an obscene hour of the day that no one should be awake for.

Briefly, "the realization that each random passerby is living a life as vivid and complex as your own." Originally from the Dictionary of Obscure Sorrows, which has a lot more beautiful neologism definitions like this you might enjoy.

A truly quite extraordinary time to be alive. Many things are reported at balls o'clock, the most common being the feeling of having balls in your mouth.