qmdaa:moro

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qmdaa:moro [2007/09/18 12:51] steko lecture #2 |
qmdaa:moro [2018/08/04 00:01] (current) |
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Philosophical positions | Philosophical positions | ||

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===== 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)