Startled, they swung around. A stooped old man stood in a tiny doorway that opened from the hall — an old man who, while he was human, seemed not quite human. His head was large and his chest bulged out grotesquely. He stood on trembly pipestem legs and his arms were alarmingly long and skinny.

A long white beard swept over his chest, but his great domed head was innocent of even a single hair. Across the space that separated them, Gary felt the force of piercing eyes that stared out from under shaggy eyebrows.

"We're looking for someone," said Gary, "to give us information.”

"Come in," shrieked the thought of the old man. "Come in. Do you want me to catch my death of cold holding the door open for you?”

Gary grasped Caroline by the hand. "Come on," he said.

At a trot, they crossed the room, ducked through the door. They heard the door slam behind them and turned to look at the old man.

He stared back at them. "You are human beings," said his thoughts. "People of my own race. But from long ago.”

"That's right," said Gary. "From many millions of years ago.”

They sensed something that almost approached disbelief in the old man's thoughts.

"And you seek me?”

"We seek someone," said Gary. "Someone who may tell us something that may save the universe.”

"Then it must be me," said the old man, "because I'm the only one left.”

"The only one left!" cried Gary. "The last man?”

"That's right," said the old man, and he seemed almost cheerful about it.

"There were others but they died. All men's life spans must sometime come to an end.”

"But there are others," persisted Gary. "You can't be the last man left alive.”

"There were others," said the old one, "but they left. They went to a far star. To a place prepared for them.”

A coldness gripped Gary's heart.

"You mean they died?”

The old man's thoughts were querulous and impatient.

"No, they did not die. They went to a better place. To a place that has been prepared for them for many years. A place where they could not go until they were ready.”

"But you?" asked Gary.

"I stayed because I wanted to," said the old man. "Myself and a few others.

We could not forsake Earth. We elected to stay. Of those who stayed all the others have died and I am left alone.”

Gary glanced around the room. It was tiny, but comfortable. A bed, a table, a few chairs, other furniture he did not recognize.

"You like my place?" asked the old man.

"Very much," said Gary.

"Perhaps," said the old man, "you would like to take off your helmets. It's warm in here and I keep the atmosphere a little denser than it is outside.

Not necessary that I do so, of course, but it is more comfortable. The atmosphere is getting pretty thin and hard to breathe.”

They unfastened their helmets and lifted them off. The air was sharp and tangy, the room was warm.

"That's better," said Caroline.

"Chairs?" asked the old man, pointing out a couple.

They sat and he lowered his old body into another.

"Well, well," he said, and his thoughts had a grandfatherly touch about them, "humans of an earlier age. Splendid physical specimen, the two of you. And fairly barbaric still — but the stuff is in you. You use your mouths to talk with and man hasn't talked with other than his thoughts for thousands and thousands of years. That in itself would set you pretty far back.”

"Pretty far is right," said Gary. "We are the first humans who ever left the solar system.”

"That is far," said the old man. "Far, far…”

His sharp eyes watched them closely. "You must have an interesting story,”

be suggested.

"We have," said Caroline and swiftly they told it to him, excitedly, first one and then the other talking, adding in details, explaining situations, laying before him the problems which they faced.

He listened intently, snapping questions now and then, his bright old eyes shining with the love of adventure, the wrinkles in his face taking on a kind benevolence as if they might be children, home from the first day of school, telling of all the new wonders they had met.

"So you came to me," he said. "You came trundling down a crazy timepath to seek me out. So that I could tell you the things you need to know.”

Caroline nodded. "You can tell us, can't you?" she asked. "It means so much to us — so much to everyone.”

"I wouldn't worry," said the old man. "If the universe had come to an end, I wouldn't be here. You couldn't have come to me.”

"But maybe you aren't real," said Caroline. "Maybe you are just a shadow. A probability…”

The oldster nodded and combed his beard with gnarled fingers. The breath wheezed in his mighty chest.

"You are right," he agreed. "I may be only a shadow. This world of mine may be no more than a shadow-world. I sometimes wonder if there is any reality at all — if there is anything but thought. Whether it may not be that some gigantic intelligence has dreamed all these things we see and believe in and accept as real… if the giant intelligence may not have set mighty dream stages and peopled them with actors of his imagination. I wonder at times if all the universes may be nothing more than a shadow show. A company of shadowy actors moving on a shadow stage.”

"But you can tell us," pleaded Caroline. "You will tell…”

His old eyes twinkled. "I will tell you, yes, and gladly. Your fifth dimension is eternity. It is everything and nothing… all rolled into one.

It is a place where nothing has ever happened and yet, in a sense, where everything has happened. It is the beginning and the end of all things. In it there is no such thing as space or time or any other phenomena which we attribute to the four-dimensional continuum.”

"I can't understand," said Caroline, lines of puzzlement twisting her face.

"It seems so hopeless, so entirely hopeless. Can it be explained by mathematics?”

"Yes," said the old man, "but I'm afraid you wouldn't understand. The mathematics necessary to explain it weren't evolved until just a few thousand years ago.”

He stroked the beard down smoothly over his pouter-pigeon chest.

"I do not wish to make you feel badly," he declared, "but I can't see how you would have the intelligence to grasp it. After all, you are a people from an earlier age, an almost barbaric age.”

"Try her," growled Gary.

"All right," said the old man, but there was a patronizing tone to his thoughts.

Gary gained a confused impression of horrific equations, of bracketed symbols that built themselves into a tangled and utterly confused structure of meaning — a meaning that seemed so vast and all-inclusive that his mind instinctively shuddered away from it.

Then the thoughts were gone and Gary's mind was spinning with them, with the vital forcefulness that he had guessed and glimpsed behind the symbolic structure that had been in the mathematics.

He looked at Caroline and saw that she was puzzled. But suddenly a look of awe spread over her face.

"Why," she said, and hesitated slightly, "…. why, the equations cancel, represent both everything and nothing, both zero and the ultimate in everything imaginable.”

Gary caught a sense of surprise and confusion that flashed through the mind of their host.

"You understand," said the faltering thought. "You grasp the meaning perfectly.”

"Didn't I tell you," said Gary. "Of course, she understands." ‘

Caroline was talking, almost as if she were talking to herself, talking her thoughts aloud. "That means the energy would be timeless. It would have no time factor, and since time is a factor in power, its power would be almost infinite. There'd be no stopping it, once it started.”

"You are right," said the old man. "It would be raw, created energy from a region where four-dimensional laws are no longer valid. It would be timeless and formless.”

"Formless," said Caroline. "Of course, it would be formless. It wouldn't be light, or heat, or matter, or motion, or any other form of energy such as we know. But it could be anything. It would be waiting to become something.

It could crystallize into anything.”

"Good Lord," said Gary, "how could you handle stuff like that? Your hyperspheres wouldn't handle it. It could mold space itself. It could annihilate time.”

Caroline looked at him soberly.

"If I could create a fifth-dimensional trap," she said, "if I could trap it in the framework of the medium from which it came. Don't you see that such a framework would attract it, would gather it in and hold it. Like a battery holds energy. Like water seeking its own level and coming to rest.”

"Sure," agreed Gary, "if you could create a fifth-dimensional trap. But you can't. It's eternity. The dimension of eternity. You can't go fooling around with eternity.”

"Yes, she can," said the old man.

The two of them stared at him, not believing.

"Listen closely," said the oldster. "By rotating a circle through three dimensions you create a sphere. Rotate the sphere through four dimensions and you have a hypersphere. You already have created this. You have bent time and space around a mass to create a hypersphere, a miniature universe.

Now all you have to do is rotate the hypersphere through five-dimensional space.”

"But you'd have to be in five-dimensional space to do that," objected Gary.

"No, you wouldn't," contended the old man. "Scattered throughout three-dimensional space are ether eddies and time faults and space traps — call them anything you like. They are a common phenomena and they're nothing more, when you come right down to it, than isolated bits of four-dimensional space scattered around through three-dimensional space.

The same thing would apply to a fifth dimension in the fourth dimension.”

"But how," asked Caroline, "would one go about it? How would one rotate a hypersphere through the fifth dimension?”

Again Gary had that sense of confusion as the thoughts of the ancient one swept over him, thoughts that translated themselves into symbols and equations and brackets of mathematics that it seemed impossible any man could know.

"Gary," gasped Caroline, "have you a pencil and some paper?”

Gary fumbled in his pocket and found an old envelope and a stub of pencil.

He handed them to her.

"Please repeat that very slowly," she said, smiling at the old man.

Gary watched in amazement as Caroline, slowly and carefully, jotted down the formulas, equations, symbols — carefully checking and going over them, checking and rechecking so there could be no mistake.

"It will take power," she said. "Tremendous power. I wonder if the Engineers can supply it.”

"They have magnetic power," said Gary. "They ought to be able to give you all you need.”

The old man's eyes were twinkling. "I am remembering the Hellhounds," he said. "The ones who would have the universe destroyed. I cannot seem to like them. It seems to me that something should be done about them.”

"But what?" asked Gary. "They seem to be all-powerful. By the time we get back they may have battered the city into a mass of ruins.”

The oldster nodded almost sleepily, but his eyes were glowing.

"We have had ones like that in our history," he said. "Ones who overrode the nations and imposed their will, standing in the way of progress. But always someone found something that would break them. Someone found a greater weapon or a greater strength and they went their way. Their names and works were dust and they were forgotten and the civilization that they sought to mold to their own selfish ends went on as if they had never been.”

"But I don't see…" began Gary, and then suddenly he did — as clearly as light. He smote his knee and yelled his enthusiasm.

"Of course," he cried. "We have a weapon. A weapon that could wipe them out. The fifth-dimensional energy!”

"Certainly you have," said the old man.

"That would be barbarous," protested Caroline.

"Barbarous!" shouted Gary. "Isn't it barbarous to want to see the universe destroyed so the Hellhounds can go back to the beginning and take it over, control it, dominate it, take over galaxy after galaxy as a new universe is born? Shape it to their needs and desires. Hold in thrall every bit of life that develops on every cooling planet. Become the masters of the universe.”

"We must hurry, then," said Caroline. "We must get back. Minutes count. We still may be able to save the Engineers and the universe, wipe out the Hellhounds.”

She rose impatiently to her feet.

The old man protested. "You would go so soon?" he asked. "You would not stay and eat with me? Or tell me more about this place at the edge of the universe? Or let me tell you strange things that I know you would be glad to hear?”

Gary hesitated. "Maybe we could stay a while," he suggested.

"No," said Caroline. "We must go.”

"Listen," said Gary to the old man, "why don't you come along with us? We'd be glad to have you. We could use you in the fight. There are things that you could tell us that would help.”

The old man shook his head. "I cannot go," he said. "For, you see, you are right. I may be only a shadow. A very substantial shadow, perhaps, but still just a shadow of probability. You can come to me, but I can't go back with you. If I left this planet I might puff into nothingness, revert to the non-existence of the thing that never was.”

He hesitated. "But there's something," he said, "that makes me suspect I am not a shadow… that this is actuality, that the Earth will follow the course history tells me it has followed.”

"What is that?" asked Gary.

"It is a thing," the old man said, "that I cannot tell you.”

"Perhaps we can come back and see you again," said Caroline. "After all this trouble is over.”

"No, my child," he said. "You will never come, for ours are lives that never should have met. You represent the beginning and I represent the end.

And I am proud that the Earth's last man could have been of service to one of the beginners.”

They fastened down their helmets and walked toward the door.

"I will walk with you to your ship," said the old man. "I do not walk a great deal now, for the cold and the thin air bother me. I must be getting old.”

Their feet whispered through the sand and the wind keened above the desert, a shrill-voiced wind that played an eternal overture for the stage of desolation old Earth had become.

"I live with ghosts," said the old man as they walked toward the ship.

"Ghosts of men and events and great ideals that built a mighty race.

"Probably you wonder that I resemble a man so much. Perhaps you thought that men, in time to come, would evolve into specialized monstrosities — great, massive brains that had lost the power of locomotion, or bundles of emotional reactions, unstable as the very wind, or foolish philosophers, or, worse yet, drab realists. But we became none of these things. We kept our balance. We kept our feet on the ground when dreams filled our heads.”

They reached the ship and stood before the opened outer valve.

The old man waved a hand toward the mighty metal building.

"The proudest city Man ever built," he said. "A city whose fame spread to the far stars, to distant galaxies. A city that travelers told about in bated whispers. A place to which came the commerce of many solar systems, ships from across far inter-galactic space. But now it is crumbling into dust and ruin. Soon the desert will claim it and the wind will sing a death dirge for it and little, furry animals will burrow in its bones.”

He turned to them and Gary saw a half-mystic light shining in his eyes.

"Thus it is with cities," he said, "but Man is different. Man marches on and on. He outgrows cities and builds others. He outgrows planets. He is creating a heritage, a mighty heritage that in time will make him the master of the universe.

"But there will be interludes of defeat. Times when it seems that all is lost — that Man will slip again to the primal savagery and ignorance. Times when the way seems too hard and the price too great to pay. But always there will be bugles in the sky and a challenge on the horizon and the bright beckoning of ideals far away. And Man will go ahead, to greater triumphs, always pushing back the frontiers, always moving up and outward.”

The old man turned around and headed back toward the doorway in the building. He went without a word of farewell and his sandaled feet left a tiny, ragged trail across the shifting sand.