The thrown stone sank gradually into the surface of the reflection pool. It left no ripple or other trace of passing. If it had been perfectly round, this would have just been a  because it was perfectly round. The young woman who caused this catastrophe did not show the least shame when the eyes turned on her.

“I told you,” she said. She had not yet become accustomed to confrontation, and her voice shook.

There was a long silence. Some of us wondered what would happen to her, and others looked to our leaders for the order to seize her. But only ancient Gauz spoke at last.

“You should know.” he paused with this fraction of an introduction, and coughed for a while, until his sleeve was dark with moisture. “Know that there are differences.” He bent over this time and wretched air from his diaphragm so violently that specks of red spattered onto the polished stone. “Between what can be done.” And paused, this time just to breathe. It was a long inhalation, full of the sweet scent of tea olives that surrounded the temple. “And should,” he finished.

I found myself mouthing the word “be.” I noticed I wasn’t alone.

The heads of the two dozen initiates then swiveled from him to her. She didn’t even have a name yet, which made the outrage incomprehensible. Of course we know her name now. Everyone does.

“You are all fools,” she said. “Fools.” The word was a bowl brimfull with contempt.

Gauz was very old, and knew very much. He could have made the earth open under the upstart’s feet open to admit her to the core of the planet. I hoped he would. Later I understood that this was because I was envious of her.

Instead of using his power in that way, Gauz showed uncommon mercy. He advanced--hobbled, really--until he could just lift his eyes to meet hers.

The woman shook now, from head to toe. The desecration of the pool had not invoked divine wrath or brought lightning down on her head, but Gauz was a different kind of force altogether. Some things are beyond logic.

Still, she trembled but did not bow her head. She made him look up.

“Show me a fool,” Gauz said, and he willed the Seven Symmetries into the space between them. The complete graph outlined itself with showy orange, glowing and dancing along the edges. The vertices sparked and called attention to themselves.

The woman who would one day be called Ede invoked a semi-group of rotation, and the arrangement began to turn in all three dimensions at once. Gauz used the opportunity to trap a subtle invocation of the Intermediate Multiples Principle, and animated the graph with its equivalent classes. Many of these were well known to us, but others served as warnings to his depth of perspicacity.

Ede ignored this altogether and demanded of the graph a new topology so severe that it shattered. This was impressive, but she seemed bothered by the the extinction, and replaced it instantly with a C40 multi-group that shifted in mind-bending ways. I had it explained to me later that it was a three-dimensional projection of a twelve-dimensional object. If I had known at the time that she could do that with her mind, I would have jumped into the pool to drown myself. But youth has its useful illusions, and at the time I thought I was anyone’s equal. None of us had any idea.

The old man who opposed her intellect considered the matter for a long time. Long enough that the shuffling of feet and muttered encouragement began to tell. He straightened his body as fully as he was able, and then did something. It shames me that I don’t know what. At the time I was convinced it was a Wiles-type form reduction, but the truth is that I’m not smart enough to understand it. In any event, it didn’t work.

The young woman then explained to him why it hadn’t worked, and the rest of us listened, but did not understand. Gauz held up his hand to slow her down, which was an admission of defeat to us. But not to Gauz, it seems. He just wanted to know. They talked, then, and we watched for a while, like ducks might watch engineers build a dam. We knew it was important, profound even, but none of us had an inkling what they were discussing.

Some of the initiates left after an hour or so, but I remained. Ede and Gauz built their incomprehensible structures in front of us, and then tore them down, or collapsed them by reduction or some new kind of transformation. No one knows.

The figure by now had enveloped them both, and it showed profane attachments to the physical frame, which they seemed to ignore. And then the Door opened. I saw it. I saw Gauz reach his hand out, and Ede smiled. It wasn’t triumph, but a kind of indulgence that she showed. She wanted the old man to see the real way of things before his body’s strength failed. And the Grand Tautology took him. He wanted it, but his last expression was of terror.

That young woman who became Ede then closed the figure as if she were putting away her robe into a chest. She’d done it before. Her invocations were confident and utter concentration showed on her face, but when it was over, her mouth quirked to one side. She looked around, meeting eyes. I tried to hold her gaze and shamed myself by failing.

Then she giggled like a little girl. When the mirth had passed, she reworked her long hair from the loose strands of an initiate into the spiral of a master. It was clear she’d practiced that too.

“I told you so,” she said.