How far back in history do you have to go before the days of the week (monday, tuesday, etc) no longer line up... in other words, how long have we been consistently keeping track of days of the week as a society before it breaks down...
Certainly as far back as the Sumerians and Babylonians, but possibly China got there before. It'd be anywhere where you need to be able to count and your society is organised and in a position to do that.