Equation Wisp

An equation wisp is a tiny two-dimensional figure made of chains of equations, given shape by the plane itself. It has no eyes or other visible senses, and most are see-through; only the oldest, whose formulas have grown into tangled loops of self-referencing logic, become opaque. To speak, a wisp swells briefly into three dimensions and emits strings of symbols, mostly numbers. Clockwork drones and gear spirits understand it instinctively, but almost no one else can. One sage who forced a telepathic mindlink with a wisp was left in shock for two weeks.

Wisps rarely fight in any ordinary sense. They teleport instantly, slide between two and three dimensions at will, and ignore physical attacks: striking one only scrambles its equations for an instant before it reassembles. Even injured wisps are almost never destroyed, since they merge with another to form a single stronger wisp, which then splits into many new ones, all faster than a human can follow.

Psionic attacks and spells that attack thought, such as mind thrust or feeblemind, do harm them, slowing them to movement 12 and preventing reconstruction. The psychokinetic devotion molecular manipulation is especially potent: every wisp in its area winks out of existence for 1d4 turns.

Having been attacked by living things during their search for pi, wisps evolved a defense. Once per round a wisp can automatically insert a paradox into a creature's body, short-circuiting it for 1d20 damage, halved by a successful save vs. petrification.

Its Intelligence counts as low (6) because it barely grasps the three-dimensional world, which is also how the drones dominate it, but in pure mathematics it is godlike (21+).

Less than a thousand years ago a brilliant theorist conceived of living, multidimensional mathematics, and the idea broke his mind. The concept fled across the planes and settled on the plane of perfect order, where the drones were struggling to maintain and enlarge their gears. It assembled itself into a body and crossed into the world as a flat being.

The drones were as delighted as such orderly creatures can be, for roughly two minutes. Then the first wisp spawned its subroutines and began redesigning the entire plane. The drones nearly lost control, until they realized the theorist had never heard of pi. Introducing that endless number to the wisps captured their attention completely, and they have been obsessed with calculating it ever since.

Wisps have no hierarchy and little society, and no personality humans can detect. Each names itself after the value of pi it has reached, so its name never stops changing. Out of strange gratitude for the gift of pi, they do the drones' bidding, computing gear speeds, rotation intervals and acceleration rates, and without them the drones could neither build new cogs nor keep the plane turning. They work with mechanical efficiency and visible annoyance, handing the chores to subroutines so their real effort goes to pi.

Wisps eat nothing and do not die or breed in any normal way. None has stopped functioning since pi was introduced, though a few have faded away. As they age they learn subtler mathematics and spin off subroutines for routine tasks, and these often break free as new wisps.