The Collected Stories of Arthur C. Clarke (13 page)

‘I did. He held the paper to the glass and looked at the reflection. Then he started to read aloud, at normal speed. But that’s a trick anyone can learn—compositors have to do it with type—and I wasn’t impressed. On the other hand, I couldn’t see why an intelligent fellow like Nelson should put over an act like that. So I decided to humour him, thinking the shock must have given his mind a bit of a twist. I felt quite certain he was suffering from some delusion, though he seemed perfectly normal.

‘After a moment he put the paper away and said, “Well, Doc, what do you make of that?” I didn’t know quite what to say without hurting his feelings, so I passed the buck and said, “I think I’ll have to hand you over to Dr Humphries, the psychologist. It’s rather outside my province.” Then he made some remark about Dr Humphries and his intelligence tests, from which I gathered he had already suffered at his hands.’

‘That’s correct,’ interjected Hughes. ‘All the men are grilled by the Psychology Department before they join the company. All the same, it’s surprising what gets through,’ he added thoughtfully.

Dr Sanderson smiled, and continued his story.

‘I was getting up to leave when Nelson said, “Oh, I almost forgot. I think I must have fallen on my right arm. The wrist feels badly sprained.” “Let’s look at it,” I said, bending to pick it up. “No, the other arm,” Nelson said, and held up his left wrist. Still humouring him, I answered, “Have it your own way. But you said your right one, didn’t you?”

‘Nelson looked puzzled. “So what?” he replied. “This
is
my right arm. My eyes may be queer, but there’s no argument about that. There’s my wedding ring to prove it. I’ve not been able to get the darned thing off for five years.”

‘That shook me rather badly. Because you see, it was his left arm he was holding up, and his left hand that had the ring on it. I could see that what he said was quite true. The ring would have to be cut to get it off again. So I said, “Have you any distinctive scars?” He answered. “Not that I can remember.”

‘“Any dental fillings?”’

‘“Yes, quite a few.”’

‘We sat looking at each other in silence while a nurse went to fetch Nelson’s records. “Gazed at each other with a wild surmise” is just about how a novelist might put it. Before the nurse returned, I was seized with a bright idea. It was a fantastic notion, but the whole affair was becoming more and more outrageous. I asked Nelson if I could see the things he had been carrying in his pockets. Here they are.’

Dr Sanderson produced a handful of coins and a small leather-bound diary. Hughes recognised the latter at once as an Electrical Engineer’s Diary; he had one in his own pocket. He took it from the doctor’s hand and flicked it open at random, with that slightly guilty feeling one always has when a stranger’s—still more, a friend’s—diary falls into one’s hands.

And then, for Ralph Hughes, it seemed that the foundations of his world were giving way. Until now he had listened to Dr Sanderson with some detachment, wondering what all the fuss was about. But now the incontrovertible evidence lay in his own hands, demanding his attention and defying his logic.

For he could read not one word of Nelson’s diary. Both the print and the handwriting were inverted, as if seen in a mirror.

Dr Hughes got up from his chair and walked rapidly around the room several times. His visitor sat silently watching him. On the fourth circuit he stopped at the window and looked out across the lake, overshadowed by the immense white wall of the dam. It seemed to reassure him, and he turned to Dr Sanderson again.

‘You expect me to believe that Nelson has been laterally inverted in some way, so that his right and left sides have been interchanged?’

‘I don’t expect you to believe anything. I’m merely giving you the evidence. If you can draw any other conclusion I’d be delighted to hear it. I might add that I’ve checked Nelson’s teeth. All the fillings have been transposed. Explain that away if you can. Those coins are rather interesting, too.’

Hughes picked them up. They included a shilling, one of the beautiful new, beryl-copper crowns, and a few pence and halfpence. He would have accepted them as change without hesitation. Being no more observant than the next man, he had never noticed which way the Queen’s head looked. But the lettering—Hughes could picture the consternation at the Mint if these curious coins ever came to its notice. Like the diary, they too had been laterally inverted.

Dr Sanderson’s voice broke into his reverie.

‘I’ve told Nelson not to say anything about this. I’m going to write a full report; it should cause a sensation when it’s published. But we want to know how this has happened. As you are the designer of the new machine, I’ve come to you for advice.’

Dr Hughes did not seem to hear him. He was sitting at his desk with his hands outspread, little fingers touching. For the first time in his life he was thinking seriously about the difference between left and right.

Dr Sanderson did not release Nelson from hospital for several days, during which he was studying his peculiar patient and collecting material for his report. As far as he could tell, Nelson was perfectly normal, apart from his inversion. He was learning to read again, and his progress was swift after the initial strangeness had worn off. He would probably never again use tools in the same way that he had done before the accident; for the rest of his life, the world would think him left-handed. However, that would not handicap him in any way.

Dr Sanderson had ceased to speculate about the cause of Nelson’s condition. He knew very little about electricity; that was Hughes’s job. He was quite confident that the physicist would produce the answer in due course; he had always done so before. The company was not a philanthropic institution, and it had good reason for retaining Hughes’s services. The new generator, which would be running within a week, was his brain-child, though he had had little to do with the actual engineering details.

Dr Hughes himself was less confident. The magnitude of the problem was terrifying; for he realised, as Sanderson did not, that it involved utterly new regions of science. He knew that there was only one way in which an object could become its own mirror image. But how could so fantastic a theory be proved?

He had collected all available information on the fault that had energised the great armature. Calculations had given an estimate of the currents that had flowed through the coils for the few seconds they had been conducting. But the figures were largely guesswork; he wished he could repeat the experiment to obtain accurate data. It would be amusing to see Murdock’s face if he said, ‘Mind if I throw a perfect short across generators One to Ten sometime this evening?’ No, that was definitely out.

It was lucky he still had the working model. Tests on it had given some ideas of the field produced at the generator’s centre, but their magnitudes were a matter of conjecture. They must have been enormous. It was a miracle that the windings had stayed in their slots. For nearly a month Hughes struggled with his calculations and wandered through regions of atomic physics he had carefully avoided since he left the university. Slowly the complete theory began to evolve in his mind; he was a long way from the final proof, but the road was clear. In another month he would have finished.

The great generator itself, which had dominated his thoughts for the past year, now seemed trivial and unimportant. He scarcely bothered to acknowledge the congratulations of his colleagues when it passed its final tests and began to feed its millions of kilowatts into the system. They must have thought him a little strange, but he had always been regarded as somewhat unpredictable. It was expected of him; the company would have been disappointed if its tame genius possessed no eccentricities.

A fortnight later, Dr Sanderson came to see him again. He was in a grave mood.

‘Nelson’s back in the hospital,’ he announced. ‘I was wrong when I said he’d be OK.’

‘What’s the matter with him?’ asked Hughes in surprise.

‘He’s starving to death.’

‘Starving? What on earth do you mean?’

Dr Sanderson pulled a chair up to Hughes’s desk and sat down.

‘I haven’t bothered you for the past few weeks,’ he began, ‘because I knew you were busy on your own theories. I’ve been watching Nelson carefully all this time, and writing up my report. At first, as I told you, he seemed perfectly normal. I had no doubt that everything would be all right.

‘Then I noticed that he was losing weight. It was some time before I was certain of it; then I began to observe other, more technical symptoms. He started to complain of weakness and lack of concentration. He had all the signs of vitamin deficiency. I gave him special vitamin concentrates, but they haven’t done any good. So I’ve come to have another talk with you.’

Hughes looked baffled, then annoyed. ‘But hang it all, you’re the doctor!’

‘Yes, but this theory of mine needs some support. I’m only an unknown medico—no one would listen to me until it was too late. For Nelson is dying, and I think I know why….’

Sir Robert had been stubborn at first, but Dr Hughes had had his way, as he always did. The members of the Board of Directors were even now filing into the conference room, grumbling and generally making a fuss about the extraordinary general meeting that had just been called. Their perplexity was still further increased when they heard that Hughes was going to address them. They all knew the physicist and his reputation, but he was a scientist and they were businessmen. What was Sir Robert planning?

Dr Hughes, the cause of all the trouble, felt annoyed with himself for being nervous. His opinion of the Board of Directors was not flattering, but Sir Robert was a man he could respect, so there was no reason to be afraid of them. It was true that they might consider him mad, but his past record would take care of that. Mad or not, he was worth thousands of pounds to them.

Dr Sanderson smiled encouragingly at him as he walked into the conference room. The smile was not very successful, but it helped. Sir Robert had just finished speaking. He picked up his glasses in that nervous way he had, and coughed deprecatingly. Not for the first time, Hughes wondered how such an apparently timid old man could rule so vast a commercial empire.

‘Well, here is Dr Hughes, gentlemen. He will—ahem—explain everything to you. I have asked him not to be too technical. You are at liberty to interrupt him if he ascends into the more rarefied stratosphere of higher mathematics. Dr Hughes…’

Slowly at first, and then more quickly as he gained the confidence of his audience, the physicist began to tell his story. Nelson’s diary drew a gasp of amazement from the Board, and the inverted coins proved fascinating curiosities. Hughes was glad to see that he had aroused the interest of his listeners. He took a deep breath and made the plunge he had been fearing.

‘You have heard what has happened to Nelson, gentlemen, but what I am going to tell you now is even more startling. I must ask you for your very close attention.’

He picked up a rectangular sheet of notepaper from the conference table, folded it along a diagonal and tore it along the fold.

‘Here we have two right-angled triangles with equal sides. I lay them on the table—so.’ He placed the paper triangles side by side on the table, with their hypotenuses touching, so that they formed a kite-shaped figure. ‘Now, as I have arranged them, each triangle is the mirror image of the other. You can imagine that the plane of the mirror is along the hypotenuse. This is the point I want you to notice. As long as I keep the triangles in the plane of the table, I can slide them around as much as I like, but I can never place one so that it exactly covers the other. Like a pair of gloves, they are not interchangeable although their dimensions are identical.’

He paused to let that sink in. There were no comments, so he continued.

‘Now, if I pick up one of the triangles, turn it over in the air and put it down again, the two are no longer mirror images, but have become completely identical—so.’ He suited the action to the words. ‘This may seem very elementary; in fact, it is so. But it teaches us one very important lesson. The triangles on the table were flat objects, restricted to two dimensions. To turn one into its mirror image I had to lift it up and rotate it in the third dimension. Do you see what I am driving at?’

He glanced round the table. One or two of the directors nodded slowly in dawning comprehension.

‘Similarly, to change a solid, three-dimensional body, such as a man, into its analogue or mirror image, it must be rotated in a fourth dimension. I repeat—a fourth dimension.’

There was a strained silence. Someone coughed, but it was a nervous, not a sceptical cough.

‘Four-dimensional geometry, as you know’—he’d be surprised if they did—‘has been one of the major tools of mathematics since before the time of Einstein. But until now it has always been a mathematical fiction, having no real existence in the physical world. It now appears that the unheard-of currents, amounting to millions of amperes, which flowed momentarily in the windings of our generator must have produced a certain extension into four dimensions, for a fraction of a second and in a volume large enough to contain a man. I have been making some calculations and have been able to satisfy myself that a ‘hyperspace’ about ten feet on a side was, in fact, generated: a matter of some ten thousand quartic—not cubic!—feet. Nelson was occupying that space. The sudden collapse of the field when the circuit was broken caused the rotation of the space, and Nelson was inverted.

‘I must ask you to accept this theory, as no other explanation fits the facts. I have the mathematics here if you wish to consult them.’

He waved the sheets in front of his audience, so that the directors could see the imposing array of equations. The technique worked—it always did. They cowered visibly. Only McPherson, the secretary, was made of sterner stuff. He had had a semi-technical education and still read a good deal of popular science, which he was fond of airing whenever he had the opportunity. But he was intelligent and willing to learn, and Dr Hughes had often spent official time discussing some new scientific theory with him.