Task 6- M&M Flashcards
What are dynamic systems?
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
What is a state space of a system?
- 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
What does it mean if a dynamic system displays chaos?
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
What is the butterfly effect?
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
What is the ‘dynamic systems challenge’ to cognitive science?
consists of the claim that, rather than understanding human thinking in computational representational terms, we should think of the mind as a dynamic system
What are the two responses to the dynamic systems challenge?
- Defender of CRUM could argue that the dynamic systems approach is very limited in its application to human thinking -> replace it
- Expand and supplement CRUM
What are linear dynamic systems?
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
What is non-linearity? What are nonlinear complex dynamic systems?
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
Which kind of behaviour can nonlinear systems show?
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
What does it mean that nonlinear equations are not additive?
- Answers often involves pattern of solutions
2. Results feed back in system itself
What usually happens to nonlinear systems over time?
Settling down (or convergence) -> results in 1 of 4 typical patterns
What are the typical patterns called which nonlinear systems settle down into?
Attractors
What is discontinuity a subcategory of?
Subcategory of nonlinear
What characterizes discontinuity?
Sudden shifts; sudden or catastrophic jumps in behaviour
What is discontinuity often preceded by?
by an increase in variability and destabilization/ loosing of old, previous pattern that can be followed by system reorganization
