"complexity alone cannot explain a phenomena that is profoundly, qualitatively different in nature."

Ah - emergent behavior - which is qualitatively different in nature, and often profoundly counter-intuitive, comes out of complexity in a functioning system. :-)

Read Hofsteader's Pulitzer Prize winning Book "Escher, Godel & Bach - an Eternal Golden Braid ". He goes into some detail, especially in Computing, a field where it was recognized as being as fundamental to how the whole Universe, not only computers, works.

On the main example he quoted, the number of users able to run in the Operating system is not a property of any part of the system - you can't go in and just change a magic number somewhere. The emergent behavior is only displayed when the system is actually running. The aspect called 'intelligence', is only displayed when the system. eg Brain, 'Black Box', traffic flow on a motorway, etc is functioning.

QUOTE (Wikipedia)
On its surface, GEB examines logician Kurt Gödel, artist M. C. Escher and composer Johann Sebastian Bach, discussing common themes in their work and lives. At a deeper level, the book is a detailed and subtle exposition of concepts fundamental to mathematics, symmetry, and intelligence.

Through illustration and analysis, the book discusses how self-reference and formal rules allow systems to acquire meaning despite being made of "meaningless" elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of "meaning" itself.

In response to confusion over the book's theme, Hofstadter has emphasized that GEB is not about mathematics, art, and music but rather about how cognition and thinking emerge from well-hidden neurological mechanisms. In the book, he presents an analogy about how the individual neurons of the brain coordinate to create a unified sense of a coherent mind by comparing it to the social organization displayed in a colony of ants.
UNQUOTE