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Intro to Complexity (Complexity (Common properties (Emergent behaviors…

- - - - hierarchical organization
      - information processing
      - dynamics
      - evolution & learning
  - - - Study of continually changing structure & behavior of systems
    - - Study of representation, symbols & communication
    - - Study of how systems process information & act on the results
    - - Study of how systems adapt to constantly changing environment
  - - - Involve just a few variables
      - Examples
        
        Pressure & Temperature, in Thermodynamics
        
        Current, Resistance, Voltage, in Electricity
        
        Population vs. Time, in population dynamics
      - problems of the end 19th - begin 20th century,
        in biology, chemistry, physics
    - - Involve billions or trillions of variables
      - Temperature example
        
        Understanding laws of temperature and pressure as emerging from trillions of disorganazed air molecules in the room or the athmosphere
        
        When we look at understanding temperature, we don't look at
        the particular position and energy of every individual air molecule.
      - Science of Averages
        
        Systems are understood through taking
        averages over a large set of variables
        
        Comes under the rubric of Statistical Mechanics
      - Statistical Mechanics
        
        key - assumes very little interaction among variables
        
        that allows to take meaningful averages
    - - Involve a moderate to large number of variables
      - key - due to their strong non-linear interactions, the variables cannot be meaningfully averaged
      - Problems which involve dealing simultaneously with a sizable number of factors which are interrelated into an organic whole
      - This organic whole refers to the emergent behavior of the system
- - - - Perfect prediction is possible even if
        we're looking at a chaotic system
      - Together with Quantum Mechanics => impossible to ...
    - - prediction becomes impossible
  - - - System's Attractor
        
        Periodic attractor
        
        FIxed-point attractor
        
        Chaotic (strange) attractor
      - Bifurications in the Logistic Map
      - Feigenbaum constant
  - - - the manner in which the system changes
    - - example: population growth
    - - Let's explore it's dynamics
    - - Systems, whose parts interact in a non-linear way
  - - - even with a simple deterministic model,
        long-term prediction is impossible