Right Angles

The fire in the grate had burnt low, and the third round of brandy and whisky was about to give way to the fourth, when the man in the corner spoke.

He’d been sitting in the corner all evening, shrouded in shadow, not moving. I would not have noticed him at all but for his hands, the only parts of him that were illuminated. They were pale and never still, moving constantly, over his thighs and knees, and over the little table by his side, on which a glass of Scotch reposed untouched. I had no idea who he was, and it didn’t matter; our discussion, by turns interesting and acrimonious, had taken up all my attention. And, really, anyone has a right to sit in a corner of the common room of an inn on a winter evening without being stared at.

So I’d virtually forgotten his existence long before young D_______, who studied science in college for two years, has once or twice tried to decipher the theories of the Swiss mathematician Einstein, and therefore fancies himself an expert, began to declaim on the Fourth Dimension.

“Now,” he said, “as we all travel along the three dimensions of Space, we simultaneously are drawn down the black river of Time, which is the fourth dimension. And, just as we could take a paddle-steamer or a steam-barge down a river of water faster than the current would bear us along, if we could only invent a machine – and someday, as Mr Wells speculated in his novel, we shall – we could travel down it faster, as far as we wish to go. And to return to the selfsame place where we started, we only have to turn it back.”

“My dear man,” someone objected. I rather think it was A________, who dislikes D________ intensely and makes a habit of objecting to anything he says. “My dear man, suppose we believe such a thing is possible. You...” He dipped a fingertip in the bottom of his glass and drew a squiggly line of moisture on the side of the mantelpiece. “Look, here’s your river of time. You start from here in your paddle steamer...” He marked an X on the squiggle, “From X, you steam down river at top speed to here.” He marked a rough Y. “Now, you’ve done whatever you wanted to, so you want to go back to X. But...” he beamed around the gathering. “But, by the time you’ve done going from X to Y and back again, the people you knew at X are no longer there!”

“What do you mean?” I asked.

“It’s simple.” A__________ was clearly enjoying himself. “The river didn’t stop flowing just because you decided to take your steam paddleboat down it. While you’ve been gallivanting back and forth, your friends and relatives, and your enemies, have come down river from X to...” he poked his finger triumphantly at the mantelpiece. “To Z!” he finished. “So what do you do then?”

D________ looked down his nose at A________. Since he is as tall and thin as A_________ is short and stout, this was not difficult for him to do. “It’s you who didn’t think it through, it seems to me,” he snapped. “If you go back only up to your Z, you’ll have disappeared from your time – the three dimensions of the world –for a period between your X and your Z, and then suddenly reappear. But if you go back to X, you’ll just have avoided creating a paradox. Do you even begin to understand?”

H_________, who has always been a nervous type, hastened to try and pour oil over troubled waters. “All this is just theoretical, anyway,” he said. “we can only travel along the three dimensions of space, and if we can ever manage to ride the waves of time, the Fourth Dimension, well, by that time, I have no doubt, we will have learnt to manage any problems we encounter. Man’s ingenuity, after all, can...”

“Poppycock!” The word slashed out of the shadows in the corner. “Absolute and utter drivel. You all make me sick.”

We turned as one man, towards where the man in the corner sat in his pool of shadow.

“I beg your pardon?” D__________ began indignantly.

“You don’t deserve it,” the reply came. “My pardon? You don’t even deserve the time I’m going to waste in setting you all straight.”

“Set us straight?” D__________ responded in his most sneering tone. “I’ll have you know that everything I said has the best scientific backing. Why, I’ve read Einstein...”

“Oh, yes, the Swiss patent clerk. I’ve read him too. And I understood what he had to say, unlike you.” The pale hands twisted as though looking for crevices to hide. “You people and your travels through time. You talk about the fourth dimension, and you haven’t the faintest idea what the fourth dimension even is.”

“What is it, then?” A___________ challenged. “Everyone knows that it’s time.”

“And how would you know anything about it anyway?” D________ added. “Are you going to pretend you’re a scientist or something?”

“A scientist?” the stranger repeated. “Dear me, no. I’m not a scientist. I’m a former army officer.”

“A former army officer.” D_________ laughed that short sarcastic laugh he used to laugh, the one that suggested a dog barking. After that evening he has never laughed that way again. “And how does that make you an expert on the Fourth Dimension?”

“Because I was one of the participants in Professor Feuergang’s dimensional project.” There was a pause as though the stranger was expecting us to say something. “You never heard of Professor Feuergang and his project, of course? I’m not surprised. Nobody wants to talk about it now, after what happened to all the test subjects. All but one.”

“What happened to the others?” H__________ asked.

There was a brief pause. “It was really rather tragic,” the man in the shadows said finally. “The fate all of them shared. All of them, but me.”

“There was something special about you, I suppose?” A_______ asked with a superior smile.

“Special?” The stranger seemed to be considering. “Perhaps. That’s for you to judge, after you’ve heard my story. So, listen now.”

****************************     ***************************     **************************

Before I talk about Professor Feuergang and his dimensional project, (the man in the corner said) I will have to set you straight about dimensions. Otherwise you’ll never understand what I’m going to say.

You have, all of you, I assume, some knowledge of basic geometry, such as any child is given in school. It’s a pity that you choose to ignore it, so I’m going to have to teach you all over again. What’s the first geometrical figure? The most basic one? A point, right? And what is a point? Geometrically, it’s something that has no length, no breadth, no height. In fact, it has no dimension at all. When you look at a full stop at the end of a sentence, however small it is, it still isn’t a point, because a genuine point would be literally invisible. Let’s suppose we have a point, then, a thinking, living, point. We can call him, uh, Mr X.

But put more than one point next to each other – even just two points, Mr X and his sister Miss Y – and what do you have? Why, a line.  And what’s a line? It’s got length, that’s all – but no breadth and no height, because it’s just a whole lot of points strung together. That, unless you’ve forgotten even basic geometry, is a one dimensional figure. It’s the smallest figure that can occupy any space at all.

Why am I telling you all this? You know it all already? Well, we shall see!

Now, suppose our point, Mr X, wants to visit his dear sister, Miss Y. To do so, he would have to travel along the line to her, wouldn’t he? And any travel, any at all, would take some time, wouldn’t it, even if it’s just a fraction of a fraction of a second?

Do you understand what I am getting at? You can’t get away from time, even in one single dimension. In fact you can’t disentangle time from the space occupied by even one dimension. There’s no such thing as separate time and space, really; it’s one quantity, called space-and-time, or, more briefly and inelegantly, spacetime. That’s what the Swiss patent clerk, your Einstein, said, as well. It’s not his fault that you didn’t understand a word.

Now let’s go back to Mr X, our point. As a point, he has nowhere to go. He’s stuck in one place. But as soon as he’s on a line, he can travel – in one plane only, along the line, but he can travel. I’m sure you can understand this, it’s simple enough. Mr X can move, but only along the line. He can’t move in any direction except the line, because there is no direction, in a one-dimensional world, but along the line.

But what if there was another direction in which Mr X could move? In order to do that – to move, as it were, left and right, instead of just backward and forward, he would have to go at right angles to the way he was moving earlier, wouldn’t he? Instead of a dimensionless point, or of a line with length but nothing else, he would have to be the equivalent of a line on a sheet of paper. That means he’s in two dimensions – and moving in two dimensions takes time, just as it does in one dimension. Do you clots understand that at least? Yes, or no?

All right. Now, in zero dimension, our Mr X can only exist as a point. He can’t possibly be anything else. But in one dimension, all of a sudden, he can not only be a point, he can also be a straight line! And in two dimensions, he can be a point, or a straight line, or a wavy line, or – and follow me carefully here – he can be a figure that encloses space, occupies an area, such as a circle or a triangle, a trapezium or a square. But all he can still do is occupy an area. He can’t have any volume, because in two dimensions there is no volume. To do that he would have to lift off the sheet of paper – he would need to be in three dimensions, the third being at right angles to the other two, just as the second is at right angles to the first. And, as we all know, to move around in three dimensions – just like I’m moving my hand here – takes time as well. So let’s get rid of this absurd idea that time is a dimension separate from the other three. Of course it isn’t.

Now, let’s consider our Mr X in zero dimensions. He can’t move. He might, if he bothered to think about it, conceive of an existence where there might be a possibility of movement, but it would be merely a theoretical exercise. In a zero-dimensional universe, remember, there’s nothing outside him, nothing at all. He, the point, is all there is.

However, when he’s in a one-dimensional world, suddenly he can move. He can only move in a straight line, but he can move. And, if he can move in a straight line, he can imagine that there may be a world at right angles to it where he could change direction; move in a curved line, even curl around his own path to make a circle and enclose space. But he can only imagine it; he can work out the mathematics of it, but it will always be a fantasy to him, a theoretical universe that he cannot possibly directly experience.

Of course, if he then ascends to the two-dimensional world, the one which has length as well as breadth, he can experience it; and he can also imagine a universe where he could not just move along the flat surface of two dimensions, but lift off at right angles to it into the world of three dimensions.

Now let’s suppose he tells his sister, Miss Y, about this idea of his. Not too surprisingly, her response is, “Well, then, where is this third dimension of yours? Show it to me.” But he can’t. He can mathematically prove that such a third dimension could exist, even that it should exist; but he can’t show it to her. Can he?

So, let’s then take pity on Mr X and bring him into the three-dimensional world of ours. He suddenly has not just length and breadth but height – he has volume! He can move, not just forwards and backwards and left and right, but up and down. He’s amazed, and so is his sister Miss Y, whom we’ve brought along with him so he has someone to talk to.

Then Mr X has a further thought. “This third dimension is at right angles to the two we lived on earlier, and they were at right angles to the world without dimensions before that. What, then, is to prevent there being a fourth dimension at right angles to this one?” Why, nothing.

Perhaps Miss Y might object, but Mr X could simply point out that her scepticism in the case of the third dimension has been proved wrong. But still, even if she accepts the possibility of this fourth dimension, how can one go to it? How can one step into a direction at right angles to length, breadth, and height, as easily as from two dimensions to three?

And, so, my young friends, we come to the crux of the problem facing Professor Feuergang. Have you ever heard of him? I didn’t think so. He’s too intimately mixed up with military research to publish papers, and he takes care to keep himself out of the public eye. As a matter of fact, I have no particular reason to believe that Feuergang is even his real name. Certainly I never found out which university he might have taught at; and if you ever met him, you would realise that it was utterly impossible to imagine this man in a lecture hall, teaching anyone anything.

But, real name or not, military research was exactly why the Professor began trying to find a way of reaching the fourth dimension. You may all be young nitwits – your conversation leaves me no reason to suspect anything else – but you will be aware that war clouds are gathering on the horizon. Within three or four years – perhaps sooner – the great powers may ignite a war the likes of which the planet has never seen before.

Some of our spies reported rumours that the Other Side had started research into the fourth dimension. If they thought it useful – and you know that they have a strong scientific base, as strong as ours – then they must have thought of some way to make it militarily advantageous. We couldn’t find out how they might do it, but it did offer some fascinating possibilities.

For instance, let’s imagine a battle where your army is besieging an enemy fort. It’s not easy to get past the tons of metal and concrete and barbed wire that constitute its defences, even without the enemy’s defensive fire. But imagine if our Mr X were in his two dimensional world and confronted by a square he needed to enter; a bank vault he wished to loot, shall we say. He couldn’t enter it in the two dimensional world without breaching one of the sides or angles. But if he could lift at right angles into the third dimension, he could pass over the boundary of the square and enter inside, to steal all he wanted to his heart’s content, as long as the bank was closed for a holiday.

Similarly, confronted by an impregnable fortress, if you could merely shift your army into the fourth dimension, it could, as it were, vault over the three-dimensional boundaries of the fort and materialise right inside it! The enemy would be helpless.

So some military council called together a team of mathematicians and physicists, put them under Professor Feuergang, and ordered him to set to work. This research, was, of course, to be conducted in total secrecy, and absolutely no effort was spared to ensure that secrecy.

To keep it hidden from prying eyes, an old copper mine – I won’t tell you where it is, but you would probably recognise it if I did, for it’s one of the deepest in the world – was handed over to Feuergang for the research. The old shafts and tunnels were enlarged, and entire halls and laboratories hollowed out of the rock, kilometres underground. I don’t know what cover story they used: probably something about reopening the mine to look for fresh ore deposits. If the locals wondered why the old miners weren’t hired, they knew well enough not to say anything.

At this time I wasn’t involved in the project; I didn’t even know about its existence until I was, one day, abruptly summoned from my office in the paymaster’s corps to army headquarters and ordered to report to General S_______ himself. Perhaps you have seen photos of the general in the papers. His shining bald head and walrus moustache are instantly identifiable in any gathering of military top brass; but newspaper photos only hint at the florid colour of his cheeks, and totally miss the cold intelligence in his little eyes. I believe that the man has no emotions at all; when he affects to have feelings, it’s merely to manipulate someone to do something he wants.

“Major V__________,” he said, without preamble, as soon as I had entered his office and identified myself. “Major V__________, you are ordered to volunteer to join Professor Feuergang’s team. You will leave for ________ right away. And this is to be treated as absolutely top secret. You can discuss it with nobody, not even your wife, if you have one.”

“May I ask what the nature of this team is, sir? I asked.

 “You may not,” he responded shortly. “Professor Feuergang will tell you all that you need to know. See my aide, he will have further orders and travel passes for you.”

So I went back to my quarters, and, as I had been commanded by the general’s aide, sent my batman out on an errand that would take up most of the day. Then I hastily packed my bags myself and, wearing civilian clothes, left for ___________ by train before the poor man could get back.

It was not a comfortable journey, for the general’s aide had procured for me the cheapest tickets, all the better to make my journey in anonymity, he said. So it was exhausted after a sleepless night that I arrived at _______ and from the station took a bus that deposited me not far from the mine which now did duty as Professor Feuergang’s research centre.

I still remember quite well my first sight of the mine. It was a gash in the red earth, with trolleys rattling along rails leading up from the depths, winches running, and the air full of the smoke and noise of the steam engines driving them. Later I discovered that all this was just a sham; the trolleys contained nothing but gravel, and would merely return to the depths to be brought back up again by the busy winches. The miners in their rough clothes I saw, as it turned out, were all either scientists or soldiers like myself.

Professor Fuergang met me in what, according to the sign on the door, was the mine manager’s office. He was tall and thin, with a nose like a knife-blade separating eyes of a peculiar grey-green colour that I have only seen before in stormy seas. “So you are the latest test subject the general has sent,” he said, in a voice reminiscent of the squeak of chalk on blackboard. “I hope you do better than the others.”

“What is the programme about, Professor?” I asked.

“It’s research concerning the fourth dimension,” he replied, and gave me a brief explanation, far briefer than the one I provided to you, because he had less time to waste and also because he assumed, correctly, that I was more intelligent than you are. “And we’ve managed to invent the mechanism,” he finished.

“You mean, we can send our armies into enemy fortresses, and even into their capital?” I asked disbelievingly.

“Hardly that yet,” he responded drily, “or we would not have required you. We would have been conducting field trials with troops under the command of combat officers, not mere majors in the paymaster corps.” Without bothering to acknowledge my wince, he tapped on the table with a neatly manicured fingernail. “We have managed a way to access the fourth dimension, yes. But it’s still in the trial phase. And the trials have not gone, shall we say, precisely according to plan.”

“What do you mean, Professor?” I asked.

“Come with me,” he said. “We will go down into the mine, and on the way I will explain.”

It was the first time I had ever been inside a mine, so I would normally have wanted to look around, but the professor’s voice was insistent. “The entire interior of the mine, except for the parts given over to disguising its real purpose, has been turned into part of the project. We’ve converted part of the upper levels into residential quarters for our really essential staff – they aren’t permitted to go to the surface without special permission, and you will be joining them. We also have a hospital, which you will be visiting shortly for your physical checks.”

“The military hospital said I was perfectly healthy at my last check-up, just a month ago,” I said.

“I don’t doubt that you are. These checks we will do here are not to see if you’re healthy. They are to measure your indices.”

“Indices?”

“The medical staff will explain in detail, but what it means is that the doctors will need to know exactly what your body’s architecture and chemistry are like so that, after your trip to the fourth dimension, they can see if anything has changed.”

“My trip to the fourth dimension?” I repeated stupidly.

“Yes, of course. Why did you imagine you’re here? We don’t need a desk warrior from the paymaster corps to handle our finances.”  

I had nothing to say for the moment; my mind was still grappling with the idea of my going to the fourth dimension. In silence I followed Feuergang into a lift, which was little more than a metal cage hung on chains, and we rattled down a vertical shaft that seemed to go down for so long I began to wonder if it would ever stop.

“The actual fourth dimensional projection chambers are in the deepest part of the mine, of course,” Feuergang said conversationally. “It’s not just a matter of secrecy. We aren’t really able to control the process fully yet. The only safe way to keep it damped down and contained is under thousands of tons of rock.”

“What is this projection chamber like?” I managed eventually, suppressing an urge to shiver. It had grown frigid in the shaft. Feuergang, who was probably used to the conditions, did not seem to notice the cold at all.

“You’ll soon see,” Fuergang said. “We tried a lot of things at first; none of them worked. But we knew that if the Other Side was working on it, then it must be possible. And if it is possible, we had only to keep trying until we were successful.

“Finally we hit on the idea of reconfiguring a chamber in the rock in accordance with the mathematical modelling of a hypercube; that is the four-dimensional projection of a regular cube. I will not waste both your time and mine with the many errors we made, but finally, by means of a series of plates projecting galvanic currents and inducing magnetism in that chamber, we managed to create a way of reaching the fourth dimension – for as long as the current was run. And, after further experiments, we...ah, here we are.”

With a slight jerk and a final clang, the iron cage came to a halt at the bottom of the shaft. It was so cold that my breath was condensing on my moustache, and I fancied that it would freeze into little icicles.

“The low temperature is essential to creating the electromagnetic fields necessary,” Feuergang said. “I trust you have a greatcoat or other warm clothes with you? If not, you will need to borrow something from one of the other staff.” Without waiting to listen to my response, he strode off down the passage, leaving me to follow.

There were lights set in the roof of the passage, and as we walked they got progressively brighter, until they reached an eye-searing level of brightness that might have rivalled the light of the midday sun. The passage kept changing direction from left to right and back in a series of hairpin bends, for all the world like the passages of a fortress, meant to limit the damage from the explosion of an enemy shell that might breach the walls. I must have made some comment on this, if only to keep my teeth from chattering, for Feuergang nodded.

“Exactly,” he said. “Only it’s not an explosion that we’re guarding against, and not from something from outside. We’re trying to put as much rock as possible between the reaction chambers and the outside world. It’s just a precaution. We have no reason to believe that the four dimensional space can spread outside the confines of our hypercube...so far.”

“But?” I supplied.

“But, given the current political situation, we’re compelled to move fast; faster than we’d have liked. Sooner, rather than later, we’re going to have to increase the power of the system and try to create the four dimensional space outside the confines of the hypercube. That’s why this passage is like that.”

As he spoke the last words we turned a final bend and were faced with the kind of heavy metal door one normally only sees in armouries. There was a guard present, too, whose miner’s clothing could not disguise his soldierly build and bearing. Nodding in response to the Professor’s greeting, he unlocked the door and ushered us inside.

I had not known what to expect, but at first sight the chamber within seemed at first sight decidedly ordinary. It was merely a large room cut into the stone, which at a glance seemed as broad as it was long and as high as it was broad; in other words, it seemed to be a perfect cube. Only on closer examination did one notice that there were subtle differences from a cube, though just what those differences were, it was impossible to tell. One was left with the persistent feeling of something wrong, in every direction one looked, whether up at the ceiling or at the walls or corners or at the floor under one’s feet. It made me shiver for a reason that had nothing to do with the bone-chilling cold.

“How does it work?” I asked. I rather fancy I stammered.

“The plates and galvanic current inducers are in adjacent chambers,” Feuergang said. “They have their own crews. You don’t need to know how they work. All you are concerned with is that.”

In the centre of the room, was a spherical object which, for some reason, I had not noticed before. It was a globe of some dingy grey metal, placed on a metal post so that it was raised above the floor to halfway to the ceiling. Looking up at it, I noticed the round opening of a hatch.

“What is it?” I asked.

“That,” Feuergang said, with pride, ‘is the actual capsule – the thing that we send into four dimensions, along with anything it contains. That’s how all our test subjects – from mice to men – have gone, and come back.”

“They did come back?” I felt compelled to ask.

“Of course they came back,” Feuergang replied sharply. “It’s just a matter of creating the four dimensional bubble inside the hypercube, and then breaking it. Why shouldn’t they come back?”

“I...” I began, but Feuergang had already turned away. There was nothing to say, anyway. I was under orders, and nothing that I could say would make any difference. Besides, the wrongness of that room was beginning to make me slightly nauseous and give me a headache. “What do you want me to do?” I asked.

“I have work to do, preparing for tonight,” the Professor said. “You will go back up and report to the medical department for your check-up. Eat something if you want, if you have time afterwards; there’s a commissary above ground. And get some rest; you’ll need it. Be back here before nine in the evening. That is when tonight’s exercise is to begin.”

*****************************************

The medical department occupied a series of passages at the topmost level of the old mine, just below ground. If I had wondered at Feuergang’s implying that I might not have enough time to eat, I soon realised that he was right. The examination I went through was more thorough than any I had ever been through before, in civilian life or in the military. Every part of me was probed and prodded, examined and noted. They sampled my blood, demanded that I provide them with urine, peered into my ears, scraped with gleaming instruments at my teeth, and with the new roentgenographic apparatus imaged every part of me down to my toes.

At last I reached the psychological department, where a Dr U________ made me look at shapes and colours and asked me questions about my mother; it seems that these are the latest techniques, created by some Viennese whose name escapes me at the moment; something like Fraud. After all the shining and frankly intimidating equipment of the rest of the medical section, the psychology department was at least familiar; it was merely a large, well-furnished office with a carpet on the floor and paintings hanging on the walls; and Dr U_______ was himself a large, reassuring, comfortably plump man with a ready smile. Apart from the lack of windows – unavoidable, since we were underground – the only jarring note was another of the heavy metal doors set in the far wall. I didn't take much notice of it until, just as we had finished our session and Dr U________ was scribbling in my file, the door opened and a muscular young orderly in white stepped into the room.

“I am sorry, Doctor,” he said. “I did not wish to interrupt you, but one of the patients is in trouble again and –”

  

“Which patient?” Dr U________ asked, rising, and at the same time pulling on a white coat which until then had hung over the back of his chair.

“It’s J_____,” the orderly replied. “And P______ C______ isn’t looking too good either.”

J______ and P_______ C________? I frowned. Where had I heard those names before? They were familiar, just on the other side of memory. I knew them from somewhere.

“I’m coming,” Dr U________ said, picking up a little black bag from a side table. “Get the sedative injections ready.” As the orderly left, he turned to me. “Major V_______, you can go now. We’ll see you after your little trip.”

“What’s going on?” I asked.

“It’s none of your concern.” His eyes were no longer reassuring, and his fat face looked as though it was carved out of granite. “We will see you later. Now go.”

As I left the office, I glanced back over my shoulder. The orderly was holding the armoured door open, and, through it, I saw a narrow corridor and a row of doors with barred windows set in them.

And, for a moment before the door shut behind me, I heard the clear sound of someone shrieking.

*****************************************

It was ten minutes to nine by my pocket watch when I returned to the chamber at the bottom of the shaft. I had not spent the time in between eating and resting as Feuergang had advised; I had spent it deep in thought. I had managed to get hold of a heavy overcoat and a hat, which I had pulled down low over my ears. And I had made one other acquisition, which lay in my overcoat pocket, within easy reach of my hand.

In contrast to the morning, when the tunnels had been deserted but for the guard, they were full of hurrying figures, many carrying notebooks in which they were writing with the new fountain pens. One of them, a tall woman in grey, was waiting impatiently at the metal door and came up as soon as she saw me.

“Major V_________?” she snapped. “I’ve been waiting for you. I’m Dr G________.”

I knew, of course, that there were a few of the gentler sex who have in these latter days taken to dabbling in science, but it was the first I had ever seen, let alone met in person. Besides, with her darting black eyes and her angular face, she was about as far from gentle as anyone I have ever seen.

“Where’s Professor Feuergang?” I asked.

“The Professor is busy. He has no time to speak to you now.” Her tone of voice clearly indicated that she did not have any time either, that I was little more than a laboratory animal, like a white rat, in fact worse because a white rat was not expected to ask questions and need instructions. “He told me he has already briefed you.”

“He told me about the programme, yes. But...”

“What?” she asked impatiently, opening the door. The cubical room was full of people now. Some of them were drawing curves and lines on the floor and walls with chalk under the direction of others. In one corner, a man bent under the cloth hood of a photographic apparatus, busily exposing plates. A couple of soldiers in mining clothes were on stepladders, at work on the outside of the sphere, swabbing it down with mops, over and over again.

“We can’t risk any dust on it,” Dr G_______ said, following my gaze. “Even a single particle of grit might introduce a fatal discrepancy in the field. Oh,” she added, “by that I mean it will ruin the four-dimensional bubble. You don’t have to worry, I don’t mean literally fatal.”

“Has it been literally fatal?” I asked.

She darted another sharp glance at me. “What do you mean by that?”

“I mean...I’m not the first test subject, am I? What happened to the earlier ones?”

“Of course you aren’t the first. We used rats at first, then a monkey, and then moved to human test subjects. None of them died. They didn’t even suffer a scratch. Why do you ask?”

“I was just wondering why you needed me, instead of just using them again.”

“I’m afraid that’s something I can’t talk about.” She did not look afraid. She looked angry and impatient. “Anything else?”

“Who were the test subjects? Scientists?”

“The first was...” she blinked and her mouth snapped shut into a thin line. “You don’t need to know who they were. You’re a soldier, so your job is to follow orders. We’re running short of time as it is.”

“I need to know what to expect, don’t I? What did the earlier subjects say they experienced?”

“You don’t need to know,” she said after a moment’s pause. “It’s better that you don’t have any preconceived notions.” She glanced upwards at the sphere, which the two men had finally finished cleaning. “Now, here’s what is going to happen.

“You’ll climb in through the hatch, which will be sealed behind you. The inside is padded and there’s a seat. All you have to do is sit still. We’ll send the sphere into the fourth dimension and bring it back in two minutes.”

“Two minutes? That’s all?”

“It’s long enough for our tests.” She motioned to one of the men who had been mopping the thing, and he opened the hatch. The black circle of the interior looked like a hungry mouth swallowing the light. “The galvanic current can’t be maintained much longer than that anyway. It takes too much power.”

“What’s the delay?” The shout was in a familiar voice, and we turned to see Feuergang at the door. “The batteries are fully charged. We can’t wait any longer.”

“He’s just going, Professor,” Dr G______ said. “I’m giving him his instructions.”

“What’s the need for that?” Feuergang shouted. “All he’s got to do is get inside. It’s not as though he’s anything more than another expendable military idiot anyway.” Turning away, he stomped off.

“He’s, uh, under a little tension. What with the situation in the world and the pressure to produce results, you know.”

I didn’t say anything. The man who had opened the hatch descended the stepladder, and Dr G________ motioned me up to the hatch. Inside there were just the one spherical wall, padded in khaki-coloured canvas, and a seat fixed to one side and covered with the same material. A tiny yellow bulb set in the padding opposite the chair threw a wan glow on the cheerless furnishings.

“It’s just two minutes, so you won’t need any additional supply of air,” Dr G________ said at my shoulder. I had not realised that she had followed me up the stepladder. “All you have to do is sit down and wait until the hatch is opened again, and tell us what you’ve felt and seen.”

“But there’s no window or anything,” I objected. “How am I supposed to see anything?”

“You don’t need to look out,” she said. “Just tell us what you feel and see here, inside. That’s all.” Without wishing me good luck, she began swinging the hatch shut.

“Wait!” I said. “Just tell me this: among the previous test subjects were military officers called J______ and P_______ C________, weren’t they?”

She stared at me, and then gave an infinitesimal nod.

“What happened to them?” I asked. “Something happened to them all, didn’t it? Something because of which you had to stop using scientists and resort to using expendable military people instead. And it didn’t happen to the rats, or to the monkey, or else you wouldn’t have moved on to people. What happened to them?”

Dr G_________ said nothing. The tip of her tongue ran over her lips, as though licking away the words that she might have been about to say.

“They went insane, didn’t they?” I shouted, but the hatch swung shut, and I did not hear if she made any reply.

*****************************************

It is difficult to explain in words you would understand exactly what happened next. Not just because of your intellectual limitations, painful as they are, but because you have never been in that situation. Still, as far as possible, I will try.

The hatch swung shut, and instantly the interior of the sphere was thrown into an even deeper gloom than before. The little lamp on the opposite wall had barely served to illuminate the interior when the hatch was open; it now proved to be so dim that the glow of it barely lit up my hands. For a long – a very long time, as it seemed to me, nothing further happened; indeed, I began to wonder if the experiment had failed completely. But, still, I took out the other thing I had acquired, the one in my pocket, and held it in my hand; just in case I had to use it.

Then the lamp suddenly glowed much more brightly, so that the entire interior of the sphere was illuminated; and a moment later there was a sudden wrenching sensation, as though something had grasped every part of me and pulled.

Pulled in all directions at the same time, both outside and inside, from my hair and skin to my blood and bones and brain; it went on and on, and at the same time the inside of the sphere, too, began to expand rapidly, or maybe it was no longer a sphere at all, but something so nearly flat that it was impossible to tell. And still it went on, and on, and on.

All around me the space fell away. Instead of being perched on a tiny seat in a little ball of metal, I seemed to be standing, or hovering, above – or maybe it was at the same time below –  a great plain. And yet it was not a plain, for in the distance it curved upwards, and yet the curve was not just upwards, it was at the same time away from me instead of towards me. I might say it was at right angles to upwards. It does not make sense unless you’ve been there and experienced it.

The time had come. I did not know exactly where or what my hand was any longer, but I could still feel it. And I brought it up, with the object grasped in it, ready for use.

Then, and only then, did I look down at myself.

****************************     ***************************     **************************

“And so,” said the man in the shadows, “I went to the Fourth Dimension and came back. I’m sure that Professor Feuergang, Dr G________, and the rest were surprised that I had retained my sanity. I am also sure that they were less than happy about how I had done it.

“Actually, in retrospect, it was obvious; the only surprising thing was that nobody had worked it out by themselves before, simply by logical progression.

“As you may have gathered, I had decided that there could not have been a physical problem to going into the fourth dimension; if the rats and monkey had been killed or otherwise damaged, then Feuergang and his team would never have proceeded to humans. Therefore the problem had to be a mental one; one which only a creature like a human, with a highly developed brain, could experience. I just didn’t know what, and unless I experienced it for myself there was no way I could know.

 “Afterwards, when I was able to talk to Feuergang and the doctors, I told them what I had deduced.

“Think of our Mr X, the point in the zero dimensional world, who then goes to the first and the second dimension. Let us say that in the second dimensional world he prospers exceedingly, and grows flat, so that eventually he is no longer a mere point, but a circle. In other words, he occupies an area.

“Now we pull Mr X up and away from his two dimensional world into that of three dimensions; but that does not mean that he is separated from his two dimensions. He can’t simply float above the two dimensional world, like a zeppelin or artillery observation balloon in the sky, and look down on the two dimensional world spread out beneath. No! At the same time that he is in this third dimension, he is also down there in the two dimensions. His centre, along with the radii, may have been pulled up into three dimensions; but his circumference is still down there. To us he would look, no longer a circle, but a cone.

“However, Mr X isn’t a rat or a monkey, which has neither the knowledge of what is happening, nor the mental capacity to understand any of it. No, he is sentient and intelligent. So just imagine his feelings when he not just enters the third dimension, but sees himself altered into a shape that he had never been able to comprehend might exist before.

“And a circle, and then a cone, is a simple progression. Imagine how much more complex the shape of a man might be!

“Also, when Mr X is a circle, he might know that there are things inside him, his organs and juices and thoughts and loves and whatever else he contains. But unless someone cuts him open, he can’t see them, can he? Not in two dimensions.

“But imagine when he is in three.

“I absolutely cannot describe to you what I saw in that instant when I looked down – or, to be accurate, at right angles to down – at myself. It cannot be put into words. Think of yourself with all your inner organs pulled out, and arranged into something like a squid or a jellyfish; heart, lungs, intestines, and all, pulled out and turned inside out; and it is you, still breathing, still thinking, still alive. Can you imagine that? Then you might have the faintest, slightest shadow of an idea of what I experienced.

“And then, as I said, I came back. Afterwards the army discharged me. I was of no further use, and for that I am grateful.

“Professor Feuergang is, as far as I know, still at work on his project, but he has stopped trying to send men through. They are now talking of inventing metal men to take the part of flesh and blood soldiers. I do not know if they will manage to do that; and I think I am afraid of their succeeding.

“Well,” the man in the shadows said, and began to rise from his seat. “That is my tale. Now, if you excuse me, it has been a long evening, and I really must be going.”

“Wait,” D________ shouted. “You can’t just end it like that. How did you manage to not go insane like everyone else?”

The man in the corner laughed shortly. “I used my penknife,” he said. “Now, if you will please clear the way to the door. Thank you, gentlemen. Pleasant dreams.”

Fetching a white cane from behind the chair, he fumbled a pair of dark glasses into place over his features, and tapped his way out into the night.

Copyright B Purkayastha 2019