It's always struck me odd that the "day" starts in the middle of the night, rather than at, say, dawn (or thereabouts). Where does this tradition come from?
The Hebrew calendar, the Islamic and Baha'i calendars end and start a day at sunset, instead of midnight.
The standard use of midnight as the start of the day is a consequence of the Roman system of time which divided the daylight time into 12 equal parts, in which the mid-point (roughly Noon) was used as the reference point for the whole day. Times during the day were expressed relative to Noon eg "2 a.m. meant 2 hours before Noon (nominally our current 10am).
They divided night time into 4 "watches" of roughly 3 hours each.
Under this system, the time at which you cease to be closest to one day's Noon and begin to be closer to the next day's Noon is half way through the night.