The Mammoth Book of Alternate Histories

CHRIS ROBERSON O One

Tsui stood in the golden morning light of the Ornamental Garden, looking over the still waters of the abacus fishponds and thinking about infinity. Beyond the walls, the Forbidden City already hummed with the activity of innumerable servants, eunuchs, and ministers bustling along in the Emperor’s service, but in the garden itself there was only silence and serenity.

Apart from the Imperial House of Calculation, which Tsui had served as Chief Computator since the death of his predecessor and father years before, the Ornamental Garden was the only place he lingered. The constant susurration of beads shuttling and clacking over oiled rods was the only music he could abide, and as dear to him as the beating of his own heart, but there were times still when the rhythms of that symphony began to wear on him. On these rare occasions the silence of the fishponds and the sculpted grounds surrounding them was the only solace he had found.

His father, when he had been Chief Computator and Tsui not yet an apprentice, had explained that time and resources were the principal enemies of calculation. One man, with one abacus and an unlimited amount of time, could solve every mathematical operation imaginable, just as an unlimited number of men working with an infinite number of abacuses could solve every operation imaginable in an instant, but no man had an infinity in which to work, and no emperor could marshal to his service an infinite number of men. It was the task of the Chief Computator to strike the appropriate balance. The men of the Imperial House of Calculation worked in their hundreds delicately manipulating the beads of their abacuses to provide the answers the Emperor required. That every click of bead on bead was followed a moment of silence, however brief, served only to remind Tsui of the limits this balance demanded. In that brief instant the enemies of calculation were the victors.

As a child Tsui had dreamt of an endless plain, filled with men as far as the eye could see. Every man in his dream was hunched over a small wooden frame, his fingers dancing over cherrywood beads, and together they simultaneously solved every possible operation, a man for each calculation. In his dream, though, Tsui had not heard the same clatter and click he’d found so often at his father’s side, with an endless number of permutations, every potential silence was filled with the noise of another bead striking bead somewhere else. The resulting sound was steady and even, a constant hum, no instant distinguishable from any other.

Only in pure silence had Tsui ever found another sensation quite like that, and the only silence he had found pure enough was that of the Ornamental Garden. Without speaking or moving, he could stand with eyes closed at the water’s edge and imagine himself on that infinite plain, the answer to every problem close at hand.

The sound of feet scuffing on flagstone broke Tsui from his reverie, and he looked up to see Royal Inspector Bai walking leisurely through the garden’s gate. Like Tsui, the Royal Inspector seemed to find comfort within the walls of silence, and the two men frequently exchanged a word of pleasantry on their chance encounters.

“A good morning, Chief Computator?” Bai asked. He approached the fishponds, a package of waxed paper in his hands. He stopped opposite Tsui at the water’s edge of the southernmost of the two ponds and, unwrapping his package with deft maneuvers, revealed a slab of cold pork between two slices of bread. A concept imported from the cold and distant England on the far side of the world, it was a dish that had never appealed to Tsui, more traditional in his tastes than the adventurous Inspector.

“As good as I might deserve, Inspector,” Tsui answered, inclining his head a fraction. As he was responsible for the work of hundreds, Tsui technically ranked above the Inspector in the hierarchy of palace life, but considering the extensive influence and latitude granted the latter by imperial decree, the Chief Computator always displayed respect shading into submissiveness as a matter of course.

Bai nodded in reply and, tearing pieces of bread from either slice, dropped them onto the water before him. The abacus fish in the southern pond, of a precise but slow strain, moved in a languid dance to nibble the crumbs floating on the water’s surface. The brilliant gold hue of their scales, iridescent in the shifting light, prismed through the slowly shifting water’s surface, sparkling from below like prized gems. The fish, the result of a failed experiment years before to remove man from the process of calculation, had been bred from ornamentals chosen for their instinct of swimming in schools of close formation. In tests of the system, though, with a single agent flashing a series of lights at the water’s edge representing a string of digits and the appropriate operation, it was found that while accurate to a high degree, the slowness of their movements made them no more effective than any apprentice of the House of Calculation. The biological and chemical agents used in breeding them from true, however, had left the scales of the languid abacus fish and their descendants much more striking that those of the base stock, and so a place was found for the failed experiment in the gardens.

“Your pardon, O Chief Computator,” Bai remarked, shaking the last dusty crumbs from the pork and moving to the northern pond. “But it seems to me, at such times, that the movements of these poor doomed creatures still suggest the motions of your beads over rods, for even in their feeding, the fish arrange themselves in columns and rows of varying number.”

Tearing off strips of pork, the Inspector tossed them onto the water, which frothed and bubbled the instant the meat hit the surface. Silt, kicked up by the force of the sudden circulation, colored the water a dusty gray.

“I can only agree, of course,” Tsui answered, drawing alongside the Inspector and looking down on the erratic dance beneath the surface of the pond. This strain of abacus fish was, in contrast to its languid neighbor, much swifter but likewise far less consistent. They had been mutated from a breed of carnivorous fish from the Western Hemisphere’s southern continent, the instinct of hunger incarnate. The operations they performed, cued by motions in the air above and enticed by offerings of raw flesh, were done faster than any but the most accomplished human operator could match, but with an unacceptably high degree of error. Like their languid cousins before them these fierce creatures were highly prized for their appearance, their strangely iridescent scales offset by razor teeth and jagged fins, and so they were relocated from the Imperial Ministry of Experimentation into the garden when Tsui was only a child. “They mimic the process of calculation as a mynah bird does that of human speech. Ignorant, and without any comprehension. Man does not, as yet, have any replacement.”

“Hmm,” the Inspector hummed, tossing the last of the pork into the water. “But what does the abacus bead know of its use? Is it not the computator only who must understand the greater meaning?”

“Perhaps, O Inspector, this may be how the Emperor himself, the-equal-of-heaven and may-he-reign-ten-thousand-years, rules over the lives and destinies of men. Each of us need not know how we work in the grander scheme, so long as the Emperor’s hand guides us.” It was not a precise representation of Tsui’s thoughts on the matter, but a more politic answer than that which immediately suggested itself, and one better fit for the ears of the Emperor’s justice.

The Inspector hummed again, and wiped his fingers clean on the hems of his sleeves. Looking past Tsui’s shoulder at the garden’s entrance, Bai raised his eyebrows a fraction and nodded.

“You may be right, Chief Computator,” the Inspector answered, grinning slightly. “I believe either of two beads, you or I, will in short order be guided from here. Can you guess which?”

Tsui turned his chin over his shoulder, and saw the approach of the Imperial page.

“Neither can I,” the Inspector said before Tsui could answer. When the page presented the parchment summons to the Chief Computator with an abbreviated bow, Bai smiled and nodded again, and turned his attention back to the abacus fish. The last of the pork was gone, but white foam still frothed over the silty gray waters.

Within the hall they waited, ministers and courtiers, eunuchs and servants, the Empress Dowager behind her screens, her ladies with faces made painted masks, and the Emperor himself upon the Golden Dragon Throne. All watching the still form of the infernal machine, squatting oily and threatening like a venomous toad on the lacquered wooden floor, its foreign devil master standing nervously to one side.

Tsui was met in the antechamber by the Lord Chamberlain. With a look of stern reproach for the Chief Computator’s late arrival, the Chamberlain led Tsui into the hall, where they both knelt and kowtowed to the Emperor, touching foreheads to cold floor twice before waiting to be received.

“The Emperor does not like to be kept waiting,” said the Emperor, lazily running his fingers along the surface of the scarlet and gold object in his hands. “Begin.”

As the Emperor leaned forward, elbows resting on the carved arms of the ancient Manchurian throne, Tsui could see that the object in his hand was a representation in miniature of the proposed Imperial Space Craft. A much larger version, at fifty per cent scale, hung from the rafters of the hall overhead. It presented an imposing image of lacquered red cherrywood and finely wrought gold, with delicately sweeping fins and the imperial seal worked into the bulkheads above the forward viewing ports. That the Emperor did not like to be kept waiting was no secret. Since he’d first ascended to the Dragon Throne a decade before, he’d wanted nothing more than to travel to the heavens and had dedicated the resources of the world’s most powerful nation to that end. His ancestors had conquered three-quarters of the world centuries before, his grandfather and then his father had gone on to bring the remaining rogue states under the red banner of China, and now the Emperor of the Earth would conquer the stars.

In the years of the Emperor’s reign, four out of every five mathematical operations sent to the Imperial House of Calculation had been generated by the Ministry of Celestial Excursion, the bureau established to develop and perfect the art of flying into the heavens. Tsui had never given it a great deal of thought. When reviewing the produced solutions, approving the quality of each before affixing his chop and the ideogram that represented both “Completion” and “Satisfaction”, he had never paused to wonder why the scientists, sages and alchemists might need these answers. The work of the Chief Computator was the calculation, and the use to which the results were put the concern of someone else.

Now, called for the first time to appear before his Emperor, it occurred to Tsui that he might, at last, be that someone else.

The Lord Chamberlain, at Tsui’s side, motioned for the foreign devil to step forward. A tall, thin white man, he had a pile of pale brown hair on his head, and wispy mustaches that crept around the corners of his mouth towards his chin. A pair of round-framed glasses pinched the bridge of his nose, and his black wool suit was worn at the edges, the knees worn thin and shiny.

“Ten thousand pardons, your majesty,” the Lord Chamberlain began, bowing from the waist, “but may I introduce to you the Proctor Napier, scientific attaché to the Imperial Capital from the subjugated land of Britain, conquered in centuries past by your glorious ancestors.”

The Emperor inclined his head slightly, indicating that the foreign devil could continue.

“Many thanks for this indulgence, O Emperor,” Proctor Napier began. “I come seeking your patronage.”

The Emperor twitched the fingers of one hand, a precise motion.

“I was sent to these shores by your servant government in my home island,” Napier continued, “to assist in Imperial research. My specialty is logic, and the ordering of information, and over the course of the past years I have become increasingly involved with the questions of computation. The grand designs of your majesty’s long-range plans, whether to explore the moon and far planets, or to chart the course of the stars across the heavens, demand that complex calculations be performed at every step, and each of these calculations require both men, materials and time. It is my hope that each of these three prerequisites might be eliminated to a degree, so as to speed the progress towards your goals.”

Tsui, not certain before this moment why he had been called before the Emperor, now harbored a suspicion, and stifled the desire to shout down the foreign devil. At the Chamberlain’s side, he listened on, his hands curled into tense fists in his long sleeves.

“With your majesty’s kind indulgence,” Napier said, “I would take a moment to explain the fundamentals of my invention.” With a timid hand, he gestured towards the oily contraption on the floor behind him. “The basic principle of its operation is a number system of only two values. I call this system ‘binary’. Though an innovation of Europe, this system has its basis in the ancient wisdom of China, and as such it seems appropriate that your divine majesty is the one to whom it is presented.

“The trigrams of the I Ching are based on the structure of Yin and Yang, the complementary forces of nature. These trigrams, the building blocks of the I Ching, are composed either of broken or of unbroken lines. Starting from this pair of values, any number of combinations can be generated. Gottfried Liebniz, a German sage, adapted this basic structure some two hundred years ago into a full number system, capable of encoding any value using only two symbols. He chose the Arabic numerals ‘1’ and ‘0’, but the ideograms for Yin and Yang can be substituted and the system still functions the same. The decoding is key. Using the Arabic notation, the number one is represented as ‘1’, the number two as ‘10’, the number three as ‘11’, the number four as ‘100’, and so on.”

The Emperor sighed, pointedly, and glanced to the spacecraft model in his lap, signifying that he was growing weary of the presentation.

“Oh, dear,” Napier whispered under his breath, and then hastened to add, “which brings me to my invention.” He turned, and stepped to the side of the construct of oily metal and wood on the floor. It was about the height of a man’s knee, almost as wide, a roughly cubical shape of copper and iron plain and unadorned. The top face was surmounted by a brass frame, into which was set a series of wooden blocks, each face of which was carved with a number or symbol. On the cube face presented towards the Emperor was centered an array of articulated brass buttons, three rows of fifteen, the brassy sheen dulled by smudges of oil and grime.

“I call it the Analytical Engine. Powered by a simple motor, the engine comprises a series of switches, each of which can be set either to an ‘on’ or ‘off’ state by the manipulation of gears and cogs. By assigning a binary value to each of the two states, we are then able to represent with the engine any numerical value conceivable, so long as there are a sufficient number of switches available. With the inclusion of five operational variables, and the ability to display results immediately,” he indicated the series of blocks crowning the device, “a fully functional Analytical Engine would theoretically be capable of solving quickly any equation put to it. Anyone with a rudimentary ability to read and input values can produce results more quickly and efficiently than a team of trained abacusists. This is only a prototype model, of course, capable of working only up to a limited number of digits, but with the proper funding I’m confident we could construct an engine free of this limitation.”

Tsui’s pulse raged in his ears, though he kept silent and calm in the view of the Emperor.

“If I may?” Napier said, glancing from the Emperor to his invention with an eyebrow raised.

The Emperor twitched, almost imperceptibly, and in response the Chamberlain stepped forward.

“You may exhibit your device,” the Chamberlain announced, bowing his head fractionally but never letting his eyes leave Napier’s.

Wiping his hands nervously on the thin fabric of his pants, Napier crouched down and gripped the wood-handled crank at the rear of the engine. Leaning in, the strain showing on his pale face, he cranked through a dozen revolutions that produced a grinding clatter that set Tsui’s teeth on edge. Finally, when the Chief Computator was sure he could stand the torture no longer, the engine sputtered, coughed, and vibrated to clanking life. Little plumes of acrid smoke bellowed up from the corners of the metal cube, and a slow drip of oil from one side puddled in a growing pool on the lacquered floor.

Licking his lips, Napier worked his way around to the front of the device, and rested his fingers on the rows of brass buttons.

“I’ll start with a simple operation,” he announced. “Can anyone provide two numbers?”

No one ventured an answer, all too occupied with the clattering machine on the floor, afraid that it might do them some harm.

“You, sir?” Napier said, pointing at Tsui. “Can you provide me with two numbers for my experiment?”

All eyes on him, not least of which the Emperor’s, Tsui could only nod, biting back the answer that crouched behind his teeth, hoping to pounce.

“One and two,” Tsui answered simply, eyes on the floor.

With a last look around the assembled for any other response, Napier hit four buttons in sequence.

“I’ve just instructed the engine to compute the sum of the two provided values,” he explained, pausing for a brief resigned sigh, “and when I press this final button the calculation will occur immediately and the result will be displayed above.”

Demonstrating a flair for the dramatic, Napier reached back his hand, and stabbed a finger at the final button with a flourish. The engine smoked and wheezed even more than before, and with a final clatter the rightmost of the blocks crowning the device spun on its brass axis and displayed the symbol for “3” face up.

“There, you see?” Napier said. “The answer produced, without any human intervention beyond the initial input.”

“I have seen horses,” the Emperor replied in a quiet voice, “clopping their hoofs on cobblestones, do more complicated sums than this.”

“Perhaps, your majesty,” the Chamberlain said, stepping forward, “a more evaluative demonstration is in order. Chief Computator Tsui?” The Chamberlain motioned to him with a brief wave of his hand, and Tsui inched forward, his fingers laced fiercely together in front of him.

The Chamberlain then snapped his fingers, and a page glided out of the shadows into the center of the hall, a small stool in one hand, an abacus in the other. Setting the stool down a few paces from the foreign devil’s instrument, the page presented the abacus to Tsui and, bowing low, glided back into the shadows.

“I would suggest, with your majesty’s permission,” the Chamberlain said, “that a series of calculations be performed, both by the Proctor Napier and his machine, and by our own Chief Computator and his abacus. Which of the two performs more reliably and efficiently will no doubt tell us more than any other demonstration could.”

The Emperor twitched his eyebrows, slightly, suggesting a nod.

“Let us begin,” said the Chamberlain.

Tsui seated himself on the stool. The abacus on his lap was cool and smooth at his touch, the beads when tested sliding frictionless over the frame of rods. Tilting the frame of the abacus up, he set the beads at their starting position, and then left his fingers hovering over the rightmost row, ready to begin.

The Chamberlain officiated, providing values and operations from a slip of paper he produced from his sleeve. That he’d anticipated this test of man and machine was obvious, though it was inappropriate for any involved to suggest the Chamberlain had orchestrated the events to his ends.

The first calculation was a simple addition, producing the sum of two six-digit numbers. Tsui had his answer while Napier’s engine was still sputtering and wheezing, taking less than a third of the time needed for the machine to calculate and display the correct answer on blocks.

The second calculation was multiplication, and here again Tsui finished first. The lapse of time between Tsui calling out his answer and Napier calling out his, though, dwindled in this second round, the engine taking perhaps only twice as long.

The third calculation was division, a four-digit number divided into a six-digit one. Tsui, pulse racing, called out his answer only an instant before Napier. The ruling of the Chamberlain named the Chief Computator the victor, even after Napier protested that he had inadvertently set his engine to calculate to two decimal places, and that as a result his answer was in fact more accurate.

The fourth and final calculation was to find the cube root of a six-digit number. This time, with his previous failure in mind, Napier shouted out after the numbers had been read that the answer should be calculated to two decimal points. The Chamberlain, eyes on the two men, nodded gravely and agreed to this condition. Tsui, who was already fiercely at work on the solution, felt the icy grip of dread. Each additional decimal place in a cube root operation increased the time necessary for the computation exponentially, and even without them he wasn’t sure if he would finish first.

Fingers racing over the beads, too tense even to breathe, Tsui labored. The answer was within reach, he knew, with only seconds until he would be named the victor. The abhorrent clattering machine of the foreign interloper would be exposed for a fraud, and the place of the Chief Computator, and of the Imperial House of Computation, would be secure.

“I have it!” Napier shouted, and stepped back from the Analytical Engine to let the assembled see the displayed solution. There was a manic gleam in his eyes, and he looked directly at the Emperor without reservation or shame, as though expecting something like applause.

Tsui was frozen, struck dumb. Reviewing his mental calculations, he realized he’d been nowhere near an answer, would have required minutes more even to come close. He looked up, saw the symbols displayed on the first blocks of the device, and knew that Napier’s answer was the correct one.

“It is decided, then,” the Chamberlain announced, striding to Tsui’s side. “Of the four tests, the methods of our tradition won out more often than they did not, and only by changing the parameters of the examination after calculations had begun was the Proctor Napier able to prevail. Napier’s device is a failure.”

“But…” Napier began, on the edge of objection. Seeing the stern expression on the Chamberlain’s face, and looking to the palace guards that ringed the room, the foreigner relented. He’d agreed that his machine should be judged by a majority of tests, and had to abide by the results. To object now would risk a loss of face, at best, and a loss of something much more dire at worst.

Tsui, too numb still to speak, rose shakily to his feet and handed the abacus back to the page who appeared again from the shadows. Bowing to the Emperor, he backed towards the exit, face burning with self-recrimination.

“The Emperor demands a brief moment,” the Emperor announced, sitting forward with something resembling interest. “British, how much time and work would be needed for you to complete the improvements you mentioned earlier? How many of your countrymen are trained in the arts of this device, who could assist you in the process?”

Napier, already in the process of packing up his engine dejectedly, rose to his feet. Rubbing his lower lip with an oil-stained finger, he answered.

“A matter of months to eradicate the current limitations, your majesty,” he said. “Perhaps a year. But I would need easily as much time to instruct a staff of men, as at present I am the only one who understands all the aspects of the engine’s manufacture.”

The Emperor, uncharacteristically demonstrative, nodded twice.

“Leave now,” the Emperor commanded, and they did.

In the antechamber, while Napier led a collection of pages and eunuchs in dismantling and boxing up his device, the Chamberlain caught Tsui’s elbow.

“A moment, Chief Computator,” the Chamberlain said in a low voice, drawing him into an alcove well out of earshot.

“My thanks, O Lord Chamberlain,” Tsui said, his tones hushed, “for allowing me to perform this small service for our master the Emperor.”

“We all serve our part,” the Chamberlain answered. “Remember, though, that the Emperor’s remembrance of this good office will serve only to balance his displeasure that you kept him waiting.”

“And for that, you have my apologies,” Tsui answered. “But it is strange, I should think, that you would send for me at the House of Computation, in an hour during which it is well known to you that I am elsewhere at my leave. Would not one of my journeymen have been a suitable representative to hear the foreigner’s presentation, and to offer any service you might require?”

“Perhaps,” the Chamberlain replied, eyes narrowed. “Perhaps it slipped my memory that you would not be found in the House of Computation at this hour, and perhaps it did not occur to me that one of your able journeymen might be as suited for our purposes. But perhaps,” the Chamberlain raised a long finger, “it was best that a member of the House of Computation in your position of leadership was present to see and hear what you have. I have always counted on you, O Chief Computator, to find solutions to problems others thought were without resolution. Even, I add, solutions to things others did not even see as problems.”

Tsui nodded.

“Yes,” he said, “but of the many hundreds who labor under me in the art of calculation there are others very nearly as adept.” He paused, and then added, “Many hundreds.”

“Mmm,” the Chamberlain hummed. “It is best, then, do you not think, that this device of the British does not meet the Emperor’s standards, that so many hundreds of adepts are not removed from their productive positions?”

That the standards proposed had not been the Emperor’s, but had instead been proposed by the Lord Chamberlain himself, was a point Tsui did not have to raise. The Emperor, in fact, as evidenced by his uncharacteristic inquiry into the production cycle of Napier’s invention, seemed not entirely swayed by the Lord Chamberlain’s stagecraft, the question of the utility of the Analytical Engine not nearly so closed as Tsui might have hoped.

“I could not agree more,” Tsui answered, thin-lipped and grave. “I thank you for this consideration, and value our exchange.”

The Chamberlain nodded, and drawing his robes around him, slid away into the antechamber and beyond, leaving Tsui alone.

The next morning found Tsui in the Ornamental Garden, eyes closed by the northernmost abacus fish pond.

The noise of shoes scuffing on gravel at his side startled him, and he opened his eyes to see Royal Inspector Bai standing at his side. He’d made no other sound in his approach.

“Good morning, Chief Computator,” Bai said, a statement more than a question.

“Yes, Inspector,” answered Tsui, looking down into the waters of the pond. They were silty and gray, the carnivorous fish almost hidden below the surface. “I would say that it is.”

“Surprising, one might argue,” Bai went on, “after the excitement of the evening.” The Inspector pulled a wax-paper wrapped lump of meat and bread from within his sleeve and, unwrapping it, began to drop hunks of dried pork into the waters.

“Excitement?” Tsui asked, innocently.

“Hmm,” the Inspector hummed, peering down into the water, quiet and still but for the ripples spreading out from the points where the meat had passed. “The fish seem not very hungry today,” he said softly, distracted, before looking up and meeting Tsui’s gaze. “Yes,” he answered, “excitement. It seems that a visitor to the Forbidden City, a foreign inventor, went missing somewhere between the great hall and the main gate after enjoying an audience with the Emperor. The invention which he’d brought with him was found scattered in pieces in the Grand Courtyard, the box which held it appearing to have been dropped from a high-story balcony, though whether by accident or design we’ve been unable to determine. The Emperor has demanded the full attentions of my bureau be trained on this matter, as it seems that he had some service with which to charge this visitor. That the visitor is not in evidence, and this service might go unfilled, has done little to improve the temper of our master, equal-of-heaven and may-he-reign-ten-thousand-years.”

Tsui nodded, displaying an appropriate mixture of curiosity and concern.

“As for the man himself,” Bai said, shrugging, “as I’ve said, he seems just to have vanished.” The Inspector paused again, and in a practiced casual tone added, “I believe you were present at the foreign inventor’s audience yesterday, yes? You didn’t happen to see him at any point following his departure from the hall, did you?”

Tsui shook his head, and in all sincerity answered, “No.”

The Chief Computator had no fear. He’d done nothing wrong, after all, his involvement in the business beginning with a few choice words to his more perceptive journeymen and foremen on his hurried return to the Imperial House of Computation, and ending in the early morning hours when a slip of paper was delivered to him by one of his young apprentices. On the slip of paper, unsigned or marked by any man’s chop, was a single ideogram, indicating “Completion” but suggesting “Satisfaction”.

Tsui’s business, since childhood, had been identifying problems and presenting solutions. To what uses those solutions might be put by other hands was simply not his concern.

“Hmm,” the Inspector hummed again and, looking at the still waters of the pond, shook his head. “The abacus fish just don’t seem interested today in my leavings. Perhaps they’ve already been fed, yes?”

“Perhaps,” Tsui agreed.

The Inspector, with a resigned sigh, dropped the remainder of the meat into the northernmost pond, and then tossed the remaining bread into the southernmost, where the languid fish began their slow ballet to feed themselves.

“Well, the Emperor’s service demands my attention,” Inspector Bai said, brushing off his hands, “so I’ll be on my way. I’ll see you tomorrow, I trust?”

Tsui nodded.

“Yes,” he answered, “I don’t expect that I’ll be going anywhere.”

The Inspector gave a nod, which Tsui answered with a slight bow, and then left the Chief Computator alone in the garden.

Tsui looked down into the pond, and saw that the silt was beginning to settle on the murky bottom, revealing the abacus fish arranged in serried ranks, marking out the answer to some indefinable question. The Chief Computator closed his eyes, and in the silence imagined countless men working countless abacuses, tirelessly. His thoughts on infinity, Tsui smiled.