This seems unclear. What is the information content of a set of
axioms, for instance? Even in deductive fields like mathematics, it
is not considered a waste of time to pursue investigations because 'no
more information is gained than what was in the original postulates.'
It is exactly the process of making explicit what patterns and possibilities
are in the original postulates which makes the enterprise exciting! The
laws of physics obviously allow for our existence, but it seems to process
of exploring those possibilities is what makes for an exciting life.
Perhaps 'information content' is a poor diagnostic of what is worth doing.
-Greg