Like all the guilds, the Akademi der Luftsmagiker took most of its students at a young age—Sif was twice as old as most new aspirants. Yet it was not unheard of for older children, nearer Sif’s age, to show a talent for the working of magic. Most guilds had some provision for bringing such students up to speed. At the Akademi, it was Leifsson’s job.

It was not an easy one. Sif and her fellows trained at three times the pace of more traditional students. For four hours each day they studied ælfish. On most days, they spent an hour in the courtyard learning to fight. Four more they spent on the theory and practice of magic.

That was the topic at hand now. Before coming to the guild, Sif had worked magic on the fly, expressively. There was no structure to it, only what controlled chaos Sif herself wrung from the order of the weave. The guilds had a better way, re-imposing order onto the disorder of magic by teaching thousands of forms. Each tiny movement or single syllable corresponded to an exertion of will, a tiny tweak of the weave. Put together in the right way, the forms’ effects built on one another. A magiker who knew them well enough, and had the creativity to put them together in the right way, could do nearly anything with them, and leave the weave more intact than she would simply working magic off the cuff.

The girl seated next to Sif elbowed her. She could nearly have been Sif’s sister: they shared wide-set blue eyes and heart-shaped faces, though the girl’s blonde hair was curly where Sif’s was straight, and her skin was pale where Sif’s was darker.

The reason for the intrusion into Sif’s thoughts became clear a moment later. Ansgar Leifsson said, “Would you care to demonstrate, Sif Hrothgarsdottir?”

Sif frantically rewound Leifsson’s lecture in her head. No good.

The girl next to her stared straight ahead. Out of the corner of her mouth, she whispered, “Five seventy-one.”

Sif stood. “Five seventy-one,” she said. Leifsson nodded, gesturing in a circle with two fingers: go on. “One of… Felmansson’s cumulations?”

Leifsson nodded again. “Very good. Show us.”

Sif made a pyramid with her thumbs, forefingers, and middle fingers, then rotated her right hand so that her right thumb touched her left forefinger. The weave hummed as she did. She reversed the motion, and the power faded away.

“Well done. Be seated.”

Sif did so. “Thanks, Lilja,” she mouthed. Her seatmate dipped her head just a fraction.