Cut and Dry (wizard adventure school, oc setting)

[filigree]

Explaining Magic 101

Overview:

In generic terms, each school of magic is a single, broadly useful spell, which is then adjusted to have different uses or effects as needed. A school's root spell is called its foundational formula, and the parts of a formula that can be altered are called its principles.

To use evocation as an example, its foundational formula could be called a matter-energy conversion equation, and its principles are elementalism (the "engine"), theory of force (the "spark plug"), storm magic (the "intake" and "output"), and constructs and artifice (magitech). It's a very popular school of magic since its use is the closest to classical physics, and has few practical limits on what it can't do as long as you know how to modify the equation correctly.

These are things the main character knows, and does on their own as part of the writing. For readers it isn't necessary to do, but doing it anyways will give you a more direct hand in spell design if you want it.

All spellcraft starts at one of these foundational formulas, then manipulates its principles to achieve specific results. Going back to the evocation example, the formula which is essentially matter-energy conversion could be made to magically convert air into fire by inscribing the sigil defining air to the formula's input and fire to its output. This would ordinarily just flash-convert all air in the spell's area to fire, which is absurdly dangerous for a wizard who hasn't figured out how to specify distance or direction yet.

By including additional sigils to define which air is being used as the input, the spell can be changed from converting all air in its area to converting a specific pocket of air, and then the output can be changed from producing fire in an undefined output to producing fire in, say, a forward stream. This is a typical flamethrower spell that creates a stream of fire from a reserve of air, and once cast will continue to spew fire until the air reserve runs out. A variation on this can create a stream of air from the reserve of air, essentially just moving the air around.

Most spells work with existing materials and resources, and so aren't very taxing for the wizard to cast. The personal cost of magic is comparable to a spark plug starting an engine, with the engine then running on gas (the intake) afterwards. Larger, more complex spells with multiple formulas will require a bigger initial spark to start up, but even then the bulk of the difficulty comes from spellcraft as a skill, not so much the actual casting.

The catch is that spellwork only rarely uses actual number math. The evocation formula is the most well researched, and cleanly works by manipulating definitions of objects, locations, and sets, and by exploiting 1:1 efficiency ratios. The less researched illumination spells appear to work by changing how destiny applies to a person. Transmutation spells work by defining a body or ingredient as a set of properties, then modifying those properties or transferring them into a separate set of properties.

Magical theory is incomplete; there is no sixth sense for magic, so wizards only know how a spell works by comparing the real results against what they expected from their equations. Whole chunks of the curriculum are guesswork built on assumptions, but all an adventuring party asks is that the spells work as expected. Some wizards will pursue arcane secrets their whole lives in a quest for true understanding, but for most it's enough that they can live to see the next dungeon delve.

Foundational Formulas and their Principles:

The evocation formula, as the example above, is an equation for matter-energy conversion. Build the magical equation from known sigils and known interactions, pay an upfront mana cost to start the process, then it operates continuously until it runs out of intake.
- Elementalism's principles takes evocation and focuses specifically on the conversion part of it. Turning rocks into fire, fire into water, water into air, or otherwise. This same process can also be used to 'convert' an element into an active state, such as causing a boulder at rest to be a boulder in motion.
- Theory of Force focuses wholly on the "spark plug" part of the evocation formula, separating it from elemental reactions to instead turn magic input into magic output. This is much more taxing on the caster since their magic reserves are the intake, but magical force behaves however you want it to, as long as you can foot the bill for it.
- Storm Magic focuses on the intake and output parts of the formula to create escalating phenomena. Their output is usually a convergence or chain reaction of several varied and synergistic inputs, and often feeds back into the system to further prolong it.
- Constructs and Artifice is the physical, mechanical application of other evocation principles to create tools, weapons, and in some cases near-magitech with elemental properties. This includes golems and flaming swords, but also horseless carriages and indoor heating.

There is no unified illumination formula, since core aspects of the school are proscribed for a variety of honestly pretty good reasons. In this case, keep in mind that what is called "formulas" are actually principles of a formula for a school that isn't formally unified.
- Divination began as astrology, but also includes water scrying, crystal balls, and other methods that reflect or refract the cosmic light. No two people see the same night sky, so prisms, mirrors, and lenses are used to approximate how another person sees the sky-spanning equations of their own infinite possibilities.
- Enchanting changes how a person is affected by the destinies of others. This can be used to create love or hatred between friends and enemies, to cause a person to fail against another when they would have succeeded, or to steal their fortunes away from them.
- Observation was at one time called abjuration, and was thought to work by forcing a particular interpretation of another person's destiny onto them. This changed following a paradigm shift in how stars were perceived, from points of light on a flat surface to points of lights in a three dimensional space, and now the principle is thought to work by changing another person's destiny relative to the observing wizard's.
- Conjuration, in technical terms, seeks parallels between the signs of the casting wizard and a cooperating extra planar being to tie their fates together. From there, and with further cooperation, the two can work with their shared signs to create an agreement that can only be broken at significant cost. Every conjuration student's first lesson is to not make contracts with beings who can afford to break them.
- Necromancy is a school that seems to exist in opposition to the other illumination schools, and is the biggest obstacle to a true unified theory. Necromancy's formula divorces an observer from their destiny entirely, trapping the living and dead alike in a state that is neither life nor death, in a lightless fate where past and future have no meaning.

The transmutation formula is softer than the hard maths of evocation or the determinism of illumination, and must be inscribed directly on the body or reagents being affected. Its foundational formula is an equation to define a body or group of reagents as a set of properties, with the wizard then using the sigils for which properties they want the spell to act on, and then closing the formula with how the spell is meant to act on those properties.
- Alchemy separates the formula into two parts, with the set of definitions being inscribed on the bottle of potion, and the closing effects being inscribed or tattooed on the wizard. This system of a separated formula that the wizard casts by "bridging" is also used in the other schools to simplify complex spellwork.
- Fleshcrafting alters the properties of a mass of flesh directly, reshaping it into homunculi with just enough biology to be alive and fulfill the purpose they're made for. The principle is certainly capable of more than this, but the royal crown is having none of that.
- The Chimeric Arts require a double ended version of the foundational transmutation formula, each end of which is inscribed on a separate body, and which when completed must resolve into an equivalency. This isn't saying each body must be identical, but rather that the additions and subtractions of properties to either body must equal one body between the two of them. From there, the two then have to be surgically conjoined to match the completed formula, and the result is a living chimera that breeds true, for reasons not yet known.
- Transformation rewrites the foundational formula as a closed loop to define a property in a reagent or body which is to be altered or transferred. Unlike the chimeric arts, this doesn't change the fundamental nature of anything involved, and any changes made can revert if the inscriptions are removed.

Sigils:

Every wizard's spellbook is written from a lifetime of research and practical testing, all in the pursuit of learning how to represent ideas or things within a magical equation. A sigil is that representation, and they are written into a formula's principles to create a spell that behaves as written. You'll learn sigils from classes directly, but can also experiment on your own to create new sigils for things you don't know yet, or for things the academy isn't likely to teach you.

tl;dr: formulas are a sentence, principles are the blanks, sigils are words you can put in those blanks. Wizards make magic by playing madlibs with the universe.