Only slowly did he glimpse the soaring structures above each discipline. Great spans joined the vistas of topology to the infinitesimal intricacies of differentials, or the plodding styles of number theory to the shifting sands of group analysis. Only then did he see mathematics as a landscape, a territory of the mind to rove and scout.

To traverse those expanses he worked in mind time-long stretches of uninterrupted flow when he could concentrate utterly on problems, fixing them like flies in timeless amber, turning them this way and that to his inspecting light, until they yielded their secrets.

Phones, people, politics-all these transpired in real time, snipping his thought train, killing mind time. So he let Yugo and Dors and others fend off the world throughout the morning.

But today Yugo himself snipped his concentration. “Just a mo,” he said, slipping through the crackling door field. “This paper look right?”

He and Yugo had developed a plausible cover for the psychohistory project. They regularly published research on the nonlinear analysis of “social nuggets and knots,” a sub field with an honorable and dull history. Their analysis applied to subgroups and factions in Trantor, and occasionally on other worlds.

The research was in fact useful to psychohistory, serving as a subset of equations to what Yugo insisted on calling the full “Seldon Equations.” Hari had given up being irked at this term, even though he wished to keep a personal distance from the theory.

Though scarcely a waking hour passed without his thinking about psychohistory, he did not want it to be a template for his own worldview. Nothing rooted in a particular personality could hope to describe the horde of saints and rascals revealed by human history. One had to take the longest view possible.

“See,” Yugo said, making lines of print and symbols coalesce on Hari’s holo. “I got all the analysis of the Dahlite crisis. Neat as you please, huh?”

“Um, what’s the Dahlite crisis?”

Yugo’s surprise was profound. “We’re not bein’ represented! “

“You live in Streeling.”

“Once a Dahlan, you’re always one. Just like you, from Helical.”

“Helicon. I see, you don’t have enough delegates in the Low Council?”

“Or the High!”

“The Codes allow-”

“They’re out of date.”

“Dahlites get a proportional share-”

“And our neighbors, the Ratannanahs and the Quippons, they’re schemin’ against us.”

“How so?”

“There’re Dahlans in plenty other Sectors. They don’t get represented.”

“You’re spoken for by our Streeling-”

“Look, Hari, you’re a Helical. Wouldn’t understand. Plenty Sectors, they’re just places to sleep. Dahl is a people.”

“The Codes set forth rules for accommodating separate subcultures, ethnicities-”

“They’re not workin’.”

Hari saw from Yugo’s jutting jaw that this was not a point for graceful debate. He did know something of the slowly gathering constitutional crisis. The Codes had maintained a balance of forces for millennia, but only by innovative adaptation. Little of that seemed available now. “We agree on that. So how does our research bear upon Dahl?”

“See, I took the socio-factor analysis and-”

Yugo had an intuitive grasp of nonlinear equations. It was always a pleasure to watch his big hands cut the air, slicing through points and pounding objections to pulp. And the calculations were good, if a bit simple.

The nuggets-and-knots work attracted little attention. It had made some in mathematics write him off as a promising young man who had never risen to his potential. This was perfectly all right with Hari. Some mathists guessed that his true core research went unpublished; these he treated kindly but gave no hint of confirmation.

“-so there’s a pressure-nugget buildin’ in Dahl, you bet,” Yugo finished.

“Of course, glancing at the news holos shows that.”

“Well, yeah-but I’ve proved it’s justified.”

Hari kept his face composed; Yugo was really worked up about this. “You’ve shown one of the factors. But there are others in the knot equations.”

“Well, sure, but everybody knows-”

“What everybody knows doesn’t need much proof. Unless, of course, it’s wrong.”

Yugo’s face showed a rush of emotions: surprise, concern, anger, hurt, puzzlement. “You don’t support Dahl, Hari?”

“Of course I do, Yugo.” Actually, the truth was that Hari didn’t care. But that was too bald a point to make, with Yugo seeming wounded. “Look, the paper is fine. Publish.”

“The three basic knot equations, they’re yours.”

“No need to call them that.”

“Sure, just like before. But your name goes on the paper.”

Something tickled Hari’s mind, but he saw the right answer now was to reassure Yugo. “If you like.”

Yugo went on about details of publication, and Hari let his eyes drift over the equations. Terms for representation in models of Trantorian democracy, value tables for social pressures, the whole apparatus. A bit stuffy. But reassuring to those who suspected that he was hiding his major results-as he was, of course.

Hari sighed. Dahl was a festering political sore. Dahlites on Trantor mirrored the culture of the Dahl Galactic Zone. Every powerful Zone had its own Sectors in Trantor, for influence-peddling and general pressuring.

But Dahl was minor on the scale that he wanted to explore-simple, even trivial. The knot equations which described High Council representation were truncated forms of the immensely worse riddle of Trantor.

Allof Trantor-one teeming world, baffling in its sheer size, its intricate connections, meaningless. coincidences, random juxtapositions, sensitive dependencies. His equations were still terribly inadequate for this shell which housed forty billion bustling souls.

How much worse was the Empire!

People, confronting bewildering complexity, tend to find their saturation level. They master the easy connections, local links, and rules of thumb. They push this until they meet a wall of complexity too thick and high and hard to grasp, to climb.

There they stall. Gossip, consult, fret-and finally, gamble.

The Empire of twenty-five million worlds was a problem greater even than understanding the whole rest of the universe-because at least the galaxies beyond did not have humans in them. The blind, blunt motions of stars and gas were child’s play, compared to the convoluted trajectories of people.

Sometimes it wore him down. Trantor was bad enough, eight hundred Sectors with forty billion people. What of the Empire, with twenty-five million planets of average four billion souls apiece? One hundred quadrillion people!

Worlds interacted through the narrow necks of wormholes, which at least simplified some of the economic issues. But culture traveled at the speed of light through wormholes, information without mass, zooming across the Galaxy in destabilizing waves. A farmer on Oskatoon knew that a duchy had fallen on the other side of the Galactic disk a few hours after the blood on the palace floor started turning brown.

How to include that?

Clearly, the Empire extended beyond the Complexity Horizon of any person or computer. Only sets of equations which did not try to keep track of every detail could work.

Which meant that an individual was nothing on the scale of events worth studying. Even a million made about as much difference as a single raindrop falling in a lake.

Suddenly Hari was even more glad that he had kept psychohistory secret. How would people react if they knew that he thought they didn’t matter?

“Hari? Hari?”

He had been musing again. Yugo was still in the office. “Oh, sorry, just mulling over-”

“The department meeting.”

“What?

“You called it for today.”

“Oh, no.” He was halfway through a calculation. “Can’t we delay…?”