Yugo said, “I’ll just bet the Emperor’s got this all analyzed.”

Dors began pacing again. “One of history’s lessons is that emperors who overanalyze fail, while those who oversimplify succeed.”

“A neat analysis,” Hari said, but she did not catch his irony.

“Uh, I actually came in to get some work done,” Yugo said softly. “I’ve finished reconciling the Trantorian historical data with the modified Seldon Equations.”

Hari leaned forward, though Dors kept pacing, her hands clasped behind her back. “Wonderful! How far off are they?”

Yugo grinned as he slipped a ferrite cube into Hari’s desk display slot. “Watch.”

Trantor had endured at least eighteen millennia, though the pre-Empire period was poorly documented. Yugo had collapsed the ocean of data into a 3D. Economics lay along one axis, social indices along another, with politics making up the third dimension. Each contributed a surface, forming a solid shape that hung above Hari’s desk. The slippery-looking blob was man-sized and in constant motion-deforming, caves opening, lumps rising. Color-coded internal flows were visible through the transparent skin.

“It looks like a cancerous organ,” Dors said. When Yugo frowned, she added hastily, “Pretty, though.”

Hari chuckled; Dors seldom made social gaffes, but when she did, she had no idea of how to recover. The lumpy object hanging in air throbbed with life, capturing his attention. The writhing manifold summed up trillions of vectors, the raw data drawn from countless tiny lives.

“This early history had patchy data,” Yugo said. The surfaces jerked and lurched. “Low resolution, too, and even low population size-a problem we won’t have in Empire predictions.”

“See the two-dee socio-structures?” Hari pointed. “And this represents everything in Trantor?” Dors asked.

Yugo said, “To the model not all detail is equally important. You don’t need to know the owner of a starship to calculate how it will fly.”

Hari said helpfully, pointing at a quick jitter in social vectors, “Scientocracy arose here third millennium. Then an era in which stasis arose from monopolies. That fed rigidity.”

The forms steadied as the data improved. Yugo let it run, time-stepping quickly so that they saw fifteen millennia in three minutes. It was startling, the pulsing solid growing myriad offshoots, structure endlessly proliferating. The madly burgeoning patterns spoke of the Empire’s complexity far more than any emperor’s lofty speech.

“Now here’s the overlay,” Yugo said, “showing how the Seldon Equations post-dict, in yellow.”

“They aren’t my equations,” Hari said automatically. Long ago he and Yugo had seen that to pre dictwith psychohistory first demanded that they post- dict the past, for verification. “They were-”

“Just watch.”

Alongside the deep blue data-figure, a yellow lump congealed. It looked to Hari like an identical twin to the original. Each went through contortions, seething with history’s energy. Each ripple and snag represented many billions of human triumphs and tragedies. Every small shudder had once been a calamity.

“They’re…the same,” Hari whispered.

“Damn right,” Yugo said.

“The theory fits.”

“Yup. Psychohistory works.”

Hari stared at the flexing colors. “I never thought…”

“It could work so well?” Dors had walked behind his chair and now rubbed his scalp.

“Well, yes.”

“You have spent years including the proper variables. It must work.”

Yugo smiled tolerantly. “If only more people shared your faith in mathists. You’ve forgotten the sparrow effect.”

Dors was transfixed by the shimmering data-solids, now rerunning all Trantorian history, throbbing with different-colored schemes to show up differences between real history and the equations’ post-dictions. There were very few. What’s more, they did not grow with time.

Not taking her eyes from the display, Dors asked slowly, “Sparrow? We have birds as pets, but surely-”

“Suppose a sparrow flaps its wings at the equator, out in the open. That shifts the air circulation a tiny amount. If things break just right, the sparrow could trigger a tornado up at the poles.”

Dors was startled. “Impossible!”

Hari said, “Don’t confuse it with the fabled nail in the shoe of a horse, that a legendary beast of burden. Remember?-its rider lost a battle and then a kingdom. That was failure of a small, critical component. Fundamental, random phenomena are democratic. Tiny differences in every coupled variable can produce staggering changes.”

It took a while to get the point through. Like any other world, Trantor’s meteorology had a daunting sensitivity to initial conditions. A sparrow’s wingflutter on one side of Trantor, amplified through fluid equations over weeks, could drive a howling hurricane a continent away. No computer could model all the tiny details of real weather to make exact predictions possible.

Dors pointed at the data-solids. “So-this is all wrong?”

“I hope not,” Hari said. “Weather varies, but climate holds steady.”

“Still…no wonder Trantorians prefer indoors. Outdoors can be dangerous.”

“The fact that the equations describe what happened-well, it means that small effects can smooth out in history,” Hari said.

Yugo added, “Stuff on a human scale can average away.”

She stopped massaging Hari’s scalp. “Then… people don’t matter?”

Hari said carefully, “Most biography persuades us that people-that we-are important. Psychohistory teaches that we aren’t.”

“As a historian, I cannot accept-”

“Look at the data,” Yugo put in.

They watched as Yugo brought up detail, showed off features. For ordinary people, history endured through art, myth, and liturgy. They felt it through concrete examples, close up: a building, a custom, a historical name. He and Yugo and the others were like sparrows themselves, hovering high over a landscape unguessed by the inhabitants below. They saw the slow surge of terrain, glacial and unstoppable.

“But people have to matter.” Dors’ voice carried a note of forlorn hope. Hari knew that somewhere deep in her lurked the stern directives of the Zeroth Law, but over that lay a deep layer of true human feeling. She was a humanist who believed in the power of the individual-and here she met blunt, uncaring mechanism, in the large.

“They do, actually, but perhaps not in the way you want,” Hari said gently. “We sought out telltale groups, pivots about which events sometimes hinge.”

“The homosexuals, f’instance,” Yugo said.

“They’re about one percent of the population, a consistent minor variant in reproductive strategies,” Hari said.

Socially, though, they were often masters of improvisation, fashioning style to substance, fully at home with the arbitrary. They seemed equipped with an internal compass that pointed them at every social novelty, early on, so that they exerted leverage all out of proportion to their numbers. Often they were sensitive indicators of future turns.

Yugo went on, “So we figured, could they be a crucial indicator? Turns out they are. Helps out the equations.”

Dors said severely, “Why does history smooth out?”

Hari let Yugo carry the ball. “Y’see, that same sparrow effect had a positive side. Chaotic systems could be caught at just the right instant, tilted ever so slightly in a preferred way. A well-timed nudge could drive a system, yielding benefits all out of proportion to the effort expended.”

“You mean control?” She looked doubtful.

“Just a touch,” Yugo said. “Minimal control-the right nudge at the right time-demands that the dynamics be intricately understood. Maybe that way, you could bias outcomes toward the least damaging of several finely balanced results. At best, they could drive the system into startlingly good outcomes.”