Numerology and Grammatica

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Arithmancy is a magical discipline that studies the magical properties of numbers, including predicting the future with numbers and numerology. Its name is derived from two Greek words: ἀριθμός (arithmos, number) and μαντεία (manteia, divination).

The study of divination through numbers has been practiced successfully for over two millennia, providing its students - Arithmancers - with the means to map their futures through in-depth analysis of both strengths and weaknesses. Advanced study of this divination method may also provide insight into the creation of innovative spells and potions to further enhance the magical way of life.

Notable arithmancers include Bridget Wenlock, who discovered the magical properties of the number 7 in the 13th century; Professor Septima Vector, a celebrated professor of both Arithmancy and Advanced Arithmancy Studies at Hogwarts in the 1990s; and William Weasley, who leveraged his O.W.L. in the subject to achieve a prestigious Curse-Breaker position at Gringotts.

History
The Ancient Greeks first used a method similar to the Agrippan Method below to divine the outcome of battles by assigning values to the names of known combatants prior to the ninth century BC. Later, the Chaldeans of Arabia practiced a similar form, bridging the gap between arithmancy and astrology by dividing their alphabet into three parts and assigning each letter within the parts to one of the seven known planets.

The Agrippan Method
To analyze an entity, the numerical values are added and reduced in the following manner: all letters, then all vowels, then all consonants. (Vowels are the letters A,E, I, O, and U.) These form the Character Number, the Heart Number, and the Social Number, respectively.

The Heart Number represents the individual's inner life, including desires and fears they may conceal from others.

The Social Number is the "face" that individual shows to the outside world.

The Character Number represents the sum total of their personality, accounting for both inner thoughts and outer appearances.

''Example: Albus Dumbledore becomes 1+3+2+3+1+4+3+4+2+3+5+4+6+9+5= 55. The reduction of this means his Character Number is 1, as 5+5=10 and 1+0=1. Likewise, this character's Heart Number is 5 and his Social Number is also 5 from the reduction of the vowels and consonants.''

Interpreting the Agrippan Method - Modern Western Numerology
It should be noted that this is not an exhaustive interpretation of the possible meanings of each number. Interpretations vary by culture according to superstition, significance, and time: what may be a positive reading now could have caused great anxiety a century prior.

Relationships
Using this method, we can quantify interpersonal relationships, both platonic and romantic. Individuals with the same Character Numbers or Heart Numbers will generally experience great compatibility, either as partners or as best friends. Individuals with identical Social Numbers will work well in public, regardless of their private feelings for one another. However, compatibility is not restricted to identical numbers; a 2 and a 4 may do great things despite their hatred of each other, and a 3 and a 6 complete one another to unparalleled degrees.

Spell Difficulty
It is obvious (or at least it should be) that various spells require different amounts of experience with magic in general to be able to cast. First years, for example, generally lack the ability to cast the Killing Curse, no matter how technically accurate their pronunciation or wand movement may be. The Theory of Basic Thaumaturgic Similarity states that all spells, regardless of type or language, share a fundamentally similar Arithmantic structure and may be measured in Lums (ʆ), from the incantation for the Wand-Lighting Charm. Arithmancy may also play a role in ritual magic, and to a lesser degree, potions crafting, but these are advanced topics best suited to individualized study. The interested student may wish to inquire about a NEWT-level Alchemy course, assuming they pass their OWLs in Runes, Arithmancy, Transfiguration, and Potions.
 * Objective Difficulty - A standardized comparison of skill required to cast a spell.
 * Apparent Difficulty - A spell's Objective Difficulty, when scaled to the year level of the caster according to the Theory of Progression.
 * Practical Difficulty - The most subjective of the three, an individual's ability to successfully cast the spell. With continued study and focus on a particular spell, the student may acquire proficiency if Apparent Difficulty reaches zero; mastery is said to have occurred if the caster produces exceptional or unusual results in addition to consistent success when casting.

Appendix I: Historical Numerology and Motifs
Medieval Europe adopted a three-pronged approach to the symbology of numbers, integrating elementary (or "self-apparent"), astrological, and Pythagorean justifications into their understanding of the world around them. Below are some interesting motifs and deviations from the above symbology, as well as an attempt to succinctly explain their sources. For an example of an extremely complex motif with a basis in numerology, one need only look at the 144,000 elect in the book of Revelation, as described in the Christian tradition. Far from being arbitrary, this number can be broken down into a square of 12 - completion completed - raised to the power of 1000, or the third exponent of ten - a divine amplification. Many other numerological motifs in Revelation and other apocryphal books may be found and thus dissected according to the tradition of the time. This is an example of the necessity of historical study for prophecies and their interpretations - meanings change over time, and the lens of each successive century will almost inevitably shift in some way away from the previously held views of the dominant culture.