The man suddenly stood and like a virtuoso directing an unseen orchestra, he gestured right and left, twisting and bowing his entire body in contortions that would have been ridiculous if the end result weren’t lightning bolts, punctuated by the occasional clap of thunder, streaming outward, picking off attackers with amazing accuracy and efficiency.

A name suddenly came to the Angel. Doktor Omweer.

She stood, her people watching, and strode to the door. The attacking spider pack had either been entirely destroyed or discouraged by the time she reached the banks of the pool and Omweer stood on his toes, his arms thrust into the sky, his back dramatically bent backward like a bow.

He heard her approaching step and whirled to face her. His full head of grey hair thrust wildly in every direction, his face was smeared with dirt and what looked to be caked blood. One lens was missing from his eyeglasses that lay crookedly upon his face and his eyes, the Angel saw, were mad. Stark, crazy mad.

“What is,” he asked almost conversationally, “the difference between the rational and irrational?”

The Angel edged a small step to her right. To her left was the open pool. To her right, the broken ground from which it was torn.

“I don’t know,” she replied, in a cunningly rational voice.

“The question is, which one are you?” Omweer replied. “There exists, irrational numbers a and b such that a to the power of b is rational.”

“Of course,” the Angel said.

“The square root of two is irrational, yet two is rational.” He approached her carefully. “Consider the number q which equals the square root of two to the power of the square root of two. Either it is rational or irrational.”

Omweer, she saw, was not going to take a chance. His right hand twitched at the wrist, giving her time to dive behind a pile of dirt that proved thick enough to protect her as his lightning bolt flashed outward, exploding it into a pillar of dust.

“If q is rational,” Omweer screamed, “then the theorem is true, with a and b both being the square root of two!”

The Angel leapt, taking to the sky as her wings appeared. Her wings beat twice as she gained height, then she suddenly turned and swerved as Omweer tried to track her flight path.

“If q is irrational,” he shouted to the sky, “then the theorem is true, with a being the square root of two to the power of the square root of two and b being the square root of two, since—”