So, lilairen and I were commenting on it being past midnight -- I said "It's fifteen minutes into tomorrow," and she countered with her usual claim that "it's not tomorrow until I've slept" figured into the equation.
And so, it being late and my brain being slightly warped by the hour, I pondered at this, and concluded that there are actually two separate date-counters, and there's no need for them to tick over simultaneously. There is the counter of which calendar day corresponds to "now" -- e.g., is it the 14th, or the 15th? -- and the counter of which calendar day corresponds to "today".
It would make sense that "now", which needs to refer to an instant, ought to tick over at midnight, so that times are given in unambiguous form. On the other hand, "today" relates to conceptions of single days, and ought tick over when one sleeps. Thus, I can accurately state that it is now tomorrow.
On the other hand, one could imagine that one could set things the other way, so that "now" doesn't tick over, but "today" does. This would, oddly enough, mean that it's so late that now is now yesterday.
This, one should note, could have dangerous effects on one's scheduling if one isn't prepared for it. Given the first situation, the time between midnight and sleep becomes enormously busy, because one is suddenly swamped with all the things that one had thought were safely put aside as "I'll do that tomorrow". Or, given the second situation, one finds that that precious core of time is a spot where one has a second chance at all the things that needed to be done yesterday but didn't get done.
In my case, I found this deeply distressing, because there's a stack of dirty dishes in the sink that I meant to do yesterday, but didn't do and put off until tomorrow. Either way, these dirty dishes land in my to-do pile right now, and I want to go to sleep!
It was only by remembering that I was going to do the dishes today that I was saved.