Listen to part of a lecture in a history class. The professor has been discussing ancient Egypt. 

Ok, so one of the challenges that faced ancient civilizations like Egypt was timekeeping, calendars. When you have to grow food for whole cities of people, it is important to plant your crops at the right time. And when you start having financial obligations, rents, taxes, you have to keep track of how often you pay.   

So today we will look at how the Egyptians addressed these problems. In fact, they ended up using two calendars, one to keep track of the natural world, or their agriculture concerns, and another one, that was used to keep track of the business functions of the Kingdom. So let's take a look at the hows and whys of one ancient Egyptian calendar system, starting with the Nile River. 

Why the Nile? Well, there's no other way to put it. Egyptian life basically revolved around the mysterious rise and fall of the river. The success of their agriculture system depended upon them knowing when the river would change. So, naturally, their first calendar was divided up into three seasons, each based on the river's changes: inundation, subsidence and harvest. 

The first season was the flooding, or inundation, when the Nile valley was essentially submerged in water for a few months or so. And afterwards during the season of subsidence, the water would subside, or recede, revealing a new layer of fertile black silt and allowing for the planting of various crops. And finally the time of the year would arrive when the valley would produce crops, such as wheat, barley, fruit, all ready to harvest. Ok, so it was important to the ancient Egyptians to know when their Nile based seasons would occur, their way of life depended upon it. 

Now, the way they used to count time was based on the phases of the moon, which, regularly and predictably, goes through a cycle, starting with a new moon, then to a full moon, and back again to the new moon. Now this cycle wes then used to determine the length of their month. So, um, one lunar cycle was one Egyptian month, and about four of the months would constitute a season. Now, 12 of these months was an approximately 354-day year. So they had a 354-day agricultural calendar that was designed to help them determine when the Nile would inundate the land.  

Well, of course it had to be more complicated than that. The average amount of time between floodings wasn't actually 354 days. I mean, although it varies, the average was clearly longer than 354 days. So how did they keep this short calendar in step with the actual flooding of the Nile? 

Well, their astronomers had discovered that at a certain time of year the brightest star, Sirius, would disappear. Actually, it'd be hidden in the glare of the Sun. And then, a couple of months later, one morning in the eastern sky just before dawn, Sirius would reappear. And it happened regularly, about every 365 days. Even more significantly, the reappearance of Sirius would occur around the same time as the Nile's flooding. And this annual event is called a heliacal rising. The heliacal rising was a fair indicator of when the Nile would flood. The next new moon, after the heliacal rising of Sirius, which happened in the last month of the calendar year, marked the New Year. And because the ancient Egyptians were using the lunar cycle in combination with this heliacal rising, some years ended up having 12 lunar months, while others had 13 lunar calender months, if Sirius didn't rise in the 12th month.  

Even though the length of the agricultural calendar still fluctuated, with some years having 12 months and others having 13, it ended up being much more reliable than it was before. They continually adjusted it to the heliacal rising of Sirius, ensuring that they never got too far off in their seasons. This new calendar was ideal, because, well, it worked well for agricultural purposes as well as for knowing when to have traditional religious festivals. So, that was their first calendar. 

But was it any way to run a government? They didn't think so. For administrative purposes, it was very inconvenient to have years of different lengths. So another calendar was introduced, an administrative one. Probably soon after 3,000 BC, they declared a 365-day year, with 12 months per year, with exactly 30 days each month, with an extra 5 days at the end of each year. This administrative calendar existed alongside the earlier agricultural and religious calendar that depended on the heliacal rising of Sirius. This administrative calendar was much easier to use for things like scheduling taxes and other things that had to be paid on time. Over time, the calendar got out of step with seasons and the flooding of the Nile, but for bureaucratic purposes, they didn't mind.