by J. G. Sandom
“It’s not like that. I don’t think: oh, this number means this or that. They’re not just symbols. They’re relationships.”
“Is that what the labyrinth is?”
Koster shook his head. “I wish I knew.”
She straightened her hem. “I don’t understand how you do it. All this geometry means nothing to me. Shapes and numbers.”
“It’s not that difficult. Geometry’s just common sense. Here,” he said. Mariane was trying to reach the buttons at the back of her dress. “Let me help.”
Mariane turned away and Koster did the buttons up, one at a time. They looked like flattened pearls.
“It may be common sense to you,” she said. “But it’s nonsense to me.”
“No, it’s not.” He turned her around in his arms. “Take this dress,” he said.
“What about it?”
“You know how to sew, don’t you?”
“A little.”
“Then you know something about geometry. It’s like when you have to fit a piece of cloth to a convex shape, like the front of your dress here at the bust. How do you do it?”
“You cut a pointed section, a dart from the material, and sew the two pieces together.”
“Exactly. And you can do the reverse by cutting the fabric and sewing a pointed patch into the slit.”
“A godet,” she said. “So what?”
Koster laughed. “Well, I don’t know how to sew,” he said, “but all of these characteristics—whether a piece of fabric splits, overlaps, or conforms to a surface—are reflective of the fabric’s geometry. You see? Without even realizing it, you already know most of the tenets of topology, a kind of mathematics that’s much more complicated than…”
There had been moments like this before. Koster remembered each one with a punishing clarity. But they had come to him so many years before, to such a different Joseph Koster, he had thought that they would never come to him again. And, now, it all seemed obvious. Now, the strange twelve-sided shape fell into place. The dodecahedron. The drawing in the missal.
“What is it, Joseph?” Mariane said. “What’s wrong?”
Koster snatched her by the shoulders. “Topology,” he answered breathlessly. “Not group theory. Topology. My God. What an idiot I’ve been. It’s been staring me right in the face.” He dashed across the room. There was a stack of papers near the armchair and he wrestled with it for a moment before pulling out a tattered pad. “My pencil,” he said, looking desperately about. “Where’s my pencil?”
Mariane pointed at his feet.
“Thanks.”
“Joseph?”
Koster leaned back in the armchair. He began to scribble madly on the paper.
“Joseph?”
“Yes.” He looked up. “I’m sorry, Mariane.”
“Do you have it? Do you know where the gospel is?”
“Not yet,” he answered, playing with the pencil. He took a step inside, and turned. The labyrinth unfurled like a medieval pennant, one step at a time, one flagstone. Around he went, one quadrant to the next, as if the winding trail were just a twisted number line within a spinning wheel, the mainspring of some great machine. “But give me ten more minutes and I’ll tell you.”
“I’ll get some coffee.”
In the end it took him over an hour, but Koster did not notice. Dimensions, sides, and edges too. These were the properties that mattered. Homeomorphs. Edge to edge. Fear to fear. Side to side. Emotion to emotion. The things which made us human. The things we shared. The touchstones. “You’d better get Nigel,” Koster said. He looked up and there was Lyman, sitting on the bed. “When did you come in?”
“Just now. Five, ten minutes ago.”
“I didn’t see you.”
“So I noticed,” Lyman said. “Well? Do you have it?”
Mariane came over and offered Koster some more coffee. He shook his head. Then he looked at Lyman, and his face broadened into a smile, a grin, stretching. “Topology,” he said.
“Topology—what’s that?”
“It’s a kind of mathematics. It deals with the fundamental characteristics of objects, the properties which make a thing what it is, properties which can’t be destroyed by stretching, bending or twisting.”
Lyman looked disgusted. “Like your theory group,” he said.
“Group theory. No, that’s different. Look, imagine a soccer ball. It has two dimensions, no edges, and two sides. In fact it retains these same basic characteristics even if you let the air out and twist it all around. Get it? Topology studies these kinds of invariant properties. Objects that are topologically equivalent are called homeomorphs.” He tore a piece of paper from his pad. “Haven’t you ever seen a Möbius strip before? Here,” he said. “A piece of paper has two dimensions—length and width. It has one edge all the way around. And it has two sides, top and bottom. You see?”
“So?”
“Now imagine if you glued the ends together. It looks like a ring. I’ve changed it topologically. It still has two dimensions and two sides, but now it has two edges instead of one.” He gave the strip of paper a half twist and brought the edges together to form a loop. “And this,” he continued, “is a Möbius strip. It’s really unusual topologically, because unlike most imaginable surfaces, it doesn’t have two sides. It has one. You see? If you run a finger along the outside, you’ll eventually end up on the inside of the paper, without ever taking your finger off. One side.”
“Fascinating,” Lyman said. “But what does this have to do with the labyrinth?”
Koster dropped the papers on the floor. “That twelve-sided shape which Thierry drew into the margin of the missal. The Chaldean Cup. I told you I’d seen it before. Well, now I remember. It looks exactly like the three-manifold which Seifert and Weber discovered at the University of Geneva, back in 1932.”
“The what?”
“Three-manifold. It’s a kind of topological space. Of course, it can’t really be depicted from the outside. To do so you’d have to view it from a higher dimension. But it can be visualized,” Koster said, “as a dodecahedron.”
“Like the one Thierry drew,” Lyman volunteered. “The Chaldean Cup.”
“Exactly. The different colors of the precious stones indicate how the identification, how the gluing of the opposite sides should be carried out: each member of each pair of faces is matched to its counterpart after a three-tenths turn about the axis perpendicular to the two faces.”
“Well, you’ve lost me,” Lyman said. “What’s this manifold do anyway?”
“Manifolds don’t do anything. They’re models for the structure of the universe.”
“But if it was discovered back in 1932,” Lyman said, “why does it look like the Chaldean Cup? What did the Babylonians know about topology?”
“I’m not sure. I know it seems strange, but I can’t believe it’s just a coincidence. The Chaldeans were the most sophisticated mathematicians of their day.”
Lyman scowled. “Look, I’m not interested in the bloody cup. I want to know about the Gospel of Thomas. What the hell does this topology have to do with the gospel?”
“It’s the answer, don’t you see? I was looking at the labyrinth in strictly Euclidian terms. I was looking at symmetry and numerical measurements instead of topological invariants. It’s a totally different perspective.”
“And.”
“And by using topology it becomes clear that the labyrinth is a kind of numerical pointer. By following the white path to the center of the labyrinth, you run a kind of topological journey. And if you apply that same topological journey or transformation to the basic numerical structure of the cathedral, it brings you to a specific point at the heart of the crypt below.”
“Where? What point?”
Koster paused. “You have to promise me something first.”
“What do you mean? Promise you what? What are you talking about?”
“That I’ll be in on it. Remember what you said, Nigel. You can�
�t dig it up all by yourself. It’s too late for that now anyway. I’m sure they’re watching every move we make.”
“For God’s sake, Joseph, you’ve already done your job. Now let me do mine. Please try to understand,” he said. “I don’t want any unnecessary casualties. Not at this stage of the game. Not again.”
Mariane gathered up the dirty coffee cups and placed them on a tray. Her face was very pale. “I’ll let you settle this alone,” she said.
“Don’t go too far,” said Lyman. “I want everyone to keep together, just in case Scarcella tries another move.”
“I’ll be right back.”
Lyman opened and shut the door behind her. Then he turned to Koster with a frown and said, “Tell me where it is, Joseph.”
“Not until you promise. You know I’m right. It would look pretty weird if Mariane and I suddenly vanished from the scene. Scarcella might get suspicious. He might send a messenger instead of coming himself. You know I’m right.”
“Where’s the gospel, Joseph?”
“Promise.”
“Oh, for Christ’s sake.” Lyman turned away. “If I do,” he added crisply, “will you do everything I tell you, down to the last detail, without any questions?”
“Of course. You’re in charge. You and Musel.”
“And if something happens, and I ask you to leave? You promise to go?”
“Nigel, I’m not stupid. I don’t want to die. But I can’t just walk away from this. Not now.”
“I thought you wanted to leave. You were the one complaining about the risks.”
“That was before.”
“Before what?”
“Before everything. Before you told me the truth about yourself. Before I knew you. It was just different then.”
“Where’s the Gospel of Thomas, Joseph?”
“You agree then?”
“Yes, I bloody agree. There. I said it. All right? I agree. Are you satisfied?”
Koster smiled. He picked up a drawing of the Chartres cathedral. “Here,” he said, pointing at it with his finger.
Lyman gathered near. “Where?”
“In that window space at the eastern end of the old Carolingian crypt. According to the records I’ve been reading, there was a great fire on the morning of September 7th, 1020, in which the Carolingian cathedral was destroyed. Guy mentioned it once back in Amiens, remember? St. Fulbert was the chancellor at the time, and he wrote to King Robert, William the Fifth, and several other noblemen for money to rebuild it.
“Eventually they kept the original Carolingian crypt underneath the choir, and built a much greater one around it. Then either Fulbert or a guy named Bernard of Chartres had the windows of the old crypt covered up. There was no point to them anymore, since they now faced the Romanesque ambulatory instead of the outdoors. It’s there, Nigel. And the Chaldean Cup as well. Thierry was Bernard’s brother. That’s how he knew about it.”
“Are you absolutely sure?”
“It all fits, Nigel. It all works perfectly.”
Lyman sighed. “Thank God,” he said.
Just then there was a loud knock on the door. Koster held his breath while Lyman moved behind the bed. “Who is it?” the Englishman said.
“It’s me,” said Mariane.
Koster exhaled. “Come on in.”
The door opened and Mariane took a step into the room, rolling her eyes. A figure loomed behind her. “Look who’s here,” she said uncertainly. “We met in the dining room downstairs. He just insisted on coming up.”
“It’s all right, Mariane. Isn’t it, Nigel?”
“Yes, do come in. Please.” Lyman stepped forward from around the bed. “How do you do? It’s a pleasure to meet you finally.”
Archbishop Grabowski pressed through the doorway with a smile. “Just fine. You must be Joseph’s English friend. I’m sorry I missed you last night.”
“I see my reputation precedes me.” Lyman shook his hand. “Well, well. We’ve got good news for you.”
Grabowski looked surprised. “You do? What? What have you got?”
Your downfall, Koster thought. Then he glanced away. Despite his size Grabowski looked so frail now, like an old oak hollowed by the wind, scooped out by the ice and the rain.
“The labyrinth, Kazimierz,” Koster said. “The Gospel of Thomas.” He tried to smile. “Everything we’ve all been looking for.”
Chapter XXIII
CHARTRES
September 27th, 1991
THERE MIGHT HAVE BEEN A TIME ONCE, LYMAN thought, when what he knew he had to do now would have seemed a kind of cowardice, the hollowest revenge. But as he walked across the open square, through the windless twilight thick with fog, he realized that the world and he had changed, and that the ends and means had grown entangled, indistinct, irrelevant. There would not be a Champ Dollon this time, no fast escape across the moors, no rotors of a helicopter turning, warming up. This time Scarcella would not get away. He would feel the world slide out from underneath him, hear the sounds of life grow distant in his ears, slip at an angle into darkness through the waves, and sleep.
It had just started to rain when they finally reached the entrance to the crypt. The archbishop held his black umbrella open over them, trying to protect them from the rain as they struggled with the lock. Mariane kept close to the American. There was a small sign posted on the door, Lyman noticed, which said the crypt was closed for renovations, and he reminded himself to congratulate Koster on his foresight. The lock tumbled, the door swung open, and Grabowski turned a torch on, illuminating the corridor within. “All clear,” said Koster forcefully, as if to fill the vacuum and displace his fear.
They filed in through the entrance, one by one. Lyman lingered in the doorway, staring at the ancient houses as they drifted on the fog across the square. He carried a pick in one hand and a chisel in the other. His long green coat hung heavily from his shoulders, the hood slightly askew, the plastic bone toggles dangling down. He wore his piebald Irish fishing hat, tilted, so that a fine line of rain spilled off the rim at the back.
“Nigel?” Koster stood in the doorway with a quizzical expression on his face.
“Here,” Lyman said, and offered him the pick and chisel. “I’m going to stay outside for a while. Go ahead. You can start without me. I get a little claustrophobic anyway.”
The light in the corridor flicked on. Mariane had found the switch. “Are you sure?” said Koster.
“Yes, of course. I’ll be down in a few minutes.”
The American took the tools. The trio disappeared around the corner, and Lyman leaned against the door frame with a sigh. He could hear their footsteps echo off the thick walls as they moved deeper and deeper into the heart of the crypt. Then there was nothing but the rain, the gentle tapping on the surface of the square. It was hardly more than a mist really, but puddles had already formed between the cobblestones, along the pavement and the ribbed depressions of the street, spilling together to the north, a trickle to a puddle to a stream. And somewhere in the valley was the River Eure, turning waterwheels, carrying boats, tying the earth.
Lyman took a step into the rain and there they were: the warden and his uncle Jack; the farmer cursing; the open empty bag; that thick trout falling once again, spilling her scales, turning as she tumbled end to end, and down into the grass beside his feet. Lyman reached into his coat.
“Hello,” he said, feeling like a fool. “Come in. Hello.” The radio crackled in his hand.
“We have you,” came the reply. It was the high-pitched voice of the Amiens police captain, Musel.
“Is everybody ready?”
“Of course we’re ready. We’ve been ready for hours. I don’t know how you talked me into this, Lyman, but it better pay off.”
There was a silence. Lyman stared across the square. Damn this fog, he thought. He could barely see a thing. The medieval houses appeared disjointed and half built, stenciled by dark beams of wood, spotted with windows. “It’ll pay off,” he sa
id.
“But Grabowski never called. I’m telling you, my men followed him all day. He didn’t take a shit without them giving him the paper.”
“They must have missed the call,” Lyman said. “Don’t get cold feet on me now, Musel. Grabowski is Scarcella’s man. I know he is.”
“One hour,” Musel said. “You hear me? And I do it only out of courtesy. If my own men tell me that there wasn’t any contact, I believe them. One hour. Then we go back to Amiens.”
The radio died in his hand. Lyman stuffed it back into his coat and leaned against the door frame. The mist was lifting slightly. The houses were more visible across the square. He could see a television flickering in the dark, magnesium bright, shaking out a story. He reached into his coat and pulled out a pack of cigarettes. Then he ducked back into the corridor.
The Romanesque crypt curved out of sight before him, a wide stone ambulatory, a few mosaics and a chapel to the side. The corridor must have been fifteen feet across. The stone looked cold, ice gray, and ancient. Lyman struck a match and lit one of his Players, inhaling deeply. A small piece of tobacco fastened itself to his lower lip, bitter and delicious. He pulled it off. The smoke made the world seem clearer, he thought, but he knew it was just the nicotine. An illusion of clarity. A myth. A footstep echoed down the corridor, and then another, and Lyman realized someone was approaching. He moved against the wall. It was Mariane.
“Oh, hello,” he said. “Any luck?”
“We were worried about you.”
Lyman smiled. “I’m flattered. How’s the digging?” He might have been querying a fisherman about his catch. His voice had the same quality of false indifference.
“Nothing yet. They’ve gone about a meter and a half, a little less. Joseph says the mortar’s surprisingly soft. He wants to know if you’re coming down.”
“I don’t think so,” Lyman said. “I’d better stay here.”
Mariane shrugged. “Whatever you say.” She looked out at the courtyard. “It’s already dark.”
“Yes,” Lyman said.
“Foggy too.”
“Yes, no wind.” Lyman smoked his cigarette quietly, watching Mariane. She seemed frightened and he cursed himself for allowing Koster to persuade him to give in to this ridiculous charade. She had no business being there. It was his war, not theirs. He had manipulated them, as certainly as Scarcella, as certainly as the Countess de Rochambaud. And suddenly he remembered the daughter of that Italian magistrate, that twelve-year-old girl in Terracina, bloody and dying in that little bed, staring wide-eyed at the rose and straight pin in Scarcella’s hands. It had been his fault Mariane had been approached by Scarcella. They had stood front to front across the counter of the photo shop, only a foot away. Scarcella had looked deep into her eyes.