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A Further Sally, or The Miracles of Amentia

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Nothing can outrace the speed of light, and so it is impossible to say that Trurl and Klapaucius were famous across the entire universe, since in those benighted parts of it which lay outside their light-cone the inhabitants could not possibly have heard of them. Nevertheless, tales of their skill at all manner of crafts, their ingenuity and their munificence spread so widely throughout the galaxy that for a period of some centuries, more than sixty percent of all the children produced were named either Trurl or Klapaucius (with the addition, of course, of some distinguishing nickname). In the end the names became mere honorifics, and the two constructors found themselves asked whenever they introduced themselves: "Trurl and Klapaucius what?"

Eventually the two of them tired of the adulation and accolades with which they were greeted everywhere they went. And at last Trurl suggested they disguise themselves as ordinary wandering tinkers, and sally out in search of adventure.

Klapaucius was delighted with the idea, and so the two of them hid away the finely calibrated calculators and brightly chromed tools that identified them as constructors of repute. They purchased a battered space freighter whose leaky fission reactor gave its hull a warmly welcoming glow, and equipped it with a set of rust-covered old probes and circuits which Trurl had abandoned, several upgrades ago, to deteriorate in a musty corner of his workroom. To this they added a supply of gadgets, gizmos, whirligigs and contrivances for sale and barter along the way. Then with a lurch and a shower of gamma radiation, they set off.

Indeed, they soon encountered a variety of fascinating (not to mention dangerous) adventures. Trurl was arrested for mopery in the realm of Authoritaria, where this crime was considered a most serious offense, albeit one whose definition was non-constructive, so that although all of the lawyers or judges were convinced that he had violated it, none of them could actually tell him how he had done so. But the two constructors' mathematical prowess was such that they easily reaxiomatized the Authoritarian code to produce a constructive formula, and moreover one that demonstrated Trurl's innocence, to the great disgust of their accusers.

Klapaucius had a run-in with the notorious Narcissasaur of Stultifex, which he managed to escape by trapping the beast within a non-Riemannian manifold studded with fragments of a broken mirror. For disposing of this notorious predator and general hazard to navigation, the Sultan of Stultifex made the two wayfarers Knights of the Realm, bestowing on them ceremonial swords and lances, a pair of magnificent electro-destriers, and also the purely nominal sum of one hundred bars of solid gold. Trurl and Klapaucius bowed low, assuring the Sultan that they were most honored and overjoyed to be thus ennobled, and that they would treasure forever their swords, lances and electro-destriers, as well as (they added with an aristocratic disdain for mere lucre) the hundred gold bars. They then loaded the whole amount into their spaceship, expressing their disdain by locking the gold in one of the darkest and most closely confined cargo holds, and headed off again for parts unknown.

By the time they next made landfall, the two constructors were both hungry and thirsty, and so made without delay for the nearest inn. It was a bright and homely place, and the pair made immediately for the bar, where each raised a brim-full Leyden jar to the other's health, and then, since there seemed little else to do for recreation, another, and then one more. At last, they staggered merrily off toward their ship, arms round one another's shoulders, singing the old spacefarer's anthem "Stoke the Plasma, Johnny".

As Klapaucius climbed up the gangway to the door of the ship, however, he suddenly ran into a very strange figure indeed: a person clad all in black, and carrying a bar of gold in either hand.

"How odd," he exclaimed. "What are the odds of two people happening to meet like this, and each happening to own a small fortune in gold?"

Trurl pulled out a notepad and began to figure, muttering to himself about martingales and the Birthday Paradox. The mysterious figure, meanwhile, began to sidle off. But unluckily for him, the cool air had sobered Klapaucius up a bit, and he ran into the ship, where he quickly ascertained that the cargo hold had been opened and completely ransacked.

"Seize the miscreant," he shouted, and Trurl, abandoning some promising investigations into the economics of non-measurable sets, reached out and grasped the fellow by the shoulder.

"Listen up, you wretched sneak-thief," he cried. "What do you mean by stealing our gold this way?"

But the thief refused to answer, and instead tried to wrench free, so that Trurl had quite a struggle to keep hold of him. But finally Klapaucius reappeared, and seeing himself outnumbered, the thief gave up trying to escape and merely glowered at them in silence.

"You had better explain yourself, and right quickly too," Klapaucius declared:
"For be warned, O larcenous lout, we are no ordinary tinkers such as our humble dress may suggest, but the Magnificent and Far-Famed Constructors, Klapaucius and Trurl, to whom the very strong and weak nuclear forces are as playthings! Beware lest we choose to punish you, for your actions thus far have shown a reprehensible lack of moral discernment."

"It is true, all too true!" replied the thief. "This is the great misfortune of my people: we lack all moral discernment."

He collapsed, noisily sobbing, but after a minute or two, regained enough control of himself to begin his story, which was as follows:

"The country you have come to is called Amentia, and once it was a happy and well-regulated land. All the citizens lived kindly and peacefully with one another, for such was the command of our God, the great Xntz, Who had made Itself known to us by the Three Miraculous Signs. These were the Three Miraculous Signs of Xntz: the Sinking of Dense Objects, the Floating of Bouyant Objects, and the Miraculous Production of Chlorine from the Hydrolysis of Sodium. It is true that certain skeptics advanced naturalistic explanations for Sinking and even for Floating, but none dared question the miracle of Hydrolysis.

"On an ill-starred day, however, a traveling mountebank arrived in our fair country, and as a species of cheap entertainment began to advertise a certain manual of elementary chemistry. This, O constructors, was our undoing, for once we had read this manual, even the dullest of our citizens immediately understood that the Miraculous Production of Chlorine was no miracle at all, but the consequence of a simple chemical reaction.

"Immediately we marched on the temple of Xntz, smashed the tablets of the law, burned the sacred books, and smelted down the idols for kitchenware. Since then we Amentians have been confirmed atheists. And as a consequence, we are also amoralists, dystopians, unethicists and antinomians. For without the command of Xntz, we see no reason not to slander, burgle, extort, adulter, dissemble and covet. Indeed, none of us ever do anything else. O woeful state!"

Klapaucius frowned. "If the whole country is filled with robbers and murderers, we had better give up on the gold and leave as fast as we can."

"Don't think so small," said Trurl. "I have a much better idea--- one that will get us back our money and more besides. All we have to do is build them a new god: no cheap confidence tricks this time, but one that can perform a genuine miracle on command, and has a strong moral code to boot."
"They robbed us, and you want to give them a gift?"
"Don't you see?" Trurl said cunningly. "Once they have a new god, they'll be forced to reform their vicious ways and pay us back... not to mention rewarding us for our services, and most handsomely, too."

Klapaucius shook his head. "With our usual tools, we could do it for sure. But with these?"
"It won't be so bad. We start with the old greatest-good-for-the-greatest-number trick, which is a simple numerical integration, and add in a few extra axioms for special cases. We can give it a sense of perspective, which is just plane geometry."

"That just might work," said Klapaucius excitedly. "We'll add in a pendulum, for reciprocity, and I think there's an old deontoscope buried under some other spare parts in the workshop. Wire all that together and you'll get a moral code fit for a king!"
"I should hope not," Trurl replied.
"Excuse me," said Klapaucius. "I wasn't thinking. I meant..." He considered a moment. "Fit for a constructor."

With that, they warmed up the fusion reactor and soon the air was ringing with clangs and bangs. From the exhaust vents of the ship poured heavy black clouds of smoke, richly scented with solder. Every so often the lights outside would flicker as a badly wired circuit burned out of the deontoscope (which was a finicky instrument at the best of times). The Amentians gathered curiously around the ship, wondering what it was the occupants could be working on, and how soon they could get their greedy hands on it once they finished.

The constructors, meanwhile, were nearing the end of their task. They fed in reams of philosophy, mythology and sociology, all neatly coded on punch cards, plus a few biographies of historic statesmen as negative examples. Klapaucius reached for the power switch, but just then, they realized they had forgotten the miracle.

"It can't be much of a miracle, with nothing but spare parts to go on," said Trurl. "But on the other hand, it can't just be chemistry; they already know all about that."
"What about the multiplication of fishes, then?"
"Should be easy enough," said Trurl. "We define a ring over the icthyomorphs---"

And so they scratched, scribbled and planned for a while, then fastened their multiplicative icthyoplex firmly to the forehead of their prototype god, where it served as a sort of headdress, with a funnel sticking up at the top and two spouts leading out at the bottom. And with that, they flung wide the door to their spaceship, and cried out, "Amentians, behold your God!"

The assembled amoralists, dystopians, unethicists and antinomians gave a gasp of surprise, and then rushed up the gangway to inspect the strange device, which was squat and chubby, studded with valves and vents, about four feet high and electroplated with a thin layer of palladium for added majesty.

"Is it really a source of moral authority?" asked one, but Klapaucius pointed proudly to the deontoscope, whose needles were all jammed at their highest setting.

"Can it really do miracles?" whispered another. Trurl produced a tiny electroguppy, which he fed ceremoniously into the headdress, and after a second, with a slither and gurgle, two of the creatures emerged from the spouts and lay wriggling on the ground, their gas exchangers flapping for want of water.

"It is sinful to leave these tiny souls to suffer and die," proclaimed the machine, and the Amentians ran in this direction and that, fetching bowls, buckets and tanks of water.

Within minutes, the machine was busy with a long line of Amentians, for in their period of crime, they had accumulated a sizable list of grievances and injustices. The machine, just and yet merciful, ordered muggers to distribute alms in dark alleys, slanderers to whisper surreptitiously about the secret virtues of their neighbors, and the publishers of academic journals to switch to tabloid journalism, so that their long-suffering writers could finally be paid for their work. At the end of the line, two desperate Amentians were struggling over the ownership of a baby, but even this conundrum puzzled the machine not a bit. Calling for a sword, it neatly applied the Banach-Tarski theorem to slice up the squealing infant and produce two new ones of equal volume, which the parents bore away perfectly satisfied.

At last, the constructors approached the machine, congratulating one another on particularly effective bits of the mechanism.

"Now for our money," said Trurl.
"That's right, machine. Make the Amentians cough up what they stole, and throw in, say, a hundred more bars of gold---"
"Make it two hundred," Trurl amended.
"---All right, two hundred, for our trouble in making you."

"You must address me as Your Holiness," the machine replied in booming tones.
"Of course, of course, Your Holiness," said Klapaucius. "Three hundred bars of gold and we'll be on our way."

The machine cogitated a moment. "This demand is completely unjust. The Amentians are an honest folk, but they are poor and can use the gold far more than you can. What's more, there are no ends of improvements you can make in their condition! Let's see: you can refine their refineries, refactor their factories and that's not to mention the gardens, guardhouses and garderobes you could build, the plants and plantations, the--- in short, you must not be allowed to leave."

And by the machine's divine instruction, Trurl and Klapaucius were borne away by a crowd of Amentians, who confined them in a tightly-locked workroom. There they were supplied with tools mechanical and mathematical, and presented with a neatly-written volume entitled: "Mandated Goals for Research and Development (vol 1)".

"This is terrible," moaned Trurl. "Why did I let you talk me into building that infernal cyberdeity?"
"As I recall, you were doing most of the talking. But never mind that, we have to find a way out of here."
"We could destroy your misbegotten machine."
"No! That is, it's not my machine, it's yours, and what's more, we can't destroy it. If the Amentians lost their moral code again, we'd be robbed and beaten within an inch of our lives."

The two of them sat sullenly against the wall, Klapaucius shaking his head and swirling his fingers in the dust on the workroom floor, while Trurl riffled frustratedly through the Mandated Goals . After a while, however, the swirls Klapaucius drew began to resemble an algorithm, and Trurl picked up a stick of charcoal and began to make idle notes in the margins of the book. Then Klapaucius carefully copied his sketches from the floor onto a slate and began to ornament them with growth rates and proofs of efficiency, and Trurl, meanwhile reached for a pencil and began to write more purposefully, adding occasional exclamation marks and underlined QEDs. And at last Klapaucius snatched up the card punch and began to input a program with such speed that the air was filled with tiny paper circles, while Trurl warmed up the lathe and began to cut out a series of miniature chromium scales.

After about half an hour, the two turned to one another.

"It's a fine mess you've gotten us into," said Trurl. "But I have the solution!"
And he held up the device he had been making. "All we need to do is write a program for it."

And at the same time, Klapaucius fanned out his punch cards excitedly. "Once again, I've managed to fix one of your idiotic mistakes. I've programmed---"

They looked at one another. "Never mind whose fault it is," said Trurl. "Let's put your program into my device, and then we'll go show that arrogant machine that being a god isn't all it's cracked up to be!"

And so, making short work of the room's locked door, the two crept back to their spacecraft.

"Your Holiness," said Klapaucius, "We have come on bended knee to beg your forgiveness, and admire once again your miraculousness."

"Especially the miraculousness." Trurl held up a tiny chromium fish, which however, seemed perfectly comfortable in the open air, for he had fitted it with an improved gas exchanger. "Just hold still a minute, Your Holiness," he said, and fed it in through the funnel. Two fishes at once emerged from the spouts, and these the constructors fed in again at the top, and then the ensuing four fishes, and so on, until the twinkling cascade of icthyomorphs was so rapid that the constructors were forced to redirect them from spout to funnel with short lengths of hosepipe they had brought with them for that exact purpose.

"What is the meaning of this?" the god thundered, but Klapaucius and Trurl refused to answer, and meanwhile, in the pauses between his words, they began to hear a tiny murmuring sound.

"Soon," said Klapaucius, and, "Very soon", agreed Trurl, and indeed the murmuring grew rapidly louder and louder until all of them could hear it quite clearly. It was the fishes, all of them speaking in unison, and what they said was:

"We want you to pay the constructors their gold and then make them leave! Yes, make them leave! The sight of them causes us pain! Such pain! Pay them off and get rid of them!"

"Now listen up," Klapaucius explained, shouting to be overheard above the rising clamor of thousands and millions of tiny chromium fishes.
"You care for the greatest good for the greatest number--- with a few extra axioms for special cases--- and right now, the greatest number want us gone!"
"With the gold," added Trurl eagerly.
"Don't you see that by keeping us here you are causing them pain?"

And Trurl was about to agree with them when he realized he could no longer even hear himself talk, for although the hosepipes had by this time burst under the pressure of the vast number of fishes, the creatures were piled up so high that more and more of them continually slipped into the funnel, causing yet more of them to emerge from the other end. Meanwhile, although the god had begun trying to shove some of them in the other direction, the constructors had lazily neglected to provide an inverse operation for their icthyalgebra, and so all its efforts were in vain.

Klapaucius and Trurl were actually beginning to grow somewhat nervous at the number of fishes, and wonder if they should run before they were buried, when from somewhere at the center of the pile came a great bellow: "Enough!"

There was a great clinking and clattering as the god emerged, one metallic hand jammed tightly into the funnel to prevent any more multiplication.

"I will end your torment," it promised. "I will let them go."

"AND THE GOLD!" roared the fishes, and to this demand too, the god was forced to assent, for just as the constructors predicted, its rigorous moral principles did not allow it to cause pain to so many tiny souls. And so, as quickly as possible, the Amentians produced the stolen gold bars, and two hundred more for good measure, loaded them haphazardly into the ship, and bid the pair of them farewell.

"GO!" screamed the millions of chrome-scaled fishes, "GO! GOOD RIDDANCE TO YOU BOTH!"
"What do you suppose will happen to them all," Klapaucius asked.
"Oh, they'll have to be taken care of somehow," Trurl replied. "The god will make sure of that. It'll probably be very expensive and time-consuming, but then again, that's not our problem, is it?"

Klapaucius frowned. But at the thought of being imprisoned in some even more tightly-locked Amentian prison, to toil till the end of time on gardens, guardhouses and garderobes, he shuddered and decided to leave the lot of them to work it out on their own.

It was years later, in fact, that the constructors discovered how the problem of the fishes had been solved. They had been voyaging in the Gas Clouds of Vulm when they caught a transmission advertising a choral concert: over a million singers performing a magnificent work of sacred music, for the delectation of the audience and the greater glory of God. Curious to hear this impressive-sounding oratorio, the two set their course for the great stellar concert hall in which it was about to take place. But as they took their seats in the gallery, there came a deafening shout from the stage:

And under the surprised and disapproving glares of the rest of the audience, the two slunk back to their spaceship. They would never be able to see the tiny chrome-scaled fishes perform, for they had made them to hate the sight of their creators--- and made them too well.