Circular Reasoning

     Socrates had lively pupils
     Who enjoyed their little jests
     They gave hemlock to their teachers
     For inventing true/false tests.
     --traditional school jingle to the tune of "Rueben, Rueben"



    She looked up from her journal and smiled, brushing a wisp of hair from her eyes. "Yes, Marrim, what is it?"

    The younger woman gestured towards the green and blue glass doorway. "I need to look over your notes on water. I'm having trouble with the weather in my new Age."

    "Go on," replied Catherine. "You know our library's open to those who respect it."

    Marrim smiled tightly at the particular wording, and headed into the other room.


    Some hours later, Marrim awoke to Catherine shaking her gently, and found her face pillowed against her forearm, pen still in hand and a sheaf of notes beside her on the worktable. She blushed and sat up. "Goodness. What time is it?"

    "After dinner. As well for you Eedrah was not expecting you back tonight. You should come eat something."

    Marrim glanced around the table hurriedly, making sure she hadn't squashed Catherine's journals. "Yes, just let me just put everything away."

    The older woman was already moving to do so, but paused as she picked up the first of her own notebooks, noting the volume. She lifted an eyebrow quizzically at Marrim. "Water experiments?"

    The girl ducked her eyes. "I was distracted. I've never seen your Terahnee notes, and Eedrah doesn't like to speak of it."

     "And so that is what you have been doing all afternoon, reminiscing."

    Marrim looked away. There were some memories one had to honor by keeping them fresh, for the sake of those who had died, but they were not pleasant ones. "Not entirely." She turned back and said in a hushed voice, "The 'closed circle?'"

    "What about it?"

    "It's more than just the resealing of D'ni from Terahnee, isn't it? You speak of time and prophecies, things Seen, things destined to happen." Marrim sounded less dazed from sleep than from several hours of thinking.

    Catherine pulled up a chair and settled beside her, glancing over the passages from her own journal which Marrim had meticulously copied out. "Yes," she said quietly. "Do you agree with my findings, such as they are?"

    "I'm not sure I know what they are." Marrim struggled for words, and eventually pointed to the top page of her notes. "Garternay. Ten thousand years ago its people migrated to the Age of D'ni. Five or six thousand years ago the Terahnee left, and there was 'a period of forgetting, so traumatic and so violent that it was a wonder anything survived to tell that tale.' A thousand or so years before Kerath." She paused, again caught up short by sheer awe at the immense age of the D'ni civilization.

    "Go on."

    "There were prophets in Garternay, some of whose words survived in collections on both Terahnee and D'ni. And they are real." She read one aloud. "'A burrowing worm blinks in the sunlight and pulls his eyes down over his eyes. Earth's mouth steams. Deep voices grumble. Time draws a jagged line upon the sand in which the woman waits.' That's the expedition Aitrus participated in that almost reached the surface, when the Council decided they should turn back. And the woman who lives in the fault zone is Anna."

    Catherine folded her hands in her lap, letting her student trace her mental path step by step. "Perhaps."

    "'He who numbers but does not name: It is he who heralds the coming tragedy. His footprints lay about the muddied pool.' Gehn, yes?" the girl asked carefully, mindful of making a verbal misstep. "He numbered his Ages. Although I don't know about the pool."

    "That part also fits," Catherine replied gravely, "from what Atrus has told me."

    "Atrus is the child who saw flowers in the desert, and a pool of stars, right?"

    Catherine relaxed back into a smile. "Undoubtably."

    Marrim circled in on her thoughts. "So all these things were seen by someone, long ago, in Garternay. So precisely, so perfectly. You say: by the Maker, and the Great King."

    Catherine leaned forward. "Yes."

    The girl shook her head slowly. "So Atrus had no choice in his whole life? He was simply fulfilling destiny? A 'thread of happening that was stitched into every aspect of Atrus' life', leading him to accomplish some purpose." She scowled. "As if somehow all those disasters, from the time Anna came to D'ni until you imprisoned Gehn, were directing Atrus' life towards the moment when he unearthed the Book of Terahnee, just so he could rescue the relyimah, even at the price of the plague."

    "I did not say he had no choice," Catherine said quietly. "He knows none of this, nor would believe it if he did. He chose each of his actions, alone, of his own free will, due to his nature: which was shaped by the humility Anna taught him, which in turn was shaped by what she saw in D'ni. Cause and effect are in their proper place. But someone forsaw all of this."

    "Or--" Marrim stared at Catherine sharply-- "simply recorded it, which makes far more sense than prophecy."

    Green eyes locked with hers. "What do you mean?"

    Marrim pulled out another page of her notes and read it aloud, voice shaking slightly. "'Written as he was, Atrus nonetheless wrote his own path, like a Linking Book back to himself.'"

    Catherine smiled faintly. "Written in the sense that prophecies were written about him, Marrim. I do not mean he was in a Descriptive Book, save perhaps in the hands of the Maker of us all."

    Marrim looked unsatisfied. "The closed circle." She returned to the phrase again, tasting it. "Catherine. Can one Link to a different time?"

    Catherine's expression became positively Sibyllean. "That is the question, isn't it?" She spread her hands. "Suppose one can."

    "Then," Marrim said slowly, "One could, accidentally, write a Link back to one's own Age, at an earlier time."

    Catherine shook her head. "No. One can never Link back to an Age without using phrases and key words drawn directly from its original Descriptive Book. No more can you write a Link to any place in the same Age, unless you are standing in that very place and, again, have phrases from the Descriptive Book to anchor the link."

    "But then, there is this problem." Marrim tapped a fingertip against the desk. "I have always wondered how the D'ni could have discovered the Art. Consider the Art's original inventor. He had to Write a Descriptive Book. Then, someone had to be the first to test it, to step into the new Age. But how did that someone get back? He had to have a Linking Book back to D'ni, before he left."

    "Did he?"

    "You said the Linking Book to an Age has to include phrases and words drawn from the Age's original Descriptive Book, or it won't work. So... he had to copy from the Descriptive Book of D'ni."

    "Right. Maker knows where it is now, of course, but there are certain phrases every Linking Book back to D'ni must have, in one variant or another, which presumably come from that original Descriptive Book."

    "Well, that works only because we now know D'ni was written as an Age. But if you take a step back to Garternay, how did the first person mad enough to test a Descriptive Book link back to Garternay to tell them he'd survived? I can't imagine Ri'neref Wrote D'ni, and then all the people of Garternay, en masse, linked to D'ni, without finding out whether the Art actually worked. Or even enough people to form a colony. It would mean fifty, a hundred, maybe even thousands of people choosing to give up their lives and link into an Age with no guarantee their journey would take them anywhere, still less that it would be a good place to go. They would only risk the experiment if Garternay was also an Age, so that they could Link back to it."

    "But then you're simply pushing the problem of the Art's inception back a stage. In that case, who Wrote Garternay?"

    "Atrus!" Marrim blurted out. "He's doing it right now!"

    Catherine eyed Marrim levelly and did not speak.

    Marrim took a deep breath. "You said it yourself! 'Atrus wrote his own path, a Linking Book back to himself.'" She brought her hands together, index fingers and thumbs touching. "The closed circle."

    Catherine exhaled slowly. "Yes, I did say that, didn't I?"

    Marrim paused, looked at her doubtfully, and continued at a more careful pace. "You said one can never write a Linking Book back to one's own Age, without using phrases from its Descriptive Book. But the problem with the Art is that whoever invented it couldn't return from his visit to his first Age to tell anyone it worked. Unless it was never invented. Unless time is a closed circle, in which the Art has always existed, because in that case, the question of 'invention' is eliminated." She looked up. "There's nothing that says we can't write the original Descriptive Book of Garternay. Only that we can't write a Linking Book to it, without the Descriptive Book in hand for study."

    Catherine nodded. "Assuming Books do not always have to link to our current time, yes. So. But you have a problem, once you have created this closed circle."

    "All kinds of problems." Marrim pressed the bridge of her nose with her thumb. "Because what happens when we step onto Garternay-- if that's what Atrus is writing now? Will time start repeating itself? Will we hit a terrible contradiction and explode? Will everything start unravelling?"

    "You're making a big assumption that Garternay is the Age he's writing now, which is a separate matter from whether time can be circular. But you're right. The Closed Circle theory would explain best the contradiction of how the Art was first invented. So let us explore it." She played with one of the strings of beads in her hair. "Ah. It would not be repeating, Marrim. Because it is a circle, not a spiral."

    Marrim shook her head. "Yes, but--"

    "Allow me." Catherine picked up her pen and began to draw carefully below some of Marrim's scribbles, which happened to be a circular diagram of the D'ni timeline crossed out sharply.

    "Think of it this way," said Catherine. "The spectrum of colors follows a sequence, yes?" Marrim nodded and watched attentatively as Catherine proceeded to sketch out the D'ni color wheel, a circle of circles. "Now, each one flows into the next, smoothly. Sometimes we find them following a linear sequence, as in a rainbow, where the pattern may repeat but the red at the top never circles around to join itself. Other times, as here, it can be a circle. Has this red--" she tapped the appropriate bead-- "been repeated, just because I have positioned it within a circular sequence? Or is there only one?"

    "Just one," Marrim was able to say, relieved that some things, at least could be answered simply.

    "Just one," Catherine echoed. "It flows smoothly from the sequence of colors before it, and connects with those immediately after it, but although part of the sequence and the pattern, it is not altered by the pattern's overall circular shape."

    Marrim frowned. "But it's static. I mean, none of the 'colors' there have free will, so to speak. They're dictated by whatever happened before them. Once you seal off the circle, don't you have a case where everything's already happened, ergo, nothing in the timeline can change-- because it would be a paradox if one altered the timeline? That explains the prophecies; they refer to things further along, which are predetermined. And it explains what you said about Atrus following a path laid out for him. But it eliminates free will entirely."

    "Following a path forseen is not the same as following something which is ordained, designed." Catherine tried a different approach. "Atrus wrote Averone, correct?"

    "Yes--" Marrim caught herself, smiling at the trick. It was, after all, the first lesson Atrus and Catherine had taught her. "No, he only wrote a Descriptive Book which matched Averone, and therefore created a Link to it."

    "And Atrus and I arrived there on Averone, just as the D'ni first arrived in Earth. But you still have free will, in spite of his writing the Age of Averone."

    "But that's not a circle, so we don't have the same paradox."

    "It helps, though. Even if Atrus wrote-- is writing-- Garternay, he did not create it, still less set in stone the events that would follow its creation. He is not writing who the D'ni are, or what they will do once they arrive there. He is not predetermining their history. So writing an Age does not affect the free will of its inhabitants."

    "It still doesn't solve the problem that-- that--" Marrim waved her hands, trying to articulate the question. "Say we're drawing to the end of the circle. We finish this time. We go back in time, and now, suddenly, Atrus and all the surviving D'ni are their own ancestors. It breaks the law of evolution. That makes no sense!"

    "Finish?" Catherine asked sharply. But after letting Marrim ponder that word for a moment, she addressed the objection. "Evolution dictates slow change. Usually over a period far longer than the history of D'ni, and perhaps of Garternay. So it may not apply here any more than two-dimensional geometry applies to gravity. But yes, by chance evolution would not create, after however many thousand years, the exact same individuals at the so-called end of the cycle as existed in the beginning. But we're not talking about a chance event, nor two groups of people. We're talking about a group of individuals who connected back up with that past time. And as for being one's own ancestors, there's plenty of generations between now and then to eliminate any problems caused by inbreeding, don't you think? It's a staggering possibility. But there's no logical reason why one couldn't be one's own ancestor, if one could 'go back in time', as you say."

    Marrim fell silent again, chewing on her lower lip. Sensing this, Catherine began to unwind one of the strings of beads from her braid. "You are still troubled about the idea that, when we get to the end of this circle, we will go back in time, and start repeating the past, yes? And that, since it has already happened, all events are fixed."

    Marrim nodded slowly. "Right."

    "Well. I think it is because you are still seeing things in a linear way, so long as you speak of 'end' and 'beginning'." Catherine laid the string of colored beads along the table, unknotted one end, and unthreaded about a third of them, scattering the beads along the table with a soft patter. "Here is the D'ni history so far," she said, running her finger back along the beads that were still strung. "And look! Here is Garternay," she said, pointing to the first several. "All laid out, moment by moment, year by year, event by event. You can't change them, yes? Because they're behind you. But what about the future?"

    Marrim looked at the unused beads. "Like an Age," she said softly. "There are certain parameters, in that one has to use beads. But shape, color, size, are a matter of choice."

    "Precisely. Only with far more variables. Choose a bead."

    Marrim did, obediently, threading a sparkling blue one onto the string.

    "And was that dictated at all by the pattern that came before?"

    "No," Marrim said slowly, "Except that I think it complemented the colors behind it."

    "Exactly. But you could have chosen a different bead, or seen a different pattern you thought more appropriate to match. Your options were simply limited by the beads available. In the same way, our choices are dictated partly by experience, partly by the constraints of the moment. Keep going."

    Marrim thoughtfully threaded several more along the string.

    "Stop." Catherine took the string from her and, carefully, tucked the ends of the "future" thread back around into the "Garternay" thread. "Oh dear. Now see. Is time repeating itself?" She touched the last "future" bead, followed by the first of the "Garternay" beads.

    "No," Marrim said slowly. "There is only one of each event, following in sequence. Like the rainbow."

    "It is not a matter of repeating, unless you make a spiral. In a circle, all the events simply connect."

    "And I suppose it's more logical, in some ways, than postulating that time has a finite starting point, which linear time requires. I've always had trouble thinking of a 'start' before which nothing exists." Marrim pursed her lips. "Each individual part of the circle still has the choice, at the time it's being formed, to shape its own part of the circle. It didn't matter what the shape of the Whole is. Its choices are dictated only by that moment--" she touched a couple of beads-- "when green decides to go to red next."

    "The shape of the Whole is fixed, but each bead represents a moment of choice." Catherine let that sink in for a little while. "Now, this is very important: the hinge of the argument, if you will. There is no way to alter the timeline or to break the circle once formed. There is no 'what if I had chosen a wooden bead instead of glass?' There are infinite possibilities, at each moment, but once you have selected one, it is fixed in place. You could have made a different choice, but you didn't; you made this one. Just as, when a tree grows a leaf, it can make it any shape, but once the leaf is grown, the tree cannot go back and regrow that same leaf in a different way. Do you see that?"

    "I think so," Marrim said softly, trying very hard to hold onto the train of thought.

    "A past choice simply is-- not because it's ordained or dictated, but because that's just how it happened to be. Living within the consequence of your own actions, there is no way to go back and explore other possibilities, other choices, which might contradict the events that got you where you are today. But that has nothing to do with the circular timeline. The same holds true even if you say time is linear: it happened, so it is. This would be more obvious to us, if we were able to see the Whole in four dimensions instead of three."

    Marrim's eyes lit up. "What we are describing is simply a circle in four dimensions!"

    Catherine smiled. "In a manner of speaking."

    Marrim exhaled. "So Atrus is the blue bead that decided on red, and the red bead he decided on happened to be the beginning of the string."

    "Not quite." Catherine ran her fingers slowly around the necklace. "There is no beginning, and no ending, here."

    A heavy silence fell. The two women looked at the sparkling beads suspended from Catherine's splayed fingers, all the various colors and shapes. Marrim sighed at last.

    "The Maker designed the circle."

    Catherine's eyes met hers through the open loop. "Whatever shape time has, the Maker's hand is behind it. But just as we do not write Ages, only describe them, the Maker has given us free will to determine what happens in this time, what we make of our world and our lives."

    Marrim dropped her eyes respectfully. "So," she concluded, almost dreading the answer, "do you really think Atrus is writing Garternay?"

    Catherine chuckled. "No, of course not." She pulled the ends of the beaded string apart, and began threading the remaining ones.

    Marrim gave a nervous puff of laughter. "Oh, good."

    "I believe in prophecy," the older woman said demurely, a teasing light in her eyes. "It explains everything so much more simply, without need for elaborate time-circles to explain why ancestors could have records of the future."

    Marrim made an exasperated snort. But before she could respond, the doors swung open, revealing a befuddled and beleaguered Atrus. "Catherine?" he said plaintively. "Yeesha says there's a wahrk under the bed, and it won't go away until her mother sings to it."

    Catherine's laughter spilled into the room as she turned and headed for the door. "Well, we can't have that, can we?"

    Marrim smiled, staring after her mentor with the bleary gaze of one whose brain was beginning to seep out of her eardrums. "I will never understand her."

    Atrus cocked his head at the slight awe in Marrim's voice and leaned against the doorframe, face relaxing into a tired smile. "Nor I. What conundrum in particular has brought you to this conclusion, Marrim?"

    Marrim sighed. "A long story." She pushed her chair back and began collecting up her notes. "Perhaps I'll tell you about it when I have energy left to think again." He smiled and moved towards the desk to help her, but she shooed him away with a wave of her hands, not really wanting to discuss Catherine's notes on prophecies with him, any more than she wanted to remind him of Terahnee. "I'll take care if it, Master."

    He had come to learn the unspoken nuances when she chose to address him formally, and stepped back. "Very well. You really should take breaks now and then. I know how easy it is for work to swallow all of your time."

    With that he left, leaving her much bemused at his parting words. As she set the books back on the shelf one by one, still hearing the sound of his voice in her mind, her thoughts drifted to another of his sayings, from that all-important journal he had written so long ago.

    "...I close, realizing that perhaps the ending has not yet been written."

    "But circles," she whispered to herself, "never end."