So here is a lecture:
https://www.youtube.com/watch?v=JR93X7xK05o
To celebrate Complexity Explorer's 10th anniversary, we're excited to share a lecture from SFI President David Krakauer sectioning the concept of complexity and exploring complexity epistemology and emergence.
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So I was thinking to define for myself 'What is complexity'
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Complex systems are system where the whole is greater than the sum of the parts.
This would violate the laws of thermodynamics if not for the fact that they are open systems.
So, complex systems are open systems in which energy from an outside system increases the energy of the whole to be greater than the sum of its parts (luckily after Goedel all (formal) systems are open systems)
This may be accomplished by creating connections between the parts.
Thus, the whole is the particles and their binding energy.
A complex system is one where the energy in the whole is greater than the energy in the particles, i.e. a system with binding energy.
As the binding energy increases, the system increases its Information and may be communicated more efficiently.
Efficient communication requires phase transitions. Thus when the energy in the whole increases beyond a threshold a phase transition occurs, whereby the parts lose their identity and are communicated as a (semi-)whole.
So a complex systems is a system which can be communicated efficiently
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note, that technically Entropy decreases and Information should decrease with the addition of binding energy, since the state of the parts are now linked, they have less freedom.
The flaw in the logic is that Entropy measured at the level of individual particles does decrease, however, the parts are now connected and at a new level they are emerging into a single whole. Thus, the Entropy and energy and Information needs to be normalized to the new whole.
