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qmdaa:moro [2007/09/18 12:51]
steko lecture #2
qmdaa:moro [2018/08/04 00:01] (current)
Line 46: Line 46:
  
 Philosophical positions Philosophical positions
 +
  
 ===== Lecture #2 ===== ===== Lecture #2 =====
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 Complex ≠ Complicated\\ Complex ≠ Complicated\\
 Simple ≠ Easy\\ Simple ≠ Easy\\
-Multitude → complexity +Multitude → complexity ​but also simplicity 
-          → simplicity+ 
 +  - Chaotic systems 
 +  - Synergy systems 
 +  - Mesoscopic systems 
 + 
 +Complexity depends on the context of study. 
 + 
 +<m>y = x^3 + a·x</​m>​ 
 + 
 +if <​m>​a=1</​m>​ or <​m>​a=-1</​m>​ the 2 resulting systems are qualitatively completely different. Mathematics catastrophe theory knows just 7 types of catastrophes described in mathematical terms. 
 + 
 +C. Renfrew 1978 
 + 
 +Cellular Automata <​m>​{S_i}^{t+1} = R ({S^t}_{i-1},​{S^t}_{i},​{S^t}_{i+1})</​m>​ 
 + 
 +Power laws 
 + 
 +Independence ​→ No prediction 
 + 
 +===== Lecture #3 ===== 
 + 
 +Fractals 
 +  * not a single statistics 
 +  * not only descriptive 
 +  * self-similar (scaling factors) 
 +  * defined by recursive algorithms 
 +  * fractional dimension compared to integer geometries (line=1, square=2, cube=3) 
 + 
 +Fractional dimension D characterizes how the mean depends on the size of the sample. 
 + 
 +Zipf 1949 
 + 
 +Strange attractors are fractals (Lorentz) 
 + 
 +Self-organized Criticality
qmdaa/moro.txt · Last modified: 2018/08/04 00:01 (external edit)