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
THE DEEP RANGE
AUTHOR’S NOTE
In this novel I have made certain assumptions about the maximum size of various marine animals which may be challenged by some biologists. I do not think, however, that they will meet much criticism from underwater explorers, who have often encountered fish several times the size of the largest recorded specimens.
For an account of Heron Island as it is today, seventy-five years before the opening of this story, I refer the reader to The Coast of Coral, and I hope that the University of Queensland will appreciate my slight extrapolation of its existing facilities.
1956
INTRODUCTION
The Deep Range began its existence as a 3,500-word story written in November 1953, first published in Frederik Pohl’s Star Science Fiction series (Number 3, 1954). I had just become seriously addicted to underwater exploration, and soon afterward bought my first scuba set. Like a motorist in those pioneering days before any interfering bureaucrat had dreamed of driving licenses, I simply ordered it from Abercrombie and Fitch, strapped it on, and plunged into the nearest convenient body of water.
This happened to be Florida’s famed Weeki-Wachi Springs, the crystal clarity of which must be unmatched anywhere in the world. I was carrying with me my first underwater camera—a Leica, in a cylindrical plastic case I’d purchased from a LIFE magazine photographer—loaded with Kodachrome (a torpid ASA 10 or so in those days, if I remember correctly).
The camera worked fine, and when I dived into Weeki-Wachi Springs the first subject I encountered was a fair-sized alligator, hanging languidly in a vertical position with its nostrils just breaking the surface. I’d never met one before and assumed (correctly) that it wouldn’t attack a strange, bubble-blowing creature heading confidently toward it. So I got half a dozen excellent shots before it became camera shy and fled up the nearest creek.
The remainder of the roll wasn’t so exciting: It merely showed a lot of fish apparently suspended in midair. The trouble with Weeki-Wachi (visibility approx. 200 feet) is that you can’t see the water, which explains a comment by the late Alfred Bester (The Demolished Man, The Stars My Destination, etc.): “Damn it, Arthur, these aren’t underwater shots. You took them in an aquarium. I can see the reflection in the plate glass.”
In December 1954, I left the Northern Hemisphere for the Great Barrier Reef, where I encountered my first whales, as well as the justly famed Australian sharks. After completing The Coast of Coral (1956), I realized that I now had the background for a whole novel, which was written in Ceylon during 1956 and published the next year. Still later, I used the same Heron Island background for another book, Dolphin Island (1963). Both novels have been purchased by optimistic movie makers. I wish them luck with their casting problems.
Back in 1957 (the year the Space Age opened!), only a few people were interested in whales, and the idea of ranching them was still quite novel, though not original: I suspect I got it from Jacques Cousteau. Now they—and cetaceans in general—are among mankind’s most favorite animals, and the ecological points I attempted to make almost half a century ago are widely accepted (vide Free Willy!).
When I wrote Dolphin Island back in 1962, I felt I was risking ridicule by having my hero actually ride a killer whale. Now it’s a regular act in oceanaria, and the trainer even puts his—often her—head inside the animal’s mouth, between those huge teeth. I once saw a hair-raising television film in which a girl trainer was grabbed by a killer whale, who wouldn’t let her go until her colleagues had prised open his jaws. He was just lonely and didn’t want her to leave! I’m happy to say that the brave girl was back in the tank the next day.
There has certainly been a revolution in public attitudes toward marine mammals, as a direct result of underwater movies like Jacques Cousteau’s famous films, the popularity of oceanaria, and the explosion of interest in diving as a sport or hobby. I often wonder what Herman Melville would have thought of today’s campaign to save the whales—especially sperm whales, the ferocious monster he described so vividly in Moby Dick. I suspect he’d now agree with the ironic saying: “This animal is very vicious—when attacked, it defends itself.”
How is it that we can so easily make friends with large and powerful carnivores in the sea—when we wouldn’t dream of doing so on land? Anyone who behaved toward a lion, a tiger, or polar bear as divers have done countless times toward sperm whales, killer whales, and dolphins wouldn’t come back to tell the tale. I’ve never seen an answer to this question.
An even greater enigma is presented by the musical repertoire of the humpback whales, something unique in nature. By comparison, all bird songs are simple: They last only seconds and are repeated mechanically year by year (though there are regional variations—perhaps the equivalent of human dialects). But whale songs last up to half an hour, and they change style in successive years.
The amount of information contained in one of these songs must be considerable: at a rough estimate, the capacity of a small computer. How is it stored? What is its purpose? If they are intended merely for location, identification, warning, mating, these songs seem far more elaborate than necessity would warrant. After all, the birds manage rather well with a much simpler repertoire.
And it’s a strange thought that the songs of the humpback whales are now, literally, on the way to the stars. The two Voyager spacecraft that flew by Jupiter and Saturn in 1979 carried with them gold-plated records on which were stored many of the characteristic sounds of Earth and messages in many languages.
In the benign and changeless environment of space, these records will still exist when all the other artifacts of man have been eroded by time, and even the Earth itself has been consumed by the Sun when it goes nova at the end of its evolutionary sequence. So perhaps these songs will be heard again, by creatures we cannot imagine, when they encounter our primitive space probe. How ironic it will be, if extraterrestrials a billion years hence grasp a message from fellow Earthlings that has been incomprehensible to us.
Colombo, Sri Lanka
I
THE APPRENTICE
CHAPTER
1
There was a killer loose on the range. The South Pacific air patrol had seen the great corpse staining the sea crimson as it wallowed in the waves. Within seconds, the intricate warning system had been alerted; from San Francisco to Brisbane, men were moving counters and drawing range circles on the charts. And Don Burley, still rubbing the sleep from his eyes, was hunched over the control board of Scoutsub 5 as it dropped down to the twenty-fathom line.
He was glad that the alert was in his area; i
t was the first real excitement for months. Even as he watched the instruments on which his life depended, his mind was ranging far ahead. What could have happened? The brief message had given no details; it had merely reported a freshly killed right whale lying on the surface about ten miles behind the main herd, which was still proceeding north in panic-stricken flight. The obvious assumption was that, somehow, a pack of killer whales had managed to penetrate the barriers protecting the range. If that was so, Don and all his fellow wardens were in for a busy time.
The pattern of green lights on the telltale board was a glowing symbol of security. As long as that pattern was unchanged, as long as none of those emerald stars winked to red, all was well with Don and his tiny craft. Air—fuel—power—this was the triumvirate that ruled his life. If any one of these failed, he would be sinking in a steel coffin down toward the pelagic ooze, as Johnnie Tyndall had done the season before last. But there was no reason why they should fail, and the accidents one foresaw, Don told himself reassuringly, were never those that happened.
He leaned across the tiny control board and spoke into the mike. Sub 5 was still close enough to the mother ship for radio to work, but before long he’d have to switch to the ultrasonics.
“Setting course 255, speed 50 knots, depth 20 fathoms, full sonar coverage. Estimated time to target area 40 minutes. Will report at ten-minute intervals until contact is made. That is all. Out.”
The acknowledgment from the Rorqual was barely audible, and Don switched off the set. It was time to look around.
He dimmed the cabin lights so that he could see the scanner screen more clearly, pulled the Polaroid glasses down over his eyes, and peered into the depths. It took a few seconds for the two images to fuse together in his mind; then the 3-D display sprang into stereoscopic life.
This was the moment when Don felt like a god, able to hold within his hands a circle of the Pacific twenty miles across, and to see clear down to the still largely unexplored depths two thousand fathoms below. The slowly rotating beam of inaudible sound was searching the world in which he floated, seeking out friend and foe in the eternal darkness where light could never penetrate. The pattern of soundless shrieks, too shrill even for the hearing of the bats who had invented sonar millions of years before man, pulsed out into the watery night; the faint echoes came tingling back, were captured and amplified, and became floating, blue-green flecks on the screen.
Through long practice, Don could read their message with effortless ease. Five hundred feet below, stretching out to the limits of his submerged horizon, was the Scattering Layer—the blanket of life that covered half the world. The sunken meadow of the sea, it rose and fell with the passage of the Sun, hovering always at the edge of darkness. During the night it had floated nearly to the surface, but the dawn was now driving it back into the depths.
It was no obstacle to his sonar. Don could see clear through its tenuous substance to the ooze of the Pacific floor, over which he was driving high as a cloud above the land. But the ultimate depths were no concern of his; the flocks he guarded, and the enemies who ravaged them, belonged to the upper levels of the sea.
Don flicked the switch of the depth selector, and his sonar beam concentrated itself into the horizontal plane. The glimmering echoes from the abyss vanished, and he could see more clearly what lay around him here in the ocean’s stratospheric heights. That glowing cloud two miles ahead was an unusually large school of fish; he wondered if Base knew about it, and made an entry in his log. There were some larger blips at the edge of the school—the carnivores pursuing the cattle, ensuring that the endlessly turning wheel of life and death would never lose momentum. But this conflict was no affair of Don’s; he was after bigger game.
Sub 5 drove on toward the west, a steel needle swifter and more deadly than any other creature that roamed the seas. The tiny cabin, now lit only by the flicker of lights from the instrument board, pulsed with power as the spinning turbines thrust the water aside. Don glanced at the chart and noted that he was already halfway to the target area. He wondered if he should surface to have a look at the dead whale; from its injuries he might be able to learn something about its assailants. But that would mean further delay, and in a case like this time was vital.
The long-range receiver bleeped plaintively, and Don switched over to Transcribe. He had never learned to read code by ear, as some people could do, but the ribbon of paper emerging from the message slot saved him the trouble.
AIR PATROL REPORTS SCHOOL 50-100 WHALES HEADING 95 DEGREES GRID REF X186593 Y432011 STOP MOVING AT SPEED AFTER CHANGE OF COURSE STOP NO SIGN OF ORCAS BUT PRESUME THEY ARE IN VICINITY STOP RORQUAL
Don considered this last piece of deduction highly unlikely. If the orcas—the dreaded killer whales—had indeed been responsible, they would surely have been spotted by now as they surfaced to breathe. Moreover, they would never have let the patrolling plane scare them away from their victim, but would have remained feasting on it until they had gorged themselves.
One thing was in his favor; the frightened herd was now heading almost directly toward him. Don started to set the coordinates on the plotting grid, then saw that it was no longer necessary. At the extreme edge of his screen, a flotilla of faint stars had appeared. He altered course slightly, and drove head on to the approaching school.
Part of the message was certainly correct; the whales were moving at unusually high speed. At the rate they were traveling, he would be among them in five minutes. He cut the motors and felt the backward tug of the water bringing him swiftly to rest.
Don Burley, a knight in armor, sat in his tiny, dim-lit room a hundred feet below the bright Pacific waves, testing his weapons for the conflict that lay ahead. In these moments of poised suspense, before action began, he often pictured himself thus, though he would have admitted it to no one in the world. He felt, too, a kinship with all shepherds who had guarded their flocks back to the dawn of time. Not only was he Sir Lancelot, he was also David, among ancient Palestinian hills, alert for the mountain lions that would prey upon his father’s sheep.
Yet far nearer in time, and far closer in spirit, were the men who had marshaled the great herds of cattle on the American plains, scarcely three lifetimes ago. They would have understood his work, though his implements would have been magic to them. The pattern was the same; only the scale of things had altered. It made no fundamental difference that the beasts Don herded weighed a hundred tons and browsed on the endless savannas of the sea.
The school was now less than two miles away, and Don checked his scanner’s steady circling to concentrate on the sector ahead. The picture on the screen altered to a fan-shaped wedge as the sonar beam started to flick from side to side; now he could count every whale in the school, and could even make a good estimate of its size. With a practiced eye, he began to look for stragglers.
Don could never have explained what drew him at once toward those four echoes at the southern fringe of the school. It was true that they were a little apart from the rest, but others had fallen as far behind. There is some sixth sense that a man acquires when he has stared long enough into a sonar screen—some hunch which enables him to extract more from the moving flecks than he has any right to do. Without conscious thought, Don reached for the controls and started the turbines whirling once more.
The main body of the whale pack was now sweeping past him to the east. He had no fear of a collision; the great animals, even in their panic, could sense his presence as easily as he could detect theirs, and by similar means. He wondered if he should switch on his beacon. They might recognize its sound pattern, and it would reassure them. But the still unknown enemy might recognize it too, and would be warned.
The four echoes that had attracted his attention were almost at the center of the screen. He closed for an interception, and hunched low over the sonar display as if to drag from it by sheer willpower every scrap of information the scanner could give. There were two large echoes, some distance apart, and one was
accompanied by a pair of smaller satellites. Don wondered if he was already too late; in his mind’s eye he could picture the death struggle taking place in the water less than a mile ahead. Those two fainter blips would be the enemy, worrying a whale while its mate stood by in helpless terror, with no weapons of defense except its mighty flukes.
Now he was almost close enough for vision. The TV camera in Sub 5’s prow strained through the gloom, but at first could show nothing but the fog of plankton. Then a vast, shadowy shape appeared in the center of the screen, with two smaller companions below it. Don was seeing, with the greater precision but hopelessly limited range of light, what the sonar scanners had already told him.
Almost at once he saw his incredible mistake: The two satellites were calves. It was the first time he had ever met a whale with twins, although multiple births were not uncommon. In normal circumstances, the sight would have fascinated him, but now it meant that he had jumped to the wrong conclusion and had lost precious minutes. He must begin the search again.
As a routine check, he swung the camera toward the fourth blip on the sonar screen—the echo he had assumed, from its size, to be another adult whale. It is strange how a preconceived idea can affect a man’s understanding of what he sees; seconds passed before Don could interpret the picture before his eyes—before he knew that, after all, he had come to the right place.
“Jesus!” he said softly. “I didn’t know they grew that big.” It was a shark, the largest he had ever seen. Its details were still obscured, but there was only one genus it could belong to. The whale shark and the basking shark might be of comparable size, but they were harmless herbivores. This was the king of all selachians—Carcharodon—the Great White Shark. Don tried to recall the figures for the largest known specimen. In 1990, or thereabouts, a fifty-footer had been killed off New Zealand, but this one was half as big again.