ANST-601 Lessons

The class quickly settles into their seats, eager to see what sort of magic will be performed at the beginning of today’s class. They watch as the professor carefully unrolls a large piece of parchment, gently hangs it on the front wall, and steps away to reveal… a map. A flicker of disappointment crosses the students’ faces, but the professor gives them a reassuring smile. 

Waving her wand, the professor focusses on the map and suddenly it seems to the students that they are flying ever closer to the ground as the map zooms in closer and closer on the area once belonging to the Maya Empire. The sensation slows as they near the ground where the image settles over a group of ruins and focuses on one impressive building.

Stunning, isn’t it? This is the ruins of the Temple of the Warriors found in the ancient Maya complex of Chichen Itza. It is not the largest of the temples found in Chichen Itza, let alone the entire Maya civilization, however I find it intensely fascinating as it is quite unlike other structures we have looked at in this class so far. We are indeed beginning our discussion on the Maya Empire today. As there is much to cover, this topic will be split into two lessons. Today we shall cover the history and knowledge of the Maya, while our next lesson will cover some of the more fascinating aspects of the civilization, namely the magic and hieroglyphs they used as well as the uses for the pyramids they constructed. Don’t forget, your midterms will be ready for you to write at the end of your next lesson, and they will include information from both this week and next, so be certain to take excellent notes! 

History of the Maya Empire

That’s enough chit-chat for today; let’s get right down to business. 

The Maya Empire (circa 1000 B.C.E. to 987 C.E.) covered the majority of the modern-day Yucatan peninsula of Mexico at its peak. It also stretched into modern-day Belize, Guatemala, and even a small portion of Honduras. As for the capital city, well, there wasn’t one, at least not the way we think of a capital city. For all intents and purposes, Tikal, towards the bottom of the empire, was the central hub for many important things like trade, but it was not like our Ministry of Magic being located in London.

In truth, the Maya Empire was not really a unified empire as we typically think of one. It was more of a group of similarly minded small regions with slightly differing mythologies and beliefs. What did unite these smaller states was primarily the extensive amount of trade between them, and also their love of mathematics and astronomy.

Wisdom of the Maya: The Calendar

There is no greater example of the Maya mastery of mathematics and astronomy than the Maya calendar, an example of which you will see below. It is a very complicated calendar to understand, much less use, however it is incredibly accurate. The basics of the calendar calculations are as follows:

There are three time cycles - Solar (365 days based on the Earth’s revolution around the Sun), referred to as a “vague year,” the ritual cycle (260 days), and the astronomical cycle, which is 584 days, based on the synodic rotation (or
the period of time it takes a planet to be seen from Earth in the same position relative to the Sun) of the planet Venus. As I mentioned, the calendar is extremely accurate in that all modern calculations place the synodic rotation of Venus at 583.92 days!

In addition to the three time cycles, there is also a k’atun, which is 20 vague years, or 7200 days. Confused yet? I know that the math doesn’t seem to add up correctly, but the k’atun is calculated slightly differently than a vague year - it is 20 tun, which is 18 20 day months, but not the last five-day “month” needed to complete a vague year. Still lost? Don’t be concerned. Most of us are when it comes to deciphering the Maya calendar. Here is another diagram that demonstrates how to read the calendar itself, but don’t worry - you will not be expected to read it for any of your examinations at Hogwarts. That said, if you wish to become a magiarchaeologist, magianthropologist, or a curse-breaker, I suggest further reading on the topic.

Many of you may have heard that the Maya calendar “ended” a few years ago, and that large groups of people believed this event signified the end of the world. The mistake that these people made was assuming that the Maya calendar is a linear calendar, such as the Roman calendar that we use in most of the Western world. In fact, the Maya calendar is cyclical in nature, which is the way the Maya believed time behaved. When one cycle ends, another begins. The Maya calendar has “ended” numerous times, however it just starts all over at the beginning - which is why it is represented as a circle.

Maya Numerals

The Maya calendar is not the only piece of daily life to differ vastly from our own. The numbers, unsurprisingly, are not the same numbers (1, 2, 53, 720.78542, for example) that we use. Have a look at the following chart of the Maya numbering system. In fact, write it down on your parchment - you will need it for your assignments later today.

Now, you may be looking at this number system and think, “well, this is just a simple substitution, that’s not so fascinating!” You would be partially correct. There is, after all, only one way to count, no matter what words or symbols (numerals) you use to represent the concepts. That said, advanced mathematics changes depending on the base form of the numbering system. Our current method of thinking about numbers is base ten. That is, we have numerals from 0-9 (ten digits) that then combine to create larger numerals, as well as decimal points. If you look at the Maya numbering system, you will note that it has different symbols for 20 different numerals (0-19). The Maya numbering system is then considered a vigesimal system, in other words, a mathematices relating to the number 20. It is also one of the earliest recorded sets of numerals to include a representation for zero or nothing. While you are all thinking “of course there is a zero!” This is actually a very advanced mathematical concept. Have you ever tried to divide by zero? That’s right, you can’t.  Zero is complicated.

Again, you may be wondering about the significance of all of these numerals. Well, let’s examine a basic subtraction problem - have a look and see just how easy it is to use these numerals:

Do you see? You are removing the part of the symbol that is “subtracted” in the problem, and it leaves you with the symbol of the correct answer. Fascinating! Yes, this does work with larger numbers, however it is a bit more complicated - and not necessary for you to know at this level of your studies. I will show you a slightly larger chart depicting how numerals are combined to create up to the numeral 100. Basically each line or level of the number depicts part of the number, and increases using the numerals 0-19 as shown above. Confused? Don’t be concerned, you are not expected to have these memorized for class.

Copy down this chart as well; it will be very handy. Another thing to note, when working on mathematics problems using this system, please be aware that the numerals are often rotated one quarter turn counterclockwise. While this practice sounds odd, it is simply to aid in the ability to solve the problems. 

Conclusion

One last piece of information about Maya mathematics that I find truly fascinating is actually based on who understood it. One Maya practice that was impressive given the time period was the education of all social classes. Everyone from the highest rulers to the lowest farmers was educated and competent in mathematics. This equality of knowledge increased the productivity and satisfaction of the working class throughout the empire, which in turn supported the empire and its longevity.

And that brings us to the end of our first class on the Maya civilization. I know that there are some challenging concepts in this material, which is why I have kept it relatively short. Our next class will not prove quite as challenging, however it will be quite a bit longer as we examine magic use, magical communities (including the location of a possible magical school), Maya hieroglyphics, and pyramids. Make sure you bring enough parchment! Your assignments today include a quiz on the material we have covered, as well as a Maya mathematics assignment. Do not panic, you have all of the information you need to complete these assignments within the lesson. Good luck!

Image credits here, here, here, here, here, here, and here
Original lesson written by Professor Liria Morgan