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From the Lexicon Edit
Arithmancy is a branch of magic that is concerned with the magical properties of numbers; someone who practices Arithmancy is called an Arithmancer. For example, in the 1200s, Bridget Wenlock, a famous Arithmancer, discovered the magical properties of the number seven. An O.W.L. in Arithmancy is required to apply for a curse-breaker's job at Gringotts.
Arithmancy at Hogwarts is taught by Professor Vector. In her class, students are expected to write essays and to be able to understand complicated number charts, which are part of their homework. Hermione Granger appears to be the only Gryffindor in her year who attempted an O.W.L. in this subject (which is her favourite).
Further Definition Edit
Arithmancy is the study of numbers and their magical properties. In actuality, it is one of the oldest documented forms of magic in the world. Among its practioners were the Chaldeans, a semi-nomadic people, who occupied the city of Ur. The Chaldeans used it in a way that, in its simplest forms, could be considered divination with numbers. However, the practice is much more complicated than that.
There are two schools of Arithmancy, based on the schism that occurred in the discipline when Europe adopted the Hindu-Arabic numeral system in the 12th century. East Asia, which adopted the system only in the 19th, developed spells and foci in remarkably different ways from that point on. All that is written here is considered part of the western mathemagical discipline, Arithmancy. The eastern form is known as Kazutama, literally "number spirit/soul" in Japanese, and presupposes that numbers and equations can magically affect objects, and that ritual usages can influence our environment, body, mind, and soul.
In Arithmancy, to study the properties of a number requires breaking the universe down into fundamental equations. People, objects, things, concepts – the arithmancer must take what is concrete and turn it conceptual. In some senses, Arithmancy is contagious magic with numbers as the channel. It is quite similar to how African cultures consider the magic of names or of personal images.
The first step towards using the discipline is in being able to analyse/interpret people on a basic level and make inferences using a combination of mathematical calculations and magical method. This is what we'd consider numerology. Most students don't progress beyond this level. Another early aspect of the discipline is simply convincing students to embrace and accept the idea that numbers have power. And that certain numbers have certain powers.
These ideas then, in turn, translate into sequencing and linking numbers to create mathematical equations – these, when performed, interpret and unlock elements of being. Arithmancy is best used as a helping magic and in conjunction with other disciplines. It is a tool of understanding, foundation and method, rather than a direct path to high magical action.
The study of mathematical magics isn't truly, in the upper levels, a study of how to cast or conjure but rather, how to think. In order to be effective, you have to have a mind that can calculate and compute, reducing not only objects but people and life itself into numbers. It is a difficult discipline to embrace – at the earlier levels, it is effectively useless and at the upper levels, you are effectively altering matter and it then cannot be used. People at the upper echelons of the field are often so far removed from reality that they can no longer effectively interact with people, people at the lower end tend to become accountants. Neither one is really a desirable fate.
Like most disciplines, you can specialize narrowly. Arithmancers are often an extremely exacting sort and will frequently target their work down to a near-miniscule scale, working on the level of the aether (1), rather than examining the life around them. These disciplines are similar in equivalent to muggle mathematical study and often developed in conjunction with or influenced those mathematicians.
Some common specializations are:
Aljabr ("reunion" in Arabic): The study of structure, relation and quantity. Developed by Persian mathematician Muhammad ibn Mūsā al-khwārizmī in 820.
Analysis: Most explicitly concerned with the notion of a limit, whether the limit of a sequence or the limit of a function. It can also be defined and studied in any space of mathematical objects that is equipped with a definition of "nearness" (a topological space) or more specifically "distance" (a metric space). This is relatively new, having been developed to a higher potential by British arithmancers in the 17th century.
Arithmantic Theory: This branch of pure mathemagics is concerned with the properties of numbers in general as well as the wider classes of problems that arise from their study. Arithmantic theorists are generally those who generate the highest number of new spells and uses for the discipline.
Geanian Arithmancy ("gape wide" in Anglo-Saxon): This studies the behavior of chaos, ie: the complexity of causality or the relationship between events. This means that any 'seemingly' insignificant event in the universe has the potential to trigger a chain reaction that will change the whole system. A well known saying in connection with this issue is "A butterfly flapping its wings in one part of the world can cause a hurricane on the other side of the earth." This is also known as the "butterfly effect".
Cryptomancy: Cryptomancy is the study of magical codes, cyphers and symbols, often tied in with runes and linguistics.
Geometria: Concerned with questions of size, shape, and relative position of figures and with properties of space. One of the oldest specializations, so old that a definite date or creator cannot be established.
Probability: This branch focuses on analysis of random phenomena and attempts to replicate such phenomena. It requires a basic understanding of arithmantic probability to brew the felix felicitas potion successfully, one reason that it is so expensive to produce.
Alchemy, Astronomy, and Ancient Runes, while not considered part of Arithmancy all work closely with this discipline.
While Numerology is an offshoot of Arithmancy, it's considered a "fringe" art and most self-respecting Arithmancers would not class it with any of the above. (Though they often still use it when examining other people.) That said, the basic numeric properties aren't secret knowledge and many people would be aware of these.
Some Sample Number Meanings Edit
These are some of the meanings associated with the base of the numbers themselves:
0. Everything or absoluteness. All 1. Individual. Aggressor. Yang. 2. Balance. Union. Receptive. Yin. 3. Communication/interaction. Neutrality. 4. Creation. 5. Action. Restlessness. 6. Reaction/flux. Responsibility. 7. Thought/consciousness. 8. Power/sacrifice. 9. Completion. 10. Rebirth.
When applied to people, the meaning of numbers shifts towards the following:
1 Creativity, independence, originality, ego, self 2 Empathy, cooperation, consideration, over-sensitivity, co-dependence 3 Practicality, application, loyalty, rigidity, repression 4 Artistic expression, sociability, friendliness, superficiality, wastefulness 5 Freedom, adaptability, travel, inconsistency, abuse of senses 6 Love, responsibility, understanding, meddling, jealousy 7 Spirituality, mental analysis, wisdom, fault finding, suppression 8 Executive ability, management, power, materiality, unscrupulousness 9 Artistic genius, humanitarianism, romance, emotionalism, dissipation 11 Intuition, idealism, invention, insensitivity, fanaticism 22 Practical idealism, material mastery, get-rich-quick schemes, viciousness
1. On aether: "Plato's Timaeus posits the existence of a fifth element (corresponding to the fifth remaining Platonic solid, the dodecahedron) called quintessence, of which the cosmos itself is made.
Aristotle included aether in the system of the classical elements of Ionic philosophy as the "fifth element" (the quintessence), on the principle that the four terrestrial elements were subject to change and moved naturally in straight lines while no change had been observed in the celestial regions and the heavenly bodies moved in circles. In Aristotle's system aether had no qualities (was neither hot, cold, wet, or dry), was incapable of change (with the exception of change of place), and by its nature moved in circles. Medieval scholastic philosophers granted aether changes of density, in which the bodies of the planets were considered to be denser than the medium which filled the rest of the universe." - from wikipedia