OPERATIONS
32. NOBODY HERE BUT US ROBOTS
Until the first decade of the new century, the great wreck and the debris surrounding it had remained virtually unchanged, though not untouched. Now, as 2010 approached, it was a hive of activity—or, rather, two hives, a thousand meters apart.
The framework of scaffolding around the bow section was almost complete, and the Mole had successfully laid twenty-five of the massive straps under the hull; there were only five to go. Most of the mud that had piled up around the prow when it drove into the seabed had been blasted away by powerful water jets, and the huge anchors were no longer half buried in silt.
More than twenty thousand tons of buoyancy had already been provided by as many cubic meters of packaged microspheres, strategically placed around the framework, and at the few places inside the wreck where the structure could safely take the strain. But Titanic had not stirred from her resting place—nor was she supposed to. Another ten thousand tons of lift would be needed to get her out of the mud, and to start her on the long climb to the surface.
As for the shattered stern—that had already disappeared inside a slowly accreting block of ice. The media were fond of quoting Hardy’s “In shadowy silent distance grew the Iceberg too’—even though the poet could never have imagined this application of his words.
The penultimate verse was also quoted widely, and equally out of context. Both the Parkinson and Nippon-Turner consortia were rather tired of being told that
They were bent
By paths coincident
On being anon twin halves of one august event
They hoped that it would be “august”—but not, if they could possibly help it, coincident.
Virtually all the work on both portions of the wreck had been carried out by remote control from the surface; only in critical cases were human beings actually required on the site. During the past decade, underwater robot technology had been pushed far beyond even the remarkable achievements of the previous century’s offshore oil operations. The payoff would be enormous—although, as Rupert Parkinson often wryly remarked, most of it would go to other people.
There had, of course, been problems, mishaps—even accidents, though none involving loss of life. During one severe winter storm, Explorer had been forced to abandon station, much to the disgust of her captain, who considered this a professional insult. His vomitous passengers did not altogether appreciate his point of view.
Even this display of North Atlantic ferocity, however, had not interrupted operations on the stern. Two hundred meters down, the demobilized nuclear submarines, now rechristened, after a pioneer oceanographer and a famous shipbuilder, Matthew Fontaine Maury and Peter the Great, were scarcely aware of the storm. Their reactors continued steadily pouring megawatt upon megawatt of low-voltage current down to the seabed—creating a rising column of warm water in the process, as heat was pumped out of the wreck.
This artificial upwelling had produced an unexpected bonus, by bringing to the surface nutrients that would otherwise have been trapped on the seabed. The resulting plankton bloom was much appreciated by the local fish population, and the last cod harvest had been a record one. The government of Newfoundland had formally requested the submarines to remain on station, even when they had fulfilled their contract with Nippon-Turner.
Quite apart from all this activity off the Grand Banks, a great deal of money and effort was being expended thousands of kilometers away. Down in Florida, not far from the launchpads that had seen men leave for the Moon—and were now seeing them prepare to go to Mars—dredging and construction for the Titanic Underwater Museum was well under way. And on the other side of the globe, Tokyo-on-Sea was preparing an even more elaborate display, with transparent viewing corridors for visitors and, of course, continuous performances of what was hoped would be a truly spectacular movie.
Vast sums of money were also being gambled elsewhere—especially in the land once more called Russia. Thanks to Peter the Great, share dealings in Titanic spinoff companies were very popular on the Moscow Stock Exchange.
33. SOLAR MAX
“Another of my monomanias,” said Franz Zwicker, “is the sunspot cycle. Especially the current one.”
“What’s particular about it?” asked Bradley, as they walked down to the lab together.
“First of all, it will peak in—you guessed it!—2012. It’s already way past the 1990 maximum, and getting close to the 2001 record.”
“So?”
“Well, between you and me, I’m scared. So many cranks have tried to correlate events with the eleven-year cycle—which isn’t always eleven years anyway!—that sunspot counting sometimes gets classed with astrology. But there’s no doubt that the Sun influences practically everything on Earth. I’m sure it’s responsible for the weird weather we’ve been having during the last quarter century. To some extent, anyway; we can’t put all the blame on the human race, much as Bluepeace and Company would like to.”
“I thought you were supposed to be on their side!”
“Only on Mondays, Wednesdays, and Fridays. The rest of the week I keep a wary eye on Mother Nature. And the weather patterns aren’t the only abnormality. Seismic activity seems to be increasing. Look at California. Why do people still build houses in San Francisco? Wasn’t 2002 bad enough? And we’re still waiting for the Big One…”
Jason felt privileged to share the scientist’s thoughts; the two men, so different in background and character, had grown to respect each other.
“And there’s something else, that occasionally gives me nightmares. Deep-water blowouts—perhaps triggered by earthquakes. Or even by man.”
“I’ve known several. A big one in ’98, in the Louisiana Field. Wrote off a whole rig.”
“Oh, that was just a mild burp! I’m talking about the real thing—like that crater the Shell Oil scientists found two kilometers down in the Gulf, back in the eighties. Imagine the explosion that caused that—three million tons of seabed scooped out! Equivalent to a good-sized atomic bomb.”
“And you think that could happen again?”
“I know it will—but not when and where. I keep warning the people up at Hibernia that they’re tickling the dragon’s tail. If Tommy Gold is right—and he was right about neutron stars, even if he struck out on moondust and the Steady State!—we’ve barely scratched the Earth’s crust. Everything we’ve tapped so far is just minor leakage from the real hydrocarbon reservoirs, ten or more kilometers down.”
“Some leak! It’s been running our civilization for the last couple of centuries.”
“Did you say running—or ruining? Well, here’s your prize pupil. How’s class going?”
J.J. lay in a transporter cradle, very much a fish out of water. It was attached to a bank of computers by what seemed to Bradley to be an absurdly thin cable. Having grown up with copper wiring, he had never become quite accustomed to the fiber-optic revolution.
Nothing seemed to be happening; the technician in charge hastily concealed the microbook she was viewing, and quickly scanned the monitor display.
“Everything fine, Doctor,” she said cheerfully. “Just verifying the expert system databases.”
That’s part of me, thought Jason. He had spent hours in dive simulators, while computer programmers tried to codify and record his hard-won skills—the very essence of veteran ocean engineer J. Bradley. He was beginning to feel more and more that, at least in a psychological sense, J.J. was becoming a surrogate son.
That feeling became strongest when they were engaged in a direct conversation. It was an old joke in the trade that divers had a vocabulary of only a couple of hundred words—which was all they needed for their work. J.J. had enough artificial intelligence to exceed this by a comfortable margin.
The lab had hoped to surprise Jason by using his voice as a template for J.J.’s speech synthesizer, but his reaction had been disappointing. The pranksters had forgotten that few people can recognize their own recorded voice, especially if it is uttering sentences that they have never spoken themselves. Jason had not caught on until he had noticed the grinning faces around him.
“Any reason, Anne, why we can’t start the wet run on schedule?” Zwicker asked.
“No, Doctor. The emergency recall algorithm still doesn’t seem to be working properly, but of course we won’t need it for the tests.”
Although the sound transducers were not designed to function in air, Jason could not resist a few words with Junior.
“Hello, J.J. Can you hear me?”
“I can hear you.”
The words were badly distorted, but quite recognizable. Underwater, the speech quality would be much better.
“Do you recognize me?”
There was a long silence. Then J.J. replied.
“Question not understood.”
“Walk closer, Mr. Bradley,” the technician advised. “He’s very deaf out of water.”
“Do you recognize me?”
“Yes. You are John Maxwell.”
“Back to the drawing board,” muttered Zwicker.
“And who,” asked Bradley, more amused than annoyed, “is John Maxwell?”
The girl was quite embarrassed.
“He’s section chief, Voice Recognition. But there’s no problem—this isn’t a fair test. Underwater he’ll know you from half a kilometer away.”
“I hope so. Goodbye, J.J. See you later—when you’re not quite so deaf. Let’s see if Deep Jeep is in better shape.”
Deep Jeep was the lab’s other main project, in some ways almost equally demanding. The reaction of most visitors at first viewing was: “Is it a submarine or a diving suit?” And the answer was always, “Both.”
Servicing and operating three-man deep submersibles like Marvin was an expensive business: a single dive could cost a hundred thousand dollars. But there were many occasions when a much less elaborate, one-man vehicle would be adequate.
Jason Bradley’s secret ambition was already well known to the entire lab. He hoped Deep Jeep would be ready in time to take him down to Titanic—while the wreck still lay on the ocean floor.
34. STORM
It would be decades before the meteorologists could prove that the great storm of 2010 was one of the series that had begun in the 1980s, heralding the climatic changes of the next millennium. Before it exhausted its energies battering against the western ramparts of the Alps, Gloria did twenty billion dollars” worth of damage and took more than a thousand lives.
The weather satellites, of course, gave a few hours” warning—otherwise the death toll would have been even greater. But, inevitably, there were many who did not hear the forecasts, or failed to take them seriously. Especially in Ireland, which was the first to receive the hammerblow from the heavens.
Donald and Edith Craig were editing the latest footage from Operation DEEP FREEZE when Gloria hit Conroy Castle. They heard and felt nothing deep inside the massive walls—not even the crash when the camera obscura was swept off the battlements.
It would be decades before the meteorologists could prove that the great storm of 2010 was one of the series that had begun in the 1980s, heralding the climatic changes of the next millennium. Before it exhausted its energies battering against the western ramparts of the Alps, Gloria did twenty billion dollars” worth of damage and took more than a thousand lives.
The weather satellites, of course, gave a few hours” warning—otherwise the death toll would have been even greater. But, inevitably, there were many who did not hear the forecasts, or failed to take them seriously. Especially in Ireland, which was the first to receive the hammerblow from the heavens.
Donald and Edith Craig were editing the latest footage from Operation DEEP FREEZE when Gloria hit Conroy Castle. They heard and felt nothing deep inside the massive walls—not even the crash when the camera obscura was swept off the battlements.
Ada now cheerfully admitted that she was hopeless at pure mathematics—the kind which, in G. H. Hardy’s famous toast, would never be of any use to anyone. Unknown to him—because the secrets of ENIGMA’s code-breaking were not revealed until decades later—Hardy had been proved spectacularly wrong during his own lifetime. In the hands of Alan Turing and his colleagues, even something as abstract as number theory could win a war.
Most of calculus and higher trigonometry, and virtually all of symbolic logic, were closed books to Ada. She simply wasn’t interested; her heart was in geometry and the properties of space. Already she was trifling with five dimensions, four having proved too simple. Like Newton, much of the time she was “sailing strange seas of thought—alone.”
But today, she was back in ordinary three-space, thanks to the present that “Uncle” Bradley had just sent her. Thirty years after its first appearance, Rubik’s Cube had made a comeback—in a far more deadly mutation.
Because it was a purely mechanical device, the original cube had one weakness, for which its addicts were sincerely thankful. Unlike all their neighbors, the six center squares on each face were fixed. The other forty-eight squares could orbit around them, to create a possible 43252 00327 44898 56000 distinct patterns.
The Mark II had no such limitations; all the fifty-four squares were capable of movement, so there were no fixed centers to give reference points to its maddened manipulators. Only the development of microchips and liquid crystal displays had made such a prodigy possible; nothing really moved, but the multicolored squares could be dragged around the face of the cube merely by touching them with a fingertip.
Relaxing in her little boat with Lady, engrossed with her new toy, Ada had been slow to notice the darkening sky. The storm was almost upon her before she started the electric motor and headed for shelter. That there could be any danger never occurred to her; after all, Lake Mandelbrot was only three feet deep. But she disliked getting wet—and Lady hated it.
By the time she had reached the lake’s first western lobe, the roar of the gale was almost deafening. Ada was thrilled; this was really exciting! But Lady was terrified, and tried to hide herself under the seat.
Heading down the Spike, between the avenue of cypresses, she was partly sheltered from the full fury of the gale. But for the first time, she became alarmed; the great trees on either side were swaying back and forth like reeds.
She was only a dozen meters from the safety of the boathouse, far into the Utter West of the M-Set and nearing the infinity border post at minus 1.999, when Patrick O’Brian’s fears about the transplanted cypress trees were tragically fulfilled.
35. ARTIFACT
One of the most moving archaeological discoveries ever made took place in Israel in 1976, during a series of excavations carried out by scientists from the Hebrew University and the French Center for Prehistoric Research in Jerusalem.
At a 10,000-year-old campsite, they uncovered the skeleton of a child, one hand pressed against its cheek. In that hand is another tiny skeleton: that of a puppy about five months old.
This is the earliest example we know of man and dog sharing the same grave. There must be many, many later ones.
One of the most moving archaeological discoveries ever made took place in Israel in 1976, during a series of excavations carried out by scientists from the Hebrew University and the French Center for Prehistoric Research in Jerusalem.
At a 10,000-year-old campsite, they uncovered the skeleton of a child, one hand pressed against its cheek. In that hand is another tiny skeleton: that of a puppy about five months old.
This is the earliest example we know of man and dog sharing the same grave. There must be many, many later ones.
“You may be interested to know,” said Dr. Jafferjee with that clinical detachment which Donald found annoying (though how else could psychiatrists stay sane?) “that Edith’s case isn’t unique. Ever since the M-Set was discovered in 1980, people have managed to become obsessed with it. Usually they are computer hackers, whose grip on reality is often rather tenuous. There are no less than sixty-three examples of Mandelmania now in the data banks.”
“And is there any cure?”
Dr. Jafferjee frowned. “Cure” was a word he seldom used. “Adjustment” was the term he preferred.
“Let’s say that in eighty percent of the cases, the subject has been able to resume an—ah—normal life, sometimes with the help of medication or electronic implants. Quite an encouraging figure.”
Except, thought Donald, for the twenty percent. Which category does Edith belong to?
For the first week after the tragedy, she had been unnaturally calm; after the funeral, some of their mutual friends had been shocked by her apparent lack of emotion. But Donald knew how badly she had been wounded, and was not surprised when she began to behave irrationally. When she started to wander around the castle at night, searching through the empty rooms and dank passageways that had never been renovated, he realized that it was time to get medical advice.
Nevertheless, he kept putting it off, hoping that Edith would make the normal recovery from the first stages of grief. Indeed, this seemed to be happening. Then Patrick O’Brian died.
Edith’s relationship with the old gardener had always been a prickly one, but they had respected each other and shared a mutual love for Ada. The child’s death had been as devastating a blow to Pat as to her parents; he also blamed himself for the tragedy. If only he had refused to transplant those cypresses—if only…
Pat began drinking heavily again, and was now seldom sober. One cold night, after the landlord of the Black Swan had gently ejected him, he managed to lose his way in the village where he had spent his entire life, and was found frozen to death in the morning. Father McMullen considered that the verdict should have been suicide rather than misadventure; but if it was a sin to give Pat a Christian burial, he would argue that out with God in due course. As, also, the matter of the tiny bundle that Ada held cradled in her arms.
The day after the second funeral, Donald had found Edith sitting in front of a high-resolution monitor, studying one of the infinite miniature versions of the set. She would not speak to him, and presently he realized, to his horror, that she was searching for Ada.
In later years, Donald Craig would often wonder about the relationship that had developed between himself and Jason Bradley. Though they had met only half a dozen times, and then almost always on business, he had felt that bond of mutual sympathy that sometimes grows between two men, and can be almost as strong as a sexual one, even when it has absolutely no erotic content.
Perhaps Donald reminded Bradley of his lost partner Ted Collier, of whom he often spoke. In any event, they enjoyed each other’s company, and met even when it was not strictly necessary. Though Kato and the Nippon-Turner syndicate might well have been suspicious, Bradley never compromised his ISA neutrality. Still less did Craig try to exploit it; they might exchange personal secrets, but not professional confidences. Donald never learned what role, if any, Bradley had played in the authority’s decision to ban hydrazine.
After Ada’s funeral—which Bradley had flown halfway around the world to attend—they had an even closer link. Both had lost a wife and child; though the circumstances were different, the effects were much the same. They became even more intimate, sharing secrets and vulnerabilities that neither had revealed to any other person.
Later, Donald wondered why he did not think of the idea himself; perhaps he was so close to it that he couldn’t see the picture for the scan lines.
The fallen cypresses had been cleared away, and the two men were walking by the side of Lake Mandelbrot—for the last time, as it turned out, for both of them—when Bradley outlined the scenario. “It’s not my idea,” he explained, rather apologetically. “I got it from a psychologist friend.”
It was a long time before Donald discovered who the “friend” was, but he saw the possibilities at once.
“Do you really think it will work?” he asked.
“That’s something you’ll have to discuss with Edith’s psychiatrist. Even if it is a good idea, he may not be willing to go along with it. The NIH syndrome, you know.”
“National Institutes of Health?”
“No—Not Invented Here.”
Donald laughed, without much humor.
“You’re right. But first, I must see if I can do my part. It won’t be easy.”
That had been an understatement; it was the most difficult task he had ever undertaken in his life. Often he had to stop work, blinded by tears.
And then, in their own mysterious way, the buried circuits of his subconscious triggered a memory that enabled him to continue. Somewhere, years ago, he had come across the story of a surgeon in a third world country who ran an eye-bank which restored sight to poor people. To make a graft possible corneas had to be removed from the donor within minutes of death.
That surgeon must have had a steady hand, as he sliced into his own mother’s eyes. I can do no less, Donald told himself grimly, as he went back to the editing table where he and Edith had spent so many hours together.
Dr. Jafferjee had proved surprisingly receptive. He had asked in a mildly ironic but quite sympathetic manner: “Where did you get the idea? Some pop-psych video-drama?”
“I know it sounds like it. But it seems worth a try—if you approve.”
“You’ve already made the disk?”
“Capsule. I’d like to run it now—I see you’ve got a hybrid viewer in your outer office.”
“Yes. It will even show VHS tapes! I’ll call Dolores—I rely on her a good deal.” He hesitated, and looked thoughtfully at Donald as if he was going to add something. Instead, he pressed a switch and said softly into the clinic’s paging system: “Nurse Dolores—will you please come to my office? Thank you.”
Edith Craig is still somewhere inside that skull, thought Donald as he sat with Dr. Jafferjee and Nurse Dolores, watching the figure sitting stiffly at the big monitor. Can I smash the invisible yet unyielding barrier that grief has erected, and bring her back to the world of reality?
The familiar black, beetle-shaped image floated on the screen, radiating tendrils that connected it to the rest of the Mandelbrot universe. There was no way of even guessing at the scale, but Donald had already noted the coordinates that defined the size of this particular version. If one could imagine the whole set, stretching out beyond this monitor, it was already larger than the Cosmos that even the Hubble Space Telescope had yet revealed.
“Are you ready?” asked Dr. Jafferjee.
Donald nodded. Nurse Dolores, sitting immediately behind Edith, glanced toward their camera to indicate that she had heard him.
“Then go ahead.”
Donald pressed the EXECUTE key, and the subroutine took over.
The ebon surface of the stimulated Lake Mandelbrot seemed to tremble. Edith gave a sudden start of surprise.
“Good!” whispered Dr. Jafferjee. “She’s reacting!”
The waters parted. Donald turned away; he could not bear to watch again this latest triumph of his skills. Yet he could still see Ada’s image as her voice said gently: “I love you, mother—but you cannot find me here. I exist only in your memories—and I shall always be there. Goodbye…”
Dolores caught Edith’s falling body, as the last syllable died away into the irrevocable past.
36. THE LAST LUNCH
It was a charming idea, though not everyone agreed that it really worked. The decor for the interior of the world’s only deep-diving tourist submarine had been borrowed straight from Disney’s classic 20,000 Leagues Under the Sea.
Passengers who boarded the Piccard (port of registry, Geneva) found themselves in a plush, though rather oddly proportioned, mid-Victorian drawing room. This was supposed to provide instant reassurance, and divert all thoughts from the several hundred tons pressing on each of the little windows which gave a rather restricted view of the outside world.
The greatest problems that Piccard “s builders had had to face were not engineering, but legal ones. Only Lloyd’s of London would insure the hull; no one would insure the passengers, who tended to be VIPs with astronomical credit ratings. So before every dive, notarized waivers of liability were collected, as discreetly as possible.
The ritual was only slightly more unsettling than the cabin steward’s cheerful litany of possible disasters that passengers on transocean flights had endured for decades. NO SMOKING signs, of course, were no longer necessary; nor did Piccard have seat belts and life jackets—which would have been about as useful as parachutes on commercial airliners. Its numerous built-in safety features were unobtrusive and automatic. If worst came to worst, the independent two-man crew capsule would separate from the passenger unit, and each would make a free ascent to the surface, ultrasonic beacons pinging frantically.
This particular dive was the last one of the season: it was getting late in the year, and Piccard would soon be airlifted back to calmer seas in the southern hemisphere. Although at the depths the submarine operated, winter and summer made no more difference than day and night, bad weather on the surface could make passengers very, very unhappy.
During the thirty-minute free-fall to the wreck site, Piccard “s distinguished guests watched a short video showing the current status of operations, and a map of the planned dive. There was nothing else to see during the descent into darkness, except for the occasional luminous fish attracted to this strange invader of its domain.
Then, abruptly, it seemed that a ghostly dawn was spreading far below. All but the faint red emergency lights in Piccard were switched off, as Titanic’s prow loomed up ahead.
Almost everyone who saw her now was struck by the same thought: She must have looked much like this, in the Harland and Wolff Shipyard, a hundred years ago. Once again she was surrounded by an elaborate framework of steel scaffolding, while workers swarmed over her. The workers, however, were no longer human.
Visibility was excellent, and the pilot maneuvered Piccard so that the passengers on both sides of the cabin could get the best possible view through the narrow portholes. He was extremely careful to avoid the busy robots, who ignored the submarine completely. It was no part of the universe they had been trained to deal with.
“If you look out on the right,” said the tour guide—a young Woods Hole graduate, making a little money in his vacation—“you’ll see the ‘down’ cable, stretching up to Explorer. And there’s a module on the way right now, with its counterweight. Looks like a two-ton unit—
“And there’s a robot going to meet it—now the module’s unhooked—you see it’s got neutral buoyancy, so it can be moved around easily. The robot will carry it over to its attachment point on the lifting cradle, and hook it on. Then the two-ton counterweight that brought it down will be shuttled over to the ‘up’ cable, and sent back to Explorer to be reused. After that’s been done ten thousand times, they can lift Titanic. This section of her, anyway.”
“Sounds a very roundabout way of doing things,” commented one of the VIPs. “Why can’t they just use compressed air?”
The guide had heard this a dozen times, but had learned to answer all such questions politely. (The pay was good, and so were the fringe benefits.)
“It’s possible, ma’am, but much too expensive. The pressure here is enormous. I imagine you’re all familiar with the standard scuba bottles—they’re usually rated at two hundred atmospheres. Well, if you opened one of these down here, the air wouldn’t come out. The water would rush in—and fill half the bottle!”
Perhaps he’d overdone it; some of the passengers were looking a little worried. So he continued hastily, hoping to divert their thoughts.
“We do use some compressed air for trimming and fine control. And in the final stages of the ascent, it will play a major role.
“Now, the skipper is going to fly us toward the stern, along the promenade deck. Then he’ll do a reverse run, so you’ll all have an equally good view. I won’t do any more talking for a while—”
Very slowly, Piccard moved the length of the great shadowy hulk. Much of it was in darkness, but some open hatches spilled dramatic fans of light where robots were at work in the interior, fixing buoyancy modules wherever lifting forces could be tolerated.
No one spoke a word as the weed-festooned walls of steel glided by. It was still very hard to grasp the scale of the wreck—still, after a hundred years, one of the largest passenger ships ever built. And the most luxurious, if only for reasons of pure economics. Titanic had marked the end of an era; after the war that was coming, no one would ever again be able to afford such opulence. Nor, perhaps, would anyone care to risk it, lest such arrogance once again provoke the envy of the gods.
The mountain of steel faded into the distance; for a while, the nimbus of light surrounding it was still faintly visible. Then there was only the barren seabed drifting below Piccard, appearing and disappearing in the twin ovals of its forward lights.
Though it was barren, it was not featureless; it was pitted and gouged, and crisscrossed with trenches and the scars of deep-sea dredges.
“This is the debris field,” said the guide, breaking his silence at last. “It was covered with pieces of the ship—crockery, furniture, kitchen utensils, you name it. They were all collected while Lloyd’s and the Canadian government were still arguing in the World Court. When the ruling came, it was too late—”
“What’s that?” one of the passengers suddenly asked. She had caught a glimpse of movement through her little window.
“Where—Let me see—Oh, that’s J.J.”
“Who?”
“Jason Junior. ISA—sorry, International Seabed Authority’s—latest toy. It’s being tested out—it’s an automatic surveying robot. They hope to have a small fleet of them, so that all the seabeds can be mapped down to one-meter resolution. Then we’ll know the ocean as well as we know the Moon…”
Another oasis of light was appearing ahead, and presently resolved itself into a spectacle that was still hard to believe, no matter how many times one had seen it in photos or video displays.
Nothing of the stern portion of the wreck was now visible: it was all buried deep inside the huge, irregular block of ice sitting on the seabed. Protruding out of the ice were dozens of girders, to many of which half-inflated balloons had been attached by cables of varying length.
“It’s a very tricky job,” the young guide said, with obvious admiration. “The big problem is to stop the ice from breaking off and floating up by itself. So there’s a lot of internal structure that you can’t see. As well as a kind of roof up there on top.”
One of the passengers, who obviously hadn’t paid attention to the briefing, asked: “Those balloons—didn’t you say they couldn’t pump air down to this depth?”
“Not enough to lift masses like this. But that’s not air. Those flotation bags contain H2 and O2—hydrogen and oxygen released by electrolysis. See those cables? They’re bringing down millions—no, billions of amp-hours from the two nuclear subs four kilometers above us. Enough electricity to run a small township.”
He looked at his watch.
“Not so much to see here, I’m afraid. We’ll do one circuit in each direction, then start home.”
Piccard dumped its excess weights—they would be collected later—and was sent back along the “up” elevator cable at Titanic’s bow. It was time to start autographing the souvenir brochure; and that, to most of the passengers, would be quite a surprise…
D.S.V. “PICCARD”
October 14, 2011
R.M.S. “TITANIC”
April 14, 1912
LUNCHEON
Consommé Fermier Cockie Leekie
Fillets of Brill
Egg à l’Argenteuil
Chicken à la Maryland
Corned Beef, Vegetables, Dumplings
FROM THE GRILL
Grilled Mutton Chops
Mashed, Fried and Baked Jacket Potatoes
Custard Pudding
Apple Meringue Pastry
BUFFET
Salmon Mayonnaise
Potted Shrimps
Norwegian Anchovies
Soused Herrings
Plain Smoked Sardines
Roast Beef
Round of Spiced Beef
Veal Ham Pie
Virginia Cumberland Ham
Bologna Sausage Brawn
Galantine of Chicken
Corned Ox Tongue
Lettuce Beetroot Tomatoes
CHEESE
Cheshire, Stilton, Gorgonzola, Edam
Camembert, Roquefort, St. Ivel, Cheddar
Iced draught Munich Lager Beer 3d. 6d. a Tankard
“I’m afraid quite a few items are off the menu,” said the young guide, in tones of mock apology. “Piccard “s catering arrangements are rather limited. We don’t even run a microwave—would take too much power. So please ignore the grill; I can assure you that the cold buffet is delicious. We also have some of the cheeses—but only the milder ones. Gorgonzola didn’t seem a very good idea in these confined quarters…
“Oh yes—the lager—it’s genuine, straight from Munich! And it cost us rather more than three pence per tankard. Even more than six.
“Enjoy yourselves, ladies and gentlemen. We’ll be topside in just one hour.”
37. RESURRECTION
It had not been easy to arrange, and had taken months of arguing across the border. However, the joint funeral services had gone smoothly enough; for once, sharing the same tragedy, Christian could talk politely to Christian. The fact that one of the dead had come from Northern Ireland helped a good deal; coffins could be lowered into the ground simultaneously in Dublin and Belfast.
As the “Lux aeterna” of Verdi’s Requiem Mass ebbed softly away, Edith Craig turned to Dolores and asked: “Should I tell Dr. Jafferjee now? Or will he think I’m crazy again?”
Dolores frowned, then answered in that lilting Caribbean accent that had once helped to reach the far place where Edith’s mind was hiding:
“Please, dear, don’t use that word. And yes, I think you should. It’s about time we spoke to him again—he’ll be getting worried. He’s not like some doctors I could mention—he keeps track of his patients. They’re not just case numbers to him.”
Dr. Jafferjee was indeed pleased to receive Edith’s call; he wondered where it was coming from, but she did not enlighten him. He could see that she was sitting in a large room with cane furniture (ah, probably the tropics—Dolores” home island?) and was happy to note that she seemed completely relaxed. There were two large photographs on the wall behind her, and he recognized both—Ada, and “Colleen.”
Physician and ex-patient greeted each other with warmth; then Edith said, a little nervously: “You may think I’m starting on another hopeless quest—and you may be right. But at least this time I know what I’m doing—and I’ll be working with some of the world’s top scientists. The odds may be a million to one against success. But that’s infinitely—and I mean infinitely—better than… than… finding what you need in the M-Set.”
Not what you need, thought Dr. Jafferjee: what you want. But he merely said, rather cautiously: “Go ahead, Edith. I’m intrigued—and completely in the dark.”
“What do you know about cryonics?”
“Not much. I know a lot of people have been frozen, but it’s never been proved that they can be—Oh! I see what you’re driving at! What a fantastic idea!”
“But not a ridiculous one?”
“Well, your million-to-one odds may be optimistic. But for such a payoff—no, I wouldn’t say it was ridiculous. And if you’re worried that I’ll ask Dolores to put you on the first plane back to the clinic, you needn’t be. Even if your project doesn’t succeed, it could be the best possible therapy.”
But only if, Jafferjee thought, you aren’t overwhelmed by the almost inevitable failure. Still, that would be years ahead…
“I’m so glad you feel that way. As soon as I heard that they were going to keep Colleen in the hope of identifying her, I knew what I had to do. I don’t believe in destiny—or fate—but how could I possibly turn down the chance?”
How could you, indeed? thought Jafferjee. You have lost one daughter; you hope to gain another. A Sleeping Beauty, to be awakened not by a young prince, but an aging princess. No—a witch—a good one, this time!—possessing powers utterly beyond the dreams of any Irish lass born in the nineteenth century.
If—if !—it works, what a strange new world Colleen will face! She would be the one to need careful psychological counseling. But this was all the wildest extrapolation.
“I don’t wish to pour cold water on the idea,” Jafferjee said. “But surely, even if you can revive the body—won’t there be irreversible brain damage after a hundred years?”
“That’s exactly what I was afraid of, when I started thinking about it. But there’s a great deal of research that makes it very plausible—I’ve been quite surprised. More than that—impressed. Have you ever heard of Professor Ralph Merkle?”
“Vaguely.”
“More than thirty years ago, he and a couple of other young mathematicians revolutionized cryptography by inventing the public-key system—I won’t bother to explain that, but it made every cipher machine in the world, and a lot of spy networks, obsolete overnight.
“Then, in 1990—sorry, 1989—he published a classic paper called ‘Molecular Repair of the Brain’—”
“Oh, that fellow!”
“Good—I was sure you must have heard of his work. He pointed out that even if there had been gross damage to the brain, it could be repaired by the molecule-sized machines he was quite certain would be invented in the next century. Now.”
“And have they been?”
“Many of them. Look at the computer-controlled microsubs the surgeons are using now, to ream out the arteries of stroke victims. You can’t watch a science channel these days without seeing the latest achievements of nanotechnology.”
“But to repair a whole brain, molecule by molecule! Think of the sheer numbers involved!”
“About ten to the twenty-third. A trivial number.”
“Indeed.” Jafferjee was not quite sure whether Edith was joking; no—she was perfectly serious.
“Very well. Suppose you do repair a brain, right down to the last detail. Would that bring the person back to life? Complete with memories? Emotions? And everything else—whatever it is—that makes a specific, self-conscious individual?”
“Can you give me a good reason why it wouldn’t? I don’t believe the brain is any more mysterious than the rest of the body—and we know how that works, in principle if not in detail. Anyway, there’s only one way to find out—and we’ll learn a lot in the process.”
“How long do you think it will take?”
“Ask me in five years. Then I may know if we’ll need another decade—or a century. Or forever.”
“I can only wish you luck. It’s a fascinating project—and you’re going to have lots of problems beside the purely technical ones. Her relations, for example, if they’re ever located.”
“It doesn’t seem likely. The latest theory is that she was a stowaway, and so not on the passenger list.”
“Well, the church. The media. Thousands of sponsors. Ghost writers who want to do her autobiography. I’m beginning to feel sorry for that poor girl already.”
And he could not help thinking, though he did not say it aloud: I hope Dolores won’t be jealous.
Donald, of course, had been both astonished and indignant: husbands (and wives) always were on such occasions.
“She didn’t even leave any message?” he said unbelievingly.
Dr. Jafferjee shook his head.
“There’s no need to worry. She’ll contact you as soon as she’s settled down. It will take her a while to adjust. Give her a few weeks.”
“Do you know where she’s gone?”
The doctor did not answer, which was answer enough.
“Well, are you quite sure she’s safe?”
“No doubt of it; she’s in extremely good hands.” The psychiatrist made one of those lengthy pauses which were part of his stock-in-trade.
“You know, Mr. Craig, I should be quite annoyed with you.”
“Why?” asked Donald, frankly astonished.
“You’ve cost me the best member of my staff—my right-hand woman.”
“Nurse Dolores? I wondered why I’d not seen her—I wanted to thank her for all she’d done.”
Another of those calculated pauses; then Dr. Jafferjee said: “She’s helped Edith more than you imagine. Obviously, you’ve never guessed, and this may be a shock to you. But I owe you the truth—it will help you with your own adjustment.
“Edith’s prime orientation isn’t toward men—and Dolores actively disliked them, though she was sometimes kind enough to make an exception in my case…
“She was able to contact Edith on the physical level even before we connected on the mental one. They will be very good for each other. But I’ll miss her, dammit.”
Donald Craig was speechless for a moment. Then he blurted out: “You mean—they were having an affair? And you knew it?”
“Of course I did; my job as a physician is to help my patients in any way I can. You’re an intelligent man, Mr. Craig—I’m surprised that seems to shock you.”
“Surely it’s… unprofessional conduct!”
“What nonsense! Just the reverse—it’s highly professional. Oh, back in the barbarous twentieth century many people would have agreed with you. Can you believe it was a crime in those days for the staff of institutions to have any kind of sex with patients under their care, even though that would often have been the best possible therapy for them?
“One good thing did come out of the AIDS epidemic—it forced people to be honest: it wiped out the last remnants of the Puritan aberration. My Hindu colleagues—with their temple prostitutes and erotic sculpture—had the right idea all the time. Too bad it took the West three thousand years of misery to catch up with them.”
Dr. Jafferjee paused for breath, giving Donald Craig time to marshal his own thoughts. He could not help feeling that the doctor had lost some of his professional detachment. Had he been erotically interested in the inaccessible Nurse Dolores? Or did he have deeper problems?
But, of course, everyone knew just why people became psychiatrists in the first place…
With luck, you could cure yourself. And even if you failed, the work was interesting—and the pay was excellent.
FINALE
38. RICHTER EIGHT
Jason Bradley was on the bridge of Glomar Explorer, monitoring J.J.’s progress on the seabed, when he felt the sudden sharp hammerblow. The two electronics technicians watching the displays never even noticed; they probably thought it was some change in the incessant rhythm of the ship’s machinery. Yet for a chilling instant Jason was reminded of a moment almost a century ago, equally unnoticed by most of the passengers…
But, of course, Explorer was at anchor (in four kilometers of water, and how that would have astonished Captain Smith!) and no iceberg could possibly creep undetected through her radar. Nor, at drifting speed, would it do much worse than scrape off a little paint.
Before Jason could even call the communications center, a red star began to flash on the satfax screen. In addition, a piercing audio alarm, guaranteed to set teeth on edge as it warbled up and down through a kilocycle range, sounded on the unit’s seldom-used speaker. Jason punched the audio cutoff, and concentrated on the message. Even the two landlubbers beside him now realized that something was wrong.
“What is it?” one of them asked anxiously.
“Earthquake—and a big one. Must have been close.”
“Any danger?”
“Not to us. I wonder where the epicenter is…”
Bradley had to wait a few minutes for the seismograph-computer networks to do their calculations. Then a message appeared on the fax screen:
SUBSEA EARTHQUAKE ESTIMATED RICHTER 7
EPICENTER APPROX 55 W 44 N.
ALERT ALL ISLANDS AND COASTAL AREAS NORTH ATLANTIC
Nothing else happened for a few seconds; then another line appeared:
CORRECTION: UPDATE TO RICHTER 8
Four kilometers below, J.J. was patiently and efficiently going about its business, gliding over the seabed at an altitude of ten meters and a speed of a comfortable eight knots. (Some nautical traditions refused to die; knots and fathoms still survived into the metric age.) Its navigation program had been set so that it scanned overlapping swaths, like a plowman driving back and forth across a field being prepared for the next harvest.
The first shock wave bothered J.J. no more than it had the Explorer. Even the two nuclear submarines had been completely unaffected; they had been designed to withstand far worse—though their commanders had spent a few anxious seconds speculating about depth charges.
J.J. continued its automatic quest, collecting and recording megabytes of information every second. Ninety-nine percent of this would never be of the slightest interest to anyone—and it might be centuries before scientific gold was found in the residue.
To eye or video camera, the seabed here appeared almost completely featureless, but it had been chosen with care. The original “debris field” around the severed stern section had long ago been cleared of all interesting items; even the lumps of coal spilled from the bunkers had been salvaged and made into souvenirs. However, only two years ago a magnetometer search had revealed anomalies near the bow which might be worth investigating. J.J. was just the entity for the job; in another few hours it would have completed the survey, and would return to its floating base.
“It looks like 1929 all over again,” said Bradley.
Back in the ISA lab, Dr. Zwicker shook his head.
“No—much worse, I’m afraid.”
In Tokyo, at another node of the hastily arranged conference, Kato asked: “What happened in 1929?”
“The Grand Banks earthquake. It triggered a turbidity current—call it an underwater avalanche. Snapped the telegraph cables one after the other, like cotton, as it raced across the seabed. That’s how its speed was calculated—sixty kilometers an hour. Perhaps more.”
“Then it could reach us in—my God—three or four hours. What’s the likelihood of damage?”
“Impossible to say at this stage. Best case—very little. The 1929 quake didn’t touch Titanic, though many people thought she’d been buried; luckily, it was a couple of hundred kilometers to the west. Most of the sediment was diverted into a canyon, and missed the wreck completely.”
“Excuse me,” interrupted Rupert Parkinson, from his London office. “We’ve just heard that one of our flotation modules has surfaced. Jumped twenty meters out of the water. And we’ve lost telemetry to the wreck. How about you, Kato?”
Kato hesitated only a moment; then he called out something in Japanese to an associate off-screen.
“I’ll check with Peter and Maury. Dr. Zwicker—what’s your worst-case analysis?”
“Our first quick look suggests a few meters of sediment. We’ll have a better computer modeling within the hour.”
“A meter wouldn’t be too bad.”
“It could wreck our schedule, dammit.”
“A report from Maury, gentlemen,” said Kato. “No problem—everything normal.”
“But for how long? If that… avalanche… really is racing toward us, we should pull up whatever equipment we can. What do you advise, Dr. Zwicker?”
The scientist was just about to speak when Bradley whispered urgently in his ear. Zwicker looked startled, then glum—then nodded in reluctant agreement.
“I don’t think I should say any more, gentlemen. Mr. Bradley is more experienced in this area than I am. Before I give any specific advice, I should consult our legal department.”
There was a shocked silence; then Rupert Parkinson said quickly: “We’re all men of the world; we can understand that ISA doesn’t want to get involved in lawsuits. So let’s not waste time. We’re pulling up what we can. And I advise you to do the same, Kato—just in case Dr. Zwicker’s worst case is merely the bad one.”
That was precisely what the scientist had feared. A submarine seaquake was impressive enough; but—as a fission bomb serves as detonator for a fusion one—it might merely act as a trigger to release even greater forces.
Millions of years of solar energy had been stored in the petrochemicals beneath the bed of the Atlantic; barely a century’s worth had been tapped by man.
The rest was still waiting.
39. PRODIGAL SON
On the bed of the Atlantic, a billion dollars” worth of robots downed tools and started to float up to the surface. There was no great hurry; no lives were at stake, even though fortunes were. Titanic shares were already plunging on the world’s stock exchanges, giving media humorists an opportunity for all-too-obvious jokes.
The great offshore oil fields were also playing it safe. Although Hibernia and Avalon, in relatively shallow water, had little to fear from turbidity currents, they had suspended all operations, and were doubly and triply checking their emergency and backup systems. Now there was nothing to do but to wait—and to admire the superb auroral displays that had already made this sunspot cycle the most spectacular ever recorded.
Just before midnight—no one was getting much sleep—Bradley was standing on Explorer’s helicopter pad, watching the great curtains of ruby and emerald fire being drawn across the northern sky. He was not a member of the crew; if the skipper or anyone else wanted him, he would be available in seconds. Busy people, especially in emergencies, did not care to have observers standing behind their backs—however well intentioned or highly qualified they might be.
And the summons, when it did come, was not from the bridge, but the operations center.
“Jason? Ops here. We have a problem. J.J. won’t acknowledge our recall signal.”
Bradley felt a curious mix of emotions. First there was concern at losing one of the lab’s most promising—and expensive—pieces of equipment. Then there was the inevitable mental question mark—’What could have gone wrong?’—followed immediately by: “What can we do about it?”
But there was also something deeper. J.J. represented an enormous personal investment of time, effort, thought…even devotion. He recalled all those jokes about the robot’s paternity; there was some truth in them. Creating a real son (what had happened to the flesh-and-blood J.J.?) had required very much less energy…
Hell, Jason told himself, it’s only a machine! It could be rebuilt; we still have all the programs. Nothing would be lost except the information collected on the present mission.
No—a great deal would be lost. It was even possible that the whole project might be abandoned; developing J.J. had stretched ISA’s funding and resources to the limit. At the very least, Operation NEPTUNE would be delayed for years—probably beyond Zwicker’s lifetime. The scientist was a prickly old S.O.B., but Jason liked and admired him. Losing J.J. would break his heart…
Even as he hurried toward the ops center, Bradley was collecting and analyzing reports over his wristcom.
“You’re sure J.J.’s operating normally?”
“Yes—beacon’s working fine—last housekeeping report fifteen minutes ago said all systems nominal—continuing with search pattern. But it just won’t respond to the recall signal.”
“Damn! The lab told me that algorithm had been fixed. Just keep trying… Boost your power as much as you can. What’s the latest on the quake?”
“Bad—Mount Pelée is rumbling—they’re evacuating Martinique. And tsunami warnings have been sent out all over, of course.”
“But what about the Grand Banks? Any sign of that avalanche starting yet?”
“The seismographs are all jangling—no one’s quite sure what the hell’s happening. Just a minute while I get an update—
“—ah, here’s something. The Navy antisubmarine network—didn’t know it was still running!—is getting chopped up. So are the Atlantic cables—just like ’29… Yes—it’s heading this way.”
“How long before it hits us?”
“If it doesn’t run out of steam, a good three hours. Maybe four.”
Time enough, thought Bradley. He knew exactly what he had to do.
“Moon pool?” he called. “Open up Deep Jeep. I’m going down.”
I’m really enjoying this, Bradley told himself. For the first time, I have an ironclad excuse to take Deep Jeep down to the wreck, without having to make application through channels, in triplicate. There’ll be plenty of time later to do the paperwork—or to input the electronic memos…
To speed the descent, Deep Jeep was heavily overweighted; this was no time to worry about littering the seabed with discarded ballast. Only twenty minutes after the brilliant auroral glow had faded in the waters above him, Bradley saw the first phosphorescent nimbus around Titanic’s prow. He did not need it, of course, because he knew his exact location, and the wreck was not even his target; but he was glad that the lights had been switched on again for his exclusive benefit.
J.J. was only half a kilometer away, going about its business with simpleminded concentration and devotion to duty. The monotonous ping… ping-ping call sign of its beacon filled Deep Jeep’s tiny bubble of air every ten seconds, and it was also clearly visible on the search sonar.
Without much hope, Bradley retransmitted the emergency recall sequence, and continued to do so as he approached the recalcitrant robot. He was not surprised, or disappointed, at the total lack of response. Not to worry, he told himself; I’ve lots of other tricks up my sleeve.
He saved the next one until they were only ten meters apart. Deep Jeep could easily outrun J.J., and Bradley had no difficulty in placing his vehicle athwart the robot’s precomputed track. Such underwater confrontations had often been arranged, to test J.J.’s obstacle avoidance algorithms—and these, at least, now operated exactly as planned.
J.J. came to a complete halt, and surveyed the situation. At this point-blank range Bradley could just detect, with his unaided ears, a piccololike subharmonic as the robot scanned the obstacle ahead, and tried to identify it.
He took this opportunity of sending out the recall command once more; no luck. It was pointless to try again; the problem must be in the software.
J.J. turned ninety degrees left, and headed off at right angles to its original course. It went only ten meters, then swung back to its old bearing, hoping to avoid the obstruction. But Bradley was there already.
While J.J. was thinking this over, Bradley tried a new gambit. He switched on the external sound transducer.
“J.J.,” he said. “Can you hear me?”
“Yes,” the robot answered promptly.
“Do you recognize me?”
“Yes, Mr. Bradley.”
Good, thought Bradley. We’re getting somewhere…
“Do you have any problems?”
“No. All systems are normal.”
“We have sent you a recall—Subprogram 999. Have you received it?”
“No. I have not received it.”
Well, thought Bradley, whatever science fiction writers may have pretended, robots won’t lie—unless they’re programmed to do so. And no one’s played that dirty trick on J.J.—I hope…
“One has been sent out. I repeat: Obey Code 999. Acknowledge.”
“I acknowledge.”
“Then execute.”
“Command not understood.”
Damn. We’re going around in circles, Bradley realized. And we could do that, literally, until we both run out of power—or patience.
While Bradley was considering his next step, Explorer interrupted the dialogue.
“Deep Jeep—sorry you’re having no luck so far. But we’ve an update for you—and a message from the Prof.”
“Go ahead.”
“You’re missing some real fireworks. There’s been a—well, blowout’s the only word—around forty west, fifty north. Much too deep to do any serious damage to the offshore rigs, luckily—but hydrocarbon gas is bubbling up by the millions of cubic meters. And it’s ignited—we can see the glare from here—forget the aurora! You should see the Earthsat images: looks as if the North Atlantic’s on fire.”
I’m sure it’s very spectacular, thought Bradley. But how does it affect me?
“What’s that about a message from Dr. Zwicker?”
“He asked us to tell you Tommy Gold was right. Said you’d understand.”
“Frankly, I’m not interested in proving scientific theories at the moment. How long before I must come up?”
Bradley felt no sense of alarm—only of urgency. He could drop his remaining ballast and blow his tanks in a matter of seconds, and be safely on his way up long before any submarine avalanche could overwhelm him. But he was determined to complete his mission, for reasons which were now as much personal as professional.
“Latest estimate is one hour—you may have more. Plenty of time before it gets here—if it does.”
An hour was ample; five minutes might be enough.
“J.J.,” he commanded. “I am giving you a new program. Command Five Two Seven.”
That was main power cutoff, which should leave only the backup systems running. Then J.J. would have no choice but to surface.
“Command Five Two Seven accepted.”
Good—it had worked! J.J.’s external lights flickered, and the little attitude-control propellers idled to a halt. For a moment, J.J. was dead in the water. Hope I haven’t overdone it, Bradley thought.
Then the lights came on again, and the props started to spin once more.
Well, it was a nice try. Nothing had gone wrong this time, but it was impossible to remember everything, in a system as complex as J.J.’s. Bradley had simply forgotten one small detail. Some commands only worked in the lab; they were disabled on operational missions. The override had been automatically overridden.
That left only one option. If gentle persuasion had failed, he would have to use brute force. Deep Jeep was much stronger than J.J.—which in any case had no limbs with which to defend itself. Any wrestling match would be very one-sided.
But it would also be undignified. There was a better way.
Bradley put Deep Jeep into reverse, so that the submersible no longer blocked J.J. The robot considered the new situation for a few seconds, then set off again on its rounds. Such dedication was indeed admirable, but it could be overdone. Was it true that archaeologists had found a Roman sentry still at his post in Pompeii, overwhelmed by the ashes of Vesuvius because no officer had come to relieve him of his duty? That was very much what J.J. now seemed determined to do.
“Sorry about this,” Bradley muttered as he caught up with the unsuspecting machine.
He jammed Deep Jeep’s manipulator arm into the main prop, and pieces of metal flew off in all directions. The auxiliary fans spun J.J. in a half circle, then slowed to rest.
There was only one way out of this situation, and J.J. did not stop to argue.
The intermittent beacon signal switched over to the continuous distress call—the robot Mayday—which meant “Come and get me!”
Like a bomber dropping its payload, J.J. released the iron ballast weight which gave it neutral buoyancy, and started its swift rise to the surface.
“J.J.’s on the way up,” Bradley reported to Explorer. “Should be there in twenty minutes.”
Now the robot was safe; it would be tracked by half a dozen systems as soon as it broke water, and would be back in the moon pool well before Deep Jeep.
“I hope you realize,” Bradley muttered as J.J. disappeared into the liquid sky above, “that hurt me much more than it hurt you.”
40. TOUR OF INSPECTION
Jason Bradley was just preparing to drop his own ballast and follow J.J. up to the surface when Explorer called again.
“Nice work, Jason—we’re tracking J.J. on the way up. The inflatables are already waiting for him.
“But don’t drop your weights yet. There’s a small job the N-T group would like you to do—it will only take a minute or five.”
“Do I have that long?”
“No problem, or we wouldn’t ask. A good forty minutes before the thing hits—it looks like a weather front on our computer simulations. We’ll give you plenty of warning.”
Bradley considered the situation. Deep Jeep could easily reach the Nippon-Turner site within five minutes, and he would like to have one last look at Titanic—both sections, if possible. There was no risk; even if the arrival estimate was wildly in error, he would still have several minutes of warning time and could be a thousand meters up before the avalanche swept past below.
“What do they want me to do?” he asked, swinging Deep Jeep around so that the ice-shrouded stern was directly ahead on his sonar scan.
“Maury has a problem with its power cables—can’t haul them up. May be snagged somewhere. Can you check?”
“Will do.”
It was a reasonable request, since he was virtually on the spot. The massive, neutral-buoyancy conductors which had carried down their enormous amperages to the wreck cost millions of dollars; no wonder the submarines were trying to winch them up. He assumed that Peter the Great had already succeeded.
He had only Deep Jeep’s own lights to illuminate the ice mountain still tethered to the seabed, awaiting a moment of release that now might never come. Moving cautiously, to avoid the wires linking it with the straining oxy-hydrogen balloons, he skirted the mass until he came to the pair of thick power cables running up to the submarine far above.
“Can’t see anything wrong,” he said. “Just give another good pull.”
Only seconds later, the great cables vibrated majestically, like the strings of some gigantic musical instrument. It seemed to Bradley that he should feel the wave of infrasound spreading out from them.
But the cables remained defiantly taut.
“Sorry,” he said. “Nothing I can do. Maybe the shock wave jammed the release mechanism.”
“That’s the feeling up here. Well, many thanks. Better come home—you’ve still plenty of time, but the latest estimate is that half a billion tons of mud is heading your way. They say it’s like the Mississippi in full spate.”
“How many minutes before it gets here?”
“Twenty—no, fifteen.”
I’d like to visit the prow, Bradley thought wistfully, but I won’t press my luck. Even if I do miss the chance of being the very last man ever to set eyes on Titanic.
Reluctantly, he jettisoned Number 1 ballast weight, and Deep Jeep started to rise. He had one final glimpse of the immense ice-encrusted framework as he lifted away from it; then he concentrated on the pair of cables glimmering in his forward lights. Just as the anchor chain of his boat gives reassurance to a scuba diver, they also provided Bradley with a welcoming link to the world far above.
He was just about to drop the second weight, and increase his rate of ascent, when things started to go wrong.
Maury was still hopefully jerking on the cables, trying to retrieve its expensive hardware, when something finally gave way. But not, unfortunately, what was intended.
There was a loud ping from the anticollision sonar, then a crash that shook Deep Jeep and threw Bradley against his seat belt. He had a brief glimpse of a huge white mass soaring past him, and up into the heights above.
Deep Jeep started to sink. Bradley dropped the remaining two ballast weights.
His rate of descent dropped, almost to zero. But not quite; he was still sinking, very slowly, toward the seabed.
Bradley sat in silence for a few minutes. Then, despite himself, he began to laugh. He was in no immediate danger, and it really was quite funny.
“Explorer,” he said. “You’re not going to believe this. I’ve just been hit by an iceberg.”
41. FREE ASCENT
Even now, Bradley did not consider himself to be in real jeopardy; he was more annoyed than alarmed. Yet on the face of it, the situation seemed dramatic enough. He was stranded on the seabed, his buoyancy lost. The glancing blow from the ascending mini-iceberg must have sheared away some of Deep Jeep’s flotation modules. And as if that were not enough, the biggest underwater avalanche ever recorded was bearing down upon him, and now due to arrive in ten or fifteen minutes. He could not help feeling like a character in an old Steven Spielberg movie.
First step, he thought: see if Deep Jeep’s propulsion system can provide enough lift to get me out of this…
The submarine stirred briefly, and blasted up a cloud of mud which filled the surrounding water with a dazzling cloud of reflected light. Deep Jeep rose a few meters, then settled back. The batteries would be flat long before he could reach the surface.
I hate to do this, he told himself. A couple of million bucks down the drain—or at least on the seabed. But maybe we can salvage the rest of Deep Jeep when this is all over—just as they did with good old Alvin, long ago.
Bradley reached for the “chicken switch,” and unlatched the protective cover.
“Deep Jeep calling Explorer. I’ve got to make a free ascent; you won’t hear from me until I reach the surface. Keep a good sonar lookout—I’ll be coming up fast. Get your thrusters started, in case you have to sidestep me.”
Calculations had shown—and tests had confirmed—that shorn of its surrounding equipment Deep Jeep’s buoyant life-support sphere would hit forty klicks, and jump high enough out of the water to land on the deck of any ship that was too close. Or, of course, hole it below the water line, if it was unlucky enough to score a direct hit.
“We’re ready, Jason. Good luck.”
He turned the little red key, and the lights flickered once as the heavy current pulsed through the detonators.
There are some engineering systems which can never be fully checked out, before the time when they are needed. Deep Jeep had been well designed, but testing the escape mechanism at four hundred atmospheres pressure would have required most of ISA’s budget.
The twin explosive charges separated the buoyant life-support sphere from the rest of the vehicle, exactly as planned.
But, as Jason had often said, the sea could always think of something else. The titanium hull was already stressed to its maximum safe value; and the shock waves, relatively feeble though they were, converged and met at the same spot.
It was too late for fear or regret; in the fraction of a second that was left to him before the sphere imploded, Jason Bradley had time for only a single thought: This is a good place to die.
42 THE VILLA, AT SUNSET
As he drove his hired car past the elaborate iron gates, the beautifully manicured trees and flowerbeds triggered a momentary flashback. With a deliberate effort of will, Donald Craig forced down the upwelling memories of Conroy Castle. He would never see it again; that chapter of his life was over.
The sadness was still there, and part of it would always be with him. And yet he also felt a sense of liberation; it was not too late—what was Milton’s most misquoted phrase?—to seek fresh woods and pastures new. I’m trying to reprogram myself, Donald thought wryly. Open a new file…
There was a parking space waiting for him a few meters from the elegant Georgian house; he locked the hired car, and walked to the front door. There was a very new brass plate at eye level, just above the bell push and speaker grill. Though Donald could not see any camera lens, he did not doubt that one was observing him.
The plate carried a single line, in bold lettering:
Dr. Evelyn Merrick, Ph.D. (Psych)
Donald looked at it thoughtfully for a few seconds, then smiled and reached for the bell push. But the door anticipated him.
There was a faint click as it swung open; then Dame Eva said, in that probing yet sympathetic voice that would often remind him of Dr. Jafferjee: “Welcome aboard, Mr. Craig. Any friend of Jason’s is a friend of mine.”
43. EXORCISM
2012 April 15, 2:00 A.M.
It was a bad time for the media networks—too early for the Americas, not late enough for the evening Euronews. In any case, it was a story that had peaked; few were now interested in a race that had been so well and truly lost.
Every year, for a century now, the U.S. Coast Guard had dropped a wreath at this same spot. But this centennial was a very special one: the focus of so many vanished hopes and dreams—and fortunes.
Glomar Explorer had been swung into the wind, so that her forward deckhouse gave her distinguished guests some protection from the icy gusts from the north. Yet it was not as cold as it had been on that immaculate night a hundred years ago, when the whole North Atlantic had lain all Danaë to the stars.
There was no one aboard who had been present the last time Explorer had paid its tribute to the dead, but many must have recalled that secret ceremony on the other side of the world, in a bloodstained century that now seemed to belong to another age. The human race had matured a little, but still had far to go before it could claim to be civilized.
The slow movement of Elgar’s Second Symphony ebbed into silence. No music could have been more appropriate than this haunting farewell to the Edwardian Era, composed during the very years that Titanic grew in the Belfast shipyard.
All eyes were on the tall, gray-haired man who picked up the single wreath and dropped it gently over the side. For a long time he stood in silence; though all his companions on the windswept deck could share his emotions, for some they were especially poignant. They had been with him aboard the Knorr, when the TV monitor had shown the first wreckage on the morning of 1 September 1985. And there was one whose dead wife’s wedding ring had been cast into these same waters, a quarter of a century ago.
This time, Titanic was lost forever to the race that had conceived and built her; no human eyes would look upon her scattered fragments again.
More than a few men were free at last, from the obsessions of a lifetime.
44. EPILOGUE: THE DEEPS OF TIME
The star once called the Sun had changed little since the far-off days when men had worshiped it.
Two planets had gone—one by design, one by accident—and Saturn’s rings had lost much of their glory. But on the whole, the Solar System had not been badly damaged during its brief occupancy by a space-faring species.
Indeed, some regions still showed signs of past improvements. The Martian oceans had dwindled to a few shallow lakes, but the great forests of mutated pines still survived along the equatorial belt. For ages to come, they would maintain and protect the ecology they had been designed to create.
Venus—once called New Eden—had reverted to its former Hell. And of Mercury, nothing remained. The System’s mother lode of heavy metals had been whittled away through millennia of astroengineering. The last remnant of the core—with its unexpected and providential bonus of magnetic monopoles—had been used to build the worldships of the Exodus Fleet.
And Pluto, of course, had been swallowed by the fearsome singularity which the best scientists of the human race were still vainly struggling to comprehend, even as they fled in search of safer suns. There was no trace of this ancient tragedy, when the Seeker fell earthward out of deep space, following an invisible trail.
The interstellar probe that Man had launched toward the Galactic core had reconnoitered a dozen stars before its signals had been intercepted by another civilization. The Seeker knew, to within a few dozen light-years, the origin of the primitive machine whose trajectory it was retracing. It had explored almost a hundred solar systems, and had discovered much. The planet it was approaching now was little different from many others it had inspected; there was no cause for excitement, even if the Seeker had been capable of such an emotion.
The radio spectrum was silent, except for the hiss and crash of the cosmic background. There were none of the glittering networks which covered the nightlands of most technologically developed worlds. Nor, when it entered atmosphere, did the Seeker find the chemical traces of industrial development.
Automatically, it went into the standard search routine. It dissolved into a million components, which scattered over the face of the planet. Some would never return, but would merely send back information. No matter; the Seeker could always create others to replace them. Only its central core was indispensable—and there were backup copies of that, safely stored at right angles to all three dimensions of normal space.
Earth had orbited the Sun only a few times before the Seeker had gathered all the easily accessible information about the abandoned planet. It was little enough; megayears of winds and rains had wiped away all man’s cities, and the slow grinding of the tectonic plates had completely changed the patterns of land and sea. Continents had become oceans; seabeds had become plains, which had then been wrinkled into mountains…
…The anomaly was the faintest of echoes on a neutrino scan, but it attracted immediate attention. Nature abhorred straight lines, right angles, repeated patterns—except on the scale of crystals and snowflakes. This was millions of times larger; indeed, it dwarfed the Seeker. It could only be the work of intelligence.
The object lay in the heart of a mountain, beneath kilometers of sedimentary rock. To reach it would require only seconds; to excavate it without doing any damage, and to learn all its secrets, might require months or years.
The scan was repeated, at higher resolution. Now it was observed that the object was made from ferrous alloys of an extremely simple type. No civilization that could build an interstellar probe would have used such crude materials. The Seeker almost felt disappointment…
Yet, primitive though this object was, no other artifact of comparable size or complexity had been found. It might, after all, be worth the trouble of recovering.
The Seeker’s high-level systems considered the problem for many, many microseconds, analyzing all the possibilities that might arise. Presently the Master Correlator made its decision.
“Let us begin.”
SOURCES AND ACKNOWLEDGMENTS
RM.S. Titanic has haunted me all my life, as is amply demonstrated by this extract from Arthur C. Clarke’s Chronices of the Strange and Mysterious (Collins, 1987):
My very first attempt at a full-length science-fiction story (fortunately long since destroyed) concerned that typical disaster of the spaceways, the collision between an interplanetary liner and a large meteorite—or small comet, if you prefer. I was quite proud of the title, Icebergs of Space—never dreaming at the time that such things really existed. I have always been a little too fond of surprise endings. In the last line I revealed the name of the wrecked spaceship. It was—wait for it—Titanic.
More than four decades later, I returned to the subject in Imperial Earth (1976), bringing the wreck to New York to celebrate the 2276 Quincentennial. At the time of writing, of course, no one knew that the ship was in two badly damaged portions.
Meanwhile I had grown to know Bill MacQuitty, the Irish movie maker (and much else) to whom this book is dedicated. Following the success of his superb A Night to Remember (1958), Bill was determined to film my 1961 novel A Fall of Moondust; however, the Rank Organization refused to dabble in fantasy (men on the Moon, indeed!) and the project was turned down. I am happy to say that the novel is now being turned into a TV mini-series by another close friend, Michael Deakin. If you wonder how we manage to find seas of dust on the Moon, stay tuned.
I am also indebted to Bill MacQuitty for photographs, plans, drawings, and documents on R.M.S. Titanic—especially the menu reproduced in Chapter 36, “The Last Lunch.” Bill’s beautiful book Irish Gardens (text by Edward Hyams; Macdonald, London, 1967) also provided much inspiration.
It is pleasant to record that Bill’s director of photography was Geoffrey Unsworth—who, a decade later, also filmed 2001: A Space Odyssey. I can still remember Geoffrey wandering round the set with a slightly bemused expression, telling all and sundry: “I’ve been in this business for forty years—and Stanley’s just taught me something I didn’t know.” Michael Crichton has reminded me that Superman was dedicated to Geoffrey, who died during its production, much mourned by all those who had worked with him.
This novel would not have been possible, of course, without inputs from the two classic books on the subject, Walter Lord’s A Night to Remember (Allen Lane, 1976) and Robert Ballard’s The Discovery of the Titanic (Madison Press Books, 1987), both of which are beyond praise. Two other books I have also found very valuable are Walter Lord’s recent “sequel” The Night Lives On (William Morrow, 1986) and Charles Pellegrino’s Her Name, Titanic (Avon, 1990). I am also extremely grateful to Charlie (who appears in Chapter 43) for a vast amount of technical information about “Bringing up Baby’—an enterprise which we both regard with very mixed feelings.
Martin Gardner’s book The Wreck of the Titanic Foretold? (Prometheus Books, 1986) reprints the extraordinary Morgan Robertson novel, The Wreck of the Titan (1898!), which Lord Aldiss refers to in Chapter 9. Martin makes a good case for intelligent anticipation on Robertson’s part; nevertheless, I cannot blame anyone who thinks there must have been some feedback from 1912…
Since many of the events in this novel have already occurred—or are about to do so—it has often been necessary to refer to real individuals. I hope they will enjoy my occasional extrapolation of their activities.
“The Century Syndrome” (Chapter 4) already has many people worried, though we will have to wait until 1/1/00 to see whether matters are as bad as I suggest. While I was writing this book, my most long-standing American friend, Dr. Charles Fowler (GCA, 1942—though neither of us can quite believe it), sent me an article from the Boston Globe entitled “Mainframes have a problem with the year 2000.” According to this, the joke in the trade is that everyone will retire in 1999. We’ll see…
This problem will not, of course, arise in 2099. By then, computers will be able to take care of themselves (as well as H. Sap., if he/she is still around).
I have not invented the unusually large mollusk in Chapter 12. Details (with photographs) of this awesome beast will be found in Arthur C. Clarke’s Mysterious World (Collins, 1980). Octopus giganteus was first positively identified by F. G. Wood and Dr. Joseph Gennaro (Natural History, March 1971), both of whom I was happy to get on camera for my Mysterious World TV series.
The useful hint on octopus allergies (e.g., what to do if you find one in the toilet) comes from Jacques-Yves Cousteau and Philippe Diole’s Octopus and Squid: The Soft Intelligence (Cassell, 1973).
And here I must put on record something that has mystified me for many years. In this book, Jacques asserts that though his divers have played with octopuses (very well: octopodes) hundreds of times, they have never once been bitten—and have never even heard of such an incident. Well… the only time I caught one, off the eastern coast of Australia, it bit me! (see The Coast of Coral, Harper Row, 1956). I am quite unable to explain this total breakdown of the laws of probability.
According to Omni magazine, the question described in Chapter 13 was actually set in a high school intelligence test, and only one genius-type pupil spotted that the printed answer was wrong. I still find this amazing; skeptics may profitably spend a few minutes with scissors and cardboard. The even more incredible story of Srinivasa Ramanujan, mentioned passim in the same chapter, will be found in G. H. Hardy’s small classic, A Mathematician’s Apology, and more conveniently in Volume 1 of James Newman’s The World of Mathematics.
For a crash course in offshore oil drilling operations, I must thank my longtime Sri Lankan friend Cuthbert Charles and his colleagues Walter Jackson and Danny Stephens (all with Brown Root Vickers Ltd.) and Brian Redden (Technical Services Division Manager, Wharton Williams). They prevented me from making (I hope) too many flagrant errors, and they are in no way responsible for my wilder extrapolations of their truly astonishing achievements—already comparable to much that we will be doing in space during the next century. I apologize for awarding their kindness by sabotaging so much of their handiwork.
The full story of 1974’s “Operation JENNIFER” has never been told, and probably never will be. To my surprise, its director turned out to be an old acquaintance, and I am grateful to him for his evasive but not unhelpful replies to my queries. On the whole, I would prefer not to know too much about the events of that distant summer, so that I am not handicapped by mere facts.
While writing this novel, I was amused to encounter another work of fiction using the Glomar Explorer, though (luckily!) for a very different purpose: Ship of Gold, by Thomas Allen and Norman Polmar (Macmillan, 1987).
My thanks also to sundry CIA and KGB acquaintances, who would prefer to remain anonymous.
One informant I am happy to identify is Professor William Orr, Dept. of Geological Science, University of Oregon, my erstwhile shipmate on the floating campus SS Universe. The plans and documentation he provided on Glomar Explorer (now languishing in Suisun Bay, California, between Vallejo and Martinez—you can see her from Highway 680) were essential inputs.
The discovery of major explosive events on the seabed, referred to in Chapter 33, was reported by David B. Prior, Earl H. Doyle, and Michael J. Kaluza in Science, vol. 243, pp. 517-9, 27 January 1989, under the title “Evidence for Sediment Eruption on Deep Sea Floor, Gulf of Mexico.”
On the very day I was making the final corrections to this manuscript, I learned that there is now strong evidence that oil drilling can cause earthquakes. The October 28, 1989, Science News cites a paper by Paul Segall of the U.S. Geological Survey, making this claim in the October 1989 issue of Geology.
The report on the Neolithic grave quoted in Chapter 34 will be found in Nature, 276, 608, 1978.
Ralph C. Merkle’s truly mind-boggling paper “Molecular Repair of the Brain” first appeared in the October 1989 issue of Cryonics (published by ALCOR, 12327, Doherty St., Riverside, CA, 92503) to whom I am grateful for an advance copy.
My thanks to Kumar Chitty for information on the U.N. Law of the Sea Convention, directed for many years by the late Ambassador Shirley Hamilton Amarasinghe. It is a great tragedy that Shirley (the hospitality of whose Park Avenue apartment I often enjoyed in the ’70s) did not see the culmination of his efforts. He was a wonderful persuader, and had he lived might even have prevented the U.S. and U.K. delegations from shooting themselves in the foot.
I am particularly grateful to my collaborator Gentry Lee (Cradle, the Rama trilogy) for arranging his schedule so that I could concentrate all my energies on the latest of my “last” novels…
Very special thanks to Navam and Sally Tambayah—not to mention Tasha and Cindy—for hospitality, WORDSTAR, and faxes…
And, finally: a tribute to my dear friend the late Reginald Ross, who besides many other kindnesses introduced me to Rachmaninoff and Elgar half a century ago, and who died at the age of 91 while this book was being written.
Mandelmemo
The literature on the Mandelbrot Set, first introduced to the non-IBM world in A. K. Dewdney’s “Computer Recreations” (Scientific American, Aug. 1985, 16-25), is now enormous. The master’s own book, The Fractal Geometry of Nature (W. H. Freeman, 1982), is highly technical, and much is inaccessible even to those with delusions of mathematical ability. Nevertheless, a good deal of the text is informative and witty, so it is well worth skimming. However, it contains only the briefest references to the M-Set, the exploration of which was barely beginning in 1982.
The Beauty of Fractals (H-O. Peitgen and P. H. Richter, Springer-Verlag, 1986) was the first book to show the M-Set in glorious Technicolor, and contains a fascinating (and often amusing) essay by Dr. M. himself on its origins and discovery (invention?). He describes later developments in The Science of Fractal Images (edited by H-O. Peitgen and Dietmar Saupe, Springer-Verlag, 1988). Both these books are highly technical.
Much more accessible to the general—though determined—reader is A. K. Dewdney’s The Armchair Universe (W. H. Freeman, 1988). This contains the original 1985 Scientific American article, with updates and information on software available for personal computers. I have been very happy with MandFXP, from Cygnus Software (1215 Davie St., P.O. Box 363, Vancouver BC, V6E 1N4, Canada), and have used this extensively on my AMIGA 2000. While making a TV documentary, “God, the Universe, and Everything Else” for U.K.’s Channel 4, I had the rare privilege of showing Stephen Hawking some beautiful “black holes” I had discovered, while expanding the set until it would have filled the orbit of Mars. Another supplier of M-Set software (for MAC and IBM) is Sintar Software (1001 4th Ave., Suite 3200, Seattle, WA 98154).
Needless to say, there are Mandelbrot “fan magazines,” containing hints on speeding up programs, notes from explorers in far-off regions of the set—and even samples of a new literary genre, Fractalfiction. The newsletter of the field is Amygdala, edited by Rollo Silver, who also supplies software (Box 111, San Cristobal, NM 87564).
Undoubtedly the best way of appreciating the set is through the videotapes that have been made of it, usually with accompanying music. Most celebrated is “Nothing But Zooms” from Art Matrix (P.O. Box 880, Ithaca, NY 14851). I have also enjoyed “A Fractal Ballet” (The Fractal Stuff Company, P.O. Box 5202, Spokane, WA 99205-5202).
Strictly speaking, the “Utter West” of the M-Set is at exactly-2, not -1.999… to infinity, as stated in Chapter 18. Anyone care to split the difference?
I do not know if there have been any cases of Mandelmania in real life, but I expect to receive reports as soon as this book appears—and waive all responsibility in advance.
APPENDIX: THE COLORS OF INFINITY
In November 1989, when receiving the Association of Space Explorers Special Achievement Award in Riyadh, Saudi Arabia, I had the privilege of addressing the largest gathering of astronauts and cosmonauts ever assembled at one place. (More than fifty, including Apollo 11’s Buzz Aldrin and Mike Collins, and the first “space walker” Alexei Leonov, who is no longer embarrassed at sharing the dedication of 2010: Odyssey Two with Andrei Sakharov.) I decided to expand their horizons by introducing them to something really large, and, with astronaut Prince Sultan bin Salman bin Abdul Aziz in the chair, delivered a lavishly illustrated lecture “The Colors of Infinity: Exploring the Fractal Universe.”
The material that follows is extracted from my speech; another portion appears at the beginning of Chapter 15. I’m only sorry that I cannot illustrate it with the gorgeous 35-millimeter slides—and videos—I used at Riyadh.
Today, everybody is familiar with graphs—especially the one with time along the horizontal axis, and the cost of living climbing steadily up the vertical one. The idea that any point on a plane can be expressed by two numbers, usually written x and y, now appears so obvious that it seems quite surprising that the world of mathematics had to wait until 1637 for Descartes to invent it.
We are still discovering the consequences of that apparently simple idea, and the most amazing is now just ten years old. It’s called the Mandelbrot Set (from now on, the M-Set) and you’re soon going to meet it everywhere—in the design of fabrics, wallpaper, jewelry, and linoleum. And, I’m afraid, it will be popping out of your TV screen in every other commercial.
Yet the most astonishing feature of the M-Set is its basic simplicity. Unlike almost everything else in modern mathematics, any schoolchild can understand how it is produced. Its generation involves nothing more advanced than addition and multiplication; there’s no need for such complexities as subtraction and—heaven forbid!—division, let alone any of the more exotic beasts from the mathematical menagerie.
There can be few people in the civilized world who have not encountered Einstein’s famous E = mc2, or who would consider it too hopelessly complicated to understand. Well, the equation that defines the M-Set contains the same number of terms, and indeed looks very similar. Here it is.
Z = z2 + c
Not very terrifying, is it? Yet the lifetime of the Universe would not be long enough to explore all its ramifications.
The z’s and the c in Mandelbrot’s equation are all numbers, not (as in Einstein’s) physical quantities like mass and energy. They are the coordinates which specify the position of a point, and the equation controls the way in which it moves, to trace out a pattern.
There’s a very simple analog familiar to everyone—those children’s books with blank pages sprinkled with numbers, which when joined up in the right order reveal hidden—and often surprising—pictures. The image on a TV screen is produced by a sophisticated application of the same principle.
In theory, anyone who can add and multiply could plot out the M-Set with pen or pencil on a sheet of squared paper. However, as we’ll see later, there are certain practical difficulties—notably the fact that a human life span is seldom more than a hundred years. So the set is invariably computer-generated, and usually shown on a visual display unit.
Now, there are two ways of locating a point in space. The more common employs some kind of grid reference—west-east, north-south, or on squared graph paper, a horizontal X-axis and a vertical Y-axis. But there’s also the system used in radar, now familiar to most people thanks to countless movies. Here the position of an object is given by (1) its distance from the origin, and (2) its direction, or compass bearing. Incidentally, this is the natural system—the one you use automatically and unconsciously when you play any ball game. Then you’re concerned with distances and angles, with yourself as the origin.
So think of a computer’s VDU as a radar screen, with a single blip on it, whose movements are going to trace out the M-Set. However, before we switch on our radar, I want to make the equation even simpler, to:
Z = z2
I’ve thrown c away, for the moment, and left only the z’s. Now let me define them more precisely.
Small z is the initial range of the blip—the distance at which it starts. Big Z is its final distance from the origin. Thus if it was initially 2 units away, by obeying this equation it would promptly hop to a distance of 4.
Nothing to get very excited about, but now comes the modification that makes all the difference:
That double arrow is a two-way traffic sign, indicating that the numbers flow in both directions. This time, we don’t stop at Z = 4; we make that equal to a new z—which promptly gives us a second Z of 16, and so on. In no time we’ve generated the series
256, 65536, 4294967296…
and the spot that started only 2 units from the center is heading toward infinity in giant steps of ever-increasing magnitude.
This process of going around and around a loop is called “iteration.” It’s like a dog chasing its own tail, except that a dog doesn’t get anywhere. But mathematical iteration can take us to some very strange places indeed—as we shall soon discover.
Now we’re ready to turn on our radar. Most displays have range circles at 10, 20… 100 kilometers from the center. We will require only a single circle, at a range of 1. There’s no need to specify any units, as we’re dealing with pure numbers. Make them centimeters or light-years, as you please.
Let’s suppose that the initial position of our blip is anywhere on this circle—the bearing doesn’t matter. So z is 1.
And because 1 squared is still 1, so is Z. And it remains at that value, because no matter how many times you square 1, it always remains exactly 1. The blip may hop around and around the circle, but it always stays on it.
Now consider the case where the initial z is greater than 1. We’ve already seen how rapidly the blip shoots off to infinity if z equals 2—but the same thing will happen sooner or later, even if it’s only a microscopic shade more than 1—say 1.000000000000000000001. Watch:
At the first squaring, Z becomes
1.000000000000000000002
then
1.000000000000000000004
1.000000000000000000008
1.000000000000000000016
1.000000000000000000032
and so on for pages of printout. For all practical purposes, the value is still exactly 1. The blip hasn’t moved visibly outward or inward; it’s still on the circle at range 1.
But those zeros are slowly being whittled away, as the digits march inexorably across from the right. Quite suddenly, something appears in the third, second, first decimal place—and the numbers explode after a very few additional terms, as this example shows:
1.001 1.002 1.004 1.008 1.016 1.032
1.066 1.136 1.292 1.668 2.783 7.745
59.987 3598.467 12948970
167675700000000
28115140000000000000000000000
(Overflow)
There could be a million—a billion—zeros on the right-hand side, and the result would still be the same. Eventually the digits would creep up to the decimal point—and then Z would take off to infinity.
Now let’s look at the other case. Suppose z is a microscopic amount less than 1—say something like
.99999999999999999999
As before, nothing much happens for a long time as we go around the loop, except that the numbers on the far right get steadily smaller. But after a few thousand or million iterations—catastrophe! Z suddenly shrinks to nothing, dissolving in an endless string of zeros…
Check it out on your computer. It can only handle twelve digits? Well, no matter how many you had to play with, you’d still get the same answer. Trust me…
The results of this “program” can be summarized in three laws that may seem too trivial to be worth formulating. But no mathematical truth is trivial, and in a few more steps these laws will take us into a universe of mind-boggling wonder and beauty.
Here are the three laws of the “Squaring” Program:
1. If the input z is exactly equal to 1, the output Z always remains 1.
2. If the input is more than 1, the output eventually becomes infinite.
3. If the input is less than 1, the output eventually becomes zero.
That circle of radius 1 is therefore a kind of map—or, if you like, fence—dividing the plane into two distinct territories. Outside it, numbers which obey the squaring law have the freedom of infinity; numbers inside it are prisoners, trapped and doomed to ultimate extinction.
At this point, someone may say: “You’ve only talked about ranges—distances from the origin. To fix the blip’s position, you have to give its bearing as well. What about that?”
Very true. Fortunately, in this selection process—this division of the z’s into two distinct classes—bearings are irrelevant; the same thing happens whichever direction r is pointing. For this simple example—let’s call it the S-set—we can ignore them. When we come on to the more complicated case of the M-Set, where the bearing is important, there’s a very neat mathematical trick which takes care of it, by using complex or imaginary numbers (which really aren’t at all complex, still less imaginary). But we don’t need them here, and I promise not to mention them again.
The S-set lies inside a map, and its frontier is the circle enclosing it. That circle is simply a continuous line with no thickness. If you could examine it with a microscope of infinite power, it would always look exactly the same. You could expand the S-set to the size of the Universe; its boundary would still be a line of zero thickness. Yet there are no holes in it; it’s an absolutely impenetrable barrier, forever separating the z’s less than one from those greater than one.
Now, at last, we’re ready to tackle the M-Set, where these commonsense ideas are turned upside down. Fasten your seat belts.
During the 1970s, the French mathematician Benoit Mandelbrot, working at Harvard and IBM, started to investigate the equation which has made him famous, and which I will now write in the dynamic form:
The only difference between this and the equation we have used to describe the S-set is the term c. This—not z—is now the starting point of our mapping operation. The first time around the loop, z is put equal to zero.
It seems a trifling change, and no one could have imagined the universe it would reveal. Mandelbrot himself did not obtain the first crude glimpses until the spring of 1980, when vague patterns started to emerge on computer printouts. He had begun to peer through Keats’
Charm’d magic casements, opening on the foam
Of perilous seas, in faery lands forlorn…
As we shall learn later, that word “foam” is surprisingly appropriate.
The new equation asks and answers the same question as the earlier one: What shape is the “territory” mapped out when we put numbers into it? For the S-set it was a circle with radius 1. Let’s see what happens when we start with this value in the M-equation. You should be able to do it in your head—for the first few steps. After a few dozen, even a supercomputer may blow a gasket.
For starters, z = 0, c = 1. So Z = 1
First loop: Z = 12 + 1 = 2
Second loop: Z = 22 + 1 = 5
Third loop: Z = 52 + 1 = 26
Fourth loop: Z = 262 + 1… and so on.
I once set my computer to work out the higher terms (about the limit of my programming ability) and it produced only two more values before it had to start approximating:
1, 2, 5, 26, 677, 458330,
21006640000
4412789000000000000000
At that point it gave up, because it doesn’t believe there are any numbers with more than 38 digits.
However, even the first two or three terms are quite enough to show that the M-Set must have a very different shape from the perfectly circular S-set. A point at distance 1 is in the S-set; indeed, it defines its boundary. A point at that same distance may be outside the boundary of the M-Set.
Note that I say “may,” not “must.” It all depends on the initial direction, or bearing, of the starting point, which we have been able to ignore hitherto because it did not affect our discussion of the (perfectly symmetrical) S-set. As it turns out, the M-Set is only symmetrical about the X, or horizontal, axis.
One might have guessed that, from the nature of the equation. But no one could possibly have intuited its real appearance. If the question had been put to me in virginal pre-Mandelbrot days, I would probably have hazarded: “Something like an ellipse, squashed along the Y-axis.” I might even (though I doubt it) have correctly guessed that it would be shifted toward the left, or minus, direction.
At this point, I would like to try a thought experiment on you. The M-Set being literally indescribable, here’s my attempt to describe it:
Imagine you’re looking straight down on a rather plump turtle, swimming westward. It’s been crossed with a swordfish, so has a narrow spike pointing ahead of it. Its entire perimeter is festooned with bizarre marine growths—and with baby turtles of assorted sizes, which have smaller weeds growing on them…
I defy you to find a description like that in any math textbook. And if you think you can do better when you’ve seen the real beast, you’re welcome to try. (I suspect that the insect world might provide better analogies; there may even be a Mandelbeetle lurking in the Brazilian rain forests. Too bad we’ll never know.)
Here is the first crude approximation, shorn of details—much like Conroy Castle’s “Lake Mandelbrot” (Chapter 18). If you like to fill its blank spaces with the medieval cartographers” favorite “Here be dragons” you will hardly be exaggerating.
First of all, note that—as I’ve already remarked—it’s shifted to the left (or west, if you prefer of the S-set, which of course extends from +1 to -1 along the X-axis. The M-Set only gets to 0.25 on the right along the axis, though above and below the axis it bulges out to just beyond 0.4.
On the left-hand side, the map stretches to about -1.4, and then it sprouts a peculiar spike—or antenna—which reaches out to exactly -2.0. As far as the M-Set is concerned, there is nothing beyond this point; it is the edge of the Universe. Mandelbrot fans call it the “Utter West,” and you might like to see what happens when you make c equal to -2. Z doesn’t converge to zero—but it doesn’t escape to infinity either, so the point belongs to the set—just. But if you make c the slightest bit larger, say -2.00000… 000001, before you know it you’re passing Pluto and heading for Quasar West.
Now we come to the most important distinction between the two sets. The S-set has a nice, clean line for its boundary. The frontier of the M-Set is, to say the least, fuzzy. Just how fuzzy you will begin to understand when we start to “zoom” into it; only then will we see the incredible flora and fauna which flourish in that disputed territory.
The boundary—if one can call it that—of the M-Set is not a simple line; it is something which Euclid never imagined, and for which there is no word in ordinary language. Mandelbrot, whose command of English (and American) is awesome, has ransacked the dictionary for suggestive nouns. A few examples: foams, sponges, dusts, webs, nets, curds. He himself coined the technical name fractal, and is now putting up a spirited rearguard action to stop anyone from defining it too precisely.
Computers can easily make “snapshots” of the M-Set at any magnification, and even in black and white they are fascinating. However, by a simple trick they can be colored, and transformed into objects of amazing, even surreal, beauty.
The original equation, of course, is no more concerned with color than is Euclid’s Elements of Geometry. But if we instruct the computer to color any given region in accordance with the number of times z goes around the loop before it decides whether or not it belongs to the M-Set, the results are gorgeous.
Thus the colors, though arbitrary, are not meaningless. An exact analogy is found in cartography. Think of the contour lines on a relief map, which show elevations above sea level. The spaces between them are often colored so that the eye can more easily grasp the information conveyed. Ditto with bathymetric charts; the deeper the ocean, the darker the blue. The mapmaker can make the colors anything he likes, and is guided by aesthetics as much as geography.
It’s just the same here—except that these contour lines are set automatically by the speed of the calculation—I won’t go into details. I have not discovered what genius first had this idea—perhaps Monsieur M. himself—but it turns them into fantastic works of art. And you should see them when they’re animated…
One of the many strange thoughts that the M-Set generates is this. In principle, it could have been discovered as soon as the human race learned to count. In practice, since even a “low magnification” image may involve billions of calculations, there was no way in which it could even be glimpsed before computers were invented! And such movies as Art Matrix’ Nothing But Zooms would have required the entire present world population to calculate night and day for years—without making a single mistake in multiplying together trillions of hundred-digit numbers…
I began by saying that the Mandelbrot Set is the most extraordinary discovery in the history of mathematics. For who could have possibly imagined that so absurdly simple an equation could have generated such—literally—infinite complexity, and such unearthly beauty?
The Mandelbrot Set is, as I have tried to explain, essentially a map. We’ve all read those stories about maps which reveal the location of hidden treasure.
Well, in this case—the map is the treasure!
Colombo, Sri Lanka
1990 February 28
38. RICHTER EIGHT
Jason Bradley was on the bridge of Glomar Explorer, monitoring J.J.’s progress on the seabed, when he felt the sudden sharp hammerblow. The two electronics technicians watching the displays never even noticed; they probably thought it was some change in the incessant rhythm of the ship’s machinery. Yet for a chilling instant Jason was reminded of a moment almost a century ago, equally unnoticed by most of the passengers…
But, of course, Explorer was at anchor (in four kilometers of water, and how that would have astonished Captain Smith!) and no iceberg could possibly creep undetected through her radar. Nor, at drifting speed, would it do much worse than scrape off a little paint.
Before Jason could even call the communications center, a red star began to flash on the satfax screen. In addition, a piercing audio alarm, guaranteed to set teeth on edge as it warbled up and down through a kilocycle range, sounded on the unit’s seldom-used speaker. Jason punched the audio cutoff, and concentrated on the message. Even the two landlubbers beside him now realized that something was wrong.
“What is it?” one of them asked anxiously.
“Earthquake—and a big one. Must have been close.”
“Any danger?”
“Not to us. I wonder where the epicenter is…”
Bradley had to wait a few minutes for the seismograph-computer networks to do their calculations. Then a message appeared on the fax screen:
SUBSEA EARTHQUAKE ESTIMATED RICHTER 7
EPICENTER APPROX 55 W 44 N.
ALERT ALL ISLANDS AND COASTAL AREAS NORTH ATLANTIC
Nothing else happened for a few seconds; then another line appeared:
CORRECTION: UPDATE TO RICHTER 8
Four kilometers below, J.J. was patiently and efficiently going about its business, gliding over the seabed at an altitude of ten meters and a speed of a comfortable eight knots. (Some nautical traditions refused to die; knots and fathoms still survived into the metric age.) Its navigation program had been set so that it scanned overlapping swaths, like a plowman driving back and forth across a field being prepared for the next harvest.
The first shock wave bothered J.J. no more than it had the Explorer. Even the two nuclear submarines had been completely unaffected; they had been designed to withstand far worse—though their commanders had spent a few anxious seconds speculating about depth charges.
J.J. continued its automatic quest, collecting and recording megabytes of information every second. Ninety-nine percent of this would never be of the slightest interest to anyone—and it might be centuries before scientific gold was found in the residue.
To eye or video camera, the seabed here appeared almost completely featureless, but it had been chosen with care. The original “debris field” around the severed stern section had long ago been cleared of all interesting items; even the lumps of coal spilled from the bunkers had been salvaged and made into souvenirs. However, only two years ago a magnetometer search had revealed anomalies near the bow which might be worth investigating. J.J. was just the entity for the job; in another few hours it would have completed the survey, and would return to its floating base.
“It looks like 1929 all over again,” said Bradley.
Back in the ISA lab, Dr. Zwicker shook his head.
“No—much worse, I’m afraid.”
In Tokyo, at another node of the hastily arranged conference, Kato asked: “What happened in 1929?”
“The Grand Banks earthquake. It triggered a turbidity current—call it an underwater avalanche. Snapped the telegraph cables one after the other, like cotton, as it raced across the seabed. That’s how its speed was calculated—sixty kilometers an hour. Perhaps more.”
“Then it could reach us in—my God—three or four hours. What’s the likelihood of damage?”
“Impossible to say at this stage. Best case—very little. The 1929 quake didn’t touch Titanic, though many people thought she’d been buried; luckily, it was a couple of hundred kilometers to the west. Most of the sediment was diverted into a canyon, and missed the wreck completely.”
“Excuse me,” interrupted Rupert Parkinson, from his London office. “We’ve just heard that one of our flotation modules has surfaced. Jumped twenty meters out of the water. And we’ve lost telemetry to the wreck. How about you, Kato?”
Kato hesitated only a moment; then he called out something in Japanese to an associate off-screen.
“I’ll check with Peter and Maury. Dr. Zwicker—what’s your worst-case analysis?”
“Our first quick look suggests a few meters of sediment. We’ll have a better computer modeling within the hour.”
“A meter wouldn’t be too bad.”
“It could wreck our schedule, dammit.”
“A report from Maury, gentlemen,” said Kato. “No problem—everything normal.”
“But for how long? If that… avalanche… really is racing toward us, we should pull up whatever equipment we can. What do you advise, Dr. Zwicker?”
The scientist was just about to speak when Bradley whispered urgently in his ear. Zwicker looked startled, then glum—then nodded in reluctant agreement.
“I don’t think I should say any more, gentlemen. Mr. Bradley is more experienced in this area than I am. Before I give any specific advice, I should consult our legal department.”
There was a shocked silence; then Rupert Parkinson said quickly: “We’re all men of the world; we can understand that ISA doesn’t want to get involved in lawsuits. So let’s not waste time. We’re pulling up what we can. And I advise you to do the same, Kato—just in case Dr. Zwicker’s worst case is merely the bad one.”
That was precisely what the scientist had feared. A submarine seaquake was impressive enough; but—as a fission bomb serves as detonator for a fusion one—it might merely act as a trigger to release even greater forces.
Millions of years of solar energy had been stored in the petrochemicals beneath the bed of the Atlantic; barely a century’s worth had been tapped by man.
The rest was still waiting.
39. PRODIGAL SON
On the bed of the Atlantic, a billion dollars” worth of robots downed tools and started to float up to the surface. There was no great hurry; no lives were at stake, even though fortunes were. Titanic shares were already plunging on the world’s stock exchanges, giving media humorists an opportunity for all-too-obvious jokes.
The great offshore oil fields were also playing it safe. Although Hibernia and Avalon, in relatively shallow water, had little to fear from turbidity currents, they had suspended all operations, and were doubly and triply checking their emergency and backup systems. Now there was nothing to do but to wait—and to admire the superb auroral displays that had already made this sunspot cycle the most spectacular ever recorded.
Just before midnight—no one was getting much sleep—Bradley was standing on Explorer’s helicopter pad, watching the great curtains of ruby and emerald fire being drawn across the northern sky. He was not a member of the crew; if the skipper or anyone else wanted him, he would be available in seconds. Busy people, especially in emergencies, did not care to have observers standing behind their backs—however well intentioned or highly qualified they might be.
And the summons, when it did come, was not from the bridge, but the operations center.
“Jason? Ops here. We have a problem. J.J. won’t acknowledge our recall signal.”
Bradley felt a curious mix of emotions. First there was concern at losing one of the lab’s most promising—and expensive—pieces of equipment. Then there was the inevitable mental question mark—’What could have gone wrong?’—followed immediately by: “What can we do about it?”
But there was also something deeper. J.J. represented an enormous personal investment of time, effort, thought…even devotion. He recalled all those jokes about the robot’s paternity; there was some truth in them. Creating a real son (what had happened to the flesh-and-blood J.J.?) had required very much less energy…
Hell, Jason told himself, it’s only a machine! It could be rebuilt; we still have all the programs. Nothing would be lost except the information collected on the present mission.
No—a great deal would be lost. It was even possible that the whole project might be abandoned; developing J.J. had stretched ISA’s funding and resources to the limit. At the very least, Operation NEPTUNE would be delayed for years—probably beyond Zwicker’s lifetime. The scientist was a prickly old S.O.B., but Jason liked and admired him. Losing J.J. would break his heart…
Even as he hurried toward the ops center, Bradley was collecting and analyzing reports over his wristcom.
“You’re sure J.J.’s operating normally?”
“Yes—beacon’s working fine—last housekeeping report fifteen minutes ago said all systems nominal—continuing with search pattern. But it just won’t respond to the recall signal.”
“Damn! The lab told me that algorithm had been fixed. Just keep trying… Boost your power as much as you can. What’s the latest on the quake?”
“Bad—Mount Pelée is rumbling—they’re evacuating Martinique. And tsunami warnings have been sent out all over, of course.”
“But what about the Grand Banks? Any sign of that avalanche starting yet?”
“The seismographs are all jangling—no one’s quite sure what the hell’s happening. Just a minute while I get an update—
“—ah, here’s something. The Navy antisubmarine network—didn’t know it was still running!—is getting chopped up. So are the Atlantic cables—just like ’29… Yes—it’s heading this way.”
“How long before it hits us?”
“If it doesn’t run out of steam, a good three hours. Maybe four.”
Time enough, thought Bradley. He knew exactly what he had to do.
“Moon pool?” he called. “Open up Deep Jeep. I’m going down.”
I’m really enjoying this, Bradley told himself. For the first time, I have an ironclad excuse to take Deep Jeep down to the wreck, without having to make application through channels, in triplicate. There’ll be plenty of time later to do the paperwork—or to input the electronic memos…
To speed the descent, Deep Jeep was heavily overweighted; this was no time to worry about littering the seabed with discarded ballast. Only twenty minutes after the brilliant auroral glow had faded in the waters above him, Bradley saw the first phosphorescent nimbus around Titanic’s prow. He did not need it, of course, because he knew his exact location, and the wreck was not even his target; but he was glad that the lights had been switched on again for his exclusive benefit.
J.J. was only half a kilometer away, going about its business with simpleminded concentration and devotion to duty. The monotonous ping… ping-ping call sign of its beacon filled Deep Jeep’s tiny bubble of air every ten seconds, and it was also clearly visible on the search sonar.
Without much hope, Bradley retransmitted the emergency recall sequence, and continued to do so as he approached the recalcitrant robot. He was not surprised, or disappointed, at the total lack of response. Not to worry, he told himself; I’ve lots of other tricks up my sleeve.
He saved the next one until they were only ten meters apart. Deep Jeep could easily outrun J.J., and Bradley had no difficulty in placing his vehicle athwart the robot’s precomputed track. Such underwater confrontations had often been arranged, to test J.J.’s obstacle avoidance algorithms—and these, at least, now operated exactly as planned.
J.J. came to a complete halt, and surveyed the situation. At this point-blank range Bradley could just detect, with his unaided ears, a piccololike subharmonic as the robot scanned the obstacle ahead, and tried to identify it.
He took this opportunity of sending out the recall command once more; no luck. It was pointless to try again; the problem must be in the software.
J.J. turned ninety degrees left, and headed off at right angles to its original course. It went only ten meters, then swung back to its old bearing, hoping to avoid the obstruction. But Bradley was there already.
While J.J. was thinking this over, Bradley tried a new gambit. He switched on the external sound transducer.
“J.J.,” he said. “Can you hear me?”
“Yes,” the robot answered promptly.
“Do you recognize me?”
“Yes, Mr. Bradley.”
Good, thought Bradley. We’re getting somewhere…
“Do you have any problems?”
“No. All systems are normal.”
“We have sent you a recall—Subprogram 999. Have you received it?”
“No. I have not received it.”
Well, thought Bradley, whatever science fiction writers may have pretended, robots won’t lie—unless they’re programmed to do so. And no one’s played that dirty trick on J.J.—I hope…
“One has been sent out. I repeat: Obey Code 999. Acknowledge.”
“I acknowledge.”
“Then execute.”
“Command not understood.”
Damn. We’re going around in circles, Bradley realized. And we could do that, literally, until we both run out of power—or patience.
While Bradley was considering his next step, Explorer interrupted the dialogue.
“Deep Jeep—sorry you’re having no luck so far. But we’ve an update for you—and a message from the Prof.”
“Go ahead.”
“You’re missing some real fireworks. There’s been a—well, blowout’s the only word—around forty west, fifty north. Much too deep to do any serious damage to the offshore rigs, luckily—but hydrocarbon gas is bubbling up by the millions of cubic meters. And it’s ignited—we can see the glare from here—forget the aurora! You should see the Earthsat images: looks as if the North Atlantic’s on fire.”
I’m sure it’s very spectacular, thought Bradley. But how does it affect me?
“What’s that about a message from Dr. Zwicker?”
“He asked us to tell you Tommy Gold was right. Said you’d understand.”
“Frankly, I’m not interested in proving scientific theories at the moment. How long before I must come up?”
Bradley felt no sense of alarm—only of urgency. He could drop his remaining ballast and blow his tanks in a matter of seconds, and be safely on his way up long before any submarine avalanche could overwhelm him. But he was determined to complete his mission, for reasons which were now as much personal as professional.
“Latest estimate is one hour—you may have more. Plenty of time before it gets here—if it does.”
An hour was ample; five minutes might be enough.
“J.J.,” he commanded. “I am giving you a new program. Command Five Two Seven.”
That was main power cutoff, which should leave only the backup systems running. Then J.J. would have no choice but to surface.
“Command Five Two Seven accepted.”
Good—it had worked! J.J.’s external lights flickered, and the little attitude-control propellers idled to a halt. For a moment, J.J. was dead in the water. Hope I haven’t overdone it, Bradley thought.
Then the lights came on again, and the props started to spin once more.
Well, it was a nice try. Nothing had gone wrong this time, but it was impossible to remember everything, in a system as complex as J.J.’s. Bradley had simply forgotten one small detail. Some commands only worked in the lab; they were disabled on operational missions. The override had been automatically overridden.
That left only one option. If gentle persuasion had failed, he would have to use brute force. Deep Jeep was much stronger than J.J.—which in any case had no limbs with which to defend itself. Any wrestling match would be very one-sided.
But it would also be undignified. There was a better way.
Bradley put Deep Jeep into reverse, so that the submersible no longer blocked J.J. The robot considered the new situation for a few seconds, then set off again on its rounds. Such dedication was indeed admirable, but it could be overdone. Was it true that archaeologists had found a Roman sentry still at his post in Pompeii, overwhelmed by the ashes of Vesuvius because no officer had come to relieve him of his duty? That was very much what J.J. now seemed determined to do.
“Sorry about this,” Bradley muttered as he caught up with the unsuspecting machine.
He jammed Deep Jeep’s manipulator arm into the main prop, and pieces of metal flew off in all directions. The auxiliary fans spun J.J. in a half circle, then slowed to rest.
There was only one way out of this situation, and J.J. did not stop to argue.
The intermittent beacon signal switched over to the continuous distress call—the robot Mayday—which meant “Come and get me!”
Like a bomber dropping its payload, J.J. released the iron ballast weight which gave it neutral buoyancy, and started its swift rise to the surface.
“J.J.’s on the way up,” Bradley reported to Explorer. “Should be there in twenty minutes.”
Now the robot was safe; it would be tracked by half a dozen systems as soon as it broke water, and would be back in the moon pool well before Deep Jeep.
“I hope you realize,” Bradley muttered as J.J. disappeared into the liquid sky above, “that hurt me much more than it hurt you.”
40. TOUR OF INSPECTION
Jason Bradley was just preparing to drop his own ballast and follow J.J. up to the surface when Explorer called again.
“Nice work, Jason—we’re tracking J.J. on the way up. The inflatables are already waiting for him.
“But don’t drop your weights yet. There’s a small job the N-T group would like you to do—it will only take a minute or five.”
“Do I have that long?”
“No problem, or we wouldn’t ask. A good forty minutes before the thing hits—it looks like a weather front on our computer simulations. We’ll give you plenty of warning.”
Bradley considered the situation. Deep Jeep could easily reach the Nippon-Turner site within five minutes, and he would like to have one last look at Titanic—both sections, if possible. There was no risk; even if the arrival estimate was wildly in error, he would still have several minutes of warning time and could be a thousand meters up before the avalanche swept past below.
“What do they want me to do?” he asked, swinging Deep Jeep around so that the ice-shrouded stern was directly ahead on his sonar scan.
“Maury has a problem with its power cables—can’t haul them up. May be snagged somewhere. Can you check?”
“Will do.”
It was a reasonable request, since he was virtually on the spot. The massive, neutral-buoyancy conductors which had carried down their enormous amperages to the wreck cost millions of dollars; no wonder the submarines were trying to winch them up. He assumed that Peter the Great had already succeeded.
He had only Deep Jeep’s own lights to illuminate the ice mountain still tethered to the seabed, awaiting a moment of release that now might never come. Moving cautiously, to avoid the wires linking it with the straining oxy-hydrogen balloons, he skirted the mass until he came to the pair of thick power cables running up to the submarine far above.
“Can’t see anything wrong,” he said. “Just give another good pull.”
Only seconds later, the great cables vibrated majestically, like the strings of some gigantic musical instrument. It seemed to Bradley that he should feel the wave of infrasound spreading out from them.
But the cables remained defiantly taut.
“Sorry,” he said. “Nothing I can do. Maybe the shock wave jammed the release mechanism.”
“That’s the feeling up here. Well, many thanks. Better come home—you’ve still plenty of time, but the latest estimate is that half a billion tons of mud is heading your way. They say it’s like the Mississippi in full spate.”
“How many minutes before it gets here?”
“Twenty—no, fifteen.”
I’d like to visit the prow, Bradley thought wistfully, but I won’t press my luck. Even if I do miss the chance of being the very last man ever to set eyes on Titanic.
Reluctantly, he jettisoned Number 1 ballast weight, and Deep Jeep started to rise. He had one final glimpse of the immense ice-encrusted framework as he lifted away from it; then he concentrated on the pair of cables glimmering in his forward lights. Just as the anchor chain of his boat gives reassurance to a scuba diver, they also provided Bradley with a welcoming link to the world far above.
He was just about to drop the second weight, and increase his rate of ascent, when things started to go wrong.
Maury was still hopefully jerking on the cables, trying to retrieve its expensive hardware, when something finally gave way. But not, unfortunately, what was intended.
There was a loud ping from the anticollision sonar, then a crash that shook Deep Jeep and threw Bradley against his seat belt. He had a brief glimpse of a huge white mass soaring past him, and up into the heights above.
Deep Jeep started to sink. Bradley dropped the remaining two ballast weights.
His rate of descent dropped, almost to zero. But not quite; he was still sinking, very slowly, toward the seabed.
Bradley sat in silence for a few minutes. Then, despite himself, he began to laugh. He was in no immediate danger, and it really was quite funny.
“Explorer,” he said. “You’re not going to believe this. I’ve just been hit by an iceberg.”
41. FREE ASCENT
Even now, Bradley did not consider himself to be in real jeopardy; he was more annoyed than alarmed. Yet on the face of it, the situation seemed dramatic enough. He was stranded on the seabed, his buoyancy lost. The glancing blow from the ascending mini-iceberg must have sheared away some of Deep Jeep’s flotation modules. And as if that were not enough, the biggest underwater avalanche ever recorded was bearing down upon him, and now due to arrive in ten or fifteen minutes. He could not help feeling like a character in an old Steven Spielberg movie.
First step, he thought: see if Deep Jeep’s propulsion system can provide enough lift to get me out of this…
The submarine stirred briefly, and blasted up a cloud of mud which filled the surrounding water with a dazzling cloud of reflected light. Deep Jeep rose a few meters, then settled back. The batteries would be flat long before he could reach the surface.
I hate to do this, he told himself. A couple of million bucks down the drain—or at least on the seabed. But maybe we can salvage the rest of Deep Jeep when this is all over—just as they did with good old Alvin, long ago.
Bradley reached for the “chicken switch,” and unlatched the protective cover.
“Deep Jeep calling Explorer. I’ve got to make a free ascent; you won’t hear from me until I reach the surface. Keep a good sonar lookout—I’ll be coming up fast. Get your thrusters started, in case you have to sidestep me.”
Calculations had shown—and tests had confirmed—that shorn of its surrounding equipment Deep Jeep’s buoyant life-support sphere would hit forty klicks, and jump high enough out of the water to land on the deck of any ship that was too close. Or, of course, hole it below the water line, if it was unlucky enough to score a direct hit.
“We’re ready, Jason. Good luck.”
He turned the little red key, and the lights flickered once as the heavy current pulsed through the detonators.
There are some engineering systems which can never be fully checked out, before the time when they are needed. Deep Jeep had been well designed, but testing the escape mechanism at four hundred atmospheres pressure would have required most of ISA’s budget.
The twin explosive charges separated the buoyant life-support sphere from the rest of the vehicle, exactly as planned.
But, as Jason had often said, the sea could always think of something else. The titanium hull was already stressed to its maximum safe value; and the shock waves, relatively feeble though they were, converged and met at the same spot.
It was too late for fear or regret; in the fraction of a second that was left to him before the sphere imploded, Jason Bradley had time for only a single thought: This is a good place to die.
42 THE VILLA, AT SUNSET
As he drove his hired car past the elaborate iron gates, the beautifully manicured trees and flowerbeds triggered a momentary flashback. With a deliberate effort of will, Donald Craig forced down the upwelling memories of Conroy Castle. He would never see it again; that chapter of his life was over.
The sadness was still there, and part of it would always be with him. And yet he also felt a sense of liberation; it was not too late—what was Milton’s most misquoted phrase?—to seek fresh woods and pastures new. I’m trying to reprogram myself, Donald thought wryly. Open a new file…
There was a parking space waiting for him a few meters from the elegant Georgian house; he locked the hired car, and walked to the front door. There was a very new brass plate at eye level, just above the bell push and speaker grill. Though Donald could not see any camera lens, he did not doubt that one was observing him.
The plate carried a single line, in bold lettering:
Donald looked at it thoughtfully for a few seconds, then smiled and reached for the bell push. But the door anticipated him.
There was a faint click as it swung open; then Dame Eva said, in that probing yet sympathetic voice that would often remind him of Dr. Jafferjee: “Welcome aboard, Mr. Craig. Any friend of Jason’s is a friend of mine.”
43. EXORCISM
2012 April 15, 2:00 A.M.
It was a bad time for the media networks—too early for the Americas, not late enough for the evening Euronews. In any case, it was a story that had peaked; few were now interested in a race that had been so well and truly lost.
Every year, for a century now, the U.S. Coast Guard had dropped a wreath at this same spot. But this centennial was a very special one: the focus of so many vanished hopes and dreams—and fortunes.
Glomar Explorer had been swung into the wind, so that her forward deckhouse gave her distinguished guests some protection from the icy gusts from the north. Yet it was not as cold as it had been on that immaculate night a hundred years ago, when the whole North Atlantic had lain all Danaë to the stars.
There was no one aboard who had been present the last time Explorer had paid its tribute to the dead, but many must have recalled that secret ceremony on the other side of the world, in a bloodstained century that now seemed to belong to another age. The human race had matured a little, but still had far to go before it could claim to be civilized.
The slow movement of Elgar’s Second Symphony ebbed into silence. No music could have been more appropriate than this haunting farewell to the Edwardian Era, composed during the very years that Titanic grew in the Belfast shipyard.
All eyes were on the tall, gray-haired man who picked up the single wreath and dropped it gently over the side. For a long time he stood in silence; though all his companions on the windswept deck could share his emotions, for some they were especially poignant. They had been with him aboard the Knorr, when the TV monitor had shown the first wreckage on the morning of 1 September 1985. And there was one whose dead wife’s wedding ring had been cast into these same waters, a quarter of a century ago.
This time, Titanic was lost forever to the race that had conceived and built her; no human eyes would look upon her scattered fragments again.
More than a few men were free at last, from the obsessions of a lifetime.
44. EPILOGUE: THE DEEPS OF TIME
The star once called the Sun had changed little since the far-off days when men had worshiped it.
Two planets had gone—one by design, one by accident—and Saturn’s rings had lost much of their glory. But on the whole, the Solar System had not been badly damaged during its brief occupancy by a space-faring species.
Indeed, some regions still showed signs of past improvements. The Martian oceans had dwindled to a few shallow lakes, but the great forests of mutated pines still survived along the equatorial belt. For ages to come, they would maintain and protect the ecology they had been designed to create.
Venus—once called New Eden—had reverted to its former Hell. And of Mercury, nothing remained. The System’s mother lode of heavy metals had been whittled away through millennia of astroengineering. The last remnant of the core—with its unexpected and providential bonus of magnetic monopoles—had been used to build the worldships of the Exodus Fleet.
And Pluto, of course, had been swallowed by the fearsome singularity which the best scientists of the human race were still vainly struggling to comprehend, even as they fled in search of safer suns. There was no trace of this ancient tragedy, when the Seeker fell earthward out of deep space, following an invisible trail.
The interstellar probe that Man had launched toward the Galactic core had reconnoitered a dozen stars before its signals had been intercepted by another civilization. The Seeker knew, to within a few dozen light-years, the origin of the primitive machine whose trajectory it was retracing. It had explored almost a hundred solar systems, and had discovered much. The planet it was approaching now was little different from many others it had inspected; there was no cause for excitement, even if the Seeker had been capable of such an emotion.
The radio spectrum was silent, except for the hiss and crash of the cosmic background. There were none of the glittering networks which covered the nightlands of most technologically developed worlds. Nor, when it entered atmosphere, did the Seeker find the chemical traces of industrial development.
Automatically, it went into the standard search routine. It dissolved into a million components, which scattered over the face of the planet. Some would never return, but would merely send back information. No matter; the Seeker could always create others to replace them. Only its central core was indispensable—and there were backup copies of that, safely stored at right angles to all three dimensions of normal space.
Earth had orbited the Sun only a few times before the Seeker had gathered all the easily accessible information about the abandoned planet. It was little enough; megayears of winds and rains had wiped away all man’s cities, and the slow grinding of the tectonic plates had completely changed the patterns of land and sea. Continents had become oceans; seabeds had become plains, which had then been wrinkled into mountains…
…The anomaly was the faintest of echoes on a neutrino scan, but it attracted immediate attention. Nature abhorred straight lines, right angles, repeated patterns—except on the scale of crystals and snowflakes. This was millions of times larger; indeed, it dwarfed the Seeker. It could only be the work of intelligence.
The object lay in the heart of a mountain, beneath kilometers of sedimentary rock. To reach it would require only seconds; to excavate it without doing any damage, and to learn all its secrets, might require months or years.
The scan was repeated, at higher resolution. Now it was observed that the object was made from ferrous alloys of an extremely simple type. No civilization that could build an interstellar probe would have used such crude materials. The Seeker almost felt disappointment…
Yet, primitive though this object was, no other artifact of comparable size or complexity had been found. It might, after all, be worth the trouble of recovering.
The Seeker’s high-level systems considered the problem for many, many microseconds, analyzing all the possibilities that might arise. Presently the Master Correlator made its decision.
“Let us begin.”
SOURCES AND ACKNOWLEDGMENTS
RM.S. Titanic has haunted me all my life, as is amply demonstrated by this extract from Arthur C. Clarke’s Chronices of the Strange and Mysterious (Collins, 1987):
My very first attempt at a full-length science-fiction story (fortunately long since destroyed) concerned that typical disaster of the spaceways, the collision between an interplanetary liner and a large meteorite—or small comet, if you prefer. I was quite proud of the title, Icebergs of Space—never dreaming at the time that such things really existed. I have always been a little too fond of surprise endings. In the last line I revealed the name of the wrecked spaceship. It was—wait for it—Titanic.
More than four decades later, I returned to the subject in Imperial Earth (1976), bringing the wreck to New York to celebrate the 2276 Quincentennial. At the time of writing, of course, no one knew that the ship was in two badly damaged portions.
Meanwhile I had grown to know Bill MacQuitty, the Irish movie maker (and much else) to whom this book is dedicated. Following the success of his superb A Night to Remember (1958), Bill was determined to film my 1961 novel A Fall of Moondust; however, the Rank Organization refused to dabble in fantasy (men on the Moon, indeed!) and the project was turned down. I am happy to say that the novel is now being turned into a TV mini-series by another close friend, Michael Deakin. If you wonder how we manage to find seas of dust on the Moon, stay tuned.
I am also indebted to Bill MacQuitty for photographs, plans, drawings, and documents on R.M.S. Titanic—especially the menu reproduced in Chapter 36, “The Last Lunch.” Bill’s beautiful book Irish Gardens (text by Edward Hyams; Macdonald, London, 1967) also provided much inspiration.
It is pleasant to record that Bill’s director of photography was Geoffrey Unsworth—who, a decade later, also filmed 2001: A Space Odyssey. I can still remember Geoffrey wandering round the set with a slightly bemused expression, telling all and sundry: “I’ve been in this business for forty years—and Stanley’s just taught me something I didn’t know.” Michael Crichton has reminded me that Superman was dedicated to Geoffrey, who died during its production, much mourned by all those who had worked with him.
This novel would not have been possible, of course, without inputs from the two classic books on the subject, Walter Lord’s A Night to Remember (Allen Lane, 1976) and Robert Ballard’s The Discovery of the Titanic (Madison Press Books, 1987), both of which are beyond praise. Two other books I have also found very valuable are Walter Lord’s recent “sequel” The Night Lives On (William Morrow, 1986) and Charles Pellegrino’s Her Name, Titanic (Avon, 1990). I am also extremely grateful to Charlie (who appears in Chapter 43) for a vast amount of technical information about “Bringing up Baby’—an enterprise which we both regard with very mixed feelings.
Martin Gardner’s book The Wreck of the Titanic Foretold? (Prometheus Books, 1986) reprints the extraordinary Morgan Robertson novel, The Wreck of the Titan (1898!), which Lord Aldiss refers to in Chapter 9. Martin makes a good case for intelligent anticipation on Robertson’s part; nevertheless, I cannot blame anyone who thinks there must have been some feedback from 1912…
Since many of the events in this novel have already occurred—or are about to do so—it has often been necessary to refer to real individuals. I hope they will enjoy my occasional extrapolation of their activities.
“The Century Syndrome” (Chapter 4) already has many people worried, though we will have to wait until 1/1/00 to see whether matters are as bad as I suggest. While I was writing this book, my most long-standing American friend, Dr. Charles Fowler (GCA, 1942—though neither of us can quite believe it), sent me an article from the Boston Globe entitled “Mainframes have a problem with the year 2000.” According to this, the joke in the trade is that everyone will retire in 1999. We’ll see…
This problem will not, of course, arise in 2099. By then, computers will be able to take care of themselves (as well as H. Sap., if he/she is still around).
I have not invented the unusually large mollusk in Chapter 12. Details (with photographs) of this awesome beast will be found in Arthur C. Clarke’s Mysterious World (Collins, 1980). Octopus giganteus was first positively identified by F. G. Wood and Dr. Joseph Gennaro (Natural History, March 1971), both of whom I was happy to get on camera for my Mysterious World TV series.
The useful hint on octopus allergies (e.g., what to do if you find one in the toilet) comes from Jacques-Yves Cousteau and Philippe Diole’s Octopus and Squid: The Soft Intelligence (Cassell, 1973).
And here I must put on record something that has mystified me for many years. In this book, Jacques asserts that though his divers have played with octopuses (very well: octopodes) hundreds of times, they have never once been bitten—and have never even heard of such an incident. Well… the only time I caught one, off the eastern coast of Australia, it bit me! (see The Coast of Coral, Harper Row, 1956). I am quite unable to explain this total breakdown of the laws of probability.
According to Omni magazine, the question described in Chapter 13 was actually set in a high school intelligence test, and only one genius-type pupil spotted that the printed answer was wrong. I still find this amazing; skeptics may profitably spend a few minutes with scissors and cardboard. The even more incredible story of Srinivasa Ramanujan, mentioned passim in the same chapter, will be found in G. H. Hardy’s small classic, A Mathematician’s Apology, and more conveniently in Volume 1 of James Newman’s The World of Mathematics.
For a crash course in offshore oil drilling operations, I must thank my longtime Sri Lankan friend Cuthbert Charles and his colleagues Walter Jackson and Danny Stephens (all with Brown Root Vickers Ltd.) and Brian Redden (Technical Services Division Manager, Wharton Williams). They prevented me from making (I hope) too many flagrant errors, and they are in no way responsible for my wilder extrapolations of their truly astonishing achievements—already comparable to much that we will be doing in space during the next century. I apologize for awarding their kindness by sabotaging so much of their handiwork.
The full story of 1974’s “Operation JENNIFER” has never been told, and probably never will be. To my surprise, its director turned out to be an old acquaintance, and I am grateful to him for his evasive but not unhelpful replies to my queries. On the whole, I would prefer not to know too much about the events of that distant summer, so that I am not handicapped by mere facts.
While writing this novel, I was amused to encounter another work of fiction using the Glomar Explorer, though (luckily!) for a very different purpose: Ship of Gold, by Thomas Allen and Norman Polmar (Macmillan, 1987).
My thanks also to sundry CIA and KGB acquaintances, who would prefer to remain anonymous.
One informant I am happy to identify is Professor William Orr, Dept. of Geological Science, University of Oregon, my erstwhile shipmate on the floating campus SS Universe. The plans and documentation he provided on Glomar Explorer (now languishing in Suisun Bay, California, between Vallejo and Martinez—you can see her from Highway 680) were essential inputs.
The discovery of major explosive events on the seabed, referred to in Chapter 33, was reported by David B. Prior, Earl H. Doyle, and Michael J. Kaluza in Science, vol. 243, pp. 517-9, 27 January 1989, under the title “Evidence for Sediment Eruption on Deep Sea Floor, Gulf of Mexico.”
On the very day I was making the final corrections to this manuscript, I learned that there is now strong evidence that oil drilling can cause earthquakes. The October 28, 1989, Science News cites a paper by Paul Segall of the U.S. Geological Survey, making this claim in the October 1989 issue of Geology.
The report on the Neolithic grave quoted in Chapter 34 will be found in Nature, 276, 608, 1978.
Ralph C. Merkle’s truly mind-boggling paper “Molecular Repair of the Brain” first appeared in the October 1989 issue of Cryonics (published by ALCOR, 12327, Doherty St., Riverside, CA, 92503) to whom I am grateful for an advance copy.
My thanks to Kumar Chitty for information on the U.N. Law of the Sea Convention, directed for many years by the late Ambassador Shirley Hamilton Amarasinghe. It is a great tragedy that Shirley (the hospitality of whose Park Avenue apartment I often enjoyed in the ’70s) did not see the culmination of his efforts. He was a wonderful persuader, and had he lived might even have prevented the U.S. and U.K. delegations from shooting themselves in the foot.
I am particularly grateful to my collaborator Gentry Lee (Cradle, the Rama trilogy) for arranging his schedule so that I could concentrate all my energies on the latest of my “last” novels…
Very special thanks to Navam and Sally Tambayah—not to mention Tasha and Cindy—for hospitality, WORDSTAR, and faxes…
And, finally: a tribute to my dear friend the late Reginald Ross, who besides many other kindnesses introduced me to Rachmaninoff and Elgar half a century ago, and who died at the age of 91 while this book was being written.
Mandelmemo
The literature on the Mandelbrot Set, first introduced to the non-IBM world in A. K. Dewdney’s “Computer Recreations” (Scientific American, Aug. 1985, 16-25), is now enormous. The master’s own book, The Fractal Geometry of Nature (W. H. Freeman, 1982), is highly technical, and much is inaccessible even to those with delusions of mathematical ability. Nevertheless, a good deal of the text is informative and witty, so it is well worth skimming. However, it contains only the briefest references to the M-Set, the exploration of which was barely beginning in 1982.
The Beauty of Fractals (H-O. Peitgen and P. H. Richter, Springer-Verlag, 1986) was the first book to show the M-Set in glorious Technicolor, and contains a fascinating (and often amusing) essay by Dr. M. himself on its origins and discovery (invention?). He describes later developments in The Science of Fractal Images (edited by H-O. Peitgen and Dietmar Saupe, Springer-Verlag, 1988). Both these books are highly technical.
Much more accessible to the general—though determined—reader is A. K. Dewdney’s The Armchair Universe (W. H. Freeman, 1988). This contains the original 1985 Scientific American article, with updates and information on software available for personal computers. I have been very happy with MandFXP, from Cygnus Software (1215 Davie St., P.O. Box 363, Vancouver BC, V6E 1N4, Canada), and have used this extensively on my AMIGA 2000. While making a TV documentary, “God, the Universe, and Everything Else” for U.K.’s Channel 4, I had the rare privilege of showing Stephen Hawking some beautiful “black holes” I had discovered, while expanding the set until it would have filled the orbit of Mars. Another supplier of M-Set software (for MAC and IBM) is Sintar Software (1001 4th Ave., Suite 3200, Seattle, WA 98154).
Needless to say, there are Mandelbrot “fan magazines,” containing hints on speeding up programs, notes from explorers in far-off regions of the set—and even samples of a new literary genre, Fractalfiction. The newsletter of the field is Amygdala, edited by Rollo Silver, who also supplies software (Box 111, San Cristobal, NM 87564).
Undoubtedly the best way of appreciating the set is through the videotapes that have been made of it, usually with accompanying music. Most celebrated is “Nothing But Zooms” from Art Matrix (P.O. Box 880, Ithaca, NY 14851). I have also enjoyed “A Fractal Ballet” (The Fractal Stuff Company, P.O. Box 5202, Spokane, WA 99205-5202).
Strictly speaking, the “Utter West” of the M-Set is at exactly-2, not -1.999… to infinity, as stated in Chapter 18. Anyone care to split the difference?
I do not know if there have been any cases of Mandelmania in real life, but I expect to receive reports as soon as this book appears—and waive all responsibility in advance.
APPENDIX: THE COLORS OF INFINITY
In November 1989, when receiving the Association of Space Explorers Special Achievement Award in Riyadh, Saudi Arabia, I had the privilege of addressing the largest gathering of astronauts and cosmonauts ever assembled at one place. (More than fifty, including Apollo 11’s Buzz Aldrin and Mike Collins, and the first “space walker” Alexei Leonov, who is no longer embarrassed at sharing the dedication of 2010: Odyssey Two with Andrei Sakharov.) I decided to expand their horizons by introducing them to something really large, and, with astronaut Prince Sultan bin Salman bin Abdul Aziz in the chair, delivered a lavishly illustrated lecture “The Colors of Infinity: Exploring the Fractal Universe.”
The material that follows is extracted from my speech; another portion appears at the beginning of Chapter 15. I’m only sorry that I cannot illustrate it with the gorgeous 35-millimeter slides—and videos—I used at Riyadh.
Today, everybody is familiar with graphs—especially the one with time along the horizontal axis, and the cost of living climbing steadily up the vertical one. The idea that any point on a plane can be expressed by two numbers, usually written x and y, now appears so obvious that it seems quite surprising that the world of mathematics had to wait until 1637 for Descartes to invent it.
We are still discovering the consequences of that apparently simple idea, and the most amazing is now just ten years old. It’s called the Mandelbrot Set (from now on, the M-Set) and you’re soon going to meet it everywhere—in the design of fabrics, wallpaper, jewelry, and linoleum. And, I’m afraid, it will be popping out of your TV screen in every other commercial.
Yet the most astonishing feature of the M-Set is its basic simplicity. Unlike almost everything else in modern mathematics, any schoolchild can understand how it is produced. Its generation involves nothing more advanced than addition and multiplication; there’s no need for such complexities as subtraction and—heaven forbid!—division, let alone any of the more exotic beasts from the mathematical menagerie.
There can be few people in the civilized world who have not encountered Einstein’s famous E = mc2, or who would consider it too hopelessly complicated to understand. Well, the equation that defines the M-Set contains the same number of terms, and indeed looks very similar. Here it is.
Z = z2 + c
Not very terrifying, is it? Yet the lifetime of the Universe would not be long enough to explore all its ramifications.
The z’s and the c in Mandelbrot’s equation are all numbers, not (as in Einstein’s) physical quantities like mass and energy. They are the coordinates which specify the position of a point, and the equation controls the way in which it moves, to trace out a pattern.
There’s a very simple analog familiar to everyone—those children’s books with blank pages sprinkled with numbers, which when joined up in the right order reveal hidden—and often surprising—pictures. The image on a TV screen is produced by a sophisticated application of the same principle.
In theory, anyone who can add and multiply could plot out the M-Set with pen or pencil on a sheet of squared paper. However, as we’ll see later, there are certain practical difficulties—notably the fact that a human life span is seldom more than a hundred years. So the set is invariably computer-generated, and usually shown on a visual display unit.
Now, there are two ways of locating a point in space. The more common employs some kind of grid reference—west-east, north-south, or on squared graph paper, a horizontal X-axis and a vertical Y-axis. But there’s also the system used in radar, now familiar to most people thanks to countless movies. Here the position of an object is given by (1) its distance from the origin, and (2) its direction, or compass bearing. Incidentally, this is the natural system—the one you use automatically and unconsciously when you play any ball game. Then you’re concerned with distances and angles, with yourself as the origin.
So think of a computer’s VDU as a radar screen, with a single blip on it, whose movements are going to trace out the M-Set. However, before we switch on our radar, I want to make the equation even simpler, to:
Z = z2
I’ve thrown c away, for the moment, and left only the z’s. Now let me define them more precisely.
Small z is the initial range of the blip—the distance at which it starts. Big Z is its final distance from the origin. Thus if it was initially 2 units away, by obeying this equation it would promptly hop to a distance of 4.
Nothing to get very excited about, but now comes the modification that makes all the difference:
That double arrow is a two-way traffic sign, indicating that the numbers flow in both directions. This time, we don’t stop at Z = 4; we make that equal to a new z—which promptly gives us a second Z of 16, and so on. In no time we’ve generated the series
256, 65536, 4294967296…
and the spot that started only 2 units from the center is heading toward infinity in giant steps of ever-increasing magnitude.
This process of going around and around a loop is called “iteration.” It’s like a dog chasing its own tail, except that a dog doesn’t get anywhere. But mathematical iteration can take us to some very strange places indeed—as we shall soon discover.
Now we’re ready to turn on our radar. Most displays have range circles at 10, 20… 100 kilometers from the center. We will require only a single circle, at a range of 1. There’s no need to specify any units, as we’re dealing with pure numbers. Make them centimeters or light-years, as you please.
Let’s suppose that the initial position of our blip is anywhere on this circle—the bearing doesn’t matter. So z is 1.
And because 1 squared is still 1, so is Z. And it remains at that value, because no matter how many times you square 1, it always remains exactly 1. The blip may hop around and around the circle, but it always stays on it.
Now consider the case where the initial z is greater than 1. We’ve already seen how rapidly the blip shoots off to infinity if z equals 2—but the same thing will happen sooner or later, even if it’s only a microscopic shade more than 1—say 1.000000000000000000001. Watch:
At the first squaring, Z becomes
1.000000000000000000002
then
1.000000000000000000004
1.000000000000000000008
1.000000000000000000016
1.000000000000000000032
and so on for pages of printout. For all practical purposes, the value is still exactly 1. The blip hasn’t moved visibly outward or inward; it’s still on the circle at range 1.
But those zeros are slowly being whittled away, as the digits march inexorably across from the right. Quite suddenly, something appears in the third, second, first decimal place—and the numbers explode after a very few additional terms, as this example shows:
1.001 1.002 1.004 1.008 1.016 1.032
1.066 1.136 1.292 1.668 2.783 7.745
59.987 3598.467 12948970
167675700000000
28115140000000000000000000000
(Overflow)
There could be a million—a billion—zeros on the right-hand side, and the result would still be the same. Eventually the digits would creep up to the decimal point—and then Z would take off to infinity.
Now let’s look at the other case. Suppose z is a microscopic amount less than 1—say something like
.99999999999999999999
As before, nothing much happens for a long time as we go around the loop, except that the numbers on the far right get steadily smaller. But after a few thousand or million iterations—catastrophe! Z suddenly shrinks to nothing, dissolving in an endless string of zeros…
Check it out on your computer. It can only handle twelve digits? Well, no matter how many you had to play with, you’d still get the same answer. Trust me…
The results of this “program” can be summarized in three laws that may seem too trivial to be worth formulating. But no mathematical truth is trivial, and in a few more steps these laws will take us into a universe of mind-boggling wonder and beauty.
Here are the three laws of the “Squaring” Program:
1. If the input z is exactly equal to 1, the output Z always remains 1.
2. If the input is more than 1, the output eventually becomes infinite.
3. If the input is less than 1, the output eventually becomes zero.
That circle of radius 1 is therefore a kind of map—or, if you like, fence—dividing the plane into two distinct territories. Outside it, numbers which obey the squaring law have the freedom of infinity; numbers inside it are prisoners, trapped and doomed to ultimate extinction.
At this point, someone may say: “You’ve only talked about ranges—distances from the origin. To fix the blip’s position, you have to give its bearing as well. What about that?”
Very true. Fortunately, in this selection process—this division of the z’s into two distinct classes—bearings are irrelevant; the same thing happens whichever direction r is pointing. For this simple example—let’s call it the S-set—we can ignore them. When we come on to the more complicated case of the M-Set, where the bearing is important, there’s a very neat mathematical trick which takes care of it, by using complex or imaginary numbers (which really aren’t at all complex, still less imaginary). But we don’t need them here, and I promise not to mention them again.
The S-set lies inside a map, and its frontier is the circle enclosing it. That circle is simply a continuous line with no thickness. If you could examine it with a microscope of infinite power, it would always look exactly the same. You could expand the S-set to the size of the Universe; its boundary would still be a line of zero thickness. Yet there are no holes in it; it’s an absolutely impenetrable barrier, forever separating the z’s less than one from those greater than one.
Now, at last, we’re ready to tackle the M-Set, where these commonsense ideas are turned upside down. Fasten your seat belts.
During the 1970s, the French mathematician Benoit Mandelbrot, working at Harvard and IBM, started to investigate the equation which has made him famous, and which I will now write in the dynamic form:
The only difference between this and the equation we have used to describe the S-set is the term c. This—not z—is now the starting point of our mapping operation. The first time around the loop, z is put equal to zero.
It seems a trifling change, and no one could have imagined the universe it would reveal. Mandelbrot himself did not obtain the first crude glimpses until the spring of 1980, when vague patterns started to emerge on computer printouts. He had begun to peer through Keats’
Charm’d magic casements, opening on the foam
Of perilous seas, in faery lands forlorn…
As we shall learn later, that word “foam” is surprisingly appropriate.
The new equation asks and answers the same question as the earlier one: What shape is the “territory” mapped out when we put numbers into it? For the S-set it was a circle with radius 1. Let’s see what happens when we start with this value in the M-equation. You should be able to do it in your head—for the first few steps. After a few dozen, even a supercomputer may blow a gasket.
For starters, z = 0, c = 1. So Z = 1
First loop: Z = 12 + 1 = 2
Second loop: Z = 22 + 1 = 5
Third loop: Z = 52 + 1 = 26
Fourth loop: Z = 262 + 1… and so on.
I once set my computer to work out the higher terms (about the limit of my programming ability) and it produced only two more values before it had to start approximating:
1, 2, 5, 26, 677, 458330,
21006640000
4412789000000000000000
At that point it gave up, because it doesn’t believe there are any numbers with more than 38 digits.
However, even the first two or three terms are quite enough to show that the M-Set must have a very different shape from the perfectly circular S-set. A point at distance 1 is in the S-set; indeed, it defines its boundary. A point at that same distance may be outside the boundary of the M-Set.
Note that I say “may,” not “must.” It all depends on the initial direction, or bearing, of the starting point, which we have been able to ignore hitherto because it did not affect our discussion of the (perfectly symmetrical) S-set. As it turns out, the M-Set is only symmetrical about the X, or horizontal, axis.
One might have guessed that, from the nature of the equation. But no one could possibly have intuited its real appearance. If the question had been put to me in virginal pre-Mandelbrot days, I would probably have hazarded: “Something like an ellipse, squashed along the Y-axis.” I might even (though I doubt it) have correctly guessed that it would be shifted toward the left, or minus, direction.
At this point, I would like to try a thought experiment on you. The M-Set being literally indescribable, here’s my attempt to describe it:
Imagine you’re looking straight down on a rather plump turtle, swimming westward. It’s been crossed with a swordfish, so has a narrow spike pointing ahead of it. Its entire perimeter is festooned with bizarre marine growths—and with baby turtles of assorted sizes, which have smaller weeds growing on them…
I defy you to find a description like that in any math textbook. And if you think you can do better when you’ve seen the real beast, you’re welcome to try. (I suspect that the insect world might provide better analogies; there may even be a Mandelbeetle lurking in the Brazilian rain forests. Too bad we’ll never know.)
Here is the first crude approximation, shorn of details—much like Conroy Castle’s “Lake Mandelbrot” (Chapter 18). If you like to fill its blank spaces with the medieval cartographers” favorite “Here be dragons” you will hardly be exaggerating.
First of all, note that—as I’ve already remarked—it’s shifted to the left (or west, if you prefer of the S-set, which of course extends from +1 to -1 along the X-axis. The M-Set only gets to 0.25 on the right along the axis, though above and below the axis it bulges out to just beyond 0.4.
On the left-hand side, the map stretches to about -1.4, and then it sprouts a peculiar spike—or antenna—which reaches out to exactly -2.0. As far as the M-Set is concerned, there is nothing beyond this point; it is the edge of the Universe. Mandelbrot fans call it the “Utter West,” and you might like to see what happens when you make c equal to -2. Z doesn’t converge to zero—but it doesn’t escape to infinity either, so the point belongs to the set—just. But if you make c the slightest bit larger, say -2.00000… 000001, before you know it you’re passing Pluto and heading for Quasar West.
Now we come to the most important distinction between the two sets. The S-set has a nice, clean line for its boundary. The frontier of the M-Set is, to say the least, fuzzy. Just how fuzzy you will begin to understand when we start to “zoom” into it; only then will we see the incredible flora and fauna which flourish in that disputed territory.
The boundary—if one can call it that—of the M-Set is not a simple line; it is something which Euclid never imagined, and for which there is no word in ordinary language. Mandelbrot, whose command of English (and American) is awesome, has ransacked the dictionary for suggestive nouns. A few examples: foams, sponges, dusts, webs, nets, curds. He himself coined the technical name fractal, and is now putting up a spirited rearguard action to stop anyone from defining it too precisely.
Computers can easily make “snapshots” of the M-Set at any magnification, and even in black and white they are fascinating. However, by a simple trick they can be colored, and transformed into objects of amazing, even surreal, beauty.
The original equation, of course, is no more concerned with color than is Euclid’s Elements of Geometry. But if we instruct the computer to color any given region in accordance with the number of times z goes around the loop before it decides whether or not it belongs to the M-Set, the results are gorgeous.
Thus the colors, though arbitrary, are not meaningless. An exact analogy is found in cartography. Think of the contour lines on a relief map, which show elevations above sea level. The spaces between them are often colored so that the eye can more easily grasp the information conveyed. Ditto with bathymetric charts; the deeper the ocean, the darker the blue. The mapmaker can make the colors anything he likes, and is guided by aesthetics as much as geography.
It’s just the same here—except that these contour lines are set automatically by the speed of the calculation—I won’t go into details. I have not discovered what genius first had this idea—perhaps Monsieur M. himself—but it turns them into fantastic works of art. And you should see them when they’re animated…
One of the many strange thoughts that the M-Set generates is this. In principle, it could have been discovered as soon as the human race learned to count. In practice, since even a “low magnification” image may involve billions of calculations, there was no way in which it could even be glimpsed before computers were invented! And such movies as Art Matrix’ Nothing But Zooms would have required the entire present world population to calculate night and day for years—without making a single mistake in multiplying together trillions of hundred-digit numbers…
I began by saying that the Mandelbrot Set is the most extraordinary discovery in the history of mathematics. For who could have possibly imagined that so absurdly simple an equation could have generated such—literally—infinite complexity, and such unearthly beauty?
The Mandelbrot Set is, as I have tried to explain, essentially a map. We’ve all read those stories about maps which reveal the location of hidden treasure.
Well, in this case—the map is the treasure!
Colombo, Sri Lanka
1990 February 28
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