by Fritz Leiber
Finally it would pop them out off the Riemannian hyper-continuum into unoccupied space two light years from the solar system and in the direction of the tiny constellation of the Pleiades. After they had made brief confirmatory observations, a simple reversal of the process would bring Wolfe and Barr back near their starting point—if the new equations had been rightly read.
As the ionic swirl became a blizzard, a dull black, dense mono-molecular layer built up from the positive to the negative pole of the transparent sphere. This opaque outer plating was an unavoidable side-effect of the process. First Earth, then Luna, then Sol was blotted out and the stars around them. The last constellation to be obscured was the Pleiades. Wolfe said a silent farewell to the Seven Sisters, though out here he and Barr could see sixteen.
The field neared climax. Wolfe gently rubbed the lopped-off first joint of his right forefinger—which was his only outward expression of tension.
A nervous grin quirked Barr’s lips in the mirror. He said, rather loudly, “I don’t care how confident the math boys are, we still must be prepared for any species of disorientation. Did you ever read about the German psychologist who wore lenses that turned everything upside down? After a couple of days his brain accommodated and he saw everything—still through the same lenses—as right-side up. Then when he finally took off the lenses…”
A gust of cosmic change swept through Wolfe and Barr with no immediate perceptible effect on them or their vehicle except that two tell-tales on the panel flashed green, one of them blinking.
Wolfe touched another button. The blinking ceased as deplating of the opaque layer began, the molecules flying off in exact reverse of the order in which they had been laid down. The two men watched the spot where the stars would first show.
“The Pleiades!” Then Barr’s voice changed. “But something’s happened to them.” He laughed oddly. “They’re not upside down, at any rate!”
“No, but they’re reversed right-to-left,” Wolfe said quietly. “The translation effect seems to have been somewhat greater than anticipated. We appear to be not two light years away from Earth but 440—twice the distance of the Pleiades—and we are seeing them from the opposite side.”
When Barr did not reply, Wolfe continued methodically to spell out the obvious to his comrade. He said, “This is possible with the Pleiades since they are an actual group of stars, physically close to one another. It would not be true of most other constellations, whose member stars differ widely in their distance from Earth. For instance, there is no place on the other side of Ursa Major or Orion whence one can see the Dippers or the Hunter reversed.”
Deplating continued. The agelessly familiar constellation of Orion appeared, but to the right of the Pleiades, not to the left as one sees it looking southwest from Earth’s northern hemisphere and Bellatrix and great yellow Beteleuse were reversed, and the Sword hung the wrong way from the Belt.
Barr said softly, “This sight is impossible in our home continuum. We appear to have been translated along a diameter of the great Riemannian hypersphere to the mirror-image universe which Muawiya hypothesized as lying at the fourth-dimensional antipodes.” And now it was Wolfe’s turn not to reply.
Deplating went on. Fierce Sol appeared, and Luna, and then quickly Earth showing the Americas—but Florida hung from the west coast and Baja California from the east, while by the narrow, near-invisible twig of the Isthmus of Panama, South America hung to the left of the northern continent, and the Caribbean opened into what should have been the Pacific.
“Since the mirror universe duplicates ours in detail,” Barr said, “our twins must just now have materialized near our home planet—a mirror you and a mirror me.”
“Wait,” Wolfe said sharply. He was staring at himself in the mirror-bright surface of the panel and holding out his hands. At first he thought all was as it had been: his right forefinger was the one lacking a joint. Then he reminded himself that plane mirrors give a reversed image, and he looked down directly at his hands. His left forefinger was the lopped one.
“Wait,” Wolfe repeated to Barr and pointed to the maimed forefinger. “Since we’ve been mirror-reversed ourselves, we can’t be in a mirror universe, because if we were, it would appear normal to us.”
“The new equations were misread completely: they don’t refer to translation but to reversion. We have only moved through the fourth dimension enough to accomplish a dextro-levo reversal in our bodies—yes, and in our vehicle too, since—look!—the panel’s console pattern is still normal to us. But with respect to the Earth we haven’t moved a fourth-dimensional micron.”
He took a breath. “Besides,” he added more cooly, “it better satisfies the Law of the Conservation of Reality to assume a mirror-reversed microcosm than a singularly reversed macrocosm.”
Barr sighed, possibly with relief. “And so all we have to do to unkink ourselves,” he said, “is to make our ‘return journey’ as planned.”
“Yes,” Wolfe allowed, “but I for one don’t approve of running needless risks. Besides, I fancy it would be wise to present the math boys with some more physical proof of the mirror-reversal than our unsupported word. They were so positive about their reading of the equation. Barr, what happened to your German psychologist when he took off the lenses?”
“Why, he’d got so used to them that the world looked upside down again. But it straightened out, I mean inverted back to normal, after a couple of days.”
Wolfe nodded. “We ought to be able to stand mirror-image people and a mirror-image environment for a couple of days, don’t you think? He waited a moment, then turned to the panel’s communication sector to raise Earth. He added, “If adjustment proves too troublesome we can come out here and unkink, though I’d enjoy always having a complete right hand.”
Barr said, “We’ll have to remember to tell our doctors our hearts lie to the right now. I’ll spend a bit of the next two days simply being thankful I’m not a virtual man on a virtual world.”
Wolfe nodded and said, “Let’s shake on that.” The two men automatically gripped left hands, and a voice came from the panel, saying: “Congratulations!”
THE 64-SQUARE MADHOUSE
Silently, so as not to shock anyone with illusions about well dressed young women, Sandra Lea Grayling cursed the day she had persuaded the Chicago Space Mirror that there would be all sorts of human interest stories to be picked up at the first international grandmaster chess tournament in which an electronic computing machine was entered.
Not that there weren’t enough humans around, it was the interest that was in doubt. The large hall was crammed with energetic dark-suited men of whom a disproportionately large number were bald, wore glasses, were faintly untidy and indefinably shabby, had Slavic or Scandinavian features, and talked foreign languages.
They yakked interminably. The only ones who didn’t were scurrying individuals with the eager-zombie look of officials.
Chess sets were everywhere—big ones on tables, still bigger diagram-type electric ones on walls, small peg-in sets dragged from side pockets and manipulated rapidly as part of the conversational ritual and still smaller folding sets in which the pieces were the tiny magnetized disks used for playing in free-fall.
There were signs featuring largely mysterious combinations of letters: FIDE, WBM, USCF, USSF, USSR and UNESCO. Sandra felt fairly sure about the last three.
The many clocks, bedside table size, would have struck a familiar note except that they had little red flags and wheels sprinkled over their faces and they were all in pairs, two clocks to a case. That Siamese-twin clocks should be essential to a chess tournament struck Sandra as a particularly maddening circumstance.
Her last assignment had been to interview the pilot pair riding the first American manned circum-lunar satellite—and the five alternate pairs who hadn’t made the flight. This tournament hall seemed to Sandra much further out of the world.
Overheard scraps of conversation in reasonably intelligible En
glish were not particularly helpful. Samples:
“They say the Machine has been programmed to play nothing but pure Barcza System and Indian Defenses—and the Dragon Formation if anyone pushes the King Pawn.”
“Hah! In that case…”
“The Russians have come with ten trunkfuls of prepared variations and they’ll gang up on the Machine at adjournments. What can one New Jersey computer do against four Russian grandmasters?”
“I heard the Russians have been programmed—with hypnotic cramming and somno-briefing. Votbinnik had a nervous breakdown.”
“Why, the Machine hasn’t even a Haupturnier or an intercollegiate won. It’ll over its head be playing.”
“Yes, but maybe like Capa at San Sebastian or Morphy or Willie Angler at New York. The Russians will look like potzers.”
“Have you studied the scores of the match between Moon Base and Circum-Terra?”
“Not worth the trouble. The play was feeble. Barely Expert Rating.”
Sandra’s chief difficulty was that she knew absolutely nothing about the game of chess—a point that she had slid over in conferring with the powers at the Space Mirror, but that now had begun to weigh on her. How wonderful it would be, she dreamed, to walk out this minute, find a quiet bar and get pie-eyed in an evil, ladylike way.
“Perhaps mademoiselle would welcome a drink?”
“You’re durn tootin’ she would!” Sandra replied in a rush, and then looked down apprehensively at the person who had read her thoughts.
It was a small sprightly elderly man who looked like a somewhat thinned down Peter Lorre—there was that same impression of the happy Slavic elf. What was left of his white hair was cut very short, making a silvery nap. His pince-nez had quite thick lenses. But in sharp contrast to the somberly clad men around them, he was wearing a pearl-gray suit of almost exactly the same shade as Sandra’s—a circumstance that created for her the illusion that they were fellow conspirators.
“Hey, wait a minute,” she protested Just the same. He had already taken her arm and was piloting her toward the nearest flight of low wide stairs. “How did you know I wanted a drink?”
“I could see that mademoiselle was having difficulty swallowing,” he replied, keeping them moving. “Pardon me for feasting my eyes on your lovely throat.”
“I didn’t suppose they’d serve drinks here.”
“But of course.” They were already mounting the stairs. “What would chess be without coffee or schnapps?”
“Okay, lead on,” Sandra said. “You’re the doctor.”
“Doctor?” He smiled widely. “You know, I like being called that.”
“Then the name is yours as long as you want it—Doc.”
Meanwhile the happy little man had edged them into the first of a small cluster of tables, where a dark-suited jabbering trio was just rising. He snapped his fingers and hissed through his teeth. A white-aproned waiter materialized.
“For myself black coffee,” he said. “For mademoiselle Rhine wine and seltzer?”
“That’d go fine.” Sandra leaned back. “Confidentially, Doc, I was having trouble swallowing… well, just about everything here.”
He nodded. “You are not the first to be shocked and horrified by chess,” he assured her. “It is a curse of the intellect. It is a game for lunatics—or else it creates them. But what brings a sane and beautiful young lady to this 64-square madhouse?”
Sandra briefly told him her story and her predicament. By the time they were served, Doc had absorbed the one and assessed the other.
“You have one great advantage,” he told her. “You know nothing whatsoever of chess—so you will be able to write about it understandably for your readers.” He swallowed half his demitasse and smacked his lips. “As for the Machine—you do know, I suppose, that it is not a humanoid metal robot, walking about clanking and squeaking like a late medieval knight in armor?”
“Yes, Doc, but…” Sandra found difficulty in phrasing the question.
“Wait.” He lifted a finger. “I think I know what you’re going to ask. You want to know why, if the Machine works at all, it doesn’t work perfectly, so that it always wins and there is no contest. Right?”
Sandra grinned and nodded. Doc’s ability to interpret her mind was as comforting as the bubbly, mildly astringent mixture she was sipping.
He removed his pince-nez, massaged the bridge of his nose and replaced them.
“If you had,” he said, “a billion computers all as fast as the Machine, it would take them all the time there ever will be in the universe just to play through all the possible games of chess, not to mention the time needed to classify those games into branching families of wins for White, wins for Black and draws, and the additional time required to trace out chains of key-moves leading always to wins. So the Machine can’t play chess like God. What the Machine can do is examine all the likely lines of play for about eight moves ahead—that is, four moves each for White and Black—and then decide which is the best move on the basis of capturing enemy pieces, working toward checkmate, establishing a powerful central position and so on.”
“That sounds like the way a man would play a game,” Sandra observed. “Look ahead a little way and try to make a plan. You know, like getting out trumps in bridge or setting up a finesse.”
“Exactly!” Doc beamed at her approvingly. “The Machine is like a man. A rather peculiar and not exactly pleasant man. A man who always abides by sound principles, who is utterly incapable of flights of genius, but who never makes a mistake. You see, you are finding human interest already, even in the Machine.”
Sandra nodded. “Does a human chess player—a grandmaster, I mean—ever look eight moves ahead in a game?”
“Most assuredly he does! In crucial situations, say where there’s a chance of winning at once by trapping the enemy king, he examines many more moves ahead than that—thirty or forty even. The Machine is probably programmed to recognize such situations and do something of the same sort, though we can’t be sure from the information World Business Machines has released. But in most chess positions the possibilities are so very nearly unlimited that even a grandmaster can only look a very few moves ahead and must rely on his judgment and experience and artistry. The equivalent of those in the Machine is the directions fed into it before it plays a game.”
“You mean the programming?”
“Indeed yes! The programming is the crux of the problem of the chess-playing computer. The first practical model, reported by Bernstein and Roberts of IBM in 1958 and which looked four moves ahead, was programmed so that it had a greedy worried tendency to grab at enemy pieces and to retreat its own whenever they were attacked. It had a personality like that of a certain kind of chess-playing dub—a dull-brained woodpusher afraid to take the slightest risk of losing material—but a dub who could almost always beat an utter novice. The WBM machine here in the hall operates about a million times as fast. Don’t ask me how, I’m no physicist, but it depends on the new transistors and something they call hypervelocity, which in turn depends on keeping parts of the Machine at a temperature near absolute zero. However, the result is that the Machine can see eight moves ahead and is capable of being programmed much more craftily.”
“A million times as fast as the first machine, you say, Doc? And yet it only sees twice as many moves ahead?” Sandra objected.
“There is a geometrical progression involved there,” he told her with a smile. “Believe me, eight moves ahead is a lot of moves when you remember that the Machine is errorlessly examining every one of thousands of variations. Flesh-and-blood chess masters have lost games by blunders they could have avoided by looking only one or two moves ahead. The Machine will make no such oversights. Once again, you see, you have the human factor, in this case working for the Machine.”
“Savilly, I have been looking allplace for you!”
A stocky, bull-faced man with a great bristling shock of black, gray-flecked hair had halted abruptly by
their table. He bent over Doc and began to whisper explosively in a guttural foreign tongue.
II
Sandra’s gaze traveled beyond the balustrade. Now that she could look down at it, the central hall seemed less confusedly crowded. In the middle, toward the far end, were five small tables spaced rather widely apart and with a chessboard and men and one of the Siamese clocks set out on each. To either side of the hall were tiers of temporary seats, about half of them occupied. There were at least as many more people still wandering about.
On the far wall was a big electric scoreboard and also, above the corresponding tables, five large dully glassy chessboards, the White squares in light gray, the Black squares in dark.
One of the five wall chessboards was considerably larger than the other four—the one above the Machine.
Sandra looked with quickening interest at the console of the Machine—a bank of keys and some half-dozen panels of rows and rows of tiny telltale lights, all dark at the moment. A thick red velvet cord on little brass standards ran around the Machine at a distance of about ten feet. Inside the cord were only a few gray-smocked men. Two of them had just laid a black cable to the nearest chess table and were attaching it to the Siamese clock.
Sandra tried to think of a being who always checked everything, but only within limits beyond which his thoughts never ventured, and who never made a mistake…
“Miss Grayling! May I present to you Igor Jandorf.”
She turned back quickly with a smile and a nod.
“I should tell you, Igor,” Doc continued, “that Miss Grayling represents a large and influential Midwestern newspaper. Perhaps you have a message for her readers.”
