Task 6- M&M

Question 1

What are dynamic systems?

Answer 1

system whose changes over time can be characterized by a set of equations that show how current values of variables depend mathematically on previous values of those variables

Question 2

What is a state space of a system?

Answer 2

• set of states it can be in as determined by the variables that are used to measure it
• e.g. weather model that keeps track of temperature, humidity, and air pressure at five locations has a total of fifteen variables, so all the different combinations of values of these variables constitute the state space

Question 3

What does it mean if a dynamic system displays chaos?

Answer 3

if it is very sensitive to initial conditions, that is, if very small differences in values of variables of its equations can produce dramatically different outcomes as the system develops

Question 4

What is the butterfly effect?

Answer 4

butterfly effect: a butterfly flapping its wings in China may have a tiny effect on the atmospheric system there that eventually leads to a major weather change elsewhere

Question 5

What is the ‘dynamic systems challenge’ to cognitive science?

Answer 5

consists of the claim that, rather than understanding human thinking in computational representational terms, we should think of the mind as a dynamic system

Question 6

What are the two responses to the dynamic systems challenge?

Answer 6

1. Defender of CRUM could argue that the dynamic systems approach is very limited in its application to human thinking -> replace it
2. Expand and supplement CRUM

Question 7

What are linear dynamic systems?

Answer 7

Linear -> two or more equations whose solutions can be combined to obtain another solution; work well in physics but cannot always describe what happens in natural systems

Question 8

What is non-linearity? What are nonlinear complex dynamic systems?

Answer 8

complex dynamic systems need to be described by nonlinear equations such as y = xz, where the value of the variable y depends on interaction of values of x and z

Question 9

Which kind of behaviour can nonlinear systems show?

Answer 9

can have very erratic behaviour e.g. jumping from one point in the state space to another, very different point in a short period of time

Question 10

What does it mean that nonlinear equations are not additive?

Answer 10

1. Answers often involves pattern of solutions

2. Results feed back in system itself

Question 11

What usually happens to nonlinear systems over time?

Answer 11

Settling down (or convergence) -> results in 1 of 4 typical patterns

Question 12

What are the typical patterns called which nonlinear systems settle down into?

Answer 12

Attractors

Question 13

What is discontinuity a subcategory of?

Answer 13

Subcategory of nonlinear

Question 14

What characterizes discontinuity?

Answer 14

Sudden shifts; sudden or catastrophic jumps in behaviour

Question 15

What is discontinuity often preceded by?

Answer 15

by an increase in variability and destabilization/ loosing of old, previous pattern that can be followed by system reorganization

Question 16

What is a cusp catastrophe?

• Which type of system?
• What does it describe?

Answer 16

o One type of a nonlinear dynamic system
o Models of sudden and discontinuous change
o One of seven elementary catastrophe models that are developed

Question 17

Why was the cusp catastrophe model developed for?

Answer 17

to describe complex natural and social phenomena

Question 18

Which two kinds of variables does the cusp catastrophe model have?

Answer 18

two control variables (asymmetry variable and bifurcation variable)

Question 19

Explain the example of the interaction between physiological arousal and cognitive anxiety.

Answer 19

• cognitive performance better when stressed until a certain threshold is reached
• if threshold reached -> catastrophic downfall
• sudden behavioural change exhibited once predictor variables cross cusp threshold

Question 20

What are 5 features of the cusp catastrophe model?

Answer 20

1. Bimodality
2. Inaccessibility
3. Divergence -> not settling down
4. Hysteresis
5. Abrupt transitions

Question 21

What are attractors?

Answer 21

• Patterns a nonlinear system tend to settle down into

- Relatively stable states

Question 22

Does a system only have one attractor?

Answer 22

No, a system may have multiple attractors ( more than one stable state)

Question 23

What is a phase transition?

Answer 23

change from one attractor state to another constitutes a phase transition e.g. when the weather moves from being cool and clear to being hot

Question 24

What are the 4 types of attractors?

Answer 24

(A) Point Attractor, (B) Cyclical or Oscillating Attractor, (C) Quasi periodic Attractor, (D) Chaotic Attractor

Question 25

What are characteristics of the ‘chaotic attractor’?

Answer 25

• pattern is bounded, but after some repetitions within the system, it becomes very irregular
• Irregularity -> unpredictable
• unpredictability associated with “sensitive dependence on initial conditions”
• general patterns of future behaviour may be predictable but specific behaviors over the long range will not

Question 26

What is self-organization?

Answer 26

process by which a structure or pattern emerges in an open system without specifications from the outside environment

Question 27

What is ‘entrainment’?

Answer 27

• change of pattern with new energy
• another behaviour will disappear
• ability of one unit
• temporal coordination of behaviour of 2 units (synchronizing)

Question 28

What are developmental transitions characterized by?

Answer 28

Periods of increased variability precede a range of developmental transitions (motor, cognitive and linguistic development; emotional behaviour)

Question 29

How is the process of recovery of substance use like?

Answer 29

process is discontinuous

Question 30

How is the system like during periods of fluctuations?

Answer 30

system is destabilized but also open to new information and to the exploration of potentially more adaptive associations and configurations

Question 31

What are discontinuous transitions in psychotherapy preceded by?

Answer 31

preceded by critical fluctuations and instabilities in the system’s behaviour

Question 32

Asymmetry variable

Answer 32

normal factor -> smooth, continuos

Question 33

Bifurcation variable

Answer 33

splitting factor -> leads to discontinous change

Question 34

Repeller

Answer 34

• negative form of attractor
• opposite of a magnet
• > chaos
• > you cannot settle
• > you’d push away

Question 35

Hysteresis

Answer 35

• collection of stickiness
• between two states
• transition; shortly before you transition to other state

Question 36

Settle

Answer 36

• cusp point
• you cannot stay there
• most unstable position