# on modelling

**URL:** http://discourse.iapct.org/t/on-modelling/14462
**Category:** CSG1996
**Created:** [March 6, 1996, 12:38pm UTC](http://discourse.iapct.org/t/on-modelling/14462 "1996-03-06T12:38:46Z")
**Posts on this page:** 1
**Page:** 1

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### Author: ![HANS\_BLOM2](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/h/f17d59/32.png) [@HANS\_BLOM2](http://discourse.iapct.org/u/HANS_BLOM2)
#### Post date: [March 6, 1996, 12:38pm UTC](http://discourse.iapct.org/t/on-modelling/14462/1 "1996-03-06T12:38:46Z")

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[Hans Blom, 960306c]

(Bill Powers (960305.0900 MST))

> Some nice posts, Hans, with which I find much agreement. But the  
> disagreements are always what call for the most words.

Thank you. And if we didn't have disagreements, there wouldn't be  
anything to talk about, would it?

> There is general problem in our discussions in the use of the word  
> "model".

Yes, as with any other word. Martin has answered this one already, and I  
agree with much that he says. I, too, look at a model in two ways: in the  
abstract, it is a mapping of some space (in the mathematical sense) onto  
another one, usually of a vastly decreased number of dimensions; in the  
concrete, as a set of laws or equations or hypotheses that provide a  
basis for predictions that test the implications of those hypotheses.

In the latter sense, I can combine those hypotheses into a computer simu-  
lation and observe what "falls out" in terms of "behavior". E.g. imple-  
ment those laws that you think describe E. coli behavior into a computer  
program and compare the movements of your simulated thing with the  
observed thing. If you have a close match, you have reached some "under-  
standing". The mapping, in this case, is to just a very few dimensions:  
position (center of gravity?) only. We do not map, for instance, the way  
in which the substructures of E. coli move. In this sense, a model is a  
simplification. If it didn't simplify, it would not be able to be a tool  
to reach understanding.

> A perceptual signal is a representation of some constructed aspect of  
> the external world, and so could be said to be a "model" of it.

Yes, in the sense of a mapping.

> But the signal does not represent the \_parameters\_ of the world -- only  
> the states of hypothetical variables that are affected by other  
> variables in the world.

Yes!

> On the other hand, the "model" in your adaptive filter scheme \_does\_  
> contain representations (although not perceptual representations) of  
> hypothetical \_parameters\_ attributed to the world.

On the other hand? Isn't that the same thing as you said above? We will  
never know the parameters of the world, only the parameters attributed to  
the world. There is always at least a transduction (mapping) between the  
two, and we can only know and use the output side of the transducer. But  
that may be enough.

> To make this as clear as I can, there is a (hypothetical) correspondence  
> between perceptions and variables in the outside world. There is a  
> (hypothetical) correspondence between the internal construction of a  
> modeling network and properties of the world. In the first case we have  
> a correspondence of \_signals\_ with \_variables\_ in the world; in the  
> second case we have a correspondence of \_forms of computations\_ with  
> \_properties\_ of the world.

Yes. The first are expressed in terms like force, position, distance,  
time, etc. Upon closer inspection, these are not "things" that exist in  
the real world but human concepts \_about\_ ... Yes, about \_what\_? The  
second are like the laws of physics that specify what we know about the  
\_relations\_ between the things of the first category. These laws are  
human inventions as well, usually with a huge reduction of dimensionality  
through the introduction of abstractions like "point mass", "center of  
gravity", "position", etc.

> So when "model" is used both to mean the signal-variable correspondence  
> and the computation-property correspondence, it really means two  
> different things.

Yes, but they go together. One would be useless without the other.

> There is a third use that comes up: the physical-computational structure  
> of a perceptual function is sometimes spoken of as if it is a model of  
> the world, too. But this hybrid usage is invalid, because there is no  
> property of the external world that corresponds to the computations  
> taking place in the perceptual function.

How deep should the model go? Sometimes we're satisfied with \_functional\_  
equivalences, where one "black box" can replace another one as long as  
the computations that they perform are equivalent. That is sufficient for  
some discourses -- at a higher level of abstraction -- but not, of  
course, when you're concerned with what is \_in\_ the black box. Just like  
in the HPCT hierarchy, one can "live" at different levels.

> Consider a simple photocell. The structure of this perceptual function  
> creates a correspondence between a light flux and an electrical current.

Is it that we \_assume\_ a light flux and \_measure\_ a current? Or that we  
\_measure\_ a light flux? What would be the difference? Watch out: this is  
a "deep" question...

> But in the environment, there is nothing corresponding to the structure  
> of the photocell. That is, in the environment there is no function  
> relating the light flux to something corresponding to the electrical  
> signal. So we should really treat a perceptual input function simply as  
> a transducer, which creates a representation of a hypothetical external  
> variable. The transducer is not a model of anything but itself. It is  
> (to speak as a naive realist) simply a way of transmitting the value of  
> an external variable to a position inside the perceiving system.

Yes, at least that's how engineers talk. Engineers are spoiled in this  
respect because they have created nice categorizations. A physiologist  
has slightly more trouble when you ask him exactly what it is that, say,  
a muscle spindle transduces.

> ... an adaptive model meant to work with a plant that is a mass on a  
> spring contains computational operations such as integration and  
> feedback which express the mass of the object, the spring constant that  
> produces a restoring force, and any coefficients of friction that may  
> exist. The model relates force and acceleration as the real object  
> relates force and acceleration.

Note that you're talking about the real object in terms of \_mapped\_ vari-  
ables (mass, spring constant, force). You're modelling it already as soon  
as you talk about it! No wonder the subsequent mapping (from your  
description of the "real" object to the model) is so simple!

> I think of a model as being a set of property-describing functions, not  
> a set of state-describing variables. A model of a spinal reflex does not  
> describe particular muscle forces or limb accelerations. It describes  
> functions which relate driving signals to muscle force, muscle force to  
> limb acceleration, limb acceleration to feedback signals, and so forth.

You need both. You cannot talk about functions that relate in some  
particular way if you don't talk about what the relation is between.

> I hope I've managed to get the point across.

What point? In other words: no. I sense in your discussion the presuppo-  
sition that you can talk about the real thing without modelling it. But  
that is impossible.

> It seems to me that many of your statements about the performance of  
> adaptive models, optimization, and so on rely to a large degree on  
> assuming a world that is mostly predictable.

Predictable isn't the correct word. Lawful maybe. Here I'm operating from  
the point of view of that philosopher who said that if he knew the  
positions and the speeds of all the particles of the universe, he could  
predict everything that would happen afterward. Note that this philoso-  
phical position implies that, with full knowledge, "feedforward control"  
would also work perfectly.

I do also know that this philosophical position is incorrect. Yet it is  
what I call a "useful lie". It is the point of view that science, most of  
all applied science, requires. So I also assume that what you call dis-  
turbance is not an inherent property of the outside world (above the  
quantum domain and on not too long time scales), but our incapability to  
model the outside world appropriately. In other words, once we have  
modelled the outside world perfectly, no (macroscopic) disturbances will  
be left.

If you argue the opposite position, I will agree with you, too. The  
concept "disturbance" is fine in case we have less than perfect -- or  
even simplistic -- models. Sometimes (often?) simple controllers may be  
adequate for a control job, due to the properties of the control loop  
through which disturbances are "controlled away". But here, again, I see  
a disturbance as a modelling error rather than a property of the outside  
world, as you seem to do.

> There is a general tendency in behavioral theorizing to overestimate the  
> reliability of the environment -- that is, to assume that consistent  
> effects can be obtained simply by producing consistent actions.

That is what science looks for. If a relation is not reliable, it is not  
a good "law". Science tries to discover laws and necessarily requires the  
position that the more reliable a relation, the better the law.

> For simple S-R theories, this assumption is vital, because what is  
> learned is an \_action\_, and if actions do not have reliable effects,  
> learning of actions becomes pointless.

Unless the model is perfect, maybe. But that might require modelling a  
large part of the world, besides the organism's reactions to it, and that  
could be too much in many cases. The control point of view is different:  
control can be adequate in many cases even if the model it is based on is  
extremely simple. In a PID controller, for instance, all the knowledge  
that is modelled about the object to be controlled are 3 parameters: the  
delay time (the time it takes before you notice any effect of an input  
change), the dominant time constant (which describes the time it takes,  
after the delay time, for the output to change to almost final value),  
and the gain (the final effect divided by the input change). Why? Well,  
many "plants" have additional nice characteristics that allow this scheme  
to work. It breaks down in other cases, such as non-minimum-phase plants,  
where a better model is required.

> I think that if you look carefully at any example of behavior, you will  
> begin to see disturbances where you saw none before.

And I think that if you look carefully at any example of behavior, you  
will begin to see modelling inadequacies where you saw none before.

> One thing you should consider about your model: the way you handled  
> disturbances actually gave the effect of real-time closed loop control

So now the basic difference might become clear: my model does not know  
about "disturbances". It assumes that the world is lawful, and that it  
can discover those laws. But it also assumes that it will not be able to  
build a perfect model, due to its inherent limitations. In its control  
actions, it uses the knowledge that it has acquired about the world to  
the best of its limited abilities. If the small artificial world that it  
lives in is so simple that it can be adequately modelled, behavior is  
nigh to perfect. The real surprise is that even if the model is far from  
perfect, some control quality is still possible. Reminds you of humans?

Greetings,

Hans

> **···**
>
> ================================================================  
> Eindhoven University of Technology Eindhoven, the Netherlands  
> Dept. of Electrical Engineering Medical Engineering Group  
> email: j.a.blom@ele.tue.nl
> 
> Great man achieves harmony by maintaining differences; small man  
> achieves harmony by maintaining the commonality. Confucius