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

A paper of this title by Francis Heylighen (2022) provides a clear and informative review of the early misconceptions about goal seeking and maintaining in biological organisms that led to the rejection of purposive behavior as a respectable scientific concept, subsequent attempts to provide a scientific account for purposive behavior, and current accounts based on system dynamics. I particularly like Heylighen’s explanation of why equilibrium systems such as a marble rolling to the bottom of a bowl do not qualify as purposive: Purposive systems must draw on external energy sources to power their disturbance-opposing actions, equilibrium systems do not.

Another feature of Heylighen’s discussion is his use of phase diagrams to convey the properties of dynamic systems, especially those systems that create basins or attractors in phase space-- states toward which the system will evolve over time from given initial states. (He takes panes to note that attractors are not forces that pull the system toward themselves but rather the states toward which the system evolves. Disturbances move the system trajectory to other states, but so long as those states lie within the same basin, the system will continue to move toward the same attractor if the disturbance is not so strong as to overcome the system’s opposing actions. You learn some interesting things about what such diagrams can tell you from Heylighen’s exposition.

To illustrate some of the information one can extract from a phase diagram, I’ve posted a video of a simulation I wrote back in 2015 of a mass-spring-damper dynamic system. A force acts for a few seconds to compress the spring, causing the spring to undergo damped oscillation; when the force is removed, the spring returns to its uncompressed state via another series of damped oscillations.

I’ve posted two videos of the simulation. In the first, live time-series graphs depict the position, velocity, and acceleration of the mass over time.
shown here:

In the second, the time-series graphs are replaced by a phase diagram that plots velocity as a function of position.
see here:

You can download a preprint of Heylighen’s paper here:
Heylighen (2022)

Bruce A.

1 Like

Thanks Bruce!

You’re welcome, Warren! If you haven’t already, check out the paragraph beginning at the bottom of page 20 of Heylighen’s (2022) paper; it might make your day…

I think the mention of PCT here gives a very misleading impression of what PCT is about. PCT explains the controlling that is seen as the behavior of living systems. The “goal-directedness” of controlling results from negative feedback processes that are are quite different than those that produce the goal-directness of dynamical systems.

PCT shows that a central feature of the goal-directedness resulting from negative feedback processes is that they are organized around the control of perceptual input variables. So understanding the goal-directedness of living systems involves determining the perceptual variables that these systems control.

This extraordinarily important point about the goal-directedness of living systems – that it involves the control of perceptual variables – is completely ignored when goal-directed behavior is seen as equivalent to that of a dynamical system.

A dynamical system is a system of variables that undergo changes over time. A familiar example is the motion of a ball free-falling in the earth’s gravitational field; the ball’s acceleration, velocity, and position all vary over time as the ball drops. System dynamics is the analysis of dynamical systems via mathematical formulas. Techniques used in analyzing dynamical systems of equations include, among others, mathematical analysis (e.g. calculus) computer simulation, time-series plots, Fourier analysis, and phase portraits.

In tracking studies, we typically display a time-series plot showing how perception, error, output, and disturbance variables changed over time during the experimental run. But this is not the only way we could display the results. In the mass-spring-damper simulations I referred to previously, by pressing a radio button the user could switch the graphical display from a time-series view to a phase diagram (also called a phase portrait). The phase portrait shows the system spiraling down toward the position where velocity is zero. The spiral occurs because the damper is draining energy from the system. This is one example of how a phase portrait can help the viewer to understand the behavior of the system over time.

Vensim is an example of a computer application that makes it relatively easy to simulate dynamical systems and analyze their behavior, and contains some mathematical procedures for finding “best-fitting” system parameters. Bill Powers used Vensim to fit system parameters of a control system to data and found that it did a better job than the “ecoli” search method he used to fit parameters to data.

In discussions of reorganization using the ecoli method, Bill Powers has talked about the “landscape” of parameters that the method must explore in order to find a set of parameters that will provide a good fit to the data in the sense of minimizing the squared error (least squares criterion). You can visualize this landscape as containing hills and valleys, with the optimal least-squares solution finding the deepest valley. But if the parameter landscape is complex, there will be many valleys, some deep, some shallow, some wide, some narrow. Depending on where on the landscape the search for optimal parameters begins, the search may lead to a relatively shallow valley in which the search becomes “stuck.”

Now here’s the kicker: The parameter landscape is nothing more than a phase portrait and the valleys are what are termed “attractors.” The landscape does nothing more than describe the behavior of the system (with respect to the size of error) as it moves through parameter space. Note that attractors are not forces that “attract” the system to a lower error state, they simply describe how ecoli reorganization will proceed from given starting points, given the data and the specific control system model whose parameters are being fitted. Phase portraits describe a dynamical system’s behavior. They do not propose a mechanism to explain this behavior. That mechanism is supplied by the system of variables that is put in motion to produce the behavior being diagramed.

It can now be seen that the above statement is incorrect. Control systems are just a particular kind of dynamical system; consequently, they cannot be “quite different than those that produce the goal-directness of dynamical systems.”

I think what you are worrying about is that dynamical systems include not only control systems, but other systems that may appear to produce goal-directedness. A nice example of this is the mass-spring-damper system of my simulation. The phase portrait of this system spirals down to a point attractor, giving the appearance that the system had the goal of arriving there. But this is merely an equilibrium system, not a control system, spiraling down to a minimum-energy state. Heylighen does a nice job distinguishing an equilibrium system from a control system, noting that control systems use energy from a source external to the system to resist the entropy-increasing effects of disturbances:

“For example, a ball that rolls down into a bowl will come to rest in the lowest point at the bottom of the bowl, having dissipated its energy of motion through friction. It does not matter where in the bowl (initial state) the ball started its trajectory: the end point will always be the same equilibrium state of minimal potential energy. This type of equifinality is not what we would intuitively see as goal-directedness, though.”

“This problem can be avoided by demanding that the final state would be a steady state “far-from-equilibrium”, i.e. a state that requires active intervention and a continuing flow of energy to reach and maintain. Indeed, life is a far-from equilibrium condition, and organisms cannot survive without a constant source of energy to keep their metabolism going.”

I like Heylighen’s discussion of phase portraits because he shows how useful they can be toward understanding a system’s behavior. For example, a control system will remain stable only so long as disturbances are not strong enough to overwhelm the system’s ability to compensate for them via its output. Cases in which disturbances can overwhelm the system are shown in the phase portrait as regions outside of the system’s attractor basin. Furthermore, a broad basin indicates a wide region of possible disturbances that the system will successfully compensate for. (See the paper for further insights into the information that can be extracted by viewing phase portraits.)

I strongly recommend reading Heylighen’s (2022) paper to those who are interested in expanding their knowledge of the philosophical problems that for millennia impeded progress in understanding the goal-directed nature of human and animal behavior, of the history of attempted solutions to the problem, of some current solutions, and of the use of phase diagrams in the analysis of dynamical systems.

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.