The Case of the Hanging Paradox

January 19, 2011

Chief's Apartment, Nürnberg, West Germany, Saturday, 12 October 198-, 1630 hrs.

“Bicycles have wheels, or pigs have wings.“


“Excellent. Now: the president is a gypsy, or flowers have petals, and your nose is bright blue.”

“False,” I said at once, pleased with myself.

Chief smiled and banged his mug on the table. “I think you've got it! I told you this logic stuff wasn't so hard. Now, for your final test: this statement is false.”

“Easy!” I said. “It's…well, now wait a minute…” I said it over to myself, “this statement is false.” It didn't match any of the tautologies Chief had taught me. Suppose it was true. Then it had to be false, since that was what it asserted. On the other hand, suppose it was false. Then—

The phone rang. Chief heaved himself out of his chair, grinning evilly at me, to answer it.

“I don't get it, Chief. It can't be true, but it also can't be false. What's the answer?”

“Ask Epimenides,” he called from the other end of the long room he used as both study and parlor, and picked up the phone.

I had worked for Chief for nearly four months, long enough to know that the appropriate thing to do at this point was to take the clue that was offered and follow it up. Accordingly, I went to the expansive shelves that walled both sides of the room and drew down a dictionary. I didn't know the spelling, and by the time I found the likeliest looking entry Chief was off the phone and looking over my shoulder.

“‘Epimenides,’” I read, “‘noun; a crater in the third quadrant of the face of the moon—’”

“No no no!” he cut in. “Webster knows nothing of these matters!” He grabbed the volume and put it back on the shelf. “It'll have to wait, anyway, Smitty. We've got a suicide.”

“Oh. Where?”

“Dickson Barracks.” He hiked up his trousers and combed his salt-and-pepper mustache down thoughtfully with his fingers. “A hanging apparently—female.”


* * * * *


Another Saturday afternoon shattered; a common occurrence when one works for a U.S. Army criminal investigator. We drove separately, so that he could get there as quickly as possible while I went to our own headquarters to fetch our official vehicle and the cases containing Chief's crime-scene investigative paraphernalia. Then a quick dodge through the tight, hectic streets of Nürnberg under a slate sky heavy with the promise of coming winter, and out into the rolling countryside of Bavaria.

Dickson Barracks was adjacent to a small town, and as I slowed to a crawl to navigate the narrow streets and admire the heavily timbered houses and medieval stone church, I reflected that any resentment over the interruption in my logic lesson was hardly appropriate. Working for Chief Tobias was probably the best thing that had ever happened to me, at least since I had enlisted. It meant almost immediate promotion, for one thing (only to Specialist—but still), and it kept me out of the motor pool (hate that), and the work was…well, the work was indescribable. Besides, just knowing Chief was an education.

Finding the right building at Dickson barracks was made simple by the presence of an MP sedan, an ambulance, and Chief's blue Toyota parked in front of the door, and by the presence of Chief himself, standing on the cobblestone walk and talking animatedly to a female officer and a senior NCO of the hard-crusted variety. Chief had his badge out, and I smiled at the trouble he always had establishing his credentials. He just didn't look like a soldier. As I approached, carrying one of Chief's cases in each hand and another tucked under each arm, an MP was being consulted. He acknowledged Chief as his superior, and, with a loud grunt from the NCO and an arch look from the officer, who was the company commander, we were led inside.

They took us to the orderly room, and through to the commander's office. This was a large, beautiful room, for the building, like so many the Army used, was built not for us but for Hitler's troops, or perhaps even for the Kaiser's. It had a high ceiling, supported by large crossbeams, and glorious windows bright even in the waning pale of a drab October afternoon.

The room's occupants, two young women, one in fatigues, stood to attention as we entered. The woman out of uniform, a Private Teresa Turner, was the roommate of the deceased. She was tall and athletic, with a square jaw and deep-set brown eyes.

“Teri,” the captain said, “this is an investigator with CID. Tell him what you told me.”

The young woman hesitated, then began:

“Jill and I were alone in our room. She had just gotten a letter this afternoon from her boyfriend, and she was very upset about it. She was crying, and saying she wanted to kill herself. I was trying to be a friend to her, but she was being impossible. Then, she asked me if I would go out and get some ice cream. There is a store nearby that carries her favorite kind. I didn't feel like going out, but she begged me to, so I got dressed and left. I forgot my keys and when I got back the door was locked and I couldn't get in. I banged on the door and hollered, but she never answered it. I decided she must have gone out. I went to the Charge of Quarters to ask him to let me into my room. That's when we found her. We could see that she had stood on a chair and then kicked it away, because it was lying on the floor beneath her. The CQ cut her down, and then I went to call the ambulance, the MP's, and the first sergeant. She must have burned the letter, because there were bits of it on the window sill, and we could smell the burned smell.”

The uniformed girl, a sergeant, was the Charge of Quarters, and confirmed that Private Turner had gone out at about 1500 hrs (3:00 pm), and returned about 25 minutes later. She had gone to her room, and almost immediately come back to ask for the pass-key. Because getting this required going to the battalion's CQ and signing it out, they had not gotten into the room until about 1550 hrs. The girl, Jill Macke, was hanging from a crossbeam when they opened the door. They cut her down with a pocket knife and attempted first aid, but it was obvious the girl was dead. The call to the MP's had been received at exactly 1610.

Chief stood staring at Private Turner during both statements, while I took notes, and when they were done he took off his glasses and started wiping them with the hem of his t-shirt.

“Well,” he said at last, “let's have a look, shall we? No,” he said to the young women, “you stay here.”

The commander led us up to the third floor, where the ambulance drivers were just wheeling a gurney out of the room. Chief stopped them and unzipped the top of the body bag.

The girl had been a blonde. I imagined she had probably been pretty, but it was hard to be certain, for her face was puffy and pale, the blue eyes bulged, the tongue was extended and blackish, and around her neck was a deep, angry gouge where the rope had bit.

Chief leaned over and studied her for a few moments. “Yeah,” he said. and then, “you boys wait for a bit. I'll take charge of this.” He pulled the gurney away from them and shoved it rolling back into the room.

“Who—?” one of the men said, looking questioningly at the captain, but stood aside at her nod.

“I'd like you to wait outside too, ma'am,” Chief said.

“I don't intend to,” she said. “I'm the commander here.”

Chief looked about to argue, but changed his mind and sighed. “Yeah,” he said. “Well, it's your stomach. Just stay out of the way.” He waived her in and shut the door, then looked at me. “Smitty, the camera.”

“Yes, Chief.”

I opened the camera case and loaded a fresh roll of film. Chief went back over to the body and yanked down the zipper the rest of the way, folding back the ends of the bag to expose the body. The girl was still in a blue terry-cloth robe, cinched tightly at the waist. Chief examined this carefully, then inexplicably slid his hands under the girl and hoisted her in his arms. He laid her back down and, after directing me to take several snapshots, undid her robe and threw it open. She was nude beneath it. Chief had me take several more pictures, particularly of the waist area.

The captain was very red in the face at this point, but she stood her ground by the door and didn't protest.

The rope used, thick cotton clothesline cord of a kind that is sold in the Post Exchange, had been tied to one of the ceiling crossbeams and apparently slung across an adjacent one, beneath which was the chair Private Turner had spoken of. The noose itself lay on the bed, the cut end pulled clear of the knot so that it lay open, like a small white snake with a knot in its tail. On the stone sill near an open window lay fragments of burned paper.

Chief put the robe back over the body and zipped the bag as far as her chest, then looked around slowly and put his hand on my shoulder.

“Well, Smitty?”


“This is a classic case. I'm glad you're here.”

“Chief?” I said again.

He picked up the remains of the noose and held its cut end to that of the rope hanging from the beam, then stretched the longer piece across towards the second beam. Eyeing the beam carefully he said, “What does it mean when a thing is true and false at the same time?” He got up on the chair and pulled the rope over the top of the beam. “A contradiction,” he continued, not waiting for me to answer, “is a sacred thing, some ways, because it tells us something serious.” He jumped down and approached me. “We're assuming this girl was hanged—like this.” He threw a loop of the longer rope over my head and pulled it snug. Lifting it so that it cinched under my jaws, he said, “like this, right?”

“Er, yes Chief.”

“All right.” He pulled the rope off and slung it around his own neck. Gathering it at the back and lifting, so that it bunched the skin on his throat into folds under his chin, he croaked, “where does the rope cut?”

“Above the Adam's apple,” I began, and then suddenly saw the light. “Oh! It's right under the jaw!”

“Right. And see on the back of my neck? See how it makes a kind of upside-down ‘V’ behind my ear where the knot would be? Now!” He led me back over the body. Pointing at her throat he said, “what's wrong?”

“The gouge is in the wrong place,” I said. “It goes straight around her neck, like a choker.”

“What an apt turn of phrase you have, Smitty.”

“Oh! This means—”

“Yeah,” he said, cutting me off, and then, “Where are you going, Captain?”

The commander had opened the door but stopped at Chief's sharp tone.

“Patience, ma'am. Nobody downstairs is apt to wander off just yet.”

“I'm still in charge here, and I intend to find out—”

“Forgive me,” Chief said, drawing her back in by the elbow and shutting the door, “but that is no longer even technically correct. Have a seat, will you? Now, Smitty—where were we? Oh yes, contradictions.” He picked up the noose again and drew me over to the chair. “Just stand up here—that's right—and put this long bit back over the beam. Pull it good and tight. There you go. How far down does it hang?”

“About ten inches below the beam.”

“Or about the level of your throat. Now—” He threaded the loose end of the noose back through the knot. “I doubt we could get this around your neck, let alone mine, which means it was cut just above the knot, and pulled apart to get it off of her. How tall are you, Smitty?”

“Six feet, maybe six-foot-one or so.”

“And you're wearing boots.” He took a tape measure from one of the cases and unzipped the body bag agin. “I'd say she was…maybe…sixty-three inches on a tall day. What do you make of that?”

“She couldn't have done it, Chief,” I said after calculating mentally, “not standing on this chair, anyway. But then how—?”

“It'll come to you. Hop down here. Okay, that's two contradictions. I'm guessing there's a third. We'll have to do the whole crime-scene thing, with all the trimmings, but first let's have a thorough look around. I notice there are no ashtrays, and that bothers me.”

“Why?” I asked, putting on the surgical gloves he handed out to me.

“Something's missing. I already checked her robe, so let's check everywhere else. Try to disturb things as little as possible.”

“But Chief—”

“Think of it as a test, Smitty. If it's here, it'll be out in the open. You'll know it when you don't find it.” Leaving me to puzzle over that characteristic epigram, he got down on his hands and knees and started scouring the floor near the window sill.

I looked under the bunks, and searched the bedding and the tops of the dressers.

The captain, after fidgeting for a few minutes, finally drolled, “Is there something I can help you find?

“No ma'am,” Chief said, carefully putting a pile of litter back into a small trash can, “apparently not. But I think it's time for guests. Would you mind bringing everyone up from the orderly room? Oh, and it would be most helpful if you avoided mentioning anything you have seen or heard in here.”

She left wordlessly.

After a couple more minutes he said, “Well, Smitty?”

“Whatever it is, I haven't found it.”

“Me neither. You really don't know what it is?”

“No, Chief,” I said apologetically. “Unless you're just looking for whatever she used to light the—”

“Hush!” he said, holding his hand up and listening.

There were footsteps in the hall, and then the captain, Private Turner, and the CQ entered the room. Behind them came the ambulance drivers, and at a nod from Chief they wheeled the body away.

After a solemn pause, Chief cleared his throat. Pulling off his gloves with the air of a surgeon who has just lost a patient, he said, “Private Turner, I know this must have been a sad shock for you.”

The girl nodded mutely.

“You were friends?”


“Well, suicide is a very difficult thing to understand. It is natural to feel that somehow we might have done something to prevent it, but it is important that we not blame ourselves. And I want you to know Teri—may I call you Teri?—that your testimony makes this kind of investigation much simpler.”

Chief's tone was enigmatic to me. It was his “favorite-grandfather” voice, the one he reserved for putting nervous witnesses at ease. This was certainly its effect on Private Turner. She began to look much less tense, and actually smiled when Chief asked if he could call her by her first name.

“Well,” Chief said, pulling a Sobranie from the pack in his shirt pocket and tamping it on his thumb. “I suppose we're about done here. Oh”—he searched in his trouser pockets—“uh, Teri, do you have a light?”

“Sure,” she said, and dug from her own pocket a small Bic lighter, and held it out to him.

He didn't take it. He stood like a stone, his eyes locked on hers.

The easy confidence in her face vanished. “Oh…” she breathed, and the lighter slipped from her fingers and bounced on the polished linoleum floor. Her eyes strayed to the window sill, and back to Chief, who was still motionless, but whose eyes were like glass. Then all at once her legs gave way, and she hit the floor with a thump, sitting Indian fashion, her head bobbing stupidly.

“Private Turner, I am arresting you for the murder of Jill Macke. You have the right to remain silent. If you choose to give up this right…”


* * * * *


“She wasn't very bright,” Chief said to me later.

“I wonder why she did it?”

“Me too.”

I was scanning Chief's bookshelves, and paused to admire his lizard, which was sunning itself under the lamp. “There's one thing I don't get, Chief. If she strangled her before she was hung—”


“—hanged, how did she get her up there? And why weren't there signs of a struggle?”

“First of all,” he said, “strangulation can be sudden. It's not blocking the airway, but pinching the main arteries of the neck that causes unconsciousness, and it can happen in as little as a few seconds. I'm guessing she surprised her from behind, possibly while she was in bed.”

“It's not like the movies, then.”

“Not necessarily. As to how she got her up there, I think that's pretty easy to see. First of all, that robe was tied very tightly, and with a heavy knot—not just folded over or looped in a bow. Did you notice the marks on her waist? I believe Teri hoisted her around using the belt as a sling. Also, Teri was a much bigger girl. Standing on the chair herself, under the other beam, she would have had little difficulty—once she'd put the noose around the girl's neck—lifting her into position by tugging on the rope.”

“It's funny she lifted her too high.”

“You have a strange sense of humor,” Chief said.

“I didn't mean…you know.”

“Well, she had to eyeball it, since she was standing on the chair herself.”

“Giving us one of our contradictions.”

“That's right. We were supposed to assume she hanged herself, and when we got contradictions, what did we conclude?”

“That,” I recited, “the assumption was flawed. Actually, Chief, I think I might almost get to like logic.” I left off stroking Nietsche, Chief's iguana, behind the ears, and got us each a Pils from the fridge and fresh glasses from the bar.

“So what about ‘this statement is false’?” I said, handing Chief his beer.

“What about it?”

“Well, is it true, or false?”

“Neither. Both. It's Epimenides' paradox, and nobody knows.”