Long ago, when most people still believed that sun orbited the earth (considered the centre of the universe), some bright spark noticed that if you put a stick in the ground it cast long shadows at dawn and dusk and that the shadow was shortest at the middle of the day; known hence forth as “midday”. It was the Ancient Egyptians who decided that the period between successive middays should be divided into 24 hours (named after the god Horus). Interestingly, Luxor – the ancient city of Thebes, the great capital of Egypt during the New Kingdom – is almost on the Tropic of Cancer so that the shadow would have just about disappeared at midday on the summer solstice when the sun is almost directly overhead.
Until well into the Middle Ages, and even later in Japan, it was accepted that the length of the 12 daylight and 12 nighttime hours would differ with the season. Indeed Japanese clocks were made to accommodate this. The more scientific Ancient Greeks detected the equinox, the dates in spring and autumn when day and night have equal length, and by the second century BC had decided that there should be 24 equal (equinoctial) hours in a day.
We don’t know who first divided the hour into 60 minutes but 60 has been a popular number since the time of the Sumerians – an early Bronze Age civilisation of southern Mesopotamia (modern-day southern Iraq). Like the Greeks, they were keen on geometry. A 60° angle can be created with a compass in two steps. Six of those 60° angles make a circle and one and a half make a very useful 90°. Moreover 60 can be divided easily and accurately by all the numbers one to six, plus 10, 12, 15, 20 and 30; the ancients could have lots of fun scribing lines with a pair of dividers. For simple mathematics the sexagesimal system has a lot more to offer than the decimal.