And fascinating, the observation that "In molecular machinery, the uncertainty of the receiver before a message is received and decoded is the Shannon entropy in the before state. When the incoming message (along with noise) has been received and decoded, the uncertainty in the molecular machinery decreases to the after state, also a Shannon entropy."
Perhaps Shannon entropy truly does refer to a "regularity" of nature -- since it would seem to hold for both the "before-case" and the "after-case" as well. If a true universal, it would be equally common to both, of course.