"It"s the same as them "mathematics" that you and that Marvin Stewart kid are always scribbling on pieces of paper," Arnie grumbled. "What do you think they"ll ever do for you?"
"Paper?" Stan repeated, blinking his eyes. "You mean with pens? They write things on pieces of paper with pens?"
Ella stared in disbelief. "You mean without any b.u.t.tonpad, even? No screen?"
"They"ve even got a game they play without a screen," Beth told them. "Chess, or something, they call it.
They push pieces of wood around on a board."
Stan gave Kenny a worried look. "You mean that"s it? They just move pieces of wood around on a board? Nothing else happens?"
"It doesn"t even have batteries," Beth moaned miserably.
"That"s what you get for your trouble, Stan," Arnie said in a hopeless voice. "You do your best, and all you get is rejection. No grat.i.tude, no appreciation. And on top of that they have to be reasonable with you all the time, and discuss everything . . . and talk in that low-key kind of way that drives you crazy-as if you"re not worth arguing with." He shook his head. "They don"t try to solve their problems, Stan. They think about them."
"That"s bad," Stan said. "You mean just sitting there, staring at nothing-not doing anything about anything?"
"Right." Beth waved vaguely at the screen, which was showing baton-swinging police clashing with demonstrators in a street riot somewhere in South America. "It ain"t as if they don"t ever get to see the proper way to handle life . . . I mean, everyone has problems, right? But people need to do something positive about them-like they throw something, scream, smash things, go out and have a breakdown and beat up on somebody, or whatever. . . . But kids these days don"t do things like that any more. All they do is sit and talk, and then say the problem"s gone away, or maybe it ain"t so bad or something.
They won"t face up to anything."
"Hyperpa.s.sivity," Ella p.r.o.nounced. "That"s what Dr. Friedmann said was wrong with Alice"s daughter in Bayview Apartments. Too much thinking is the first sign of losing touch with reality. It"s a big problem everywhere with kids. There are some pills that will get him back up to a normal level of hype."
"Thanks, but I"m sure I can manage fine without," Kenny said hastily.
"Don"t keep thanking people," Arnie complained. "It ain"t good manners. It sounds like people are doing you favors or something . . . as if they"re n.o.bodies trying to get liked."
"Well that G.o.d-awful music you play in there won"t get you anyplace," Beth said to Kenny. She turned toward Ella and Stan. "You know the kind of stuff I mean-no beat or feel to it all, just noise."
"The kids across the street from us are always playing it out the window," Stan said, nodding. "It"s primitive, not even electronic. I went over there one night and set fire to their rose bushes."
"What"s that place you were talking about the other week?" Arnie asked Kenny. "Beat Heaven or something? I mean, what"s it all about, huh? Where in h.e.l.l is Beat Heaven supposed to be?"
"Beethoven," Kenny said with a sigh.
"Same difference. So where in h.e.l.l is that?"
"Is that where they wear all the freaky clothes, Kenny?" Ella asked, giggling and waving her hand at his general appearance.
"They don"t say anything, kid," Stan told him. "Are you ashamed to be yourself? Is that what it is, huh?"
He gestured down at his own crotch-hugging white pants with scarlet side-stripes, tucked into calf-length astronavigator boots, officer"s belt with Alpha Centauri Squadron buckle, and navy, white-trimmed blouse, complete with Strikefleet shoulder patch. "See. You should try to find yourself, and then tell the world who you are-like a starship admiral, for instance. It"s easy once you find yourself and make the effort to fit in."
"But I never lost myself," Kenny said. "And I"m not a starship admiral."
"You have to be something sooner or later," Ella insisted. "You can"t spend your whole life staring at books and listening to crazy music. You have to get involved eventually. It ain"t all gonna change to suit you."
There was short pause. Then Beth lowered her eyes and said dismally, in the voice of someone finally revealing a long-concealed secret of congenital madness in the family, "He says he wants to be some kind of scientist." She looked at Arnie. "What was it, a fizzy-something?"
"Physicist," Kenny supplied. Arnie looked away to hide his shame.
"But that kind of thing is for n.o.bodies, like schoolteachers, technical waddyacallits, or people who make things," Ella protested. "Why would anyone wanna do something like that?"
Arnie showed his empty palms. "That"s the way they are, Ella. They want to work, and learn things.
They say it shouldn"t be the government"s job to keep them. Something to do with "ethics" and that kind of c.r.a.p. . . . I don"t know."
Kenny looked around and shook his head. For the first time his expression betrayed rising exasperation.
He pointed at the screen. "Look . . . that idiot behind the desk is telling you how the U.S. is more respected in the world today because of the way we"ve strengthened our strategic forces, right? But they only voted the appropriation a year ago. They haven"t actually spent any money yet. They"re still only talking about what to spend it on. And even if they had spent it, it couldn"t have made any difference on that kind of time scale. It would be ten years at least before any new weapons ordered through last year"s budgets could be produced and deployed. But they"re talking as if it had all already happened, and taking the credit for it.
"Can"t you see what"s happening? Things in the real world don"t happen fast enough to be entertaining any more. So the media have created a make-believe world that runs at several times the speed of real time, with a crisis every half hour and always an instant solution.
"It"s the same with all the other "crises" that they invent and then say they"ve solved. How could a crime wave of "epidemic proportions" that n.o.body had heard of before suddenly materialize in two months, just before Ed Callones ran for governor-and with a program already worked out to fight it? . . . And then have been "successfully eliminated" in just as short a time after he was elected? It couldn"t have. Things don"t change that quickly. The "economic recoveries" that somebody or other is always supposed to be masterminding every six months are from slumps that never happened. The "environmental catastrophes"
that are always supposed to be imminent never materialize. And yet people everywhere believe it all and carry on paying . . ."
Kenny looked from one to another of the four faces staring blankly back at him. He exhaled a long sigh.
"It doesn"t matter. . . . I guess I got carried away a little. I was going out anyhow. I"ll just be on my way.
You folks have a good evening." With that he turned away quickly and left, closing the door behind him.
An uncomfortable silence persisted for a while. Finally Stan said, "Gee, I didn"t realize you guys had it so bad. . . . I guess he"ll probably grow out of it, huh?"
"What was he talking about?" Ella asked, still dazed after Kenny"s outburst.
Arnie was still looking down at the floor. Beth came over and leaned her head against his shoulder. "Oh Arnie," she sobbed. "We tried, didn"t we? Where did we go wrong?"
Outside, Kenny pulled his parka on over his jacket and walked around to the back of the house to pick up the backpack, suitcase full of selected books, and crammed briefcase that he had dumped from his bedroom window. He carried his things to the end of the street and waited in the shadows of the shrubbery by the corner streetlight. After about ten minutes, Marv Stewart"s battered "95 Chevy van appeared. Marv was at the wheel, with Bev Johnson and Harry wedged in next to him up front. Kenny slid open the side door and hoisted his bags inside. Then he climbed in to join the crush of young people jammed in the back amidst coats, rucksacks, suitcases, sleeping bags, and bundles of books. "Okay, Kenny?" Marv called from the front as the van pulled away. "Any problems?"
"No," Kenny answered. He felt drained, now that the worst was over and he was committed. "It went okay. Did everyone else make it?"
"All here," Tom Pearce"s voice said from somewhere in the shadows nearby. "You"re the last."
Kenny gradually made out the forms as his eyes adjusted to the darkness. Tom, who could read IBM microcode and wanted to get into AI research, was propped just behind him, next to Nancy, who had painted the murals in Giuseppe"s restaurant in Oakland. Sheila Riordan, who understood tensor calculus and wrote plays, was behind them, with Kev, the chess expert, and Charlie Cameron, who was into number theory and could recite pi to fifty places. . . . And yes, the others were all there, too, farther back. Kenny leaned back and made himself comfortable between his backpack and a pile of blankets.
"So what"s the schedule?" he called out to Marv.
"Down the Interstate and on through L.A., bound for Phoenix. We"ll probably stop for breakfast somewhere near the Arizona border."
"When do you think we"ll make Boston?" Kenny asked.
"Aw . . . should be sometime around Tuesday, I figure."
"Uh-huh."
Kenny settled back into the shadows and closed his eyes to rest. He wondered if it really was the way people said. Boston-home of the revolution of the New Wave generation, who were sweeping away the rejected, outmoded values of an era that was ending, and replacing them with new ways born of the rebelliousness of youth.
It was said that there were bookstores on every block there, galleries exhibiting paintings and sculptures, theaters, science labs, and symphony orchestras playing to packed halls. The University had allegedly closed down its faculties of paranormal phenomena and ant.i.technology to make room for arts, sciences, engineering, and business, and there were free public lectures on everything from differential geometry and molecular evolution to s.p.a.ce engineering and nuclear physics. People ate real steaks with wine in restaurants with candlelit tables; portrait painters worked at easels set up on the sidewalks; and string quartets played in the streets.
It had been a tough decision in some ways; but sooner or later people had to take responsibility for their own lives, Kenny thought to himself-even if it did cause some upsets and misunderstandings in the short term. His folks would miss the money he"d been getting from working illegally at the computer store on Sat.u.r.days to supplement their phoney welfare checks, but they"d manage okay in the end. He was satisfied in his own mind that he had met his responsibilities to the best of his ability; he owed them no more. Eventually, the time came when you had to think of yourself. He"d explained it all as best he could in the letter that he"d left in his room. They"d come to understand in the end, he was sure . . . even though it might take them a while.
RULES WITHIN RULES.
Patrick and Michael Flynn were twin brothers, the sons of a family doctor who practiced in a sleepy Irish village called Ballaghkelly. The village was little more than a crossroad buried in a huddle of houses and outlying farms, and boasted one church, a school, a few tiny stores, a newsagent"s that was also the post office, and three pubs. Little ever happened to change the routine of a typical day in Ballaghkelly. At six o"clock every morning, Willie Maherty"s one-horse dray would clatter off on its round of the farms to collect the churns from the previous day"s milkings before the day warmed. Twice in the day and once in the evening-exactly when was always a standby topic of conversation if the weather looked settled-the bus from Kilkenny would arrive and depart again. And after nightfall, the farmers would begin gathering in O"Toole"s, Mulligan"s, and O"Shaughnessy"s to nod and murmur over their pints of porter while they reiterated worldly wisdoms that had been handed down from father and grandfather for generations. Life had always been that way, and n.o.body-in the unlikely event of such a thought entering his head-could have conceived of its being any other.
Patrick was a voracious reader and did brilliantly in school. Kevin Halloran, the schoolmaster, became convinced that the boy was a prodigy and persuaded him to try for a scholarship to study mathematics at the university in Dublin. Patrick was accepted, gained a degree with honors after some years, and then departed to pursue postdoctoral studies in America, which was somewhere across the sea, in the opposite direction from England-whichever way that was. Michael, too, was studious, but his vocation lay in a different direction. He left home to train at the Catholic seminary in Waterford, and shortly after Patrick left for America, Michael was installed as the new parish priest in a town not far from Limerick.
Although the brothers corresponded, they did not meet again for several years. Then Patrick wrote from America to say that he had been offered a research fellowship at Cambridge, England, and that before taking up his new position he would come back to Ballaghkelly on a short holiday, which he referred to in his letter as a "vacation." Michael, too, obtained leave of absence and came home for the big family reunion. There was a fine party at the Flynns", as good as any wedding or funeral wake that even the oldest in Ballaghkelly could remember, and in the course of the evening it seemed that every pair of feet from twenty miles around had pa.s.sed over the threshold, bearing some well-wisher to join the family in a gla.s.s of stout and perhaps sample one-or two, or maybe a few-of the choice blends of whiskey brought in for the occasion. At last, after it was all over, and their father had tottered unsteadily but contentedly away to his bed, with their mother closing the door after him and warning them sternly not to touch any of the mess until morning, Patrick and Michael found themselves alone with their gla.s.ses, staring at the logs crackling in the large brick fireplace in which, as boys, they had watched faces and dragons together, many years ago.
"Ah, "tis a wonderful place ye"ve been tellin" me about, Patrick," Michael said distantly. "With them Americans drivin" their motorcars along roads as wide as ten boreens, and flyin" around in the sky as naturally as the likes of us would take the bus into Kilkenny . . . and walkin" around on the moon itself, if you"re not after pullin" me leg."
Patrick took a sip from his gla.s.s. "And that isn"t the half of it, Michael. There"s the size of the place. . . .
Do you know, the nearest part of the U.S.A. is two hundred times farther away from here than Dublin, yet it"s still nearer to us than it is to the other side. Can you imagine that?"
Michael tried to visualize what it meant, but in the end shook his head with a sigh and sank back in his chair. "Anyhow, about yourself, Patrick," he said. "Ye told us enough about America in the letters ye wrote. But there was never a time when ye said anythin" about what ye were doin" in that university." His brow creased uneasily. "Ye wouldn"t have gone and got yourself mixed up with the makin"s o" these bombs and things, now, would ye, Patrick? "Tis the devil himself"s work ye"d be doin"."
Patrick gave a short laugh. "You don"t have to worry yourself about anything like that, Michael. There are some areas of research that aren"t connected with the weapons program, you know." Michael looked relieved. Patrick went on, "In fact I"m not involved with any aspect of applied research at all. My work is all to do with pure mathematics-in fact, an area called number theory, if you"d really like to know." Modesty had prevented him from saying much about this in his letters. Now, however, with the euphoria of being home again-and perhaps also from the effects of the party and the drink-he was unable to keep just a hint of a swagger out of his voice.
Michael seemed not to notice. "Ah, so that"s what it"s called, is it?" he replied, nodding slowly. "And what would ye be doin" with the numbers? Is it some kind o" computin" with them electronic machines?"
"We use computers a lot, but that isn"t really what it"s all about," Patrick said. "Number theory is simply the study of the properties of the whole numbers themselves, and of the rules for manipulating them."
"And that could keep an honest man busy for a lifetime?" Michael sounded dubious.
Patrick laughed again. "A lot more than that, Michael, believe me. People have been developing it for centuries, and they"ve still only scratched the surface. My work only touches upon one little piece of it."
"Is that a fact, now?"
"It has to do with the implications of something known as G.o.del"s Incompleteness Theorem. It, er . . . it deals with the inherent limitations of any formal system of rules, no matter how complex."
"Ah." Michael gazed silently into the fire for a few seconds. "G.o.del, you say, eh?"
"Kurt G.o.del . . . an Austrian mathematician. He formulated the theory in 1931. What it says is that all consistent axiomatic systems of number theory include undecidable propositions." Patrick paused for a second. "Well, actually the original was expressed in more technical terms, and it was in German, of course . . . but that"s about what it boils down to."
Michael squinted and rubbed his nose with the crook of a finger. "Well, it might as well be in German still, for all the sense I can make of it," he confessed. "It"s havin" a bit o" fun at your brother"s expense, ye are, if I"m not mistaken. Now could ye imagine me in the pulpit on a Sunday, railin" me congregation with that kind o" talk? Why, wouldn"t Mother McCreavy from the village be down to the post office at the crack o" dawn the next mornin", writin" letters to the Holy Father himself? Away with ye now, Patrick. If what ye just told me can"t be said in G.o.d"s own English, then it"s likely as not that it"s without any meanin" at all. I"m thinkin"."
Patrick grinned apologetically. "I guess I just couldn"t resist it." He refilled their gla.s.ses from the bottle standing between them. "It concerns the systems of rules that govern mathematical proofs. What it says is that no set of rules can ever be complete enough in itself to enable every true statement to be proved.
There will always be at least one statement that can only be proved by bringing in another rule from outside the system. And if you add that rule to make a new, bigger system, then the new system will contain at least one statement that would require yet another rule to prove it, and so on. There"s no end to the process. However big you make the system, it can never be complete enough to prove all true statements. That"s why it"s called the Incompleteness Theorem."
A silence fell while Michael tasted his drink and sat back to reflect on this. Eventually he said, "You"d think, now, wouldn"t you, that rules and such would be somethin" a priest would know all about, for isn"t every day of his life just a matter of pa.s.sing on a few simple rules of livin"? But I"m blessed if I can tell the head from the tail o" what you"re tellin" me now, Patrick-blessed if I can at all."
"Actually, that"s not a bad a.n.a.logy," Patrick said. Michael looked puzzled. Patrick sat forward and spread his hands to explain. "People, nations, society in general . . . they all have systems of rules-laws-that govern the ways they behave. Now this comparison is only a loose one, you understand, but it gives an idea-no system of social rules is ever complete, is it? For who writes the laws that govern the lawmakers? You see my point-such laws would have to be written from outside the system. But then the same questions would still apply: Who would write the laws to govern whoever wrote those laws? You could go on as long as you like, but you could never completely solve the problem."
Michael considered the proposition for a while. " "Tis a sad picture of the human race that you"re paintin"," he commented at last. "Ye make it sound as if everybody in the world is unable to live a decent life without rules to stop them from robbin" each other and cuttin" each other"s throats."
Patrick sighed. "True, but what can you do? That"s the way the world is out there. They"re all in a rat race, scrambling and trampling over each other to get a bigger piece of the cake. And when a bunch of them get into a position where they can write their own rules, it brings out the worst. Sooner or later they have to be regulated somehow, but that never solves the problem. All it does is shift it another level higher up."
"How would ye be meanin"?" Michael asked.
"Oh, the legal system over there in America is a good example," Patrick replied. "The lawyers make money by complicating the problems that they"re supposed to be solving, which suits them fine, but doesn"t suit the clients. They can get away with it because the rules let them, and they write the rules. It"s the same with price-fixing cartels in business, or the lobbying that corporations can do to get tariff laws and other restrictions pa.s.sed to get an edge over their compet.i.tors. And it"s the wealthy who get to influence how loopholes are written into the tax code. You see-whenever a group can write its own rules, it writes them in its own favor. Everyone else loses."
Michael shook his head sadly. "That"s a terrible thing . . . that with all these machines and all, and them fellas walkin" around on the moon, they"d still be havin" this kind o" trouble with each other. Ye"d think, now, that with all their talk about puttin" the Russians in their place, the government would have somethin"
to say about these carryin"s on. Have they no care at all for the people that"s payin" the money for the motorcars for them to go paradin" themselves around in with all their grand speeches and smilin" faces?"
"That"s my whole point, Michael," Patrick agreed, nodding. "You"re right-in theory the government ought to be able to prevent things like that through the power of law. But in practice it doesn"t work out, because the government in turn isn"t subject to any law but its own, and the same thing happens. The federal bureaucracy is out of control. A bureaucrat"s status and income are geared to the size of the department he runs and the number of people in it. Therefore they all want their departments and budgets to grow bigger. To justify that, they have to have problems that are getting bigger instead of being solved, and the legislation that emerges makes everything worse, not better. Take the welfare system as an example-it costs more than anything else in the government budget. If everybody in the country became self-sufficient, the agencies would be out of business. So laws get pa.s.sed which guarantee that there"ll always be a bottom layer of dependents who"ll never able to climb out of the trap-such as minimum wages that make them unemployable, or housing standards that drive prices above anything they can afford. And then, of course, we"ve got the defense industry and the military-they don"t want any relaxation of tensions with the Soviets. And the banking system that finances the government also owns the contractors that the government spends the loans with-so they"re making money with both hands by billing the taxpayer for lending their own money to themselves. It"s a good deal-you sell a few billion dollars worth of sophisticated weaponry, put it down holes in the ground for ten years and wait for it to become obsolete, then sc.r.a.p it all and start over again. And while the banks are owed money, they write the rules."
Michael stroked his chin thoughtfully as he stared into the fireplace. "And there"s honest people toilin"
away the lives that G.o.d meant them to enjoy, just to pay for it all, eh? And to think, with all them machines and the clever fellas in the universities, couldn"t they all be livin" like kings?"
"I guess so." Patrick sighed. "But they won"t. Too many people would have to come down a peg or two, and they"re the ones who write the rules. Oh, I suppose you could think in terms of a world government or something one day, but the same would happen eventually because there wouldn"t be any rules to control them."
"Maybe they should try lookin" in that number theory that ye were tellin" me about," Michael suggested.
"Wasn"t it all to do with writin" rules within rules, and isn"t that what we"re talkin" about now?"
Patrick frowned. "Number theory doesn"t apply here," he said. He kept his voice even to avoid sounding as if he were talking down to his brother. "The a.n.a.logy was only a loose one. G.o.del"s theorem merely deals with sets of formal symbolic axioms. It doesn"t have anything to say about social rules and how people should behave toward one another. You"re reading too much into it."
"I have to disagree with ye, Patrick," Michael said. "It has everything to say-about some very good social rules that were written down a long time ago now, and very concisely."
Patrick stared across with a puzzled frown. "I"m not with you, Michael," he said. "What do you imagine G.o.del"s theorem says that has anything to do with people?"
"Tch, tch." Michael shook his head reproachfully. There was a faint smile on his face, and his eyes twinkled in the glow from the fire. " "Tis a shame ye"ve never seen it, Patrick," he replied. "It"s been all these years now, and ye mean to tell me that ye"ve never noticed what the first three letters of G.o.del are?"
THE ABSOLUTELY FOOLPROOF ALIBI.
The phone on Professor Osbert Osternak"s desk rang. "Excuse me," the snowy-haired chief scientist of the Erwin Schrodinger Memorial Research Inst.i.tute said to the younger man sitting across from him.
"Yes? . . . This is Professor Osternak, yes. Who is this, please? . . . Oh?" The old man"s eyebrows shot upward almost to his hairline. "Oh really? That is most interesting." He settled back in his chair and sent an apologetic shrug across the desk. It seemed that this was going to take a while. "Yes, that is true, quite true. . . . Yes. That is so. But how do you . . . of course. Amazing! And so it happens. . . . So, what can I do for you?. . ."
Dr. Rudi Gorfmann, Osternak"s deputy, wearing a black bow tie and dress shirt beneath his white lab coat, sighed impatiently. The old fool would be prattling on for half the evening now, and Gorfmann wanted to be on his way to Innsbruck for the Celebrity Club"s charity fund-raising banquet. He stood up and turned to face away across the office. With its antiquated wooden bookshelves and panelling-even a chalkboard!-it was as much of an anachronism as the mind it belonged to. Gorfmann paced across to the window of the Gothic "Keep," which on its rocky eminence formed an incongruous focal point for the Inst.i.tute"s modern laboratory blocks and reactor housings, and stared out at the peaks of the Bavarian Alps, frosty against the darkening sky. His reflection stared back from the gla.s.s: a clean-shaven face, neatly groomed blond hair, gold-rimmed spectacles. Meanwhile, Osternak"s voice babbled on behind.
"This is unbelievable. When does he intend to do this?. . . Ach, so. . . . Can we get together and talk about this?. . ."
Old scientists should be forcibly retired at forty, Gorfmann fumed to himself. Newton, Einstein, anyone of brilliance . . . none had done anything useful beyond their twenties. All they had achieved after that was to place the seal of unchallengeable authority on ideas that had become outmoded, making further progress impossible until they died off and made room for new blood with new vigor. If it weren"t for such tyranny of age and tradition, Columbus would have landed on the moon, Watt would have harnessed fusion energy, and the Wright brothers would have built the first starship. And Rudi Gorfmann would have . . . He realized that Osternak had stopped talking on the telephone, and turned back to face the desk.