ARIT-601 Lessons

Upon entering the classroom, you notice that Professor Buchanan is talking with Professor Salvatrix at the front of the room. Once everyone has taken their seats, he turns to greet everyone with a bright smile. “There was some great work on last week’s assignments, which I will hand back to you on your way out today. For now, make sure you’re comfortable and ready to pay attention, please.”

Introduction

I know that the content of last week’s class might have been a little too intense for the people who are not huge fans of numbers, so I figured that this was the perfect time for a little break. No, don’t leave the classroom just yet! Today, rather than work with more calculations and formulae, we will take a closer look at Arithmancy through the eras and how certain civilisations or people came to discover the special properties of some numbers. In order to aid me in this endeavour, please put your hands together for our very own Ancient Studies professor - Professor Salvatrix, who has kindly agreed to provide half of today’s lecture on the topic in spite of her busy schedule. Professor Salvatrix, the stage is all yours!

Mayas and the Number Zero

Ah, thank you so much for inviting me here today, Professor Buchanan. It’s not often I get to venture into the world of numbers so it’s a pleasure to give your class a short lecture on a couple of ancient civilisations and their association with numbers!

Our first stop is the Maya, a civilisation that lived in parts of modern day Mexico, Belize, Guatemala and Honduras between 1000 B.C.E. to 987 C.E. When it comes to numbers, the Maya were very advanced and used them for everything. But before I spend all day discussing everything they’ve ever accomplished, I’ll just focus on one of the numbers that was highly important to them: zero. It may seem like an odd choice, but you’ll understand why I’ve chosen this one in a bit. I would have mentioned twenty, the number the Maya used as their base, as well, but there really is nothing magical going on there. The simple reason they chose twenty is because the average person has ten digits on their hands and ten digits on their feet so they could use those to count.

Back to zero! Although the Maya weren’t the first to discover the number or concept of zero, they definitely made it their own. In the most basic definition, we all know zero stands for nothing, but for the Maya, it was more than just that. Everything was symbolic and the most common symbol for zero was a shell, or to be more specific a conch shell. There were other symbols used as well depending on societal positions, where they lived, etc, but it was usually the conch shell. What do you think of when you hear the word ‘shell’? If it was the sea, or water, then you’ve just made the same connection as the Maya! The shell symbolised the watery underworld the Maya went to upon death and with that association was the idea of the completion of a cycle. In this particular case, that cycle was life. You may now be wondering how zero can be nothing but also mean completing a cycle? Well, for the Maya, the end of a cycle didn’t mean it was all over, but that a new cycle would start. So, in a way, it was perceived as an infinite loop, or infinity. 

Having these concepts proved very useful for the magical population among the Maya. By including zero into their already advanced astronomical calculations, they were able to open up a whole new world of ideas and concepts to explore. Honestly, I don’t understand most of the concepts they looked into there, but any kind of magic that involved time or dates was where they excelled. From what I’ve found in my research, there was a wizard from that civilisation who used zero in his spellwork to try and time travel to different periods of time at the exact moment a cycle ended and the next one began. He wasn’t successful but, if he had been, we may have seen a lot of witches and wizards appear in 2012 when the Maya long calendar last ended. Although that idea may have been a bit out there, those who practised Divination through physical objects would sometimes etch the shell symbol onto their equipment to try and boost its power to see further into the future more accurately. 

Honestly, the Maya had many magical number associations, but I think zero is probably one of the most important ones.

Chinese and the Number Eight

Now let’s move onto the Chinese and lucky number eight. In many different numerological systems, the number eight tends to have positive associations whether that’s victory, wealth or as we’ve already mentioned, luck. Most Muggles say that it’s lucky due to the pronunciation of the word being so similar to that of the Cantonese word for ‘wealth’ and yes, that is true, but it isn’t a coincidence. In fact, it was very intentional, as you will see. 

Let’s go back to Ancient China during the first half of the Han Dynasty (206 BCE–220 CE). Our story starts with a wizard, Cheng An Lin, who lived in the Kweilin Hills area of China where he was one of the people employed by the government to ensure the safety of the Qilin. This meant he was highly educated but he led a rather simple life and wasn’t wealthy by any means. During his time there, a number of poachers had been attacking and killing Qilin. Nobody knew who was doing it or why, which made it much more difficult in figuring out how to stop them. That was until Cheng managed to without even meaning to. It was purely by luck and chance that he was in the right place at the right time. He started his day like any other walking the same route and, when it was around 8am, the man felt the strong urge to take a different path. Not one to ignore his gut feelings, he went that way. He encountered a group of eight people surrounding a Qilin and, without thinking, he jumped into action and somehow managed to take them all down. It was a struggle, for sure, but he did it. 

It didn’t seem like much, but Cheng reflected on the incident afterwards and noticed a connection - everything came back to the number eight. Eight in the morning. Eight people. He’d been in this job for eight years. The list was endless. As everything seemed to go his way and the fact his gut told him to go down a different path, he theorised that eight was a very lucky number. He wanted to test it further so with what little money he did have, he saved for a while and then invested it into a business ensuring everything aligned to the number eight - the name of the business had eight letters, it started on the eighth of the month. Anything you can think of, he had it covered with the number eight. Unsurprisingly, the business did exceedingly well and Cheng became an incredibly wealthy man very quickly. He was, essentially, an overnight success. 

This caught the attention of the emperor’s chief advisors and they demanded to know how he managed to achieve so much in such a short time. Cheng told them his findings and, although they were skeptical at first, they wanted him to join them to continue his work but also to help grow the wealth of the country. Cheng’s success continued as the Han Dynasty saw huge amounts of economic growth and many advances in science and technology.

Since then, eight has been seen as lucky and, with the Cantonese language originating shortly after the end of the Han Dynasty, it’s no surprise that ‘eight’ and ‘wealth’ sound incredibly similar in that language.

And with that, I will hand it back to you, Professor Buchanan. Again, thank you for inviting me here today. If anyone has any questions related to what I discussed today, feel free to ask me any time.

Bridget Wenlock and the Number Seven

Fascinating, isn’t it? Thank you, Professor Salvatrix. Now, let us direct our attention to a period that is certainly more modern than the ancient Maya or Chinese civilisations; our next stop is 1237, in a place that is much closer to home. We will visit the wizarding village of Tinworth, a place that must be familiar to all of you given the fact you’ve already studied it in History of Magic.

Tell me, who was likely the most famous resident of Tinworth? That is correct - Bridget Wenlock takes the cake in that regard! Wenlock was a celebrated Arithmancer who attended this school from 1213 to 1220, and she was considered a very bright student at the time. Her affiliation to Hufflepuff certainly helps to dispel the myths that only Ravenclaws are academically-inclined, as all sorts of traits can be found across all four Hogwarts Houses!

Anyhow, let us proceed. Wenlock might have been a genius in her own regard, but she was also considered to be quirky by many of her peers, even throughout her school days. Certain journals indicate that Wenlock always made sure that she took ten steps in front of any door before opening it, and that she’d click her fingers twice before asking a question.

It was around the time of her graduation that Bridget Wenlock started to develop her main theory, which is currently known as the Theory of Numerical Complementarity. In simple terms, Wenlock defended that numbers sought to feel complete, and that imbalances in numerical values or sums created certain types of weak points or defects in the objects associated with those numbers. However, she had no idea what number was associated with the state of completeness she so desperately sought, and her tests also didn’t help her shed light on the matter. No matter how many magical artifacts she created or how she structured them, there was always a flaw to be found.

To make matters worse, Wenlock was extremely absent-minded and had a horrible tendency to misplace her notes, which was further aggravated by the fact that she tended to write all of her important studies in invisible ink and never in the direction you’d expect. You see, Wenlock felt like she was so close to a breakthrough that her expectations gradually converted into caution and even paranoia. Due to this, she spared no method to make sure her notes were kept hidden from other people. As you may expect, this meant that she frequently lost her observations and notes on working theories, drastically delaying her progress.

One day during breakfast, Wenlock realized that a certain wand movement she used for a cooking charm was approximately 49 centimeters long, which brought her attention back to the number seven. However, owing to the fact that she had considered that digit before, Wenlock didn’t have high hopes when revisiting her notes. Still, luck was on her side that day; while searching her kitchen for hidden notes, she came across a compendium of notes that indicated the objects she used when testing the number seven were also strongly associated with the number two, which might have introduced some degree of instability in her results. Excited about this new development, Wenlock ran some tests and identified that the more strongly an object is associated with the number seven, the more stable it is. She quickly jotted down her observations on a nearby paper scrap and went on her merry way, forgetting to store her notes somewhere safe.

Later on, Wenlock sent a letter to her cousin through owl, but soon remembered that she likely wrote her observations on the envelope that was used to enclose that letter! Unwilling to part with her valuable discovery, she tried to wrangle the letter from the owl’s clutches, which refused to hand out the missive to anyone that was not the intended recipient. Long story short, Wenlock had to travel some 600 miles to reach her cousin at John O’Groats, cast the Revealing Spell on the envelope… and actually realize her notes were written on a packet of sugar that was in her kitchen all along!

Nevertheless, Wenlock’s discoveries shook the entire world of Arithmancy. Her observations are currently used in many fields of magical engineering, including broom manufacturing, spell-repellent clothing and more, as the number seven is related to both physical integrity and receptivity to magic alike. This is a corollary of the added properties of both three and four - which many of you might recall are considered, respectively, as an energy-stable number and a materially stable number!

One final note I’d like to add is that modern-day healers believe that Bridget Wenlock might have had a psychological disorder named Obsessive Compulsive Disorder, frequently identified by its initialism OCD. In a nutshell, those who have OCD take on specific rituals as obsessions, such as constantly washing their hands, checking whether doors are locked or open and - particularly in Wenlock’s case - counting objects and actions. Bridget Wenlock is clear proof that you are not defined by your disorders, and that those who have any type of psychological condition are not relegated to being second-rate citizens - they certainly can be fully-functioning individuals in our society, and perhaps even become a source of geniality and inspiration to others.

Deagoll Adkins and the Number Forty-Two

Time for our last stop in our time journeys! This time, we are going to talk about a much more recent discovery - in fact, many of the staff members here at Hogwarts were already alive when the properties of 42 were first identified! For the final section of today’s lesson, we will return to 1978.

It was in this year that Deagoll Adkins, an up-and-coming Arithmancer, was finally able to get his hands on some rare Mesopotamian clay tablets. Adkins suspected that these tablets would provide insights on environmental spells - particularly with regards to drought and heat - but he did not have enough expertise on Curse-Breaking to try and search for these tablets on his own. After several years of waiting for these texts to surface, Adkins had a breakthrough as soon as he heard that a group of magianthropologists had found a collection of tablets when investigating a secret passageway in the ruins of Girsu.

This was all that he needed to start his research. Adkins already knew that the number 60 was used as the base of their counting system, but abstract experiments with that number posed no tangible result - he needed to try something else, but could not attempt random numbers blindly. Upon inspecting the clay tablets, Adkins realized that a string of numbers tended to repeat itself over and over again when dealing with environmental spells: 12357.

If you’ll recall our past lessons, you may notice that this string is equivalent to the single digit prime numbers in order, in addition to the number one. Theories on why the number one was added to the sequence are still inconclusive, but some believe that the Sumerians - the people from the region of Sumer in southern Mesopotamia - might have a different definition on prime numbers, and that this definition may have included the number one as a prime.

Back to the case at hand. Adkins quickly identified the presence of the number 12, which is one of 60’s divisors - the number that supports the entire Sumerian counting system. However, not knowing what to do with the remainder of the numbers, Adkins tried several operations with them, until he multiplied 12 by 35, obtaining 420 in the process. He soon realized that indeed, the number 420 seemed to be extremely effective when dealing with the sowing or harvesting of magical plants, as well as environmental spells that dealt with extreme heat; however, that number was far too large to be used effectively. In a stroke of luck, Adkins tested whether the same properties would hold true for the number 42, and it did!

Nowadays, it is believed that the path paved by Adkins may be crucial in solving modern issues, such as global warming and the loss of nutrients in soils used for monoculture (i.e., the planting of a single type of botanical specimen). Research on the topic is still ongoing, but many believe that we might have some very effective tools on how to address environmental concerns soon. As a final note, we still do not know why the number seven was mentioned in the tablet researched by Adkins - although many Arithmancers devote their full efforts in trying to solve that riddle.

Closing

This is, naturally, just a brief overview of some individuals or civilisations that were important in Arithmancy. Unfortunately, I do not have the time to cover every single discovery in this class - and it is for that very reason I will entrust this task to you, in addition to the weekly quiz on the lesson’s contents.

Dismissed.

Original lesson written by Professor Vaylen Draekon and Professor Epona Salvatrix

Improvements made by Professor Calum Buchanan
Image credits here and here