At first glance, they are thought to be a contrast. There could be a possibility that our private ideas would include the interactions that are typically found in the public world in which we inhibit. So, public and private sphere are codependent.
"Public" sometimes implies a lack of monitoring and oversight. Public water coolers and recreation areas may be unclean literally. Since the public area is being exposed to scrutiny by people, conduct that is permitted in private may be forbidden in public.
When would the public becomes the private and vice versa? For an individual to be designates as 'the public' would be one that is not part of a given profession. For example, the same commoner as 'the public' in an art museum would be known as the physician in a hospital and not 'the public' anymore. Public in this sense are constantly resifted and recomposed and everyone belongs to part of everything. So, if employed as a noun, the term 'public' is relative.
How can private art be made public? Ever see a label that state artist's private collection? That means the art institution doesn't own that work. That's private art made public.
Can 'public' be considered 'nonprivate' then?