"Obviously I have made an error."
* * * * *
Doctor Hanson again shrugged, wondering what the man was getting
at. Electrical engineers confronted with a tough problem in vector
analysis consulted other electrical engineers; they did not bring their
unruly vectors to a psychiatrist or physician and hope to have them
solved. They came to medicine and psychiatry when they began trying
to integrate and plot the rhythmic sway of their secretary's hips,
or began to see the outline of a woman's lips in the catenary of a
suspension bridge.
"Obviously," nodded Hanson.
"So here it is again, Doctor. I've been back and forth across my
equations for the past eleven months and always come back to the same
errata."
"But what can I do?"
"Someone must check my equations--someone who is viewing them as a
competent, but unbiased, observer."
"An excellent idea."
Maculay spread helpless hands wide. "I sound like an egomaniac," he
said, "but there is no other man on earth who can follow my mathematics
but I."
"Not even the thirteen fellows who understand Einstein?"
Maculay snorted. "Understood," he said emphasizing the last syllable.
"Einstein was difficult when first made public; nowadays there are
plenty of men who know more about Einstein's theories than the man
himself. In my own case it is similar. No other man has had a chance
to study my theories; I have a few adherents who try to follow them,
but they have not the full time to put to the job and so they are far
behind. Besides, I'd trust none of them."
"I see."
"Ergo, Doc, what I say is this: You are to hypnotize me. You are to
give me a post-hypnotic suggestion that I am to forget the error in
my calculations, that I am to recheck them carefully and completely,
without knowing that some factor in them is in error. Then and only
then can I locate it; as soon as I locate this error, I am to remember
everything."
"Supposing your mathematics is not in error but is entirely
correct--suppose no error truly exists?"
"There is that possibility; but if the paradox is true, I will have at
least been forced to forget that I once believed an error existed. But
I must check this math as a competent and unbiassed observer."
"That can be done."
"Good; now let's get going and let's have no more nonsense about my
glands."
"This I can do; I will help you."
Maculay relaxed while the doctor produced his hypnoscope and set it up
on the table. With Maculay's cooperation, he was in the hypnotic trance
in a matter of seconds.
* * * * *
Doctor Hanson looked at the man. This was probably the first time that
the entire man had relaxed, mind and body, in years. But Hanson did not
see the point: Maculay may have run into a mathematical paradox, but
it was not of honest mathematics. Figures do not lie, but liars can
figure; it is more than possible that a brain will introduce an error
in order that the facts of the case be unrecognized. Hanson nodded
quietly. Man was mind and glands and body and appetite, bones, hide,
and ulcers. If a sick mind can produce a sickness of the body, the
reverse is true. Cliff's error was not in his mathematics; it was in
his life.
Of all the things Maculay needed, more work along the same line with
no relaxation was not among the list. What Maculay needed--or would
eventually get in a sanatorium--was a long period of relaxation. Fun
and games; a bit of competition; a hangover, and the sheer physical
delight of wrapping an arm about the slender waist of a female and
swaying to and fro to the rhythmic beat of tomtoms and the howl of a
well beaten clarinet.
At seventy, Jay Hanson had learned the impatience of youth. Maculay had
a lot of time to finish his equations. Scissor a year of Maculay's life
and he could then finish this; let him go on as he was and he would
burn himself out at a mere fifty.
He looked at Maculay seriously. "You have been working too hard," he
said.
The reply came instantly, like the echo of an automaton.
Hanson nodded to himself. It was obvious; when the burning drive of
that demanding brain was stilled, the subconscious recognized the fact
that Maculay was working too hard.
"Maculay's Equations are in error," said the doctor.
Cliff Maculay stirred, shook his head, and began to disagree violently.
Then he relaxed, since he had come there to solve an error; but he had
become tense again.
Hanson shook his head unhappily; this was going to take time and
effort. He must take this conversion slowly, since it was apparent that
the slightest touch upon dangerous ground would trigger the big brain
into reaction and perhaps undo in the space of a second the work of
several hours.
Gradually, prying and working, Hanson began to elicit information from
Maculay. Bits of character traits, an impulse suppressed, an attitude
formed in youth, an impediment created to shut out the demands of
normal living, desires for this and wants for that. Hanson looked at
them clinically, then either reversed them or let them stand, depending
upon their possible affect. Each phase took time; it is not simple to
take a man who has never held a billiard cue and make him believe that
excellence at the pool table is an evidence of a sharp eye and fine
coordination instead of the result of a misspent youth. And Cliff's
attitude towards women was troublesome. His mother, the youthful
reading of too much of King Arthur, or Lord knew what, had given
Maculay the odd idea that a woman was a sort of goddess, not to be
touched by the hand of clod-like man. To reverse this attitude towards
a more practical attitude was difficult, since the reversion must not
be complete. Hanson did not want Cliff to reverse completely, to the
other extreme, where the man would go out and start treating women like
galley slaves, punching bags, or chattels--which, in fact, was about
the way Maculay had expected to be treated.
Hanson took a brief rest from the hard job, by recalling and telling
Maculay every risque story he could remember.
Then he was at it again, prying and probing, and reversing Maculay's
attitude on gambling, liquor, tobacco, and politics. He made a slight
revision on Cliff's idea of proper dress; the physicist had a horror
of appearing dirty, even when engaged in the dirtiest of jobs. With
some effort the doctor convinced Maculay that a mechanic emerging
from beneath a car with a face full of grime was not automatically an
undesirable character, either to men or women. The crux of the matter
was whether he liked that condition of dirt or not.
* * * * *
With a number of factors accomplished, Hanson took a deep breath, felt
his pulse, counted his heartbeat and respiration, and fished for a pill
from his desk and swallowed it quickly before he went on. The hardest
part was to come.
Cliff took himself seriously, far too seriously. With delicate verbal
barbs, Hanson began to poke fun at some of the imbecilities of pedantic
reasoning. Maculay offered resistance at first, but Hanson worked him
over the ground carefully, pointing out that Maculay, the only man in
the world capable of understanding the variable-matrix wave mechanics,
was in no position to snort at his fellow man. After all, Gertrude
Stein had once gained great popularity on the theory that no one could
understand her and therefore she must be sheer genius. Eventually he
had Cliff laughing over an old limerick:
_The wonderful family Stein,
There's Gert, and there's Ep, and there's Ein.
Gert's poems are bunk;
Ep's statues are junk,
And nobody understands Ein._
Hanson worked over Maculay's Equations with a bit of acid humor. In
third person, he had Maculay chuckling over the physicist who worked
for years on some mathematics that did not come out even. Gradually,
the doctor convinced his patient that he was not Clifford Maculay, the
renowned abstract mathematician, but Maculay's nephew--the black sheep
of the family--who viewed the brainy members with as much distaste as
they viewed him. Young Cliff had often been mistaken for his brilliant
uncle, and found this funny, since he felt himself smarter than his
namesake; he, young Cliff, had fun whereas his uncle had only hard work
to show for his life. Actually, any pondering of his uncle's work made
young Cliff sick to his stomach, and he was glad to ignore such things;
the whole theory was so much stupidity.
And for one year, Clifford Maculay, physicist, would be as different
from his former self as was possible without breaking the law to bits.
"At the end of this year, you will return to your apartment in
Washington, take a good night's sleep, and awaken as Doctor Clifford
Maculay. Then, and only then will you remember; and you will realize
furthermore that this job of relaxation has been forced upon you
for your own good. You will then be able to solve the error in your
calculations."
Hanson paused for a moment, pondering as to the advisability of
giving the hypnotized physicist a key-word to bring him out of the
post-hypnotic suggestion. But Doctor Hanson was seventy years old; he
knew all too well that a year from this moment he might be dead and
gone. He viewed it calmly, but not disinterestedly, and decided against
a key-word; it only introduced a conflicting factor.
Let the man awaken of his own accord.
Then he awakened Maculay, who sat back in his chair with a chuckle,
reached for a cigarette from the box on Hanson's desk, and puffed at it
with relish.
"How do you feel?" asked the doctor.
"Like a million," said Maculay.
"Good. Come back in one year. I'll have my girl make an appointment.
For now, we're all finished."
* * * * *
Doctor Hanson stood and watched Maculay head for the door; the
physicist's step had a certain bounce, curtailed by the fact that the
unused muscles of his body were not used to the catlike stride of the
completely balanced, healthy man. A few days of that sort of bounce and
Maculay would have it. The door closed exuberantly and Cliff was on his
way to a one-year binge.
He paused once outside of the doctor's office. Ava Longacre was bent
over some notes, and Cliff viewed her contemplatively. She stood up and
smiled at him. It was a sort of professional smile, the kind she gave
all of the doctor's visitors; it made no difference to Ava whether the
visitor were seventy or seventeen. She gave each of them the same dry
smile.
Cliff crossed the office in a quick stride and put both hands on her
shoulders. He drew her forward, felt her instant stiffening relax; with
a cheerful upsurge of spirit he put an arm around her, tilted her face
upward with his free hand and kissed her. He felt her yield to him,
press against him softly, then respond.
Cliff knew he could have her, but in that moment he also knew that he
really did not want her. Ava was a bit over thirty; she had a quiet,
mature quality--good-looking, but far past the radiant flush of youth.
A hard-working woman, efficient, intelligent, Hanson's nurse, medical
aide, and receptionist, did not offer the fun and frivolity that Cliff
Maculay sought.
He stepped back and smiled down at her. "Nice," he said with a chuckle.
Then he kissed her again, lightly on the mouth, turned, and left the
office.
Her cheeks burning, Ava Longacre stamped into Hanson's office.
"What goes on?" she demanded. "What on earth did you do to that man?"
"Why?"
"He came in here like the proverbial absent-minded professor, his eyes
blank and sort of muttering to himself about radiation mechanics or the
like. He didn't even look at me."
"Then?"
"On his way out he sort of grabbed me and kissed me."
Hanson nodded appreciatively. "You liked it?" he chuckled.
Ava sat down, landing in the chair with a thud. "When a man puts a hand
on me and my knees turn to jelly," she said quietly, "I oscillate madly
between hating his guts and wanting him to try it again. That sort of
thing would play hell with a girl's morals."
"Shucks," chuckled Hanson. "I've just violated all of the rules of
medicine. I've just treated a man against his will--and turned an
introvert inside out."
"You sure did," nodded Ava.
"He'll be back again in a year--and normal, then."
"But how do you turn an introvert inside out?"
"Reverse his sense of values."
"But--"
"His memory pattern? That's difficult. To make him more or less stable
for that year, I sort of tampered with his memory on a temporary basis,
also. He thinks he is all sorts of things that he has never been--but
has probably wanted to be from time to time."
"Is that why he kissed me?"
"Partly. But you're the woman he should have when normal, not as he is
now. That's--"
"So you gave him a false memory, complete with a lot of details to
explain just about every possible question, hey?"
"Yep."
"And just how was this background furnished?" she demanded.
"Remember it is only temporary and need not be complete. Just
sufficient to justify its being."
"Don't quibble."
Hanson laughed. "Well, when a man of seventy starts to furnish a bit
of background for a youth of thirty-odd, what better than a few true
experiences from the old man's past."
Ava Longacre snorted. "I'll bet you were a hellion in your youth," she
snapped. "And in your old age you're a nasty old lecher."
Hanson squinted at her. "I wish I were forty again," he leered. "But
worry not, m'lady. Maybe the basic idea was mine, but Maculay kissed
you on his own account. And I commend his taste."
Ava uttered a single, explosive "Oh!" and stalked out angrily, slamming
the door behind her. She leaned against the hardwood panels and
listened to the roar of Hanson's laughter die in a slow gurgle. She
pegged it properly as part hysteria; the hours of hard mental effort
spent on Maculay would have taken a lot of pep out of the Old Boy,
and he would then clutch at anything remotely amusing and make an
uproariously funny incident out of it. But this was not funny.
She remembered Maculay's hand on her, and her body went supple against
the door. Then by sheer mental effort she snapped her head erect and
walked from the door, determined to forget it.
Ava did not recognize the fact that for hours, days, or months--and
perhaps forever--she might be telling herself that it was a good thing
to forget about.
2
The _Island Princess_ took off on schedule, arrowed into the blackness
of space, and set her nose-sight on Venus. She was forty hours a-space
when it happened. And the _Island Princess_ was one of the four
spacecraft close enough to the thing to have its presence recorded in
the celestial globe.
It came with a roar of sound from the radio, which eliminated all
communications instantly, and continued on a diminishing power for an
hour until it fell below the cosmic noise level. It appeared in the
celestial globe as an ebon shaft; measurements made it a half mile
in diameter but extending from beyond the range of the globe in both
directions. It was as straight as it could be. On the other ships, the
same facts were noted.
Upon the several planets of the solar system, cosmic-ray counters
went crazy. Showers of unprecedented violence bathed the solar system
in a raging torrent of high-energy particles. The showers continued,
diminishing in intensity as time went on; the slower particles arriving
last, of course.
But the one thing that caused consternation throughout the entire solar
system was a sickening _shift_. Spacecraft and planet gave a tiny,
queasy slip, sort of like a heavy man who has just trod upon a grape.
Things move according to their mass and according to their distance
from the black shaft of energy. On planets, it was just enough to
cause fear; the most infinitesimal waver in the constant course of the
planets awakens racial fear. In spacecraft, the shift was more violent,
but here people were prepared for a bit of wobble.
[Illustration: On planets, the shift was just enough to cause fear;
auroras flamed for an hour....]
The auroras flamed bright for an hour; as soon as the shift had
shaken the wits out of every human in the solar system, the big
observatories set their big glasses on the fixed stars and consulted
quadrant-protractors to ascertain what the shift had done. On
photographic plates of operating telescopes, the shift was barely
noticeable upon the images of brighter stars. The dimmer ones had
danced aside and back too swiftly for the emulsion to register. But it
had been a swift jiggle up and back; now things were as they had been
once more save for the big mystery that caused the radio lanes to buzz,
and made men ask their neighbors what it could have been.
* * * * *
Captain Bardell of the _Island Princess_ went to the salon after the
radio had told him what little could be told about the incident. He
told the passengers what he knew as a matter of interest, and because
they had been as close to the phenomenon as any other human being.
Cliff Maculay, bent back across the bar with his elbows hooked over the
edge and a glass in his right hand, chuckled amusedly.
"But this isn't funny," complained a comely woman in a strapless gown
at his left.
"Dorothy, darling, you're wrong," he laughed.
"I suppose you know what it is?" came the cynical reply from the
red-head on Cliff's right.
"Helen, that 'thing' was a manifestation of the application of
variable-matrix wave mechanics to intrinsic space by the real and/or
unreal roots of negative space."
"That's utter gibberish."
Maculay laughed. "Verily," he chuckled. "But my revered Uncle Clifford
will--about now--be telling the world the same thing in about the same
incomprehensible collection of dictionary fodder."
Captain Bardell heard, and came to stand before Maculay. "Clifford?" he
said uncertainly. "Clifford Maculay?"
"Right name but the wrong character," said Maculay, sipping from his
glass. "Doctor Clifford is the genius in the family; Cliff, the nephew,
has only genius for getting into mischief without getting into trouble
about it. To each his own," he chanted, lifting his glass in a toast.
Bardell was openly disappointed. "I'd hoped you might give us an idea
of what was going on."
Maculay turned, rapped the bar with the heel of his glass to get
attention, and then turned back to the captain. "I can," he said
cheerfully. "But do you have the faintest idea of why nephew was
relegated to the Outer Darkness?"
Everybody, listening to Cliff, shook their collective heads.
Maculay laughed. "They had me studying under him for years. Doctor
Maculay is a slave driver and a martinet. Cigarettes, liquor, and wild
women are annoying things that detract from the single-purposedness of
life. Doctor Maculay is the kind of duck who would rather work overtime
than make frolic with a dame--and he expects everybody who works with
him to do the same. He also pays them accordingly, since a small room,
a sterile diet, and a minimum of clothing are all that is necessary for
any man dedicated to science."
"So?" asked Bardell, a bit angry at this man for belittling one of the
solar system's greatest minds.
"So Cliff, the ne'er-do-well, used to take a few of Uncle Clifford's
well-flanged ideas, add a character, stir well with a villain and a
dame, and emerge regularly with a bit of science fiction. I was Ed
Lomax, one of Larimore's cover names until John used the right name
instead of the pseudonym, and people started to write fan letters to
Clifford Maculay, MM, PhD, et al. Shortly afterwards I was out of a
job."
"Then you do understand some of this?"
Maculay grinned and nodded.
"But Doctor Maculay will be able to figure this thing out?"
Cliff nodded again, and smiled. "Good thing, too," he chuckled. "He
is the only man in the system that can handle it without going off
half-cocked. Maculay may be a stuffed shirt but he is no imbecile.
Tinkering with inverted space--or pouring a quart of nitric acid over
a half-gallon of glycerine--might be deadly unless you understand
what you're doing. Maculay is super-cautious about anything that
he does not understand completely. I cannot say the same for his
underlings, who casually point out that mankind had been using
electricity for years and years before they knew anything about it.
But," he said with a laugh, "enough of the manifestation of the unreal
roots of variable-matrix wave mechanics. Maculay's wastrel--but
interesting--nephew is about to enjoy life."
Cliff winked at Dorothy, patted Helen on a bare shoulder, and then led
Alice towards the dance floor.
"Doesn't this mean anything to you?" she asked him.
"Uh-huh," he said with a smile. "At about three cents per word; that
black shaft of energy is an idea coming to life."
"What kind of idea?"
"Um--let's see. That black shaft of energy was really a spacecraft,
passing through the solar system at a velocity higher than the speed of
light. Some extra-solar race, colonizing the galaxy. What we detected
was the space-wake of such a craft. You have no idea of the energy
kicked up when a body passes through space at a velocity higher than
that of light. Then Our Hero, bullied by his superiors, shows that he
has measured the energy-curve and solved the secret of interstellar
travel."
A slight frown came to Maculay's face. "The trouble is that this
super-galactic race has learned how to create negative space before
the ship and re-create positive space behind it to keep from having
the--the--" A bead of sweat came upon Maculay's face and he became
nervous. He looked around, almost wildly, before continuing,
"the--entire universe," he concluded lamely. "Negative space is
self-propagating, you know." Maculay finished this last with a wince of
pain.
Then Maculay straightened up with a laugh. "That's lousy," he said.
"Larimore wouldn't buy it. We'll have him go out and meet some
four-armed monsters who think that human meat is superb. That's crummy
too, but it's an idea. C'mon, m'lady, let's dance!"
* * * * *
The telephone rang on Doctor Hanson's desk. It was Ava, from the outer
office. "Man by the name of Redmond to see you, doctor," she reported.
"Has he an appointment?"
"No, that's why I'm calling. He claims it is a matter of impor--No,
Mister Redmond, you cannot go--"
The doctor's door opened abruptly and the man called Redmond strode in.
"Where is Maculay?" he demanded sharply.
Doctor Hanson looked up at Redmond calmly. With insulting deliberation,
Hanson eyed the man, while Redmond began to fume. Redmond was tall and
thin, a bit too tall and a bit too thin in the doctor's estimation.
He was thirty to Maculay's thirty-eight, but did not smoothe his
impatience and ambition behind a cloak of politeness.
"Sit down, Mister Redmond. I'm interested in you."
"Where is Maculay?" came the repeated demand.
Hanson smiled slowly. "I'm interested in trying to discover just what
it is about abstract mathematicians that makes them think that they
can stamp their way through life, disregarding not only the rights of
others, but their own as well."
"Enough of this damned foolishness--"
"Shut up, you young whippersnapper!" roared the doctor in a voice that
rattled the windows. Redmond shut up. "I'll have respect from you,
Redmond. And if I don't get it, you'll leave. Understand?"
Redmond bristled.
"Relax," said Hanson. "I'm no longer able to punch your face as you
request by your actions, but I know several men who would be most happy
to help me in this matter. Now, what is it that you want?"
"I want to know where Maculay is."
"I don't know."
"Damn it, you do know."
"Redmond, I'm not a liar."
Redmond leaned forward over the doctor's desk. "Maculay came here," he
said, "and I know why. Maculay did not return from here, and I want to
know why."
Hanson leaned back in his chair. "Doctor Maculay came here and
discussed his difficulties with me," he said. "During the course of
the discussion, it became quite evident that Maculay was on the verge
of a nervous breakdown because of too much hard work and too little
relaxation. I convinced him that a long vacation would enable him to
live and be productive longer than he might enjoy if he went back and
killed himself on his job."
"So where did he go on this vacation?"
"Maculay admitted that if a single soul knew his address, they'd be
sending him problems within a week. He took off, destination unknown."
"Did he say when he would be back?"
"In one year."
"A year! My God! We can't wait!"
"Can't is an impossible word," remarked Hanson.
"But we must find him."
"You might start combing the solar system," suggested the doctor.
"Impossible. Yet--"
"Redmond, there have been many indispensable men in history who were
not so indispensable that their leaving caused affairs to stop short.
I admit that their plans often flopped, or that history took a little
longer to get itself made when their driving force died. But not a man
on record has ever been truly indispensable."
"But you don't understand," complained Redmond. "It's about that blast
of energy that shocked space."
"I guessed as much. What is--or was it?"
"We don't know; Maculay does, or can deduce its meaning."
* * * * *
Redmond started to stride up and down the office at this point, talking
half to himself and half to the world in general. Through the still
open door. Ava could hear him, and since the danger of attack had been
averted, she decided to close the door. But Hanson waved her inside
where she sat in one of the inconspicuous chairs along the far wall.
Both Ava and the doctor watched Redmond quietly.
"From what little we know of it by direct observation it came all at
once--a shaft of energy as instantaneous as birth. Where once was empty
space, this bolt of energy was created. The energies it created showed
no directional qualities, and it extends as far in either direction
from here as we care to imagine. The distant energies are still
coming in from both directions, diminishing because of the tremendous
distances, but still showing nothing directional."
"But this shaft of energy must have come from somewhere?"
"Did it?" exploded Redmond. "Did it come from somewhere--or did
it burst into being instantly from one end of the universe to the
other like the creation of a rope from nothing all along its length?
Actually, we know this: Its duration was as close to instantaneous as
anything might be. The rest of the phenomenon was merely persistence of
the energies it created."
"Those are questions that I cannot answer."
"Maculay could."
"You assume that this thing might be in Maculay's field?"
Redmond nodded. "We charted the energy-curve," he said. "Then one of
the boys integrated the curve and came up with a formula for the curve
which I saw and without any trouble at all reduced to one of Maculay's
Equations. Do you know what this means?"
"No. Of course not."
"This means that the validity of Maculay's Equations is proven
fact. Just as Maxwell's Equations were proved by the existence of
electromagnetic waves in nature, so are Maculay's Equations proved by
the existence of this manifestation of the real and unreal roots of
space, occurring in nature." Redmond resumed pacing again. "What is
maddening," he said, "is the fact that we do not know where it came
from."