CLARITY

Clarity of writing and thought. Belief and knowledge

Unedited posts from archives of CSG-L (see INTROCSG.NET):

Date: Fri Dec 17, 1993 11:55 am PST

Subject: Clarity, Martin's assertion

[From Dag Forssell (931217 1050) Rick Marken (931215.0830)

> One of the first things that attracted me to PCT was the clarity andcrispness of Powers' "Behavior: The control of perception". ...But I could tellthat Bill knew what he was talking about because he was saying everythingclearly and simply. ... I took the clarity of Bill's prose style as evidencethat he knew EXACTLY what he was talking about. ...

> I have a strong suspicion that prose style depends on the substance ofwhat is being expressed. If the writer really has something clear and preciseto say, the prose style is clear and precise (read anything by Tom Bourbon, forexample).

This discussion by Rick speaks to me. I too am attracted by the clarity ofBill's writings. I notice that Bill provides detailed discussions of theunderlying mechanisms of the phenomena he discusses, not just high levelabstractions, derivations or categorizations of things that don't exist assuch, like bandwidth, gaussian distributions, entropy, energy, attractors andmany others.

Mathematics tells us NOTHING about nature. It is a pure abstraction. It isa tool for generalizations and description, and a very handy and useful one (--whencorrectly applied, something that is not verified by mathematics but bysuccessful physical experiments). To understand nature's mechanisms, there isno substitute for the underlying physical mechanisms, below the phenomena westudy and discuss.

In a christmas letter just received, I was reminded of the Swedish poetEsaias Tegner (1782-1846),who wrote in a poem entitled "Epilogue" for an academic graduation in 1820:(translation by Dag)

.....

What clearly you cannot say, you do not know;

with thought the word is born on lips of man;

what's dimly said is dimly thought.

.....

Original Swedish:

......

Vad du ej klart kan saega, vet du ej;

med tanken ordet foeds pa mannens laeppar;

det dunkelt sagda aer det dunkelt taenkta.

.....

---------------------------------------------------------

(Cliff Joslyn, 931217 10:12) to Martin Taylor

>> There exist in nature many, many negative feedback systems thatstabilize structures, sometimes structures of considerable complexity.

> It seems to me that this is the key point. We know that controlrequires negative feedback, but what is negative feedback WITHOUT control?Where does it occur?

> For the benefit of my feeble mind, could you please lay out inmathematical detail the simplest occurrence of negative feedback in naturalsystems? A harmonic oscillator in a certain domain?

> Perhaps a private reply would be in order.

Martin said in the same post [931215 17:20]

> Whence cometh this great resistance to allowing the normal ideas ofelementary physics to enter discussions of PCT? I don't have the tolerance Maryascribes (with good reason) to Bill, giving kindergarten lessons day afterday.

Martin, you do not easily stoop to the level of elementary physics. I thinkthat is what can be so exasperating. If you did try to give kindergartenlessons, you might find that your high-falutinabstractions (what you call elementary physics) often don't make much sense.The net is calling your unfounded assertion:

> There exist in nature many, many negative feedback systems thatstabilize structures, sometimes structures of considerable complexity.

PRIOR to this last claim, Bob Clark (931208.1410 EST) Professor Emeritus ofphysics, elementary and otherwise, had said:

> BALANCE OF FORCES

I am repeatedly troubled by attempts to apply negative feedback conceptsto cases of balance of forces, ordinary energy relationships, and other "ball-in-the-bowl"situations. Even, recently, feedback has been suggested for geological andcosmic events!! Amazing!

> ENERGY AND VORTICES

I have been surprised at recent discussion of vortices in terms ofnegative feedback and "energy flows." A vortex is a form of motion that canoccur in a fluid under certain conditions. If linear movement of a fluid isinterfered with by its surroundings, some energy is transferred to rotationalmotion --a vortex. This can occur for the fluid in a pipe, or the banks of a stream, oraround an airfoil. This is a dissipative effect: energy is removed from thestream. The vortex has acquired rotational energy and angular momentum. Thevortices rub against their surroundings, converting their energy to heat. Thisinvolves nothing beyond classical physics. Their is no feedback involved withvortices.

This to me is a sufficiently clear discussion of elementary physics.

I second Cliff's request above, but would suggest that a simple, clearkindergarten discussion of elementary physics --underlyingmechanisms--is much preferable to mathematical detail. Your answer belongs on the net,since you have made the claim and keep insisting.

Best, Dag

Date: Thu Jan 13, 1994 9:15 pm PST

Subject: Clarity

[From Dag Forssell (940113 1700)]

Now that my project with the second article [Perceptual Control: ManagementInsight for Problem Solving] has arrived at the milestone of preliminaryfinalization, I shall turn to the issues of clarity. I take for granted thatnetters have noted my discussions of Language, Logic and Reasoning,Measurement, Statistical Analysis and my distinctions between DescriptiveGeneralization, Descriptive Non-Explanation,and Causal Mechanism. Seeing no comments on the net, I conclude that my papermet with 100% acceptance. (No disturbance --no response). :-)

Here in it's entirety is Martin's post to me, followed by my reply.

I feel strongly about these issues. I perceive that much energy is wastedon the net because of a lack of clarity, which starts threads on orthogonalissues. I hate to see waste of the limited PCT research and educationalresources, wherever it is coming from. At the same time, I acknowledge thatseemingly irrelevant questions may occasion the most interesting newexplanations and additions to our body of knowledge.

---------------------------------

Date: Mon Dec 20, 1993 8:31 am PST

From: mmt

Subject: Re: Clarity, Martin's assertion

Dag, (Personal reply)

> I too am attracted by the clarity of Bill's writings.

I envy it.

> I notice that Bill provides detailed discussions of the underlyingmechanisms of the phenomena he discusses, not just high level abstractions,derivations or categorizations of things that don't exist as such, likebandwidth, gaussian distributions, entropy, energy, attractors and manyothers.

None of the things Bill talks about "exist as such" either. But hisabstractions speak more directly to him, and apparently to you, than do theones that I feel comfortable with. He tends to look to specific examples thatsay nothing in themselves about how things really work, unless he has in thebackground a set of assumptions that I try to bring to the foreground.

> Mathematics tells us NOTHING about nature. It is a pureabstraction.

I disagree strongly with this statement. One of the most dramatic counter-examplesis the prediction of a few events in a deep mine based on the mathematicsderived from observations in physics laboratories, when the supernova explodedin the Large Magellanic Cloud. What ARE neutrinos? What, for that matter, arestars? It is a very long mathematical extrapolation that tells us an enormousamount about nature, passing from meter readings or patterns of light and shadeon photographic film, through abstractions like atoms, nuclei, mesons andquarks of different kinds, neutrinos, the production cross-sectionsfor elements under different conditions of temperature and pressure, andfinishing with a few sparks in a tank of water, or a few atoms of germanium ina gallium block. Any failures in the mathematics would have lost the linkentirely between what happened in a physics laboratory in the 1950's or 60's,what happened in a star 180,000 years ago, and what happened a couple of yearsago in that mine.

Mathematics without observation tells us nothing about nature. Observationwithout mathematics likewise.

> Martin, you do not easily stoop to the level of elementary physics. Ithink that is what can be so exasperating. If you did try to give kindergartenlessons, you might find that your high-falutinabstractions (what you call elementary physics) often don't make much sense.The net is calling your unfounded assertion:

There exist in nature many, many negative feedback systems that stabilizestructures, sometimes structures of considerable complexity.

How so, unfounded?

> PRIOR to this last claim, Bob Clark (931208.1410 EST) ProfessorEmeritus of physics, elementary and otherwise, had said:

Oh well, if we are going to appeal to authority, I first encountered theconstruct of entropy at age about 10, in George Gamow's wonderful children'sphysics books. They were what induced me initially to become a physicist, Ithink. I graduated with first class honours in Engineering Physics, and haveretained membership in a professional society that is part of the AmericanPhysics Society ever since, despite becoming a psychologist. I may not be aprofessor of physics, but I do not think I am an ignoramus in that area. Andwhat Bob says is a weird mixture of fact and fiction. I have tried to point himto at least one source wherein he may be able to correct one of his strangercomments--thatthe concept of entropy applies only to closed systems.

>> BALANCE OF FORCES

>> ENERGY AND VORTICES

This to me is a sufficiently clear discussion of elementary physics.

Clear, but only partial. It omits the role of the energy transfer from themain flow, which is where the negative feedback gain occurs. He is dealing withvortices that are started by some means that provides their initial energy andthen are left to disappear. There is indeed no feedback involved in theirdisappearance stage, because there is no energy source to power it.

> I second Cliff's request above, but would suggest that a simple, clearkindergarten discussion of elementary physics --underlyingmechanisms--is much preferable to mathematical detail. Your answer belongs on the net,since you have made the claim and keep insisting.

I have done so. But I still can't see what it has to do with PCT.

Dag, if you remember Durango, you said that you had never understood mywritings on the net, but that you did understand my talk with pictures, andliked it. It was about mechanisms that underlie the kind of dynamical systemswe have been discussing recently on the net. You understood it then. Do younow?

I tend to think pictorially, which perhaps hampers my writing clarity. Iregret not being able to write like Bill Powers, and not being able toincorporate detailed pictures in my postings, but there's not much I can doabout it except to keep trying. Have faith.

Martin

---------------------------

Martin, I appreciate your reply. It helps me understand some of yourbiases; where you are coming from. Much of the recent discussion of feedback isindeed irrelevant to PCT. I think it started with your post:

>[Martin Taylor 931129 11:45]

> Generally, when we draw control loop diagrams, we show something likethis:

> | reference

> V

> ---comparator----

> | |

> perceptual output

> function function

> ^ |

> | V

> ======|=======etc=======|====

> | |

> | <-effects--

> on CEV

>

> We should show something more like this:

>

> | reference

> V

> ->-comparator-->- -<-energy source

> | | |

> perceptual output

> function function

> ^ | |

> | V V

> ======|=======etc=======|=|==

> ^ | |

> | power--<-- ---->energy sink

> to CEV

I appreciate that you think pictorially. I do too. Therefore, I should haveobjected to the above diagrams. They are incomplete and misleading.

Here is another portrait of a control system, taken from Rick Marken'sspreadsheet paper.

FIGURE 1: A BASIC CONTROL SYSTEM

r

|

______v_____

| |

o-->|comparator |---o

p | |____________| | e

_____|_____ _____v_____

| | | | Control

| sensor | | amplifier | System

=======|___________|========|___________|=================

^ | Environment

_____|_____ _____v_____

| controlled| | amplified |

| input | | output |

| variable | | variable |

| i |<-------| o |

|___________| |___________|

^

_____|_____

| disturb-|

| ance |

| d |

|___________|

I am now of the opinion that this too is incomplete. When a control systemis represented algebraically, some transfer functions are 1. It is convenientto omit them from a picture. I am consistently using this diagram, here takenfrom my first article, fully dressed up in non-technicalterms.

Exhibit 3.

_______________

| | HUMAN

| Purpose, | CONTROL

| goal | SYSTEM:

|_______________|

|

| + goal signal

what is going on: ______v______

perception signal -| | = difference signal (variance)

(report) o--->| Compare |----o

| |_____________| | arrows

______|______ ______v_____ signify

| Input: | | Output: | signals

| interpret | | convert |

| data | | difference |

|____________ | |____________| INSIDE THE BRAIN

^ /

Input signal --| / ----outputsignal

(raw data from | sensors) / (to muscles)

===============|================/============================

| / OUTSIDE THE BRAIN

______|___ ____v____ __________

| VARIABLE:|<--| |-->|EFFECTS: | The influence

|__________| |_________| |__________|

^

| PHYSICAL ENVIRONMENT

_____|_________________________________

| |

| DISTURBANCES: | arrows

| other influences on what you work on, | signify

| can be natural, random or deliberate. | influences

|_______________________________________|

I think of the most simplistic ECS's the same way. Memory is not shownhere, of course. I distinguish between the brain and the environment of thebrain. In the brain, the "energy flow" is minimal. Energy is added at theACTION stage. The output signal serves as instruction to modulate the "energyflow." In a thermostat/furnace, this means turning the flame on and off. In abrain/muscle, this means converting blood sugar etc. into contraction. Usingyour imaging, I can see an energy drain at the PHYSICAL VARIABLE. As I see it,all of your "energy flow" takes place in the environment of the control system.I reject your 931129 picture as invalid for purposes of PCT. This genericproblem arises often when we use shorthand --incomplete pictures. That I believe is why in the end the whole argument wasrecognized as irrelevant.

HPCT shows us how everyone grows up and develops systems concepts. The factthat we develop them does not make them right or wrong, but they are of varyingusefulness. In my engineering studies, I was exposed to Entropy and Entalpy (Inthermodynamics). I could never visualize what they stood for and have nowforgotten which is which and what their formal definitions were. I am stillmost comfortable thinking in terms of molecular motion and such. Therefore, Iam uncomfortable with some of your writings. For example:

>Re: VORTICES (and others)-RKC [Martin Taylor 931215 17:20]

>(Bob Clark, Bill Powers, Rick Marken et al, many posts Dec 14)

> Sure, but either may be determined as a function of the other two, ifit is asserted that only the force-distanceenergy is to be included in the calculation. Force can be expressed as energyand distance, or distance as force and energy. Why bother? In those terms, youcan sense force and distance more directly than energy. When your face getswarm near a dark stove element, you can sense energy better than force ordistance.

and

>[Martin Taylor 931220 1830] (Bob Clark 931218.1530)

Martin:

>>> When your face gets warm near a dark stove element, you cansense energy better than force or distance.

Bob:

>> You sense "temperature" not "energy." Your skin is well equippedwith temperature sensors. "Energy" is still a derived concept, not directlysensed.

Martin:

> I think actually you sense energy flow through the skin, from whichyou derive a temperature differential between inside and outside. Anyway, yousense what your nerves signal, and I don't think we have any that vary theiroutput according to their temperature. But I could be wrong.

They are ALL derived quantities, anyway, as we both pointed out to Bill P.What we think of as being "derived" depends on what we think of as being morefundamental and/or tied to direct sensory observation.

I would love to see your kindergarten, elementary physics explanationof:

"I think actually you sense energy flow through the skin, from which youderive a temperature differential between inside and outside".

I have a very hard time with this. I suppose that makes me "ignoramus inthat area." My understanding of engineering practice is quite the reverse, justlike Bob says, that engineers derive energy flow from a temperaturedifferential (plus data about the thermal qualities of matter in between). Ican easily visualize that neurons sense molecular vibrations around them--temperaturein one location. I cannot visualize how they would sense "energy flow." I getthe impression that your systems concepts have lost touch with the principlesthat created them, and that this creates difficulties for you to expressyourself and others to understand you. That shoots your physics credibilitywith me to hell.

You don't have to envy Bill's clarity. You can change your reference signalfor level of causal explanation at which you write if you want to.

I think your writings would gain clarity tenfold and be much shorter if youstepped down from entropy, energy flow and such, which are not specific enoughto be useful and relevant, to the lower causal mechanisms of neural currents,molecular motion and such. I will certainly agree with you that

> None of the things Bill talks about "exist as such" either.

because "it is all perception," but lower (deeper) levels of causalmechanisms provide better understanding than the higher ones do. They allow ameaningful argument on the details, which higher levels do not.

> He tends to look to specific examples that say nothing in themselvesabout how things really work, unless he has in the background a set ofassumptions that I try to bring to the foreground.

Bill's examples speak volumes to me about how things really work because hetends to stay at lower levels. Your efforts have certainly on occasionstimulated Bill to reconsider and see additional implications --I can't cite specifics, but that is my impression. (Just to be clear; that ismeant as an acknowledgement and a compliment). You have also in the past yearasked Bill to take the lead role in questioning the basic ideas of PCT andHPCT; the systems concepts Bill has spent a lifetime developing. (Which I readas an insult). Perhaps you would benefit from taking the lead role inquestioning the systems concepts Martin has spent a lifetime developing.

>> Mathematics tells us NOTHING about nature. It is a pureabstraction.

I disagree strongly with this statement.

I was hoping you would. You have asserted before that mathematics tells mesomething about nature. Thank you for giving me some specifics this time I candeal with, just like I am giving some specifics I hope you can deal with inthis post. I conclude that

Martin's Math = Dag's (Math + Physics + Chemistry + Astronomy + +)

My goodness, with your own unspoken, unconventional definitions, you winany argument.

You also say:

> Mathematics without observation tells us nothing about nature.Observation without mathematics likewise.

My full statement was:

Is this so different from your quote immediately above? I conclude that youboth disagree strongly with me and agree at the same time, in the same post.Some clarity.

Just so I don't give the impression of agreeing with your statement

> Observation without mathematics likewise.

Organisms function just fine with experience (descriptive generalization)alone. No high level formalized language, math, statistics, measurement orcausal mechanisms required.

Martin, I generally object to drawing conclusions about control systems andother physical phenomena from inappropriate mathematics. (Such as when Ricksays o = -d,which requires INFINITE amplification). I will now belatedly object to thefollowing:

>[Martin Taylor 930312 12:03] butting in recursively on

>(Bill Powers 930311.1530) butting in to Hans Blom (930311)

------------

>>>Hans:

>>> Your intuition is right. Such simulations have been performed.The PCT-typecontrol will indeed keep the car closer to the middle of the road on average.The avoiding-typecontrol will keep the car on the road for a longer time, however.

>>Bill:

>> Longer than forever? I don't follow this at all. Why should the PCT-typecontrol system EVER let the car go off the side of the road?

>Martin:

> I suspect Hans is talking about a linear system that will show aGaussian distribution of error if the distribution of disturbances is Gaussian.The tail of a Gaussian distribution is infinitely long, so the PCT car willeventually go off a road of any width, no matter how high the gain. At sometime, in this model, the car will be subject to a cross-windof Mach 3, and even if it didn't slip or get blown off its wheels, the enginewouldn't be strong enough to compensate. I don't think the edge avoider woulddo any better, but even the edge-avoideris a perceptual controller, so there is no theoretical issue of PCT versus non-PCTcontrol to separate the centre-seekerfrom the edge-avoider, In fact, the driver might control both perceptions simultaneously.

To me, this makes sense only in the context of your apparent systemsconcept that mathematics is superior to physics, not merely a tool. In my book,there is NOTHING that is infinite in the universe. Not the number of electrons,for instance. This is offered as an example of what I mean with the notion thathigh level systems concepts lose touch with the physical principles that gaverise to them. I interpret the application of a Gaussian distribution todisturbances to be an approximation over a short range. To draw physicalconclusions from conceptual, mathematically infinite Gaussian tails strikes meas absurd. I should have objected at the time, of course. You may have meant itas a joke, and Bill may have taken it as such, but I cannot be sure.

-------------------

Martin, I have spent the time to put this post together because I ambecoming convinced that much more clarity is needed about levels of causalexplanation and the proper role of mathematics and measurement, for cleardiscussion and rapid progress on CSGnet. You have seen my progression from mypresentation of dimensions of theory in Durango last summer to the paper posteda few days back (940107 1210). I expect to learn still more by picking afight.

> ....except to keep trying. Have faith.

I have faith in your commitment to PCT as well as my own. That is why I amposting this frustrated, argumentative post. We all keep trying. We all havemuch more to learn. As Mary says in INTROCSG.NET: "It is frustrating but alsotremendously exciting to be a part of the group who believe that they areparticipating in the birth of a true science of life". The excitement keeps megoing.

Best personal regards and best to all frustrated CSGnetters,

Dag

Date: Fri Jan 14, 1994 10:24 am PST

Subject: info in perception; mathematics and nature

[From Bill Powers (940114.0700 MST)] Martin (940112.1700) Rick(940112.1400)

After the "information in perception" debate has been submerged for sometime, it comes up again. It must be lighter than the medium in which it'sfloating. From my vantage point it looks like two people arguing aboutdifferent subjects using the same words.

First, is there _sufficient_ information in the perceptual signal toexplain the behavior of a control system? The answer is clearly no. You alsoneed information about the output function, the external feedback function, theform of the perceptual input function, the reference signal, and thecomparator. Given only that the perceptual signal is following a waveformdescribable as p = a*sin(b*t), there is no way to deduce what the system iscontrolling for, or how well, or in what way. This behavior of the perceptualsignal might represent tight control relative to a sine-wavereference signal, or loose control with a constant reference signal and a sine-wavedisturbance, or any combination of the two. Knowledge of the perceptual signalALONE, or its externally observable counterpart, does not provide sufficientinformation to explain the behavior of the system.

Second, is information in the perceptual signal _necessary_ for anexplanation of the behavior of the control system? Yes and no. If you knoweverything BUT the perceptual signal (including the effect of the externaldisturbance), its state can be deduced as the only unknown in the systemequations. You must know the state of all but one variable in the whole system+ disturbance to deduce the behavior of the remaining variable. If a differentvariable is unknown, then you must know the perceptual signal (as well as theother factors) to deduce it. Of course you must also know the forms of allfunctions, for that is information, too.

There obviously must be a perceptual signal representing the state of anexternal variable in some respect in order for control to occur at all, sowhatever information is in the perceptual signal is _necessary_, although not_sufficient_, to explain the system behavior.

-----------------------------------------

All of this takes the word "information" in the you-know-what-I-meansense. If we narrow the definition to the technical one --a measure of a signal expressible in bits per second --then clearly the information in a perceptual signal is insufficient to explainany part of the system's operation. Predicting the operation of the system, thesolution of the system equations, requires knowing the time-courseof each signal, and no measure of technical information content can providethat. It is the other way around. You must know the time-courseof a signal before you can begin to calculate its information content (even interms of how much it reduces the uncertainty in some arbitraryreceiver).

---------------------------------------

Is there anything that information theory has to say about control systemsthat PCT cannot say? Yes, there is. Information theory can predict the maximumaccuracy of control achievable in the presence of noise. It can predict thedynamic range of control given the noise level and the amplitude range of asignal. There may be other things it can tell us, but these two show thatinformation theory is not irrelevant to control theory. It addresses questionsother than those we have tried to answer in PCT, but it can provide answers tothose questions.

---------------------------------------

I haven't said anything intended to be controversial so far.

---------------------------------------

As to the role of mathematics in natural phenomena, I disagree with MartinTaylor in at least some basic regards. The question to me is whethermathematical abstractions directly represent laws of nature, or whether theyare consequences of laws of nature expressed at a more detailed mathematicallevel.

Consider energy relationships (again). Are energy relationships basic, ordo they derive from more basic relationships? If energy relationships arebasic, then objects behave so as to conform to basic energy relationships. Thissays that energy relationships impose a constraint on the way objects behave:objects must behave so as to satisfy the known energy relationships.

Pressing down on one end of a lever to lift a load at the other ends obeysthe law f1*d1 = f2*d2. If energy relationships impose constraints, thenrelationships between forces and distances are caused by these energyrelationships to be as they are. We observe that f1*d1 = f2*d2 BECAUSE energyinput must equal energy output. Conservation of energy explains WHY f1*d1 =f2*d2.

I think this is exactly the sense in which Martin claims that informationtheory explains WHY control systems work as they do. This claim explains whyMartin considers temperature sensing to be dependent on energy transfer ratherthan on temperature (molecular agitation) itself. Energy transfer is the morefundamental phenomenon, apparently.

I think this claim is equivalent to saying that energy conservation isapplied purposively by nature. The very term "conservation" suggests a goal,not an inevitable outcome. Given f1*d1, f2*d2 must have the same value _inorder that energy be conserved_. If f2*d2 were not equal to f1*d1, then energyconservation would have been _violated_. Nature "forbids" such a violation: thelaw is enforced. The language of conservation laws is purposive.

Consider, in contrast, the implications of saying that energy conservationis simply shorthand for f1*d1 = f2*d2. All forms of energy can be expressed interms of forces acting through distances; heat energy is molecular agitationbeing transformed into molecular agitation; electromagnetic energy is forces oncharged particles or magnetic dipoles acting through distances. When therelationships are understood at the level of observation, there is nothing leftto explain at the abstract level. The geometrical relationships in a leverdetermine that f1 and f2 will be of different sizes and will be applied throughdifferent distances, depending on the location of the fulcrum. If the leverremains straight, it follows that f1*d1 will be equal to f2*d2. That is thephysical explanation of the observed equality, and also of the generalizationin terms of energy.

In all physical equations, energy can be expressed in terms of positionsand time; so can momentum; so can fields. The abstract terms of physics areinvented intervening variables. All can be eliminated by substituting variablescloser to observation: they are all functions of position and time.

The observation of something like energy conservation is not _in additionto_ the observation that force*distance = force*distance. It is simply ashorter way of saying the same thing. Energy is conserved BECAUSE f1*d1 =f2*d2, not the other way around. The BECAUSE is logical and definitional, not aforce of nature. Dogs and cats are quadrupeds because they have four legs; theydo not have four legs because they are quadrupeds.

Given a complete model of the basic physical interactions involvingposition and time, one can DEDUCE conservation laws, because the conservationlaws follow from the fact that objects behave as they do. The same holds forinformation theory: given the way objects interact, information theory follows.But information theory does not explain WHY they act as they do. It onlydescribes, in shorthand, how they do in fact interact.

-------------------------------

As to the wonders of physical prediction from mathematics, I think it iseasy to overlook the amount of interpretation that is involved. In the case ofpredicting neutrinos from a supernova explosion, in fact no neutrinos weredetected; flashes of light were detected. Any number of intervening processescould have produced the flashes of light. There might be no neutrinos at all.The elaborate story that connects cause and effect contains so manyunobservables that there is no way to verify the explanation. The unobservablesare adjusted until the prediction of observables fits the facts.

This in itself is legitimate; it's the basic method of modeling. But themore steps of reasoning there are between observable inputs to the model andobservable outputs from it, the greater the chance that the intervening stepsare spurious. As the number of imagined entities and free parameters grows, theimpressiveness of the predictions rapidly declines. This is why the mathematicsneeds to be tested against observation at EVERY step, if possible. There is nounique mathematical way to get from a starting expression to a finalexpression. Some ways of parsing mathematical relationships yield factors andterms that turn out to have measurable counterparts; most don't.

---------------------------------------

How an alternate physics might arise

Consider two objects orbiting around a common center of gravity. Object 1is at radius 1 moving at velocity 1, and object 2 is at radius 2 moving atvelocity 2. Given: the force acting between the objects is the same for each:f1 = -f2= f. Equating centripetal forces, we have

m1v1^2/r1 = -m2v2^2/r2

But by definition, m1 = f/a1 and m2 = f/a2, so

v1^2 v2^2

---- = -----

a1*r1 a2*r2

By geometry, v1 = r1*dw/dt and v2 = r2*dw/dt, where dw/dt is angularvelocity, the same for both objects. This gives

r1/a1 = -r2/a2

where a1 and a2 are the central accelerations of the objects. If ourinitial observations had been in terms of distances and accelerations, thisequation would have been found immediately, and perhaps the concepts of massand force might never have arisen. We would consider this equation to be thebasic observation.

We have now reduced the relative behavior of the objects to a simpleexpression in functions of position and time. What has happened to mass andforce? They have dropped out. They are unnecessary abstractions. It wouldappear that there is a law relating the motions of particles which expressesradius of curvature in terms of acceleration, as if space itself were curved bythe presence of the particles. We would characterize particles not in terms ofmass, but in terms of r/a, to which we would give a name.

Now we could generalize to particles in noncircular orbits, but we would bethinking in terms of curvatures and accelerations instead of masses and forces.We would develop a whole line of thinking based on this fundamental ratio, r/a.On that we would build new generalizations and new abstract variables, endingup with dynamical equations that would hardly be recognizable to a conventionalphysicist, although they would be entirely equivalent. What new entities wouldbe created from this different beginning? What new conservation laws wouldappear? What new explanations would there be for "why" objects obey the lawthat r1/a1 = -r2/a2,suitably generalized for noncircular orbits?

I think it's hard to see the arbitrariness of mathematical representationsuntil two different representations can be compared. Representations that aresimple and obvious in one scheme can become complex and baffling in another.Entities which appear naturally in one scheme are missing from theother.

All this tells me that mathematics is simply a mode of perception, a way ofcreating an orderly world. It can't provide a single unique picture of theworld; there are many different mathematical representations of the world,linked only by the fact that they are based on the same observable phenomena.The mathematics does not constrain the world; the world is what it is, andmathematics can only create a representation of it --any number of representations.

Best, Bill P.

Date: Fri Jan 14, 1994 3:56 pm PST

From: tbourbon

Subject: RE: Clarity

Dag [direct],

>[From Dag Forssell (940113 1700)]

That was an excellent post to Martin. Thanks, for saying so many importantthings --with such clarity.

Warm regards, Tom

Date: Fri Jan 14, 1994 4:11 pm PST

Subject: Re: Clarity

[Martin Taylor 940114 1340] >Dag Forssell (940113 1700)

Wow, what an assault! I had no idea I was perceived as such a villain. Andeven reading your message, I can't figure out my evil, lest it be containedin

> You have also in the past year asked Bill to take the lead role inquestioning the basic ideas of PCT and HPCT; the systems concepts Bill hasspent a lifetime developing. (Which I read as an insult).

Who is better suited than Bill? If he thinks that my admiration for him andfor PCT generally is faked, and that I want him in some way to deny hisaccomplishment, then he might perceive insult.

I am unaware of insulting you. I have passed your documents and tape aroundour management here, in the (vain) hope of arousing interest. I have notcommented on them much, because I already spend more time on the technicalaspects of PCT than I should be taking from my paid work (though PCT is comingmore and more to be intrinsic to my paid work, which makes me feel less guiltyabout it). Management has never interested me much, so even when I might havesomething to say, I think "Dag knows his target audience better than I, so letit be." Is that the insult, perhaps?

I think the basic ideas of PCT and HPCT need to be understood. I find ithelpful to understand them on the base of principles that work in all otherareas in which they have been tried. I find they work (for me) in understandingPCT. I also believe that ANY worthwhile concept is much better understood whenit is seen from a variety of viewpoints than when it appears to rest on onlyone conceptual foundation. So, yes, I think it very important that Bill inparticular, but also anyone else on the net, should question and therebyreinforce the basic ideas of PCT and HPCT.

Your comment reminds me very much of one that shocked me a year or moreago, from Rick. I can't quote directly, but it was more or less: "What do youthink you are trying to do? Improve PCT?" To which my answer was (more orless): "Yes. Of course. Isn't that what everyone on CSG-Lis trying to do?." Well, isn't it? If not, I have no interest in participatingin an adulation-festfor a living god in a static religion.

I take CSG-Lto be THE place where PCT should be questioned. Elsewhere, it should bepromoted as the only way really to understand how people function. That aswell, I do. Outside, I sell Powers as the genius he deserves to be recognizedas. Not here.

> Perhaps you would benefit from taking the lead role in questioning thesystems concepts Martin has spent a lifetime developing.

You think I don't? But doing so does not stop me from finding it usefuland from saying so when I think it would be beneficial.

> Martin's Math = Dag's (Math + Physics + Chemistry + Astronomy + ++)

> My goodness, with your own unspoken, unconventional definitions, youwin any argument.

I don't understand either line of this. Mathematics is a tool in all of theobservational sciences. It is mathematics that links observations. If you wantto say that, when I refer to astronomical observations in support of theproposition that mathematics tells you about nature, I am saying thatmathematics IS astronomy, you misunderstand me. What I am saying is that theSAME mathematics, in the sense of internal consistency, has been found to workin connecting observations within AND BETWEEN the sciences of physics,chemistry, astronomy ...

That the same mathematics, for the most part born in abstract thought,actually does link observations that have no obvious connection, tells meclearly that mathematics tells us about nature.

> My full statement was:

> Mathematics tells us NOTHING about nature. It is a pure abstraction.It is a tool for generalizations and description, and a very handy and usefulone (--whencorrectly applied, something that is not verified by mathematics but bysuccessful physical experiments). To understand nature's mechanisms, there isno substitute for the underlying physical mechanisms, below the phenomena westudy and discuss.

What I argued was not whether one needs observation to check theory. Onthat we agree. I argued, and still argue, that the constructs of mathematicswork in the observational sciences. Their abstractions work. My position onrealism is that if we have a perception that we are able to control through ouractions, that perception corresponds to something "real." If application ofmathematical constructs to observations leads to predictions of observationsthat agree with those in nature, then we are as justified in saying that themathematical constructs tell us about nature as we are in saying that anyperception does. In other words, the perception works; the mathematicsworks.

It may all be wrong. There are an infinite number of perceptions that mightcorrespond to any sensation. Likewise, our whole structure of mathematicalabstractions may be flawed and need replacing wholesale. At present, theperceptions we have are the only connection we have with reality. Next week, wemay have different perceptions (perceptual functions, not values). Does thismean that reality changed? Of course not.

> Just so I don't give the impression of agreeing with yourstatement

>> Observation without mathematics likewise.

> Organisms function just fine with experience (descriptivegeneralization) alone. No high level formalized language, math, statistics,measurement or causal mechanisms required.

True. I wasn't thinking about everyday life, but about science, which ISformal. Correction accepted.

On infinities: Of course we could never compare observations with themathematics of infinity, so you are correct in

> In my book, there is NOTHING that is infinite in the universe. Notthe number of electrons, for instance. This is offered as an example of what Imean with the notion that high level systems concepts lose touch with thephysical principles that gave rise to them. I interpret the application of aGaussian distribution to disturbances to be an approximation over a shortrange.

All descriptions, including causal models, are approximations. The simplerthe description, and the better the approximation, the more useful andplausible is the description.

> To draw physical conclusions from conceptual, mathematically infiniteGaussian tails strikes me as absurd.

One way of treating "infinity" is as "greater than any particular fixedlimit" so

>> I suspect Hans is talking about a linear system that will show aGaussian distribution of error if the distribution of disturbances is Gaussian.The tail of a Gaussian distribution is infinitely long, so the PCT car willeventually go off a road of any width, no matter how high the gain.

merely says that if you wait long enough AND the system is linear (anotherimpossible approximation), the car will go off the road, but that you can'tbeforehand say how long is long enough. In practice, of course it is absurd.The road would have crumbled, road repair crews would have erected barriers,the driver would have died of old age... and it would still be unlikely thatthe linear control system would BY THEN have driven off the road.

In fact, what you quoted was as much a warning about taking modelsliterally as about control under idealized conditions. All realistic models areunrealistic, strange as that may sound. A model that includes all the variablesand nonlinearities of the real world is computationally impossible to manage.It is unrealistic in the sense that nobody could realistically use it. Manyvariables must be combined or ignored, nonlinearities smoothed, assumptionsmade. The model becomes unrealistic as an exact model of the situation, butrealistic in being usable and providing, if it is a good model, goodapproximations to what happens MOST OF THE TIME.

Now go back in your posting. You complain that my picture isincomplete:

>> Generally, when we draw control loop diagrams, we show somethinglike this:

>> | reference

>> V

>> ---comparator----

>> | |

>> perceptual output

>> function function

>> ^ |

>> | V

>> ======|=======etc=======|====

>> | |

>> | <-effects--

>> on CEV

>>

>> We should show something more like this:

>>

>> | reference

>> V

>> ->-comparator-->- -<-energy source

>> | | |

>> perceptual output

>> function function

>> ^ | |

>> | V V

>> ======|=======etc=======|=|==

>> ^ | |

>> | power--<-- ---->energy sink

>> to CEV

> I appreciate that you think pictorially. I do too. Therefore, Ishould have objected to the above diagrams. They are incomplete andmisleading.

Of course they are incomplete. If they misled you in understanding whatthey were supposed to illustrate, then they were misleading. But you can'tcorrect them by substituting more detailed diagrams that add elements suited toSPECIFIC situations while eliminating the diagram elements that illustrated themain point to be made.

If you make a diagram that includes all the elements that are important forany discussion, nobody will understand what you are trying to illustrate in anyspecific discussion. I was pointing out that an amplifier doesn't get itsenergy from its input signal, but from another independent source, and thatsome energy from that source goes to the output signal of the amplifier, therest to a sink. For most discussions of control, that doesn't matter, so youcan drop the source-sinkflow. In the context, it was the main point. The rest of your elaboration,while correct and useful in many discussions, would be distracting in thatdiscussion.

> I distinguish between the brain and the environment of the brain. Inthe brain, the "energy flow" is minimal.

Is that why we can determine from moment to moment what parts of the brainare working by variations in the local glucose metabolism? What is that energyused for? Just to signal to researchers "look at me--I'mworking"?

> In my engineering studies, I was exposed to Entropy and Entalpy (Inthermodynamics). I could never visualize what they stood for and have nowforgotten which is which and what their formal definitions were. I am stillmost comfortable thinking in terms of molecular motion and such.

Fine. So Entropy and Enthalpy aren't much help to you in understanding whatis going on. No problem. They are to other people, and some people can use themto make predictions about what can and what cannot happen. You don't have to,yourself. Doesn't bother me.

> I can easily visualize that neurons sense molecular vibrations aroundthem--temperaturein one location.

How would they do this if the temperature were the same all around them?You may easily visualize this. I can't. In my visualization, you have to havean energy flow, or else the neuron and the environment are in equilibrium andnothing will be sensed.

> I cannot visualize how they would sense "energy flow."

What they "sense" depends on your (you, the observer's) level ofabstraction. They sense molecular rearrangements, or electrical impulses, ortemperature differentials, or energy flows, or light quanta (in the case thatintroduced this, it was infrared quanta), or nearby stove elements, or mealscooking, or ... The theoretician can describe the processes involved. Theneurons can't. They sense "energy flow" insofar as when there is energy flow,they produce output, the more energy flow, the more output. The more energyflow, the greater temperature differential, and vice-versa.Which you see as more important to focus on is up to you, not up to theneuron.

> I get the impression that your systems concepts have lost touch withthe principles that created them, and that this creates difficulties for you toexpress yourself and others to understand you. That shoots your physicscredibility with me to hell.

Why does my relative inability with words lead you to insult myphysics?

> I think your writings would gain clarity tenfold and be much shorterif you stepped down from entropy, energy flow and such, which are not specificenough to be useful and relevant, to the lower causal mechanisms of neuralcurrents, molecular motion and such.

I doubt it. At that level, one loses generality, and adds the complexitiesthat are required for each specific situation. There are occasions when this iswarranted. Maybe I should look more carefully to detect those occasions, butyour comment certainly isn't true in general. I have found (as you doubtlesshave noted) that the concepts of entropy, energy flow "and such" are useful andrelevant, at least sometimes.

> I will certainly agree with you that

>> None of the things Bill talks about "exist as such" either.

> because "it is all perception," but lower (deeper) levels of causalmechanisms provide better understanding than the higher ones do. They allow ameaningful argument on the details, which higher levels do not.

I find your use of "higher" and "lower" a bit bizarre. It is true that thelower levels of causal mechanism provide better understanding, but this isbecause they apply more widely and generally than do the higher ones. But thenyou add that contradictory last sentence. I have been using arguments fromdeep, general levels, because they are widely applicable, and can be used inunderstanding PCT. Up to this point, you criticize me for that. But now you saythat I could be more detailed if I were to go even deeper. Puzzlement reignssupreme.

> Bill's examples speak volumes to me about how things really workbecause he tends to stay at lower levels.

"Higher" "lower" I'm really confused about what you mean. Bill usesspecifics more than deep causal mechanisms, which makes them easy to understandwithin the specific context of PCT and control generally. If you are happy withthat viewpoint, fine. I'm happy with it, too, but I like to see more as well.Just greedy, I guess.

> I have faith in your commitment to PCT as well as my own. That is whyI am posting this frustrated, argumentative post.

Appreciated. I don't understand the source of your frustration, but acceptthat it exists.

Martin

Date: Fri Jan 14, 1994 7:53 pm PST

Subject: Re: info in perception; mathematics and nature

[Martin Taylor 940114 17:10] Bill Powers (940114.0700)

I don't know whether I will surprise Bill by saying that I agree withALMOST everything in his fine posting. I hope it is no surprise.

I'm pretty happy with Bill's discussion of the value and role ofinformation theory. When it comes to detailed discussion, it is possible thatsome problems might crop up, but I don't see them immediately.

> As to the role of mathematics in natural phenomena, I disagree withMartin Taylor in at least some basic regards.

I can't tell from the posting to what degree this is true. Maybe myresponse will help you to determine it.

> The question to me is whether mathematical abstractions directlyrepresent laws of nature, or whether they are consequences of laws of natureexpressed at a more detailed mathematical level.

This strikes me as requiring some a priori knowledge that there AREknowable laws of nature. My position is that there are not. All our perceptionsare abstractions based on control, which in part depends on there being aconsistency about the way the unknowable outer world works. We don't know howit works, but we have developed abstractions that we call perceptual functionsthat produce results that change in some non-randomway when we act on the world. Those perceptual functions are our reality. Someof them relate to "things" some to "processes," since we in the Western worldhave come to agree that the world consists of "things" that "act on" eachother.

"Laws of nature" are perceptions of processes. We create them, and so longas our perceptions remain controllable when we use them, we remain satisfiedwith them. When our perceptions don't change as we expect from ourunderstanding of the "laws of nature," we may reorganize so as to see the lawsof nature differently.

I do not see mathematical abstractions as anything special. Like laws ofnature, or the colours yellow and blue, they are perceptions that we havedeveloped because when we use them our other perceptions tend to be wellcontrolled. We rely on the "law of nature" gravity to help us dump a load ofjunk out of an attic window. It's easier than hand-carryingthe junk down the stairs, but we have to imagine that letting the stuff go whenit is held out of the window will result in our perceiving it later to be onthe ground outside. So with a mathematical abstraction. We have to imagine thatif we have an infrared frequency-doublinglaser we will get a green beam, not one that changes between blue, red, andgamma. Doubling is something that works on things that have attributes that canbe represented numerically. Like wavelength, weight, or Reynoldsnumber.

I'll appropriate Bill's comment here.

> I haven't said anything intended to be controversial so far.

==================================

Now,

> Consider energy relationships (again). Are energy relationships basic,or do they derive from more basic relationships?

Is this an answerable question? I think it is not. Bill seems to be leaningto this conclusion with his lovely later discussion of "How an alternatephysics might arise."

> Consider two objects orbiting around a common center ofgravity.

....

> We have now reduced the relative behavior of the objects to a simpleexpression in functions of position and time. What has happened to mass andforce? They have dropped out. They are unnecessary abstractions. It wouldappear that there is a law relating the motions of particles which expressesradius of curvature in terms of acceleration, as if space itself were curved bythe presence of the particles. We would characterize particles not in terms ofmass, but in terms of r/a, to which we would give a name.

Yes! And this sounds very like the KIND of thinking that led to relativity(not the same thinking, of course). It's just what would be expected tohappen.

> We would develop a whole line of thinking based on this fundamentalratio, r/a. On that we would build new generalizations and new abstractvariables, ending up with dynamical equations that would hardly be recognizableto a conventional physicist, although they would be entirely equivalent. Whatnew entities would be created from this different beginning? What newconservation laws would appear? What new explanations would there be for "why"objects obey the law that r1/a1 = -r2/a2,suitably generalized for noncircular orbits?

Yes, yes!!! We really ARE on the same wavelength, it seems.

> I think it's hard to see the arbitrariness of mathematicalrepresentations until two different representations can be compared.Representations that are simple and obvious in one scheme can become complexand baffling in another. Entities which appear naturally in one scheme aremissing from the other.

Right on. Beautifully put. Why would you think we disagree on this, as itseems you do?

ANY controllable perception is a valid representation of something in theouter world. That's an article of faith, no more, but as far as I can see, it'sthe only place we can start. Any controllable perception may at some point bereplaced with another that can be better controlled. We do that all the time,by reorganization. If the two perceptions are incompatible, the first is likelyto be replaced by the second. If they contribute to control of another higherperception, the first may be abandoned simply because tighter control of thesecond permits tighter control of the higher perception.

Now we come back to this weasel-word"basic."

> Are energy relationships basic, or do they derive from more basicrelationships? If energy relationships are basic, then objects behave so as toconform to basic energy relationships. This says that energy relationshipsimpose a constraint on the way objects behave: objects must behave so as tosatisfy the known energy relationships.

Basic where? In the "real" laws of nature, or in the way we perceive natureto behave? Who knows what the "real" laws might be? They are the only ones thatimpose a "must" on the way objects behave. All we can say is that all objectswe have observed HAVE behaved this way, and we have, over time, less and lessreason to believe we will ever observe an object that doesn't. If we do happento make such an observation, we are likely to question its validity unless wecan make another one that corresponds to it in some way we can see.

> Pressing down on one end of a lever to lift a load at the other endsobeys the law f1*d1 = f2*d2.

There's no MUST about that. Only, such a relation has been observedapproximately so often that it makes sense for us to perceive an abstraction welabel fn, an abstraction we label dn, and two mathematical abstractions welabel * and =, and to fit them together this way. Each of these abstractionshas been useful in other circumstances. We find that when we link theseabstractions just so, we get a stable perception. It works. And "it works" is,I think, the ONLY justifiable reason for accepting any theory (model, ordescription). (Actually--seebelow--thisparticular generalization works only approximately.)

> If energy relationships impose constraints, then relationships betweenforces and distances are caused by these energy relationships to be as theyare.

Possible, in the unknowable world of real natural law. We don't know a"cause" for anything in that sense. We may be caused to expect therelationships between force and distance to be as they are because we believethe energy relationships to be as they are. But that's different.

> We observe that f1*d1 = f2*d2 BECAUSE energy input must equal energyoutput. Conservation of energy explains WHY f1*d1 = f2*d2.

This might be a red herring, but conservation of energy was not found untilpeople began asking question like why the constant f*d relation failed, andbegan to understand that in such conditions there was always a conversion ofthe f*d energy into heat energy. It was because f1*d1 != f2*d2 that the notionof conservation of energy gradually came to be accepted as a "basic"law.

> I think this is exactly the sense in which Martin claims thatinformation theory explains WHY control systems work as they do.

I ordinarily take "why" in a very pragmatic sense. If there is a perceivedlaw that has been found to work in a wide range of conditions, and thecircumstances under consideration seem to fit in that range, and the law stillseems to work, then I find "why" a legitimate term. In the deeper theo-philosophicalsense, I regard "WHY" as a non-answerablequestion.

> This claim explains why Martin considers temperature sensing to bedependent on energy transfer rather than on temperature (molecular agitation)itself. Energy transfer is the more fundamental phenomenon, apparently.

Not so. See my response to Dag earlier today. Energy transfer, nottemperature (but yes temperature differential) is required for temperaturesensing to occur. What is fundamental depends on the range of phenomena youconsider.

I once read a quote I put (and still keep) on my board, by somebody orother called W.T. Powers: "The curse of the theorist is the discovery that allis not as it seems."

> I think this claim is equivalent to saying that energy conservation isapplied purposively by nature.

I disagree, as the above discussion may show.

> The very term "conservation" suggests a goal, not an inevitableoutcome. Given f1*d1, f2*d2 must have the same value _in order that energy beconserved_. If f2*d2 were not equal to f1*d1, then energy conservation wouldhave been _violated_.

Apart from the fact that conservation of energy would actually enforce aninequality, the "suggestion" of a "goal" is imputed by one reader to theunknowable Mother Nature. Another reader only understands that certainobservations are to be expected.

> Nature "forbids" such a violation: the law is enforced. The languageof conservation laws is purposive.

A possible problem in how we use language.

> In all physical equations, energy can be expressed in terms ofpositions and time; so can momentum; so can fields. The abstract terms ofphysics are invented intervening variables. All can be eliminated bysubstituting variables closer to observation: they are all functions ofposition and time.

Sure, you can rewrite any specific situation in other terms. You might evenrewrite the general propositions in terms of "variables closer to observation"but the way you write will be much more complex, and it will be harder to seehow the always-to-be-expectedobservation will be expressed in any specific situation. The point about havingperceptions at higher levels of abstraction is that if you control using them,your control works. You keep your house near the temperature you want by usinga control system. But it helps if you have computed the amount of energyavailable in your fuel and ensure that it can be obtained at a rate greaterthan the rate the energy escapes through your walls and windows. It is easierto do that by looking at tables of energy content and insulation than byconsidering the chemistry of combustion and the vibrations of the molecules ofthe windows. Energy conservation is a useful concept that has not yet beenshown to fail when tested.

> As to the wonders of physical prediction from mathematics, I think itis easy to overlook the amount of interpretation that is involved.

On the contrary, it is precisely the amount of interpretation that makesthe whole story so marvelous.

> In the case of predicting neutrinos from a supernova explosion, infact no neutrinos were detected; flashes of light were detected.

Does one REALLY have to go to that level of obviousness? All observationsare flashes of light, or feelings of heat or touch, or vibrations of the air.So what? And depending on the neutrino detector, what is detected is theexistence of atoms of (I think) a germanium isotope. (By way of light flasheswe call meter readings, photographs,....)

> Any number of intervening processes could have produced the flashes oflight. There might be no neutrinos at all.

Possible, but the design of the detectors was intended to make it asdifficult as possible for there to be other causes.

> The elaborate story that connects cause and effect contains so manyunobservables that there is no way to verify the explanation.

You want REAL truth? The point is that experiments and observations inlaboratories and of the universe, interrelated by careful mathematicalanalysis, had led to predictions that IF there were to be a supernova of thatkind at that distance, THEN there should be some detectable neutrinos thatwould generate the specific kinds of human-sensedobservation that occurred. There were some open parameters, such as the restmass of a neutrino, and these observations led to a new upper limit that can beapplied in other situations.

> The unobservables are adjusted until the prediction of observablesfits the facts.

If by "unobservables" you mean the rest mass of the neutrino, then you areright. But I infer that this is not what you mean. In which case this is one ofthe more breathtaking statements of the (yet young) year.

> This in itself is legitimate; it's the basic method of modeling. Butthe more steps of reasoning there are between observable inputs to the modeland observable outputs from it, the greater the chance that the interveningsteps are spurious. As the number of imagined entities and free parametersgrows, the impressiveness of the predictions rapidly declines.

In the abstract, this is true. In the implication that the number of freeparameters and imagined concepts in physics is commensurate with the number ofobservations, it is not.

> This is why the mathematics needs to be tested against observation atEVERY step, if possible.

I think most people--certainlymost physicists--wouldagree with this.

> There is no unique mathematical way to get from a starting expressionto a final expression. Some ways of parsing mathematical relationships yieldfactors and terms that turn out to have measurable counterparts; mostdon't.

Yes. We are back to where this response began. Those factors and terms thatwork, in that they assist us in controlling our perceptions, will survive.Others won't.

You could apply the same analysis to religious constructs (as I think youhave). They also assist people to maintain control of some perceptions, but thekinds of perceptions involved tend to be more social than are the perceptionsinvolved in science. Not entirely, but they tend that way.

All our perceptions are abstractions in one way or another. All (in myview) survive only insofar as they, or some perception of which they form part,can be controlled through action in the outer world. Some are valuable in awider range of circumstances than are others. We use these in saying "why" theother ones are as they are. "Democracy" is "why" we "vote." "Temperaturedifferential" is "why" "energy" "flows."

I don't know what's "basic." I know that if a construct that has been showngenerally to work in a wide range of conditions works also in a new condition,I have greater faith that the construct tells me something about the unknowable"real" world, and that I can say that the construct to some degree "explains"the new condition. To "explain" is only to use a construct for free, not havingto invent it for the new occasion.

I think the places where we disagree are more minor than the latter part ofthis response might suggest. I hope you agree.

Martin

Date: Sat Jan 15, 1994 10:47 am PST

Subject: Generalization vs modeling

[From Bill Powers (940115.0930 MST)]

RE: insults

The dictionary has a great deal of trouble with the word "insult." Most ofthe definitional loops are small and tight (see "insolent"). The larger loopshave to do with being attacked or treated with contempt. I deduce that the maineffect is an injury to one's self-image.In George Herbert Mead's world, where the self is defined by society, everyoneelse in the world controls your self-image,so insults must be common. If, on the other hand, your evaluation of yourselfis not strictly a function of other people's opinions, you are much lessvulnerable to insult --you might even be impervious to insult (which implies that you are alsoimpervious to flattery). In that case, the occurrence of an insult says moreabout the source than the destination.

So far I have not felt insulted by anything I have read on this net. I haveoccasionally been embarrassed by reading certain posts, written by me.

----------------------------------------------

Martin Taylor (940114.1710)--

> I don't know whether I will surprise Bill by saying that I agree withALMOST everything in his fine posting. I hope it is no surprise.

I expected, and hoped for, a good deal of agreement. For the most part Iwas trying to say things which I judged would meet with your approval. Ofcourse that wasn't _entirely_ the point.

RE: mathematical abstractions

> Why would you think we disagree on this, as it seems you do?

We do still appear to have a disagreement which is worth exploring further.I was describing how mathematical abstractions can be derived by offeringdifferent interpretations, different treatments, of observations. You agreedwith me that the description fits how it works. In the past, you have said thatall theory is description, a statement that also fits this phenomenon ofabstraction from observation. I claim, however, that there is a different modeof theorizing that is used in the method of modeling, a mode that does notdepend on deriving more abstract representations from more detailedones.

Let's try a parable to see if it helps in making the distinction I have inmind.

Suppose you are in a small power distribution station watching the metersover the shoulder of the operating engineer. The engineer shows you the metersindicating input current, voltage, and phase angle from the generating station,and the set of meters indicating output current, voltage, and phase angle onthe multiple output lines. As a physicist, you know that the total outputenergy flow must be nearly equal to the total energy input (the only differencebeing losses that occur between the places where the meters are connected). Sothe product of output current and voltage, times the cosine of the phase angle,summed over all outputs, should nearly equal the produce of voltage and currentin, times the cosine of phase angle.

Now you observe that the current output on one of the output lines hasdropped to zero. On the basis of the physics involved, what can you say? Allyou can really say is that there is zero output power on that line, and thatthe sum of all the other output powers must still be nearly equal to the inputpower. Checking the meters shows that this is true. So the behavior of thesystem still fits the generalization. There is nothing left to explain, becausethe theory still applies --it continues to describe the observations.

The operating engineer, however, says "Oh, damn, there's a broken line outthere," and he calls the repair truck to go find the break and fix it.

You might say that the operating engineer is working from a generalization,but he's doing something more. He is proposing a FACT. The observed meterreadings are _consequences_ of this fact; given the proposed fact, the meterreadings follow deductively from it (and the rest of the theory of electricityaccompanying it). So the meter readings are to the proposed fact as theequality of energy in and out is to the meter readings.

If you apply the method of mathematical representation and abstraction tothe existing meter readings, you can make a series of true statements ofincreasing generality. But none of these statements will be "there is a brokenwire on line AX3211."

What I visualize is a layer of observations that we take to be the world ofevents and processes, the world we take as given and about which we theorize.Mathematical abstractions begin with descriptions of this world, which lead tomore compact and general descriptions, and so forth to E= MC^2. That leads toone kind of theorizing. But we can also go in the other direction, proposingimagined events and processes which, if they really existed, would demand thatthe world of observation be as it is. Once we have posited such an underlyingworld, we can base a structure of mathematical abstractions on it, too,beginning at a more detailed level of a hypothetical world, building up to thelevel where we make observations, and continuing to higher levels which aremore general representations still.

In the power-plantexample, the meter readings are at the level of observation. On those readingswe can build mathematical abstractions such as energy, conservation laws,principles of entropy and information and the like. Those abstractions aresimply more and more general descriptions of what the meter readingsshow.

The engineer's hypothesis that a wire is broken goes in the oppositedirection; it explains the meter readings not by fitting them into a moregeneral descriptive scheme, but by introducing a proposed fact at a levellower, more detailed, than that of the meter readings. The engineer proposesthat the reason for the disappearance of the current reading on one meter isthat somewhere in the world that is not represented by the meter readings, aphysical situation exists which would explain why the current has dropped tozero. The meter reading does not indicate a break in the line, but it if therewere such a break, it follows logically (from a model of the physicalelectrical distribution system) that the meter reading would have to be zero,and that the power output on that line is zero.

The engineer is proposing a premise, from which the meter reading can bededuced as a conclusion. The physicist is taking the meter readings as apremise, and from them deducing (calculating) the implied energy relationshipsas conclusions.

------------------------

Thus there seem to be two quite distinct ways of explaining observations.One is by building more and more general descriptions of them, taking theobservations as the premises and deducing their implications, and the other isto reason backward, reverse-engineeringreality in the attempt to find more detailed mechanisms from which theobservations follow deductively.

Thermodynamics would be an example of building abstract descriptions on agiven body of observations. Quantum chromodynamics would be an example ofproposing underlying facts from which observations can be deduced.

Best, Bill P.

Date: Fri Jan 14, 1994 7:10 pm PST

Subject: Clarity

Tom, Direct

Thanks for moral support.

I don't suppose it will do any good, but I had a large error signal.

Perhaps as time goes on, something will sink in, or inspire someoneelse.

I got your note and Martin's response at the same time. Of course he willdefend his self. Perhaps he got it, perhaps not. I still say what's dimly saidis dimly thought.

I note that Martin did not respond to my challenges, but avoid them andcome back with other nonsensical statements, such as his comment on energyflows in the brain.

I would like to see the net respond to Ed's postings instead of Martin'sabout vortices. Ed told me the other day on the phone, he is consideringdropping off the net, for lack of interest in applications. I don't think hewill. He was tired. Why are so few netters interested in applications? Why areso few trying to use PCT on the net? (My post was not PCTish, that's forsure).

I expect to drop the matter. I have nothing more to say, and do not enjoychallenging anyone at a personal level. It gets my heart pumpinguncomfortably.

Sunday, I expect to mail you my care package, including the new DEMODISK.Will you pass a copy to isaac? He asked, but I have misplaced hisaddress.

Keep up your good work! Thanks again, Dag

Date: Mon Jan 17, 1994 1:24 am PST

Subject: What is a "deeper" explanation?

[From Bill Powers (940116.1100 MST)] Martin Taylor (940113.1800)

> You describe control of what we call the CEV, not of perception.There is a difference. I've often had a bit of a linguistic scramble trying totalk about situations like "the Test" in which two (or more) control systemsact on related parts of the outer world in controlling their own perceptions.That may be the source of your comment:

>> There's a related subject, however, which came up in some ofMartin's posts, concerning what we mean by controlling something.

> If you don't mean that, I presume you mean my efforts to get an answerto that question, now answered. Apart from the question of whether the CEV orthe perceptual signal is controlled, I am quite happy with the answer.

My proposed definition concerns the way we identify another control system.We do it by finding something in the environment that is controlled by theactions of the other system, in the presence of variable disturbances. "Theenvironment" is, of course, our perception of it. We presume that the othersystem perceives the same way we do. So it is perception that is actuallycontrolled, although when we speak in terms of (presumably) shared models, weposit a stable relationship between perceptions and hypothetical environmentalvariables. We assume, in short, that there is a perception in the other systemcorresponding to our own perceptions, and for purposes of communication welocate that perception in "the environment."

This assumption can be proven wrong, if either our own or the othersystem's perceptual functions change. Then we have to redefine the controlledvariable before going on.

--------------------------

That isn't what I intended to start writing about. I'm trying to pin downan insight into some of our basic disagreements about explanations, and what isa more "basic" explanation. This problem shows up in many guises. Forexample:

> [Neurons] sense "energy flow" insofar as when there is energy flow,they produce output, the more energy flow, the more output. The more energyflow, the greater temperature differential, and vice-versa. Which you see as more important to focus on is up to you, not up to theneuron.

I think you are confusing temperature gradients with energy flow; they arenot the same thing. For a given temperature difference, there can be any amountof heat flow, depending on the thermal resistance. Thermocouples produce avoltage proportional to temperature difference, not to energy flow. Twothermocouples will produce identical readings only if the temperaturedifference between their junctions is equal. If the thermal conductivity of themedium between the junctions is different, there will be different energyflows, but not different thermocouple output voltages. The temperature-sensingneurons in the hypothalamus are sensitive to temperature, not temperaturegradient. Note that the rate of chemical reactions doubles for --if I remember right --each 10 degrees c. This is a temperature (molecular collision) effect, not anenergy effect.

Temperature, not energy content, determines how much physical effect a hotbody can have on a cooler one (energy content is proportional to heat capacityfor a given temperature). Two bodies can have quite different energy contentseven though their temperatures are the same, without the higher-energybody being able to affect the lower-energybody. There can be heat flow between two bodies with equal energy content, butnot between two bodies of equal temperature.

The basic problem here is that you are treating energy as if it has thesame properties as mechanical force, electromotive force, magnetomotive force,temperature difference, and so on. Energy per se can't have any physicaleffects; rather, energy transfers are the result, not the cause, of physicalprocesses. Energy computations are a way of keeping track of forces exertedthrough distances.

Start my lever example from a different place. The arms of the lever (withthe fulcrum between them) have lengths L2 and L1. The motion d2 of the secondend is L2/L1 times the motion d1 of the first end, so d2/d1 = L2/L1, bygeometry. The ratio of forces is f1/f2 = L2/L1, by balance of moments.Combining to eliminate L2/L1, we get f1/f2 = d2/d1, or

f1*d1 = f2*d2

So we have derived conservation of energy from the basic measurements offorce, position, and length that define the lever. This conservation law is nota separate law of nature; it is a derived property, a shorthand way ofexpressing the basic observed relationships. It does not need to be verified,because it is true by definition.

You objected to this by pointing out the presence of friction, whichconverts some energy to heat. But that, too, is only a derived relationship.The friction at the fulcrum results from the translation of one bearing surfaceover another. If r is the radius of the bearing, then d3, the motion of themoving surface relative to the stationary one, is r/L1 times the motion d1 atthe first end of the lever, and the force f3 is L1/r times the force f1 at thefirst end. So we have, altogether, f1*d1 = f2*d2 + f3*d3. The friction resultsfrom collisions of molecules in the moving surface with molecules in thestationary surface, transferring velocity (or momentum) from the one to theother, increasing the molecular agitation in both surfaces, and thus accountingfor the reaction forces and the rise in temperature. We have derived theconservation of energy again, this time including heat energy.

Nowhere is it necessary to discuss energy --although it is, of course, computationally convenient to do so. Energy is anabstract way of describing a relationship between forces and distances. As anabstraction, it is completely determined by the less abstract variables fromwhich it is derived. It is thus a less fundamental representation of thesituation, not a more fundamental representation. The energy representationcontains less information about the physical situation, not more. Conservationof energy explains nothing that is not already explained in terms of thedetailed physical relationships.

In a neuron, the basic mechanism as I understand it is the raising of anelectromotive force in the axon hillock past a threshold where a relaxationdischarge is triggered. This can be caused by injecting ions, by mechanicaldeformation, or by increasing the electrical fluctuations (or lowering thethreshold) due to molecular agitation (the effect being nonlinear). All ofthese effects work by applying mechanical forces to charged molecules in anelectrical field.

A very small change in the electrical potential, brought about by smallflows of ions against the gradient, can trigger the discharge of a much greaternumber of ions down the gradient. In terms of energy relationships, the productof triggered ionic flow and the discharge voltage differential is much greaterthan the product of the triggering ionic flow and the triggering voltagedifferential. The discharge is followed immediately by chemical reactions thatopen channels and force ions back against the gradient, restoring the originalelectromotive force and re-cockingthe neuron, making it ready for another discharge.

As a result, a very small energy input triggers the expenditure of a muchlarger amount of energy from metabolic stores. But it is not the energy inputthat causes the triggering; the physical cause is the force exerted on ionsagainst an electrical gradient. This process of exerting a force over adistance can be represented as an energy process, but the triggering effectcannot. The triggering must be explained in terms of balances of physical(electrical) forces independently of ionic flows.

One of the factors determining neural sensitivity is membrane capacitance.If there is a high capacitance, more ions must be forced up the gradient toeffect the required change in voltage. So the output of the neuron depends on apassive property of the cell as well as on energy input. The critical factor isnot how much energy has been input, but what voltage has resulted. Essentiallynone of the energy output comes from the energy input. Most of the energy in aneural signal is supplied by metabolism --by the pumping of ions against an electromotive force, by a greater force. Mostof the energy input is dissipated as heat or changes in molecularconfigurations. The triggering ions do not end up in the output axon.

In any case, it is not necessary to discuss energy to explain how a neuronworks. The energy relationships follow by definition from the underlying force-distancerelationships. No explanatory power is added by the more abstractrepresentation. The only gain is in explanatory convenience.

-------------------------------------

All this is just the tip of an iceberg. We have a fundamental disagreement,still, about what constitutes a "deeper" explanation of a phenomenon. In yourpost to Dag Forssell we find:

(Dag)

>> Bill's examples speak volumes to me about how things really workbecause he tends to stay at lower levels.

(Martin)

> "Higher" "lower" I'm really confused about what you mean. Bill usesspecifics more than deep causal mechanisms, which makes them easy to understandwithin the specific context of PCT and control generally. If you are happy withthat viewpoint, fine. I'm happy with it, too, but I like to see more as well.Just greedy, I guess.

What I am contending is that the more abstract representation lets us seeless deeply, or at least not more deeply. I do not equate abstraction withexplanation. Abstraction is simply substituting a function of several variablesfor the variables themselves. If the abstracting is done consistently, it canadd nothing to what the underlying variables tell us. If it is not doneconsistently, it is worse than useless --it introduces arbitrary assumptions, usually violations of the underlyingrelationships. When the abstractions become complex, such violations can easilypass unnoticed.

An example of what abstractions CAN do for us is seen in the way thedynamical equations for the jointed arm are developed. The most efficientcomputational method starts with a relationship equating potential and kineticenergy. Then this relationship is expanded into the underlying relationshipsamong accelerations, velocities, positions, and physical parameters of the armsegments. In the final solution, there are no energy terms; the arm behavior isexpressed entirely in terms of observables: functions of position andtime.

Of course the energy terms in the starting form are already completelydefined in terms of functions of force and position. The arm equations could bederived, in principle, without ever mentioning energy. But there are greatcomputational advantages, both here and in many other applications, in usingalready-developed energy expressions, and then expanding them into their actualmeanings.

A while ago I used the analogy of matrix algebra. Computing in matrixnotation is very much easier than handling the detailed additions andmultiplications required to solve a set of simultaneous equations. In mostcases it would be impossible for a person to perform the equivalent detailedoperations with pencil and paper, without mistakes or in a single lifetime. Butthe meaning of the matrix notation is nothing but those detailed operations,neither less nor more --whether or not we can intuitively see that this is true. When we program acomputer to do matrix operations, it does not actually do matrix operations: itdoes all the procedures implied by the matrix notation and conventions, down tothe last detail.

By the use of matrix algebra or calculus, we can arrive at results thatwould be humanly impossible to derive by any other means. This is the power ofabstract notation, abstract conceptualizations. But as I have pointed outbefore, the matrix algebra does not explain how the described system works anybetter than the detailed computations do. The two descriptions are --had better be --completely equivalent. There is no increase in explanatory power in theabstract approach.

-------------------

The risk in the abstract approach is that one can fail to connectabstractions to the most fundamental level in all of the required detail. Forany abstract treatment to be valid, it MUST be derived in a consistent way fromthe detailed representations that underlie it. And for validity in terms ofexplaining phenomena, it must derive from _observable_ relationships. At anypoint in a series of abstract computations, it should be possible to pause andexpand the abstract representation into its component detailed variables andrelationships. I have not seen this property in very many abstract discussions:at critical points, the reduction to underlying relationships tends to fade offinto vagueness.

----------------------

What I consider a deeper explanation is one that treats observables as ifthey were abstractions from a more detailed level of description. This is whatmodel-makingis about, as I think of it. The problem in model-makingis to propose a deeper level of description (inventing entities andrelationships as required) that, if it were observable, would explain what wesee at the available level of description. The method of abstraction, as Itried to say yesterday or the day before, works in the opposite direction: ittreats observations as the arguments, and invents functions of those argumentsthat create higher-levelvariables. The states of higher-levelvariables depend on the observations. In the method of modeling, theobservations are treated as if they depend on the behavior of a deeper level ofvariables --as the behavior of protons depends on the behavior of quarks.

Best, Bill P.

Date: Tue Jan 18, 1994 1:39 pm PST

From: tbourbon

Subject: RE: Clarity

Dag [direct],

> I got your note and Martin's response at the same time. Of course hewill defend his self. Perhaps he got it, perhaps not. I still say what'sdimly said is dimly thought.

I just read his reply. I will say that he is a skilled debater. And he iscorrect to say that PCT and CSG-Lshould not become an ossified orthodoxy, devoted to the worship of WTP. But Idon't think there is much danger of that anyway.

Beyond that, he has yet to post *any* demonstration, in the form ofmodeling, that information theory, entropy, bandwidth, or any other term helikes to use, in any way improves upon any prediction by PCT, or thatinformation theory leads, necessarily, to PCT. Any time he is pressed on thematter of lack of evidence, he backs off, changes the subject, and asserts theimportance of other ideas he holds. I cannot assert, out of hand, that he hasnothing important to say. Neither can I say the opposite. Sometimes it becomesvery frustrating.

> I would like to see the net respond to Ed's postings instead ofMartin's about vortices. Ed told me the other day on the phone, he isconsidering dropping off the net, for lack of interest in applications. Idon't think he will. He was tired. Why are so few netters interested inapplications? Why are so few trying to use PCT on the net? (My post was notPCTish, that's for sure).

Applications have all but disappeared, haven't they?

Glad to learn that your family made it through the earthquake!

Later, Tom

Date: Wed, 17 May 1995 05:24:50 -0600

Subject: Friction

Hello, Martin -- (no CCs)

I have become increasingly frustrated with our communications and have beentrying to figure out what is wrong. In the middle of the night a possibilityoccurred to me. A bit of browsing through the archives --not exhaustive --has brought up a number of topics all of which have led me to the samefrustration with your approach that I am currently experiencing. The ones Irecall now, which are probably not all of them, are (in no particularorder)

----------------------------------

Information about the disturbance flowing through the perceptual signal toenable control to take place.

The perceptual function composed of an S-shapedresponse followed by an integrator.

A discussion on bandwidth in relation to maximum realizable gain in acontrol system.

The "bomb" effect.

Flip-flopsor cross-connectionsas explanations of category perceptions, association, contrast.

Categories as existing parallel to the analogue hierarchy.

Control system organization as being a model of the environment.

----------------------------------

I finally realized that there is a common element in your treatment of allthese subjects. It is very much like the way you took off on the basis ofassuming that my limitation of the disturbance magnitude in Hans' set ofdisturbances was due to insufficient output strength in my model, which in turnwas caused by too short a word length. Having assumed the truth of your premisewithout particularly checking to see if it was true, you then built a series ofplausible deductions from the assumption, which happened to support a generalprinciple you were trying to get across. Unfortunately, the premise was false.I would not be surprised, however, if you decided that even if the premisehappened to be false in that case, the deductions you made from it wereprobably true.

In each of the above subjects, you began with a theoretical possibility anddeveloped it just far enough to see some possible implications of it. Then youquickly built a plausible and ever-more-detailedseries of deductions from those implications, and arrived at what seemed to youan interesting new phenomenon. You could see in your mind's eye how the Bombwould sit there ticking, ready to go off if the right combination ofdisturbances occurred. You could imagine information flowing from thedisturbance through the perceptual system to the output, where it got used upin producing the effects that would counteract the disturbance. You could seethe s-shapedcurves and integrators acting like a perceptron for the input part of a controlsystem. You could see a whole hierarchy of discrete categories with hysteresis,running in parallel to the analog hierarchy. And the fact that you could see inprinciple how certain other phenomena might flow from the initialconceptualizations was enough to convince you that the initialconceptualizations must be correct.

So what happens is that the tail wags the dog: the attractiveness andrichness of the conclusions drawn from the initial assumptions convinces youthat the initial assumptions must have been right. And once that has happened,you forget completely that the initial assumptions were never established astrue, and you speak of the conclusions as if they were now established facts;you even start using them to prove other conclusions.

The name of this type of reasoning process, or one name, is of course"mathematics." In mathematics (including logic, or is it the other way around),it doesn't matter whether the initial assumptions are factually true or in someway supportable by evidence. The assumptions are simply the initial process ofsetting up the chessboard with a problem, so you can work out a solution to it.Once the field of play is established, you can then start working out thetheorems and proofs, encountering beauty and entertainment at many stages alongthe way. You begin to get a feel for the system you have created, so its majorconclusions become familiar parts of that conceptual world. These majorconclusions become theorems on which to build further; they get names like"information about the disturbance" and "The Bomb" and "cross-connections."Since they have been derived by correct reasoning from the premises, there isno reason to doubt them any more; they become real. The premises drop out ofsight; they were never very important anyway, except as a way to get the gamestarted. The real fun is in building the structure of ideas on thosepremises.

Judging from various comments you have made about your interests andpreferences, I don't think that this is a completely inappropriate assessmentof your modus operandi. Your approach is not the engineering approach to aphysical system, but the mathematical-logicalapproach to a hypothetico-deductivesystem.

This hypothesis explains to me your disdain for "mere demonstrations." Ifyou have worked out the logic correctly, what is the point in doing an actualdemonstration of it, and doing different demonstrations to bring out one pointor another? If you understand addition, what is the point of demonstrating that9 + 1 = 10, and 8 + 2 = 10, and so forth? If you understand the completestructure of information theory from Shannon on up, what is the point indemonstrating what you already know to be true: that the signals inside acontrol system must contain or pass along information about the disturbance,and that it is this information that makes control (and everything else)possible? And most important, if you have shown that there are no logicalerrors in reaching a conclusion about real behavior, what is the point in goingthrough the labor of showing by direct experiment that the conclusion actuallyfits the data? If the data do not agree with the conclusion, there must havebeen some error or something unaccounted for in the experiment.

That last if-thenis the only way I can explain your reaction to difficulties when we actuallytry out some of your proposals. In the long information-in-perceptiondebacle, we tried computing the reduction in the uncertainty in the perception,then in its first derivative, then both again with temporal shifts, and inevery case the results disagreed with your deductions about what we shouldfind. By rights, this should have brought you up short and caused you toquestion the very basis on which you built your deductions. But that didn'toccur: you simply abandoned the attempt to make a correct deduction that wouldfit the data and turned to other subjects.

If I had been in your shoes, I would have had to backtrack through thelogic trying to find the error, and eventually (if no logical mistake could befound that would fix the problem) I would have gone all the way back to thesimple starting premises on which the whole logical structure is built: ifthere are no mistakes in the logic, yet the conclusions do not fit observation,then the only place left to find an error is in the premises. And for me,however painful the decision, the only conclusion I could then reach is thatthe entire system is built on false-to-realitypremises.

When I went through the process of computing reduction in uncertainty aboutthe disturbance due to the perceptual signal, under your tutelage, I noticed afact, and mentioned it, that seemed significant to me. In the process ofcomputing the conditional probabilities, I noticed that I would get the sameconditional probabilities no matter in what order I did the sampling of thedisturbance waveform. So in principle there was an infinity of differentwaveforms that would allow me to compute the same quantity of information inthe perception. This made it very hard for me to see how the outcome could bean output waveform based on the "information" that was arranged in the samesequence as the elements of the disturbance waveform, which of course isnecessary if the effect of the disturbance is to be canceled.

Your reply was brief and dismissive: you just compute the conditionalprobabilities on pairs of successive values of the waveform, and get theprobabilities of the first derivatives. But after thinking that over, Irealized that the same problem still existed: one could rearrange the pairs andget the same conditional probabilities. So how could the information passed inthe perceptual signal possibly be responsible for producing the RIGHT outputwaveform?

When I mentioned this (I am pretty sure I mentioned it), there was no replythat I recall. The failure to get the right results when we used the firstderivatives as elements, even time-shifted,reinforced my doubts about the process, but not being an expert in informationtheory I did not feel competent to ferret out the cause of the problem.

I now realize that you did not search for the cause of the problem bybacktracking through information theory. You just gave up on it. This did notsolve the problem, but it left the intellectual structure of information theoryin your head undisturbed. If PCT is correct, we can use this phenomenon toguess at the nature of the variable you were --and are --controlling.

I remember getting a frantic phone call from Chris Love shortly after thestart of the Little Baby project. He had tried to set up a big complexhierarchy of control systems in which, per the boss's suggestion, theperceptual function was an S-shapedcurve followed by an integrator. The reason he called was that he hadn't beenable to get even a single elementary control system to work. I tried to explainto him that a control system organized that way would be trying to control avariable that was the inverse function of the proposed form, namely a nonlinearfirst derivative that went to infinity at zero and maximum perceptual signal.He was not then knowledgeable about control theory, so I just suggested that hemove the integrator to the output function, and preferably make the inputfunction linear. He tried that, and got a working control system for the firsttime, several months into the project. I felt very sorry for Chris, because hehad to try to make the suggested model work, and it could not work.

On other occasions, I have pointed out to you a shortcoming of theperceptron approach, in that it doesn't yield perceptual signals which arecontinuous representations of controlled variables. The nonlinearities andother properties limit the output to a yes-nosignal, which is good only for discrete control. However, in the fairly recentpast, I noticed that you were still referring to the S-shapedinput function with an integrator as part of the model. Chris' problems do notseem to have shaken your faith one bit. Or perhaps they have simply led you toabandon that problem, and go to modeling discrete systems. Obviously it has notled you to re-examinethe premises behind the perceptron approach.

--------------------------------------

I think that in deciding to be an abstract theoretician, you have simplycut off your higher level systems from lower-levelperceptions, operating the higher-levelsystems in the imagination mode. And I think that this is a mistake. If youdon't continually check your higher-levelmodels against experiences by interacting with the outside world at the lowestlevels, you run the risk of creating a systematic delusion about the nature ofthe world; one that is internally consistent, but which is not consistent withwhat your senses could tell you if you consulted them. Abstract thought aloneis simply not a reliable way to learn about nature.

This is why I am so adamant about demonstrations and experiments. You haveto close the loop through the external environment if you're to achieve realcontrol. No matter how self-evidentor obvious or logically necessary a conclusion may seem, it is still necessaryto find a way to test it by interacting with the world. And when you do suchtests, it is necessary to pay attention to the outcome, because if the outcomesdon't agree with the logic, it says that something is wrong with the logic orwith the premises on which it's founded. No matter how convinced you are thatyou have the right idea, nature is perfectly capable of contradictingyou.

And this says something else, too. It says that there is really very littlepoint in building up big deductive structures on premises that have not beenexperimentally demonstrated. Your cross-connectionideas about category perception may prove to be quite right, but you have noway to verify that such cross connections exist or work in the ways you assumethey work. Technology has simply not reached the stage where we can do this ina living working brain. Perhaps it would be possible to do experiments tocheck, at least, the conclusions, to see if people actually work in the waythat your hypothetical model works. But unless you can also check the premises,you are on very uncertain ground. For any circuit that accomplishes a givenresult, there are a dozen different ones that would do the same thing. Therewill always be uncertainties in our models, but why deliberately make them aslarge as possible?

---------------------------------

I have no illusions about changing your style to correct what I see asmistakes. What you make of what I say is in your hands alone. But if you wantto understand where our frictions come from, you have to know how I perceivethe way you work, and how limited it looks to me. You have to understand thateven where you think you see agreement, you may be considering only a narrowrange of meanings of what I or others say, meanings that fit your world-viewbut that may only represent one point of intersection of trajectories that areheaded in different directions. And you have to realize that you often readhastily, making assumptions that a more careful reading would quickly setstraight and then leaping ahead to draw unwarranted conclusions --largely, seeing agreement where there is actually no agreement, or only a verypartial agreement. This is another penalty for working in the imagination mode.You are far from the only person to work this way, of course.

Obviously, I have considered only YOUR problems, not my own. I am sure thatall of this looks quite different to you. If you want to turn the tables, youhave every right.

Bill

Date: Wed, 17 May 1995 10:28:00 -0600

Subject: Wrong address

[From Bill Powers (950517.1020 MDT)]

When I woke up this morning, I found that in the depths of the night I hadsend a direct post to Martin Taylor to CSG-Linstead. I hope my words were considered enough to withstand publicinspection.

Best to all, Bill P.

Date: Thu, 18 May 1995 07:40:50

{from Joel Judd 950518.0730 CST}

Bill P. (950517):

About 1/3 into your post to Martin, I had the uncomfortable feeling it wasa direct post. But since all you always act purposefully, I asked myself whythe post would be on the net. I think that given the amount of space devotedto the discussions you summarized and, more importantly, the number of peoplewho potentially read them, it was appropriate for you to state explicitly howyou view what has been said.

It was helpful to me, at least.

Joel Judd

Date: Sun, 21 May 1995 22:18:31 -0400

Subject: Martin, Knowledge and belief

[From Dag Forssell (950521 1900)]

Bill Powers on Friction, Wed, 17 May 1995 05:24:50 -0600,

Joel Judd 950518.0730 CST

> I think that given the amount of space devoted to the discussions yousummarized and, more importantly, the number of people who potentially readthem, it was appropriate for you to state explicitly how you view what has beensaid.

I agree with Joel that it was appropriate and valuable that Bill's post goton the net. I have read Bill's post three times. I think it is valuable onmore than one level.

Addressing Martin, I think it parallels a post on clarity [Dag Forssell(940113 1700)], where I vented my frustration with reading Martin's posts andblasted him for his reluctance [as I saw it] to stoop to kindergarten physics.I suggested that

> I get the impression that your systems concepts have lost touch withthe principles that created them, [I might have said: observations on whichthey were based] and that this creates difficulties for you to expressyourself and others to understand you. . .

Bill notes that his post is only an expression of his perception offriction and imagined reasons for it; Bill's guess, reasoning from theprinciples of PCT.

I think Bill's post is even more valuable if it is read as a discussion ofbelief and knowledge in the context of the recent thread on CSGnet.

When discussing belief versus knowledge, it is easy to think of religionand belief in GOD as a prime example of belief without possible verification.That, and the great variety of religious beliefs, is in fact a good example,but it is far from the only one or necessarily the most significant one.

To recognize the significance of the discussion of belief versus knowledge,it behooves us to notice how much of our culture, interpretation of history[written by victors and survivors], trade relations [understanding of foreigncultures and their values], eating habits, expectations of career success[employer appreciation and loyalty], and even sciences are based on stories andbeliefs derived from them. We have a mixture of verifiable knowledge andunverifiable belief in every subject area. Since knowledge and belief look thesame from inside -- both are made up of stored memories at the program,principle and systems concept levels -- I am totally oblivious to thedifference between what I think I know and what I may only believe. I mayharbor as many unfounded prejudices, unwarranted assumptions, and gullibleinterpretations of things I have experienced as the next guy. But I cannottell which is which without great effort and a willingness toreorganize.

Bill's post to Martin really addresses all of us and gives us all reason tostop and think. The challenge Bill throws down before us is to be willing tobacktrack and question everything to the basic premises; to test and verifyevery program, principle and systems concept against experience as much aspossible.

Best, Dag