"Fechner's house," said Luca. "You know what its number was?"
Of course she didn't.
"Think of two numbers," said Luca, "then add them together to make a third."
Tris did what she was told, though she kept the numbers small so that the sums were easy.
"Now add the second number to the third, which will give you a fourth."
That was a bit harder.
"Now add those two together to give you a fifth."
As they walked Tris added numbers until she lost count of how many times Luca had asked her to do this.
"Finished adding the last two?"
"Yeah." Tris nodded.
"Good," said Luca, "now take that final number and the one before and calculate the ratio between them." He walked in silence while Tris worked out first what his instruction meant and then whether she could answer it.
"Well?"
"One point six?" Tris said finally.
"You sure?"
"Pretty much."
Luca smiled. "That's Fechner's number," he said. "You need to remember it." Tris was going to ask why but the boy now stood in front of a shimmering silver wall, concentrating hard while he did something complicated with his fingers.
Luca Pacioli lived in a palace. More precisely, he lived in part of the Emperor's palace, the one everyone recognized from the feed. Not in the actual Qiangquing Gong, obviously enough, but definitely a replica of what was intended to be a suite in a guest wing.
"That's the Jiulongbi, the Nine Dragon Screen!"
"Yes," Luca said sadly, "it is."
Someone had painted the Jiulongbi onto cloth and nailed it to the window frame, so the canvas faced inwards. The painting was crude and most of the nails holding it in place had rusted to the colour of dried blood. When Tris reached out to touch the canvas, flakes of dragon scale came off on her fingers.
"We used to have a real picture," said Luca. "One that did light and dark and showed eunuchs scurrying past the window and soldiers gathering on parade. The sky even showed black cranes flying."
"What happened?" she said.
"It broke." He shrugged. "My father kept it going for as long as he could. Far longer than was reasonable but in the end... you know. Things break." Luca gave her water and what might have been some kind of dry bread. And while Tris wolfed down the food, Luca told her about his childhood.
His father had brought him to Rapture so long before that Luca couldn't even remember when his father had died.
The pavilion had been glorious then, crowded with family, retainers, animals and servants who wore drab but functional smocks and wooden clogs for when the courtyard got waterlogged.
Ambassador Pacioli had chosen the servants and animals, just as he'd chosen his retainers and those who made up his secretariat. An important person in his own civilization, his luck had always been bad. A lucky man would have found reasons why someone else should go instead.
The replica of the guest wing in which Luca now lived had been the idea of Lady Pacioli, Luca's mother. It was not a particularly original idea because endless ambassadors had undergone training in replica palaces before taking up their posts. The novelty lay in Lady Pacioli's suggestion that the replica should be taken with them.
A feat less difficult than it sounded since all she needed was to acquire enough spiders to create whichever replica was appropriate. The secret was to instruct the spiders so they knew in advance exactly what they were meant to be doing.
The way Luca said this made Tris decide that he was reciting it from memory rather than actually understanding what spiders were or how they could grow a palace from the ground up.
"It's falling apart," Luca said.
"What is?"
"All of this." The stare he turned on the girl seemed heavy with too much knowledge and a realization that he'd never reach wherever it was he once thought he was going. "I'm sorry it's not better."
Luca looked so sad that Tris decided she probably had to sleep with him. It wouldn't be her first time and Tris wasn't worried about getting pregnant because Luca was obviously other than human and the mix never took in cases like that.
This piece of information came from Doc Joyce. And though the Doc had talked about exceptions, Tris felt it unlikely that Luca would carry the kind of germline fix needed to let him father children on stray humans... Of course, Tris didn't exactly think like this. She just thought, It's not going to happen.
And somehow that was enough.
"You own a bath?"
Luca's face froze and it took Tris a second to realize she'd just offended him. "I'm not saying you need one," she said hurriedly. "I mean, I've never had a bath. So if you've got one can I borrow it?"
"It's been a while," Luca said.
"What has?"
"Since I talked to anyone alive."
Tris decided not to think too deeply about that. Nodding at a random door, she said, "Through there...?"
"Sure," said Luca. "Why not?"
When Tris reached the doorway the room on the other side was busy rearranging itself, a divan melting into a wall as floor tiles stretched and sank to produce a bath twice her length.
"Too large," said Luca behind her and the tiles shifted again. "You'll still need some water," he said. "There should be water."
He led Tris to a courtyard where a huge cauldron stood, filled to the brim with rainwater. The cauldron was green with verdigris and the dragons that supported it had oxidized so badly in the rain that their scales were almost flat.
Below the cauldron stood a hearth heaped with ashes and when Luca swept these away Tris could see filaments of gold, some of which had melted and run together.
"We'll need some wood," Luca said. Instead of heading for a log pile, he wandered back into the pavilion, grabbed a gilded stool and smashed it hard against a doorpost. Scars on the post suggested this wasn't the first time it had been used that way.
"Try the table," suggested Luca.
Made from a honey-dark wood new to Tris, the table's top was carved into an ornate and aerodynamically sleek dragon, with vast wings which caught the wind like sails. On the back of the beast was a monk whose robes, beads and beard fluttered in the slipstream.
"Yes," said Luca, "that one."
So Tris picked up the table and carried it to the door. "It's beautiful," she said.
"Isn't it?" agreed Luca. "Here, let me." Taking the table from Tris's hands, he swung it hard into the doorpost, cracking monk and dragon into three. "It's not hard when you know how," he said. "The trick's in the wrist."
A temple carving followed the table, reduced to tinder in a single swing. "That should do us for now," said Luca.
To build his fire, Luca simply banked up fragments of table around a core of temple carving. And when both wood and kindling were ready, he flicked the fingers of his right hand across his thumb, like flint across steel.
"The water will take about a minute," he promised.
"How...?"
"The cauldron multiplies the heat. Whatever the cauldron takes in, it gives out more."
"That's impossible," said Tris.
"Most things are," Luca said, "if you think about them for long enough."
Kneeling next to the kindling, he reached out and Tris watched fire dance from his fingertips, catching ragged wood on a fragment of screen and turning those edges to gold.
"Watch," he said.
Flames caught the splintered screen and fire soon licked the underneath of the ancient cauldron, sliding up its sides until the flames grew, lost colour and disappeared into a heat so hot it was sufficient to make Tris stand back a little. All the same, the flames were nothing compared to the quantity of cold water in the cauldron and yet the inside rim was already beginning to birth bubbles, which grew fatter and fatter, until suddenly the whole slick surface began to roil and break.