Death's End (The Three-Body Problem)

by Cixin Liu

  “A bottomless abyss exists in every inch.”

  The experience of high-dimensional spatial sense was a spiritual baptism. In one moment, concepts like freedom, openness, profundity, and infinity all gained brand-new meanings.

  Chu Yan said, “We should return. The warped points remain stable for only a brief period of time before drifting away or disappearing. To find a new warped point requires moving in four-dimensional space. That’s a dangerous undertaking for novices like you.”

  “How does one find a warped point in four-dimensional space?” Morovich asked.

  “Simple. A warped point is usually spherical. Light is refracted inside the sphere, and objects inside are distorted, causing a visual break in the image of the objects. Of course, this is just an optical effect in four-dimensional space, not a real change in the shapes of the objects. Look over there—”

  Chu Yan pointed in the direction they had come from. Morovich and Guan saw those tubes again, which now also lay open so that all the liquids flowing through them could be seen clearly. Inside the spherical region, the tubes were curved and distorted, and the sphere appeared like a drop of dew hanging on a spiderweb. This was different from how the region had appeared in three-dimensional space. There, the warped point didn’t refract light, and so appeared completely invisible. Its presence could only be made known via the disappearance of objects that had entered four-dimensional space inside the bubble.

  “If you come here again, you must wear space suits. Novices can’t always tell locations accurately, and finding a new warped point for the return trip might result in landing outside the ship in three-dimensional space.”

  Chu Yan indicated that the other two should follow, and entered the dewdrop-like bubble. In an instant they were back inside the three-dimensional world, back in the corridor inside the ship, in exactly the place where, ten minutes ago, they had entered four-dimensional space. In fact, they had never left—the space they were in had just gained an extra dimension. The round opening in the bulkhead was still there, and they could still see the “broken” tubes inside.

  But to Morovich and Guan, the world no longer seemed familiar. They now experienced the three-dimensional world as narrow and smothering. Guan dealt with it slightly better—he had at least experienced four-dimensional space once before, in a semiconscious state. But Morovich was feeling claustrophobic, as though he was being suffocated.

  “This is normal. You’ll get used to it after a few times.” Chu Yan laughed. “The two of you now know what real vastness means. Even if you put on space suits and go take a walk in space now, you’ll feel confined.”

  “How did all this happen?” Morovich tore open his collar and gasped.

  “We entered a region of space where space has four dimensions. That’s it. We call this region a four-dimensional fragment.”

  “But we’re in three-dimensional space now!”

  “Four-dimensional space contains three-dimensional space, just as three-dimensional space contains two-dimensional space. To make another analogy: We’re located inside a three-dimensional sheet of paper in four-dimensional space.”

  “Let me propose a model,” said Guan excitedly. “The entirety of our three-dimensional space is a large, thin sheet of paper, sixteen billion light-years across. Somewhere on this sheet of paper is a tiny, four-dimensional soap bubble.”

  “Perfect, Dr. Guan!” Chu Yan clapped Guan’s shoulder, making him tumble in weightlessness. “I’ve been trying to come up with a good analogy, and you hit it in one try. This is why we need a cosmologist! You’re exactly right. We were on this three-dimensional sheet of paper, crawling over the surface. Then we came into the soap bubble. From a warped point, we can manage to leave the surface of the paper and entered the space inside the bubble.”

  “Though we were in four-dimensional space just now, our bodies remained three-dimensional,” Morovich said.

  “That’s right. We were flat, three-dimensional people drifting in four-dimensional space. It’s not clear how our bodies are able to survive in four-dimensional space, given that the physical laws are likely different. There are many such mysteries.”

  “What exactly are warped points?”

  “The three-dimensional sheet of paper is not completely flat everywhere. Some places are warped, reaching into the fourth dimension. That’s what a warped point is: a tunnel from lower dimensions into higher dimensions. We can get into four-dimensional space by jumping into them.”

  “Are there many warped points?”

  “Oh yes. They’re everywhere. Blue Space was able to discover their secret earlier because we have more people aboard, and so there were many more opportunities to encounter warped points. Gravity, besides having fewer people, also had a much stricter psychological monitoring regime—even those who encountered warped points dared not discuss them.”

  “Are all warped points this small?”

  “No. Some are much bigger. There’s one mystery we’ve never been able to solve: We once observed that the rear third of Gravity had warped into four-dimensional space, and stayed there for several minutes. How could you have not noticed anything odd?”

  “Well, the last third of the ship usually had no crew. Oh, wait, he was there.” Morovich turned to Guan Yifan. “You must have experienced that. I think I heard about it from Dr. West.”

  “I was only half awake. Later, that idiot convinced me that I was only hallucinating.”

  “It’s not possible to look into the fourth dimension from three-dimensional space. But it is possible to be in four-dimensional space and see everything happening in three-dimensional space and to affect things in it. We were able to lay an ambush against the droplets from four-dimensional space. No matter how powerful the strong-interaction probes were, they were still three-dimensional objects. In a sense, three-dimensionality is synonymous with fragility. Viewed from four-dimensional space, it was an unrolled painting, defenseless. We approached it from the fourth dimension, and, without understanding its principles of operation, sabotaged its internal mechanisms—completely exposed—at random.

  “Is Trisolaris aware of the existence of the four-dimensional fragment?”

  “We think not.”

  “The soap bubble—uh, four-dimensional fragment—how big is it?”

  “Talking about the size of four-dimensional space from three-dimensional space is kind of meaningless. We can only discuss how big the projection of the fragment is in three dimensions. Based on preliminary investigation, we think the three-dimensional projection is spherical. If that’s true, based on the data collected so far, its radius is between forty to fifty AU.”

  “About the size of the Solar System.”

  The round opening in the bulkhead next to the three of them began to move slowly and to shrink. When it was just over ten meters from them, the opening disappeared completely. But the information window floating near them indicated that two more warped points had appeared aboard Blue Space.

  “How could a four-dimensional fragment appear in three-dimensional space?” Guan Yifan muttered to himself.

  “No one knows. Doctor, this is your puzzle to solve.”

  After the discovery of the four-dimensional fragment, Blue Space had explored and studied the space inside extensively. The addition of Gravity brought more advanced equipment and techniques, so the crews could conduct more comprehensive and in-depth exploration.

  In three-dimensional space, this region appeared very empty and showed no irregularities. Much of the exploration had to be conducted in four-dimensional space. Since releasing probes into four-dimensional space was no trivial matter, most of the research was conducted by inserting a telescope into the fragment through a warped point. Manipulating a three-dimensional instrument in four dimensions required some practice, and a period of adjustment, but once the scientists got the hang of it, they immediately made shocking discoveries.

  Through the telescope, they discovered a ring-shaped object. Since it was impo
ssible to determine its distance from the ship, it was also impossible to estimate its size. The best guess was that its three-dimensional diameter was between eighty to one hundred kilometers, and the band of the ring was about twenty kilometers thick. The whole thing resembled a giant wedding band spinning in space. Complex patterns resembling circuitry could be discerned on the surface of the band. Based on the evidence, it seemed reasonable to conclude that the ring had been constructed by intelligent beings.

  This was the first time humanity had observed another civilization outside of the Earth and Trisolaris.

  But the most shocking thing was that the “Ring” was sealed. It existed in four-dimensional space, but didn’t reveal its interior as a three-dimensional object would have. Since its inside was concealed, that meant it was a true four-dimensional object. This was also the first true four-dimensional object detected by humanity since entering four-dimensional space.

  People initially feared an attack, but the surface of the Ring showed no signs of any activity. They also detected no emission of any electromagnetic, neutrino, or gravitational wave signals. Other than a slow, stately revolving motion, the Ring showed no acceleration. The working theory was that this was a ruin, perhaps a long-abandoned space city or spaceship.

  Further observations revealed more unknown objects in the depths of four-dimensional space. They were all sealed four-dimensional objects of different sizes and shapes, and many seemed to be artifacts fashioned by intelligence: pyramids, crosses, polyhedral frames, and so on. Other objects were irregular forms composed from simpler shapes, also clearly not natural. More than a dozen of these objects had shapes that could be discerned by telescope, though farther away were many more objects that appeared only as point sources. In total, about a hundred such objects were found. Like the Ring, none of them showed signs of activity, and they emitted no detectable signals.

  Guan Yifan proposed to Captain Chu the plan of piloting a pinnace to the Ring and studying it up close. If possible, he wanted to enter the Ring. The captain denied this proposal unequivocally. Navigating through four-dimensional space was fraught with risks. To precisely fix one’s location required four coordinates, but equipment brought from three-dimensional space could only determine three coordinates. This meant three-dimensional explorers could not determine the location of any object in four-dimensional space with precision. An explorer could not ascertain the location or distance of the Ring using instrumentation or visual observation, so it would be possible to collide with the Ring at any moment.

  Similarly, locating a warped point to return to three-dimensional space would be very difficult. Since the coordinate in one of the four directions could not be determined, when a warped point was found, all that was known was its direction, not its distance from the observer. The crew of the pinnace could use a warped point to return to three-dimensional space and, to their surprise, find themselves far away from Blue Space.

  Finally, most of the radio waves linking Blue Space and the pinnace would spill into the fourth dimension, leading to far faster decay of signal strength and causing communication difficulties.

  After that, Blue Space and Gravity suffered six micrometeoroid strikes in one day. A 140-nanometer micrometeoroid struck and completely destroyed the magnetic levitation controller of Blue Space’s fusion reactor core. This was a key system aboard the ship. The fusion reactor core could reach temperatures as high as a million degrees, which would vaporize any material it came in contact with. A magnetic field kept it centered within the reaction chamber. If the controller failed, the superheated reactor core could escape from the magnetic field and instantly destroy the ship. Fortunately, the backup unit kicked in immediately and shut off the reactor—which was operating at minimal power—and averted catastrophe.

  As the two ships sailed deeper into the four-dimensional fragment, the density of micrometeoroid strikes increased, and even larger meteoroids, visible to the naked eye, passed near the ships. Their velocity relative to the ships was several times the third cosmic velocity. In three-dimensional space, the critical parts of the ships were wrapped in layers of protection, but here, they lay exposed to the fourth dimension, completely defenseless.

  Chu Yan decided that the two ships should retreat from the four-dimensional fragment. The fragment as a whole was moving away from the Solar System, heading in the same direction as the ships’ course; thus, although Blue Space and Gravity were sailing away from the Solar System at a high speed, their velocity relative to the fragment was small, and they had only slowly caught up to the fragment. They weren’t deep within the fragment and should be able to decelerate and leave it easily.

  Guan Yifan raged against this decision. “The greatest mystery in the universe is right in front of us. The answers to all our cosmological questions may be found here. How can we leave?”

  “Are you talking about the three and three hundred thousand syndrome? The fragment did remind me of it.”

  “Even if you focus only on the practical, we can probably recover unimaginable knowledge and artifacts from that ring-shaped ruin.”

  “Such gains are only meaningful if we survive this ordeal. Right now, both of our ships could be annihilated any moment.”

  Guan sighed and shook his head. “Fine. But before you leave, let me ride a pinnace to explore the Ring. Give me a chance. You spoke of survival, but perhaps our future survival depends on what I can discover here!”

  “We can consider sending a drone.”

  “In a four-dimensional world, only a live observer can understand what is seen. You know this better than I.”

  After a brief discussion, the senior staff of both ships approved Guan’s proposal. Guan Yifan, Lieutenant Zhuo Wen, and Dr. West made up the exploratory team. Lieutenant Zhuo was the science officer aboard Blue Space and had comparatively extensive experience navigating in four dimensions. Dr. West, on the other hand, simply insisted that he come; the request was ultimately approved because he had studied Trisolaran language before the voyage.

  Prior to this, the longest voyage in four-dimensional space had been the attack on the droplets and Gravity. During the attack, a pinnace had sailed through four-dimensional space to approach Gravity, and then three people, including Lieutenant Commander Park Ui-gun, had entered Gravity via a warped point to reconnoiter. Thereafter, more than sixty marines had boarded Gravity in three separate waves. The attack on the droplets had relied on smaller shuttles. But this voyage of discovery to the Ring would be far longer.

  The pinnace entered four-dimensional space from a warped point between the two ships. At the tail of the pinnace, the small fusion reactor’s core turned from dim red to a faint blue as its power level increased. This flame, together with the balls of fire in the reactors of the two larger ships, illuminated this world of infinity times infinity. Blue Space and Gravity quickly receded, and as the pinnace sailed deeper into four-dimensional space, the high-dimensional spatial sensation intensified. Although Dr. West had already been to four-dimensional space twice, he exclaimed, “How grand is the spirit that can grasp such a world!”

  Lieutenant Zhuo piloted the pinnace using voice commands or by moving the cursor with his gaze—it was a good idea to avoid using hands and risking contact with some sensitive piece of equipment that now lay exposed in four dimensions. To the naked eye, the Ring was still but a barely visible dot, but Zhuo cautiously kept the pinnace flying at a very low speed. Due to the extra unmeasurable dimension, visual judgments of distance were completely unreliable. The Ring might be as far away as an astronomical unit or as close as the pinnace’s bow.

  After three hours, the pinnace had already exceeded the previous record of distance sailed from the ships in four-dimensional space. The Ring remained but a dot. Lieutenant Zhuo grew even more cautious and was prepared to decelerate at full power and to change the heading at a moment’s notice. Guan Yifan grew impatient and asked Zhuo to fly faster. Just then, West cried out in surprise.

  The Ring turned
into a real ring—it just happened. One moment, it was still a dot; the next moment, it was a ring the size of a coin. There was no gradual process of change at all.

  “You’ve got to remember that we’re basically blind in the fourth dimension,” Lieutenant Zhuo said. He decreased their speed again.

  Two more hours passed. If they were still in three-dimensional space, they would have sailed about two hundred thousand kilometers.

  All of a sudden, the coin-sized Ring turned into a gigantic structure. Lieutenant Zhuo banked sharply and barely managed to avoid collision. The pinnace passed through the Ring like an arch in space. The pinnace decelerated, turned around, and came to a stop a short distance from the Ring.

  This was the first time humans had come close to a four-dimensional object. Similar to high-dimensional spatial sense, they felt the magnificence of high-dimensional materiality. The Ring was completely sealed, and they could not look inside the band, but they could feel an immense sense of depth and of containment. What they were seeing wasn’t just a Ring, but an infinity of Rings all stacked together in concealment. This sensation of four-dimensionality impressed itself upon the soul, and gave the observers the experience of seeing the mountain contained in a mustard seed described in Buddhist parables.