As more and more messages accumulated, the physical size of the information “bits” has to shrink to be accommodated. Not a problem in the magical mathematical realm of a manifold, but in the real world—Eron could hear the Founder smiling—things got hairy when the Bureaucrats of Filing were eventually faced with the archival problem of finding space inside a cubic Planck-length for, say, the history of the Emperors. Yet how have bureaucrats everywhere always solved such an information overload problem? They condense the original into a brief memo, hide the memo inside the papers on their desktop, and hand the original report to an office boy with orders to lose it. Physicists have invented a fancy name for this bureaucratic procedure—they call it decoherence.
Of course, by time-symmetry, the events of the future were also sending messages to be stored in the same bulging cabinets and getting the same treatment. “Hello. This is your future speaking. Have I got news for you. But please make room in your storage space for my message.” Those famous branchings into alternate futures (the classical emperor-in-a-coffin conundrum) weren’t branches into other worlds at all; each branch simply represented one question (“Is the emperor alive?”) that was unanswerable because the procedures of the Bureaucrats of the Present didn’t yet have a place to store the answer. A bit of information about the past must be erased to make room for every new bit of information about the future.
Definition: The information content of an event, in bits, is exactly the number of yes/no questions needed to differentiate it from all other possible events. Consequently, if information is never lost—a deterministic requirement—any message describing an event had to carry from the past to the present exactly the same number of bits as were in the original event. Was it possible for such a transmission to be lossless?
The Founder was making sport with the determinists, catching them, teasing them, tweeking their noses, and letting them go. How could Remendian ever have mistaken this cat for a mouse? The Founder waxed with exaggerated humor about the trials and tribulations of a deterministic universe in which information conservation was a fact: every event that had ever happened was still out there transmitting its own information load, clogging every possible transmission line of space-time in a simultaneous attempt to wash ashore onto the present.
Eron tried to comprehend the preposterous magnitude of such a load. A whimsical analogy crossed his mind. He imagined the communication network of Splendid Wisdom burdened with the continual lossless transmission of every message that had ever been generated on Splendid Wisdom for the last fourteen millennia! Somewhere in there would be a wandering packet carrying Thanelord Remendian’s deathless order for breakfast on the morning of...consisting of three pig embryos in buttered thyme sauce on toast. He laughed, imagining the fate of a universe whose very survival depended upon the pristine maintenance of that message!
So much had been lost.
The universe was still here.
The Founder wrote out equations that illuminated the error.
Deduction: Determinism requires a transfinite channel capacity in order to maintain the transmission of all of its lossless messages. Space must be infinitely divisible.
At that point in his essay, the Founder took off his gloves. In a mere four lines he developed the formula for the real channel capacity of space. Prominent in the formula was the Planck length. The bandwidth of the universe wasn’t great enough to deliver the past’s messages losslessly to the present. Nor the future’s messages losslessly to the past. The real universe seemed to be “printed” in an “ink” whose “particle size” could never be less than the Planck length.
The Founder proceeded to outline some of the ways in which the universe was known to lose information.
1] What drops into a black hole can’t get out again, not even under time reversal. Black holes eat information permanently. Loss of information creates more uncertainty about the past, which is the same as saying that the information consumed by a black hole increases entropy.
2] Information is stored ambiguously at the quantum level to conserve bandwidth—for instance, data about position and momentum overwrite each other in the same “registers”—playing havoc with a physicist’s ability to pin down past or future. To operate in the present the universe never needs to know a particle’s position and momentum at the same time, so it doesn’t store that information independently.
3] A physicist may predict the pattern of hits that an electron beam makes in passing through two slits, but he cannot predict where any particular electron will hit; that information involves processes that are not derivable from any initial condition. The universe minimizes its use of bandwidth with such a compression technique. A physicist can look at a particular “hit” after the fact but cannot then backtrack the path of the electron that made the hit.
4] A physicist can predict how many alpha particles will be ejected from a gram of uranium in the next jiff; but he cannot tell you when a particular uranium 238 atom will changes State to thorium 234. Worse, the wave equations that describe uranium’s radioactivity, by time-symmetry, say that uranium has the same half-life whether it is moving forward or backward in time. But we know that the atoms in the uranium 238 sample we hold in our lab have been stable for the billions of years they have existed outside the supernova that created them! Quantum mechanics will not allow us to assume that, if we reverse time, these same uranium atoms will all remain stable for the billions of years it will take them to travel back to their mother nova. Bandwidth is limited. The universe eliminates inessential information. The uranium will not be able to return through time via the same path by which it arrived because the information that described that path no longer exists. A uranium atom’s moment of death is independent of its history.
The Founder concluded his discussion of physics with an elegant proof that in a deterministic universe, since nothing can be uncertain, entropy, the measure of uncertainty, must always be zero and so cannot increase. In a world without information loss, thermodynamics is impossible. Constant entropy is another word for stasis. Very little of interest could exist under a deterministic regime.
Eron threw the book across the room and sat down cross-legged on the floor to sulk. It was a mighty sulk. If entropy increases and information is lost as we move into the future, then entropy must decrease while information increases as we trace events back into the past. That was only logical— but how could such an antisymmetric conclusion square with the time-symmetry of physical law? Eron cried himself to sleep. He couldn’t understand the simplest things anymore. He was a moron, an animal!
But when Eron awoke, he understood. His sleeping mind had resolved the dilemma—a joyous miracle to Eron. It had produced a simple model within which even a famless mind could play. Its laws were time-symmetric. It was not deterministic because its future was only partially predictable and its past was only partially knowable. The model contained no arrow of time; entropy increased regardless of whether one took the model forward or backward in time.
He had dreamed a circular necklace of beads along a wire, the black and white beads stationary, the mobile blue beads always moving either clockwise or counterclockwise.
1] The black beads sometimes changed state from black to white—emitting a mobile blue bead as they did so with equal probability to right or left.
2] A blue bead passed through any black or blue bead it hit but was absorbed by contact with a white bead.
3] When a white bead absorbed a blue bead it changed state from white to black.
4] The black beads emitted their blue beads with a random frequency dependent upon how many blue beads had passed through them.
A simple universe.
At time zero, knowing which beads were black and which beads white, how could the future state of the necklace be predicted? What had been its past? Because of time-symmetry, both problems were the same. Because the system was nondeterministic, neither the future nor the past could be known with certainty, but the proba
bility of any particular future or any particular past could be computed absolutely. From those probabilities one could compute the uncertainty—the entropy—of any future or past. Entropy increased as the model was stepped into the future, and yes, just as the Founder said, the entropy increased as the model was stepped back into the past.
In a deterministic universe where each action had its certain outcome, reversibility and time-symmetry were the same thing.
But in a probabilistic universe, reversibility and time-symmetry were very different concepts.
So much for Eron’s wishful desire to go back and start all over again as a twelve-year-old; to time-travel back to his younger self he’d have to violate all the laws of thermodynamics. He laughed.
The equations of motion for smashing a goblet against the wall were exactly the same as the equations for assembling a goblet out of flying pieces of glass—but the probabilities were vastly different. The picture was beautifully time-symmetric. A process can be totally reversible—yet what is easy in one direction can be daunting in the other.
Eron felt reborn. It was exhilarating to find out that he could think without a fam—even if he did his best thinking while asleep. The feeling made him smile again and again. He picked the Founder’s book off the floor and began again at the beginning. He still had to struggle with the words, pronounce them until they made sense, read and reread the sentences. He found the place where he had left off and smoothed the battered page. He was beginning to understand how an unaided brain functioned—a problem he hadn’t faced since he was three.
The Founder continued:
In our search for the future does a lack of deterministic equations cripple us? Not at all.
Our psychohistorical tools CAN predict the critical branching points of our most probable social futures. Complexity has its own metalevel of simple modes. We can predict social structures to a high degree of accuracy along a millennial time scale just as physics can predict the orbit of a given planet on a scale of thousands of years. We do not pretend to predict the life of a single individual just as the physicist doesn’t pretend to be able to predict the path of a molecule in his given planet’s atmosphere.
We compute many futures, not all with the same likelihood. It is not pleasant to see, dominating the timescape, a full 30,000-year galactic-wide interregnum, but our math has examined less severe, if much less probable, branches. One under current investigation promises a simpler dark age on a much-collapsed time scale. There are nudge-nodes where the probabilities can be drastically altered by small forces within our command.
Can there be a nonfatalistic role for individuals in our branching vision? Of course! Our large sample-size social model assumes that SOME humans will take advantage of ALL of the degrees of freedom permitted. Psychohistory shows us ways of constraining various degrees of freedom so that...
On the other hand, psychohistory does not allow us Thanelord Remendian’s Total Freedom. Freedom unrestrained implies that every equation of action will contain an Infinity of Solutions—forcing the future to be totally unreadable. All prediction becomes impossible once every event is equally likely. Try speaking without being able to predict what your mouth will do. Try reaching for a glass of water when your fingers refuse to obey the constraints of any physical law. Without prediction, power cannot be applied rationally; even omnipotent power is helpless.
Psychohistory is neither deterministic nor licentious. It defines the constraints under which history must unfold and spotlights the low-effort choice points. Our model operates within a phase-space. The degrees of freedom allowed are far LESS than the dimensionality of the space of “total freedom” but far GREATER than the “deterministic” model which allows NO choices at all.
Gently Eron lowered the sacred book into his pocket. He wondered how much freedom he had left. Steady reading with little sleep had tired him, but he felt good. The exercise had pulled up fresh memories. One of the images was especially vivid, but he couldn’t place it. He saw a public square
in front of a hotel, yes, on a strange planet whose name escaped him. When was it? Well, it was the memory of a young boy. He was gripping his first book, bought much to the dismay of, yes, his tutor. A huge book about the Galaxy’s ancient Emperors. And his tutor hadn’t been pleased at the prospect of paying starfreight on a book whose content was more properly stored inside the head of a pin!
8
YOUNG ERON BEGINS HIS ADVENTURE, 14,790 GE
Emperor Daigin-the-Jaw
b: 5561 GE d: 5632 GE
reign: 5578 GE to 5632 GE
... during the midphase of Our Awesome Empire's inexorably patient sweep across the Galaxy, Daigin-the-Jaw ascended at seventeen. ..A charismatic mover, he sought to abandon Splendid Wisdom’s centuries old policy of sly political assimilation for an impetuous strategy of rapid conquest. The Imperial bureaucracy flushed with millennia of successful expansion, saw this youth as the embodiment of its ambition. They assembled and deployed for him the most formidable array of armies ever to swarm the human starways.
... only thirty-four when his strike forces numbered seven billion soldiers... exploits legendary. At forty-eight, personally in command of the Thirteenth Fleet...
...a stellar tide of rebellion marred his final victories, ending only with his death by perfidious ambush at the second battle of Blackamoor Cross...more than six thousand planned invasions put on hold...
—A Short History of Our Splendid Emperors
In a weaker gravity than Agander’s, Eron Osa bounded down the stairs of the narrow street with his newly acquired Short History gripped in both hands under one arm. He had been running all morning up and down the hillwalks and over the rideways of the Ulmat Constellation’s capital metropolis, poking into stores and botanical gardens, even exploring the hallowed grounds of the Vanhosen Scholarium at a lickety-split pace that no registrar would be able to match. (Having narrowly escaped the fate of being forced to study at Vanhosen, he was in no mood to be tapped inside its halls for years by unhappy lackeys in the thrall of his father.)
He did stop once at a collegiate caf£ to memorize the faces of the students he would never mix with long enough to know—silly girls with golden finger claws and arrogant boys with funny hats. Then he ran on. He had embraced as much strangeness as he could soak up before lunchtime. Down the stairs! Leap and fly!
Tutor Kapor sat, unsweating, at the appointed table in the little caf§ in the square across from their hotel. Eron plunked his book on the tabletop. “I’m not late!” He sank down in his seat with relief.
“A book?” queried his mild tutor.
“I bought it at a used-data emporium. Chip displays, all upstaging each other! I was bogglefied! You’ll never find such stuff trawling through an archive! It was enough to transmute the brain! I was staggering around the aisles dazed when I bumped into a bookshelf on the third terrace. Books are a lot quieter. What a relief!”
“You’ve never seen a book in your life!” admonished his tutor.
“I know!” Eron exclaimed happily. “That’s why I bought one.” He added defensively, “It’s not on your money stick— it was my credit. It’s all about the lives of emperors.” He saw less than approval in the eyes of Murek so he added accusingly, “You told me to study history!”
Eron’s elder companion nudged die volume. “I’m thinking about the freight charges. You didn’t, by any lucky chance, pick up the book’s template? With a piece of junk this massive, it’s easier to manufax a new copy every time you want to read it than to lug it around with you between the stars.”
“I can’t keep it?” Eron was stricken.
Tutor Kapor spun the tome a half turn on the tabletop to read the title. A Short History of Our Splendid Emperors: Kambal-the-First to Zcuikatal-the-Pious. He hefted it to make a more scholarly assessment. “Ooof. My arm exercises for the morning,” he added dryly. He examined the title page. “It’s an old book.” He sniffed it. “Cellomet. Old for sure. If I recall right,
Zankatal-the-Noose predates our Founder by about a century.” A tip of the head meant that Eron’s tutor was about to elaborate on his comment. “‘Noose’ is not his official name, of course—it’s just what Zankatal was called out here in the nether reaches of the Galaxy where he was not thought to be so pious.”
He leaned back and slapped the heavy cover. “Sure, you can keep your book, Eron—as long as you learn what every young traveler has to learn: the freight to Faraway on this book is far more than the book will ever be worth. Since those charges will be on my stick, I’m going to ask a favor of you; you’re going to have to read the damn book. And it’s an old book—there’s no famfeed; it’s all eyefeed, page by page.” He laughed. “That’ll teach you to buy books!”
“It’s not really a book!” sulked Eron. “It’s automated!” He flipped out a fold-in back-cover flatplate. “It’s got an index. Press a button and it flips open to the right pages in sequence. There aren’t any pictures on the pages, but the flatplate will give you any picture you want.” He produced the animated vizeo of some emperor who offered them a posed benediction against a Splendid palatial interior. “Hot zits!” he exclaimed while looking at the grand architecture, which dwarfed even the majestic furniture. “They lived like that?”
“Look at the words, the words,'' admonished his tutor, who couldn’t stop for a jiff being a teacher.
“You don’t know what I’ve already read,” replied the stung student. “You think it was Daigin-the-Jaw who conquered the Ulmat. You told me that. You’re wrong. It was his son, Arum, in the reign of Daigin-the-Mild, who dropped in with his fleet and cut off our balls and then went home to Splendid Wisdom and cut off the Emperor’s balls just to show the Galaxy who was boss. When I found that, that’s when I bought the book. They don’t put stuff like that in the archives on Agander! Here!” He opened the pages at the right section, just to prove that he had found out something his tutor did not know.
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