Weeks

Why do we have a seven day week?
The cycle of the moon repeats about every 28 days, which is where we get the length of the month from. The only recognizable subdivisions of this are when the moon is full, the moon is new, and when the moon is half full. (We are able to tell convex from concave easily, but telling whether the moon is more or less than 1/3 full is difficult. This isn't just a cultural habit, but derives from the nature of orthogonality.) This divides the cycle of the moon into four equal sections.
If a holiday is going to be celebrated regularly, it makes sense to have it be on the day of the new moon, the full moon, and the half moons. (The same thing is true for the cycle of the year-- it makes sense to have the big celebrations timed for the equinoxes and the solstices, because they are the easiest dates to be sure of.)
This connection with the lunar cycle is explicit in the Babylonian calendar, but by historical times the Hebrew calendar had become a repeating cycle of seven days, disregarding the phase of the moon.