Division by Zero

Board first — evidence photos, timestamps, the axe found forty yards from where Emil died, Delaney's silence sitting in its own column like a variable with no assigned value yet. He doesn't write theories on the board. He writes conditions. What has to be true, given what is already true.

Emil's stream — 800,000 witnesses and not one usable account of the ten seconds that mattered, because ten seconds of raw signal drowns in a chat scrolling too fast to read. Markan has spent three nights extracting the six frames that count out of forty thousand that don't. He does not call this tedious. He calls it filtering entropy, and means it exactly the way it sounds — coldly, gratefully. He has, at various points, referred to the chat log as "beautiful" out loud, to no one, and startled himself both times.

Delaney's silence he has already priced. Not an absence. A number. The lack of a statement is itself the loudest thing in the file, and he has treated it that way since hour one : a storm on the verge of breaking, he wrote once, in the margin, half to himself, and has not been able to improve on it since, which irritates him more than the case itself does some nights. He is a man capable of modeling a killer's psychology to four decimal places and incapable of writing a second good sentence about her.

What he has, as of tonight, is a shape. Not a name yet, but a shape close enough to one that he allows himself, alone in the office at 1 a.m., something almost like satisfaction — the small, private satisfaction of a man who has just beaten himself at chess and has no one to gloat to about it. The curve has stayed convex. Everything Delaney has done since Emil's death has continued in the direction her earlier behavior already promised — the fixation, the need for narrative control, the singular gravity of one person she has never stopped orbiting.

The Fighter.

Zeroed out, in his model, months ago. A man who left the equation before Markan ever opened the file , vanished, untraceable, functionally absent from every variable that mattered. Markan had not ignored him. He had solved him, the way you solve for a constant that doesn't move: by setting it aside, and had felt, at the time, a faint smugness about it, the way he feels about any elegantly discarded term.

He almost doesn't take it — three days of half-sleep have taught him to let the small pings go — but the caller ID is a name he flagged two weeks ago and forgot he'd flagged, back when it was still theoretical, filed under a header in his own notes that reads, only half as a joke: variables I am choosing not to worry about.

He listens. Doesn't write anything down at first, which is unlike him. His pen sits capped in his hand the entire call, an object he is, for once, not using as an extension of his own thinking.

The Fighter is in Chicago. Has been for over a week. Living, eating breakfast, having conversations — a full re-entry into the exact geography Delaney's entire post-Emil trajectory has been quietly, obsessively orbiting.

For the first time in this case, he does not reach for the marker.

Because here is the problem, and it is not a problem of missing data ; he has solved for missing data a hundred times, that's what the whole apparatus exists to do. This is a different kind of gap. He had built the entire curve, every convexity check, every posterior update, on a system with one variable permanently fixed at zero. And a variable that has been zero for months, in a system this finely tuned, does not simply become non-zero.

He thinks, unbidden, of the phrase he used with his lieutenant last week, trying to sound clever: division by zero. He'd meant it as color. A flourish, the kind of line he collects the way other men collect ties. He is starting to understand it was closer to literal than he intended — because there is no way to smoothly re-integrate a term you defined as absent. The function doesn't bend to accommodate it. It breaks, and everything downstream of the break is now unknown in a way nothing else in this file has been unknown.

It is the first time in the entire case that Damien Markan has put something on that board he does not yet know how to solve. He looks at the two words ; a man's name, and the word undefined, sitting side by side ; and has the sudden, useless thought that it looks less like a case file and more like the beginning of a very bad theorem.

He does not find this exciting, the way he has found every other stage of this case exciting. He finds it, for the first time, frightening — and cannot immediately locate the mathematics for why one feels so different from the other. He eats the rest of the egg anyway, cold, on principle, and does not go home.