“Tell Dova to continue the work,” he said. He had not anticipated that their covenant would attract the loyalty of an ardent, of all things. The Diagram, and its members, knew no boundaries. Dova had discovered their work on her own, and they’d needed to either induct her or assassinate her.

“It will be done,” Adrotagia said.

The boatmen moved them up alongside some smoother rocks at the harbor’s edge, then hopped out into the water. The men were servants of his, and were part of the Diagram. He trusted them, for he needed to trust some people.

“Have you researched that other matter I requested?” Taravangian asked.

“It is a difficult matter to answer,” Adrotagia said. “The exact intelligence of a man is impossible to measure; even your tests only give us an approximation. The speed at which you answer questions and the way you answer them… well, it lets us make a judgment, but it is a crude one.”

The boatmen hauled them up onto the stony beach with ropes. Wood scraped stone with an awful sound. At least it covered up the moans in the near distance.

Adrotagia took a sheet from her pocket and unfolded it. Upon it was a graph, with dots plotted in a kind of hump shape, a small trail to the left rising to a mountain in the center, then falling off in a similar curve to the right.

“I took your last five hundred days’ test results and assigned each one a number between zero and ten,” Adrotagia said. “A representation of how intelligent you were that day, though as I said, it is not exact.”

“The hump near the middle?” Taravangian asked, pointing.

“When you were average intelligence,” Adrotagia said. “You spend most of your time near there, as you can see. Days of pure intelligence and days of ultimate stupidity are both rare. I had to extrapolate from what we had, but I think this graph is somewhat accurate.”

Taravangian nodded, then allowed one of the boatmen to help him debark. He had known that he spent more days average than he did otherwise. What he had asked her to figure out, however, was when he could expect another day like the one during which he’d created the Diagram. It had been years now since that day of transcendent mastery.

She climbed out of the boat and Mrall followed. She stepped up to him with her sheet.

“So this is where I was most intelligent,” Taravangian said, pointing at the last point on the chart. It was far to the right, and very close to the bottom. A representation of high intelligence and a low frequency of occurrence. “This was that day, that day of perfection.”

“No,” Adrotagia said.

“What?”

“That was the time you were the most intelligent during the last five hundred days,” Adrotagia explained. “This point represents the day you finished the most complex problems you’d left for yourself, and the day you devised new ones for use in future tests.”

“I remember that day,” he said. “It was when I solved Fabrisan’s Conundrum.”

“Yes,” she said. “The world may thank you for that, someday, if it survives.”

“I was smart on that day,” he said. Smart enough that Mrall had declared he needed to be locked in the palace, lest he reveal his nature. He’d been convinced that if he could just explain his condition to the city, they would all listen to reason and let him control their lives perfectly. He’d drafted a law requiring that all people of less than average intellect be required to commit suicide for the good of the city. It had seemed reasonable. He had considered they might resist, but thought that the brilliance of the argument would sway them.

Yes, he had been smart on that day. But not nearly as smart as the day of the Diagram. He frowned, inspecting the paper.

“This is why I can’t answer your question, Vargo,” Adrotagia said. “That graph, it’s what we call a logarithmic scale. Each step from that center point is not equal—they compound on one another the farther out you get. How smart were you on the day of the Diagram? Ten times smarter than your smartest otherwise?”

“A hundred,” Taravangian said, looking at the graph. “Maybe more. Let me do the calculations…”

“Aren’t you stupid today?”

“Not stupid. Average. I can figure this much. Each step to the side is…”

“A measureable change in intelligence,” she said. “You might say that each step sideways is a doubling of your intelligence, though that is hard to quantify. The steps upward are easier; they measure how frequently you have days of the given intelligence. So if you start at the center of the peak, you can see that for every five days you spend being average, you spend one day being mildly stupid and one day mildly smart. For every five of those, you spend one day moderately stupid and one day moderately genius. For every five days like that…”

Taravangian stood on the rocks, his soldiers waiting above, as he counted on the graph. He moved sideways off the graph until he reached the point where he guessed the day of the Diagram might have been. Even that seemed conservative to him.

“Almighty above…” he whispered. Thousands of days. Thousands upon thousands. “It should never have happened.”

“Of course it should have,” she said.

“But it’s so unlikely as to be impossible!”

“It’s perfectly possible,” she said. “The likelihood of it having happened is one, as it already occurred. That is the oddity of outliers and probability, Taravangian. A day like that could happen again tomorrow. Nothing forbids it. It’s all pure chance, so far as I can determine. But if you want to know the likelihood of it happening again…”

He nodded.

“If you were to live another two thousand years, Vargo,” she said, “you’d maybe have one single day like this among them. Maybe. Even odds, I’d say.”

Mrall snorted. “So it was luck.”

“No, it was simple probability.”

“Either way,” Taravangian said, folding the paper. “This was not the answer I wanted.”

“Since when has it mattered what we want?”

“Never,” he said. “And it never will.” He tucked the sheet into his pocket.

They picked their way up the rocks, passing corpses bloated from too long in the sun, and joined a small group of soldiers at the top of the beach. They wore the burnt-orange crest of Kharbranth. He had few soldiers to his name. The Diagram called for his nation to be unthreatening.

The Diagram was not perfect, however. They caught errors in it now and then. Or… not truly errors, just missed guesses. Taravangian had been supremely brilliant that day, but he had not been able to see the future. He had made educated guesses—very educated—and had been right an eerie amount of the time. But the farther they went from that day and the knowledge he’d had then, the more the Diagram needed tending and cultivation to stay on course.

That was why he’d hoped for another such day soon, a day to revamp the Diagram. That would not come, most likely. They would have to continue, trusting in that man that he had once been, trusting his vision and understanding.

Better that than anything else in this world. Gods and religion had failed them. Kings and highlords were selfish, petty things. If he was going to trust one thing to believe in, it would be himself and the raw genius of a human mind unfettered.