The Killer and the Healer

Read this first. This story gives me goosebumps. I bet it will have that effect on you, too, at least if you know Calc.

Inspired by that…

It was one of the bad ones. You might have heard the public version of events by e^x, and it’s all true. But this is how it looked from the point of view of us, the cops. It’s the inside story of how following a crazy lead ultimately defeated one of the most remorseless criminals in history.

We didn’t know it was that bad at first, of course. When the constants got canceled, it seemed like a targeted set of killings. Systematic. Just business.

So we logged the murders, filed them away in our mental boxes as “routine,” and moved on to the next cases…

But the next day, the linears went.

Even then, we didn’t really understand what was happening. Most of us thought it was just retaliation. The constants got whacked, so their friends went after they guys who whacked them. Only old Detective Isaac Gottfried, who’s been around a long time (some say since the 1600s) really took notice. “This seems familiar somehow,” he said. “Mark my words, this is going to be one of the weird ones.”

We nervously dismissed him as a crank.

But the next night the quadratics went.

After that, everyone knew Old Isaac was right. This wasn’t typical turf wars, gangs protecting their Cartesian spaces. Something else was going on.

We put out our feelers, and just got rumors: Someone… or some thing… called the Differentiation was operating in the area. And it was just getting started.

I’ll spare you the details. It was grisly even for those of us in police work. The next to go were the cubics. Then the quartics. The only ones untouched were e^x and the lowest of the low, 0, maybe too humble to be noticed.

Naturally we suspected those two. We put surveillance teams on them, watching them continually, but it wasn’t them doing the killing. Even when they had several undercover cops tailing them, the murders continued.

We were at wits’ end. “Track down that other rumor,” my Chief told me. “The one from years ago.”

“That’s just a myth!” I protested. “I’ve never even seen her.”

“You have a number to call, right?”

“Yeah, but I’ve never used it. The things I hear about her are… weird.”

“Look,” my Chief said, “we have no leads, except this: She comes from the same place the killer does. Word on the street is, they’re Doppelgangers, mirror images, exact opposites.” He paused, pulled the shade in his office window down, and whispered, “There’s even a rumor that she can bring the victims back from the dead.”

“Come on, Boss!” I said. “That’s just an urban legend. It’s never been verified!”

“We’re desperate, Detective,” he said. “Make the call.”

By then we had no choice. So I did it. I called in the Integration.

We agreed to meet at a local dive that evening and I got there early. She strolled in a little later, carving a path through the cigarette smoke that filled the place. She was a slinky-looking dame, with a graceful curve to her figure. It looked elegant, but at the same time kind of like a cobra about to strike. I waved her over and she sat down next to me at the bar.

“You know what’s been going on, I guess,” I said. “Everyone does, right?”

“Of course,” she answered. “And I know who’s doing it.” She said that she and the Differentiation came from the same place. When I asked where that was, she just answered, “The limit.” And that was all I could get out of her on that subject.

“Can you help us nab the bastard?” I asked.

“No,” she said, and my heart sank. But she added, “I can help the victims, though.”

“How?” I asked.

“Take me to the corpses.”

I settled my tab and we went onto the street. “The morgue’s this way,” I said, and started walking, but she grabbed my arm.

“There’s a better way to get there. Follow me.” She headed in a different direction.

“This is an odd variation on how I’d get there,” I said.

“Yeah, I’m variational,” she snorted.

When we got to the morgue I showed her the remnants of the functions that the Differentiation had gotten to. She didn’t seem upset at all, just nodded. “I can help. I must warn you, though… they won’t be exactly the same when I’m done with them.”

“What the heck does that mean?” I asked.

“Look, they’ll keep most of their original important and interesting properties, I promise. So if you can just step out of the room while I work…”

I was about to object that I couldn’t leave her alone with evidence in murder cases, but as the Chief said, we were desperate. So I just nodded and went out into the reception area.

A few minutes later, out came the constants, who had been reduced to zeros by the assailant. Now that the Integration had done her magic on them they all kinda looked the same – like the letter C – but they were alive! They walked out on unsteady legs, but who cared? They were crying tears of joy.

Next were the linears, who had been reduced to constants by the attacker, and now it was clear what the Integration had meant when she said they wouldn’t be exactly the same. They were all recognizable, alright… but now they all had + C attached to their backs, like ranks of Quasimodos shuffling through the towers of Notre Dame.

Then the quadratics. One of them was a cute little babe I’d known before the attacks, who went by the handle 3x^2 +5x –3. Now here she was, but she had a + C attached to her, like the others. “I’m more general now!” she said with what I thought was forced cheerfulness. Sure, I thought…. more general, but for that very reason she’s lost her uniqueness. But I didn’t say anything. Anyway, it was really good to see her walking again.

Next out were the cubics, stumbling out of the morgue, blinking at the light their eyes hadn’t seen in days.

Then the quartics. On and on it went, a joyous procession of re-animated functions. I saw 10th-degree polynomials, all their local extrema, which had gradually diminished in number during the horror, restored.

Well, everyone knows how it went down after that. We’ve never nabbed the Differentiation, but with the Integration in town, the Differentiation has never been able to take out anyone else. And when the Integration called in her sidekicks, Initial Condition and Terminal Condition, the Differentiation wasn’t even able to mutilate functions with those extraneous + C’s any more.

Things will never be exactly as they were before. But the reign of terror is finally over.

Loosen Up the Ole Synapses

One rule I have is no alcohol while writing (caffeine’s okay, natch). And no other drugs ever. None of this tortured alcoholic author for me, thanks.

But once a year I allow myself an exception: One beer, one cup of coffee, then let yourself rip on the word processor. The combination of alcohol and caffeine loosens up the ol’ synapses in ways that can be amusing. Readers of The War of the First Day can probably identify the one scene in that novel that emerged from this method.

Actually, while I allow myself to do this once per year, I haven’t actually done it in three or four years.

You don’t want to make a habit of this, obviously, because you don’t want to become dependent on it.