The Poetry of Number
Lore by Sagwort
Credit to Toxzero & Phil for commentary
“Mathematics are most necessary in magic, for everything which is done through natural virtue is governed by number, weight, and measure. By mathematics one can produce without any natural virtue, operations which seem natural, statues and figures which move and speak. Pythagoras said that numbers have more reality than natural things, hence the superiority of mathematical magic to natural magic.”
STOP, READ THIS
Arithmancy, the distilled beauty of man’s knowledge of reality. Like the poet composes inspiring verses and prose within the age old rules of rhythm and linguistics, so too does the arithmancer bend the will of nature utilizing the very fabric of its being, that is, the wonders of ratios, numbers, and their relation. While the voidal magi might spend their days observing and recording natural phenomenon in hopes of reproducing it through their nixian magic, the arithmancers busy themselves within some fetid study pouring over charts and equations, distilling the abstract essence of these same natural phenomenon through language and number. In this way, arithmancy is inherently “rational” in its execution while normal voidal magics are empirical. While arithmancy is not technically a distinct magical discipline within its own right, it is a form of magical study, a curiosity for magi and scholars alike. However, arithmancy’s focus on mathematics, pattern identification and symbology links it more closely to alchemy and glyph enchanting than the traditional voidal magic.
Concept art from FFXIV arcanist class, which is where this magic was inspired
Arithmancy, as a field of study, is a composition of three distinct skill sets which are: gematria, metrica, and formulae writing. Together, these makes up the breadth of arithmancy, all of them required to effectively practice this abstruse magic.
The Governing Laws
The entirety of arithmancy is built upon two laws: the law of names, and the law of abstract reality. They are described herein.
Law of Names
The law of names suggests that since all magi have a connection to the void through thought, so too does language, as language is but a translation of thought. Just as the magi might use their own mind to weave spells of the void, language may be utilized by arithmancers in a similar fashion. Of course, being a translation, much of the original thought loses its potency upon utterance so the magi must use arithmancy to strengthen this power of language.
Law of Abstract Reality
The law of abstract reality states that reality, finding origin in the void, is nothing more than organized and materialized chaos that is the void. This is, to mortal minds, represented through relation, number, measure, space, etc… Giving order to discord.
These two laws are used in tandem by the arithmancers. Words have power, and mathematics is the ordering of voidal chaos, thus, by ascribing mathematics to language one is able to bolster these inherent laws of reality and manipulate it to some degree. This is the discipline of arithmancy, manipulating language and mathematics to alter and reorder. These methods are described through Gematria, the assigning of value to words and Metrica, the study of ratio and numerical relations and their meaning to language.
While more commonly known as numerology, Gematria is one of the three primary disciplines of arithmancy and is the study of assigning linguistic meaning and symbolism to numbers. Study of gematria provides arithmancers with foundational knowledge in performing their magic.
The Mather’s Table
Perhaps the most widely utilized tool of the artihmancer is the Mather’s Table which is is the table of single digit numbers and the letters which they represent.
Using this table words or entire phrases may be assigned numeric value. For instance, the letters used in the word fire are 6, 9, 9, and 5. These values can be added together to produce 29. 2 and 9 can then be added together to produce 11. 1 and 1 can be added together to produce 2. This single digit value is the vibrational value of the word fire. This value reveals a certain hidden nature of the word which is what defines the practice of numerology or gematria.
There is a more “disputed” practice among arithmancers to attempt to predict future events utilizing this technique and the names of people or certain dates.
For instance, the name Billy Bob has the values 2 + 9 + 3 + 3 + 7 + 2 + 6 + 2 = 34. 3 + 4 = 7. Thus, the vibrational value of Billy Bob is 7.
Or, the date 2/13/1619 is added to produce 2 + 1 + 3 +1 + 6 + 1 + 9 = 23, 2 + 3 = 5. The vibrational value of the 13th of the Amber Cold, 1619 is 5.
These vibrational values can, theoretically, be used to provide insight into a particular person, family, or date. Granted, whether or not vibrational values can be used in divination is up for debate.
Metrica, or arcane geometry, is the fine science of ratios and proportions. While a great deal of useful magic can be produced using basic gematria, by applying metrica more complex and specific magic formulae can be produced, which will be elaborated on later.
One of the most integral concepts in metrica is the prime numbers: 2, 3, 5, 7, 11, 13, 17, etc...
A visualization of prime numbers
While any word can be summed to produce any number, in order to have any amount of significant power the word must initially sum to produce a prime number. For instance, fire is 6 + 9 + 9 + 5 = 29. This is a prime number and, thus, the word fire has strong voidal ties. We shall call these prime number words, words of power, in that, prime numbers are only divisible by themselves and the number one which makes them the “fundamental values” of arithmancy. Notice that when summing words, only use vibrational values, that is, never sum values with more than one digit.
When producing magical formulae only words of power may be used. This makes producing magical formulae exceedingly tedious and the need to construct lexicons of words of power to easily be pulled from is useful. In this way, spells are not created but discovered.
Another fundamental property in metrica is the vibrational sequences or a sequence of numbers which all sum to the same vibrational value.
Any number within a vibrational sequence can also represent its vibrational value in a magic square. This allows arithmancer to utilize larger and larger squares for more powerful formulae. This will be explained next.
A Brief Lexicon of Words of Power
These words of power are used in formulae to determine “how” the magic takes place.
Summon - 23
Induce - 29
Disperse - 41
Hurl - 23
Ward - 29
Ignite - 37
Energy Descriptor Words
These words of power are used in formulae to determine “what” magic takes place.
Fire - 29
Aqua - 13
Ice - 17
Wind - 23
Stone - 19
Sand - 11
Burn - 19
Light - 29
Bugs - 13
Avoirdupois - 59
Addle - 17
Weariness - 41
Force - 29
Aegis - 23
These words are used to modify descriptor words.
Evocation - 41
Illusory - 41
Orb - 17
Aegis - 23
Shard - 23
The magic square is founded on basic arithmetic concepts where the numbers in any direction on the square add up to the same number. More complex square are considered to produce more powerful formulae. There exists five practiced magical squares, though there is theoretically infinite.
The value each row adds up to is known as the magic constant.
Generally speaking, the larger the square the more powerful the spell. For this reason, arithmancers use vibrational sequences so they can represent vibrational values as larger numbers and, thus, use larger squares. Essentially each square is a “tier” in magic totalling in five, the progression of use of quite similar to normal magic tier progression, except less subjective.
Tier 1 Magic Square
All numbers add up to 45, each row adds up to 15
Tier 2 Magic Square
All numbers add up to 136, each row adds up to 34
Tier 3 Magic Square
All numbers add up to 325, each row adds up to 65
Tier 4 Magic Square
All numbers add up to 666, each row adds up to 111
Tier 5 Magic Square
All numbers add up to 1225, each row adds up to 175
Creating magical formulae is the cornerstone technique in practical arithmancy which utilizes all the above techniques. The process can be broken into 4 steps:
An arithmancer produces a magical formulae
1. Describing intent
At this point, the arithmancer must decide what they want their formulae to depict and produce.
For example, we wish to produce a magic formula that will protect against fire evocation. Thus, the arithmancer must determine the most efficient way to produce such instruction clearly and without any potential misinterpretation, exact language is crucial. Remember, only words of power can be used when describing intent. For instance, to produce a magical formula to ward against fire evocations one would use the words of power ward fire evocation.
2. Reducing intent to numeric cipher
Once the intent has been clearly described it must then be reduced into its numeric cipher. Note that one should refer to individual letters and their respective vibrational values when reducing. If one were to use the vibrational values or one of the sums of a word in the phrase and then drew the formula, it would be impossible to interpret.
First, all vowels are removed from the intent: WRD FR VCTN
This becomes the numerical cipher 5-9-4 6-9 4-3-2-5
Stumped by a particularly difficult formula
3. Select magic square
Now, the arithmancer must select a magic square to produce the formula upon. The larger the numbers used in the formula the more powerful the formula. Thus, advanced arithmancers use vibrational sequences to increase the values in their formula which then requires the use of larger squares.
Notice that words cannot start and/or end on a number which is repeated anywhere else in the cipher.
Assuming our arithmancer has full knowledge of all magical squares, he will maximise their spell power by first changing all numbers to their largest possible form.
41-45-49 42-45 49-48-47-41
Then, he will change any repeated numbers at the start or end of words to a lower value within its respective vibrational sequence.
41-45-49 42-36 40-48-47-32
This is the most powerful form of the given magic cipher.
4. Drawing the formula
The most intriguing part of magical formulae is the actual drawing of them upon the magic square. Each word is drawn individually, each number connected by a straight line. Each word starts with an open circle (o) and ends with a short perpendicular line (⟂) or arrow. Note that in order for a number to be considered part of the word it must have a point, circle, or sharp curve. A straight line passing through a number does not include the number it passes through. If the line does happen to move straight through a number but that number should be included in the word, it is marked with a bump in the line over the appropriate number. To indicate two of the same number in a row the line is made with with two bumps in it.
All good arithmancers carry a compass to measure angles for their formulae
If the end of a line and the start of another line are on the same number, a triangle is placed there.
Thus, the words ward, fire and evocation respectively using the above cipher is:
When layered atop each other they produce the full formula.
Induce Weariness | NDC WRNSS | 5-4-3 5-9-5-1-1 | 41-49-48 32-45-23-46-37
Would produce an illusory fatigue to the wearer
Ward Fire Evocation | WRD FR VCTN | 5-9-4 6-9 4-3-2-5
Protects wearer/object against fire evocation
Ward Aqua/Ice Evocation | WRD Q/C VCTN | 5-9-4 8/3 4-3-2-5
Protects wearer/object against water/ice evocation
Ward Stone Evocation | WRD STN VCTN | 5-9-4 1-2-5 4-3-2-5
Protects wearer/object against earth evocation
Ward Wind Evocation | WRD WND VCTN | 5-9-4 5-5-4 4-3-2-5
Protects wearer/object against air evocation
Induce Burn | NDC BURN | 5-4-3 2-3-9-5
Causes wearer to feel burning sensation, or any who touch object feel burning sensation
Ignite | GNT | 7-5-2
Formulae ignites spontaneously
Induce Avoirdupois | NDC VRDPS | 5-4-3 4-9-4-7-1
Causes object to feel heavier
Summon Light | SMMN LGHT | 1-4-4-5 3-8-7-2 | 46-49-49-41 48-44-43-47
Causes object to glow
Summon Aegis Orb | SMMN GS RB | 1-4-4-5 7-1 9-2
Summons a spherical arcanic shield around wearer
Summon Aegis Barricade | SMMN GS BRRCD | 1-4-4-5 7-1 2-9-9-3-4
Summons an arcanic shield wall before the wearer
On Roleplaying an Arithmancer
Arithmancy is, of course, not for everyone and, I believe, would require a very distinct sort of playstyle that goes beyond spell slinging. One might be turned off by the amount of independent work required to perform arithmancy. In fact, the very act of being an arithmancer forces the player to produce a character willing to live a quiet scholarly life pouring of charts, formulas, magic squares, tables, etc…
Women can be arithmancers too!
One visual goal of the arithmancer image was to produce a magi that, may not, be entirely grounded in reality or even practicality even though an arithmancer might consider themselves above a far more practical and… even “powerful” voidal magi due to arithmancy’s “logical purity”. It is a magic for high society scholars, professors, and academics. Imagine walking around, always with a hefty tome at your character’s side containing all myriad of charts, graphs, formulae, drawings, and, of course, a lexicon of words of power.
IDK, maybe he just activated one of his formulae and is now using it