Paradox (15 page)

“So? What do they need?” asked Tom.

“I don't know.” Jak fingered the wispy moustache he had been trying to grow for the last six tendays. “You're to go to the Sorites School, is all I know.”

“All right.”

“At least you'll probably know what they're talking about.”

“If they speak slowly enough.” Tom smiled, slyly.

“Don't give me that.” Jak checked his display again. “Seminar-suite epsilon. Don't go showing them up, hear?”

Black glass pyramids. Twelve dodecahedral buildings, rippling with gold and emerald, slowly changing shape in unison: growing taller, extending towers, extruding annexes. Later, they would shrink in size, and begin a different growth pattern. What would it be like inside them?

I've never been so far from the Palace.

The cavern was enormous, so that the architecture looked like buildings beneath a dark open sky, and it made Tom queasy. The Sorites School, his destination, was a simple crimson cube, stellated with black, slowly revolving.

“—drunk again last night?”

Tom stood by a row of statues—famous Lords and Ladies wearing scholarly frowns—while a group of red-caped young men and women passed him, heading for the school.

“I certainly was…”

He waited until their voices faded with distance.

Hung-over.
Don't you know how lucky you are?

Tom shook his head, then followed.

“Ah, there you are.” Long, patrician nose, white hair pulled back into a queue.

“Sir?”

The room was bare: ivory walls, float-pad seats, a tiny infotablet hovering beside each one. Only the black-robed Lord was there, making adjustments to a master tablet floating at the front.

“The seminar's starting soon.”

Seating for fifteen. Tom wondered what it would be like: for half a year now, he had been attending Mistress eh'Nalephi's exacting one-to-one tutorials.

“What can I do to help, sir?”

“None of that ‘sir' stuff, laddie. We're all scholars here.”

Tom looked around. By one wall, flagons of fruit juice and daistral were standing on a table.

“Shall I serve the…?”

“Oh, no.” The Lord raised one white eyebrow. “We need your brain, laddie: not your brawn.”

“I—” Tom's back straightened. “That's interesting.”

“I'm Velond. No, don't bow—That's better.” Lord Velond: cousin to Lady Darinia, the High Lady of this demesne, and a Lord Minor in his own right. “My niece informed me, some time ago, of the puzzle known as Tom's paradox.”

A flush rose in Tom's cheeks. “A veridical paradox, sir, as you know.”

He meant, it was a puzzle only to a child who did not know how an infinite series might converge.

“She was five SY old. To her, it was a real antinomy.”

Tom inclined his head. “That was why I chose that example.”

“Mm.” Lord Velond's stare was penetrating. “And an example of true antinomy?”

“This statement is a lie.” Tom glanced at the nearest infotablet, then decided he could elaborate without its help. “Though that becomes veridical, if you allow meta-contextual recursion.”

“Ah.” An odd smile creased Lord Velond's long face. “And an example we can't dispose of so easily?”

“I don't know.” Tom frowned. “But the nature of time would be involved, I'm sure…No, that's too difficult for now.”

Turning to the infotablet, Tom opened up a display and wrote a tricon by gesture:
This statement is a paradox.
He made ten copies of the tricon, then linked each “this statement” identifier to the next tricon by two relations: one labelled “is true,” the other labelled “is false.”

Finally, he linked the identifier of the last tricon to the verb-attribute of the first, completing a strange loop.

“Not in our universe,” murmured Lord Velond. “But an interesting way of looking at it.”

What about a universe whose dimensions are fractal?

Tom's skin crawled. The thought had popped out of nowhere. Yet, to someone who knew that Pilots really existed, it was not ridiculous.

The possibilities
…

If you could close off the infinite series, perhaps Gödel's theorem became invalid: allowing logic to be complete, so that every true statement was derivable from axioms—

But the others were arriving. Red capes were tossed over shoulders as they sat: scholars-designate, Lords and Ladies of Tom's age, making themselves comfortable, powering up the floating infotablets.

Lord Velond spoke quietly. “Tom, I'd like you to sit in on this.”

I don't belong here.

A migraine pounded over Tom's left eye as he sat miserably in the front row. He wanted to make notes of everything Lord Velond was
saying, but the other holodisplays around him remained still. Veridical qualification in self-referential representations was obviously child's play to scholars-designate.

“And how,” asked Lord Velond, “may we contextually analyse paradox classes?”

Silence.

What does the question mean?

Sickened, Tom wished he could get up and leave without attracting attention. He looked around at the others—and saw puzzled frowns, carefully blank expressions.

But there were only three kinds of paradox: falsifiable, veridical and antinomy. Mistakes, misunderstandings and the real thing. Any other distinctions must be terminology.

“Er…”

“Yes, Corcorigan?”

“Well, if we start with the most difficult set…” Tom began to draw a branching logic-tree, as
This statement is a paradox
spread through successive versions of truth and falsehood. “The instantiations can be labelled with indices,
i
and
j
, alongside a loop formula…”

At some point Tom became aware of a latecomer joining the group, but he pressed on with his discourse until Lord Velond called a halt.

“Interesting exposition,” he said. “Comments, anyone?”

No-one spoke.

Then a babble of voices broke as they questioned Tom's model, and he froze, throat paralysed, until a female voice spoke up: “But can't we equate Tom's indices to metarelations? Then it becomes analogous to the standard method, doesn't it?”

“No, of course not—”

But that lone supporting voice was all that Tom needed. Guessing what they meant by “standard method,” he proceeded to show that his notation was shorthand for the same thing.

“What's more…” Inspired, he dreamed up examples whose
veridical status was immediately revealed in his model, while the other approach took a dozen calculations to produce the same result. There was a chorus of objections—

“Enough.” The authority of Lord Velond's voice reduced the room to silence.

It was only then that Tom realized who had spoken up for him: Lady Sylvana, sitting at the rear of the group.

“That opens up some interesting possibilities,” Lord Velond continued. “Let's explore them.”

Using Tom's exposition as a starting-point, Lord Velond launched into dazzling realms of logical exploration—almost dancing on his toes, as holodisplays blossomed around him, often flaring with random bursts of colour as he gesticulated excitedly, forgetting to turn off gesture mode.

Tom watched in awe, oblivious to the scholars-designate except when Lord Velond said: “So it is intuitively obvious that—” and there were sniggers from the back row and an audible groan from one young Lord.

How can one man know so much?
Tom wondered, as Lord Velond continued.

He felt a sudden lurch as Lord Velond brought his lecture to an end. Two hours had passed.

“Not bad, Tom.” Lady Sylvana smiled. “See you tomorrow.”

As Tom was leaving, Lord Velond said: “We'll be working you hard, Tom. Very hard.”

Fate
, thought Tom as he stepped through the membrane.
I hope so.

Shyed'mday was the next rest day. Sleeve rolled up, Tom scrubbed out a processor-oven which refused to self-clean, wondering where his fellow students might be: partying at the Outer Courts, racing arachnargoi in Cavernae Brachialae.

After his duties, his private tutorial with Mistress eh'Nalephi, his
training-session at the salle d'armes…he reviewed the tenday's studies, and prepared for the next.

It became a pattern—of hard self-discipline which no-one ever saw—with tangible results: soon only Lord Velond himself could withstand Tom's ferocious attacks on the consensual view of matters logosophic.

“For most of us,” remarked Lady Sylvana after one gruelling seminar, “logodiscipline is a world-view, maybe even therapy.”

“I hadn't thought of it that way.”

“For you, though”—she stared at Tom intently—“logosophy is a weapon.”

The next day, she was missing from the group.

Disturbed, for no reason he could think of, Tom was more blunt than usual in his presentation.

“I don't see—” began an intense, pale youth: Viscount Humphrey.

“By symmetry,” said Tom, dispensing with an hour's worth of tedious calculations, “it's obvious that—”

He ignored the sniggers as he drew a dozen meta-related sorites together in one triconic knot.

“—as inevitable as an Oracle's predictions,” he finished. “Any questions?”

Some of the scholars-designate looked stunned or angry. One or two were either bored—having given up trying to follow the argument—or quizzically amused.

“Could you—” Viscount Humphrey coughed politely. “No, that's all right. I'll read my download later.”

Lord Velond was impassive.

“Do you have truecast access?” Tom addressed the room in general.

An angry murmur rippled through the group. Having a jumped-up servitor in the group was bad enough: but to discuss matters of noble interest—

“Truecasts are really artists' impressions—correct me if I'm
wrong—of future events, based on Oracles' perceptions of their personal futures. OK so far?”

A vicious silence.

“So my argument is as inevitable as an Oracle's truecast…unless the Oracle lies.”

Even Lord Velond's face hardened.

“I'm treating this as a logical exercise,” Tom continued. “But there's an antinomy here…for another day, I think. Lord Velond?” He bowed in the Lord's direction. “My apologies, everyone. I got a little carried away today.”

Then someone clapped.

Suddenly, the whole group was applauding, and Tom, stunned, let the sound wash over him.

Arlanna was waiting for him at his quarters.

“I need your help, Tom,” she said. “Actually, Lady Sylvana suggested it.”

“She wasn't at the Sorites School today.”

“I know.” Turquoise eyes unreadable. “She was trying on bridal gowns.”

The ground seemed to fall away beneath Tom's feet; Arlanna's voice came from some distant place.

“You and I,” she added, “are in charge of the wedding ceremony.”

There was one good point: working on the wedding organization—
Sylvana's wedding, Fate damn it
—meant that he gained access-control codes for the sensor web. In his room, Tom twisted open his stallion talisman and downloaded a new module for the first time in nearly four Standard Years, and solved the opening paradox.

He had no chance to execute the storyline; details of the marriage plans took up all his time.

“Shantzu Province, Byelasavyetski Commissariat, a dozen Lords-Meilleurs-sans-Demesne…” Arlanna's fingertip traced the gantt-lattice. “That's besides the contiguous surrounding demesnes.”

“And a Commissario Proconsul is the equivalent rank?” Tom looked up from his display.

“Fate knows. I hope so.” She sighed and leaned back, massaging her forehead above the good eye.

“How many settlers do you think there were?” Tom minimized his displays to a string of shining beads suspended in mid-air. “Originally, I mean: twelve centuries ago.”

“Oh, I don't know.” Arlanna rubbed her forehead again. “The current world population is ten billion.”

“It is? I didn't know that.”

“If you were alpha-class,” she began, smiling.

“An urchin like me? I don't think so. But the colonization logistics…For that matter, isn't it strange how the multiculture's been so stable?”

“Oracles, though there are only five thousand of them.” Her
expression grew serious. “They're the real basis for—” She turned away, and bit her lip.

“What's wrong, Arlanna?” He could only see her jewel-like left eye: turquoise, amber-flecked, but expressionless.

“You don't—The day of the explosion, remember that? Remember how Lady Sylvana and Lord d'Ovraison hurried out, away from the balcony?”

“Uh, yeah. Yes, I remember. You'd just handed Syl—Lady Sylvana—a message.”

“It was from an Oracle.” She took in a deep breath, then slowly let it out. “It said:
‘While you are reading this, a disaster has occurred. My apologies
—' There was more, but I didn't get to read the rest.”

Tom stared at her.

Not a message from just any Oracle, I'll bet.

And he thought, as often before, that it had been worse for Arlanna: while he had been knocked unconscious by the explosion's percussive wave, she, at the balcony's rear and shielded by a buttress, had dealt with the aftermath.

But he was not going to discuss treason with Arlanna. Why would she broach this subject the day after he had mentioned truecasts in the Sorites School?

Instead, he said: “So what about this seating plan?” Dredging up a display, he drilled in with a fingertip. “A minimax co-ordinate in a sixty-dimensional phase-space. Just to determine where a bunch of people are going to sit…”

Arlanna remained silent for a moment. “You could request a transfer, Tom,” she then said quietly, “to other duties. They'll probably allow it.”

“There's nothing too onerous about this, really.” Tom forced good cheer into his voice. “Do you fancy a walk around Aleph Hall?”

They were laughing by the time they reached the main doors. Behind them, the wide corridor glistened white, with rippling hints of pink and green.

“Can you believe those old guys?” Arlanna shook her head.

Shoulders hunched, two white-haired servitors had hurried past them, muttering: “There were none of these freeflow panels in eighty-nine,” and, “I've walked this tunnel every year since Lord Rilker's accession, and we always used to…”

“Since Lady Darinia's predecessor took power.” Tom looked back, but the two old men had gone. “Thirty years, walking up and down the same length of corridor, working with the same bureaucracy—”

“Wait a minute.” Arlanna stopped. “Didn't we just spend ten hours devising a seating plan?”

“That's different.”

“How?”

“Er…”

There were two dark-uniformed Dragoons at the main doors. “I know you're in charge of the seating,” one of them said before Arlanna or Tom could speak, “but we can't let you in. Lieutenant Milran's orders.”

Arlanna started to look annoyed, but Tom thought diplomacy might be in order: “Makes sense. We hadn't really thought about security.”

“He'll be here himself in an hour.”

“I'll wait.” Arlanna had regained her normal composure.

“The kitchens are beckoning me,” said Tom.

“Wait a minute.” Arlanna drew him aside. “You're really OK about the…ceremony, and everything?”

“Of course.” Tom spoke lightly. “Why shouldn't I be?”

“It's just that…Talefryn Tunnel, there, is where they're going to start from. Their honeymoon grand tour. I hear they need extra—”

Tom shook his head.

“Sorry.” He turned away. “I must be getting back.”

“Would you like company, sir?” The woman's face was creased with the pressures of a life Tom could not imagine. “We have nice girls waiting for you.”

He shook his head and walked on, wondering what he was doing back in the Caverna del'Amori. Behind him, the woman was making coarsely worded invitations to a pair of off-duty labourers.

Should have dressed down
, he thought,
if I wanted to blend in.

“Hey, honey.”

Tom held up his hand. “There used to be a woman called Lora—”

“Nothing wrong with me, is there?” But her eyes had shifted to the left. Tom nodded abruptly and headed for the alcove she had not quite looked at.

“Hello?”

The hanging was half-open, and he leaned inside.

White, glistening. It covered her face: wet, weeping fungus. The thing on the cot was skeletal, all flesh sunken in, cheekbones like razor-sharp protrusions.

A smile: an awful parody of invitation.

“Sorry,” he muttered, and pulled back.

He walked away, shaking inside.

A rack of edged weapons: redmetal poignard, titanium chainflick, white ceramic darts and throwblades. Over the display a crude holo hung:

A stuffed narl-serpent, fangs agape, reared stiffly in a jar fitted to the rack.

This was Tertium, Fate-knew-how-many strata above the stratum of Tom's childhood, but this market was sleazier than any Tom had visited. The chamber was low-ceilinged, lit by randomly floating crimson glowclusters; the marketgoers moved heads-down, not talking, many of them with hoods drawn to hide their features.

Very pleasant.

Shaking his head, Tom started to move on, then stopped. The semiliterate holo was cast by an ancient laser, pulsing through translucent smoky ceramic on which arcs had been hand-carved: by knife-point, it seemed.

That's clever. Working out the interference pattern and drawing it directly.

Perhaps there was more to this than shabby first appearances. Behind the weapons display, a black velvet tent had been directed, closed to public view, and—apparently deep inside it—a virtual holo showed a tiny scarlet tricon:

He stepped inside the darkened tent.

“Worried about vendetta, my Lord?” The voice was high, genderless; the speaker was dark-robed, sitting in shadows.

“I'm not a Lord.”

“But a gentleman. Still. What's the one factor that determines a weapon's suitability for a given occasion?”

Wary, Tom said nothing.

“Detectability.”

“Er, OK.”

“Some environments disallow energy weapons, or disable smarttech with microwave bursts. But an edged blade may always be used to settle a gentleman's quarrel, provided it conforms to
Les Accords d'Honneur.”

Tom shook his head. “I'm not really—”

“But there's a level that deepscan can't go beyond. Implanted pseudatoms and other femtotech: no-one can nondestructively seek them out.”

Scared of the direction this was taking, Tom said: “You're talking about mindware.”

A clucking sound. “Perhaps, perhaps.”

Tom turned away.

“We'll see you again, sir.”

Tom had read Lord Pelishar's speculations on attotwist geodesics in the original Mardu, and enjoyed Arlanna's historic Laksheesh holodramas with translation disabled. He had smatterings of Zardais and Valraig. These were languages of regions passed through by the grand tour.

I would be an asset, to accompany them on their honeymoon.

“Loop, please,” he said to his empty room.

A small loop appeared on the ceiling. On tiptoe, Tom hooked his little finger through the loop and pulled himself up—a one-finger chin-up—five times. He repeated the process for each finger, then did a last set with a full grip, then switched to one-hand press-ups—
the only kind I'll ever do
—for five sets of twenty.

Tomorrow night he would run to the big vertical shaft and clamber around on its walls for a while. But tonight—

“I'd like to run without going outside.”

Laminar flow swept the black floor endlessly away beneath his feet as he began to run on the spot.

He gestured the infotablet into voice mode.

“Activate.”