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 probability 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.