The Meaning and Origin of Goal-Directedness: A Dynamical Systems Perspective

Yes, that’s what I was worried about and Heylighen does do a nice job of distinguishing equilibrium from control systems.

That’s fine. But I still think Heylighen’s paper isn’t of much use if one is interested in learning about PCT. A far better paper that deals with the same issues (but without the phase diagrams) is Powers’ 1978 Psych Review paper “Quantitative analysis of purposive systems”.

Best, Rick

Why not do both? Each provides useful information that is not available in the other.
Bruce A.

I figured that, given the “esteem” in which my opinions are held in this forum, I could get more people to read the Heylighen paper by suggesting that they not read it;-)

Best, Rick

RM: I now have a better reason for suggesting that people interested in learning PCT not bother reading the Heylighen paper. I re-read the abstract and found this comment a bit disturbing:

“We show that all these features [of goal-directedness as they define it – RM] can be explained by interpreting a goal as a far-from-equilibrium attractor of a dynamical system”.

So they are going to show how goal-directedness (which is what we call “control”) can be explained as the behavior of a " far-from-equilibrium attractor of a dynamical system". This will be done using dynamical systems theory (R. D. Beer, 1995; Sternberg, 2010; Strogatz, 2000), which they define as " a mathematical framework that generalizes and extends Newtonian mechanics, so as to be applicable to complex, non-linear systems with many components". This is not a control theory model and it can’t account for even the simplest examples of control. So the paper is, at best, a good example of how not to understand purposeful behavior (control).

Best, Rick

Yes. In the next sentence they describe how such a system behaves:
“This implies that perturbations that make the system deviate from its goal-directed trajectory are automatically compensated—at least as long as the system stays within the same basin of attraction.” I think you will agree that this nicely describes the behavior of a control system.

You are correct to say that system dynamics is not a control model. System dynamics is a suite of techniques (mathematical, graphical) used to analyze the behavior of dynamical systems. You create a dynamical system by writing a system of equations describing the system’s variables and their linkages. Examine its phase portrait. Does it include an attractor basin located far from equilibrium? If so, the system described by those variables and linkages is goal-directed. As Heylighen indicates in his paper, the systems that meet this criterion are control systems.

When you state that "systems dynamics . . . can’t account for even the simplest examples, I suspect you are confusing a particular analytic technique (examining phase portraits) with systems dynamics as a field of mathematics concerned with modeling and analyzing dynamic systems. To be clear: if you said that a time-series plot of control-system variables “is not a control theory model and can’t account for even the simplest examples of control,” you would be making the same kind of error.

I haven’t looked at the subject paper. I just note that nowhere in the first 10 messages of this thread is it noted that control loops (of which control systems are composed) have one special characteristic, which is their essential asymmetry. The gain on one side of the loop (reference to CEV) substantially exceed the gain on the other (disturbance to comparator).

No, I don’t agree. Rather than detail everything that’s wrong with the sentence as a description of control system behavior (which is almost everything) I’ll just write a corrected version using as much of their terminology as possible:

Perturbations that would make a controlled variable deviate from its reference state are automatically prevented from doing so by the output of the system that is controlling that variable — at least as long as the system has sufficient output gain; that is, as long as the system is able to produce sufficient output to compensate for the disturbance (see Taylor, 2022).

Then how is it an “explanation” of goal-directedness? Heylighen promised an explanation and gave us an analytic technique instead. But we don’t need no stinkin’ analytic techniques. We’re here (I thought) to understand (get an explanation of) the goal-directedness (purposeful behavior) of organisms. This site is dedicated (I also thought) to the assumption that the best current explanation of goal-directedness is the PCT model of behavior (and mind) developed by W. T. Powers, which comes along with its own analytic techniques that are appropriate for testing the model (because they recognize the existence of controlled variables; see Marken, 2021).

I think we should be talking about how best to test (and use) the PCT model rather than about how to use analytic techniques that are based on a lack of understanding of the nature of the phenomenon (purposeful behavior aka control) that PCT purports to explain.

Best, Rick

I introduced the Heylighen (2022) paper because I thought it would be of interest to PCTers, for several reasons:

  • It reviews the evolution of thinking about goal-directedness from the early Greek philosophers to the present time.
  • It concludes that goal-directedness should be understood as the product of control systems, which as Heylighen notes are closed-loop systems employing negative feedback to oppose disturbances that would carry them away from their reference values.
  • It mentions hierarchical control systems and references Powers in a positive light in that regard.
  • It places control theory squarely within the field of systems dynamics, which means that all the tools of systems dynamics (e.g., mathematical analysis, computer simulation, and graphical techniques such as time-series analysis and phase diagrams) can be applied to analyze, predict, and understand how specific examples of control systems will behave in given environments.
  • It has a nice discussion about what one can learn about control-system behavior by examining a given system’s phase diagrams (e.g., resistance to disturbance, behavior if disturbances exceed the ability of the system to resist them, presence of nearby hills and valleys that can affect the system’s stability if pushed to those regions.) In this regard, I noted that finding the best-fitting control-system parameters involves a search through such a landscape and can result in the search terminating in less-than-optimal parameters–a weakness of the “ecoli” strategy employed in most (if not all) PCT analyses aimed at optimizing those parameters for a given participant’s data.

Given all that, I believed that the information presented in Heylighen’s paper would be of interest to PCTers. I still do. For this reason I encourage interested parties to read the paper and make up their own minds about it.

Bruce A.

Of course. People should read Heylighen’s paper and make up their own mind about it. But since this is a discussion group that is ostensibly dedicated to understanding, testing, applying and promulgating PCT, I think it behooved me to point out the important ways in which Heylighen’s approach to understanding goal-directedness differs from that of PCT.

Best, Rick

Certainly not “all”. See my CSG2005 presentation of tests of three different approaches to fitting data from real control experiments at

To me, this statement defines as a discussion group opposed to science. It simply asserts that within this group, PCT must be taken as an incontrovertible truth, and any analytic methods not introduced by Powers must be eschewed as inappropriate to this basic fantasy.

Having now read the Heylighen paper, it is my opinion that some of its arguments fail, notably its total failure to consider that anti-catalysts exist as well as catalysts when discussing negative feedback’s non-existence in autocatalytic loops (the ultimate refinement of which is the formation of chemical control loops).

In its relevance to this group, I would also fault it (and Bruce) for not making clear that systems analysis describes what a system is likely to do. In no way does the analysis cause the system’s behaviour. The phase diagrams are useful in helping one visualize behaviours, but what makes things happen in ways described by the phase diagrams are things like energy flows and forces, not pretty pictures.

To me, the phase diagrams that describe control are well presented by Heylighen and by Bruce.

Apparently you didn’t notice that I said “I think we should be talking about how best to test … the PCT model”. If I were actually recommending that PCT should be taken as incontrovertible truth I certainly wouldn’t recommend that it be tested, since those tests might produce results that controvert the theory.

And I certainly wasn’t saying that “any analytic methods not introduced by Powers must be eschewed” as an inappropriate way to test PCT. I said that PCT can’t be properly tested using “analytic techniques that are based on a lack of understanding of the nature of the phenomenon …that PCT purports to explain”; the phenomenon of control.

Analytic methods that are the appropriate way to test PCT would be ones that recognize the fact that behavior is organized around the control of perceptual aspects of the environment – what are called controlled variables. There are probably many such methods, yet to be developed, that were not introduced by Powers.

Pertinent to this conversation I should mention that I just published a paper (with Richard Kennaway and Tauseef Gulraz) that explains why PCT can’t be properly tested using analytic methods that don’t recognize the fact that behavior is organized around the control of perceptual variables – controlled variables. And it also explains the basic approach to testing a theory that does recognize this fact.

Best, Rick

Martin, is this not clear enough?:

Bruce A.

The fallacy here is that the analytic techniques under discussion in this thread (Heylighen,2022) are NOT “based on a lack of understanding of the nature of . . . control.” They are techniques (such as phase portraits) for analyzing dynamical systems. Because control systems are dynamical systems, such techniques are appropriate for analyzing them.

I should have been more specific: The analytic techniques you describe are based on a lack of understanding of the controlling done by living systems, which involves control of many different types of controlled variables. These analysis techniques ignore the question of the type(s) of variable(s) that the organism is being controlled.

Recognition of the fact that the behavior of organisms is organized around the control of different types of perceptual variables is what distinguishes PCT from all the other applications of control theory in psychology. And as you surely know, control theory was being applied in psychology since at least 1947, well before the publication of B:CP.

I describe the difference between PCT and other applications of control theory in psychology in a review of a book on non-PCT applications of control theory to human behavior and in my chapter in the Handbook of PCT.

As they say, “that’s not a bug, it’s a feature”. You [RM] are asserting that if something applies everywhere, it therefore does not apply to PCT.

In my view, PCT is a science, not a fantasy in a world walled off from the rest of science. As a science, one of the features of PCT is that even the most complex of PCT hierarchies and social interactions among hierarchies all have their (to quote Eetu from years ago) “ways of being”, and their ways of being described. A two-dimensional phase plot is one way that sometimes is useful, in that it helps some people understand a bit more about what to expect of a simple control loop.

The concept of a “basin of attraction” does not apply usefully if the control loop is linear. It applies to a linear system, but there is only one basin, and that extends to infinity. The concept is more useful for non-linear systems, such as control loops that have a limit to how much force they can apply to the environmental variable that corresponds to the perceptual variable. Such a loop can be driven out of its basin of attraction by a strong enough force. And so forth.

Wrong again, Rick. They are not “based on” either an understanding or lack of understanding of control systems. They are “based on” system dynamics, which subsumes control systems.

I read the book review you linked to, which includes the following statement:
" we can use the tools of control theory (linear systems analysis, Bode plots and so on, which are described so well in Control theory for humans ) to evaluate how well this control is being carried out." You approve of these tools “of control theory” (more generally, of system dynamics). Yet you reject another useful system-analytic tool for visualizing control system behavior–phase portraits–by making spurious claims about them not being an appropriate technique for analyzing control systems.

Phase portraits simply describe a dynamic system’s behavior over time, based on a mathematical model of the system under analysis. If your model is that of a control system and its environment (including disturbances), then phase portraits based on the system’s variables will describe the behavior of the control system with respect to those variables. Such portraits can reveal interesting properties of the system, such as regions in which the system will stabilize at or near its reference value versus those in which it will go into oscillation or even behave chaotically. (You might observe such a portrait when varying the loop gain of the system or delays around the loop.) Given its usefulness in this regard, I am at a loss to explain your rejection of phase portraits for describing control-system behavior.

Nice paper, thanks Bruce, I liked the historical overview. I haven’t used phase diagrams in tuning control systems. I suppose I’ve used speed over time and position over time separately, I’ll give them a go sometimes.

What do you think about the Gaia hypothesis (p. 23)? There are dynamic system that receive external energy from the Sun, but are there control systems?

I was going to bemoan my persistent inability to be right when I realized that the system dynamics on which these analysis techniques are based are the dynamics of physical variables. So they work when the variables being controlled as the variables that are part of the physics model of realty. I’m pretty sure that these system dynamics no longer apply when we are dealing with systems that control variables that are complex functions of these physical variables; variables like the sequences and programs that are controlled in my demonstrations (here and here) of control of higher level perceptual variables.

I don’t reject any of the analysis tools you like; my complaint about your approach to understanding living control systems is that you leave out the most important analysis tool; the one that should be the first tool you use in the analysis of the behavior of a living control system: the test to determine the variable(s) it is controlling, if any.

Which is fine. I just don’t think they tell you much of interest unless you know what variable is being controlled. Which you probably do know pretty well in the case of the simple physical variables you are dealing with.

Thanks, Adam. I’ve long viewed the presence of life on Earth as a stabilizing factor, but I see it as establishing an equilibrium system, not a control system. There’s no reference value, not even an implicit one. In fact, at one point in Earth’s history the Earth was entirely covered with ice.

In this equilibrium system, pants and certain forms of bacteria break down carbon dioxide and release oxygen; animals and “decomposers” remove oxygen and release carbon dioxide. As carbon dioxide builds up in the atmosphere, plants flourish (up to a point, at least), increasing oxygen concentration and lowering carbon dioxide. As oxygen concentration increases (up to a point), animals flourish, taking up oxygen and increasing carbon dioxide concentration. Thus there is negative feedback between atmospheric oxygen and co2 concentrations. Similarly, increased atmospheric co2 raises the Earth’s surface temperature through the “greenhouse” effect; the resulting “hothouse” Earth increases plant production, reducing oxygen concentration.

I speculate that the difference between the fates of Earth (hospitable to life here) and Venus (Earth’s “twin” but a veritable Hell) may have been a failure of life to develop on Venus (or to develop sufficiently early enough) to counteract rising co2 levels. Instead, co2 levels continued to build, and that, together with the greater input of solar radiation, led to a runaway greenhouse condition, with surface temperatures on Venus now hot enough to melt lead.