\_Taylor](http://discourse.iapct.org/u/Martin_Taylor)\
**Post date:** [December 19, 1999, 5:33am UTC](http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446/19 "1999-12-19T05:33:08Z")

</div>

[Martin Taylor 991219 12:02]

> [From Bill Powers (991216.0824 MDT)]

> I know I'm being lazy, but could you repeat for us, but perhaps in  
> different words, exactly what's wrong with the way Rick's spreadsheet  
> works?

Nothing is wrong with the way it works. It's a fine demonstration of  
multi-level control with both logical and analogue variables. It does  
what one would hope such a system would do, and illustrates what is  
likely to happen in the more complex systems of real life.

> All I remember at the moment is that you found it incapable of  
> controlling a higher (logical) perception if a lower variable were fixed at  
> a negative value, although it could succeed if the variable were kept  
> positive (or perhaps it was the other way around).

Not so. I know you are very busy with more important things, so you  
are excused for your self-proclaimed laziness (which I don't believe).

What I actually found was that in the spreadsheet one can fix as many as  
three of the six intermediate reference levels with no apparent effect on  
the ability of any of the six top-level systems to control. I also agreed  
with Rick that if a particular high-level system has only one input from  
the intermediate level, and you cut off its only input, the high-level  
system no longer can control it's perception.

> You are now talking as if his  
> spreadsheet, contrary to what he said, allows you to fix any reference  
> signal at any arbitrary value without interrupting its ability to control  
> at higher levels.

Any except when the fixed one(s) fix the entire input to the higher-level  
perceptual input function--at least that's what the spreadsheet seems  
to demonstrate. I'm sure one could find specific values for which  
fixing the intermediate references would make it impossible for the  
higher-level ones to retain control, but it's not easy, at least not  
in Rick's spreadsheet, unless you totally cut off the ability of the  
higher level system to influence its input.

> When three levels, three systems per level, and three environmental  
> variables, it's hard for me to understand how that could be.

Actually, its six systems per level and six environmental variables.  
As for understanding how it could be, did you read my message  
[Martin Taylor 991211 11:37] in which I showed how it is possible  
when the upper levels are categoric/logical but not when they are  
analogic? In that message, I used Rick's spreadsheet only as an example  
to show that the mathematics actually works in practice.

Mathematically, the point is that N equations in M\>N continuous  
variables have a solution only if at least M-N of the equations are  
degenerate (can be collapsed into repeats of some combination of the  
others). But N equations in M \> N logical variables are quite likely to  
be soluble, and may sometimes be soluble even when M \>\> N.

The nature of the controlled perception makes a difference.

Martin

---

<div class="post-metadata">

**Author:** ![Erling\_O\_Jorgensen](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/e/7ba0ec/32.png) [@Erling\_O\_Jorgensen](http://discourse.iapct.org/u/Erling_O_Jorgensen)\
**Post date:** [December 19, 1999, 5:00pm UTC](http://discourse.iapct.org/t/fixed-intermediate-reference-value/4446/20 "1999-12-19T17:00:08Z")

</div>

[From Erling Jorgensen (991219.0900 CST)]

> Rick Marken (991216.0730) -- replying to:
> 
> > Martin Taylor (991216 0:43)

> > Since the spreadsheet, used as directed, demonstrates  
> > exactly the opposite of the point you wanted to  
> > demonstrate, I fail to see how you can claim you did  
> > a "pretty good job" using the existing tool.
> 
> You're right. It does a pretty good job of demonstrating  
> my point (that forcing a hierarchical control system to  
> control a perception at some arbitrarily selected fixed  
> level is likely to destroy the system's ability to control  
> other perceptions)

Rick, you are disrupting the learning of some of us on  
this one. Can you find a way to \_gently\_ back away?

Martin has already given a fairly convincing demonstration,  
(several times and with some degree of patience,) that  
control at the higher levels is more robust than you make  
it out to be. Yes, there are special limiting cases where  
your point holds. But he has been able to "arbitrarily fix"  
several intermediate level references without undue  
damage to upper level control. He has also articulated  
a useful distinction between logical and analog systems  
at such a higher level, and their differential ability to  
maintain control.

You use to accuse Martin quite often of only doing  
thought experiments, and not producing data from  
working models. Here he has used your own model  
to provide several sets of data that counter the breadth  
of your assertion. Could you reread his posts closely,  
and see if the polemics really are needed? I for one  
would appreciate it, (in the interest of my own learning.)  
Thanks.

All the best,  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Erling

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