The Book of the Ler

by M. A. Foster

  Parleau reflected, and said, “So they are, in effect, feeding us off the top of their system?”

  Eykor interjected angrily, “Programming us, I’d call it!”

  Parleau looked blandly and without rancor at the chief of Security. “There’s no denying that if they are, it’s been to the general welfare. I say, if it works, then let it be. Unless Control can project some nefarious purpose in these manipulations.”

  Plattsman said, “Control until this minute was unaware that we were being manipulated. And I hardly see evidence of detail work, the kind that would be necessary to bring us to some point desirable to them. But I’ll certainly send this through Research, to see if we can prove it, and if so, find out where it’s going.” He spoke slowly, as if unwilling to believe the implications of what they had uncovered here: Control was totally unaware that a more subtle system was probably being applied to them all, a macrosystem involving—and here Plattsman’s mind took a giant, risk-filled leap across normal deductive logic—yes, very likely the large-scale nudging and controlling of the whole damn planet! And for what purpose? As Parleau had most accurately put it, “to the general welfare.” That could not be denied. He added, as an afterthought, “Yes, I’ll have those crazies down in Games-Theory Branch get cracking on it right away.”

  Parleau nodded approval, and said, “I want to hear about that girl and this Game they play. How old is it?”

  Klyten answered, “According to the annals, the Game appeared coincident with the move into the reservation. It seems to be tied up deeply in the popular religion, a kind of movable morality play. They have factions, rivalries, the whole thing. It is very Byzantine, and the fine points are shrouded in layers of allegorical nonsense.”

  Parleau observed, “So they sublimate aggression into sports? That’s nothing new. We’ve done that, ourselves, for aeons.”

  Klyten persisted, “No, no, it’s that there is an aggression present within the Game that isn’t present anywhere else. Literally. And by no means does it reach all the people. In fact, on the whole, the people are rather uninterested in it. Less than half even bother with it in any degree and the number of real fans is probably less than ten percent, counting the Players themselves.”

  The data made no more sense to Parleau than it did to anyone else. He pondered on that for a moment, then asked, “Well, what in hell is this Game? We’re talking about another of these things we can’t see, or are we fishing in the dark there, too?” A sudden light had been illuminated in Parleau’s mind. If he could but penetrate into this system, which he sensed was part of a larger, elaborate plan, then by opening it up, he would pave his way, beyond Denver. If he could only prod these blockheads to find the answers. Yes. Suddenly merely surviving his assignment to Seaboard South seemed petty, unvisioned, lacking scope.

  Plattsman said, “It’s a recursive system. . . .”

  Klyten added, interrupting the Controller, “Yes, recursive. The Game itself, as we see it, appears to be very distantly related to chess, or checkers, but of course it is almost inconceivably more complex than either of those examples. It is manifestly difficult even to try to describe it. . . . They normally play on a two-dimensional field, which can be divided at will into one of several tiling arrays: triangles, squares, and hexagons, those being equilateral and regular, and also quite a number of irregular pentagons and hexagons. These divide the field up into cells. Inside the cell, one can have a number of conditions, ranging from binary on-off two-state on up. I don’t think there is a limit to the number of states a cell can have, although obviously there are some practical limits. The Game begins with some simple, and I use this word guardedly in this context, patterns of states in cells . . . a move in the Game, or a time-component unit, is the sum of all the changes produced by considering each cell, serially, in relation to a surrounding number of cells, sometimes by raw sum, and sometimes by position of cells of different state arrayed about the referent cell. This neighborhood can also be varied, from close in to far away. Then they apply transition rules, some statistical, some arbitrary, and make the changes. When all the cells have been processed according to the program, then the whole changes and they start over again. The object of the Game appears to attain certain desirable configurations in shape and color and dynamics, while the opposing team tries to manipulate certain parts of the rules and other factors to prevent it; but they, too, operate under elaborate rules covering what they can do.”

  Plattsman contributed, “You have to understand recursive math to comprehend the Game.”

  Klyten added one more thought, “We think that this is why they evolved their cumbersome number system of variable-numbers with no permanent fixed base, as our decimal system. It makes it easier to understand the Game, when you have to or want to, in the case of the spectators.”

  Plattsman continued, “We in Control have tried to explore recursive systems also, because the concept is deeply tied up with decision-making, controlling functions, and programming. The concept was first worked out in the twentieth century, about the middle, if I have my history straight. There was an extensive literature on the subject well into the twenty-first century.”

  Klyten said, “They were playing random-start Games even then: just fill it up, more or less randomly, and watch it evolve.”

  Plattsman counterpointed, “But simple Games with unchanging rules and neighborhoods. Most people played on computers when they could get access, but a few fanatics were known to play it on graph paper, some of which they had to have specially printed for the purpose. Absolute maniacs!”

  Parleau asked, “Why the difference?”

  Plattsman answered, “The computer-players could see the motion and the patterns of change, and spot productive patterns faster, but the graph-paper players, while vastly slowed down by the need to run every single step in the program manually, were able to see farther into the scope of it, and the things it could lead to. Eventually, however, they were also forced into computers by the sheer volume of transactions, but they used the computers only as working aids. All ongoing work in the Game tended to originate from the minority Graphists, and what we know from the Archives indicates that the ler built upon one particularly active Graphist faction—one could almost call it a cult—that was active in the latter third of the twentieth century.”

  Parleau shook his head exaggeratedly from side to side. He sighed, looked at the ceiling, scratched his neck, and returned his attention to the group. “Tell me no more! I do not wish to become one of these Players—just relate this unknown girl to what she was doing and why, and why she insisted upon withdrawing into herself rather than answer a few simple questions. I will accept your description of things as provisionally accurate in substance, although I admit to incomprehension. By what means do they control the display?”

  Klyten said, “By a keyboard, something rather like an organ of the old days.”

  “I fail to see why they would devote so much energy to something that demonstrably produces no results. What is the use of it?”

  Klyten observed, “We have been unable to determine that. Obviously it is of great importance to them, and nobody thinks that its sole purpose is entertainment. I mean, after all, the Players have a certain regard, an exclusiveness, but hardly are they lionized as popular figures.”

  Plattsman offered, “Chairman, we have some tapes of some Games material, if you would like to see them. It makes more sense if you can see it in action, perceive the motion in it.”

  “Yes, by all means,” said Parleau. “I would like very much to see this Game. Perhaps we can all learn something from it. You have prepared recordings?”

  Plattsman replied, “We have an extensive file of them, Chairman. Control has been studying the Game for many years. From that, we have selected what appears to be a typical, although short, round of a Game.”

  Klyten added, “This recording was made a few years ago, at their Solstice Tournaments. I have it on the good word of those who claim to b
e authoritative on such matters that this particular Game is a classic of its type, but is rather short in duration. The curtuosity here is after the manner of chamber music, rather than oratorios, symphonies, and grand operas. We mutually apologize, Plattsman and I, for the lack of sound, but none had been thought necessary, since the play is almost exclusively visual as medium.”

  Plattsman motioned to an unseen operator. The office dimmed, a section of the far wall opened, and the panels slid back into cleverly hidden recesses in the walls, revealing a softly glowing screen occupying most of the space between floor and ceiling. After an uncertain pause, the screen flickered, flashed bright momentarily, then went completely dark. Then gradually a moving series of images began to fade in, growing in brightness and contrast until it seemed natural to the viewers’ dark-adapting eyesight.

  The screen showed an open space in the forest, a pleasantly bucolic environment, a natural depression that had been subtly modified into an amphitheater. The show was in color, and though it appeared from the light within to be evening, there was no fading or overexposure; they saw as if they were there. They watched and became absorbed in it. It was a summer evening, deep evening shades and shadows in the small gathering-place of the Players and their audience; they sensed, rather than saw, that somewhere offscreen the sun was yet in the sky; nevertheless it was evening, not merely late afternoon. A subdued, middling crowd was present, all ler, at least as far as could be seen. Some wore summer clothing, light overshirts, loose robelike affairs, which were the everyday, general-purpose ler garment; others wore a garment suggesting a kimono, but with the belt or sash looped and hung loosely over one hip or the other. Many of the younger ones present wore only a saronglike wraparound about their lower bodies, leaving their chests and abdomens bare, while the ends of it fell to their ankles. Even then, with the identical haircuts, it was difficult at first glance to tell boy from girl, to Parleau’s eye. You simply could not differentiate. . . . Only if he picked one and watched it for some time could he determine which sex it belonged to. It was as if the whole secret of defining lay in dynamics and motions, rather than in states-of-being, a disturbing notion indeed. He watched what he believed to be a boy, who was engaged in teasing, very subtly, what appeared to be a girl. What was it, the difference? She seemed softer, more delicate, smoother perhaps. He couldn’t say just what it was. The way she moved, smiled? They were both trying to appear most serious and attentive, but of course it was a summer evening, warm and scented, and their minds were elsewhere, as well they might have been, with the soft shadows falling across the leafy little glade. The one who had recorded this little drama unawares had not even been observing the boy and the girl, for in the image they both were far off-center, and as Game time came closer, he lost them entirely, expanding the image and zooming closer to take in the display board and the Players.

  The board itself was a large, square unit, supported on a simple, broad base, completely unadorned. It looked simple, but in no way did this display board suggest primitiveness, or crudity; to the contrary, it seemed the product of a highly professional technological civilization. Before it was a small, desklike console, furnished with several rows of buttons, while to either side were two larger consoles with imposing multiplex keyboards, which resembled organ consoles more than they did anything else. The Players were already in place, the Reds to the right and the Blues to the left, two Players by each console, and two more behind them. An announcer, was addressing the crowd, apparently in a most relaxed, easygoing manner, as if he (or she—Parleau could not tell) were among friends and acquaintances.

  The announcer finished whatever remarks were required, and then retired offstage with a fluty little flourish, to be replaced by a stern and imposing couple, elders by the look of them and the twin long pigtails of iron-gray hair that hung down the fronts of their garments. Their color was dark; Parleau thought black, although he could not be sure . . . the light of day was slowly fading in the recording. These would be the referees. They made no speeches or gestures to the spectators, but turned to the center console and one of them made a chopping motion with his hand. And on the board, immediately appeared a preliminary figure, a mildly complex geometrical figure in five colors. It stayed in place a moment, winked out, and then reappeared.

  The whole board shimmered, came alive, changed to a hexagonal cellular array, retaining the figure as well as it could be accommodated into the new matrix; a series of indecipherable symbols began flowing across the top of the screen, and the figure began changing rapidly, evolving into different shapes and densities as the initial moves of the Game proceeded. Parleau watched in attentive astonishment, riveted to his plush chair, as the figure first lost all its color, becoming black against the illuminated background, and then abruptly began to change shape, colors flowing over it like firelight flickering over a wall, or perhaps summer lightning. The most basic color appeared to be green, and it seemed that the Reds were trying to control the figure and manipulate it into other shapes, desired configurations, while at the same time, the Blues, just as tenaciously, attempted to hinder this operation and tried to arrange things so that the developing figure would fly apart and dismember itself. The symbols flowing across the top of the screen changed constantly, scoring? A running commentary while the game was in progress?

  At first, despite the interference of the Blues, the Reds seemed to be having the better of it; they manipulated the vibrating figure into a larger shape that seemed more impervious to attack, but this lasted only minutes. Soon, Blue attacked with increased zeal and dedication, their centers laboring mightily over the keyboards, arms and heads blurred in motion, moving faster than the scan rate of the recording device. Soon, the advances of the Reds were blunted, dissipated, brought to a halt. Parleau looked back to the Reds: they were playing, if anything, with even more vigor than the Blues, and as they occasionally turned, he could see that the expressions of intense concentration, indeed, they grimaced with effort.

  Suddenly, a foul was called on Blue, and the referees engaged their controls; the Blues were forced to sit helpless for a measured time, their keyboard locked out, while the Reds advanced and rebuilt their figure into an impressively complex configuration. But when they returned, they reentered the Game furious with zeal, and by dint of extreme effort and a brilliant, virtuoso attack, forced the Reds to give up much they had gained, and in fact, as Parleau remembered, forced them to return to an earlier configuration. A foul was now called on Red, and now they also had to sit helplessly aside while Blue, with glee, dismembered the complex figure. But returning, they did not give up, were not routed, and hung on gamely. The Reds began to advance again, slower now than before, but inexorable, like the tide coming in. Blue sensed that there was nothing to be gained by further delay, and they changed the array to square cells, and after a moment, to the triangular lattice, all apparently in an effort to disorient Red and keep them off balance. At first, it seemed to succeed. Red seemed to lose momentum and drift, uncertain of what to do next. Parleau, now indeed caught up in the swirling patterns of the Game, sensed that this had been a reasonable course on the part of Blue, for Red had, he sensed, been gaining, if slowly. Perhaps this could lead to a stalemate, which would of course favor the defending Blues. But soon it became apparent that the maneuver was to be unsuccessful, for Red was still gaming. They had ridden with the attack, drifted with the changing current, and were now fully in possession of the field again. Blue riposted by a move of desperation, changing the field to a beautifully weird pentagonal tesselation, the cells irregular polygons, and after a moment, back to the square grid. But it appeared to be too late, this rearguard action; the audience was waving little red pennants, while partisans of the Blues stood about glumly, their heads lowered, expecting the worst.

  It was not long in coming: in an amazing tour de force, Red finally manipulated the figure somehow into an astonishing and enigmatic shape, one which hung on the display board screen for a long time, emitting cohe
rent sparks and particles that fled to the edges and vanished. Across the top of the board, the cryptic symbols flowed on for a moment, as if they had fallen behind the action, and then they stopped, abruptly, and without warning the board went blank, dimmed, and went out. Red partisans and their friends waved their pennants and applauded, rather restrainedly, while Blue fans began to walk away, dejected and expressionless. Some, however, despite their loss, also joined in the subdued approval, showing that they could appreciate a good Game, even if their team had lost. One of the centers of the Red team turned from the console and made a short speech. The view expanded, as if the operator had wished to take in more of the crowd; Parleau looked for the boy and girl he had noticed earlier, but they were almost conspicuously absent. The screen went blank. . . .

  Parleau breathed deeply, once. The rest said and did nothing.

  After a time, he asked, “Control, what can you tell us about that particular Game?”

  “We can set up simplex sequences back in the labs; that is, Games with unchanging parameters. Now, this one you just saw,” said Plattsman, “escapes detailed analysis. We think that this one was held to a minimum deliberately, probably varying between three-state and, say, fifteen-to-twenty-state for an upper limit. They use color to symbolize states; in some of the higher-order games, this can get serious, because they have greater color-discrimination than we do. The grid changes you saw yourself. By and large, most cellular arrays are pretty straightforward—equilateral triangles, squares, hexagons. But the pentagonal arrays are all irregular and have some tricky rules; the neighborhood can vary, even when it’s at minimum closest to the reference cell. And the rules! Here is where we really are at sea! We think that none of those remained stable for more than a few moves, two to three. We have to deduce it by effect. They used to say, back in the old days, that one insurgent could tie down ten regulars; it’s the same ratio here: to compute backward takes about ten times the number of computations, and without long time-strings of steady states of rules, that does us no good. The rules are never symmetrical with respect to time—they only work as rules one way. When you try to work them backward and figure back, you get an uncertainty factor. . . .”