I ran across a term recently on LinkedIn, about introverted extroverts, sometimes called 'ambiverts'. Now, I've always found dichotomous arguments beginning "There are two types of people in this world..." to be tiresome. Just like the stupid Myers-Briggs & Stratton, Pierce, Fenner & Smith personality tests. "Would you rather do 'x' or 'y'?" Dude, you gotta give me more context - sometimes x, and sometimes y (and sometimes y not).
Just as with introverted extroverts (I consider myself an extroverted introvert, not as a contrarian, but because at my core I am more private), there are many paradoxes in life: Sadness and loneliness in a sea of people, isolation in a hyper-connected society.
I've always thought this was a beautifully haunting Elton John song.