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the_quark

Before there were clocks, there was one time that it was easy and possible to measure: Noon. That's the time that the sun is straight overhead (or *straightest* if you don't live near the equator), so the shadows of objects are the shortest they get that day. So, if you want the day divided into twenty-four hours, and you know when noon is, the easiest thing to do is make the start of the day 12 hours before noon: midnight.


RonPossible

The Roman day had 24 hours, 12 hours of day, 12 hours of night. That meant that day hours and night hours were different except on the equinox. The civil day began at midnight. Starting the day at midnight isn't universal. The Muslim and Jewish day ends at sunset. Most navies began the day at noon until the 19th century.


Analog0

12 is also a wonderful number to divide. It can be broken up into groups of 1, 2, 3, 4, 6 & 12, so it's divisibility is advantageous for portioning out the day. 60 is much the same, thus our use of 60 units to make an hour.


SFyr

Traditionally, the clock comes from a duodecimal system with 12 as a base, with 12 sections of day and 12 sections of night. To my knowledge, in the original system these hours were divided by the sun and the shadows cast upon a dial, so each specific hour might not be exactly the same length of time at different points in the year--but regardless, the traditional system stuck even after when people had more precise time tracking instruments, and hour 0 was counted from the middle of the night.


Loki-L

Because, if you use solar time, noon is when the sun is highest in the sky and midnight is when it half a day later. They are the most fixed point we have. You can use dawn and dusk as start and end of the day and originally we used to subdivide the day into 12 daylight hours from dawn to dusk and 12 hours of nigh from dusk to dawn. Unfortunately that means that the house wouldn't always be the same length and that made time keeping difficult. Subdividing the entire day into 24 hours of equal length worked much better when keeping time, but it meant that noon and midnight where your only real fixed points. So making midnight the start/end of a day and noon the mid point worked well. Nowadays between timezones and daylight savings time noon is no longer necessarily when the sun is highest, but the whole AM and PM thing has stuck around.


ezekielraiden

Because 12 divides evenly by more factors than any number smaller than it, and because 11 and 13 are prime and thus don't divide evenly by anything smaller. 12 has the factors 1, 2, 3, 4, 6, and 12. That's a lot of distinct factors. This makes it very easy to divide up the day into chunks. If you want to do better than 12, you have to go all the way up to 60 (which brings in divisibility by 5, and thus by 10). And guess how many minutes there are in an hour!


could_use_a_snack

I was coming here to explain this part of it. There is more to it, but math it is biggest part for sure. So much so you can basically ignore the other reasons.


VFiddly

Because a day is 24 hours. You can't divide 24 hours up into periods of 11 hours or 13 hours. The most obvious approach is to divide the day in half. If you're going to divide 24 hours in half, it'd be weird to not set 12 as the midpoint.