Yalda stayed kneeling against the bush, shouting with frustration at all her stupid failed scrawls. A teacher and a writing partner made it easier; rest and guidance and encouragement made it easier.
But when the sun had crossed half the sky, the figure from her memory was there on her chest, imperfect but legible, hers to command.
3
On the day after her twelfth birthday, Yalda woke before dawn and forced herself to open her eyes before the cool soil lured her back to sleep. The vines that crisscrossed the low ceiling above her were studded with tiny yellow blossoms; thumps and scraping sounds filtered through from the floor of the markets as the stallholders made their preparations.
Zeugma’s public beds were much in demand, and Yalda preferred to be gone before the night shift workers came down grumbling and prodding for spaces of their own. She rose and threaded her way between her sleeping neighbors, aware of other shapes moving softly nearby. The slender vines gave out just enough light to let her see where she was going, but it took care and practice not to step on a sleeper, or collide with someone else on the way to the exits.
She bounded up the stairs and ducked into the markets to buy a loaf, then made it out onto the street in time to see the stars before the pale sky extinguished them completely. In Zeugma, only the wealthiest inhabitants with their private, walled gardens had the choice of sleeping in the open air; if you dug an indentation beside the flowers in the parks you were beaten for damaging city property. But Yalda preferred to spend her nights beneath the markets rather than waste money on an apartment in the towers, where your bed was cooled by a thermal conduit of calmstone columns, buried in the ground but stretching up to drain the heat from the highest of those dreary cages.
She still had five chimes before her appointment with Eusebio, but she wanted to be thoroughly prepared in order to ensure that the session didn’t run over time; there was a mid-morning lecture by a visiting scientist on new developments in optics that she didn’t want to miss. So she paced the grimy streets between the markets and the university, planning her lesson in detail, composing diagrams as she walked. There weren’t many pedestrians about, and in any case the people she passed showed no surprise at the strange shapes forming and shifting on her skin. Some academics went to great pains to conceal their priceless musings, learning to make purely mental sketches or to ensure that anything showing on their body was at least writ small on the palms of their hands, but Yalda had never felt the need to cultivate those furtive habits.
She had timed her peregrinations perfectly; the university clock made its doleful noise just as she entered the stone tower where Eusebio lived. Yalda took the stairs quickly; to arrive right on the chimes would have been ill-mannered, but a sprint to the fourth floor would be enough to take the edge off her punctuality.
When she reached the apartment the curtained entrance was already parted to welcome her; she called out “It’s Yalda!” and stepped through. The room smelled of dye and paper; there were dozens of textbooks stacked against the walls, and Eusebio’s own notes rivaled them in bulk. A merchant’s son hoping to break into the railway business, he took his engineering studies seriously. Even the three small clockwork figurines, marching back and forth beside one pile of books, were evidence of a diversion equally concerned with the subject of what a machine could or could not be made to do.
“Good morning, welcome!” Eusebio was sitting on the floor in the corner, loose pages spread out in front of him. He was bulky for a man, but no less agile for it; Yalda suspected that he’d strived from childhood to match the deftness of smaller peers, much as she had.
She sat facing him, cross-legged, and got straight to the point. She knew exactly what he would have been told in the lecture he’d had the day before; not one word had changed in the introductory physics course since she’d taken it herself, four years previously.
“Conservation of energy and momentum,” she said. “How much did you understand?”
“Maybe half,” he confessed. But Eusebio didn’t claim understanding lightly; Yalda suspected that he’d followed the whole lecture, but longed for a deeper grasp of the subject.
“Let’s start with something simple,” she suggested. “Suppose an object is free to move, without friction. It starts out at rest, and you apply a constant force to it. After some time has passed, tell me how the force, the time, and the object’s velocity are related.”
Eusebio said, “Force equals mass times acceleration; acceleration by time gives velocity. So, the product of force and time equals the product of the object’s mass and its velocity—also known as its ‘momentum’.”
Yalda widened her eyes approvingly. “And in the general situation, where the object need not start from rest? The product of the force and the time for which it’s applied gives…?”
“The change in the object’s momentum.” Eusebio lifted a sheet of calculations. “I confirmed that.”
“Good. So, if two objects interact—if a child throws a stone at an approaching train, and it bounces off the front carriage—what happens to their momenta?”
“The force of the train on the stone is equal and opposite to the force of the stone on the train,” Eusebio replied. “And since both forces act for the same amount of time, they cause equal and opposite changes of momenta: as much as the stone’s momentum rises—measured in the direction of the train’s motion—the train’s will fall.”
Yalda said, “So the total, the sum of the two, is unchanged. What could be simpler?”
“Momentum is simple enough,” Eusebio agreed. “But energy—”
“Energy is almost the same!” Yalda assured him. “It’s just that instead of the product of force and time, you use the product of force and distance traveled. What’s an easy way to turn the first into the second?”
Eusebio thought for a moment. “Multiply it by distance over time, which is the average velocity. For an object that started from rest and accelerated smoothly, that’s half the final velocity it’s reached. So the product of the force and the distance traveled is the product of momentum and half the velocity… or half the mass times the velocity squared. The kinetic energy.”
“Exactly,” Yalda said.
Eusebio understood these calculations well enough, but he was less happy with the bigger picture. “Energy is where the ‘conservation laws’ start to sound more like a long list of exceptions,” he complained.
“Maybe. Tell me about the exceptions.”
“Gravity! Drop a book from my window; its kinetic energy certainly won’t stay the same. And the fact that the book pulls the world up toward it with as much force as the world pulls it down doesn’t help; that keeps momentum balanced, but not kinetic energy.”
“Sure.” Yalda brought one of the diagrams she’d rehearsed onto her chest.
“If you plot the downward force on the book against its height above the ground,” she said, “it’s a constant, a flat, straight line. Now think about the area under that line, up to the point representing the book’s current height. When the book falls, the reduction in the area—the little rectangle that gets chopped off—will equal the force on the book times the distance it travels—which is precisely the amount by which its kinetic energy increases: force times distance.”