You have fallen into the trap of assigning some sort of meaning to the numbers themselves, when the difference between them by modulo arithmetic is the importan

You have fallen into the trap of assigning some sort of meaning to the numbers themselves, when the difference between them by modulo arithmetic is the important part. Some time systems roll over at midnight (24-hour base-60 clock) some roll over at noon (Julian day) and some roll over at both (12-hour base-60 clock). You shouldn't assume anything about a timekeeping system that has never actually been used. Besides that, if such a clock had time zones, they certainly wouldn't be aligned to hours. If it had no time zones, you would have to know where on Earth the hypothetical conversation took place, and what the typical sleep schedule is there. Though I'm sure people like me would be irritated by that leftover 400 second bit every day, where you don't get a whole kilosecond before rollover, and it may be that everyone arranges things by consensus such that it usually happens while people are sleeping, wherever they may be. So you might be right. Zero could correspond roughly to around 3 AM by the old clock, just like with the DST transitions.