Steven Crane Compiled Section Handouts. Human Behavioral Biology 2012

Chaotic systems

1. 
   Understanding "deterministic" and "periodic:"
   
   1. 
      Deterministic and periodic. Like a simple "add one" rule. 1, 2, 3, 4, 5…
      
   2. 
      Deterministic and aperiodic. You can't just repeat the same step over and over, the state changes with every iteration. It also NEVER actually repeats a previous state or else it would be periodic. The difference might be 10 orders of magnitude down the line, but the difference is there. This is what we're usually talking about in chaos.
      
   3. 
      Non-deterministic and aperiodic. This would be utter randomness, with each new generation not even following any rules, but just generated at random. This ISN'T what we're talking about in class.
      
2. 
   Ex: The water wheel
   

• 
  At some speed of water going in, you get aperiodic oscillations. They ARE deterministic, just NOT predictable.
  
• 
  You can figure out what's going on at time T+1, but you can't extrapolate to T+10 without going through T+1 then T+2 then T+3, etc.
  

3. 
   Ex: Strange attractors
   
   1. 
      Attractor: The name you give to the "ideal solution"
      
      1. 
         Perturb a non-chaotic system and the curve will return (be attracted to) its original path.
         
      2. 
         Chaotic systems never achieve this. Perturb them and you're just off on a different chaotic path.
         

iii. There is no perfect idealized point that we're all failing to achieve. There is no norm, no correct answer. The variability, the fluctuation: that is the norm.

4. 
   Ex: Inherent variability and fractals
   
   1. 
      The variability never goes away, even as you zoom in with more and more powerful tools. "The average" maybe doesn't actually represent the true nature of the system. Maybe variability is inherent.
      
   2. 
      "fractal" can be talked about in a number of ways/definitions.
      
      1. 
         Noun: "A pattern whose variability remains constant, independent of scale."
         
         1. 
            Like the strange attractor
            
         2. 
            Like Sapolsky's testosterone meta-analysis
            
      2. 
         Noun: "A pattern that is self-similar over a range of scales."
         
         1. 
            Like the Mandelbrot set:
            
         2. 
            Like bifurcating systems in the body
            
      3. 
         Noun: "A pattern with complexity best described as being a fraction of a dimension."
         
         1. 
            Like the Koch snowflake, Cantor Set, or Menger Sponge
            
         2. 
            Sort of like the circulatory system: huge surface area and minimal volume.
            
      4. 
         Adjective: describing any of the above patterns.
         
5. 
   Reductionism isn't ALL bad though. Great for crude answers and explanations. Or for predicting things 99% of the time. Reductionism can be great on the average. But it’ll rarely give you a 100% clean, predictive system.
   

Emergence and Complexity
1. Context: instead of "you can't predict anything complicated, you can't understand it, you can't manipulate anything to control complex outcomes" consider all that is to follow. It's about a type of "predictive" power pretty different from things you've probably considered before.

How do we solve the problems of insufficient numbers of component parts?

1.