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The purple number cruncher

By Marc Whiteley


The bedside computer belched out a wisp of aroma calibrated to put its owner in a good mood just before he woke, put the power shower on standby alert and beeped softly at the correct frequency determined to wake Professor Thaddeus Hobgoblin quickly but gently from sleep without disturbing his wife. He leaned over, slapped the metal sensor that detected the micro currents across his skin and when the beeping had stopped, thumbed the directional transceiver switch. Now the talking from the terminal would not wake his wife either, as long as his head was between the small screen and her. Neither would she be woken by his talking as the directional mike could pick up and amplify a whisper from the right direction.

"What?" he grumped into the microphone. He didn't like being woken up.

"Time to get up professor," spoke the intentionally annoying voice from the computer, "the countdown has just started, you've got about three hours. The car's on the way over to pick you up now and you asked me to remind you that your new technician, a Doctor Saskins, is starting this morning. He'll meet you there." There was a soft sound, almost subconsciously heard as the computer finished its talking. It was a noise that you hardly noticed but managed to convincingly convey the fact that the computer had finished.

Wide awake now, thanks to the tone of the computer's voice which was sufficiently irritating to wake the professor without counteracting the aroma and making him grumpy, Professor Hobgoblin whispered, "Thanks, tell Saskins, I'll be there in about three quarters of an hour." The professor flicked the switch to turn the computer back to standby mode and climbed out of bed carefully, to avoid waking his wife. After a quick shower he threw on a pair of jeans, pulled a t-shirt over his head and slipped his feet into an old but comfy pair of running shoes. Downstairs he grabbed a quick cup of coffee and a chocolate biscuit, recorded a note for his wife on the memo-box, threw on a clean lab-coat and was out the door, lighting a cigarette just as the car pulled up at the kerb.

Fifteen minutes later the car pulled up outside the Institute of Bizarre Science and Professor Hobgoblin ran up the steps to the main door. He barged through the entrance, waved hello to the security guard and sprinted up the two flights of stairs to the Inscrutable Numbers laboratory. Awake now and with a bit of a dramatic flair he kicked open the door, stood framed in the doorway, backlit from the corridor and demanded of Saskins, who had arrived five minutes before and was looking round, "How long does the converter say we have left?"

Saskins glanced about to locate what seemed most likely to be a converter and checked the screen, "Two hours, seven minutes..........now."

The professor grimaced, flicked the stub of his second cigarette accurately into the ashtray and replied, "A relatively short time but an annoyingly long wait." The two men shook hands and exchanged nods of greeting. Each was well aware who the other was.

"I guess so," replied Saskins. "Popular rumour around the Institute tells me that the machine is about to finish doing its thing and spit out an answer any day now, in about two hours judging by the converter. Is it right that you're trying to calculate a value for infinity?"

"Exactly," grinned Professor Hobgoblin, "as long as it doesn't just keep saying '42' and giggling like the prototype did."

"Pardon?" asked Saskins, "Do these hypercomputer jobbies do that sort of thing a lot then? I haven't used them much. My most recent doctorate was in five dimensional topographics and the one I'm currently working on is in irrational logic. I've mostly done particulate chemistry and plasma physics here at the institute before I asked for the transfer to your department."

"It wasn't really the computer's fault Saskins. No-one has ever actually seen a computer go insane before so I didn't predict that it might happen. The prototype was the most powerful artificial intelligence unit in the world, it had been specifically designed for this task. Its lucky I realised what had happened to it otherwise I may have guessed that this computer had reached the limit of electronic intelligence, that it had found and crossed the maximum value for that thin and theoretical line which separates genius and madness in machines."

"So why 42? What has that got to do with anything? That can't be the value for infinity or somebody would surely have realised by now."

"The computer was exposed to as many relevant bizarre ideas as possible to help it cope with the conceptual nightmare of it's program. I fed it C.S. Lewis and Lewis Carroll. It read Douglas Adams and Arthur C. Clarke. It was given Frank Baum and The Brothers Grimm. It read Erich Von Daniken and Stephen Hawking, Asimov and James Herbert, anything that had strange concepts or where the characters had no idea what was going on but all was explained at the end, good or bad. The computer was pumped full of examples of abstract ideas and suspension of logic. In fact it tended to be fed anything you yourself were reading at the time."

Saskins eyebrows rose in surprise. "Me? How did that come about?"

"Well, you amongst others. I asked the other professors to keep an eye on what their young technicians were reading in the way of conceptual literature, especially science fiction, fantasy and pseudoscience. It just seemed that the computer particularly liked your reading material. That is also one of the reasons I accepted your application to transfer here. I only fed the prototype 'The Hitch-hiker's Guide to the Galaxy' because you were reading it at the time. The computer liked it so much that it kept wiping it from its memory banks and reading it again. 6.02252 x 1026 times it read that series of books."

"A mole of Hitch-hiker's Guides?"

"Yes. I was teaching it to fully understand other numerical constants as well, to prepare it for calculating the infinity constant and it had recently taken in Avogadro's number. I'd just fed it a small piece of pi when you started reading the Lensman series. The prototype read it 3.14159265358979323846264 times."

"Exactly?"

"It got a short way into 'First Lensman' for the fourth time and stopped partway through a letter in the middle of a word in the middle of a sentence. The prototype had some very wierd stuff in it." The professor sighed, "It should have been able to handle almost any strange concept that could possibly be imagined. And it's got to be admitted, Saskins, that the program I gave it was a very strange concept."

"If it read the Hitch-Hiker's Guide that many times I can see why '42'. But how exactly does it work?"

Professor Hobgoblin was glad of the chance to explain his wonderful toy to a scientist who didn't know much about it, he got so fed up with the pretentiousness of the other professors sometimes. "Cup of tea Saskins?" He gestured at a chair and flicked on the kettle as Saskins took a seat. The two men engaged in polite and civil small talk as they settled themselves and started on their cuppas. Soon enough the conversation turned back towards the Purple Number Cruncher. Professor Thaddeus Hobgoblin settled back for a brief lecture.

"Well Saskins, the machine is set to count up to infinity and thereby quantify for us one of the physical constants of our Universe. Infinity can, for most purposes, be considered the reciprocal of zero. Zero is a very abstract concept but most people don't realise how weird it is, they just file it away in their heads as meaning roughly nothing. Most people handle infinity in a similar, vague way, they just file it away as meaning roughly going on forever or not really meaning anything at all.

"I hoped that if I fed the prototype concepts of a strange nature it would be able to think of infinity in the same way most humans do. The neural net understood the concept of fiction so literature seemed the best way to introduce new ideas. It would take the ideas on board, realising that they were fiction and it gave me a base to work from to program its task. I hoped that it would be able to treat the program as a conceptual task, possibly assuming it was fiction but still using all its mathematical skills to solve the problem without crashing.

"Most computers would have short circuited and completely malfunctioned at being asked to calculate infinity but the prototype retreated into insanity because it could handle bizarre ideas. It didn't blow a fuse, it just retreated into some very dodgy logic. I don't think that it really understood the difference between what was fiction and fact at the end. It failed its purpose but provided the psychiatrists with some fascinating data.

"I think I know what went wrong with the prototype so I've exposed the Purple Number Cruncher to a more selective range of literature this time. Do you know the story 'By His Bootstraps' by Robert Heinlein?"

Saskins nodded, "I know that one, it's about a man who gets caught up in a circular time segment and ends up being nearly all of the characters at some point or another."

"That's the one. Well it was circular logic, infinity type things like that, specific examples of people trying to work out something inscrutable then finally understanding in broad terms the concept they were attempting to grasp. I also unhooked most of the circuits that I think allowed the prototype to go insane.

"With any luck this one will do its job without going mad at how impossible it is. Once it has quantified infinity it will be able to go back through its calculations and resolve all the equations it was working using infinity as an unknown amount. Hopefully that way it will ignore the fact that the equations it is using make no sense and keep it from going insane. After being exposed to all the weird literature it will hopefully just keep working on the problem in the hope that all will be explained later. Unfortunately the most dangerous time for the computer is as it gets towards infinity and realises what is about to happen. We should keep an eye on the controls and readouts,"

He walked over to the control panel, gave Saskins a brief explanation of the readouts and controls as he glanced at the McAdams compensator, frowned and adjusted the Planck resistor. "That's partly why I added the countdown and the converter." He gestured at the large opaque, coloured case of the Purple Number Cruncher and the black cased readout of the converter, "The computer also counts down from infinity and the converter picks up the countdown from about three zillion googols then converts it to time left. The computer will hopefully ignore the fact that it is a paradox to count down from infinity while it is trying to work out infinity and, as I said, all will be resolved when it actually understands the concept."

The professor glanced back up at Saskins and continued, "And in case the Institute grapevine didn't explain and you were wondering why it doesn't take an infinite amount of time to calculate infinity..." he paused and Saskins looked like he had just been about to ask that very question, so he continued. "As anything less than infinity is by definition finite, I started the computer counting from ten so that it only had a finite amount to calculate. Similarly, the countdown is only going to ten. That way it will only take a finite amount of time and I know when I'll have an answer." Saskins looked suitably impressed and wondered whether the professor had also studied irrational logic.

The Professor glanced at the converter, "Forty-three minutes and nine seconds, plus however long it takes the Number Cruncher to resolve the paradox, retain its sanity and give us an answer."

"But how exactly does this Purple Number Cruncher thing know when it has reached infinity?"

"Good question, Saskins," replied the Professor. "You understand Heisenberg's Uncertainty Principle, of course," he laughed at his foolish question, who didn't understand it? "As your certainty of the position of an electron reaches infinity, your certainty of its momentum tends towards zero. I set the Number Cruncher to determining the exact position of an electron. As it does so it also calculates the odds of it knowing the right answer. Once it has determined the exact position of the electron, the odds of it being right will be infinity to one. Obviously the certainty of the momentum of the electron will at that time be zero, the Number Cruncher won't have a clue where the electron is going or how fast. That's how it will know when it has reached infinity."

There followed a forty-five minute debate on the equations involved in Heisenberg's Uncertainty Principle (delving extensively into the Schrödinger equation, Dirac's constant and Planck's law) and an equally lengthy discussion of how exactly the Purple Number Cruncher set about determining the position of an electron but we'll skip over that. If you want to know the details of the Purple Number Cruncher's workings you should purchase the book 'Mission Improbable:Purple Infinity.' by Professor Thaddeus Hobgoblin published by the Institute of Bizarre Science Press and priced £24.99.

A man of lesser brain than Saskins would have spent the time during this rather boring and involved conversation wondering what pattern of wallpaper he should put up in his new loft conversion and trying to hint that he would like another cup of tea. Saskins, possessing a brain the equal to the professor's but less obsessed with abstract thoughts and more firmly grounded in reality didn't have any trouble keeping up.

By the time they had finished talking and the conversation had turned to more understandable concepts for another two cuppas, the readout on the converter said slightly less than ten minutes were left of the countdown. Saskins and he both went over to the control panel and began adjusting dials and tapping commands into the keyboard. The adjustments were not really necessary but they both felt better to be actually doing something rather than just standing waiting for the last ten minutes for the answer.

"So what do you intend to do with infinity once you've discovered it, Professor? I can see several possible uses, or is it just a 'because-it's-there-and-no-one-else-has-ever-done-it' kind of thing?"

"Oh, there's endless uses Saskins. Probably not an infinite number of uses for it, but lots at least. The main uses will be in the fields of mathematics and physics. There is a lot more we could learn, or at least theorise, about the nature of space-time and the various aspects of what we call reality. With a decent idea of what infinity actually is then we may be able to understand our supposedly infinite Universe a lot better. If you want later I'll explain fully my theory on subatomic particles. We have discovered many of these; protons, photons, neutrinos, quarks, gravitons and quadriphasons to name just a few.

"Some of these particles are much, much larger than any atom. Gravitons for instance have almost literally no mass, but are about thirty metres across. It took a solid piece of lead two miles thick to even detect one of these things as they are so insubstantial and invisible to the eye. I think that there are subatomic particles that are even larger than that."

"I believe that one day we will discover that the Universe itself is a subatomic particle. Obviously it is made up of smaller particles, like neutrons, electrons and all the others we are used to. I think if we look far enough we'll find that the universe is a constituent particle of every atom and is a particle of itself, round and round in a strange cosmic dance. Knowing what infinity is will allow me to get a better idea of whether it may be true. It's a bit of a strange idea and I haven't published because I don't think anyone will believe it yet and it may harm my reputation.

"However, if the Purple Number Cruncher does its job properly and gives a good answer then I will be able to use it to sort out a proper mathematical proof that the Universe is a particle of itself and everything is a part of everything else in an infinite regression. Being able to use infinity properly in my calculations will help gain some evidence in one way or another, whether it agrees with me or tends to disprove me."

The Professor frowned, "I suppose there's always the danger that those military chaps want to use it in some sort of weapon but hopefully they won't be able to find a way or even think of trying."

"Erm, I'm sorry Professor but I worked for a while recently in the weapons lab and the boffins there think they can use it to find a way of controlling nuclear fission so they can use atomic bullets in rifles that will make a controlled explosion not a runaway chain reaction. It will be a definite one hit-kill bullet. Maybe with little or nothing left of the body, maximum soft target take-down, what. Whatever they're going to do with it, they seemed quite keen on getting their hands on it."

The Professor really didn't like the idea of his research being used for war but there was not really a lot he could do about it. He couldn't afford to run a research project this expensive without funding from the Institute and the Purple Number Cruncher had nearly finished its task.

Professor Hobgoblin was the only person who could possibly have built the Number Cruncher, but now it was running there were two or three people who knew how to keep it running and would be able to get an answer from it. If he refused to work the machine, someone else would just do it and Professor Hobgoblin would be expelled from the Institute Of Bizarre Science. He'd be buggered if he was going to let anyone else take the credit for his work.

At least atomic bullets would be too expensive for general use on civilians. The idea behind them was a partly psychological one with the idea that if you knew you would almost totally disintegrated if you got shot anywhere would be quite scary (it was hoped) to enemy soldiers. The Professor consoled himself with the thought that the only people likely to get shot with the bullets would be people stupid enough to want to join an army, go to war and get shot at anyway.

By this time, the countdown was well into the last minute. The two men fell completely silent, just mouthing the countdown from the last ten seconds. When it reached zero, the Professor broke the silence, "It should take about thirty seconds to resolve its internal equations and the various paradoxes set up by its program, then we should know whether have an answer or another insane computer."

They waited again in silence for nearly a full minute. Suddenly there was a sound something like the pop of a million daisies all opening at the same instant and the Purple Number Cruncher spoke in a bland, uninflected but still deep and resonating voice, "Ah. Very interesting. I understand infinity." It thought for another microsecond, "I also seem to understand zero, fascinating."

The Professor's face lit up. Of course! By using Heisenberg's Uncertainty Principle to calculate infinity, it had also given itself an exact idea of zero. Computers could use it but they didn't understand it, there was no need. That's why when the the professor found infinity it would not take computers this powerful to understand it, they would just use the symbol. The Purple Number Cruncher actually understood the concept. Even more amazing, it seemed to be able to handle and understand completely the concepts of zero and infinity at the same time! Could it be true? He decided to ask.

"You understand zero?"

"Yes."

"You understand infinity?"

"Yes."

"You understand them both at the same time?"

"I shall try." This gave the Professor pause. Maybe the Number Cruncher didn't understand them both at the same time, maybe it could handle one or the other as long as it didn't think about both. He hoped he hadn't suggested something that might be bad for it.

Before he could order it to stop thinking about both and give him just the answer to infinity, the Purple Number Cruncher spoke again, "I understand infinity, I understand zero. I am infinite. I am nothing." It vanished leaving a flattened square of carpet against the wall.

Professor Hobgoblin and Saskins gasped in astonishment as it went, then gasped in amazement when it reappeared in the same position but with the eye twisting illusion of seeming as if it was viewed from a great distance. "I am infinite and nothing." It chuckled in its deep voice, "I'm everywhere and nowhere, baby. That's where I'm at." It seemed to expand without changing size and then vanished again. It reappeared behind the three men saying, "Such sights, such wonders, such beauty in the Universe," then vanished for the last time.

The incredulous silence was again broken by the faint hum of the control panel lighting up and its screen flashing with a sequence of strange symbols and numbers. The professor heaved a sigh of relief, it was the answer the Purple Number Cruncher had been working on. Obviously it had found time to complete its program and download the information. He would study it now and later he would definitely try to work out what had just happened here. This was almost as exciting as having calculated infinity. He had a sneaking suspicion that the Number Cruncher had become quantum. Infinite and zero at the same time, maybe expressing something like wave-particle duality, although he couldn't be sure.

The two men looked carefully at the screen. Neither of them by themselves could have imagined a number so large that you couldn't add one to it and get a bigger number. What they saw on the screen changed that. The number represented was actually an equation which was so cunning and complex that it would be impossible to make the answer it would give out any larger. Professor Thaddeus Hobgoblin had discovered the true meaning of infinity. Saskins pressed the button to print the equation out. He wanted to keep a copy. Later he would frame it and put it up on the wall of the laboratory in his house, or maybe get it printed on a T-shirt. He would definitely put the equation into a spreadsheet on his home computer to see what happened, just out of interest.

The professor rubbed his hands together gleefully, "Excellent!" He rushed over to a computer terminal and sat down. Frowning in concentration as he tried to remember the shortcut keys for the symbols in the infinity equation, he typed his discovery into the middle of a page of text showing on the computer. He cut and pasted the equation into another, smaller document, saved both and worked his way through menus that culminated in both files being encrypted and sent directly to his publisher.

"That's another best selling book and another award winning new thesis published."

"Simple as that?"

"Well obviously I'd already written them, I was just waiting for the actual equation. There's no point writing a book after the discovery, that's when you write a sequel. You get everything you want written while you're working on it, while you're still excited and inspired and turning it all about in your head. I think you get better writing that way. You're still considering all angles and it shows in the writing, it's a more interesting read if you write it when you don't actually know.

"Then, when you've published your paper, had a while to think things over and read the responses to your paper and book, you write a sequel. It sells almost as well as the first because the subject is still hot and you've got the book out in time to catch the market, as well as being the discoverer or inventor, you ensure your reputation as the foremost authority on the subject. Especially if you print a coffee table edition in dumbed-down language and with lots of glossy pictures for the plebs. Be one step ahead, that's the key."

Saskins grinned, this wierd logic appealed to him. From seeing what had just happened with the Purple Number Cruncher, this strange attitude to publishing and the professor's reputation, he was beginning to feel quite glad that he had asked for a transfer to work with him.

"Anyway," continued the professor, "I'll worry about the infinity equation later. Right now I want to know what happened to my hugely expensive computer. I had hoped to use it for all sorts of other things afterwards. Once I'd calculated infinity I was hoping to use that in the Number Cruncher's next program. I was going to calculate pi right to the end, to it's last digit. Mathematicians and computer experts have been working on it for centuries but I thought I'd be able to do it in weeks. Not without a hypercomputer I can't."

"The last digit of pi?" enquired Saskins, grinning. "Already been done. I did that for my most recent doctorate. I needed it to calculate the circumference through the fourth dimension of a particular 5D hypersphere. The last digit is a seven. Didn't you read my paper?"

The professor looked stunned. He spluttered a bit then asked, "You've already done it?

Why on earth hasn't the whole world heard about it by now? A seven? Does it ever start to show a pattern? Does it ever repeat itself? Where's a copy of your paper? Why has no-one shown me it? Have you got the whole of pi printed out somewhere? How many digits does it run to?"

"I don't know," replied Saskins to the professor's babbled questions, "I didn't work all of it out, I only needed the first few digits and had to know what the last was so I worked it out. I didn't need the rest of it because that cancelled itself out later in the equation. I just needed to know the very last digit to determine exact accuracy. Obviously, however many decimal places you measure to, the last digit is innacurate because it si rounding up or down from the next digit that you aren't measuring. If you calculate the very last digit then obviously it is accurate as there is no digit after it to estimate."

The professor was speechless again, filled at once with a sense of joy that his marvellous idea hadn't already been done and disappointment that Saskins hadn't already done it. The next best thing to discovering something wonderful was someone else doing it first and saving you the bother. The professor had experienced a brief moment of hope that he would be able to get his hands on the entirety of pi immediately. That was not to be, but on the bright side he would still have the fun of working out how to do it for himself....if he could get funds to build another hypercomputer that was. No matter how good a seller his book was, it still would not bring in enough money to fund another hypercomputer project. Even if everyone on the planet bought ten copies of the book, the royalties would not cover the cost of another project that would almost certainly be as difficult and expensive as was the Purple Number Cruncher.

He did of course have a gadget around somewhere in his office that could replicate money quite easily and to a very high standard but it would be difficult to explain, walking into his bank with several trillion pounds worth of forged notes. Besides, it might accidentally ruin the economy. Which, incidentally, had been more than embarassing enough the last time.

No, he had to get away with losing one of the most expensive computers e
ever built without either getting fired or having trouble getting funding in future. Probably the best way would be to explain it away as something that was bound to happen, that he had expected to happen and that he was dissapointed his bosses hadn't remembered him mentioning a year ago when they agreed funding. Maybe even make it sound like it was a bonus that it had happened. Now would probably be a good time to start working on a cover story.

"Erm....I suppose that if the computer is everywhere and nowhere like it said then it is here in the lab with us just as much as it isn't?" Saskins, with his recent studying into irrational logic might be able to help him out here.

"I guess so," replied Saskins.

"So even though it can't be seen, it is still here. Definitely still here."

"Well of course it can't be seen," said Saskins, guessing what was going through Professor Hobgoblin's mind, "If you could see it here in the lab, enclosed by the lab and physically contained in the lab then it couldn't be everywhere could it? If it was still sitting there in the corner on that flat patch of carpet then it would be here and nowhere else. It said it was everything and nothing, nobody can percieve everything and nobody can percieve nothing so it's not surpriding that we can't see it, feel it or detect it an any way at all. How could it possibly understand infinity and zero at the same time without becoming - in part - the concepts it was trying to understand? All knowledge becomes part of us, helps define who we are, changes us by our very exposure to it. How could the Number Cruncher be anything else but what it is?.........Is that the sort of thing you were hoping for? We could probably work out a mathematical proof for it if we tried but to be honest I don't think the board would understand it. If we just show them a graph that says 80% of the population would be more willing to trust the findings of a computer that had actually tried to fully understand its task then they'll probably be happy. They like graphs. Just tell them the computer is walking a mile in the mocassins of both infinity and zero."

"That sounded very convincing. You're right about the graphs. When I was trying to get the funding for the computer approved I showed them a graph that proved that even the best scientists in the world were all at exactly the same point in there search for infinity. Easy really. Nobody had got anywhere near it and compared to infinity, all amounts smaller are the same. I convinced the board that we would be breaking a scientific deadlock, solving a problem that had all the other scientists in the world stumped exactly the same amount. Even the technical director on the board doesn't understand anything that goes on here and nearly drowned in his own drool when I showed him the 3D graph I'd done."

"So what are we going to do? Go with that story? Maybe add that we are actually at the most tricky and risky but potentially rewarding part of the experiment? Now that the Number Cruncher understands both concepts and is exploring them fully, maybe you should act like you expect it to manifest itself at any time with masses of information about how zero and infinity relate to each other. The great thing is that the nature of it means that it is impossible to tell when it will reappear. It would obviously be anywhere between immediately and an infinite time later."

Professor Thaddeus Hobgoblin stood with a huge grin on his face. "I think so. You're the irrational logic expert, how about you have a go at knocking up a quick report explaining it all away? Take the rest of the day off to think about it. I'll bash on with my second book and try to put in some rousing stuff about what we can expect from the Number Cruncher if it ever comes back."

"I'll do that," replied Saskins, pleased at having a short day, even if it did start early. "Well, this has been a most interesting first day Professor. Thanks again for allowing me to transfer to your department. I'll see you tomorrow morning and I'll have a rough draft of a report that we can work on."

"Thank you for your help. I think I'm going to like having you as an assistant, Saskins. You keep up the good work and the ideas and you'll go far. I hope you can stand working with me longer than most of my assistants have so far managed. See you tomorrow." The two men shook hands and Saskins turned to leave as the professor turned towards his computer terminal to work on his next book. He worked for nearly an hour, collating data he needed and downloading it to his computer at home so he could work from there. Finishing his last cup of tea and flicking off the computer terminal, he left the lab to return to his wife and write up the first couple of chapters.

As Professor Hobgoblin said goodbye to the security guard and left the building there was a slurping noise and the Purple Number Cruncher reappeared in the Inscrutable Numbers lab. A Cheshire Cat grin had somehow appeared on the front of it and it giggled hysterically. In a conspiratorial whisper but still in its dead flat, uninflected voice, the completely insane hypercomputer confided in the teapot. "I hope the professor likes my little joke. I didn't really find infinity and vanish, I went through the wardrobe. I've been hiding from him in Narnia."

The end

Copyright c)2001 Marc Whiteley

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