Task 6-Dynamic systems, nonlinearity, discontinuity, cusp catastrophe, attractors, self-organization Flashcards
Dynamic systems:
A system whose changes depend on the previous values of involved variables
The problem with cognitive science: Assumption of proportionality and unimodality. Behaviors are not always smooth functions of their causes.
Unimodality = only 1 outcome without disturbances
Non-Iinear: a big change can occur suddenly
Bimodal: two initial states can lead to one outcome
Both felxible and stable
Behavior is constant and fluid
Explains real life mind well and stuff like sleep and mood
Butterfly effect
Butterfly effect: a small change somewhere might have a big impact somewhere else
Attractors
stable states that the system settles to (soft assembly to attractor states)
Phase Transition:
change from one attractor to another due to multiple attractors
Chaos
very small difference in values of variables can produce big different outcomes: abrupt unpredictable changes. = CATASTROPHE THEORY
Can be seen as a supplement to CRUM theory (T1) and simulated annealing (T2))
Global minimum is the ultimate goal state!
Cusp catastrophe
Sudden change in performance due to change in X,Y,Z
Control surface (top): Determines e.g. performance
Bimodal system: In the bifurication set bimodality occurs; various outcomes possible.
= Sudden change in behavior=Catastrophic jumps
catastrophe models characteristics
Hysteresis: „Sticking tendency“ (prior conformity = consistency)
Divergence: Different effects of splitting factor (depending on individual)
Splitting factor: outside influence (social pressure)
Self-organization without any executive agent
Nested timescales: behavior change occurs over different timescales that interact with each other
bifurcation set
that area of bimodlaity
bimodality
one combination of independent variables can have multiple dependant variables
divergence
different effect of splitting factor on behaviour in catastrophe theory
hysteresis
tendency to stick
nonlinearity
changes do not happen gradually , but in a discontinuous nonlinear way that includes destabilisation
have very erratic behavior, jumping from one point in state space to another in short period of time
Example: weather can change dramatically within couple of hours
state space
all different combinations of values or variables of a system a system can be in
set of states the system can be in as determined by the variables that are used to measure it
Example: weather model keeps track of temperature, humidity and air pressure at five locations has a total of 15 variables, so all different combinations of values of these variables can constitute state space
self organization
a structure / pattern emerges without specification from teh outside world / environment
dynamics system 2
system – a system whose changes over time can be characterized by set of equations that show how current values of variables depend mathematically on previous values of those variables
Example: weather (variables like temperature, humidity, air pressure)
• Many phenomena in physics, biology, and even economics can usefully be understood in terms of dynamic systems ideas such as state space, attractors, phase transitions, and chaos
Dynamic systems challenge cognitive systems
instead of understanding human thinking in computational-representation terms, we should think of mind as dynamic system
we should follow the successful example of physics and biology and try to develop equations that describe how the mind changes over time
Responses to Dynamic Systems Challenge
• Denial
Dynamic system is very limited in its application to human thinking
Connectionist models have been more precise, but connectionism is part of CRUM, not an alternative to it; so dynamic systems theory is best seen as just an adjunct to connectionism rather than as an alternative to CRUM
• Expand and supplement CRUM
Dynamic system embodies several aspects that are neglected in CRUM
Deals more gracefully with time than CRUM
CRUM (connectionist version) seems open to expansion and supplementation with dynamic systems ideas
approach might be useful for explaining nonrepresentational aspects of human behavior
mind is a dynamic system is not yet a credible alternative to CRUM, since there is so much about problem solving, learning, and language that is explainable with CRUM and that proponents of the dynamic systems approach have not even addressed Nevertheless, a full account of the nature of mind that incorporates human biology and interactions with the world may find it useful to draw on dynamic systems explanations
conflict attractors
states/patterns that unfold overtime in situations of conflict which resist change or which resume after changes have been initiated
People can have many different types of conflict attractors and move between them during progression of conflict
Conflict attractors are psychological, social and cultural patterns people display overtime in conflicts and to which they return after temporary changes occur
high resilience
high level of stability
Support for a complex systems perspective on psychopathology (foresee levels
• Sudden shifts in symptoms are observed in patients (abrupt symptom changes are quite common which is in line with the expectations from complex system theory)
• Verbal descriptions of patients suggest that sudden and discontinuous changes in their symptom experience may occur in the absence of an obvious, temporally proximal cause or reason
in line with complex system theory which predicts that when resilience becomes very low (can be due to distant causes) even minor disturbances can tip over the system to an alternative state
• Elements within complex systems are in a continuous and complex interplay with each other
in many complex systems reinforcing feedbacks are present that, if strong enough can push the system to another alternative state
such feedback loops are also likely to occur between mental states
people with higher levels of psychopathology have more pronounced feedback loops
• Transitions in symptom levels can be anticipated by directly assessing changes in the stability of the system
it is known that these changes in stability can be observed using certain “EWS”
if psychopathology also behaves as a complex system we may be able to find EWS that we can use to foresee important shifts in symptoms in an earlier phase and in a personalized manner
bridge system
symptoms that connect across boundaries
• Since bridge symptoms facilitate most of the communication between the clusters (syndromes) changes in the states of these bridge symptoms may be particularly good candidates for the prediction of the direction of phase transitions in psychopathology networks
specific patterns of connections between symptoms (like the EWS) may provide us with clues regarding the likelihood of a transition to a particular set of symptoms
development as dynamic system
multi causality (a not b error)
nestled timescale
Sensitive Dependence on Initial Conditions
• Characteristics of self-organization
readiness to exhibit:
1. multiple stable states that can change suddenly from one to another when a parameter value crosses a critical threshold
2. cyclical state changes
3. the structural coupling of component processes
4. temporal, spatial, and behavioral organization
5. localized instabilities that can lead one part of the system to organize itself differently from another part of the system
6. the ability of one unit to cause other units to oscillate at a harmonically related frequency (entrainment), and
7. behavior that can sometimes be modeled by a system of nonlinear equations
Psychological systems lack the precise temporal or spatial symmetry seen in physical systems and instead involve complex neurological structures and behaviors
some self-organizing properties can only be found in living things
hysteria (kim)
– impact of previous demand conditions on current demand conditions
hysteria (catastrophe model cusp)
The dependence of the state of a system on its history and the same set of current circumstances can produce very different behaviors
A change in behavior is not always reversible and a “sticking” tendency is known as hysteresis in physics
For example, if love and behavior start out low, there is a tendency for the behavior to remain low even though love has increased substantially
divergence
refers to differing effects of the splitting factor on behavior
Sometimes increases in the splitting factor increase the behavior and sometimes they decrease behavior
This is explained by conformity, that is conforming to the social pressure, or reactance to it
In the example above the splitting factor is social pressure
• The Newborn Stepping Reflex is an example of multiple systems in motor development:
Newborn infants, when held upright with their feet on a support surface, perform alternating step-like movements
Within a few months, these movements “disappear” and infants do not step again until late in the first year, when they intentionally step prior to walking
The traditional explanation of the stepping response was single-causal, but the insight that kicking and stepping had the same movement pattern refuted this view
According to the new view, movement arises from a confluence of processes + constraints in the organism and the environment
A change in posture is a change in the relationship between the mass of the body and the gravitational field and it requires more strength to lift a leg
Therefore, as infants’ limbs get heavier but not necessarily stronger, the reflex disappears by the confluence of increasingly heavy legs and a demanding posture
ome patterns are preferred under certain circumstances and act as Attractor States in that the system “wants” to perform them
Developmental change can be seen in dynamic terms as a series of states of stability, instability and phase shifts in the attractor landscape
