The following is a companion-piece to the talks given at Mykonos in July 2005 at a conference on "Mathematics and Narrative."  Mykonos is a Greek island next to Delos, an island sacred to Apollo.

From Secret Passages, by Paul Preuss
(hardcover, August 1997, Tor Books)

Peter followed the Sacred Way of this once most-sacred island, which led him into a field of ruins only a classical scholar could have made sense of. He was not a classical scholar. He could not see what was once there, only what was there now: the hard ground, the tough grass, the low courses of stone relaid to sketch out the building plans of the ancient sanctuary, with a few column drums, a few white marble herms, set upright to suggest the vanished third dimension. And underfoot, the paving stones and low stone steps of the Sacred Way, a riverbed of stone deeply carved into smooth hollows by a centuries-long stream of shoes and sandals and bare feet . . .

To the uninitiated, to Peter, it could only be glittering wreckage. More than the ruins were bright; every crystal in the granite of the low barren hillside glistened with refocused sunlight. He came upon a curious pair of white boulders looming in the ruin field and stopped to peer at them.

Minakis, stalking him silently, wondered what he made of the pitted and eroded gobbets of stone. He approached, making no effort to be silent but moving up silently nevertheless.

"We will not ever know his legendary head," he said, "Wherein the eyes, like apples, ripened."

Peter turned to find a man as tall as himself, as slim and erect, but darker, more used to the sun -- and upon inspection much older, his eyes as black as lava and his teeth, under his broad gray mustache, whiter than marble. Teeth and eyes and height, that is what registered; Minakis was used to it.

"Professor Minakis. I didn't see you." He offered his hand.

Minakis shook it neatly, then turned his eye to the weathered remains. "You know the poem?"

"Rilke, isn't it?"

"Yes, 'An archaic torso of Apollo.' I was inspired to learn it because of this ruin. Not every kouros was Apollo, but this one certainly was."

"This one?" Peter looked at the two trapezoidal boulders that were once a statue. One would have been the upper torso, now chopped off and set upon its waist; the other, two or three yards away, must have been the pelvis.

"It was almost twenty feet tall, made on Naxos at the end of the eighth century. The pedestal -- it's still over there, by what's left of the Naxian house -- is inscribed, 'I am the same stone, figure and base.' The Naxians had a habit of carving these things in one piece, right out of the mountainside."

Peter looked across the grassy court to the rows of stone Minakis had indicated. "What happened to it?"

"Pirates tried to carry it off. It was so heavy they had to cut it up just to drag it this little distance. They must have decided it wasn't worth the trouble. Delos had been in ruins for more than half a millennium, but the unfortunate thieves were hundreds of years too early to capitalize on our modern appetite for stolen antiquities."

"Do you remember all of it?"

Minakis's eyebrow lifted. "All of it?"

"The poem."

He began again without preamble. His accent was educated British overlying native Greek.

We will not ever know his legendary head
Wherein the eyes, like apples, ripened. Yet
His torso glows like a candelabra
In which his vision, merely turned down low,
Still holds and gleams. If this were not so, the curve
Of the breast could not so blind you, nor this smile
Pass lightly through the soft turn of the loins
Into that center where procreation flared.
If this were not so, this stone would stand defaced, maimed,
Under the transparent cascade of the shoulder,
Not glimmering that way, like a wild beast's pelt,
Nor breaking out of all its contours
Like a star; for there is no place here
That does not see you. You must change your life.

"Change your life?" The imperative caught Peter by surprise. His laugh was a dry sound in the dry surroundings. "Easy to say."

"Perhaps not so easy for the poet." Minakis stepped back. "Forgive me. I've thoughtlessly interrupted you."

"Nothing to interrupt."

Minakis persisted. "The others went that way. You came this way. I assume to be alone."

"They have guidebooks. I'm following my nose."

"Then your nose is good. But of course you've been here before."

"No. What makes you think so?"

"You were at the first Delos. Your paper on neutral kaons made a stir. You had interseting things to say about field theory."

"I never left Mykonos, actually; I hardly left the villa. In those days I didn't pay as much attention to . . ." Peter waved his long fingers and, after a momentary pause, passed them through his hair. And then, almost absent-mindedly, he walked off. Minakis caught up and walked beside him in silence, moving with easy strides over the bare ground, listening as Peter spoke. "Delos One was ten years ago -- quantum theory seemed as natural as water to me then; I could play in it without a care. If I'd had any sense of history, I would have recognized that I'd swallowed the Copenhagen interpretation whole."

"Back then, you insisted that the quantum world is not a world at all," Minakis prompted him. "No microworld, only mathematical descriptions."

"Yes, I was adamant. Those who protested were naive -- one has to be willing to tolerate ambiguity, even to be crazy."

"Bohr's words?"

"The party line. Of course Bohr did say, 'It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.' Meaning that when we start to talk what sounds like philosophy, our colleagues should rip us to pieces." Peter smiled. "They smell my blood already."

"Do not think I am not after your blood." Minakis bared his teeth in a happy grin.

"Thanks for the warning."

"But do consider that I am an old man, well past my theoretical prime. Not averse to philosophy."

They came to a row of stone lions, some shattered, some almost whole, crouched on stone pedestals -- lean female creatures carved to show their ribs, their skins stretched over coiled haunches. The iron rods that propped up the marble fragments had seeped rust, staining the marble like dried blood. To the east, where the lions stared, a drained lakebed full of reeds lay motionless under the high sun. The stillness was broken by a bright green lizard, breaking cover to swim across the bending reed-tops.

Peter glanced at Minakis. "Let's say there are indications -- I have personal indications -- not convincing, perhaps, but suggestive, that the quantum world penetrates the classical world deeply." He was silent for a moment, then waved his hand at the ruins. "The world of classical physics, I mean. I suppose I've come to realize that the world is more than a laboratory."

"We are standing where Apollo was born," Minakis said. "Leto squatted just there, holding fast to a palm tree, and after nine days of labor gave birth to the god of light and music -- who was a bloodthirsty savage. What did the world know of laboratories then?"

Peter said, "Even to me, my search seems foolish. Worse than philosophy. Metaphysics. Ideology." He pressed his lips together. "So if you are after my blood . . ."

Minakis held up a thin hand, his fingers as long as Peter's and, in the everywhere-reflected light, almost transparent. Peter, usually so fluent, stood as if transfixed.

Maintaining his hieratic gesture, Minakis turned to face the rocky hill that loomed to the east. On the far side of the vanished lake a woman was descending the path from the temple of Isis, her bright cotton skirts flowing about her knees, her dark hair stirring in the breeze of her passage.

Minakis dropped his hand. Peter's gaze slipped away, upslope. He squinted in puzzlement, then called out, "Anne-Marie!"

She walked toward them, raising a well-used 35mm Canon to her eye. She tweaked the focus and adjusted the exposure with practiced skill while she levered the film forward and clicked off half a dozen frames, never losing her stride. Watching her, Peter brushed his scalp absently, lost in admiration.

Suddenly she was standing in front of him. "Hello, handsome." Dropping the camera into her bag, she took his hands and gave him a wifely peck on the lips.

"You weren't coming until tonight. I would have met you."

"I caught an early plane. I just missed your boat. I've climbed over half this pile of rocks." She brushed at her dusty skirts, then looked up and smiled at Minakis.

"Professor Minakis," Peter said, "my wife, Anne-Marie."

"I'm very glad to meet you, Mrs. Slater."

"Actually it's Brand," Peter said. "Her own name."

"Call me Anne-Marie." She offered her hand and watched with approval as he shook it firmly, not trying to kiss her hand or bow or do anything smacking of fake charm. "You're from Crete?" she asked.

"What makes you think so?"

"Well, a name that ends in akis."

"Not much of a clue."

"Your broad shoulders, then, and your wasp waist, and your height -- and, if you will forgive me, your very good looks. Vaivaios, eisai apo tin Kriti, apo ta oroi Kriton."

"You speak Greek?" Minakis's eyes were fixed upon hers.

"Pend'-exi lexeis, mono."

"More than five or six words, I think."

"Anne-Marie speaks eight modern languages fluently," Peter said proudly. "She studied literature at the Sorbonne."

"I was a poor scholar. But I lived on Crete a short while."

"Doing magazine photography," Peter said. "She's an excellent photographer."

"Mostly I was doing drugs. Then I got married." She darted Peter a warning look: Let me speak for myself. "Not to Peter. That was later."

Minakis watched the edgy exchange. "I can't resist asking you what any other Greek would have asked by now. . . ."

She smiled. "Two. Not Peter's, though."

After an instant Peter caught on. "Oh yes. Jennifer lives with us, she's one. . . . She's with her grandmother now?" He raised an eyebrow at Anne-Marie, who nodded. "And Carlos is six; he, uh, he's going to spend time with us this summer."

"When do you plan to have . . . ?"

"No plans," Anne-Marie said, cutting off the inquiry.

Minakis nodded. "I will now stop being a Greek. Have you been to Delos before, Anne-Marie?"

"Once. I spent my time running up and down rocks, glancing at things out of the corner of my eye, scared I'd miss the boat back. So far, this trip is no different."

"We can walk around a bit without worrying about the boat," Minakis suggested. "I know the curator. If necessary, she'll send us back in her launch."

"Shouldn't we check with the woman first?" Peter asked. "I can't be stuck here all night."

"It's true, my friend will probably insist we stay for dinner," Minakis said, nodding solemnly. "And if we get too jovial, we may have to be her guests overnight. Yes, Peter, I think you do risk missing tomorrow morning's talk . . . what's it called?" -- the peremptory hand came up -- "I remember now: 'Amplitudes versus probabilities in reduplicated space-time,' isn't that it?"

"I'll take your word for it."

"Warmed-over Hawking. You can afford to miss it, in my opinion." Minakis hesitated. "Oh my, please forgive me. I've just remembered that Hawking was your thesis advisor."

Anne-Marie's expression made her preference plain. Peter thrust his hands into his pockets. "Never mind. We'll be glad to have you show us around."

Minakis grinned a glittering grin that said, of course you would. He turned and walked away, pausing at a discreet distance to admire the afternoon sun on the columns of the temple of Poseidon.

Meanwhile Peter leaned toward Anne-Marie and wrapped his fingers around her bare arms, on the verge of pulling her to him -- "I'm just so happy to see you!" -- but she evaded his hungry gaze. He leaned to kiss her, a light kiss on her mouth. Then, feeling her tension, he let her go. "Jennifer's okay? Your mother's all right?"

"Yes."

"Anne-Marie . . ."

"Let's talk later. When we're alone."

Together, not touching, they walked toward Minakis. He was an indistinct silhouette in the afternoon's shimmering light.

Hours later, after a tour of the island and its museum that would have exhausted even a scholar, they gratefully agreed to an early dinner with the ephor of antiquities and her husband in their square little house beside the square little museum above the sacred compound. Through clerestory windows, the westering light was honey-colored on the walls of the airy dining room and on the fragments of statues that decorated it. The long table was set with dishes of gleaming black olives and slabs of white cheese, bowls of pink taramosalata and plates of green salad, loaves of bread and sweating jugs of wine; the aroma of roasting lamb came from the kitchen.

"My good friend Manolis here has often tried to enlighten me concerning reality," said the ephor, Popi Gorgopoulou, an energetic woman in her forties whose stiff, yellow-blond hair was prematurely streaked with gray, "but I have never been able to make sense of his explanations." She directed her fierce attention upon Peter. "You are famous for your theoretical work, according to my friend. Also according to my friend, you are interested in the nature of reality." She lifted a glass of purple wine. "So I made him promise to bring you to meet me. I invite you to explain reality to me."

There was a moment's silence during which Popi's husband took the opportunity to make a trip to the kitchen; so far he had added little to the conversation besides his hearty smile, for he was not confident of his English, which the others were speaking in deference to Peter, who did not speak a word of Greek. Meanwhile Peter savored a morsel of marinated octopus and wondered just when Minakis had promised to produce him.

"Two years ago," Peter said, after pausing to swallow, "I would have had to decline your invitation. I was as much a logical positivist as Werner Heisenberg, who was suspicious of the word reality."

"Was he really?" Gorgopoulou asked, amused.

"Because, said Heisenberg, while such words lend themselves to sentences that produce pictures in our imagination -- he used the example, 'Besides our world there exists another world, with which any connection is impossible' -- such sentences have no consequences and therefore no content at all."

"But surely reality is what we can see and hear and feel," said the ephor. "Our experience. Our sense impressions."

"Most of us can agree on that," Peter said, "but if that were all we had to go on, we wouldn't know much about the world. We continually make assumptions, we fall into habits, we build little rational constructs on top of our sense impressions. I've seen the sun come up most days of my life, unless it is cloudy, so early on I concluded that the sun really does come up every day whether I see it or not. And I can think of good reasons why it should do so. And that becomes part of reality."

"A modest assumption," said the ephor.

"Not so modest. The realm of sense impressions plus the rational constructions we base upon them extends a long way, all the way from distant quasars down to the smallest virus. But try to look at anything much smaller . . ." Peter shrugged and speared another fragment of octopus tentacle with his fork.

"Please don't keep us in suspense," Anne-Marie said dryly, twisting her wine glass between her fingers.

"When we try to look inside atoms," Peter said, "not only can we not see what's going on, we cannot even construct a coherent picture of what's going on."

"If you will forgive me, Peter," Minakis said, turning to the others. "He means that we can construct several pictures -- that light and matter are waves, for example, or that light and matter are particles -- but that all these pictures are inadequate. What's left to us is the bare mathematics of quantum theory."

"As you've said before, Manolis" -- Popi Gorgopoulou broke in enthusiastically -- "and according to quantum theory, the microworld doesn't really exist?"

"More precisely," Minakis suggested, "according to the prevailing interpretation of quantum mechanics, the question of whether the microworld has an independent existence is meaningless."

"Yes, but do you believe that?" she asked. "You, Peter. Do you really believe there are two worlds, one that doesn't exist and one that does?"

Peter found Minakis looking at him across the table with an expression of wolfish amusement. "I used to," he said. "No more. Quantum theory works, but it doesn't tell the whole story."

"Then you believe in one world," said the ephor. "One really real world."

For a moment, no one said anything. Finally Peter nodded. "I'd like to."

Anne-Marie said, "Note the conviction."

Minakis said to Gorgopoulou, "Whatever the really real world is like, my friend, it is not what you might imagine."

"And you, Manolis?" she asked. "Can you imagine it?"

"I can imagine the real world." Minakis's smile was enigmatic. "Alas, in the time available to us tonight, I could not begin to describe it to you."

After dinner they took up their glasses of sweet mavrodaphni and moved away from the table. The ephor and her husband took Anne- Marie to see the Cycladic sculptures whose fragments were displayed in the hall of the adjacent museum; speaking Greek, kyrios Gorgopoulos was not at all reticent.

Meanwhile Peter followed Minakis onto the stone terrace that overlooked the ruin field of Apollo's sanctuary. The fat sun was wobbling toward the horizon across the narrow strait between Delos and its neighbor island Renia, backlighting the marbble rubble with orange light.

"Professor Minakis, people speak highly of you, but I'm afraid I'm not familiar with your work." Talking physics, Peter tended to bluntness. "Tell me more about this real world you imagine but can't describe."

Minakis turned away from the view of the sunset. "Are you familiar with John Cramer's transactional interpretation of quantum mechanics?"

"No I'm not."

"Some years ago Cramer followed up Feynman's and Wheeler's proposal that the self-energy of the electron can be eliminated if one assumes the existence of advanced-wave solutions to Schrodinger's equation for electromagnetic waves."

"Which proved to be a red herring."

"I'd prefer to call it a useful mistake, given the subsequent course of cosmology and quantum electrodynamics."

Peter shrugged.

Minakis leaned closer, his back to the spectacle of the setting sun. "Also possibly useful, I think, for removing the absurdities of quantum mechanics generally. Cramer takes Feynman and Wheeler several steps further, you see; he develops the notion of an exchange, or transaction, between what he calls 'offer' waves -- analogous to the wave function describing any quantum event -- and 'confirmation' waves, which are emitted backwards in time by the absorber of the consequences of the event."

Peter cocked his head quizzically. "That makes it sound as if every quantum event is a negotiation between the past and the future -- between a cause and its effect." In full sunlight Peter's skepticism was plain.

"Although Cramer's scheme is only an interpretation," Minakis replied, his shadowed expression unreadable, "in my view it is much more sensible than the Copenhagen interpretation and at least as logical as the many-worlds interpretation. But Cramer assumes it can't be tested. . . . that it makes no predictions which differ from those of standard quantum mechanics."

"You disagree?"

"Theory is indispensable, of course, but I was always one of those chaps who is happiest getting his hands dirty in the laboratory," Minakis said. "Read Cramer. I'll give you his papers. Then we can talk."

Popi Gorgopoulou came onto the terrace, leading Anne-Marie by the hand. "Time to go, you two, while there's light to see by."

Peter saw his wife radiant in the orange light, her pale eyes afire, her soft clothes wrapping her form in the evening breeze like a statue of Victory. He felt a rush of desire, having nothing whatever to do with the abstract matters he had been discussing a moment before.

But her pale gaze was fixed on the man behind him. On Minakis.

* * *