The Library of Laplace

(With apologies to Jorge Luis Borges.)
The universe, which others call the cellular automata, is composed of an indefinite (and perhaps infinite) number of square rooms, each room having four doors (in what we can, for lack of a better choice, assumelie in the cardinal directions of north, south, east, and west.) Each door leads to an adjoining room which is identical to the other rooms except for one salient feature. In the middle of each room stands a monstrous monolith whose color is not fixed, but changes regularly every forty two seconds.
Like most inhabitants of the universe, I have often contemplated the mysterious workings of the monolith…

For many years, when heathens beat their chests and ran amok across the universe, it was thought that the colors and their changes were a sign sent from the heavens to signal to the inhabitants of the universe how they should live their lives. One cause of this unorder was that the color shadings of the monolith were subtle. Which is to say that one man’s atrous was another man’s melanic. Thus these olden days were filled with wars of epic proportions, where the meanings and differences between the colors caused the heathens to fight hand to hand across the halls of the universe.
The first discovery which brought civilization to the universe was the finding, by the autodidact Roy G. Biv, that the colors of the monoliths were not arbitrary. Biv, as his associates always called him, was playing one day with a piece of glass left over from the recently finished “Battle over Mauve.” Curiously this piece of glass was of a shape which had been called “prism,” a word whose origin has been lost to the ages of time but who some claim had mystical origins. Biv had been having some problems at home and had thus been outcast four rooms north and five rooms east of the room he inhabited with his wife and four children. In other words, he had some time on his hands. Biv noticed that by using some cardboard (also left around from the Battle) he could direct the light from the monolith into his prism shaped piece of glass. When he did this, to his amazement, a distinct line appeared on a part of his cardboard contraption, apparently emanating from his prism and of the same color as the monolith.
Curious, Biv scratched into the cardboard a line where the first color he saw had appeared as a line. Forty two seconds later, when a new color appeared, Biv excitedly noticed that the line for this new color did not appear in the same place as the former, but appeared in a slightly different location. Many hours later, Biv and his cardboard contraption had a large number of markings for different colors, but already Biv had seen the same line appear many times. There were many surprises in these lines. For example the colors aubergine and magenta, which a certain tribe five hundred rooms to the east swore were the same color, appeared with different lines! Thus this heresy for that tribe was something that did not need to be fought over, but could be resolved by using Biv’s contraption. If the lines were different, the colors were different.
And thus began the age of monolith spectroscopy. For many years following Biv’s discovery, Bivometers, contraptions like Biv’s prism and cardboard construction, were invented, refined, and put to use in an ever widening circle of knowledge within the universe. Biv himself discovered that there were exactly 255 different lines which would appear in his Bivometer (which he never called a Bivometer, but instead called a triangular prism spectrometer.) I have traveled far and wide across the labyrinth of square rooms, taking my hand held Bivometer with me wherever I go, and have yet to observe a room in which exactly those 255 different lines did not appear. Indeed this has become a central dogma of the universe: that the monoliths can appear in only 255 colors, no more, no less, and these colors are the same in whichever direction you should choose to walk.
The age of monolith spectroscopy was marked by a sharp increase in the precision with which wars could be waged in the universe. Now instead of arguing over the colors of the monoliths, one could argue instead over what the monoliths were actually trying to say to the inhabitants of the universe. With great care careful observation of a room’s monolith could be performed, and this record of colors could then be translated into a message from the deity which inhabited that monolith. But one man’s cyan, cyan, fuscous, indigo, while being seen as the same colors by co-inhabitants of a room, would mean to one person that they should marry the neighbor to the north, and to another person it would mean exactly the opposite (that one should not marry to the neighbor to the south.) Long sequences of monolith colors, inspired great and bloody battles, epic poems, and many romantic love triangles. The age of monolith spectroscopy was the age of the song of the monolith colors.
For many years the age of monolith spectroscopy reigned and pressed its strange kind of order across the universe. But then a journeyman who made it his purpose to see as many rooms as he could in his lifetime passed through this very room and told my grandfather of a startling discovery made some five thousand rooms to the north and two thousand and fifty nine to the east of here. This journeyman, who went by the moniker Update, told my grandfather of a startling discovery of order in the universe. It had long been noted that the colors of monoliths in adjoining rooms changed at exactly the same time. By standing with your back to one of the monoliths one could look through the door to the adjoining room, place your hand in front of your face, and see the color from the monolith in your room reflected off your hand change at exactly the same time as the monolith in the adjoining room. This fact had long been noted, but little remembered.
But the journeyman told my grandfather that recently he was talking with an old gentleman who claimed that if one were to look not just through one door, but through each of the four doors, at the same time, one could, depending on the colors in those rooms, and the color of the monolith in your room, exactly predict the next color your monolith would be in the next time interval. Such heresy, my grandfather had never heard before in my life, and he covered his ears upon hearing it so as to not let more such visions of order enter into his head. That the color changes of a room’s monolith depended only on the color of the monolith and the colors of the four adjoining room’s monoliths? What madness! The number of ways that four rooms plus ones own room can each take on 255 colors is 255 x 255 x 255 x 255 x 255 = 1078203909375, a very large number. When one considers how long it would take for each of these different colors to appear, even assuming every combination where to appear once and exactly once, over a million years would be needed write down all of these combinations. How could anyone claim that there were rules such as those described governing the colors of the monoliths?
But like all madnesses, what one generation sees as absurd, the next sees as an opportunity. And thus my father, who had learned of this possible order in the universe from his father, took up this idea and began to ponder it more deeply. Having nowhere to start, he began by make a few tens of thousands of observations of the color changes, obtaining a huge catalog of six columned data. The first column contained the color of the monolith, the second through fifth column contained the color of the monolith to the north, east, west, and south, and the final column contained the color the monolith changed to under those previous five columns conditions. This list my father and his associates guarded as their secret treasure. Secret, for if the ruling faction of the local area of rooms ever found out about this list they might expel or even execute my father and his associates for heresy of the highest order.
For many years my father studied his lists. I remember fondly sitting beside him on the ground in the room in which I was born, watching him stare, deep in thought, at his laboriously constructed lists. And then, one day, my father disappeared. My suspicions were immediately for the local junta who were worshipers of the azul means war sect, and felt they had probably snatched him away and murdered him in a room not to far from my own. Adding to my suspicions just following my father’s disappearance, a strange rumor began to spread. This rumor had to do with the way the colors changed in the rooms. In particular when one took a Bivometer the lines produced could be laid out in a line and onecould pick a dividing line between what one might call “top lines” and what one might call “bottom lines.” The rumor was that if one looked at the colors of the four adjoining rooms and the color in your own room, if more top lines appeared in those five monoliths, then your monolith would change to one of the top lines. If more bottom lines appeared in those five monoliths, then a bottom line would appear. While one didn’t know how to predict which bottom and which top line would appear, one could be certain that if the majority of colors you could see (including your own monolith) where top lines, in the next 42 second interval your own color would be a top line.
Upon hearing this idea, I immediately thought that my father, whose name was Toom, had probably been the source of this rumor. And because rumors can spread outside the grips of tyranny, it soon became known that this rule was in fact observed to be true! This discovery, of course, made me cry for my lost father, and rocked our understanding of the universe to its foundations. There was an order in the way in which the rules changed which had nothing to do with the desires of a deity, at least when it came to top and bottom lines, but instead was completely and totally determined by the monoliths color and the color of the monoliths in the adjoining rooms. News of this result spread out in a circle of knowledge from my local community and bounced back to us with news that indeed this observation holds true as far as the news has traveled.
Thus the secrets of the monoliths began to be unlocked, and a new generation, my generation, took hold of this idea and began to explore deeper and seriously the idea that the color changes of a monolith depend only on its own color and the color of its neighbors. Beyond the law which became known as Toom’s rule, we soon began to unravel deeper and deeper order in the patterns of the color changes. Many revolutions later we know have a master rule, first written down by a good friend of mine known as Laplace–a rule which generates in a simple and elegant manner the answer to the question, “If the monolith in my room is color X and the adjoining rooms monoliths are N,E,W, and S, then the monolith in my room will change to color Y.” These rules have never been found in error, except by charlatans who play tricks with colored paper to fool gamblers who should know better.
And thus the age of Laplace has begun. Since the monoliths have now yielded an order which is so profoundly simple, harmony has descended upon most rooms in the universe. Today inhabitants are soothed by the slow stead change of the predictable monoliths. All one needs to know is the color of your neighbors monolith and your own to feel you know what will happen in life. Life lived in forty two second intervals is as simple as equations plus some small observations.
But lately, at night, when I’ve covered my face in my bed to hide the monoliths glow, I wonder and I worry. I worry about that exact instance where the color of my monolith has changed, but the light from the adjoining rooms has not had time to get to my eye. In that instance, which I cannot observe, but I know must exist, I know the color of my monolith, but I do not know, I cannot know, the colors of the adjoining room’s monolith. In that instant, I cannot predict how my monolith will change. Those with whom I’ve shared this nightmare simply glaze over and respond that such hypotheticals are the tools of evildoers who will wreck havoc on the order of the monoliths. And so I’ve kept this idea to myself and shared it with few. But at night, when others are asleep, my dreams are of that instant when I cannot predict the future, when the light from the adjoining room is old information, and the future is wonderfully, beautifully, undetermined.