Note that uncertainty is a meaningless concept without a predictor and his specific prediction. The uncertainty associated with a single jar of colored balls is very different if we predict (1) that we will pull out a ball, (2) that we will pull out a white ball, or (3) that we will pull out a white ball weighing one gram. A sophist can turn quantum mechanics into a deterministic system simply by making the absolutely certain prediction that only outcomes specified by his wave equation will be realized. That is a useful prediction but it merely tells us with certainty what won't happen; what will happen still has a computable uncertainty. Certainty can become a taskmaster who requires more answers than quantum mechanics is able to extract from any set of initial conditions, no matter how accurately measured.
It is an instructive and deeply pleasurable exercise for the superior student to derive the irreducible uncertainty associated with any physical system he can formulate as a quantum wave equation— and this author strongly suggests that he do so. Hint: First specify all the outcomes and their probabilities. Use the integral form of H and...
A magical world opens to those who master the tools of uncertainty. For instance, it is then a trivial matter to derive the second law of thermodynamics from first principles. The student can go even further; by using the time-symmetry of the quantum wave equation, it will be possible for him to decant the second law's time-symmetric corollary from his first solution: if time is reversed, past events will NOT recapitulate themselves in reverse in such a way that entropy decreases; a time-reversed observer will still see a world of increasing entropy.
Can you build a convincing proof that a time-reversed traveler will continue to grow old and die? that, for a few moments after time-reversal, rivers might slosh uphill but will very soon reassert their downward flow to the sea? Show mathematically that the velocities and positions necessary for the water molecules to flow upriver, rise into the groundwater, and levitate upward into the sky as raindrops require an accuracy many orders of magnitude greater than allowed by the irreducible uncertainties imposed by quantum mechanics.
Explain why deductions about the past contain the same irreducible uncertainties as predictions about the future, the same proliferating branch-points. Prove that only in a universe with an unlimited capacity to store detail within volumes smaller than a quantum length cubed could time-reversal induce corpses to crawl out of the grave and grown men to shrivel up into babies and slip back into their womb and uranium to cease being radioactive.
Calculate the radius of a sphere such that the uncertainty of pi gives a ten percent probability that pi is less than 3.
—Elementary Physics Course, Asinia Pedagogic
Eron hardly knew where to begin his studies. He had no tutor creating a program for him and driving him through it. He had no regular classes. He had no exams. He belonged to no group. It was impossible to skip school because there was no school to skip. It was was very disconcerting and disorienting. Jak took pity on him, with a laugh, and hauled him off to a few lecture series, which were fascinating tours into obscure areas of high physics, the details of which were all incomprehensible. It was like having acrophobia and crawling to the rim of a precipice to look down upon normally large things reduced to a very tiny status—while a knowledgeable mountain climber stood behind you, firmly nudging your ass forward with his boot.
In desperation Eron went to his advisor to plot out a course for himself. Reinstone spoke about poetry. Eron listened to him patiently, dutifully posing as a student in awe of his master. Reinstone was so enthused by an audience that he began to quote large passages from his own Saga—recklessly developing his performance into a drama that first required him to stand and then to pace while wild gestures brought fire to his words. In time Eron got him back onto the subject of constructing a course of studies. It was no use. A happy Reinstone gave him some poems to read. “They will inspire you,” he said.
Marrae took pity on him and sat at his console guiding him through lists of possible course studies while mumbling encouragement. The tri-D screen was a cacophony of scrolling text advisements, scurrying between little animations intent upon competing with each other for his attention while still on stage, their frenzied antics made even more overwhelming by Marrae’s tendency to countermand his command gestures with her own so that the console was always aborting the ongoing performance to follow up a lead he hadn’t intended. Then Marrae spotted one of the new books Reinstone had lent him, a translation of the Iliad and the Odyssey into standard galactic, and disappeared with it into her own room.
Doggedly he persisted. He tried narrowing the glut down to the directions a student of psychohistory might profitably pursue. There were lots of opinions but no one was sure and the Fellowship wasn’t telling. That came as a shock to Eron. The Fellowship was picking up students from schools like Asinia and wasn’t prescribing any course of action to guide them? Absurd. He sulked for a round of watches, sleeping long hours and eating food. He skipped his meeting with Reinstone. He carefully avoided all presentations, programmed tutorials, lectures, and demonstrations. He left his console on idle. He was as mad as an inactive nova, erupting only occasionally.
Then he met a student in Asinia’s parkland while they sat on a bench together each lost in his own thoughts. The student happened to spot a tiny flowering weed in the grass and was so surprised that he commented aloud to Eron about the diffusion of life through the Galaxy. The home planet of this specimen, he knew for a fact, was seventy-seven thousand leagues distant. He wouldn’t let Eron pick the delicate flower.
“You’re a biologist?”
“No. My father is a florist who breeds the flower gengi-neered from that weed. I just dabble, really, in everything except botany.”
“I don *t dabble. I don’t do anything. Even the water in this damn university refuses to wet my hands. What’s your favorite dabble?”
“Really not much. This watch it’s real math. I really joined the math club because of a girl I make the bumps with. I’ll be doing math as long as we are bumping. It’s really interesting—the math, I mean. We’re working on this really difficult problem in tertiary kanite algebras which keeps my mind off her unreal boobs. It’s really driving us crazy—the problem, I mean. Nobody at Asinia seems to know anything. But we’ll solve it really soon now. We’re brainstorming it again this afternoon.”
“Really?” Eron mocked. He tagged along.
The math club met in a study room with its own mnemoni-fier and a clunky-looking link to Asinia’s symbolic manipulator. Eight members had brought their lunch in anticipation of a rowdy session. They gesticulated. They punched each other jocularly and talked at the same time. The club’s president, their “chairsucker,” as they called him, continually raised his voice to shout “Quiet!” or, when he was really exasperated, “Please be quiet, for crap’s sake!” Eron dutifully remained quiet while he observed and listened.
He heard a serious undercurrent of math beneath the joking. The girl with the boobs seemed to be the intellectual in charge. She had slipped out of her shoes and, silently, was rubbing her toes together—only when some male made a hopeful suggestion did she demolish him by quoting an exotic property of kanite algebras from memory. One dark youth with bushy eyebrows did strange things such as trying to yank out his hair when frustrated by his impotent attempt to “intrant homogamous kanite gnomoids,” which he was certain would eventually solve all their problems. “Quiet!” yelled their chairsucker. “Let Hasal have his say, for crap’s sake!” Eron didn’t have the slightest idea what a kanite algebra was. It sounded like one of those awful surprises Murek Kapor was always pulling on him.
He was beginning to notice that their enthusiasm was totally dispersed. Murek had taught him very methodical ways of organizing an approach to a problem that wasn’t providing easy answers. Their hop-around discipline grated on his nerves. After a full morning of watching, he began to explain his ideas about how the club might organize its attack on kanites. The chairsucke
r was now dodging artillery rounds of hard bread rolls and had commandeered a basket of rolls to return fire. His attention wasn’t on keeping order. Eron turned to the club’s doyenne, who merely crossed her arms. “Not now. I’m thinking.” Across the table three of the main arguers retorted that being organized was mentally restrictive. A hungry mathematician was under the table chasing after a bread roll that had missed its target.
All right. Reasoning and common sense wasn’t going to work on these anarchists.
They should be enlisted in the Imperial Shock Troops with Murek as their top sergeant. Eron grinned, remembering Murek’s diabolical ways. He relaxed and waited for an opening. The doyenne was still thinking. The chairsucker was busy with a sandwich in his left hand and a ready round or hard roll in his throwing hand. The boy under the table now rose with paws on the bench, roll devoured and stomach satiated, to take up the lapse in conversation, announcing to his companions on the right and left his latest bright idea. So...at the exact moment this scholar finished his speculation, Eron directed a question at him in the same voice Murek always used when demanding an answer. It was like unloosing a smelly rabbit across the path of a talking dog who had been thinking about rats. Eron let the dog run off at a gallop after the lure, then turned his total attention to the doyenne, armed with another question, this one crafted to ratde her pretentious authority. But the timing had to be right. She had to drift out of her loop first. He waited, ready to pounce.
He was interrupted. “Really!” his real friend complained in alarm from across the room. “Those are my boobs your eyes are coveting!” So far as Eron could see, he was boobless. “You’re too wet behind the ears for her!” Possessiveness had cleared away all visions of mathematics, and he was standing at attention near his abandoned whiteboard, eyes fixed on Eron. Eron ambled over. The doyenne would have to wait. “I’ve a question I’ve been meaning to ask you.” That was a ruse; what Eron “really” wanted to know was how to scroll and erase a whiteboard, since when he’d tried to use the damn thing it didn’t seem to have a visible tactile input, nor did it respond to verbal commands. But a question about kanite algebras would have to do as a diversion. “Clear up something for me,” he cajoled. “Why are we trying to use one of the kanite algebras to solve this problem? I don’t understand.” He put on his best woebegone air.
The florist’s son groaned but was only too happy to distract Eron. He began to scribble on the whiteboard, which turned out to be such a primitive device that it didn’t even correct his illegible handwriting. Eron watched hawk-eyed as the board filled, waiting to see what would happen when it was time to erase. “Got that?” chimed his friend, pausing just long enough for Eron to memorize the scribbles before wiping them away with the flat of his palm. It was the second time Eron had seen this, and it suddenly dawned on him that the whiteboard wasn’t defective! Ingenious! But there didn’t seem to be any way to scroll. Instead of scrolling, new symbols were added to odd blank comers and arrows guided one through the maze.
It was hopeless. Eron figured that it was going to take him at least a couple of turns on Faraway’s axis to bring this low-technology group under control. So back to his cave. As he left he whispered the special question he had saved for the doyenne’s ears alone—prudently first glancing to check that his really real friend was still puzzling over his own handwriting on the whiteboard.
Faraway had a leisurely rotation, and Eron stayed up all of a long night in his room with the plastic camel lamp he had found in the trash on one of his walks. Camels were reputedly mammals and so related to humans. Marrae didn’t believe it because they didn’t have hands and couldn’t climb trees; she was sure they couldn't have evolved on Rith and, maybe, were just gengineered freaks, even mythological beasts. But Eron thought their haughty expression was very human. He believed. “Anthropomorphism,” grumbled Marrae. At any rate the camel’s belly glowed comfortingly. The light wasn’t bright enough to read by, but he did all his reading at the console. After dinner he had been hard at work with a tutorial on kanite algebras. Its library use-log said it hadn’t been booted in almost a sixtyne of years. Perhaps that was a warning about the quality of the presentation, or perhaps just an indication that kanite algebras weren’t fashionable. The subject was exciting, the tutorial as bland as if its creators hadn’t quite grasped the power of the material they were teaching.
He allotted himself a modest nap before breakfast—it didn’t do to live without any sleep. Why hadn’t someone gengineered a bug-fix for sleep—it was such a waste of time. After all, those lazy gengineers had had seventy-odd millennia to perfect the human genome. Of course, maybe the original humans had been camels, and transmogrifying a camel would have taken some doing, especially for a camel!
Jak was the only one up for breakfast. Eron rattled off about the amazing properties of kanite algebras. Jak listened patiently while the cuisinator prepared him a plate of poached eggs on muffin topped by ham in a creamy sauce of butter, egg yolks, and darkmoon juice. He poured a jigger of ersatz Armazin over the benedictine concoction before interrupting Eron’s monolog. “What you need is a little practical math.”
“Ugh,” said Eron. “That’s your genteel word for physics. What do I need physics for? I’m interested in human beings!” He was calling up a sprinkling of ground cinnamon beetloid for the butter on his toast
“You need to know physics to know thyself. Right now you’re just a walking wave-function with a silly smile. Your fam is a quantum computer. Your penis is another swollen-wave function. Your conscious mind is a teeny-weeny quantum agent that can’t possibly keep track of all the things going on inside your head. Dismiss physics at your peril.”
“I want to solve problems that have never been solved before.”
Jak laughed with his face full of eggs and ham sauce. “Come to today’s problem seminar. Our chief prestidigitator, Prof Sledgehammer—”
“Sledgehammer?”
“His real name is unpronounceable. You don’t want to know. He comes from a planet where the larynx has devolved but the hands move quicker than the eye! He runs our problem sessions. Usually he’s kind-hearted and gives us problems we can solve if we cheat a bit by brainraiding our friends, but this watch he wants us to relax while he gives us a lecture on a problem that was posed back during the Interregnum. He’s going to give us tips on how to play with an intractable problem. He’s been working on it for thirty years—off and on, of course, not being deranged like you math freaks.”
A problem that hadn’t been solved? Eron was intrigued. After humanity’s eighty thousand years of number-juggling, a problem without an answer was hard to come by. Of course, humans were more ambitious now that they used fams instead of clay. He let Jak drag him to the lecture.
It was a class smaller than the math club, but more formal—no lunches allowed. No throwing rolls at the prof. Old Sledge lounged in his easy chair and chatted with wry humor about his love of sailing. He used that to segue into apocryphal tales about the legendary Faraway physicist Malcof who had also loved sailing, reputedly spending much time in his one-masted sloop creating conundrums. The one on today’s agenda had appeared twenty-five centuries ago in an early version of Asinia’s Encyclopedia under unsolved physics problems. No one knew if it was Malcof’s own problem or one he had purloined from a source now vanished into the chaos of the Dark Ages.
When Old Sledge finally tacked into the wind—after abandoning the telling of tall tales to return to the problem on the agenda—he still couldn’t keep his ship on course. He bobbed around at sea by using analogy rather than careful mathematical symbolism. Such euphemism annoyed Eron. Physicists! They pulled out of the bilgewater clunky concepts like standing waves in a cup of water or speeding bullets when what they meant was a space-time probability distribution! Sledge’s choices of analogy were always colorful, often startling, but like all analogies, each held an arsenal of potential traps. Analogies were never perfect. Eron’s mind drifted. He remembered an episode fro
m that Rithian epic Reinstone had lent him—Rith must be quite some place if you could find on it winged women with three-toed claws and feathered boobs! He made an analogy of his own: listening to an analogy was about as safe as trying to sail past the island home of Rith’s sirens while at the same lime enjoying their singing.
The wakedream grew more complex—better than listening to a physicist talk—as his fam conjured an ocean with the fog of dawn drifting across a distant rocky shore, the beautiful sirens barely visible on their crag. He felt the ropes tying him to the mast. He felt himself strain against them as he harkened to those enchanting voices that drifted out to sea above the wind and the clunk of deaf sailors dipping their oars in the brine. How could a physicist compete with the lilting of a siren’s poetry?
Come, great Odysseus, Hero in thy Glory,
Stop, bring your Ship to rest and Hear our honeyed story.
Turn that black prow to Shore; Taste the Sweet Delights
Waiting here for heroes through Magic Days and Nights
We know the Noble Past, know the Future’s Plan.
Pause... then go thy way, a joyful, wiser man.
Old Sledge tired of farting around with the half-truths of analogy and suddenly he stood erect, spryly energetic, to attack the whiteboard. At last! Mathematical rigor! Eron began to pay close attention. The problem was new to him but its structure was familiar from his sparring matches with Murek. Eron had already set his fam to automatically clean up, memorize, organize, and cross-index the ramblings that these crazy Faraway types scribbled on their ubiquitous whiteboards. Now that thinking had turned precise, pieces fit together cleanly—except for the known contradictions and puzzles. He was able to translate Sledgehammer’s awkward perambulations into Murek’s categories while developing his own interpretations faster than the prof could scrawl out his thirty years of thinking. The one convenient thing about whiteboards was that they were ten times slower than disciplined thought. Fam-aided thought, of course. Maybe that fam upgrade they had cobbled into his old clunker was actually working! Or maybe he was pretematurally smart.
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