Eifelheim

“Why not?” she said. “In the real sciences, theory has to fit the facts; not vice versa.”

Tom’s face went red, for she had touched (as she had known she would) upon one of his hot buttons. “Does it, a cuisla? Does it really? Wasn’t it Dirac who said that it was more important that the equations be beautiful than that they fit the experiment? I read somewhere that measurements of light speed have been getting lower over the years. Why not throw out the theory that light speed is constant?”

She frowned. “Don’t be silly.” She had her own hot buttons. Tom did not know what they were, but he managed to hit them all the same.

“Silly, hell!” He slammed his hand down sharply on the terminal and she jumped a little. Then he turned his back and faced the screen once more. Silence fell, continuing the quarrel.

Now, Sharon had that peculiar ability to stand outside herself, which is a valuable skill, so long as one comes back inside now and then. They were both being silly. She was angry at having her train of thought derailed, and Tom was angry because some simulation of his wouldn’t work out. She glanced at her own work and thought, I’m not helping me by not helping him, which might be a poor reason for charity, but it beats having none at all.

“I’m sorry.”

They spoke in counterpoint. She looked up, and he turned ’round, and they stared at each other for a moment and ratified a tacit armistice. The geodesic to peace and quiet was to hear him out; so Sharon crossed the room and perched on the corner of his desk.

“All right,” she said. “Explain. What’s this Zip-whatever theory?”

In answer, he turned to his keyboard, entered commands with the flourish of a pianist, and rolled his chair aside for her. “Tell me what you see.”

Sharon sighed a little and stood behind him with her arms folded and her head cocked. The screen displayed a grid of hexagons, each containing a single dot. Some dots were brighter than others. “A honeycomb,” she told him. “A honeycomb with fireflies.”

Tom grunted. “And they say physicists make lousy poets. Notice anything?”

She read the names beside the dots. Omaha. Des Moines. Ottumwa… “The brighter the dot, the bigger the city. Right?”

“Vice versa, actually; but, right. What else?”

Why couldn’t he just tell her? He had to make it a guessing game. His students, waiting beak-open for his lectures, often felt the same disquiet. Sharon concentrated on the screen, seeking the obvious. She did not regard cliology as an especially deep science, or much of a science at all. “Okay. The big cities form a partial ring. Around Chicago.”

Tom gri

“A ring of not-so-big cities. How fractal! But the pattern isn’t perfect…”

“Life’s not perfect,” he answered. “Microgeography and boundary conditions distort the pattern, but I correct for that by transforming the coordinates to an equivalent, infinite plain.”

“A manifold. Cute,” she said. “What’s your transformation?”

“Effective distance is a function of the time and energy needed to travel between two points. Non-Abelian, which complicates matters.”

“Non-Abelian? But then—”

“B can be farther from A than A is from B. Sure, why not? The Portuguese found it easier to sail down the coast of Africa than to sail back up. Or, take our own dry-cleaners? The streets are one-way, so it takes three times longer to drive there than it does to drive back.”

But Sharon wasn’t listening any longer. Non-Abelian! Of course, of course! How could I have been so stupid? Oh, the happy, unquestioning life of an Abelian, Euclidean, Hausdorff peasant! Could Janatpour space be non-isotropic? Could distance in one direction differ from distance in another? It’s always faster coming home. But how? How?

His voice shattered her reverie once more. “… oxcarts or automobiles. So, the map is always in transition from one equilibrium to another. Now watch.”

If she didn’t hold his hand while he complained, she would never get her own work done. “Watch what?” she asked, perhaps in a harsher voice than she had intended, because he cast her a wounded glance before bending again over the keyboard. While he did, she slipped across the room and retrieved her notebook so she could capture her butterfly thought.

“Christaller’s original survey,” said Tom, who had not noticed her sortie. “Land Württemburg, 19th century.”

Sharon spared the screen a cursory glance. “All right—” Then, almost against her will, she leaned toward the computer. “Another honeycomb,” she said. “Is that a common pattern?”

He didn’t answer. Instead he showed her a series of maps. Johnson’s study of Late Uruk settlements around Warka. Alden’s reconstruction of Toltec polities in the Valley of Mexico. Ski

“Now check out this map. Verified sites of ancient Sumerian and Elamite pueblos.”

To her own a

Tom regarded the screen with indulgence. “My claim to fame. There was no known pueblo at that site. But ancient writings are full of references to places we’ve never pi

So his patterns had predictive value, too. Patterns were interesting. They could lead, like astrology, to real science. “There has to be a cause,” she said.

He gave her a satisfied nod. “Ochen khoroshó.”

“Okay, I’ll bite. What is it?”

He tapped a fingernail against the display. “You’re looking at the equilibrium of a reaction-diffusion process. Each locus provides some degree of bio-psychological reinforcement to its inhabitants. Rich bottomlands, a vein of silver, a plentiful supply of guano, anything. Andere Lände, andere Sitte. The intensity of that reinforcement defines a potential function over the landscape, and the gradient of that potential is a force we call affinity.”

Sharon withheld comment. She had never considered Tom’s ‘forces of history’ as anything more than a metaphor. She was a physicist, and physicists dealt in real forces.

“If affinity were the only force,” Tom continued, “the entire population would be sucked into the local maximum. But population density itself creates a second potential because, cæteris paribus, people prefer wide open spaces to getting someone’s elbow in their ear. So there’s a counter tendency for the population to spread out evenly across the landscape in a kind of cultural heat death. The interaction between these two forces generates the differential equations for a reaction-diffusion process. Population accumulates at the equilibrium sites, with settlement sizes distributed according to Zipf’s rank-size law. Each settlement generates a cultural potential field whose strength is proportional to its wealth and population and which diminishes with the square of the distance. Geographically, these settlements and their hinterlands form hexagonal patterns called Christaller grids. Ert, Nagy kisasszony?”

“Ertek jol, Schwoerin ur,” she answered. Sharon wasn’t entirely convinced, but if she argued the point, they’d be up all night, settle nothing, and she’d never get back to Janatpour space. Besides, the model did account for that remarkable consistency of settlement patterns. She pursed her lips. If she wasn’t careful, she’d get sucked into solving his problem instead of her own. “So, where does this Eifelheim of yours fit in?”