The Impossible Cube

“Just listen.” He set the new machine down and pulled the protectors over his ears. They were wooden cups stuffed with wool, apparently designed to keep out sound. Then he turned the machine’s crank.

From the speaking trumpet emerged an unearthly sound. It sounded like a chorus of ghosts sighing from high to low and low to high all at once. Gavin continued turning, and the sound repeated endlessly. The pitch rose higher and higher and higher and fell lower and lower and lower, but it never seemed to reach the top or bottom of any scale. It turned endlessly, the tonal equivalent of a figure eight, always moving and going nowhere. It made Alice’s skin crawl.

“I don’t understand,” she said when he stopped.

Gavin pulled the protectors off his ears. “I think I broke Dr. Clef.”

Dr. Clef sat motionless. He stared into space without blinking, and only the faintest breath fluttered from his chest. A line of spittle drooled down the side of his mouth. The engine blew its whistle, high and shrill.

“Good heavens.” Alice shook Dr. Clef’s shoulders, and he didn’t respond. Gavin handed her a bottle of smelling salts, and she opened it under his nose. He coughed awake and waved the bottle away.

“Where am I, then?” he asked. “What is happening?”

“I think only Gavin can explain that,” Alice said.

Gavin gestured to the new machine. “It generates a tritone paradox,” he said. “Kind of hard to explain. The machine plays a one-octave scale that goes down and another that goes up. When the machine reaches the top of the ascending scale, it drops back down to the bottom and starts over, but the volume changes so that you don’t notice the switch. It does the same for the descending scale. But then things really get interesting.”

“It’s just a noise,” Alice said doubtfully. Click squirmed in her arms, so she set him down.

“Not really,” Gavin said. “The machine also adds another pair of ascending/descending scales, but those are a tritone above the first two. It creates the illusion of a sound that’s always going up or always going down—it depends on your ear—but it never actually goes anywhere. Clockworkers, though, are sensitive to tritones and have perfect pitch—”

“—so it creates an unsolvable paradox for us,” Dr. Clef put in. “And the addition of the other tones does away with the pain and makes the entire scale hypnotic. I remember only a lovely sound that— Wait! Wait!” He clapped his hands and his face flushed. “Du Lieber! Ach, das ist ja nicht zu glauben! Wie habe ich das verpa?t?”

“What’s wrong, Doctor?” Alice asked. “What did you miss?”

“This tritone paradox is an auditory version of my Impossible Cube! Play it again! Play it now!”

“Just a moment,” Alice said, holding up a hand. “We don’t know everything this does yet. Is it harmful?”

“I don’t know,” Gavin replied. “It seems to have helped Dr. Clef. He’s talking to me instead of arguing.”

“Why, so I am!” Dr. Clef exclaimed. “We should be fighting, yet we are not. I am filled with goodwill toward you, my boy. What an amazing thing! Did you create it just for this purpose? So that we can work together?”

“No,” Gavin said. “I created it because I think it’s possible to slow time.”

There followed a long, long pause. Wind whistled through the cracks in the shanty walls, and Click’s steel wool tongue rasped as he cleaned his paws.

“Sorry,” Alice said. “Did you say—?”

“It’s possible to slow time,” Gavin repeated.

“How?” Dr. Clef said in a low, steady voice.

“With your new alloy, Dr. Clef.” Gavin gestured at the rolled-up wiring that still lay on the deck. “I saw your calculations, the ones that prove gravity distorts time.”

Dr. Clef held up a finger. “That is not quite correct. I proved that time isn’t a constant. The flow of time speeds up or slows down based on a number of forces, including the power of gravity, but we don’t notice because we’re in whatever passes for local time. If you could somehow put a clock two or three thousand miles above the surface of the planet, for example, within a few days you will find it is running faster because Earth’s gravity is weaker up there. Time for an object also changes based on how fast it moves. I have reason to believe—though I have not yet proved it mathematically—that if you could somehow accelerate to the speed of light, time would stand still for you.”

“This is more than I can follow,” Alice admitted.

“But”—Gavin lifted a finger—“you used your electric alloy to make the Impossible Cube, and it warped the universe around itself. Have you thought of why the alloy does this?”

Dr. Clef shrugged. “I assumed it was to do with the nature of electricity. Electric current cycles back and forth between negative and positive, like a mouse running back and forth between its hole and a piece of cheese. We measure the distance between the two points and call it volts.”

“But,” Gavin said again, “we don’t actually measure the farthest distance. I’ve been reading your notes. We measure from a point just below and above the two extremes. To use your metaphor, it’s as if the mouse paused on the way to the cheese, and then paused again on the way back to its hole, and we actually measure how far the mouse ran from the pauses, not from the cheese or the hole. We do that for convenience because it’s very hard to measure electricity at its peak and its low.”

“What does this have to do with anything?” Alice asked.

Gavin turned his eyes on her, and they all but glowed with intensity. “To get the distance between the stopping point and the peak, that is, the distance between the pause and the cheese—”

“Oh!” Alice interrupted. “You’re going to tell me it’s the square root of two.”

“Well, you multiply by the square root of two, but yes.”

“God in heaven!” Dr. Clef dropped his pencil and scrabbled for it on the rocking deck. “I knew this fact, my boy,