Not many possess the arcane potential to cast even the simplest spell, until recently it was impossible for people with that limited potential to draw arcane energy from any source.
Many, who lacked magical potential but still wished to pursue the study of arcane, simply became theoretical researchers of spells.
What is precise magic? It's magic, that contrary to usual practices, focuses on fine control of source rather than drawing enough magical potential.
It's different than standard control of arcane in such a way, that levels of arcane manipulation are minuscule, smaller than molecules or atoms.
On such levels, mana tends to behave differently and tends to draw out more power than usual. Such power, of course, is dangerous. Precise magic performed with high amounts of mana could in most, but not all cases, lead to instability and chain reaction, which would result in failure of spell or a rather violent explosion.
That's why students with a low amount of mana are perfect to pursue precise magic, although it's a demanding and hard subject, so not many manage to pass.
How to differentiate between precise magic and standard magic?
For example, let's take standard an arcane shield. For the starters, its defensive potential would be based on the density of barrier and thickness, and the shield itself would be a pretty uniform body.
In terms of precision magic, one would develop a very thin shield made of millions of tiny triangular shields, then would carefully study enemy spells. What type is it, the flow of the arcane energy, and other intricate details. It often requires strenuous calculations and approximations. Upon performing such, the defender would adjust the gradient of his shield to effectively counteract the spell by dispersing it, or by deflecting it in another direction.
Another example would be arcane missiles. While the standard version is a simple accumulation of force and usually the size of a fist, the precise version is no langer than a tip of a finger, and works in such a way that the caster effectively tries to find gaps in the enemy arcane defense and flexibly adjust the tip of a missile to squeeze or pierce through the weaker section of the surface.
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Another aspect of precision magic is its relation to density and thinness. If strands of mana are in an entity are exceptionally thin and at the same time sufficiently dense, then the entity can experience full effects of precision magic.
One of such effects is changes in time dilation, which is the basis of haste spell or in extreme cases, stopping the time altogether. Of course, not only reducing the thinness of one's mana strands to the proper level is a time-consuming process and requires preparation, but requires high levels of stamina to sustain the control of the spell for sufficient time.
Now, let's return to users with a high amount of powers and capable of advanced precision magic. Currently, only a few spells are available for such casters. They're all basing their power on singularities.
For the magic of destructive type, there theoretically exists a spell that can be cast by just one person and is capable of destroying entire cities.
There exist gravitational singularities that pull everything towards the source point in a short period of time.
There exist time singularities that slow the movement of nearby entities.
It's still in an experimental phase, but it's predicted that healing singularities might allow complete removal of diseases and toxic substances from one's body.
Another appliance of precision magic is dynamic, programmable spellcasting, where the caster doesn't have to sequentially cast an advanced spell, but instead, the spell casts itself based on implemented procedures, which allows users of precise magic to access more complex spell as long as they possess required stamina, level of control and someone implements those spells for them.
Programmable spellcasting not only applies to students of the arcane, but also to the new branch of arcane, that is intelligent arcane devices.
We're currently in a phase of testing, but it was possible to build a first arcane processor – a non-living entity - capable of theoretically casting any type of programmable spell on its own. We still lack materials and conductors required for higher-level spells that would have some use in the industry, but it is within the realm of possibility in the next twenty to fifty years.
At last, one of the omitted appliances of precision magic was manipulation of space itself. Currently, it's a matter of very precise control and unimaginable amounts of energy at the same time, but we believe it's theoretically possible to construct small spheres of pocket universes, or bridges (portals) between two destinations.
The spatial magic is a whole new subject, which could lead to spells such as temporarily shrinking or enlarging desired entities or spaces between entities, reversibly shifting their position in space, or even teleporting them. One should not forget a subject of intangibility, which is a stronger version of already available displacement.