ReVISIONS

by Julie E. Czerneda

  Moral: Do not play games with a cad.

  As the stork was flying yet again to the forest, he passed a lion. The lion said, “Friend stork, you seem tired. Perhaps you should land beside me and rest.” “I am not that foolish,” the crane replied, “but I am tired. The monkey is playing tricks on me, and will not give me what I wish unless I bring her bananas.” “Where is this monkey?” the lion asked. The stork gave the lion detailed directions. This time, when the stork returned from the forest, he found the monkey gone, the lion walking away well-fed, and a white stone lying among the walnut shells.

  Moral: O children of Greece, gambling may

  seem like a glamorous path to easy rewards,

  but it’s a cesspool of crime and betrayal,

  even if you know the odds.

  When the stork finally returned to his unattended children, they’d all been eaten by ferrets.

  The end!

  The Angle of the Lord

  Now it came to pass in the second year of the reign of Nebuchadnezzar that the king dreamed dreams, wherewith his spirit was troubled and his sleep broke from him. Then the king commanded to call the court mathematicians for to show the king his dreams.

  When they came, they asked the nature of the dreams, but the king could not say for the memory had gone from him. Yet still he demanded they give their interpretations, on pain of death. The mathematicians answered him, saying, No man upon the earth can show the king’s matter; none can but the gods, whose dwelling is not with the flesh.

  Yet in the king’s household lived Daniel, a son of Judah and a righteous man whom God had given understanding of dreams. He came before Nebuchadnezzar and said, “The Lord God of Israel has revealed thy dream’s secrets unto me—not for mine own sake, but that thou shouldst know the wisdom of the Ancient of Days.

  “Thou, O king, sawest, and beheld a great image. This image’s head was of fine gold, his breast and his arms of silver, his belly and his thighs of brass, his legs of iron, his feet part of iron and part of clay. Four great chains ran up from the ground to the head, that the fiercest gale should not topple the image. And thou stood beneath the southernmost chain in such manner that thine own head but touched a single link. Each link of the chain was a cubit in length, and the link at thy head was the tenth from the ground.

  “As thou watched, a stone was cut out without hands, which smote the image upon his feet that were of iron and clay, and broke them to pieces. Then was the iron, the clay, the brass, the silver, and the gold, broken to pieces together, and became like the chaff of the summer threshing floors; and the wind carried them away, that no place was found for them. Only the chains remained; and thou sawest the southernmost chain had four hundred links, which had run from the ground to the image’s top, but now lay flat on the plain.

  “This was the dream; and I will tell the interpretation thereof before the king.

  “Thou stood at the tenth link of the chain, which was like unto a hypotenuse of a right-angle triangle whereof the farthest leg was the graven image itself (if we but ignore the sag in the chain, which was drawn very tight, thereby making the variance negligible). The chain was four hundred links long, which is two score tens. Therefore, O king, since thy head just touched the chain, by divine similarity of ratios, the image was two score times thine own height. Though the image and its feet of clay were sore destroyed, the wisdom of the Lord yet enables thee to take the image’s measure.”

  Then Nebuchadnezzar said unto Daniel, “I care not the image’s height, but rather its portent. Is there some meaning to these ratios? The height of the image to the length of the chain?”

  “Verily,” said Daniel, “that ratio foretells what is to come, for surely it is a sine. . . .”

  The Confucian Analytics

  The Master said:

  Piety toward one’s ancestors and submission to one’s prince: are these not the origin of all benevolent actions?

  The superior man measures himself with respect to this origin. He charts his piety and submission on two perpendicular axes.

  Positive piety and positive submission lead upward to the rising sun, while negative piety and negative submission lead downward to hell.

  Positive piety without submission rises straight toward heaven, but does not spread outward to the people.

  Positive submission without piety lies flat and does not rise.

  When piety equals submission, the superior man’s life passes through the origin and rises with balanced harmony.

  (Those who would rise more quickly must appeal to a higher power.)

  The people may be made to follow a path of action, but they may not be made to understand it.

  However, the superior man studies diligently, that he may comprehend all paths—even those of exponential difficulty.

  He also learns to factor polynomials.

  By nature, men are nearly alike; by practice, they get to be wide apart.

  The degree of divergence at any point depends on the slope of the tangent.

  What the superior man seeks is in himself. What the inferior man seeks is in others.

  The difference between the two is the square root of (Δp)2 + (Δs)2.

  Many of the Master’s sayings generalize to higher dimensions.

  Without recognizing the geometry of Heaven, it is impossible to be a superior man.

  Without knowing the rules of algebra, it is impossible for character to be established.

  Without logarithmic scales, it is impossible to conserve paper.

  Achilles and the Tortoise: The Second Heat

  SOCRATES: I went down yesterday to the Piraeus with Glaucon the son of Ariston, that I might offer up my prayers to the goddess; and also because I wanted to see how the city would celebrate the festival. I was delighted with many of the events, particularly the sports competitions. But then that old madman Zeno showed up and began to rant loudly to his neighbors during the races.

  POLEMARCHUS: No doubt he declaimed his paradox?

  S: Can he speak of anything else?

  THRASYMACHUS: What paradox is this?

  P: Zeno pictures a race between the swift Achilles and a tortoise, in which the tortoise is given a head start of perhaps ten paces.

  T: Unless the race length is ten paces and the width of a fingernail, Achilles would surely win.

  P: Zeno contends otherwise. For before Achilles can close the ten-pace gap, he must run the first five paces. And before he can close the remaining five-pace gap, he must run the first half of that: two and a half paces. And before he can close the remaining two and a half paces, he must run the first half of that distance, too. You see the pattern?

  T: Yes, certainly.

  P: Therefore Zeno says Achilles must run an infinite number of these half-distance races; and although each such race is half the distance of the previous, yet there are still an uncountable number of them. How can a man run an infinite number of races in a finite lifetime? Zeno claims Achilles will never catch up with the tortoise, and moreover that all movement is impossible.

  T: I do not agree with Zeno’s conclusion though I see no error in his argument. Socrates, can you help me resolve the dilemma?

  S: Zeno’s error is simple. He assumes that distance is infinitely divisible but will not grant a similar favor to time. For suppose swift Achilles can run ten paces in a single heartbeat. Then he runs the first five paces in half a heartbeat; he runs the next fraction of the race in a quarter of a heartbeat; he runs the next in an eighth of a heartbeat; and so on. Achilles therefore has an infinite number of ever-smaller time segments to run an infinite number of ever-smaller distance segments. In the limit, as the distance segments D go to zero, the time segments

  T also go to zero. Therefore there is no paradox.

  P: Yet what of Achilles’ speed? For speed is distance divided by time . . . and if both D and T go to zero, do we not have a case of zero divided by zero? You must realize, Socrates, that in Athens, advocating division by zero is a crime punish
able by death. Do you wish to corrupt our youth with seditions against the very foundations of mathematical discourse?

  S: I preach no seditions. My Socratic method is merely to slice ever more finely until I arrive at the truth. Do you realize my techniques can analyze all manner of phenomena? The fall of an apple. The movements of stars and planets. Why bubbles are round and how to calculate pi.

  P: None of that matters, Socrates—not if you divide by zero! Such talk offends the gods. I beg you, abandon these notions. Do you wish to be executed? [Silence.]

  S [stiffly]: I do not divide by zero itself. Merely by values approaching zero.

  P: That is an extremely delicate distinction, Socrates . . . and I am afraid the elders of Athens will not be able to differentiate.

  The Death of Ideals (by Plato)

  My mentor Socrates is dead. Compelled to take poison because his ideas transgressed the status quo.

  Never mind that Athens pretends to venerate ideas. Our ambassadors have traveled the entire world—to Persia, the Indus, the court of the Chou emperor, and everywhere in between—deliberately seeking out systems of thought, to make our city a paragon of wisdom.

  Yet we are incapable of honoring one of our own.

  Now Socrates is dead. His writings have been destroyed. His knowledge is lost—his vast vast knowledge. For the notions that led to his death were infinitesimal compared to the greater body of work he never made public. The secrets known only to his most intimate students.

  Those who loved him.

  Like me.

  I watched him die. I saw the best mind of my generation destroyed by intolerance, called heretical, stripped naked, dragged through the hemlock streets at dawn by angry fanatics.

  An agile-headed trickster burning with an ancient Zoroastrian grasp of the fiery calculus running the machinery of night.

  Who bared his brain to Heaven under the Parthenon and heard algebraic angels totaling Buddhist zeros into infinite chanted sums.

  Who got arrested in pubescent years returning through Sparta with a contraband copy of Lao Tzu under his robe.

  Who studied Aesop, Mahavira, Pythagoras, and fourteen forbidden Upanishads to find the cosmos instinctively ordering itself in probabilistic sample spaces.

  Who read Daniel’s writing on the wall, walked with saints and angels in the Babylonian furnace, slept in the lions’ den, slept with all the lions, triangulated their manes to five decimals.

  Who wept at his first glimpse of analytic geometry, wept copiously asymptotically exponentially logarithmically, all the while on his way to becoming a superior man.

  Who took T to zero in the company of epsilon and delta, then worked backward as infinite Σ became smoothed-out, and slopes reversed themselves into areas-under-the-curve always always plus a constant or marks would be deducted.

  Who journeyed to Athens, who differentiated in Athens, who came back to Athens & integrated in vain, who factored over Athens & X-the-unknowned in Athens and finally went away to take Athens’ measure, & now Athens is lonesome for her hero.

  Who dreamed and made incarnate more secret things still: the transfinite aleph, the rank-clashing matrix transforms, the groups and the rings and the prime-power fields, the stretched deformations of bourgeois space into patchy coordinate manifolds, the torn topologies, the random walks, the bloom of cardinalities, series and sequences, the functors, the metrics, the lemmas, the postulates, the perfect perfections of perfected forms, now with the absolute magnitude of the poem of mathematics butchered in Socrates’ body, gone and dead for the next two thousand years.

  Light. Dark. Light. Then fire.

  Light. Dark. Light. And fire.

  Light. Dark. Light. Ahh, fire!

  Fire is light. And fire, it burns. Burns the dark.

  Fan . . . the . . . flames!

  Revision Point

  As noted at the beginning of the story, the Axial Age (600-400 BCE) was a sort of Renaissance wherein many old tribal beliefs were questioned and replaced. Throughout Europe and Asia, several generations of thinkers tried to make sense of the world in a way that had never been tried before. As a result, the Axial Age saw the birth of Zoroastrianism (the first religion that combined true monotheism with a strong belief in an afterlife), Buddhism, Taoism, Confucianism, Jainism, and modern Hinduism, as well as the late Jewish prophets and the most important Greek philosophers. The religions and philosophies created during this time set Eurasia’s intellectual agenda for more than two thousand years.

  What the Axial Age didn’t give us was much advancement in science. A few small steps were taken, but nothing comparable to the great developments in philosophical thought. Why not? Perhaps because it was still the Bronze Age, and humanity hadn’t yet invented useful things like telescopes, mechanical clocks, sextants, etc. People could think, but they couldn’t measure. What kind of science could flourish in such an environment?

  Well, there’s one realm of science where abstract brainpower is all that counts: math. It occurred to me that if all those prophets and philosophers had just spent a little time putting their ideas into mathematical form, the Axial Age would have been a lot more fun . . . at least to a math geek like myself. Therefore, I’ve attributed the invention of various mathematical concepts (from positive and negative numbers, up to calculus and beyond) to appropriate thinkers of the Axial Age. It’s scary just how easily the math and the people lined up. . . .

  J.A.G.

  THE TERMINAL SOLUTION

  by Robin Wayne Bailey

  IN the matter before us which now threatens us so direly we have relatively few facts, and the hypotheses and opinions we now offer are subject to so many caveats and arguments as to invite ridicule not just from numerous of our fellow colleagues, most notably Dr. Joseph Lister of the King’s College Hospital and in Paris M. Louis Pasteur, but from clergy and from political circles throughout the empire as well.

  Nevertheless, the facts are the facts, and I take no great pleasure in noting that the British Medical Association as well as leading figures within the Royal College of Surgeons, if somewhat slowly—indeed, and without leveling judgments, I might say too slowly—have come to concur with much of what I now report.

  We can state as fact that the epidemic which now confounds and menaces us had its origins in the darkest heart of Africa, perhaps somewhere along the Ruvuma River or along the banks of the great lakes of Mweru and Bangweulu. It is impossible to more precisely determine where it first appeared. As fearful as this disease is to us, it has struck a far more devastating blow there. Many of the key settlements and villages where important clues might have been found are now either abandoned or completely wiped out. Ujiji and Kolobang were burned. Capetown has completely quarantined itself.

  We know as fact, however, that the renowned explorer and writer, David Livingstone was already quite ill when he returned to London on July 23, 1864. His physician, one Doctor Samuel Overton, diagnosed his several maladies as symptomatic of malaria, and there can be no doubt that malaria was present. However, Doctor Overton also indicated the occurrence of several purplish lesions of an unknown and possibly cancerous nature upon Livingstone’s torso. These lesions seemed to defy all treatment.

  So, detracting no honor from his famous name, it is with David Livingstone that we find the first evidence of this plague, which I now call African Invasive Disease, upon our shores. And it is with David Livingstone that we begin to document a curious and notable progression of subsequent, and I might add inevitably fatal, occurrences. Most immediate among these are Dr. Overton, himself, and a number of his patients. Overton’s copious notes describing his own symptoms and pathology provided useful groundwork for my investigations.

  From this point, I must speak with some delicacy about matters that may shock or offend, for in charting the progress of this plague. . . .

  Dr. Joseph Bell laid his pen aside, leaned his elbows on his writing table, and in the dim, yellowish light from a single gas lamp, rubbed his eyes. In his mind,
he’d gone over this passage a dozen times and on paper at least half that many. He felt tired, so very deeply tired. The summary of his investigations at which he was working and which he would soon present to the British College of Physicians was proving difficult, requiring wording that was foreign to his blunt nature.

  “Devil damn us all!” he grumbled, wadding his pages up and hurling them across the room of his cluttered apartment. He stared in disgust after the parchment ball as it bounced off a bookcase full of medical texts and settled into a shadowy corner. Then, recovering from his outburst, he settled back in his chair and rubbed his eyes a second time as he muttered to himself, “Indeed, he already has—damned us every bloody one.”

  Weary to the bone, he tried to push all thought from his mind. He knew he needed sleep, but there was no time for that. There were riots in Whitechapel, in Aldgate, and Spitalfields, demonstrations at the gates of Buckingham, itself.

  He squeezed his temples as he rose and paced back and forth over the carpet which Mrs. Hudson, his housekeeper, had once kept so clean. Poor, sweet woman. She was dead, too, like so many others.