This is a series of lores found within the game
Arthmancy and its Application to Magic
Part I
"The Aspiring Arthmancer
No subject in Academagia is as wide spread, and sometimes lamentable, as Mathematics. Quite frankly, there’s a disturbing number of students who wonder what the purpose of Mathematics is, in a world where variables are changed as swiftly as a wave of a wand.
What is the purpose of learning what 2 + 2 equals… when a defiant young wizard can put four apples into a basket, wave his wand, and suddenly there will be five? How can you begin to say 2 + 2 does not equal 5 when the boy can say: “Sure it does. Look!”
In practical, non-magic application - Math is a discipline that is invaluable. Mathematicians have the prestige given to potentates and merchant princes, and ever more advanced algorithms are daily being created to understand natural phenomenon. But for mages, the importance of Mathematics has often been dismissed.
That was until a brilliant young mage named Horace Godfreed began to look at magic in a non-practical way. He began to see how words and gesticulations were used to formulate spells and realized, at its core, magic is mathematically based. How to say the words of power were a function of when to wave the wand or hand.
A wizard who has ingrained formulae into their heads could produce amazing results with spells, doubling - sometimes even tripling their efficiency. Later chapters give examples of how Arthmancy can be applied to the mainstream schools of study."
Part II
"The Practice of Arthmancy
Magic is the study of Phemes. On the surface, it seems relatively straightforward: from thin air, roses. A shimmering illusion appears in the night. A spoken command is uttered to dispel the magic of others. Mathematics seems to have no application here at all.
But while drawing the Phemes, and speaking the words of power, a skilled Arthmancer can add the power of Mathematics to his spell. It’s a complex discipline, but it boils down to a simple understanding of the natural laws.
By employing the Phemes which are expressions of these laws, you can change your spells in any number of ways. For instance, you could create double the amount of objects you were planning to - or divide the size of an object by 12. Using more complex functions, you could create a Spell which only has effect every 10 days, or one which waxes and wanes in power over a period of time.
One practical application is illustrated by the fell wizard Destrobeign. It was said, during a Duel, he created two daggers floating in the air before him. Using a complex group of Phemes, he was able to infuse the spell with the 6th power of 2, which any mathematician can tell you, is 64. Thus, 2 daggers immediately became 64 - and, with but a single word of power, they all flew at his enemy at once.
Part III
"Arthmancy in Astrology
No magic is more open to Arthmancy than the mathematical projections which are determined by careful study of the stars. While no magic has been able to alter or change the stars, the mathematical principles and arithmetic values in physics still remain applicable to the stars.
A skilled Astromancer can utilize the position of the stars, and glean today’s secrets of the cosmos. But one who is skilled in the art of Arthmancy can also determine the alignment of the stars tomorrow, next week… even next year.
Should their calculations be correct, and they are able to plot the course of the stars through the sky, it’s said that one may indeed achieve a level of omnipotence, with no fate a mystery to him or her.
Thus far, the most successful Arthmancer/Astromancer has only been able to predict the future within seven months time, by effectively plotting the course of a thousand stars, and determining what their alignment would be seven months later. While the effort took him almost thirty years, he was able to glean all the events within a seven month window, and - for that time - no man, woman or event was capable of surprising him.
Or so he claimed."
Part IV
"Arthmancy in Glamour
There is no greater way to create convincing glamour than allowing some degree of randomness. Even the best illusionists are sometimes discovered by other illusionists simply because they create every glamour the same way, with the same signature appearances and aura - for those keen enough to perceive it.
By adding certain Mathematical Phemes to introduce randomness, a skilled illusionist is able to conjure Glamours which surprise even himself, by allowing the principles of his mathematics to dictate the little features within his illusions.
For example, Melvin Chames - one of the only few known Glamour specialists who practice Arthmancy as well - is able to create one-hundred thousand disguises, without duplicating more than five common features between them. All this the product of one Spell, with no need to adjust or think about it!
Another of his Spells enables the creation of an illusion of a random location, populated with the level of detail that would take a regular illusionists hours of consideration to replicate, simply by employing Mathematical functions to create randomness. Every little detail from the foreground, background - even whether there is a lost sandal in a tree, or an ant colony in the ground, can be determined by the spell, if properly cast."
Part V
"Arthmancy in Incantation (1 of 2)
At first, there seems little that could be applied mathematically to the ability to throw fireballs, or shoot lightning from ones fingertips - until you break that down to its basic concepts. What is a fireball but a sum of Phemes, incantations, gestures and primordial force?
When magic fails, your Palette simply could not contain the magic which was channeled - and the spell fizzles, the extra power defusing either in a harmless puff of smoke… or setting your robe on fire!
But a skilled Arthmancer can be a master of failed magic. By superior knowledge of the mathematical Phemes they can govern and limit channeled magic over time - and they are able to create simply astounding effects.
There have been few notable Arthmancers who have specialized in Incantation - after all, there’s only so many interesting variables in how to translate magic into the powers of natural forces, however exciting to the imagination it may be. Even few of the best duelists bother with the clumsiness of channeled, raw magic - instead favoring finesse, the devious abilities manifested by Revision or the defensive powers of Negation."
Part VI
"Arthmancy in Incantation (2 of 2)
Discus Hatias Tekariat was, perhaps, the most noteworthy Arthmancer/Incanter. He was one of the first members who attended Academagia from Alesfa. On his return journey, his caravan was attacked by outriders from Ghawan.
He hurled incantations toward the desert riders… fireball after fireball, lightning bolt after lightning bolt. All of them arced toward the enemy. Wisely, they took cover, expertly breaking their formation so that the fewest among them might be struck. Yet, before each spell impacted, they fizzled out halfway to their destination.
The riders laughed, and laughed, as the young man struggled with his magic, throwing ineffective balls of fire their way. After approximately twenty such failed spells, the chieftain grew impatient and ordered Discus killed.
The riders of the rose from their dune shelters and protections, and rode as swift as the wind towards the young man, their spears eager for his blood!
Discus smiled, and uttered a simple incantation. Suddenly, every single spell he had cast, all twenty, emerged from their failed states at the same time, blasting the exposed army with fire. By simply withholding the exact, correct gesture and vocalization, his spells had remained active, just waiting to be completed."
Part VII
"Arthmancy in Negation
Negation has a great deal of uses for a skilled Arthmancer, well beyond that of the average school. One technique, pioneered by the legendary wizard Delric d’Onyx, is based heavily around the principles of Calculus.
A typical wizard learns Shield Negation before the end of his first year. Yet, this simple shield negation can become so much more by using mathematics to describe a deflection function.
When an offensive spell is cast upon you, with a touch of Arthmancy, one can not only protect oneself from the spell, but shape their shield as they see fit to deflect the offensive spell in whatever direction they preferred… even back at the original caster, if one is able to solve for the aggressor's position in time.
The famous story of the Wizardress Blanche of Meryonne is made more interesting by learning that her renowned duel was won because she spent the entire night before it calculating the shape of the shield necessary to reflect the spells her spies had told her her opponents would use first. She remains to this day the only mage to ever win a 15 to 1 duel… in exactly 1 move. When each of her foes cast a spell on her, each one was redirected back upon another, and - when the smoke cleared - she stood alone."
Part VIII
"Arthmancy in Revision
In truth, no field of magical study is more closely linked with Arthmancy than Revision. In fact, to the untrained eye, Arthmancy is merely Revision in the form of mathematical pretext. Both are used to alter the effects of specific spells.
However, where they differ is in complexity. Even a simple mage with a limited understand of Revision is capable of applying it to their spells, changing their effects on the fly. By using different one of a million alterations on phonetics, gesticulations and calligraphy, a skilled Revisionist can create many effects - but no human mind can possibly grasp all the variations.
Arthmancy allows you to create new effects upon the fly, and even discover the exact phonetic used to create whatever effect you wish without prior knowledge. Just as a mathematician doesn’t know the value of X before he’s solved an equation - neither does a skilled Arthmancer. By process of mental math, he’s capable of determine the exact change is needed to produce an effect.
For example, if you know what original magical effect you want to create, and you know in order to alter an existing spell to create it, you need to change a single Pheme… that Pheme becomes your only unknown. From there, it’s a mental process to “solve for X”, and determine exactly what the Pheme should be. Of course, it is never that simple- if you do not have knowledge of the Phemes, Arthmancy cannot help you- at least, not without significant study and further research."