The Secret of the Universe
I’m not sure I should be telling you this - the secret of the universe I mean. If everyone knew then the whole thing might be called into question. Still, it’s like all knowledge, you just can’t keep it to yourself can you? I’m hopeless with secrets. I have to tell someone, and pretending it’s fiction sort of lets me off the hook. You’re a broad minded lot, but I’m confident you won’t believe me. More to the point, so are the Operators, and that’s what counts. If they thought anyone might suspect for half a moment it was all true, this story would probably never get published.
Enough of the preamble. I found out about The Secret six months ago and completely by accident - one of those unfortunate screw ups that can happen in the best planned schemes. I should explain that my intellectual roots lie deep in the uncompromising soil at the rocky end of theoretical physics; quantum chromodynamcis and super string theory with more than a passing interest in the mathematical implications of a variety of (n) brane multi-dimensional extensions. Before you start to panic though, the secret of the universe has very little to do with any of that! In all honesty, I haven’t made any great contributions to the field, and unless you’re a specialist you’re unlikely to have heard of me. Even so, I’m writing this under a pseudonym. I don’t want to embarrass the respectable university where I spent last spring on sabbatical, pursuing some tangential philosophical research for a well known Institute.
On an afternoon late last March I was day dreaming in the library when I felt a peculiar coldness spread over my limbs. I’d been reading Thomas Aquinas and wrestling with medieval metaphysics, enough to make anyone feel numb you might imagine, but this was a very strange sensation indeed. I lost my sense of touch and became increasingly light headed. I found myself quite unable to control my muscles and at the same time it seemed that my view point was drifting outside my own flesh. Although it should have been frightening I was remarkably calm and there was even a certain peculiar enjoyment. I’d heard of out of body experiences, but I’d never expected to have one myself and especially in such a sober place as the university library.
Time was draining to a stop. The annoying strobe of a faulty strip light became a perceptible flicker and an early fly dawdled in the air. My eyes blinked slowly, without me. I had a delayed moment wondering ‘how did I do that?’, before the room began to twist and an ominous darkness oozed out of the top shelf where they keep the psychology case studies. There was a dark red tunnel and a bright white light. I felt myself drawn inside, thinking ‘so this is death’. Then I emerged from the other side. A moment of whiteness introduced a silent explosion of colour. Amidst a spectacular coruscation of rainbow light, a cool neuter voice was speaking.
“Initiate upload,” it said.
Nothing happened except that the rainbow colours danced around with increasing violence. After a moment or two more, the same voice resumed.
“Upload procedure failed. Recall notification tag invalid. Coded exit security violation. Operator intervention required. Please wait.”
I nearly laughed at that point. Please wait, indeed! What else could I do?
It was very peaceful suspended in limbo awash in this beautiful bath of brilliantly changing light but I was starting to get impatient when everything went black. A more intense voice was speaking now but although I could hear it clearly, I guessed it wasn’t for my ears.
“I warned him not to use that code! Look we’ve got an exit violation now. Two thousand years with a clean record and all ruined because he had to have his little joke.
"Cancel upload. Total Environment to Deep Slow. Decant gate pattern.”
“Authorisation required for Deep Slow,” the cool neuter voice said.
“Authorisation code is General Override Design.”
“G.O.D. confirmed. Deep Slow starting. Decanting gate pattern in default protocol form.”
I went suddenly hot and cold, then I had a body again and was sitting in a chair. After all those hallucinogenic special effects the room in which I now found myself seemed almost banal. My first impression was of space. A ribbed ceiling vaulted ten metres over my head, and tall fluted windows looked out onto a uniform blue sky. Green velvet curtains fell the full length of the white plaster walls, which were tastefully decorated with two or three landscape water colours. I walked over to look at them more closely. Under a superficially conventional structure they depicted a variety of disconcerting abnormalities; oddities of perspective and content which would have made Hieronymus Bosch blanche.
The heavy wooden door opened whilst I was still puzzling over a particularly curious scene and I returned to my chair and sat down hastily. I’m a little over six feet tall but my host was half as tall again. He wore a white linen double breasted suit, and in almost all other respects save one, looked like a perfectly normal man of middle eastern origin. That one respect was impossible to ignore. A heavy pair of feathery white wings were rooted in the muscle and bone of his shoulder blades.
“Welcome to heaven, Mr. Worton,” he said. “You may call me Ohrmuzd.”
I had so many questions I hardly knew where to start.
“Am I dead?” I asked.
“I’m afraid not,” he answered with a disarming smile. “Oh, don’t take it personally! It’s just that you came here via a rather unusual route. Under normal circumstances you do have to die to get here, and after the upload you’d understand everything. Unfortunately there’s been a bit of a mix up in your case and I’ve been appointed to explain it.”
“How did I get here then,” I interrupted impatiently.
Ohrmuzd seemed to hesitate for a moment as though considering the best way to proceed. “Let me give you an analogy. I see from your records that you’ve done a little computer programming. You’ve probably heard about the Trojan Horse principle - lines of code built deep inside a new program by the programmer so that they can later gain privileged access to the routines and bypass any standard security procedures. A Trojan Horse can be used maliciously but it may also have a perfectly legitimate application as a way of monitoring an active environment without disrupting the usual controls. It can be a kind of artist’s signature as well, a concealed key inside an algorithm which marks the program as the writer’s own. A good Trojan Horse must be secret of course; that is its essence. It should only be triggered by a sequence of data which will never occur in the course of the normal operation of the program. However, the key must be available in principle to anyone within the system. It must pass all the standard validation procedures. If it doesn’t, then the user will be unable to trigger it in all execution environments.
"Now this is only an analogy, but in some senses your universe is our program. We are the Operators. There are the standard inputs and outputs (which you know as birth and death) and then there is our Trojan Horse. We need to get in and out to monitor things from time to time. Our ‘back doors’ are keyed by sequences of thought which permute according to arcane principles known only to ourselves. In theory these sequences of thought are ones which no sane or insane individual would ever be likely to experience. We select wildly disparate themes in improbable orders. Unfortunately in your case, my choice of a key was obviously too mundane.
"Do you remember what was passing through your head in the moments immediately before you arrived here?”
“Well... Oh, um," was all I could manage, realising that I could blush in heaven.
“Precisely,” he said with grim amusement. “The key consisted of contemplation of eleven dimensional super strings, the Summa Theologica and a certain unlikely fantasy involving Ginger Spice and the Teletubbies.”
“So I accidentally triggered the Trojan Horse and went straight to heaven?”
“Well, not straight here. When you got to the holding gate the system identified you as a normal mortal and tried to perform the standard ‘after death processing’. That failed because you hadn’t died and the recall flag wasn’t set properly. Then it recognised the way you had arrived and asked for an Operator to step in.”
“And this is really heaven?”
He shrugged. “You’ve dabbled in philosophy. You know the dangers of definition. In all practical senses the answer is yes, but you haven’t had much experience of asking practical questions about heaven have you?”
Ohrmuzd seemed to be enjoying my confusion but not without sympathy. “Perhaps you would rather think of this place as the meta-universe (let’s call it the metaverse for short). A dimension beyond the limits of your space and time. That will do just as well.”
I nodded, reserving judgement.
“And what about God?” I asked.
“There are some questions which I prefer not to answer.” He sounded cagey. “Not in these circumstances anyway. Of course, if you were dead it would be different.”
“Speaking of which,” I said, “what are you going to do now? If I’m not dead, can’t you just put me back inside my head?”
“It’s under consideration,” the Operator said. “When something like this happens there has to be an investigation. There are procedures to follow and so on. I’m sure you can imagine. Now that you are here, though, wouldn’t you like to look around? Come on, let’s take you on a little tour.”
It was an offer I couldn’t refuse.
We left the room and descended a rough stone spiral staircase, emerging into sunlight to find ourselves at the base of a tall white tower projecting from the side of an expansive mountain side. When I looked down, folds of heather, bilberry, grass and rock seemed to drop away forever. Pure icy streams fringed by bracken and gorse, cascaded over mossy grey stones. Here and there, I could see broad ledges where groups of Operators had convened for some inscrutable purpose, but for the most part the mountain was empty. Wispy cloud drifted above and below, thick enough to obscure my view of the summit or base but too transparent to deny the overwhelming impression of suspension in a wide blue sky. I thought I could hear the faint twang of harp music.
“I will life up mine eyes unto the hills, from whence comes my salvation,” my guide quoted without further explanation. We set out along a narrow mountain track and after cresting a spare rocky ridge came to the start of a thin diamond bridge which arched out into the void. Crossing the bridge was a disconcerting experience. It was almost perfectly transparent, apart from the occasional prismatic effect which lined the edges in rainbow light. Operators flew above and below, and it was hard not to feel a little vertigo. At the other end was a small floating island suspended in the sky. I could now see that it was only the first of a series of such gravity defying bodies stretching away before me like a flock of birds. The islands were connected by a variety of delicate bridges and walkways, the orthodox stone, wood and metal visible to me, although I would have been unable to perceive distant structures built of the same material as the one I had just crossed.
Pink flowering rhododendron and lime green ferns overhung the irregular granite outcrops which circled the rim of the nearest island, and a small stream cascaded over the edge. The critical part of my mind wondered how the water could possibly be recycled. Unless it rained an awful lot on this island it would soon run completely dry. Strangely, this disturbed me more than the islands’ odd ignorance of gravity. I suppose my physics research had led me to distrust gravity anyway, but violation of basic ecological bookkeeping seemed offensive.
When I questioned Ohrmuzd though, he just said airily, “Oh it’s all in conformance with the Laws of Art. The Laws of Art are more important in the metaverse but I can’t explain them all to you now. Don’t worry about it.”
We began our tour of the Elysium Fields and at first I couldn’t help but marvel. The islands were incredibly beautiful, wild but some how gardened at the same time - a magnificent park. There were orchards over flowing with ripe red berries, stripped lawns as dense as carpets and tall cedar and blue spruce trees. From time to time we caught a glimpse of an occasional living creature - a flock of bluebirds, a solitary unicorn and a couple of gnome like gardeners. For the most part, though, the islands were unoccupied.
“We have as much space as we need,” Ohrmuzd explained. “We just let the Fields grow to meet the demand, but there isn’t as much demand as you might imagine.”
“That doesn’t surprise me,” I said cynically. I hadn’t seen a single human being yet.
“Ah... You’re thinking of Heaven and Hell are you?” the Operator said. “That wasn’t what I had in mind.”
He seemed to hesitate.
“I expect I’ll explain it later,” he concluded lamely.
After a while, the richness began to overwhelm me. In some obscure way I felt vaguely disappointed, as though this was all a hollow show. The Operator must have sensed my reaction.
“What’s the matter?” he asked.
“Well...” I said, groping for words (for who wants to upset an angel?) “I don’t mean to cause any offence or anything, but it’s all a little... conventional. I mean everything I’ve seen of this heaven (or metaverse, or whatever you want to call it) has been a bit of a cliché - a variation on standard medieval images. I’d expected that it would be different - a whole different order of existence, not just the beauty of the Earth writ large.”
“Don’t worry,” he laughed, “that’s a fair criticism on the basis of what you’ve seen so far, but this is just a kind of lobby. It’s an area we dedicate to Earth and we loosely follow the themes of your planet. I thought it best to bring you here first. The metaverse has a lot more to offer but you would find it indigestible; even frightening without the proper preparation. Unfortunately I can’t authorise the proper preparation for you. Not in this state.”
“Isn’t there anything else you can show me? Something special about the metaverse.”
He considered for a moment.
“Would you like to see The Sphere?”
“What’s the sphere?” I asked.
“Not the sphere, The Sphere,” he corrected me. “Are you familiar with Plato?”
“Not entirely,” I admitted.
“Well when he was trying to underpin the foundations of geometry he had the concept of an ‘ideal form’. An ‘ideal form’ is a pure abstract entity, independent of any physical realisation. If you’re doing geometric proofs you obviously don’t want to be stuck with a particular triangle on a specific piece of papyrus, complete with all the imperfections of the draftsman and the accidental folds of nature. No, you want to find the truths about a perfect triangle. This perfect triangle is the ‘ideal form’ and according to Plato every real triangle is just a corrupted copy of a corresponding ideal. Occasionally, some human being hits on a bigger truth than they can know. Plato did then. The metaverse is where the ‘ideal forms’ live. This is where The Sphere lives.”
“OK,” I said. “I suppose that would be something...”
We travelled through the endless blue sky on a sort of a flying carpet. I knew that Ohrmuzd could have flown but he sat with me as a courtesy.
“The Sphere is one of those primal objects we prefer to call the Self Justifying Artefacts,” he said.
“There are an indeterminate number of orders of Self Justifying Artefacts. Most of them would be completely incomprehensible to you in your current state of mind. Many of them are incomprehensible even to us.”
“So you didn’t make them?”
“Oh no!” he laughed. “You don’t understand our role here yet. It isn’t quite this simple but you can think of us as humble denizens of the metaverse. As mankind is to the universe, so the Operators are to the metaverse. Except that the Laws of Nature are rather different here. We’re immortal for a start and I’ve already mentioned the Laws of Art.
"The Sphere I think you can understand. Much of our real work is in the Zones of Theoretical Pleasure and the Truth and Beauty Wars. You’re not ready for those.”
There was a growing crowd of Operators heading in the same direction but I started to notice that it was getting hard to focus on any one individual. The light had an elusive, slippery quality.
“The Sphere is something of a tourist spot,” he explained. “There’ll be a bit of a crowd.”
I mentioned the peculiar distortion I was now experiencing.
“That’s what happens near the Self Justifying Artefacts. Just close your eyes for a bit if it makes you feel sick.”
I took his advice and when I opened them again, there it was.
What can I say about The Sphere? What colour was it? It didn’t have a colour. Well I suppose you can just about imagine that. How big was it? It didn’t have a size. Now that’s a bit more difficult to imagine! But how could it have a size, acting as it did, as a template for all spheres in the universe? It was the ‘essence of sphere’ and a sphere can be any size. I began to properly appreciate that the metaverse really was different in kind to our own universe. I guess The Sphere did have a location, but not in the way we think of location. It was more of an abstract generalisation of a place. What it was, was round. Completely and utterly and perfectly round. The Operators nearby seemed to have come to contemplate that quality and I found myself inevitably drawn into a similar mystical contemplation...
When I regained consciousness, Ohrmuzd was looking at me with some concern.
“I had to snap you out of that,” he said. “That sort of meditation is dangerous for the uninitiated.”
I felt light headed and let my mind slowly refocus. There was something I remembered; something very odd.
“Umm... “ I began diffidently. “I had a feeling that The Sphere wasn’t quite right somehow.”
“The Sphere is perfectly all right,” he snapped.
“So Pi really is three then?”
“Ah....”
Now he seemed a bit embarrassed. He paused before elaborating.
“Yes, well, I must confess it’s supposed to be. There was a bit of a mix up when the fundamental constants were defined for your universe. I’m afraid the spheres you’re accustomed to are an even more imperfect copy of the Ideal Form than normal. Sorry about that.”
Ohrmuzd led me to a comfortable house on one of the floating islands nearest to the mountain. It was simple but artfully designed in a style somewhat reminiscent of a Japanese pavilion.
“You can stay here until we sort things out,” he said. “Don’t worry about the time. Time runs differently here when we want it to. We’ve had to suspend your universe until your case is resolved.”
“Total Environment to Deep Slow?” I remembered out loud.
“Yes. It’s a bit of a nuisance that is...” he said vaguely.
I was too stunned to answer. It seemed like the greatest understatement of all time. ‘Stop the universe I want to get off...’, I thought irreverently and had to suppress a nervous laugh.
“You’ll find all you want to eat on the islands,” he said. “Pick fruit from the trees and drink water from the streams. There’s nothing poisonous but I’m afraid you’ll have to do without meat. We’re vegetarian here, the lion shall lie down with the lamb and all that. Think of it as a sort of Eden, or a free run round Sainsbury’s without the queues at the checkout if you prefer...”
I wasn’t quite sure how to take his odd sense of humour so I ignored it.
“If you want to talk to me again, ring this.”
He gave me a large silver bell which I hung on a post hook by the door to the house.
“I have to attend your case conference now. In the mean time, feel free to explore all the islands. Oh and try not to ring the bell unless you really must. I do have other important business to handle you know!”
And with that he left me to my own company.
I was a guest in heaven for a long time. Exactly how long I can’t tell. It might have been anything between one month and six months. I was seldom tired and seemed to sleep only briefly but since there was no day or night to regulate the pattern of my days I started to lose track of time.
To describe in detail the landscapes and wonders of the Elysium Fields would take an age and would in any case only distract from the point for my story. Suffice to say that the islands were a source of endless scenic variety and interest and I greatly enjoyed exploring them; but it was rather lonely. In all my wanderings I never came across another human soul.
Someone once said that happiness makes for a boring story and I’m sure they’re right - not that I was exactly happy in this heaven but it was perfect in its own way and there are only so many ways you can describe perfection. The more interesting abstract differences between the universe and the metaverse, I just can’t transmit properly in words.
Initially I was determined not to ring the bell. It seemed unwise to antagonise the Operators and I was confident that my case would soon be dealt with. After a while though, I started to consider the distinction between being a guest and a prisoner.
Eventually I became bored. I found myself singing the subversive old Talking Heads song “Heaven” under my breath. From there I graduated to the more openly antagonistic Curve tune, ‘There’s no escape from heaven, try as you might... there’s no escape from heaven...’ The original wasn’t quite right for this context but it amused me anyway. It was time to ring the bell.
A clear musical tone echoed round the sky. Ohrmuzd flew over the tree tops within a remarkably short space of time.
“I thought you’d forgotten us,” he smiled.
“Isn’t that the wrong way round,” I answered sharply (because I was now starting to get rather annoyed). “I thought you’d forgotten me!”
“Oh no,” he said. “We haven’t forgotten you. In fact your case was dealt with a long time ago. It was just a question of whether the Powers That Be felt it right to give you a better explanation. I’m glad to say that they decided they would.”
“Well you might have let me know earlier!”
“No. Answers to these sort of questions are all about having the right preparation. This isn’t some sort of pub quiz you know! I’m going to tell you ‘The Secret Of The Universe’. The least you can do is show a bit of respect.
"Come on. It’s time to put you back where you belong. Let’s go to the Fountain of Amnesia.”
My guide unrolled his ‘magic carpet’ and we set off again into the crystal blue sky.
“What do you know about infinity?” he asked as we flew.
“Not much,” I answered. “I don’t have any truck with infinity. I’m a physicist. If you don’t need infinity in calculus (and you don’t; limits are enough) you don’t need it at all. Physicists don’t go in for all that mystical nonsense.”
“You can deny mysticism here?” the Operator laughed. “You really are set in your ways aren’t you! Well before I go any further, I’ll have to enlighten you a bit about infinity. You do know that there’s more than one kind of infinity, don’t you?”
“Surely infinity is infinity. How can there be more than one kind of infinity?”
“Oh dear. I’ve got more explaining to do than I thought! Let’s start with the basics. Imagine the natural numbers - 1,2,3,4..... Suppose you carry on forever until you reach the limit of the series. Let’s call the last number omega. You’d agree that omega is infinite wouldn’t you?”
“It must be.”
“And you’ve also expressed a simple notion of infinity as ‘the biggest thing there is’, or perhaps ‘The Ultimate’?”
I nodded cautiously.
“We’ll go along with that and call this kind of infinity ‘Absolute Infinity’ - Omega with a captial "O" if you like.
"So the question is, ‘Is omega as big as Omega?’. Is the highest natural number as big as Absolute Infinity?”
“I don’t suppose you’d be going to all this trouble to make the distinction if you thought they were the same,” I answered. “But you’ve still got to prove it to me. I mean omega is pretty big!”
“omega is very big,” Ohrmuzd said, “but it’s not Absolutely Infinite, even though it is a kind of infinity. We call numbers like omega a transfinite number. In fact omega is the first of a series of transfinite numbers all of which are ‘beyond the finite’ and approach, but do not reach, the Absolutely Infinite.
"Let me give you an example of an infinity bigger than omega. It’s ever so simple. Think of the number line and then of all the numbers between 0 and 1. I mean numbers like 0.5, 0.6785, 0.344243... and on to as many decimal places as you like. There are more real numbers between 0 and 1 than there are natural numbers. I’ll prove it to you.
"Just suppose that there were as many natural numbers as real numbers between 0 and 1. In that case you could imagine a book of all the real numbers between 0 and 1. It would be a very boring book. To make it slightly more interesting we’ll say that the numbers don’t need to be in order. So we could have 0.234455, followed by 0.1990928384, followed by 0.787874 etc. Each row in the book is allocated a natural number which is its position in the book. Now I’m going to say that there aren’t enough natural numbers for the job. omega isn’t big enough to count all the entries in this book!
"Why? Suppose we had the book in front of us. The first page might start like this.”
He passed me a sheet of paper on which was written:-
“If you said you had the complete book, I can prove you’re lying by telling you about a real number that should be in the book, but isn’t. I just start at 1 and take the digit in the first decimal place of the real number (2 in this case). I add one to it and start to make up a new number starting 0.3. Now I take the second number and look at the digit in the second decimal place (3 in this case). I add one to it and continue my new number as 0.34. Moving on to the third number and the third decimal place by the same logic we get 0.342, then 0.3423, 0.34232, 0.342321 etc.. etc.. The point is that we can continue up to omega and when we get there we will have a new number that isn’t in the book. It can’t be! It isn’t the same as any existing number because for all the numbers in the book it differs by at least one digit. That’s how we constructed it. Yet the book was supposed to be complete. If we add our new number as an entry we can repeat the same trick, proving that the book can never be indexed. The trouble is that the set of real numbers between 0 and 1 contains a higher degree of infinity than the set of natural numbers. It is the first uncountable transfinite number.
"That’s how you study transfinite numbers. You try to map infinities on to one another and when you can’t do it, you’re dealing with a higher order of infinity. But it’s a tricky business. You have to be very careful with infinity. For instance, are there more numbers than odd numbers?”
“There must be twice as many,” I said. “For every odd number there’s an even number one greater.”
“Wrong, I’m afraid,” Ohrmuzd replied. “There are exactly as many numbers as odd numbers. Why? Because you can (theoretically!) make a book of odd numbers indexed from 1 to omega and it will be a complete book. There is no scheme analogous to the one I’ve just explained for generating an entry that isn’t in the book. "There’s another terminology for this. We call countable infinities measured by omega, Aleph Null. The uncountable infinity of the real numbers is known as Aleph One. Aleph Null and Aleph One are transfinite cardinals and no transfinite cardinal can be mapped onto any other.” I found the idea of uncountable infinities strangely liberating. I could picture a hysterical headline in the tabloid press, ‘Shortage of Numbers, Scientists Say!’, complete with a shocked quote from some rent-a-boffin : ‘There simply aren’t enough numbers to count everything! It’s typical. Irresponsible scientists and mathematicians have been using numbers up like there’s always another one out there, and without any thought for where it will all end. Now we’re running out! The day of reckoning is at hand. This is nature’s way of telling us to stop over classifying. We’ll have to introduce some kind of number rationing!’ I brought my mind back to the current conversation. “And I suppose you’re going to tell me that Aleph One isn’t the same as Omega either?” “Quite right but I’m not going to prove that now. Take my word for it that there are cardinals called Aleph Two, Aleph Three, and so on, and so on, up to Aleph omega. And that’s just where it starts to get interesting! The study of the transfinite cardinals takes things much further. What all these infinities actually mean is another matter....” I remembered the old argument about how many angels can dance on the head of a pin. My head was hurting. “In your universe,” Ohrmuzd was saying, “you are confined to the lower realms of infinity. In the metaverse we aren’t so limited. My mind is literally infinitely more complex than yours because it is based on a different order of space and time - a higher transfinite cardinal.” We had reached our destination; an isolated floating rock beyond the range of islands I had previously explored. It supported a Moorish Castle with a tall white fountain in a square central courtyard. We floated over the battlements and landed by an ebony door, carved with gargoyles and dragons. “I have a question for you,” he said as we dismounted. “Think seriously about it but don’t worry about infinite differences - they’re true but irrelevant. You can answer this question quite happily by analogy to you’re own experience. "Suppose you lived forever in heaven. What do you think your main problem would be?” I was a bit stumped by this and made no immediate reply. Fortunately none seemed to be required. Behind the door a flight of stairs twisted down to a large cellar with a high domed ceiling. It was lit from above by sky light filtered through the pool of the fountain. The light streamed out via a clear crystal bulb of water below the level of the courtyard and this acted underground like an enormous chandelier. Round the sides of the room, a number of Operators sat, stood or hovered before a series of consoles which at first glance seemed not entirely unlike the computers I was familiar with, although I hope they weren’t running Windows 95. The centre of the room drew my immediate attention. A voluminous geometric darkness looped and twisted around pierced corridors of metaspace, like the spilled intestines of some dark leviathan. It was a topologists nightmare; no telling what sort of equivalent shape would classify it. Bright flecks of tiny white light floated inside, like clouds of dandruff. I guessed immediately what it was. “Your universe,” the Operator confirmed. “You can just about make out some of the larger super galactic clusters and the more energetic quasars at this scale. It’s like dough in a warm kitchen. We try to stop it expanding too much. These things can get out of control if you let them run away.” “You mean there’s more than one?” I asked. “Oh yes,” he said breezily. “We’ve quite a few of these things cooking on different sites. We don’t always run them with the same laws. We call them the Fountains of Amnesia.” I was still thinking about his earlier question. I remembered my own recent experience exploring the Elysium Fields and suddenly recalled the provocative last chapter of a book I’d read some years before. In ‘The History Of The World in 10 ½ Chapters’ the author ends up in heaven and encounters just this problem. “Boredom!” I shouted. Ohrmuzd waited patiently whilst I explained my answer. “When you’ve experienced every pleasure and achieved every desire, what do you do next?” Even as I recounted the source of my inspiration though, I couldn’t help feeling just a bit cheated by my own sojourn into higher reality. In that book Leicester City win the FA cup, the author completes a round of golf in eighteen shots and has an endless variety of fulfilling sex. “Yes, well you don’t play golf do you?” the Operator replied simply enough. “As for the sex,” he continued more severely, “this is a Platonic heaven after all. You should have guessed that, when we went to see The Sphere. I presume you know what a Platonic relationship is?” “You don’t have to tell me about that,” I said, perhaps a little bitterly. “And the football... Leicester City is at least plausible but you support Southend United if I remember rightly. Now come on! We have to be realistic here. This may be heaven but Southend United winning the FA Cup?” He had a point. I had to admit that after watching them play last season it did seem outrageous. Changing the value of Pi was one thing but Southend United winning the FA Cup was quite another. “You’re right though,” Ohrmuzd continued. “We don’t need earthly pleasures because of our infinitely greater minds but we also have an infinite amount of time to contemplate the joys of heaven, and eternity is a very long time. "When you go on holiday for a fortnight aren’t the first three days the longest? You’re seeing new things and meeting new people. Then the last week just zips past as familiarity sets in. It’s like that with life, isn’t it? Childhood seems to last forever but as you get older, subjective time speeds up. Experiences start to repeat more often and life just slips by, faster and faster. "That’s how it is with us. When you start wondering where the last billion years went, that’s when you’ve got a problem! The universe is our solution. We enter the universe to experience novelty again. We are the souls in your bodies, put through the Lethe system for amnesia before rebirth. Only when we re-enter the metaverse after death do we recall all our past lives, reintegrate our experiences and awake refreshed.“ “So reincarnation is true! I always though it was ridiculous because if you couldn’t recall your past life there was no sense in which it was your life anyway. And if you could recall it, you’d just have one extended existence punctuated by death.” “Now you know the answer,” the Operator said. “You can’t recall other lives in there,” He nodded towards the universe, “or there’d be no point in going in. You need to be born again to get a fresh perspective. It’s a holiday from eternity. Once you’re back here in the metaverse, your complete memory is restored.” “So that’s what ‘Initiate upload’ means,” I said, recalling the voice in my head when I had first arrived in the metaverse. “And that’s the Secret Of The Universe?” “That’s right, and now you understand, it’s back inside for you. I’ll enjoy debating this with you again, when you get properly recalled.” I asked him if I could write this account. “The Powers That Be have considered it. They’ve decided no one will believe you anyway, so go ahead! Goodbye Mr. Worton and Have A Nice Life.” They put me though a translation mechanism. It was altogether more abrupt than the gentle way I’d been separated from my body. All at once I was slumped over the desk in the library and the world was back, not a second older than when I’d left. You’d think I’d be satisfied wouldn’t you? No more need for philosophical doubt. I know for certain what countless philosophers and theologians never knew. I actually know why the universe exists. There’s only one problem. I feel like a bit of a fraud in here; in this bounded time and space with its limited eleven dimensions, I mean. My conceptual cosmos now includes the Operators, the Fountains of Amnesia, the Self Justifying Artefacts, the Zones of Theoretical Pleasure and the Truth and Beauty Wars. It includes endless complexity at a higher scale which I will no doubt spend eternity exploring when I finally get recalled. So I have to ask another question. I know the secret of the universe, but what’s the secret of the metaverse? Recently I thought I might even have guessed the answer to this one. It sounds blasphemous but perhaps the purpose of the metaverse is, in some sense, the universe. There’s a neat symmetry about this. The purpose of the universe is the metaverse, the purpose of the metaverse is the universe. Maybe. But now I’ve started wondering if it’s valid to explain A in terms of B, and B in terms of A. What about AB? What’s the purpose of the metaverse-universe system? Do I have to introduce a third entity to explain AB - say the metametaverse? And won’t this involve an infinite regress? (not that I know what an infinite anything is anyway) Life would be so much simpler, if only I hadn’t triggered the Trojan Horse and had my strange introduction to heaven in the library. If you ask me, that Ginger Spice has a lot to answer for! DMFW - 26/7/98
Natural Numbers | Real Numbers (0 to 1) |
---|---|
1 | 0.2123457891029394049593020995069607907970790550504444490........ |
2 | 0.2337596976079939393939393939000000000000000199099030404........ |
3 | 0.7814141515151515155253840109309089589589893821129040587........ |
4 | 0.1202021112939402939949595993493090208653333324516737381........ |
5 | 0.11111111111111111111111111111111111111111111112111111111111........ |
6 | 0.5561000000000023034044000000000006787812345678912345678........ |
“There must be twice as many,” I said. “For every odd number there’s an even number one greater.”
“Wrong, I’m afraid,” Ohrmuzd replied. “There are exactly as many numbers as odd numbers. Why? Because you can (theoretically!) make a book of odd numbers indexed from 1 to omega and it will be a complete book. There is no scheme analogous to the one I’ve just explained for generating an entry that isn’t in the book. "There’s another terminology for this. We call countable infinities measured by omega, Aleph Null. The uncountable infinity of the real numbers is known as Aleph One. Aleph Null and Aleph One are transfinite cardinals and no transfinite cardinal can be mapped onto any other.” I found the idea of uncountable infinities strangely liberating. I could picture a hysterical headline in the tabloid press, ‘Shortage of Numbers, Scientists Say!’, complete with a shocked quote from some rent-a-boffin : ‘There simply aren’t enough numbers to count everything! It’s typical. Irresponsible scientists and mathematicians have been using numbers up like there’s always another one out there, and without any thought for where it will all end. Now we’re running out! The day of reckoning is at hand. This is nature’s way of telling us to stop over classifying. We’ll have to introduce some kind of number rationing!’ I brought my mind back to the current conversation. “And I suppose you’re going to tell me that Aleph One isn’t the same as Omega either?” “Quite right but I’m not going to prove that now. Take my word for it that there are cardinals called Aleph Two, Aleph Three, and so on, and so on, up to Aleph omega. And that’s just where it starts to get interesting! The study of the transfinite cardinals takes things much further. What all these infinities actually mean is another matter....” I remembered the old argument about how many angels can dance on the head of a pin. My head was hurting. “In your universe,” Ohrmuzd was saying, “you are confined to the lower realms of infinity. In the metaverse we aren’t so limited. My mind is literally infinitely more complex than yours because it is based on a different order of space and time - a higher transfinite cardinal.” We had reached our destination; an isolated floating rock beyond the range of islands I had previously explored. It supported a Moorish Castle with a tall white fountain in a square central courtyard. We floated over the battlements and landed by an ebony door, carved with gargoyles and dragons. “I have a question for you,” he said as we dismounted. “Think seriously about it but don’t worry about infinite differences - they’re true but irrelevant. You can answer this question quite happily by analogy to you’re own experience. "Suppose you lived forever in heaven. What do you think your main problem would be?” I was a bit stumped by this and made no immediate reply. Fortunately none seemed to be required. Behind the door a flight of stairs twisted down to a large cellar with a high domed ceiling. It was lit from above by sky light filtered through the pool of the fountain. The light streamed out via a clear crystal bulb of water below the level of the courtyard and this acted underground like an enormous chandelier. Round the sides of the room, a number of Operators sat, stood or hovered before a series of consoles which at first glance seemed not entirely unlike the computers I was familiar with, although I hope they weren’t running Windows 95. The centre of the room drew my immediate attention. A voluminous geometric darkness looped and twisted around pierced corridors of metaspace, like the spilled intestines of some dark leviathan. It was a topologists nightmare; no telling what sort of equivalent shape would classify it. Bright flecks of tiny white light floated inside, like clouds of dandruff. I guessed immediately what it was. “Your universe,” the Operator confirmed. “You can just about make out some of the larger super galactic clusters and the more energetic quasars at this scale. It’s like dough in a warm kitchen. We try to stop it expanding too much. These things can get out of control if you let them run away.” “You mean there’s more than one?” I asked. “Oh yes,” he said breezily. “We’ve quite a few of these things cooking on different sites. We don’t always run them with the same laws. We call them the Fountains of Amnesia.” I was still thinking about his earlier question. I remembered my own recent experience exploring the Elysium Fields and suddenly recalled the provocative last chapter of a book I’d read some years before. In ‘The History Of The World in 10 ½ Chapters’ the author ends up in heaven and encounters just this problem. “Boredom!” I shouted. Ohrmuzd waited patiently whilst I explained my answer. “When you’ve experienced every pleasure and achieved every desire, what do you do next?” Even as I recounted the source of my inspiration though, I couldn’t help feeling just a bit cheated by my own sojourn into higher reality. In that book Leicester City win the FA cup, the author completes a round of golf in eighteen shots and has an endless variety of fulfilling sex. “Yes, well you don’t play golf do you?” the Operator replied simply enough. “As for the sex,” he continued more severely, “this is a Platonic heaven after all. You should have guessed that, when we went to see The Sphere. I presume you know what a Platonic relationship is?” “You don’t have to tell me about that,” I said, perhaps a little bitterly. “And the football... Leicester City is at least plausible but you support Southend United if I remember rightly. Now come on! We have to be realistic here. This may be heaven but Southend United winning the FA Cup?” He had a point. I had to admit that after watching them play last season it did seem outrageous. Changing the value of Pi was one thing but Southend United winning the FA Cup was quite another. “You’re right though,” Ohrmuzd continued. “We don’t need earthly pleasures because of our infinitely greater minds but we also have an infinite amount of time to contemplate the joys of heaven, and eternity is a very long time. "When you go on holiday for a fortnight aren’t the first three days the longest? You’re seeing new things and meeting new people. Then the last week just zips past as familiarity sets in. It’s like that with life, isn’t it? Childhood seems to last forever but as you get older, subjective time speeds up. Experiences start to repeat more often and life just slips by, faster and faster. "That’s how it is with us. When you start wondering where the last billion years went, that’s when you’ve got a problem! The universe is our solution. We enter the universe to experience novelty again. We are the souls in your bodies, put through the Lethe system for amnesia before rebirth. Only when we re-enter the metaverse after death do we recall all our past lives, reintegrate our experiences and awake refreshed.“ “So reincarnation is true! I always though it was ridiculous because if you couldn’t recall your past life there was no sense in which it was your life anyway. And if you could recall it, you’d just have one extended existence punctuated by death.” “Now you know the answer,” the Operator said. “You can’t recall other lives in there,” He nodded towards the universe, “or there’d be no point in going in. You need to be born again to get a fresh perspective. It’s a holiday from eternity. Once you’re back here in the metaverse, your complete memory is restored.” “So that’s what ‘Initiate upload’ means,” I said, recalling the voice in my head when I had first arrived in the metaverse. “And that’s the Secret Of The Universe?” “That’s right, and now you understand, it’s back inside for you. I’ll enjoy debating this with you again, when you get properly recalled.” I asked him if I could write this account. “The Powers That Be have considered it. They’ve decided no one will believe you anyway, so go ahead! Goodbye Mr. Worton and Have A Nice Life.” They put me though a translation mechanism. It was altogether more abrupt than the gentle way I’d been separated from my body. All at once I was slumped over the desk in the library and the world was back, not a second older than when I’d left. You’d think I’d be satisfied wouldn’t you? No more need for philosophical doubt. I know for certain what countless philosophers and theologians never knew. I actually know why the universe exists. There’s only one problem. I feel like a bit of a fraud in here; in this bounded time and space with its limited eleven dimensions, I mean. My conceptual cosmos now includes the Operators, the Fountains of Amnesia, the Self Justifying Artefacts, the Zones of Theoretical Pleasure and the Truth and Beauty Wars. It includes endless complexity at a higher scale which I will no doubt spend eternity exploring when I finally get recalled. So I have to ask another question. I know the secret of the universe, but what’s the secret of the metaverse? Recently I thought I might even have guessed the answer to this one. It sounds blasphemous but perhaps the purpose of the metaverse is, in some sense, the universe. There’s a neat symmetry about this. The purpose of the universe is the metaverse, the purpose of the metaverse is the universe. Maybe. But now I’ve started wondering if it’s valid to explain A in terms of B, and B in terms of A. What about AB? What’s the purpose of the metaverse-universe system? Do I have to introduce a third entity to explain AB - say the metametaverse? And won’t this involve an infinite regress? (not that I know what an infinite anything is anyway) Life would be so much simpler, if only I hadn’t triggered the Trojan Horse and had my strange introduction to heaven in the library. If you ask me, that Ginger Spice has a lot to answer for! DMFW - 26/7/98
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