Part 4 of a series
Niall Ferguson Complexity Theory Excellent video of Niall Ferguson, Harvard University Professor.
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1.3 Definition of Complexity Theory
The main current scientific theory related to self-organization is Complexity Theory, which states:
Critically interacting components self-organize to form potentially evolving structures exhibiting a hierarchy of emergent system properties.
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3. Edge of Chaos
The main current scientific theory related to self-organization is Complexity Theory, which states:
Critically interacting components self-organize to form potentially evolving structures exhibiting a hierarchy of emergent system properties.
[ ... ]
3. Edge of Chaos
3.1 What is criticality ?
A point at which system properties change suddenly, e.g. where a matrix goes from non-percolating (disconnected) to percolating (connected) or vice versa. This is often regarded as a phase change, thus in critically interacting systems we expect step changes in properties.
A point at which system properties change suddenly, e.g. where a matrix goes from non-percolating (disconnected) to percolating (connected) or vice versa. This is often regarded as a phase change, thus in critically interacting systems we expect step changes in properties.
3.2 What is self-organized criticality (SOC) ?
The ability of a system to evolve in such a way as to approach a critical point and then maintain itself at that point. If we assume that a system can mutate, then that mutation may take it either towards a more static configuration or towards a more changeable one (a smaller or larger volume of state space, a new attractor). If a particular dynamic structure is optimum for the system, and the current configuration is too static, then the more changeable configuration will be more successful. If the system is currently too changeable then the more static mutation will be selected. Thus the system can adapt in both directions to converge on the optimum dynamic characteristics.
The ability of a system to evolve in such a way as to approach a critical point and then maintain itself at that point. If we assume that a system can mutate, then that mutation may take it either towards a more static configuration or towards a more changeable one (a smaller or larger volume of state space, a new attractor). If a particular dynamic structure is optimum for the system, and the current configuration is too static, then the more changeable configuration will be more successful. If the system is currently too changeable then the more static mutation will be selected. Thus the system can adapt in both directions to converge on the optimum dynamic characteristics.
3.3 What is the Edge of Chaos (EOC) ?
This is the name given to the critical point of the system, where a small change can either push the system into chaotic behaviour or lock the system into a fixed behaviour. It is regarded as a phase change. It is at this point where all the really interesting behaviour occurs in a 'complex' system, and it is where systems tend to gravitate give the chance to do so. Hence most ALife systems are assumed to operate within this regime.
This is the name given to the critical point of the system, where a small change can either push the system into chaotic behaviour or lock the system into a fixed behaviour. It is regarded as a phase change. It is at this point where all the really interesting behaviour occurs in a 'complex' system, and it is where systems tend to gravitate give the chance to do so. Hence most ALife systems are assumed to operate within this regime.
At this boundary a system has a correlation length (connection between distant parts) that just spans the entire system, with a power law distribution of shorter lengths. Transient perturbations (disturbances) can last for very long times (infinity in the limit) and/or cover the entire system, yet more frequently effects will be local or short lived - the system is dynamically unstable to some perturbations, yet stable to others.
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