Dynamical Systems Theory is efficient, not sufficient

Written by hand in a COG250Y1 (Introduction to Cognitive Science) term test on February 3, 2025. Edited here for grammar and clarity; the argument is unchanged.

Thesis: while Dynamical Systems Theory provides an efficient way to achieve intelligent behaviour, it is not powerful enough to explain human-level intelligence.

Dynamical Systems Theory (DST), as exemplified by the Watt governor, provides an intriguing way to explain cognition: one that is energy-efficient, simple in its constructs, and highly complex in its behaviour compared to the simplicity of its internal structure. Set against the GOFAI model of cognition, which relies heavily on internal representation of knowledge, DST achieves an impressive range of capabilities with near-zero internal representation, and so offers a route to intelligence that is cheap in storage and in computation.

The Watt governor

To better understand the advantages DST provides, we can formalize a dynamical system as two components: a state $S$, and a transition function $F$ that converts one state into its next without knowledge of any previous state. In the Watt governor, the state is a collection of the flywheel speed, the steam speed, and the configuration of the physical structure. The transition function takes the current combination of those and updates it using simple physical rules, the kind that fit in a short formula. The result, however, is significant: the flywheel speed is well balanced through the feedback loop without any explicit knowledge of “balance”, “speed”, or “acceleration”, whereas a GOFAI approach would program a great many conditionals to examine the speed and use logic to compute the change of speed needed.

In that example, DST exhibits its efficiency precisely through its avoidance of abstraction and internal representation. Human-level intelligence, however, requires language, logic, and mental representation, which calls into question whether DST can explain minds like ours.

Language and logic

“Every human is an animal; Socrates is a human; therefore, Socrates is an animal.” This simple argument exemplifies the use of logic in language. To understand it correctly, one must understand the internal logic relating the three components, which relies on concepts like “human”, “animal”, and “Socrates”, and on logical operators like “every” and “is”. Given its lack of internal representation, it is impossible for DST to process abstract concepts and logic, since these require a memory that can be operated on while an arbitrarily given logical expression is being processed. Yet logic evidently exists in language, and humans use it effectively when they speak. DST’s lack of logic processing therefore challenges its candidacy as a plausible explanation of human-level intelligence.

Thinking about the future

Humans have the capability to plan for the future, which relies on manipulating mental representations of objects. DST, by contrast, has no way to store such representations, because its simplistic structure allows only a fixed number of variables in each state. That absence presents a substantial challenge to explaining human-level intelligence: DST does not provide the same flexibility to store and manipulate arbitrary input from the external environment, which makes it incapable of “thinking about the future”.

Alternative: a complement to existing models

While DST holds a significant advantage over earlier computational models through its low reliance on representation, its energy efficiency, and its speed, it lacks the components necessary for human-level information processing. It can still be useful, though, as part of a subsumption architecture for human cognition. It cannot account for the higher-order cognitive functions of the mind, but it can offer a plausible account of the motion systems, given that we do not “compute” our walking steps or our balance. Those lower-level functions are integral to cognition as a whole, as evidenced by the extended mind theory, and DST can work with the existing neural network approach to help us better understand cognition.

Conclusion

DST provides an efficient alternative to earlier computational models that relied on internal representation. But that same lack becomes a disadvantage as soon as the task is explaining human-level intelligence. Dynamical Systems Theory is simple, and it works as a complement to the neural network model in explaining human cognition. It does not provide a better explanation of minds: the lack of internal representation significantly hinders DST’s ability to process language and logic, as well as to store and manipulate a mental representation of the world in order to plan for the future. As both capabilities are central to the explanation of human-level intelligence, lacking them leaves DST unable to explain minds like ours on its own.