I have always been puzzled when people talk about "3 o'clock in the morning." Is that really morning, or is it night? I admit that the sections of the day -- morning, afternoon, evening, and night -- are not well defined. Only the distinction between morning and afternoon is marked clearly by the noon boundary. I draw the line between afternoon and evening at 5 p.m., but I doubt everyone does, and I'm sure I violate the distinction occasionally. Still, there is general agreement that 3 p.m. is not evening, and 7 p.m. is not afternoon.
The difference between evening and night is even less clear. You might say that night begins when the sun goes down, although most people seem to use evening to mean the entire time between getting off from work and going to bed. Ten or eleven p.m. would seem to be a reasonable dividing point. When it comes to the division between night and morning, however, confusion dominates. When does the morning begin? For most people, it begins when they wake up for good to have breakfast, get dressed, and so forth. If they wake up earlier, say, at 3 a.m., they would describe it as "the middle of the night," and they would tell people that they had trouble sleeping that night.
The problem is that people are inclined to assign midnight the same dividing power that they do to noon. Thus, although they might describe 3 a.m. as the middle of the night, they almost invariably say they woke up at "3 in the morning" rather than "3 a.m." The tendency to equate a.m. with morning is understandable. Midnight does mark one definite boundary -- the boundary between one calendar day and the next -- and we naturally associate a.m. with morning: when we're awake, the coming of the post meridiem means the end of morning. But the a.m./p.m. boundary only works to divide morning from afternoon; it makes little sense as a division between night and morning. Do people really consider 12:30 a.m. morning? Or 2 a.m., or 3 a.m.? 90% of people are sleeping by 3 a.m.; of those that aren't, 90% wish they were (they are working 3rd shift), and 90% of the remainder are still up from the day before partying. (Did you know that 87% of statistics are made up on the spot?) I'm willing to grant that a reasonable percentage of people (though probably less than 1%) get up by 5 a.m.; that could be considered morning. I doubt, however, whether one person in 10,000 gets up at 4 a.m. on a regular basis.
The next time you begin to say that something happened at 3 in the morning, stop to think whether it wasn't really 3 at night, or simply 3 a.m.