Now, there's being up past two because you're doing something really, really fun that you don't want to stop, despite the fact that you'll pay for it in exhaustion the next day. Then there's being up until past two because you got into an unexpectedly serious, heavy discussion that became fraught with meaning and importance merely because you were so tired that you had to keep reminding yourself to finish your sentences, so you didn't notice that while the things you were saying were on topic and true enough, they were also things you never would have said at, say, 9:30. At 9:30, you would say "This just isn't even a thing. Don't worry about it."
One of those things is fun, and one of those things is stupid.
At 2:00 am, I am just stupid.