Excerpt: Arithmantic Lemmata in Antipodal Matrices, or: a Concise Compendium of Alchemical Directed Set Theory, as Revised and Annotated by Brother Siclevoldus the Pallid, Fourth Degree Secant to the Order of Catenary Argent

News that the second plague in Rimur had been vanquished reached the ears of Siclevoldus a scant two days later in his cloister within the Barksminster monestary. Two acolytes walking noisily past his door argued amongst themselves about whether there was any cause to worry.

“Surely,” one claimed, “Rimurmann arithmancy is a weak and inferior sort, rough grunts from barbaric wastrels who can scant lift their heads from their cups long enough to discern a planar secant from a lunar tangent, let alone calculate the formulae necessary to tell building from bacteria. What if their Order overlooked a merchant convoy? Or failed to clean one storehouse. The next shipment of pelts here could scourge all of Vandermeer.”

“Don't be daft,” his friend scoffed, “Discerning is the easy part, which you'd know if you paid any attention in the Compositional Trigonometry lectures, instead of daydreaming about Executrix Ellynear.”

“It's Ellynore, you dolt,” the first replied angrily, “and don't be ridiculous. You know as well as I do the ordinances against that.”

“Aff,” he agreed, “but even so, you should remember that simple life forms are much easier to key precepts towards than more complex ones. A bacterium for instance is just a few base elements, you can nearly count its alchemical vectors on one hand. The hard part is the sheer number of them you have to factor in to the polynomial. Cleansing one is easy, but a whole plague requires a sizeble Array of arithmancers to solve the matrix–”

Their voices trrailed off with their footsteps as they continued down the corridor, leaving Siclevoldus awake and irritated in the murky dawn. Several reasons vied for the most irritation, but they shifted maddeningly around as he tried to quantify their relative irk. Not least of all, however was that the dolts' lax grasp of basic math was greatly overshadowed by their assumption of how much they actually knew. As if one would even use a polynomial to address a shifting set like a swarm of plague bacteria when a cubic differential would massively decrease the time necessary to approximate the cardinality.

The second most annoying thing about their intrustion, he decided, was that their quarrelsome ineptitude had distracted him from the game he played every morning– counting every brick in his ceiling, and determining how many factors they derived into from the current day, month, and year.

Then as an added treat, he paired every factor together, beginning at the ends and working inwards, subtracting one from the other, then plotting each sequential pair of sums as an X and Y coordinate on a Kharakizhin plane, and seeing if any of the intersecting angles matched the dipole alignment of the twin suns Mimis and Yfr that morning. Depending which quadrant contained the most matches, he could then determine which direction to roll out of bed and prepare for his day. Most arithmancers of his Degree slept with their beds against one wall or another, to catch the warmth of a sun, or shelter from the wind through the wall grates. Siclevoldus by necessity of ritual had his bed stationed precisely in the middle of his quarters, measured with the singular compulsion he was variously known mocked and loved for, such that he could quit his sleep over any of the four corner posts in the appropriate vector.

Cursing briefly, he began his silent count again, while reciting a series of primes to calm himself again. Today would start half an hour later than planned, but getting up from the wrong corner of the bed was so unthinkable he felt his gorge rising and panic tightening the sides of his eyes.

“Five score and thirteen,” he murmured to quiet his breathing, “six score and seven, six score and eleven, six score and seventeen, six score and nineteen, seven score and nine..”