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“Spivey,” Teresa said, though clearly she did not want to.

Manella nodded. “He’s almost got a monopoly on data about these breathtaking, intimidating new technologies. But who knows even more about singularities and gravity lasers than his tame physicists?”

They looked at each other. No one in the world understood the gazer phenomenon better than the people in this room.

This is no good, Alex decided. Manella might be right. Dammit, he probably is. But I’m not letting him hypnotize my team.

“Clever, Pedro,” he told the newsman. “Have you also worked out what I’ve decided to do about it?”

“Is that all?” The big man grinned. “You forget that I know you, Lustig. I’d bet my tooth-implant radio and half a year’s pay you intend showing Colonel Spivey just who he’s dealing with.”

Damn you, Alex thought. But outwardly he only shrugged. Looking at the others, he announced — “Anyone who chooses to leave the island may do so now. All civilians will be warned away from a two-kilometer radius.

“As for me, though, I don’t plan taking this—” he hefted the bomb ” — lying down.”

He looked again at Teresa, who nodded. She understands. The next few days will decide the future of everything.

Alex watched as the assembled workers, one by one, stepped toward him and the great swiveled bulk of the resonator. Their silent vote was unanimous. “Good,” he said, feeling a wave of warmth toward his comrades. “Let’s get to work then. I had a dream not long ago, and it gave me an idea. A possible way we just might get the good colonel’s attention.”

□ Worldwide Long Range Solutions Special Interest Group [□ SIG AeR.WLRS 253787890.546], Special Alert to Members.

There are times for discussion, and other times when only action counts. None of our fancy schemes will help anybody if we don’t make it through this present craziness! So the coordinators of the Worldwide Long Range Solutions SIG hereby suspend all conference forums. Instead we encourage all of you, as individuals, to seek ways to help solve the crisis many see looming, hour by passing hour.

“But what can a single person do to influence events of such magnitude and momentum?” One answer may surprise you. We’ll shortly hand over these channels, on loan, to the Federation of Amateur Observation Special Interest Groups [□ sig BaY, FAO 456780079.876]. Their spokesper will describe how each of you can assist the worldwide effort to track the gremlins down.

It may surprise many of you how much science relies on amateur observers, from bird-watchers, to meteor counters, to hobbyists with private weather stations. But now, with so many weird phenomena taking place worldwide, these amateur networks are truly coming into their own. It’s private citizens, with sharp eyes and ready cameras, who are even now tracing patterns the big boys think they can keep secret from us.

We’ll show them whose planet this is! So stay on-line for a list of groups you can join. Then get off your lazy asses, dust off your Tru-Vus, go outside, and look! You may be the one to catch that vital clue, to help track these gor-sucking gremlins to their source.

• MESOSPHERE

Goldman didn’t have much to do anymore. Others ran the scans now, reduced the data, constructed ever-subtler models of the inner Earth, even traced the involute geometries of that refulgent, renitent entity below… the thing called Beta. A midget town had sprung up around the lonely

Tangoparu dome on a rocky plain below the vast Greenland ice sheet. High-powered tech types bustled with armloads of data cubes, arguing in the arcane new language of gazerdynamics. Of the original team, only he remained now, the others having gone home to New Zealand long ago.

The NATO scientific commander had specifically asked him to stay. So Stan sat in on all the daily seminars, struggling to keep up with younger, more agile minds, even though his understanding grew more obsolete with each fast-breaking discovery. No matter. They all treated him with utter deference. Hardly a moment passed without hearing the name Alex Lustig spoken with an awe customarily lavished on the shades of Newton and Einstein and Hurt, and as the great one’s former teacher, Stan shared in that glory.

Singularities. There was a lot of talk about singularities, by which the bright young men and women meant the kind you made inside a cavitron — micro black holes and those newer innovations, tuned strings and cosmic knots. Of late, though, Stan had found himself thinking about another kind of “singularity” altogether. It was on his mind as he passed a saluting sentry and left the bustling encampment, swinging his walking stick across the moraine-strewn valley.

In mathematics, a singularity is a sudden discontinuity, where one expression suddenly ceases being valid, and a completely different one takes its place.

You got the simplest kind of singularity — a delta function — by dividing any real number by zero. The result, converging on infinity, was actually undefined, unknowable. That’s where we’re at right now… a singularity in the life history of mankind.

It wasn’t just the present crisis. Oh, certainly he was worried. Would the world’s institutions — or the planet itself — survive the next few hours or days? Stan was as concerned as the next man. Still, even if tomorrow the spectre of reborn international paranoia evaporated like a bad dream, and all the gorgeous, terrifying new technologies were tamed, nothing would ever be the same.

Earlier today, some of the youngsters had been discussing notions about gravitational circuits… equivalent, in collapsed mass and stressed space, to capacitors and resistors and transistors, for heaven’s sake! To Stan it was proof the time had come. The moment he’d secretly been waiting for all his life.

There’s another kind of singularity… having to do with society, and information.

Technological breakthroughs had happened before — when farming was invented, for example. Or metallurgy. Or writing. Each time, men and women gained new power over their lives, and thinking itself changed. With each such naissance, human beings were in effect reborn, remade… reprogrammed.

In early times, change came slowly. But each breakthrough laid a foundation for those that followed. And with the Western breakout of the sixteenth century, it became self-sustaining. Inventions bred wealth, which spread education and leisure to broader masses. Printing dispersed literacy. Transport distributed food. Food meant more people.

He paused near a sandy bank in the wind-shadow of a boulder, and used his walking stick to trace a rough figure. It was the standard doom scenario, depicting the fate forecast by Malthus for any species that outbreeds the carrying capacity of its niche.

The curve portrayed human population over time, and it rose very slowly at first. All through the late Stone Age — when Stan’s ancestors had chipped flint, scratched fleas, and thought fire the final terror weapon — there were never more than five million homo sapiens at a time. This changed with agriculture, though. Human numbers doubled, then doubled again every fifteen hundred years or so — a rapid climb — until they reached five hundred million around the time of Newton.

Impressive progress, achieved by people who had hardly a glimmer of what the laws of nature were, let alone concepts like ecology or psychology or planetary history. But then it accelerated even faster! New foods, sanitation, emigration… babies lived longer. Humans reproduced copiously. The next doubling, to a billion souls, took only two hundred years. The next, less than a century. Then, from just 1950 to 1980, two billions became four. And still the curve steepened. Stan recalled the elegant, symmetrical projections proclaimed by pessimists when he was young. No population boom can be sustained forever on a finite world. There must inevitably come crash.