Robert Weinberg - A Calculated Magic

A sea of fiery lava bubbled and fizzed fifteen feet below the crater’s rim. Jack gasped for air. The ravens hadn’t exaggerated when they described the place. It was hot as Hades in the crater.

Directly in the middle of the molten rock was a circular finger of stone twenty feet across. Sitting on it as a small cinder-block cottage. “That’s where the sphinx is holding Megan prisoner,” said Mongo unnecessarily. “Which is your second obstacle. The first one is sitting on the bridge over there.”

“Over there” was thirty feet around the rim of the crater, A white marble bridge, ten feet wide, extended from the edge of the pit to the island at its center. Chained to the foot of the span by two massive chains waited Cerberus, the three-headed guardian of the gate.

“You birds positive you know exactly what to do?” asked Jack. “One mistake and Cassandra and I are dog chow.”

“I’m set, Johnnie,” said Mongo.

“Me too,” answered Hugo. “Let’s do it.”

Drawing in a deep breath, Jack started walking toward the immense hound. All three heads growling faintly, the huge beast rose to its feet. Adamite steel links rustled with its every movement. Six saucer-size eyes glared at them as they approached. Jack, never a dog person, forced one foot after another. He felt as if he were walking right into the mouth of Hell. The three mouths of Hell, to be exact.

“He won’t hinder our passage across the bridge,” said Cassandra. “The hound is trained to let people enter the infernal regions. Coming back is when we’ll experience problems. Crossing should be a snap.”

“I know that,” said Jack. “You know that. I’m praying that the big, nasty dog knows it.”

Step by step, they advanced until they stood directly in front of the beast. While it glared ferociously at them, the monster otherwise made no move to halt their progress.

“Get out of my way, hound,” commanded Jack, trying to keep his voice from trembling. Dogs sensed your fear and reacted to it, he recalled someone once telling him. Act unafraid and they would step out of your path. “We want to cross the bridge.”

Snarling in triplicate, the three-headed monster shifted position to let them pass. Gaze fastened on the cottage that was their final destination, Jack slid by the hound. It wasn’t just the heat rising from the pit making him sweat. The bridge was littered with smashed and broken bones. Human bones. According to Alis, the Old Man of the Mountain disciplined unruly followers by leaving them in Hell for a few days. Evidently, more than a few had unsuccessfully tried to escape.

Fifteen feet beyond the beast, Jack started breathing again. They had gotten past the first obstacle. The sphinx was next. Mentally, Jack reviewed his trivia question. Though it had been years since he taught elementary calculus, he nevertheless remembered Zeno’s paradox perfectly. Some problems were too good to forget.

The door to the building stood wide open. As they drew closer, two figures emerged. Jack’s heart leapt for joy when he spotted Megan. His girlfriend was still dressed in her red silk nightgown. She looked a bit frazzled but otherwise unharmed. Unfortunately, she was not alone. Standing next to her, watching them with suspicious eyes, was the sphinx.

If Cerberus was a zoologist’s bad dream, then the sphinx was his worst nightmare. The monster combined body parts of human, lion, reptile, and bird into a bizarre living jigsaw puzzle. Though it possessed the head of a beautiful woman, Jack noted that when the sphinx opened its mouth to speak, it had the teeth of a lion. They worked better, he concluded grimly, when it devoured its victims.

“Who are you and what do you want?” asked the sphinx. It spoke with a woman’s voice, but there were hints of a reptile’s hiss, a bird’s trill, and a lion’s roar in its tone. “I expected no one for another day.”

“Plans have changed,” announced Jack. Megan, watching without much interest, stiffened in shock. She hadn’t recognized Jack or Cassandra, with their disguised features and unusual outfits, until she heard her fiancée’s voice. Her smile of relief vanished almost instantly as she looked at the sphinx, then at Jack, then again to the monster. She obviously realized that Jack had come to rescue her but had no idea how. She was about to find out.

“I heard of no change,” said the sphinx, staring at Jack and Cassandra with undisguised hostility. “Hasan always telephones me if there is a change.”

“Telephones you,” repeated Jack, his mind racing for a reply. “Well, the phone company is working on the lines today. The Old Man of the Mountain sent me here to get the girl. He wants her right away.”

“Nonsense,” said the sphinx. “She stays…”

“I’ve heard that you brag that you know the answer to nearly every question in the world,” interrupted Jack hurriedly. “I find that difficult to believe.”

“You do?” said the sphinx, unfurling its wings. There was a nasty edge to its voice. “Why is that, human?”

“Because my friend Zeno has been hunting the solution to his riddle for years and hasn’t been able to find it. And he’s remarkably intelligent.”

“Zeno?” growled the sphinx. “A common Greek name associated with several ancient philosophers. Tell me this conundrum, mortal, and it better be an interesting one. I don’t take kindly to being insulted. Brag, indeed.”

The sphinx’s display of teeth made it quite clear what she did to those who disappointed her. Jack hardly noticed. He had hooked his fish. Now it was time to reel her in. It had taken mathematicians over two thousand years to resolve Zeno’s paradox. He doubted that the sphinx could solve it in less time.

“I’ll state the question in simple terms,” said Jack. “Achilles and a tortoise decided to have a race. The famous hero, feeling sorry for his slow-moving opponent, decides to be fair and gives the turtle a head start. But according to my friend, Zeno, this simple act of charity leads to the conclusion that no matter how fast Achilles runs, he is unable to pass the tortoise.”

“Are you sure this question has an answer?” asked the sphinx warily. “It isn’t one of those stupid riddles about barbers and shaving?”

“Let the Kindly Ones tear the flesh from my bones if I lie,” declared Jack solemnly. Cassandra had suggested the oath, one not given lightly, in view of recent happenings at the resort. “This question is asked and answered in high schools throughout the United States.”

“Continue,” said the sphinx. “I’ve read plenty about the state of education in this country,” The monster contemplated the claws in one gigantic paw. “If your wretched students can unravel this riddle, then so can I. Ask and I will answer.”

“Since Achilles gives the turtle a head start,” continued Jack, “he first has to reach the point where the turtle starts, which we will name A1. However, during this time, the tortoise has advanced further, to point A2. Thus, Achilles must cover the distance from Al to A2. But, while he does that, the turtle continues on to point A3. Each time Achilles crosses the distance to the next point, the turtle has inched on to yet a further point.”

The sphinx frowned. “But Achilles must pass the turtle sooner or later.”

“Must he?” asked Jack. “To pass the turtle, Achilles must complete an infinite number of acts in a finite amount of time. Since traversing each distance takes some time, traveling an infinity of them will take an infinite amount of time. Thus, while Achilles draws nearer and nearer to the tortoise, he never overtakes him,” He spread his arms in bewilderment. “How can such things be?”

The sphinx scratched its head. The expression on its face was indescribable, though Jack had seen it many times before on the faces of his students. The monster was lost in a mathematical wilderness. “I need a moment or two to think things through. Give me a second.”