A Guide to Hogwarts Arithmancy

by Baelkaz

Hogwarts third years may schedule this elective. A NEWT is necessary in this subject for Department of Mysteries employment, and an OWL is required for a position in education. Enclosed are key samples of Professor Septima Vector's lesson plans from every year in the curriculum. This is intended as a course supplement, not a replacement. Please support your education professionals.

2. Basic Spell Strings

Lesson Two:

Welcome back, class. Today, we're going to talk about how the symbolic aspects of natural numbers combine. To make things a little simpler, I'll introduce you to the professional Arithmantic term. The symbolic aspects of natural numbers are called Sympatheticals. To reference the aspects of the number four, for example, is to reference the Fourth Sympathetical. So, we left off last time discussing the purpose of Sympatheticals in daily life, and the possible meanings of Zero. I'm going to address this right now and say that Zero is not called the Zero Sympathetical. Because zero is not a natural number, it has a different name. Zero is what is known as the Null Center, or just the Null. The Center references the inclusion of negative numbers in our theorems, but we won't cover that until your fourth year.

So, to begin with combinations of Sympatheticals, we'll start simple. Some of the combinations may seem obvious, but others are not as much. For example, take two and three. Multiplied, they equal six. This is a good example of how Knowledge combined with Time would equal Memory. Similarly, it is possible that Fungi combined with Choice would equal Poison. However, this combination does not make sense for every possible aspect of a Sympathetical. Plant-life and Luck will very rarely yield Evil. Part of why we study Arithmancy is to be able to understand why certain Sympatheticals work with others. If everything followed conventional wisdom all the time, we could merely hand you a list of the Sympatheticals, pat you on the head, and send you on your way knowing everything about Arithmancy. It does not work like that.

This aspect of Arithmancy is what mostly affects potions and spell creation. Every spell in existence could actually be broken down into a string of numbers and equations. This is what is known as a Spell String, not to be confused with Spell Stringing. Stringing is the practice of smoothly casting spells in a series, flowing from one movement directly into the next in ways that complement each other. Spell Strings are numbers, or, in the case of more complicated spells, full formulas. These tend to depend on factors like Kinesis of the caster, outside conditions, astronomical positioning, and so on. We'll be starting out with basic number strings.

Wingardium Leviosa is a charm you're all familiar with. It may be no shock to you that the Fifth Sympathetic, representing Air plays a prominent part in this String. The String for Wingardium Leviosa is as follows: 765030. This opens up a few interesting discussion pieces. For example, every spell begins with a Seven. This invokes Magic, as you might suspect. Six almost always follows, save for a handful of exceptions. This invokes Intent. In this case, the content of the unique String begins with Five. As stated, this invokes the Fifth Sympathetical of Air. What follows is an interesting aspect of the Null Center. A Zero in a Spell String begins a series of opposite effects. In this case, the Null effects the Third Sympathetical of Earth, adding to the effect of the Fifth Sympathetical. The second Zero is used as almost a Close to what some liken to parenthesis. A second Zero halts any opposite effect on the enclosed numbers between the Null. This can be used in conjunction with opposing Sympatheticals to increase potency. In this case, combining Air with an absence of Earth will be focused by your Intent to fuel a spell.

In a different example, the Avada Kedavra curse has a fairly simple String as well. It follows as such: 673077104. Analyzed, experts in the DOM have identified that the Sympatheticals at play to be Intent, Magic, Death, Null(Fate, Connection, Rejuvenation), Peace. This curse is a rare example of Intent being given Primacy over Magic. Without the proper feelings of hatred and absolute certainty powering this spell, no magic will respond to the caster's call. The other two Unforgivable Curses are of the same sort, as well as most Dark Magic. What is interesting about this curse is that the Sympathetical for Evil does not appear, as it does in most instances of Dark Magic Strings. It is possible that this is because the Avada Kedavra was used in Arthurian days as a means of peaceful execution.

For the next lesson, we will start on more advanced Strings, breaking into basic formulae.