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 realized, 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 energized 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 center, 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 O.K."
"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 skeptical 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 math
ematics 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.
"You say that Nelson has been rotated in the Fourth Dimension; but I thought Einstein had shown that the Fourth Dimension was time."
Hughes groaned inwardly. He had been anticipating this red herring.
"I was referring to an additional dimension of space," he explained patiently. "By that I mean a dimension, or direction, at right-angles to our normal three. One can call it the Fourth Dimension if one wishes. With certain reservations, time may also be regarded as a dimension. As we normally regard space as three-dimensional, it is then customary to call time the Fourth Dimension. But the label is arbitrary. As I'm asking you to grant me four dimensions of space, we must call time the Fifth Dimension."
"Five Dimensions! Good Heavens!" exploded someone further down the table.
Dr. Hughes could not resist the opportunity. "Space of several million dimensions has been frequently postulated in sub-atomic physics," he said quietly.
There was a stunned silence. No one, not even McPherson, seemed inclined to argue.
"I now come to the second part of my account," continued Dr. Hughes. "A few weeks after his inversion we found that there was something wrong with Nelson. He was taking food normally, but it didn't seem to nourish him properly. The explanation has been given by Dr. Sanderson, and leads us into the realms of organic chemistry. I'm sorry to be talking like a textbook, but you will soon realize how vitally important this is to the company. And you also have the satisfaction of knowing that we are now all on equally unfamiliar territory."
That was not quite true, for Hughes still remembered some fragments of his chemistry. But it might encourage the stragglers.
"Organic compounds are composed of atoms of carbon, oxygen and hydrogen, with other elements, arranged in complicated ways in space. Chemists are fond of making models of them out of knitting needles and colored plasticine. The results are often very pretty and look like works of advanced art.
"Now, it is possible to have two organic compounds containing identical numbers of atoms, arranged in such a way that one is the mirror image of the other. They're called stereo-isomers, and are very common among the sugars. If you could set their molecules side by side, you would see that they bore the same sort of relationship as a right and left glove. They are, in fact, called right—or left-handed—dextro or laevo—compounds. I hope this is quite clear."
Dr. Hughes looked around anxiously. Apparently it was.
"Stereo-isomers have almost identical chemical properties," he went on, "though there are subtle differences. In the last few years, Dr. Sanderson tells me, it has been found that certain essential foods, including the new class of vitamins discovered by Professor Vandenburg, have properties depending on the arrangement of their atoms in space. In other words, gentlemen, the left-handed compounds might be essential for life, but the right-handed one would be of no value. This in spite of the fact that their chemical formulae are identical.
"You will appreciate, now, why Nelson's inversion is much more serious than we at first thought. It's not merely a matter of teaching him to read again, in which case— apart from its philosophical interest—the whole business would be trivial. He is actually starving to death in the midst of plenty, simply because he can no more assimilate certain molecules of food than we can put our right foot into a left boot.
"Dr. Sanderson has tried an experiment which has proved the truth of this theory. With very great difficulty, he has obtained the stereo-isomers of many of these vitamins. Professor Vandenburg himself synthesized them when he heard of our trouble. They have already produced a very marked improvement in Nelson's condition."
Hughes paused and drew out some papers. He thought he would give the Board time to prepare for the shock. If a man's life were not at stake, the situation would have been very amusing. The Board was going to be hit where it would hurt most.
"As you will realize, gentlemen, since Nelson was injured—if you can call it that—while he was on duty, the company is liable to pay for any treatment he may require. We have found that treatment, and you may wonder why I have taken so much of your time telling you about it. The reason is very simple. The production of the necessary stereo-isomers is almost as difficult as the extraction of radium—more so, in some cases. Dr. Sanderson tells me that it will cost over five thousand pounds a day to keep Nelson alive."
The silence lasted for half a minute; then everyone started to talk at once. Sir Robert pounded on the table, and presently restored order. The council of war had begun.
Three hours later, an exhausted Hughes left the conference room and went in search of Dr. Sanderson, whom he found fretting in his office.
"Well, what's the decision?" asked the doctor.
"What I was afraid of. They want me to re-invert Nelson."
"Can you do it?"
"Frankly, I don't know. All I can hope to do is to reproduce the conditions of the original fault as accurately as I can."
"Weren't there any other suggestions?"
"Quite a few, but most of them were stupid. McPherson had the best idea. He wanted to use the generator to invert normal food so that Nelson could eat it. I had to point out that to take the big machine out of action for this purpose would cost several millions a year, and in any case the windings wouldn't stand it more than a few times. So that scheme collapsed. Then Sir Robert wanted to know if you could guarantee there were no vitamins we'd overlooked, or that might still be undiscovered. His idea was that in spite of our synthetic diets we might not be able to keep Nelson alive after all."
"What did you say to that?"
"I had to admit it was a possibility. So Sir Robert is going to have a talk with Nelson. He hopes to persuade him to risk it; his family will be taken care of if the experiment fails."
Neither of the two men said anything for a few moments. Then Dr. Sanderson broke the silence.
"Now do you understand the sort of decision a surgeon often has to make," he said.
Hughes nodded in agreement. "It's a beautiful dilemma, isn't it? A perfectly healthy man, but it will cost two millions a year to keep him alive, and we can't even be sure of that. I know the Board's thinking of its precious balance sheet more than anything else, but I don't see any alternative. Nelson will have to take a chance."
"Couldn't you make some tests first?"
"Impossible. It's a major engineering operation to get the rotor out. We'll have to rush the experiment through when the load on the system is at minimum. Then we'll slam the rotor back, and tidy up the mess our artificial short has made. All this has to be done before the peak loads come on again. Poor old Murdock's mad as hell about it."
"I don't blame him. When will the experiment start?"
"Not for a few days, at least. Even if Nelson agrees, I've got to fix up all my gear."
No one was ever to know what Sir Robert said to Nelson during the hours they were together. Dr. Hughes was more than half prepared for it when the telephone rang and the Old Man's tired voice said, "Hughes? Get your equipment ready. I've spoken to Murdock, and we've fixed the time for Tuesday night. Can you manage by then?"
"Yes, Sir Robert."
"Good. Give me a progress report every afternoon until Tuesday. That's all."
The enormous room was dominated by the great cylinder of the rotor, hanging thirty feet above the gleaming plastic floor. A little group of men stood silently at the edge of the shadowed pit, waiting patiently. A maze of temporary wiring ran to Dr. Hughes's equipment—multi-beam oscilloscopes, meg
awattmeters and microchronometers, and the special relays that had been constructed to make the circuit at the calculated instant.
That was the greatest problem of all. Dr. Hughes had no way of telling when the circuit should be closed; whether it should be when the voltage was at maximum, when it was at zero, or at some intermediate point on the sine wave. He had chosen the simplest and safest course. The circuit would be made at zero voltage; when it opened again would depend on the speed of the breakers.
In ten minutes the last of the great factories in the service area would be closing down for the night. The weather forecast had been favorable; there would be no abnormal loads before morning. By then, the rotor had to be back and the generator running again. Fortunately, the unique method of construction made it easy to reassemble the machine, but it would be a very close thing and there was no time to lose.
When Nelson came in, accompanied by Sir Robert and Dr. Sanderson, he was very pale. He might, thought Hughes, have been going to his execution. The thought was somewhat ill-timed, and he put it hastily aside.
There was just time enough for a last quite unnecessary check of the equipment. He had barely finished when he heard Sir Robert's quiet voice.
"We're ready, Dr. Hughes."
Rather unsteadily, he walked to the edge of the pit.
Nelson had already descended, and as he had been instructed, was standing at its exact center, his upturned face a white blob far below. Dr. Hughes waved a brief encouragement and turned away, to rejoin the group by his equipment.
He flicked over the switch of the oscilloscope and played with the synchronizing controls until a single cycle of the main wave was stationary on the screen. Then he adjusted the phasing: two brilliant spots of light moved toward each other along the wave until they had coalesced at its geometric center. He looked briefly toward Mur-dock, who was watching the megawattmeters intently. The engineer nodded. With a silent prayer, Hughes threw the switch.
There was the tiniest click from the relay unit. A fraction of a second later, the whole building seemed to rock as the great conductors crashed over in the switch room three hundred feet away. The lights faded, and almost died. Then it was all over. The circuit breakers, driven at almost the speed of an explosion, had cleared the line again. The lights returned to normal and the needles of the megawattmeters dropped back onto their scales.
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