“Sounds great,” Lily agreed. “I still have plenty of soggy money we can use. I could certainly stand a change of attire and a few days’ rest from all this hysteria. Once we’re all shipshape, where do you propose we head?”
“New York,” said Solarin, “by way of the Bahamas and the Inland Waterway.”
“What?!!” Lily and I both cried in unison.
“That must be four thousand miles,” I added in horror, “in a ship that barely survived three hundred in a storm.”
“Actually, it’s closer to five thousand miles by the route I propose,” said Solarin with an easy smile. “But if it worked for Columbus, why shouldn’t it for us? This might be the worst season for sailing the Mediterranean, but it’s the mildest for crossing the Atlantic. With a decent breeze, we’ll make it in under a month—and you’ll both be excellent sailors by the time we’ve arrived.”
Lily and I were too exhausted, dirty, and hungry to argue with conviction. Besides, more recent than my memory of the storm was my memory of what had happened between Solarin and me just after the storm. A month of that wouldn’t be entirely unacceptable. So we set off in search of a town on the tiny island while Solarin stayed behind to clean up the wreckage.
Days of hard work and beautiful golden weather mellowed us a bit. The isle of Formentera had whitewashed houses and sandy streets, olive groves and silent springs, old women dressed in black and fishermen in striped shirts. All this, set against the backdrop of the endless azure sea, was a balm to the eye, a soothing salve to the soul. Three days of eating fresh fish from the sea and fruits ripe from the tree, of drinking good strong Mediterranean wine and breathing healthful salt air, had worked wonders on our dispositions. We had leathery tans—even Lily was getting lean and well muscled from all the work we shared around the boat.
Each night Lily played chess with Solarin. Though he never let her win, he explained after each game what mistakes she’d made, in painstaking detail. After a while she began not only to take these defeats in good grace, but to question Solarin when a move of his puzzled her. She was once again so wrapped up in chess that she hardly noticed when—beginning that first night on the isle—I elected to sleep on deck with Solarin rather than adjourn to the cabin when she turned in.
“She really has it,” Solarin told me one night as we sat alone on deck, looking up at the sea of silent stars. “Everything her grandfather had—and more. She’ll be a great chess player, if she can just forget she’s a woman.”
“What does being a woman have to do with it?” I asked.
Solarin smiled and tugged my hair. “Little girls are different from little boys,” he said. “Shall I prove it to you?”
I laughed and peered at him in the pale moonlight. “You’ve made your point,” I said.
“We think differently,” he added, sliding over to lie with his head in my lap. He looked up at me, and I realized he was serious. “For example, to discover the formula contained in the Montglane Service, you’d probably go about it far differently than I.”
“Okay,” I said with a laugh. “How would you go about it?”
“I’d try to itemize everything I knew,” he told me, reaching up to help himself to a sip of my brandy. “Then see how these ‘given’ items could be combined into a solution. I admit, however, I’ve a small advantage. For example, I may be the only person in a thousand years who’s seen the cloth, the pieces, and who’s also had a glimpse of the board.” He glanced up as he felt me move slightly in surprise.
“In Russia,” he said, “when the board surfaced, there were those who quickly arrogated for themselves the responsibility of finding the other pieces. Of course, they were members of the white team. I believe Brodski—the KGB official who accompanied me to New York—is one of them. I ingratiated myself with high government officials by suggesting, as Mordecai directed, that I knew where other pieces were and could obtain them.”
He returned slowly to his initial thought. Looking up at me in the silvery light, he said, “I saw so many symbols contained in the service, it led me to believe there might not be just one formula, but many. After all—as you’ve already guessed—these symbols don’t represent only planets and signs of the zodiac, but also elements in the Periodic Table. It seems to me you’d need a different formula to convert each element into another. But how do we know which symbols to combine in what sequence? How do we know any of these formulae really works?”
“With your theory, we wouldn’t,” I said, taking a sip of the brandy as my brain began to work. “There’d be too many random variables—too many permutations. I may not know much about alchemy, but I do understand formulas. Everything we’ve learned points to the fact there’s only one formula. But it may not be what we think.…”
“What do you mean?” said Solarin, glancing up at me.
Since our arrival at the isle, none of us had mentioned those pieces stowed in their bag beneath the galley. As if by unspoken common consent, we agreed not to disturb our brief idyll by mentioning the quest that had placed our lives in such great danger. Now that Solarin had jarred me by raising the specter, I again began to probe the thought that, like a toothache, had throbbed in my head these many weeks and months.
“I mean I think there’s just one formula, with a simple solution. Why hide it in such a veil of mystery if it was so difficult no one could understand it? It’s like the pyramids—for thousands of years people have been going on about how hard it was for those Egyptians to haul all those two-thousand-ton blocks of granite and limestone with their primitive tools. And yet there they are. But what if they didn’t move them that way? The Egyptians were alchemists, weren’t they? They must have known you can dilute those stones in acid, toss them in a bucket, and slap them together again like cement.”
“Go on,” said Solarin, looking up at me in the moonlight with a strange smile. Even from upside down, I thought how beautiful he was.
“The pieces of the Montglane Service glow in the dark,” I said, my mind racing ahead. “Do you know what you get if you break down the element mercury? Two radioactive isotopes—one that decays in a matter of hours or days into thallium, the other to radioactive gold.”
Solarin rolled over and leaned on his elbow as he looked at me closely. “If I may be devil’s advocate for a moment,” he said, “I should point out that you reason from effect to cause. You say, if there were pieces that were transmuted, there must be a formula that did it. Even if so—why this formula? And why only one, rather than fifty or a hundred?”
“Because in science, as in nature, it’s often the simplest solution—the obvious one—that works,” I said. “Minnie thought there was only one formula. She said it had three parts: the board, the pieces, and the cloth.” I stopped cold as something suddenly occurred to me. “Like rock, scissors, paper,” I said. When Solarin looked puzzled, I added, “It’s a children’s game.”
“You remind me of a child.” He laughed and took another sip of my brandy. “But so were all the greatest scientists children at heart. Go on.”
“The pieces cover the board—the cloth covers the pieces,” I said, working it out in my mind. “So the first part of the formula may describe what, the second tells how, and the third … explains when.”
“You mean the symbols on the board describe which raw materials—elements—are used,” Solarin said, rubbing the bandaged cut on his head, “the pieces tell in what proportions to combine them, and the cloth tells in what sequence?”
“Almost,” I said, jittery with excitement. “As you said, those symbols describe elements in the Periodic Table. But we’ve overlooked the first thing we noticed. They also represent planets and signs of the zodiac! The third part tells exactly when—in what time, month, or year—each step of the process is to be executed!” But as soon as I said it, I knew that couldn’t be it. “What difference could it make what day or month you begin or end an experiment?”
Solarin said nothing for a moment, and when he spoke it was sl
owly, with that clipped, formal English he used when under great strain.
“It would make a very large difference,” he told me, “if you understood what Pythagoras meant when he used the phrase ‘the music of the spheres.’ I think you’re on to something. Let’s get the pieces.”
Lily and Carioca were snoring in their respective bunks when I went downstairs. Solarin had remained behind to light a lamp on deck and set up the pegboard chess set he and Lily played on each night.
“What’s going on?” Lily said as I fumbled around for the bag I’d stored under the galley.
“We’re solving the riddle,” I said cheerfully. “Care to join in?”
“Of course,” she said. I could hear the mattress creaking as she climbed off the bunk. “I was wondering when you two were going to invite me to your nightly covens. What exactly is going on between you, or shouldn’t I ask?” I was thankful for the darkness—my face felt hot. “Forget it,” said Lily. “He’s a handsome enough devil, but not my type. One of these days I’ll beat his ass in chess.”
We clambered up the stairs, Lily throwing on a sweater over her pajamas, and sat on the cushioned seats of the cockpit at either side of Solarin. Lily poured herself a drink as I removed the pieces and cloth from the bag and spread them out in the lamplight on the floor.
Quickly recapping for Lily what we’d discussed, I sat back, leaving the floor to Solarin. The boat was swaying, the waves lapping gently. A warm breeze stroked us as we sat beneath the universe of stars. Lily was touching the cloth, looking at Solarin with a strange expression.
“What exactly did Pythagoras mean by ‘the music of the spheres’?” she asked him.
“He thought the universe was comprised of numbers,” said Solarin, looking down at the pieces of the Montglane Service. “That just as notes of a musical scale repeat octave after octave, so all things in nature form such a pattern. He began a field of mathematical inquiry in which major breakthroughs have been made, we think, only in recent times. It is called harmonic analysis—the basis of my field, acoustical physics, and also a key factor in quantum physics.”
Solarin stood up and started pacing. I remembered what he’d once said about having to move in order to think.
“The basic idea,” he said as Lily watched him closely, “is that any phenomena of a periodically recurring nature can be measured. That is, any wave—whether sound, heat, or light—even the tides of the sea. Kepler used this theory to discover the laws of planetary motion, Newton to explain the law of universal gravitation and the precession of the equinoxes. Leonhard Euler used it to prove that light was a wave form whose color depended upon length. But it was Fourier, the great eighteenth-century mathematician, who revealed the method by which all wave forms—including those of atoms—could be measured.” He turned to us, his eyes glowing in the dim light.
“So Pythagoras was right,” I said. “The universe is made up of numbers that recur with mathematical precision and can be measured. Is that what you think the Montglane Service is all about—harmonic analysis of molecular structure? Measuring waves to analyze the structure of elements?”
“What can be measured can be understood,” said Solarin slowly. “What can be understood can be altered. Pythagoras studied with the greatest alchemist of them all—Hermes Trismegistus, who was considered by the Egyptians to be the incarnation of the great god Thoth. It was he who defined the first principle of alchemy: ‘As above, so below.’ The waves of the universe operate the same as the waves of the tiniest atom—and can be shown to interact.” He paused and turned to look at me.
“Two thousand years later, Fourier showed just how they interact. Maxwell and Planck revealed that energy itself could be described in terms of these wave forms. Einstein took the last step, and showed that what Fourier had suggested as an analytic tool was so, in reality—that matter and energy were wave forms that could be transformed into each other.”
Something was working in my mind. I was staring at the cloth where Lily’s fingers were running over the gold bodies of the twined serpents that formed a figure eight. Somewhere deep inside, a connection was forming between that cloth—the labrys/labyrinth Lily had described—and what Solarin had just said about waves. As above, so below. Macrocosm, microcosm. Matter, energy. What did it all mean?
“The Eight,” I said aloud, though still lost in my thoughts. “Everything leads back to the Eight. The labrys is shaped like an eight. So is the spiral that Newton showed us was formed by the precession of the equinoxes. That mystical walk described in our journal—the one Rousseau took in Venice—that was an eight, too. And the symbol for infinity …”
“What journal?” said Solarin, suddenly alert. I stared at him in disbelief. Was it possible Minnie had shown us something of which her own grandson was unaware?
“A book Minnie gave us,” I told him. “It’s the diary of a French nun who lived two hundred years ago. She was present when the service was removed from Montglane Abbey. We haven’t had time to finish it. I have it here.…” I started to extract the book from my bag, but Solarin leaped forward.
“My God,” he cried, “so that’s what she meant when she told me you had the final key. Why haven’t you mentioned this before?” He was touching the soft leather cover of the book I held in my hand.
“I’ve had a few things on my mind,” I said. I opened the book to the page where the Long March—that ceremony in Venice—was portrayed. The three of us bent over it in the candlelight, and we studied it in silence for a moment. Lily smiled slowly and turned to look at Solarin with her big gray eyes.
“These are chess moves, aren’t they?” she said.
He nodded. “Each move on the figure eight in this diagram,” he said, “corresponds to a symbol in the same location on this cloth—probably a symbol they saw in the ceremony as well. And if I’m not mistaken, it tells us what kind of piece and where it would logically land on the board. Sixteen steps, each comprised of three pieces of information. Perhaps the very three you guessed: what, how, and when.…”
“Like the trigrams of the I-Ching,” I said. “Each group containing a quantum of information.”
Solarin was staring at me. Then he laughed. “Exactly,” he said, reaching over to squeeze my shoulder. “Come, chess players. We’ve figured out the structure of the Game. Now let’s put it all together and discover the gateway to infinity.”
We labored over the puzzle all that night. Now I could see why mathematicians felt a transcendental wave of energy washing over them when they discovered a new formula or saw a new pattern in something they’d looked at a thousand times. Only in mathematics was there that sense of moving through another dimension, one that didn’t exist in time and place—that feeling of falling into and through a puzzle, of having it surround you in a physical way.
I wasn’t a great mathematician, but I understood Pythagoras when he said mathematics was one with music. As Lily and Solarin labored over the chess moves on the board and I tried to capture the pattern on paper, I felt as if I could hear the formula of the Montglane Service singing to me. It was like an elixir running through my veins, driving me on with its beautiful harmony as we beat ourselves into the ground trying to find the pattern in the pieces.
It wasn’t easy. As Solarin had implied, when you were dealing with a formula comprised of sixty-four squares, thirty-two pieces, and sixteen positions on a cloth, the possible combinations were far more than the total number of stars in the known universe. Though it looked from our drawing as if some of the moves were Knight moves and others Rook or Bishop, we couldn’t be sure. The entire pattern had to fit within the sixty-four squares on the board of the Montglane Service.
This was complicated by the fact that, even if we knew which pawn or Knight had made the move to a certain square, we didn’t know which had been sitting on which square when the Game was first designed.
Nevertheless, I was certain there was a key even to these things, so we forged ahead with the information we did h
ave. White always makes the first move, and it’s usually a pawn. Though Lily complained this wasn’t de rigueur historically, it seemed clear from our map the first move was a pawn’s—the only piece that could make a straight vertical move at the beginning of the game.
Were the moves alternating black and white pieces, or should we assume—as in a Knight’s Tour—they could be made by a single piece hopping randomly about the board? We opted for the former choice, as it narrowed the alternatives. We also decided, since this was a formula and not a game, that each piece could only move once, and each square could only be occupied once. To Solarin, the pattern didn’t form a game that made any sense in actual play, but it did reveal a pattern that looked like the one on the cloth and on our map. Only, oddly, it was backward—that is, a mirror image of the procession that took place in Venice.
By dawn we’d come up with a picture that looked like Lily’s image of the labrys. And if you left the unmoved pieces still on the board, they formed another geometric figure eight on the vertical plane. We knew we were very close:
Bleary-eyed, we looked up from our figuring with a camaraderie that transcended our individual competitive streaks. Lily began laughing and rolling on the ground with Carioca jumping on her stomach. Solarin raced to me like a madman, picking me up and whirling me around. The sun was rising, turning the sea blood-red and the sky a pearly pink.
“Now all we need to do is get the board and the rest of the pieces,” I told him with a wry grin. “A piece of cake, I’m sure.”
“We know there are nine more in New York,” he pointed out, smiling at me with an expression that suggested he had more than chess on his mind. “I think we should go have a look, don’t you?”