Rescued From Paradise

by Robert L. Forward

  AS THE day drew to a close, Adam and Dirk crossed back over the river by swimming across the rain-sprinkled Wide Pond where the river currents were not as strong, towing their sodden catch on a small makeshift wooden raft behind them. It seemed to Adam that the catch got wetter from being in the heavy downpour than the hunters did from being in the pond. Adam sent Dirk up the muddy trails of Meander Valley with their catch, while he headed down to the Jolly village with the stone tablet.

  As Adam approached the thook barrier, he gave a whistle and the thorns obediently rolled away to let him through, showering the ground with water droplets as they twisted themselves back from the entrance. As he walked through the Jolly village, he took time to look around carefully at the shapes of all the huts and storage sheds, even though he knew the general arrangement of the village well, having been in it many times. Not one of the structures looked like the drawing on the tablet. The sloped roofs of the Jolly huts were all flat, so that the constant rain dripped off down the back of the hut, while the houselike drawings on the tablet had a peaked roof like the humans' Meeting Hall. Also, the Jolly huts were tall and narrow, to fit the Jollys, while the houselike things in the tablet were short and squat.

  He went to the chief's hut. Seetoo was settled just inside the opening, out of the wind, resting on four limbs while two other limbs were working away slowly at the task of attaching one of Weehoob's blackglass spear points onto a long shaft. The chief had two nested eyes watching the work of the strong root fingers carefully braiding the complicated knot.

  Adam came to a halt in front of Seetoo and waited patiently in the warm rain—water dripping off his thick black ringlets and down his dusky shoulders—until his presence was finally noticed. One of Seetoo's long root-limbs ponderously lowered the partially finished spear to the ground. At the same time, the chief's mouth opened and a gatherer inside whistled a greeting.

  "Welcome! Aadaam of the curly black fronds; seed of Jeenjuur and pollen of Jhaan."

  Adam had no problem understanding and talking with the Jollys, for like all human children, his parents had made sure he had been exposed to the Jolly language at that critical portion in a child's life when learning languages came easily, even to the point of boarding each of the children for a few months in the Jolly village as fast-moving, intelligent, "gatherers" for the tribe as a whole. As a result, Adam and all the other children were bilingual. The Jollys in turn, found it much easier to communicate with the younger generation of humans than their elders, since the children and Jollys had rapidly evolved a pidgin mixture of human and Jolly languages that they both were comfortable with. Often, the children were called upon as interpreters when complex concepts needed to be exchanged between a Jolly and an adult.

  "Dirk found this pictotablet," said Adam, putting the stone slab down on the muddy ground in front of the hut entrance so it would not move while Seetoo's eye fluttered down to take a close look at it. Seetoo added the image to the worldview in its mind and then examined the image closely as Adam continued talking. "It is a drawing of something. But it is made of scratches on a stone tablet instead of indentations on a clay pictotablet. We thought it might be important, so I brought it here for you to look at."

  Seetoo ponderously stretched out a forelimb into the rain outside and ran sensitive root tips over the polished stone tablet, feeling the scratches carefully.

  "This is not a stone of this tribe," said the chief. "My worldview does not contain any tribe on this island or any other island that would make this stone."

  "I think those crosses and bars might be numbers. I know how to count in Jolly language—" Adam knew that the Jollys used a base six number system and knew how to count all the way up to 216, the Jolly equivalent of 1000 "—but these don't look like Jolly numbers. Your numbers are all circles, with line patterns inside indicating the numbers from zero to five. This tablet has only two symbols, like your symbols for one and four, but they don't have circles around them."

  "You are correct. Those are not Jolly numbers. This is not a Jolly tablet."

  "I guessed as much. Since there are only two symbols, it must be a binary number system," said Adam, who had gone farther than most of the firstborn in his mathematical studies program on his Teacher.

  "Binary number system?" repeated Seetoo, showing interest in learning something new.

  "Never mind," said Adam, bending over to pick up the tablet. He knew that the Jollys—unlike the flouwen—were mathematically illiterate. They used mathematics solely for counting; things like the number of days between high tides, and the number of fish they had caught. They didn't own plots of land that needed surveying, and they didn't build massive structures that needed precise construction, so they had yet to learn multiplication in order to calculate areas. They were also ignorant of geometry, including the Pythagorean theorem for calculating the length of the long side of a right-angled triangle from the lengths of the two shorter sides. They even thought that pi was three. It would have taken Adam seasons to explain to Chief Seetoo what the base-two binary numbering system was.

  Adam rose and put the tablet into his hunting net, then held himself still again in front of Seetoo until he was sure that his new position had been recorded into Seetoo's worldview.

  "I, Adam, seed of Jinjur and pollen of John, bid farewell to his friend, Seetoo, Chief of all the Keejook." He turned and trotted away through the rain. It was getting toward evening, and he didn't want to travel the slippery muddy trails in the weak light that Gargantua would supply under the heavy overcast sky.

  With the clouds pouring rain down in a steady torrent, after the communal meal everyone settled in together for the long evening in the refurbished Meeting Hall. The children got out their Teachers, which had been charging all day with their ultraefficient wide-spectrum photoelectric converters facing toward the blazing cooking fire, and most of them played games.

  Adam, his heart still heavy over the recent loss of both of his birth-parents, and beginning to feel the weight of responsibility of being an adult, couldn't get in the mood to play games. Instead, he opened up the mathematics studies program on his Teacher and started in on the puzzle of the numbers on the tablet. When Shannon heard the distinctive chime that the math program used to announce itself, she stopped playing chess with her Teacher and came over to see what Adam was doing. In the past, Adam had always treated the tom-boyish Shannon as just another guy, but now, primarily because they spent a great deal of time together, and especially now, as she snuggled up beside him, he and his body were beginning to notice the softness of her curves. Shannon went into her artistic mode as Adam showed her the tablet. Her long fingers brushed appreciatively over the polished surface of the stone.

  "It's beautiful," she said, admiring its simplicity.

  "Just a drawing," said Adam, as he ran the scanner edge of his Teacher across the tablet. Instantly, a replica of the tablet was on the screen of his Teacher. He looked at the image critically, and using the bit-map expander feature, touched it up by erasing extraneous dots caused by dirt specks and filling in missing portions of the lines. "Looks like a hut, but it's not like any Jolly hut. I was going to try to see if I could figure out what the marks mean. It only uses two symbols, cross and bar. Sure complicates things that they are just like our plus and minus signs, but since there are only two symbols, it's obviously written using a binary number system. It should be simple."

  "Splendorious! Let me help!" exclaimed Shannon with excitement, switching from artistic mode to scientist mode. Adam was glad she was helping, for of all the firstborn, she was farthest along in the Teacher's math program. Shannon looked at the tablet itself in the firelight, turning it around and around, first one way, then the other.

  "That's the first thing we need to figure out," said Adam. "Which way is 'up' on that diagram? That should help us figure out which way the numbers go."

  "We don't need to know which way is up to determine that," said Shannon. "Besides, it could be that whoever wrote
the numbers wrote them from right to left, instead of from left to right ... could even have been written from bottom to top. But, to figure out which way the numbers go, all you need to do is look at the numbers themselves. One end of all the numbers is always a cross, while the other end can be either a cross or a bar. That means the cross is one, while the bar is a zero—you don't put leading zeros in a number."

  Adam felt stupid. He should have thought of that.

  "Well, that makes it easy," he said. "Let me list the numbers that we have, leading cross first. Lessee, the smallest is a two-digit number consisting of two crosses, then three crosses—no other three-digit numbers ..."

  "But three crosses occur twice," said Shannon. "Once in the 'cross-beam' of the diagram of the small house, and once in the 'wall' of the big house diagram."

  Adam paused and put the Teacher in measurement mode. "Let me check that—to see if jookfruit are jookfruit." After a few seconds, he grunted. "Yeppa. The two lines that have the three crosses next to them are the same length."

  "Lemme try something," said Shannon, her brain racing faster than Adam's, her fingers twitching as she reached for the screen. Adam stretched his long arms out to keep the Teacher away from her and she backed off.

  "Measure the height of the two houses," said Shannon. "It looks like the big one is exactly twice the size of the little one." Adam quickly applied the measurement program to the diagram. Sure enough, the dimensions of the smaller one were exactly half that of the larger one.

  "Good," said Adam. That means that the numbers on the large house are twice those of the numbers on the small house. That gives us five equations to work with. Plus, we have two right-angled triangles that we can apply the Pythagorean theorem to."

  "Don't forget, there's another right angle triangle in the slope of that long thing," Shannon reminded him. "We just have to subtract the short end from the long end to get the third side."

  By now, Adam had listed the twelve numbers on the diagram in order of increasing length and started converting them. "If it is straight binary, and a cross is a one, then two crosses is one plus two, or three, while three crosses is one plus two plus four, or seven ..." he paused "Hmm."

  "That kills that idea, doesn't it," remarked Shannon. "In the small house, one side is marked with two crosses, while in the big house, that same side, which is supposed to be exactly twice the size, is marked with three crosses. If two crosses is three, and three crosses is twice as large, then three crosses is six—not seven. It must not be a binary numbering system."

  "But only two symbols are used," replied Adam, bewildered. "It has to be a binary system."

  "The facts are ... that it isn't," said Shannon, taking the Teacher away from him and nestling into his lap as her long slender fingers played over the touch-screen. Adam, his arms now full of well-filled sarong, didn't mind this time.

  The puzzle, however, wasn't easy to solve, even by the nimble brain of Shannon backed up by the calculational abilities of the Teacher, and late that evening the Teacher was turned off and the stone tablet placed on a storage shelf, its mystery still intact.

  The next evening, after their usual communal dinner in the Meeting Hall, instead of gathering with the adults for some evening conversation, Richard went to the children's corner with Freeman to look over the mineral samples that the fifteen-year-old had brought home from his latest expedition. Freeman had them lined up on a shelf, and as Richard picked them up and examined them with his permalight, Freeman explained where he had found them and what he thought they were. The youth was usually right, and even Richard had to call up a color image from Freeman's Teacher to categorize one unfamiliar rock sample.

  "Some of these are unusual enough that they should go into the sample return box," said Richard, picking out three of the rock samples. Freeman felt quietly proud that some of his findings would someday be taken up for analysis on Prometheus, and perhaps even be taken back to Earth.

  "What's this rock?" asked Richard, reaching down to the shelf below.

  "That's something that Adam and Dirk found on the beach," said Freeman. "Just an ordinary piece of hardened lava. Looks just like any other lava sample that you'd get anywhere else on this island. Only thing that makes it interesting is that one side has been cut and polished and marks made on it."

  "Hmm," said Richard, taking out a pocket microscope from his carrying pouch and looking carefully at the polished portion of the stone. "But this lava sample is different."

  "It is?" said Freeman as his father handed him the stone and the microscope.

  "Look how smooth it is," said Richard. "What is the biggest vesicle that you can see?"

  "I can't see any," said Freeman initially, then after looking for a while longer, he added, "now I see them, but they're real tiny." He looked up in partial understanding and partial puzzlement. "This lava sample has the same color and has the same crystal inclusions as the other lava samples I've looked at, so it came from the same volcano, but the vesicle bubbles are really tiny in this sample. How come?"

  "It solidified while it was under high pressure," explained Richard. "The gas and steam emitted by the lava couldn't expand into the big bubbles you normally see in lava samples from Hoolkoor. This uncut side is obviously the original surface of the pillow of lava after it hardened, so there wasn't any pressure from the weight of the lava itself, so the lava pillow must have formed in the deep ocean under high water pressure."

  Richard, being a geologist, had looked at the material in the stone tablet first. Now, he began to look at the diagram itself. "Where did this drawing come from?" he asked.

  "Nobody knows," answered Adam, joining them. "At first I thought it was a Jolly pictotablet. But Chief Seetoo said it wasn't produced by any Jolly tribe known. Besides, the numbering system is wrong. It's obviously binary, while the Jollys use a base six numbering system. On every island we, Spritz, and the stronglimbs have visited, the local Jollys may speak and write differently, but they all use the same base six counting system."

  "It's not binary, either," said Shannon with surety. "In fact, I don't think it has a base."

  "A number system has to have a base," said Adam.

  "The Roman number system doesn't have a base," retorted Shannon. "Each symbol represents a different number weight; 'I' equals one, 'V' equals five, 'X' equals ten, 'L' equals fifty, and so on. But the weights alternate from base five to base ten. In a base number system, the symbols are usually ordered according to weight, but that's not always true for the Roman number system. For example 'I' usually comes after 'V' but not when you write 'IV' for four. In fact there are two ways to write some numbers. Four can be either 'IV or four 'I's. The Romans showed that you don't need a base to make a useable number system."

  Richard, trying to get back to the subject, interrupted. "But what's really important, is: who made this drawing?"

  "Don't know," replied Adam. "But whoever did it made the lines very straight. They are precisely made, as if guided by a straight edge. I hardly had to do anything to the image after it had been scanned into my Teacher."

  "Let me see those lines again," said Freeman, taking the tablet from his father and looking at them with his pocket microscope. "The lines are very straight, while the symbols have a slight bit of waver, and vary slightly in length, like they were drawn free-hand ..." He paused while he scanned all the lines carefully. This is interesting! The bottoms of the lines are rounded and smooth, while the edges are relatively sharp. If the marks were scratched into the surface with a sharp tool, you would expect scratch lines on the bottom, and rough edges where pieces of stone broke away. These marks look like they were etched by a powerful chemical."

  "Well, if no Jolly tribe made this drawing, then who did?" said Richard. "Is there another intelligent species on this moon that we don't know about?" Reiki, hearing the discussion going on between Richard and the children, left the last of the after-dinner pot scrubbing to Everett and Sarah and came over to see what they were talking abo
ut.

  "Another intelligent species?" repeated Reiki. Freeman handed her the stone tablet and she looked at it carefully as Adam and Shannon explained what they had learned and not learned about the diagram.

  "So ..." concluded Shannon "... it's not a binary-base number system, and I have yet to make any logical sense of the symbols as numbers, even though there are lots of right-angle triangles that allow me to check different guesses for the different strings of symbols."

  "I'm intrigued by the fact that Richard said this lava had formed in the deep ocean," said Reiki. "Could there be an intelligent creature that lives in the ocean that we have yet to meet?"

  "An intelligent creature that has the technology to cut, polish, and etch stone—which the Jollys can't do," added Richard.

  "And that need sloped roofs on their buildings to shed the rain ..." added Adam "... under water," he continued.

  "Which probably indicates that this diagram is not of a building," said Shannon.

  "But it is a diagram," Reiki reminded them. "And it does have symbols that seem to be related to parts of the diagram—although whether the symbols are numbers or words or something else has yet to be determined. Whoever made this diagram certainly shows signs of intelligence, and it is important that we find them, meet them, and learn more about them."

  "If they really live underwater, then we have the right allies to find them," said Richard.

  "I'm sure the flouwen would have already told us if they had discovered another intelligent lifeform on the planet," said Reiki.

  "I'm not so sure of that," said Richard. "If it had been Little Red that discovered them, he might have dismissed them as being unworthy of reporting if they didn't know how to surf. But to be sure, I'll show the tablet to the flouwen tomorrow morning at P—" He looked at Reiki and modified his language. "Necessity Beach. At the very least, it will inspire them to look harder and deeper."