p236

“usual ‘complex systems studies’ are off the mark”

Whether a symbol sequence is complex or not is not determined by the intrinsic property of the sequence itself, so we cannot answer the question about the complexity of a sequence how much we study its syntactic properties. Consequently, all the attempts to characterize ‘complex systems’ in terms of entropy, mutual information, etc., are off the mark. Shostak proposed to define complexity with the surprisal of useful or meaningful sequences. However, if 111111· · · is meaningful, then this sequence would be called a complex sequence (its surprisal is large usually, because continuing many one’s is rare). 

 Incidentally, whether one can judge a living object alive or not may be a better intelligence test than the Turing test. This may give a deep suggestion about for what natural intelligence has evolved.