The antonyms for the phrase "art at the head of" would depend on the context it is being used in. If we consider the word "art" as a synonym for skill or talent, then the antonyms could be amateurism, incompetence, or ineptitude. On the other hand, if we consider the phrase in the context of hierarchy or position, the antonyms could be followership or subservience. As a general antonym, one could use "disorganization" or "chaos," as "art at the head of" suggests a sense of order and leadership. It's important to consider the context of any phrase or word when trying to find its antonyms.