Psychohistorical Crisis

7

RECOVERING FROM CAPITAL PUNISHMENT, 14,810 GE

As psychohistorians we like to claim that our mathematical methods allow us to make predictions about the future when we start with a certain critical set of carefully measured initial conditions. Our detractors dispute this. Still others attack our philosophical stance. Is Thanelord Remendian correct when he portrays us as callous Determinists who view all men as automata performing the motions of some scripted fate? Thanelord Remendian, as self-appointed advocate of Total Freedom, sees quite the opposite: humanity as a noble collection of souls each applying Free Will to attain his own Special Destiny.

We need not answer Remendian, but we must have our philosophical position well thought out among ourselves. It is a gross mistake to believe that an accurate ability to predict implies determinism. It does not.

—The Eighth Speech” given by the Founder to the Group of Forty-six at the Imperial University, Splendid Wisdom,

12,061 GE

The first time Eron Osa opened Admiral Konn’s copy of the Founder's Selected Essays after being executed, he never got past the initial two paragraphs. Some of the words he had to sound out before he could recognize them. Without fam access to the instant “gestalt-meanings” of a ten-million-word dictionary, his effort was leaden. Often Eron just gazed blankly at the open book in frustration— half expecting the ghost of his dead fam to imbibe the page all in one glance, to project vivid images based on the contents, to run simulations while exploring the mathematical ramifications, to traipse with him down byways of associated thought.

None of this happened. He was left bobbing in his aerochair in a dim room, staring at squiggles on thin cellomet in a typeface no one had used for two millennia. It was a book laid out with pride and craft, some pages wondrously illustrated with presspoint animation and active equations. The room’s light glared harshly over his shoulder, having lost its baffles and half its lum-tiles. There were no famfeed jacks in the archaic book. The actual reading of the manuscript seemed to be a one-word-at-a-time chore. Real drudgery ! And he had to think about the words without any handy tools to think with. He would have given up but he still had the strong illusion that he was a psychohistorian and on the verge of understanding everything.

The concepts seemed familiar, but Eron wasn’t sure if he had actually read any of the Founder’s words in their original format. The baud rate of eyefeed was shockingly slow. He was used to a leisurely comprehension rate of something like 2,048 words per jiff by famfeed and vastly higher input for storage mode. Reading was horrible! He could live faster than he could read about it!

Unfortunately, large chunks of the information input during a famfeed—even the selected parts of it that was used by the organic brain—were cached in the fam. That, thought Eron sourly, was probably the reason his own brain was now so empty. He wondered how much storage space was actually available inside the human head. Not much, obviously! Neurons were gross macromachinery!

How was he going to learn without famfeed! Where was he going to store his thoughts—in his stomach? He glanced covetously at the government-issue fam tossed carelessly over the back of a chair. Not that one, but he was going to have to beg-borrow-steal a real fam somehow—and spend the painful years training it.

During his “rebirth” Eron’s wardens had arranged for him a cheap hotel room on one of the lower levels of Splendid Wisdom near the Lyceum. The furniture morphed from the

wall, stark white, old, used, cramped. The plumbing in the dispozoria needed replacing. The holographic projections made by the comm console were fading and didn’t seem to adjust to a sharp definition. The picture wall didn’t work.

All they had left him of his old life were his clothes and his little red metricator. He seemed to know what that was for. It was a physicist’s pocket tool, small enough to be gripped inside a fist. It would measure almost anything: hardness, distance, spectra, acceleration. Maybe he couldn’t recall all the things it could do. He had one vivid memory of sitting at a table eating a sandwich and using it to measure the local pull of gravity, but he couldn’t remember which planet or why.

He needed to get out of this prison, take a walk maybe— not too far. Timidly he left the tiny apartment. Out in the city corridor he felt bolder and began a quick-paced exploration romp.

Eron spent the next terrifying interim trying to relocate his hotel. Had he gone down a level? Up? One clothing shop seemed familiar until he discovered that it was a common franchise in this neighborhood. He had completely lost his sense of orientation. The discreet signs seemed mostly to be of the fam-readable kind, where information was overlaid in tri-D on the visual cortex when needed—and he wore no fam. He asked directions and got answers in the off-planet dialect of some recent immigrant. Perhaps a fam could have deciphered the well-intentioned garble of sounds and gestures.

In the whole of this vertical neighborhood, there were no multilevel spaces that he could find, no reckless use of vegetation. Not everybody was working. Some residents were old and vacant and even sat in the corridors or the levitator lounges to watch the world flow by. Two tough youths assessed his wealth. Or maybe it only seemed that way because here was a class of people of whom he had been oblivious in his previous life. Maybe, just maybe, they were all right. Maybe they were dangerous only to strangers. Maybe they weren’t dangerous at all. Still, he fled from them in a kind of childish panic that took him down corridors and zigzagging commercial alleys and well-lit levita-tors that lost him completely but miraculously delivered him “home” again. The surprise of finding himself in front of his hotel astonished him into a burst of tearful thanks.

After awakening from a restless sleep, he remembered— and chose safety over adventure, spending the next multiple watches alone in his apartment—doors sealed, averse even to a brief restocking excursion—while he continued to struggle with the Founder’s first essay, polishing his painful reading skills. His troubles did not stem only from a lack of the utilities usually provided by a fam—he didn’t even command all of his organically based faculties. His mind was used to the brain/fam dialog, and some critical areas of his wetware seemed to be accessible only by key stimulation via fam-cue. The mental paths leading into these sepulchers were effectively blocked by his famlessness—and, to find their barricaded treasures, he had to guess his way blindly through neural codes. Being a moron was hard labor. Well, back to his studies!

Determinism. And more determinism. He reread the opening of the Founder’s “Eighth Speech” many times. Psychohistory was a science of prediction. Did an ability to predict imply determinism? In this Galaxy where an elite controlled the future in which the society was destined to live, people were apt to debate such philosophical points. Did it matter?

To distract himself from the reading, Eron sniffed the pages of this book that had been shaped into pocket size for carrying close to the heart by someone who loved to read. It smelled as if it had been printed a thousand years ago, and the title page said so. That spoke of a time well after the Founder had been reduced to a holographic glimmer in some vault and well past the farthest reach of that great man’s primitive mathematical vision—yet still centuries before the birth of anyone presently alive.

Enough sniffing. Keep the book open and try to read. Eron did his best to imagine the ancient debate between Thanelord Remendian and the Founder. There would be flamboyant clothes, snuff, perfume, gestures, and admonitions—but without his fam’s visualizers he saw only ghosts on a darkened stage. He plodded on.

The essay began its demolition of Thanelord Remendian’s thesis by fielding a clear definition of determinism, one that struck Eron as weirdly familiar. At the same time, it startled him—the way things do that have been around for a long time, unnoticed. He concentrated. He was still enough of a mathematician to realize that definitions are the framework of sound argument. They must be understood. He tried.

A deterministic universe requires One Future and One Past, immutable. It requires that every governing equation of motion have a Unique Solution whether worked forward or backward in time—even if we can only approximate that Solution in ever refinable steps. Choices become illusions. Determinism allows no branches, no random events, no errors, no noise. In such a universe even an omnipotent god is powerless to intervene. A universe cannot, by definition, be deterministic when man or god has choice, or if the guiding equations, given the same initial conditions, can be made to yield more than one result through branching, randomities, quantum superposition, error, or noise.

Remendian is mistaken to tar us as determinists. Psychohistory fails as a deterministic system simply because NONE of its probabilistic equations have unique solutions. This should not surprise us. After all, even the most rigorous equations of physics have long been framed in such a way that two identical initial states will not lead to exactly the same outcome. The neomystic philosopher Bohr...

At this point in his discourse the Founder went off into a technical discussion of the mathematical underpinnings that a deterministic physics would require. Eron had the comfortable illusion that he understood all the symbols and how the meanings were related, but when he actually got excited and tried to manipulate the dynamic symbols...he could do nothing. It was humiliating. Not to be able to follow the Founder when he was glossing over the easiest of the conundrums of primordial physics! Eron summarized the Founder’s points for himself to get a grip on them, using the apartment’s decrepit console as a doodle-pad.

All viable physical descriptions of our universe seem to require:

1] Time-symmetry. The physical equations determining state change are unaltered by the substitution of negative-t for t, where t is time. (The laws of our physics cannot be modified by a time reversal.)

Imposing determinism as an additional constraint then implies:

2] Reversibility. The physical equations determining state change cannot contain traps. (The system will not be determinable if it can dispatch information to conveniently inaccessible states like alternate worlds or black holes.)

The (perhaps apocryphal) father of physics, Newton, had been claimed by no less than eighteen worlds of the Sirius Sector. The great synthesis of the ancient newtonian theur-gists was deterministic because it naively contained no information traps. Being that, newtonianism failed to derive entropy from first principles; thermodynamics requires a built-in mechanism for lossy information compression. Even after careful experimentation by the mystical heisen-bergians had established the uncertainty of position/momentum, many of these dawn theurgists still clung to theological dogma that all information about the past was somehow retained in the positions and momenta of the current superposed states of the universe; nothing could be forgotten. The universe has mostly forgotten these men.

The Founder speculated that this stubborn conception of the universe as an all-remembering entity had been inherited from a then-common belief in an all-knowing God whose eye saw the whole of eternity. The tacit (and false) assumption that the underlying fabric of the universe was described by the artificial mathematical entity called a manifold fostered the illusion because a manifold has no upper limit on the amount of information that can be impressed upon it.

Gripped by a fit of industry, Eron confirmed the Founder’s careful proof that a deterministic universe requires more info storage space than the physical nature of die universe allows—using a marker on the cleanable wall because his holopad was down. Neat. He left it there as wallpaper.

In the real world, information about past states is continually being lost—quantum wave-functions decohere, things fall into black holes—and so present initial conditions never contain enough information to reconstruct the past (except on a probabilistic basis). Because of time-symmetry, an inability to reconstruct the past is mirrored as an inability to predict the future (except on a probabilistic basis). The job of accumulating information about a future time is never complete until the moment when that future becomes the present.

Our “now” contains neither the whole of the past nor the whole of the future, or, to put it another way, “now” contains the roots of all possible pasts—but won’t tell us which particular root is ours—and contains all possible futures in the branches of its tree—but won’t tell us which of those limbs we are about to climb out on.

No psychohistorian, no matter what godlike powers he might acquire, can predict an absolute future—too much information about the future is missing in the initial conditions of the present; no historian, no matter how meticulous, can write the definitive history—too much information about the past has been irretrievably lost.

That established, the Founder went on to describe how mathematics could determine the maximum upper limit on the amount of information that the present held about the future. Once the limits were known, mathematical method was free to give its best estimates of which futures we faced and what variables controlled the probability attached to a future.

The Master began to play amusing games with his audience—“the Group of Forty-six,” long dead, plus Eron, recently dead. They were asked to pretend that every Past Event was trying to encode itself in digital form to be transmitted through time to be filed by a harried Present in its bulging storage cabinets. He made it sound like he was chatting with the past over a wire. Eron grimaced. “Hello. This is the past. Get out your decrypter and I’ll tell you what really happened back here—hope you have enough storage room.”

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 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!