In the traditional
computational approach,
representations are viewed as static structures of discrete
symbols.
Cognition takes place by transforming static symbol structures in
discrete, sequential steps.
Sensory information is transformed into symbolic inputs, which produce symbolic outputs that get transformed into
motor outputs. The entire system operates in an ongoing cycle. What is missing from this traditional view is that human cognition happens
continuously and in real time. Breaking down the processes into discrete time steps may not fully
capture this behavior. An alternative approach is to define a system with (1) a state of the system at any given time, (2) a behavior, defined as the change over time in overall state, and (3) a state set or
state space, representing the totality of overall states the system could be in. A typical
dynamical model is
formalized by several
differential equations that describe how the system's state changes over time. By doing so, the form of the space of possible
trajectories and the internal and external forces that shape a specific trajectory that unfold over time, instead of the physical nature of the underlying
mechanisms that manifest this dynamics, carry explanatory force. On this dynamical view, parametric inputs alter the system's intrinsic dynamics, rather than specifying an internal state that describes some external state of affairs. These networks were proposed as a model for
associative memory. They represent the neural level of
memory, modeling systems of around 30 neurons which can be in either an on or off state. By letting the
network learn on its own, structure and computational properties naturally arise. Unlike previous models, “memories” can be formed and recalled by inputting a small portion of the entire memory. Time ordering of memories can also be encoded. The behavior of the system is modeled with
vectors which can change values, representing different states of the system. This early model was a major step toward a dynamical systems view of human cognition, though many details had yet to be added and more phenomena accounted for.
Language acquisition By taking into account the
evolutionary development of the human
nervous system and the similarity of the
brain to other organs,
Elman proposed that
language and cognition should be treated as a dynamical system rather than a digital symbol processor.
Neural networks of the type Elman implemented have come to be known as
Elman networks. Instead of treating language as a collection of static
lexical items and
grammar rules that are learned and then used according to fixed rules, the dynamical systems view defines the
lexicon as regions of state space within a dynamical system. Grammar is made up of
attractors and repellers that constrain movement in the state space. This means that representations are sensitive to context, with mental representations viewed as trajectories through mental space instead of objects that are constructed and remain static. Elman networks were trained with simple sentences to represent grammar as a dynamical system. Once a basic grammar had been learned, the networks could then parse complex sentences by predicting which words would appear next according to the dynamical model.
Cognitive development A classic developmental error has been investigated in the context of dynamical systems: The
A-not-B error is proposed to be not a distinct error occurring at a specific age (8 to 10 months), but a feature of a dynamic learning process that is also present in older children. Children 2 years old were found to make an error similar to the A-not-B error when searching for toys hidden in a sandbox. After observing the toy being hidden in location A and repeatedly searching for it there, the 2-year-olds were shown a toy hidden in a new location B. When they looked for the toy, they searched in locations that were biased toward location A. This suggests that there is an ongoing representation of the toy's location that changes over time. The child's past behavior influences its model of locations of the sandbox, and so an account of behavior and learning must take into account how the system of the sandbox and the child's past actions is changing over time. This CPG contains three
motor neurons to control the foot, backward swing, and forward swing effectors of the leg. Outputs of the network represent whether the foot is up or down and how much force is being applied to generate
torque in the leg joint. One feature of this pattern is that neuron outputs are either
off or on most of the time. Another feature is that the states are quasi-stable, meaning that they will eventually transition to other states. A simple pattern generator circuit like this is proposed to be a building block for a dynamical system. Sets of neurons that simultaneously transition from one quasi-stable state to another are defined as a dynamic module. These modules can in theory be combined to create larger circuits that comprise a complete dynamical system. However, the details of how this combination could occur are not fully worked out.
Modern dynamical systems Behavioral dynamics Modern formalizations of dynamical systems applied to the study of cognition vary. One such formalization, referred to as “behavioral dynamics”, treats the
agent and the environment as a pair of
coupled dynamical systems based on classical dynamical systems theory. In this formalization, the information from the
environment informs the agent's behavior and the agent's actions modify the environment. In the specific case of
perception-action cycles, the coupling of the environment and the agent is formalized by two
functions. The first transforms the representation of the agents action into specific patterns of muscle activation that in turn produce forces in the environment. The second function transforms the information from the environment (i.e., patterns of stimulation at the agent's receptors that reflect the environment's current state) into a representation that is useful for controlling the agents actions. Other similar dynamical systems have been proposed (although not developed into a formal framework) in which the agent's nervous systems, the agent's body, and the environment are coupled together.
Adaptive behaviors Behavioral dynamics have been applied to locomotive behavior. Modeling locomotion with behavioral dynamics demonstrates that adaptive behaviors could arise from the interactions of an agent and the environment. According to this framework, adaptive behaviors can be captured by two levels of analysis. At the first level of perception and action, an agent and an environment can be conceptualized as a pair of dynamical systems coupled together by the forces the agent applies to the environment and by the structured information provided by the environment. Thus, behavioral dynamics emerge from the agent-environment interaction. At the second level of time evolution, behavior can be expressed as a dynamical system represented as a
vector field. In this vector field, attractors reflect stable behavioral solutions, whereas
bifurcations reflect changes in behavior. In contrast to previous work on central pattern generators, this framework suggests that stable behavioral patterns are an
emergent, self-organizing property of the agent-environment system rather than determined by the structure of either the agent or the environment.
Open dynamical systems In an extension of classical
dynamical systems theory, rather than coupling the environment's and the agent's dynamical systems to each other, an “open dynamical system” defines a “total system”, an “agent system”, and a mechanism to relate these two systems. The total system is a dynamical system that models an agent in an environment, whereas the agent system is a dynamical system that models an agent's intrinsic dynamics (i.e., the agent's dynamics in the absence of an environment). Importantly, the relation mechanism does not couple the two systems together, but rather continuously modifies the total system into the decoupled agent's total system. By distinguishing between total and agent systems, it is possible to investigate an agent's behavior when it is isolated from the environment and when it is embedded within an environment. This formalization can be seen as a generalization from the classical formalization, whereby the agent system can be viewed as the agent system in an open dynamical system, and the agent coupled to the environment and the environment can be viewed as the total system in an open dynamical system.
Embodied cognition In the context of dynamical systems and
embodied cognition, representations can be conceptualized as indicators or mediators. In the indicator view, internal states carry information about the existence of an object in the environment, where the state of a system during exposure to an object is the representation of that object. In the mediator view, internal states carry information about the environment which is used by the system in obtaining its goals. In this more complex account, the states of the system carries information that mediates between the information the agent takes in from the environment, and the force exerted on the environment by the agents behavior. The application of open dynamical systems have been discussed for four types of classical embodied cognition examples: • Instances where the environment and agent must work together to achieve a goal, referred to as "intimacy". A classic example of intimacy is the behavior of simple agents working to achieve a goal (e.g., insects traversing the environment). The successful completion of the goal relies fully on the coupling of the agent to the environment. • Instances where the use of external artifacts improves the performance of tasks relative to performance without these artifacts. The process is referred to as "offloading". A classic example of offloading is the behavior of
Scrabble players; people are able to create more words when playing Scrabble if they have the tiles in front of them and are allowed to physically manipulate their arrangement. In this example, the Scrabble tiles allow the agent to offload
working memory demands on to the tiles themselves. • Instances where a functionally equivalent external artifact replaces functions that are normally performed internally by the agent, which is a special case of offloading. One famous example is that of human (specifically the agents Otto and Inga) navigation in a complex environment with or without assistance of an artifact. • Instances where there is not a single agent. The individual agent is part of larger system that contains multiple agents and multiple artifacts. One famous example, formulated by
Ed Hutchins in his book
Cognition in the Wild, is that of navigating a naval ship. The interpretations of these examples rely on the following
logic: (1) the total system captures embodiment; (2) one or more agent systems capture the intrinsic dynamics of individual agents; (3) the complete behavior of an agent can be understood as a change to the agent's intrinsic dynamics in relation to its situation in the environment; and (4) the paths of an open dynamical system can be interpreted as representational processes. These embodied cognition examples show the importance of studying the emergent dynamics of an agent-environment systems, as well as the intrinsic dynamics of agent systems. First, the foundation of this dynamical system approach, the dynamical hypothesis in cognitive science, is based on a set of equations. This fact means that to describe each specific system, it is necessary to introduce data on its specific initial conditions: a specific dynamic system cannot be defined without primary data. Indeed, van Gelder's dynamical hypothesis in cognitive science regards the initial conditions. Even though a dynamical system tracks primary data less than it does internal dynamics, according to the hypothesis, it still needs external input of primary data. So, the dynamical system requires external data input to trigger it. Second, in light of the above difficulty, embodied cognitivists introduced the notion of dynamically embodied information. It refers to the pairing of a stimulus with the particular symbol saved in the sensorimotor neuro-structures and processes that embody meaning (sense). In a chaos of environmental stimuli, the link between specific stimuli and neural "patterns of activity" is unpredictable, owing to irrelevant stimuli that can be randomly associated with this embodied meaning. This bond is possible only when "the context of the system's structural coupling with its environment" has already been established, which is impossible for the naive organism in an unfamiliar environment. So, the evidence supporting embodiment abounds across the different sciences, yet the interpretation of results and their significance remains disputed, and researchers continue to look for appropriate ways to study and explain embodied cognition. The dynamical systems approach is not the only way to explain cognitive development in early-stage organisms. ==Mother-fetus cognitive model==