Davorak comments on The Futility of Emergence - Less Wrong
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You ITprimer seems to disagree with your statement:
ITprimer:
Non-trivial interactions of individual components -> Self organization -> New behaviors labeled to have 'emerged'
Where did they emerge from? The non-trivial interactions. This description runs counter to your discription "Emergence is NOT the sum of the parts." It is the sum of the non-trivial parts by the above description and a loose definition of sum.