Produced by Greg Weeks, Mary Meehan and the Online
Distributed Proofreading Team at http://www.pgdp.net









ORIDIN'S FORMULA

By R. R. WINTERBOTHAM

The formula was a simple equation, but
Caddo had to have it--for knowing its
answer meant he would rule the universe.

[Transcriber's Note: This etext was produced from
Planet Stories March 1943.
Extensive research did not uncover any evidence that
the U.S. copyright on this publication was renewed.]


Oridin the Recluse listened to the threat wirelessed from the spaceship
that was hoving to in a landing orbit about the planetoid Azair.

"I've a bead on your atmosphere plant," said the snarling voice. "One
false move and I'll blast it to star dust."

Oridin shrugged as he heard the words. One more fool had come to Azair
looking for the secret that the Recluse of the Asteroids was supposed
to possess.

"Your threats are unnecessary, stranger," Oridin replied in the
microphone of his radio. "Everyone is welcome here as long as he
behaves. I have ways of dealing with those who don't."

"I'm warning you," came the voice again, "that I will stand for no
foolishness. I'll kill you if you try to resist."

Oridin smiled. "Land, stranger, you need not fear me."

The hermit arose and went to the galley of the warm little house that
seemed to grow from the solid rocks of the tiny planet. He pressed a
button, waited a second and then opened a small compartment. In the box
was a steaming pot of coffee, freshly made by Oridin's automatic cook.

Outside the transparent shelter, the air grew blue from the reflection
of landing rockets. Oridin glanced to the leveled surface on which the
ship was coming to rest. He saw a turret training on the little house.
Oridin was not afraid; the visitor probably would be interesting. Even
a recluse can grow lonesome on a minor planet.

A figure emerged from the spaceship. He wore an oxygen helmet, although
Oridin plentifully supplied the planetoid with artificial atmosphere
from a small plant at the north pole. The stranger did not believe that
Oridin would not resist. Again Oridin smiled. Deep in the rocks of
Azair were guns that could have blasted the visitor a thousand times,
had Oridin wished. But there was nothing clever about blowing a foe to
pieces. The foe too often was killed before he sensed defeat. Oridin
enjoyed an equal battle, or even one against odds.

[Illustration: _"Open up," Caddo snarled, "or I'll blow my way in!"_]

"Open up! Open up, I tell you, or I'll burn my way in!" demanded the
visitor.

"He's certainly not deceiving me as to his intentions," Oridin decided.

The recluse pushed a button on the wall, and a giant gate swung outward
admitting the stranger.

The fellow was as tall and as muscular as Oridin himself, but the space
suit and the gaping blaster he held in his hand made the visitor seem
much more formidable. Oridin himself was dressed in bell-bottomed
slacks and a loosely fitting, slipover coat. His beard softened his
countenance and made him seem quite gentle, except for a certain
glitter in his eyes that seemed to warn that Oridin loved a contest.
And this would seem to be a deadly contest.

Oridin bowed.

"You are welcome, stranger," he said. "Take off your helmet, for the
air is pure. Put aside your gun, for I am unarmed and I do not intend
to harm you."

The stranger hesitated, uncertainly.

"No tricks, Oridin!" he warned.

"Tricks?" Oridin laughed tauntingly. "You are not very confident for a
man of your caliber. I've heard of you often, Caddo Velexis. They say
you have conquered whole nations single-handed, and yet you are afraid
of an unarmed hermit."

"I'm not afraid of you," Caddo said in a tone that hinted he was.

Caddo removed his helmet and holstered his blaster, but Oridin noted
that the terrestrial giant did not move the firing button to safety.

"Will you have some coffee?" Oridin asked. "It will refresh you after
your long trip, and you must have had a long trip, for we are in a very
sparsely filled part of the sky."

Oridin lifted the pot and poured the brown steaming liquid into a
thick, metal mug.

Caddo waved it aside.

"I have no time!"

"Do not be alarmed," Oridin said. "The patrol will not be near Azair
for three days."

Oridin sat down. His fingers felt under the arm of the chair where a
series of buttons controlled other mechanisms in the room. Caddo had
relaxed his watchfulness.

"In three days I'll be well toward the other side of the solar system,"
Caddo said.

Oridin lifted his eyebrows.

"Toward the earth? You have undertaken something this time!"

"Yes!" Caddo said. "It's the Earth I am after! I have all I want of the
outlying planets and planetoids. You can capture a hundred of them and
be no better off than you were at first. But if you capture the Earth,
you can rule the universe."

Oridin touched one of the buttons. A tiny pinhole in the wall of the
room seemed to blink. There was a blinding flash and the smell of
burned leather permeated the place.

       *       *       *       *       *

Caddo gave a cry of alarm and sprang back, knocking over his chair. He
was on his feet holding his blaster in his hand in a second. Across the
top of his helmet was a scorched streak.

"You tried to kill me!" Caddo screamed. "You dirty swine."

Oridin's lips parted in a smile as he looked without fear into the
mouth of the trembling weapon.

"Don't underestimate yourself, Caddo," he said. "The hot beam was only
a warning--something to let you know that I could kill you anytime
I wished. Even now, before you could squeeze the trigger on the
weapon, I could cause certain things to happen--no, no! You are safe,
Caddo--I could cause you to die if I wish, but you are interesting, a
dangerous man. It would be a better accomplishment for me to give you a
punishment you deserve."

The fear that shone in Caddo's eyes faded away. For a moment he watched
Oridin. Then he laughed.

"So it's that kind of a game, is it? I can play it too! Your threats do
not frighten me. Nor am I afraid of your hot beam. Look!"

Caddo thrust his arm forward into the path of the beam. There was a
puff of smoke as the tremendous heat vaporized particles of dust on the
leather sleeves. Then nothing happened.

"I have a neutralizing force, powered with a small battery in my
clothing," Caddo said. "Foolishly, I did not have it turned on a moment
ago. But you can't hurt me now."

Oridin shrugged. "I am still not afraid of you Caddo. If you had come
here to loot, you would have killed me long ago. But what you want is
something you cannot gain by killing me. What is it?"

"You are going to give me the secret that will make me the master of
the earth, and the master of the universe," Caddo announced.

Oridin poured himself a mug of coffee.

"I knew you did not want gold, although Azair is filthy with the
stuff," he said. "But what secret have I that is so powerful?"

"The _Discovery_!" Caddo said.

"I have many." Oridin nodded toward the wall, and the pinhole of light
blinked out.

"I want the secret of the universe!" Caddo spoke tensely.

"Come! Don't be so melodramatic," Oridin chided. "The universe is full
of secrets."

"You're stalling. You know what I mean!"

"I think I do," Oridin agreed. "My erratic experiments have revealed a
certain mathematical function, _J_, which theoretically opens the door
to action without probability. Is that what you want, Caddo? The value
of _J_?"

"The mathematical bombsight!" Caddo said. "It removes probability and
makes certainty of everything. With my calculations based on certainty,
I'll be fate itself! I can conquer the world, chain the universe and
govern creation."

Oridin laughed quietly.

"Alexander, Caesar, Napoleon, Genghis Khan and Hitler spoke those words
and they were willing to bargain with the devil himself to make them
come true," he said. "I suppose I am the devil, for I know the answer
and I can tell you the answer--for a price."

"You'll give it to me for nothing!" Caddo patted the blister, now in
the holster at his side.

"Is that your only offer?" Oridin asked, still wearing an amused
half-smile.

"It is!"

Oridin rose and moved toward a safe under two clocks on the wall across
the room. One of these clocks gave the terrestrial days, hours and
minutes according to the General Meridian time. The other registered
the four-hour rotation of Azair.

"Wait!" Caddo halted Oridin. "No tricks. Give me the combination and
I'll open the safe!"

Oridin turned to the space pirate.

"The safe is unlocked. The formula is inside."

Caddo's eyes betrayed his suspicion. The most valuable secret in
the world was in an unlocked safe! Warily Caddo stepped forward. He
hesitated, wondering if even his neutralizing force was enough to
protect him.

"There's no danger. Go ahead. Help yourself," Oridin urged.

Caddo was desperate. He touched the handle of the door. It was
unlocked. He flung it open. Inside the safe was a single sheet of white
paper.

Caddo seized it eagerly. His eyes widened in amazement as he read:

"The certainty of success in any course of operations, expressed in
mathematical terms, represents the sum of all factors, beginning at the
starting point, which must be described as _real zero_, and ending with
the objective, also reduced to a real numerical value. The constant of
certainty, _J_, can be the determining factor which leads an operation
from the beginning to the objective."

Caddo read the paper and reread it again and again.

"Is this all of it?" he asked, turning to Oridin.

"Every bit," Oridin replied. "The formula is simple, like the one to
determine the sum of an arithmetical progression--the first number of
the progression plus the last number, multiplied by the number of terms
in the progression and divided by two. In your case the progression
lies between what you have and what you want. The certainty of getting
it is the sum of all the factors."

       *       *       *       *       *

Caddo sat down in a chair at the desk. He seemed to forget his
suspicions of Oridin, who had placed a stack of paper beside him.
Caddo was engrossed in the formula and Caddo, as a mathematician, knew
that everything in the world could be expressed in figures. What would
Napoleon, or Hitler, have given for this formula!

"The beginning is _real zero_!" Caddo spoke aloud.

"Which is different from a mathematical zero," Oridin said. "I might
say that zero, like absolute vacuum, never occurs. Even if we have two
apples and eat two of them the atoms of the apples continue to exist.
In the formula you have a small fraction instead of zero. It serves the
same purpose. If you multiply a number X by zero, the answer is zero.
Multiply a fraction approaching zero, .000,000,001 by another number
and that number approaches zero too. If that number is a fraction it
will be even closer to zero than our _real zero_. In fact, we are
dealing with trans-zero numbers, just like the transfinite numbers
discovered by Georg Cantor."

"Yes, yes!" Caddo said eagerly. He picked up a pencil. He scribbled
furiously. His objective was all of the power in the world expressed in
ergs; all of the gold in the world, expressed in dollars; all of the
land, expressed in acres; the people, in individuals.

Oridin moved softly behind him. A multiple-calculator made its
appearance in the room. Paper flew from under Caddo's pencil. Sweat
poured from his space-browned face.

The two clocks on the wall recorded the turning of the earth and the
planetoid Azair.

Caddo forgot about Oridin. He forgot about everything except the
figures that revolved in his brain.

Oridin moved out into the warm artificial atmosphere of his planetoid.
He was a recluse again. He was alone. A momentary contact with the
greed, and avarice of the human race had been wiped away.

Far out in space was a glow of rockets. A ship was going to land. It
had seemed only a short time since Caddo had landed. But that was three
terrestrial days ago. This was the patrol.

"I've a prisoner for you," Oridin informed the captain. "It's Caddo."

"Caddo! He's the No. 1 universal enemy. Man, you'll grow rich with the
rewards offered on nine planets for his capture."

"You can have the reward," Oridin said. "Take him away. He's a
nuisance."

They found Caddo in the lounge of Oridin's house chewing on a book
of logarithms. His mind was gone. He could only babble figures. His
fingers twitched with cramps from writing with a pencil and punching
the keys of the calculating machine. Every spark of vitality had been
taken from his body. The batteries of his force armor had burned out.

"What's the matter with him?" the captain asked.

"He wanted too much," Oridin replied. "I gave him a simple little
formula for success, but the formula ceases to be simple as the
definition for success grows more demanding. Had he sought perfection,
Caddo would have seen that even this was unrecognizable, although the
certainty was only halfway to infinity--"

"Sorry, Mr. Oridin, but I'm not a mathematician," the captain said.

"There's nothing difficult in the formula. It proves that certainty
is unrecognizable. You'll have to admit that a goal, to be reached
has to follow a path and that path is determined by two points. The
beginning is one and the second one makes the ultimate objective
certain. Therefore the second point is certainty. But certainty is
unrecognizable--"

Oridin brought forth his formula and allowed the captain to read it.
The patrol officer blinked his eyes and scratched his head. Oridin
wrote his formula out:

J = (a + 1) times infinity/2

"_J_ is certainty, _a_ our starting point and 1 is unity, or
perfection," Oridin explained. "Our starting point is close to zero,
but not zero. But for convenience we'll say that it's a fraction so
close that we can call it zero. Then certainty, _J_, is one-half of
infinity, which you'll have to agree does not approach infinity and may
be well within the realm of human comprehension, although we will not
recognize perfection because we do not know what number is halfway to
infinity. Caddo overlooked the fact that he went further and further
into the transinfinite with each number he added to his equation, for
there are an infinity of numbers between any two whole numbers and any
two fractions and their sum is always infinity."

The patrol captain already was muttering to himself and Oridin hurried
him out of the house and into the patrol ship with his prisoner.

After the space craft had gone, Oridin returned to his living quarters
and replaced his formula in the unlocked safe. He cleaned the litter
made by Caddo and sat down. Once again, Oridin was a recluse and he
would remain so until someone else had a dream of conquering the
universe.