by Jeff Sutton
What was a paradox? Stripped to its essential, it was an unanswerable question; unanswerable merely because it lay beyond the realm of human comprehension. Multidimensional space was wrapped in such paradoxes—was paradoxical itself, he reflected. Yet he was utterly convinced that such space existed.
Yet space, layered or intermingled with space, still added up to nothing. As such, the concept possessed no meaning. Space only held meaning as it was measured by the objects within it; ergo, the existence of multidimensional space implied the existence of objects beyond the realm of the known dimensions. Other worlds. He breathed the words wonderingly. Man stood in a black cave, through the narrow entrance of which he could see but a single star. Yet galaxies littered the skies. His thoughts were musing.
Gordon Maxon believed in other dimensions, also, but he saw the key to them as psychical rather than mathematical. Did it matter how man went through the door? Not really, Kane reflected. The important thing was to find the door, swing it wide.
He could understand Maxon's excitement over the possibility that John Androki was a downthrough. Maxon's other sensitives—telepaths, clairvoyants, psychokinets—inhabited the same space-time continuum as normal people. But not John Androki. Alone among the hoped-for sensitives that peopled Maxon's studies, he projected his sensory apparatus into time. Like a fisherman, he flung his net into the time stream, seining from it the events of tomorrow. Was that possible? Or was it all Gordon Maxon's imagination?
Anita met him at the door, still wearing her dressing gown. "Be ready in a jiffy." She eyed him speculatively. "You look tired."
"A trifle."
"Small wonder with the hours you keep."
"I lose track of time," he admitted. "It's an elusive world."
"Multidimensional space?"
He nodded. "It's like trying to snag mercury with a fishhook; it just won't stay hooked."
"The real world is much better." She wrinkled her nose at him. "Or didn't you know?"
"At times it seems overly grim."
"Not if you take from it what you want."
"You make it sound easy," he accused.
"No one ever said it was easy." She held his glance. "The most difficult part is in knowing what you want."
"Do you know what you want?"
She frowned. "Yes and no. I believed I did once but my wants keep changing. They ebb and flow with the possibilities."
"That's being realistic," he acknowledged.
"Is it? I don't know." She smiled brightly. "I'm learning to take a little from this world, a little from that—take the best of several worlds."
"That takes a bit of juggling."
"Yes, of course, but how else does one get what one wants? You have to juggle, make concessions. But isn't that part of the excitement?"
"I never quite thought of it in that way," he admitted.
"You can't drift through life, Bert."
"Drift?" He looked inquiringly at her.
"You have to steer the boat."
He smiled. "We steer in different ways. My rudder is mathematics."
"Toward an invisible shore," she reproved. "Now fix yourself a drink. You'll feel better."
He was sipping a Scotch-on-the-rocks when Anita reappeared from the adjoining room. Still wearing the dressing gown, her body moved sinuously under it. The sight stirred his pulse. She paused, smoke from her cigarette curling up past her face.
"Did you hear about the ten million dollars John Androki's giving LAU for a library?" she asked.
"Gordie mentioned it."
"Isn't that marvelous, Bert?"
"I suppose."
"You don't sound overly enthusiastic."
"The fellow bothers me," he confessed.
"Poof, he's an interesting man."
"He moves too fast for me."
"That's what makes him interesting, Bert." She sat beside him on the couch.
"Don't get caught by glamour," he warned.
"Why not?" she asked mockingly.
"It's an ethereal quality."
"But substance for the soul."
"In what way?" he asked quizzically.
"Glamour is a magnet, a food; it draws response."
"I can't see him as glamorous."
"Because he might be a downthrough?" She stared levelly at him, her face holding an emotion he couldn't decipher.
"That would make him twice as exciting. Imagine being able to look at a woman and knowing whether or not you were going to have an affair."
"That might excite him," he admitted, "but would it excite the woman?"
"If she knew that he knew the answer? That would be absolutely intriguing," she declared.
"Wouldn't she feel like a pawn, knowing she didn't have any control of the situation?"
"But she would have." Her eyes glinted wickedly. "He wouldn't know the answer unless she had already made the decision."
He smiled. "Suppose he didn't agree with the decision?"
"That variable largely would depend on the woman." She tossed her head smilingly.
"In other words, he's the pawn?"
"Do you expect me to answer that?" She eyed him steadily. "Men sometimes don't know what they want until someone points the way."
"Ah, this brazen age." He laughed.
"You're living in a lost world, Bert." She leaned toward him, her face turned up. He slipped his arms around her, feeling a sudden urgency. Her lips were cool. He pulled her closer, kissing her more ardently. Releasing her, he drew back.
"We'd better quit that," he warned huskily.
"Why?" Her face held a hard, glossy smile.
Kane's phone was ringing when he returned to his apartment. Throwing the door shut behind him, he flicked on a light and lifted the instrument from its cradle.
"Bert?" Maxon's voice came urgently through the earpiece. "I've been trying to reach you all evening."
"Had a date with Anita," he explained tersely. "What's up?"
"I heard a news flash a few hours ago," Maxon said. "Doctor Cantrup of Chicago was killed."
"Killed?" Kane sensed a sudden shock.
"Murdered," Maxon said.
VI
noted scientist slain in Chicago—Kane stared heavily at the black headlines in the Times before dropping his eyes to the story.
Chicago (AP)—David Cantrup, famed University of Chicago mathematician renowned for his studies of multidimensional space, last night teas shot to death by an unknown assailant as he stepped from his car in the driveway of his home. An eyewitness reported that the gunman sped from the scene in a black sedan. Police could offer no explanation. …
He finished the story and pushed the paper aside, staring blankly at the wall. David Cantrup dead! He wanted to deny it. Although he had met the mathematician only a few times, they had carried on an occasional correspondence related to their work. Cantrup, like himself, advanced the belief that space had many dimensions. It was he who had first used the Bornji transformations to project mathematics into that unknown realm.
Kane felt a deep personal loss. It was a loss, he knew, that would be felt keenly by the relatively small handful of men scattered throughout the world who were pioneering in the same field, and who in many respects were Cantrup's colleagues. Now it was up to Freyhoff of Germany, Vosin of Russia, Bernardi of Italy, Tanaki of Japan. And himself! But Cantrup had been the foremost among them. His loss would leave a big gap.
The door to his office opened and Maxon came in. Kane greeted him soberly.
"I know exactly how you feel," Maxon said. "It's a damned shame."
"Why him?" he asked bitterly. "The act was senseless."
"Not to the person who did it, Bert."
"How could a man like David Cantrup have enemies?" he asked wonderingly.
"What do we know of him?" Maxon parried gently. "We know of his work, but not the man."
"To destroy such a mind was still a senseless act."
"You feel particularly keen about it because he was i
n your field," Maxon said; "but to how many people was he great? A mere handful over the entire face of the planet."
"Is fame what determines greatness?"
"Of course not. I only made the point that not many people would feel the loss."
"He was so close to the breakthrough, Gordie."
"There are others," the psychologist consoled. He looked at Kane. "You are one."
"I'm not a David Cantrup," he denied bitterly.
"Was he, at your age?"
"Oh, I know, the pieces can be put together again." He gestured wearily toward the paper. "According to the story, there were no clues, nothing—just a man shooting him in the darkness and speeding off in a black car. It's inconceivable that such a thing could happen."
"It happens every day, Bert. What would you expect a murderer to do, carry a neon sign? Aside from that, every murder is a tragedy to someone."
"I've only seen him a few times, but somehow he always seemed like a father to me," Kane answered. "Mentally, I've lived with him for years."
"We all have our gods, Bert."
"But to be cut down at this point of his life—"
"You have to take up where he left off," Maxon interrupted firmly.
"But can I?"
"Certainly you can."
"At times it's like walking through a pitch black night, searching for a tiny glimmer of light," Kane confessed. "I know there's a key, but can I find it? Has man been endowed with the mental power to break out from the reality into which he is born? It leaves one with a quite humble feeling, Gordie."
Maxon nodded. "I feel that way at times. I catch glimmerings, enough to tantalize me; then the door is slammed in my face. But you have to keep trying."
"Oh, I'll keep trying," Kane protested, "but I can't help the self-questioning. I'm like a blind man trying to chart the universe, Gordie. I know the stars are there, but where? Now it'll be all the more lonely."
Maxon turned back at the door. "Incidentally, there's a rumor making the rounds that Rowland is going to throw a reception for Androki." Rowland was the chancellor of LAU.
"Androki." Kane spoke the name like a swear word.
"We might meet that cookie yet."
"The thought leaves me cold."
"Shake the blues and you'll feel better," Maxon advised. "You know damned well you're dying to meet him."
"Only to see what makes him tick."
"Isn't that what we all want—to see what makes Androki tick?" Before Kane could answer, Maxon went out and closed the door.
Kane remained at his desk, staring musingly through the window. David Cantrup's death was a hard blow. But Maxon was right: the full impact of the tragedy would be felt only by his immediate family, a few colleagues and students, and a scattering of scientists around the world. Freyhoff of Germany, Vosin of Russia, Bernardi of Italy, Tanaki of Japan— those men would be grieving this day.
Yet David Cantrup had left the entire world a legacy, he reflected. One day, when men flung wide the door, it would be because of David Cantrup. He had been the pioneer.
Kane remembered his own initiation into that abstract field. As a math major in his senior year at Berkley, he had attended a lecture given by Hans Wulff, a star in a firmament which had been largely unknown to him.
With a piece of chalk and a blackboard, speaking in a dry, unemotional voice, Wulff had opened to Kane's eyes vistas he'd scarcely dreamed of. This was not a world of the microcosm or macrocosm; it was discernible neither through the microscope nor telescope, nor through any of the probing waves or instruments that hectic man had flung against the waiting stars.
Wulff's world was far greater.
Kane still remembered the hush in the auditorium, broken only by the lecturer's somewhat reedy voice. The world he had uncovered that night existed around Kane on every side; it existed but was not sensed, for nature had not given man the sensory equipment with which to penetrate beyond the dimensions which formed his reality.
"What do we mean by reality and unreality?" Wulff had asked that question at the beginning of his lecture. Reality and unreality, he said, were but artificial constructs of the mind. In that regard, unreality was synonymous with the limits of sensory perception; unreality began where the mind left off.
How could limits exist within a universe which itself was limitless? Kane had wondered at the time. Men knew that limitless galaxies lay beyond the probes of the most sensitive radiotelescopes. The vistas Wulff had drawn on the blackboard were like those unseen galaxies; a more powerful telescope was needed to uncover them. Only this telescope had to be built of mathematics.
It had to be built in the minds of men.
Perhaps man could never reach Far Centauri, but he could achieve a vastly greater leap through the magic of numbers.
That's what Hans Wulff had said.
Kane drove to Anita's apartment in the early evening. Their affair, as he thought of it, perturbed him; yet he found himself drawn ever more deeply into the entanglement, for it also was that. He wasn't quite certain how it had started. One moment they had been discussing Androki; the next she was in his arms.
I should propose marriage—'the thought had come to him the first night he was with her. She expected that, certainly; yet there were times when he wondered if she really did. "I think you have to take a little from this world, a little from that"—those had been her words. At the time he had placed no great significance in them; but he since had wondered.
Did he really want to marry Anita? The question plagued him. Or was his thought of marriage a manifestation of "an old-fashioned morality that somehow he had clung to while the rest of the world raced off on a tangent? A desire for marriage, or an obligation? He fretted, torn first one way, then another.
But he couldn't deny her attraction. If anything, she was even more eager for their clandestine meetings than he. Her excitement communicated itself to him in ways he had scarcely imagined possible. She was, in fact, at times quite wanton. He winced at the admission. Still, he thought, he had to be tolerant of the past; this new age, of which he'd never quite gotten into the swing, demanded that.
"We're old fuddy-duddies," Margaret once had laughed.
"I guess we are." He had laughed with her. Yet what more could one have from life than he had had with Margaret? Nothing, he reflected. But that was because he and Margaret had known what they had; there had been no reason to chase will-o'-the-wisps.
Margaret, too, had been beautiful, but her beauty had been of a different kind. It had been an inner beauty radiating outward, disguising her rather plain features. One didn't see that Margaret was beautiful; one knew it. Anita's beauty, by contrast, was surface, yet she had a depth of mind he couldn't deny. Was it fair to judge Anita by Margaret?
You have to get with it, boy, he told himself. He had to smile, realizing that even that thought wasn't his own; Maxon had given him that advice a long while before.
Anita met him at the door with a quick smile. She kissed his cheek, then stepped back and surveyed him. "You look unhappy," she observed.
"Cantrup's death sort of threw me," he explained.
"Cantrup? Oh, the Chicago professor."
"Merely one of the world's greatest mathematicians," he answered stiffly.
"Don't expect me to feel as you do, Bert. Does the name Yves Tanguy or Chaim Soutine mean anything to you?" When he shook his head, she said, "They are as important to many artists as your Cantrup was to mathematicians."
"I'm sorry," he apologized. "I didn't mean to bite at you."
"You don't play enough, Bert."
"I'm trying." He attempted a laugh. "How would you like to run down to the beach for supper?"
"Is that what you really want?" She wrinkled her nose mischievously, but there was no mischief in her eyes; they suddenly were bright and intent.
"Well…"
"Don't try to think up an excuse," she murmured. She lifted her face, offering her lips. He kissed her, then slipped his arms around her and cru
shed her lips savagely. Her body, warm and yielding in his embrace, stirred him violently. It was the thing she always did to him, nor could he prevent his response. Margaret! Margaret! The name was a hollow ring in his mind. That was then and this was now.
She struggled free. "You're just a natural-born brute," she said severely.
He laughed. "What man wouldn't like to hear that?"
"Brutes are nice." She arched an eye, then said quickly, "I can whip up a snack here."
"Okay, you've sold me on it." Grinning, he kissed her again, rumpling her hair, then all at once felt serious. Damn it, he did want her, for now and always. To hell with his strait-laced thinking. He stepped back and said quietly, "I think we should get married."
She smiled, a hard, tight smile. "You're a doll, Bert."
^Well, I do."
"Marriage." She put a demure note into the word, studying him levelly. Her face was inscrutable. "I'm not ready for it," she finally said.
"Why not?" He felt both hurt and relieved.
"There's something more I want of life, Bert."
"More of what?"
"I'm not quite certain." She moistened her lips. "I want to be one of life's winners."
"Life's winners?" He eyed her perplexedly.
"Oh, I know, I'm saying it badly, but there's something more I want of life, something I haven't had. It's something I sense, feel, without quite knowing how to put into words." She caught his bewildered glance and rushed on. "Oh, I've hurt you. Don't think that you haven't given me a great honor, Bert, but I'm just not ready. Can't you understand that? You've been a widower for three or four years, and you're just getting ready."
"If that's the way you feel—"
"It has nothing to do with you," she cut in. "It's just me. Please try to understand."
"Well, sure."
"It's just that when I get married, I want to be absolutely certain, Bert."
"So do I," he declared.
"Are you certain now? Can you really say that?"
He asked stiffly, "What do you mean by certain?"
