"I can teach you the "decimal" system much more easily," said Soth. "Whenever they discover it on some planet they engrave the discoverer"s name among the heroes." He saw Jonnie wouldn"t buy it and sighed. "All right," he said. He got a sheet of somewhat crumpled paper. "I will write down the "undenary" numerals for you."
Jonnie said he already knew the Psychlo numerals but Soth shook his head.
"No, no," said Soth. "I doubt very much if you do. To really understand a symbol, you have to know what it came from. Now all numerals as symbols were originally either the first letter of the word that spelled them or a number of dots or lines. Or they were pictographs that then became stylized until they were only a part of the original picture or a shorthand version of it.
"Now Psychlo numerals were originally pictographs. And then as time went on, they were written in a more and more simplified form until they now are what you see as the eleven separate Psychlo numerals. They were once called "the road to happiness."
Jonnie had not known that. He saw these numbers, these symbols, every time he flew. He began to get interested.
Soth was writing the numerals as pictographs, little pictures. "Zero is an empty mouth; see the teeth? One is a claw; just one talon. Two is a being and a pick. Three is a being, a shovel, and a rock. Four is a mine cart; see the four corners? Five is what we call the "off" paw, the one with five claws. Six is what we call the "on" paw, the one with six claws. Seven is an ore chute. Eight is a pot smelter; see the smokestack and the smoke? Nine is a pile of metal ingots made like a pyramid; nine of them originally but now just the pyramid. Ten is a lightning bolt; symbol of power, now just a slash. Eleven is two paws clasped; that represents contentment.
"It"s a little moral lesson, you see. If you dig and smelt ore, it lifts you from starvation to power and contentment." He laughed. "Very few people know this. All they know is what time and haste boiled them down to." And above his pictures, he rapidly wrote the eleven Psychlo numeral symbols as they commonly appeared. They still bore the traces of the pictographs.
"I"m very glad to know that," said Jonnie. And he was amused by it. The Psychlos had been miners from the start! "I can do a little arithmetic in this system." He decided to really push it. "Where I get hung up is the Psychlo force equations." And that was no lie. They gave him headaches.
Nothing ever balanced.
Soth was looking at him very keenly. "I think you are digging for the teleportation formulas."
Jonnie shrugged. "We have a rig running. We are making rigs."
"Yes, I heard that," said Soth. "That"s where all the new breathe-gas and goo-food came from. I heard there was a planet, Fobia, n.o.body could live on." He was plainly puzzled. "Ah!" he exclaimed. "One of your scientists reevolved it in some other mathematics and you are trying to verify it against Psychlo equations." He laughed and laughed.
Jonnie gave him another bite of kerbango.
"Ah, well. Not that it will do you much good. But it"s small wonder you can"t work it out. He laughed again. "You"d have to be a native of Psychlo!"[3]
He laughed so hard he had to wipe his eyes.
"Oh, well," he said at last, "you already have teleportation so what"s the difference." He took another big piece of paper and drew a huge circle on it. Then he had second thoughts and sat back and looked at Jonnie. "If I give you this," said Soth, "what"s it worth?"
"Money?" said Jonnie.
"A separate dome, access to compound libraries, and tools to experiment with computers. And not to be cross-fired elsewhere!"
"All right," said Jonnie.
Soth made a fast list of what he had said. Then he added, "Breathe-gas and proper food for the rest of my life. I"m sorry to have to add this. But I"ve only ten years or so to go so it"s only ten years" worth. I won"t add anything else."
Jonnie signed it. He even put a paw print on it, using his fingernails. Soth looked like he had lost ten years of age.
With a flourish, Soth pulled the circle to him. Then he put another piece of paper on top of it. "Do you know anything about codes and ciphers?
Cryptography? Well anyway, here is the Psychlo alphabet." And he wrote it out. "And here are the Psychlo numerals." And he wrote them under the letters and then started the numerals over again until there was one written under each letter. "Do you see, here, that each letter has a number value?"
Jonnie said he did. Soth laid aside the top sheet and again addressed the big circle.
"This," said Soth impressively, indicating the circle, "is the perimeter of the imperial Palace of Psychlo." He made a series of small slashes around the circle. "These are the eleven gates. A lot of people even on Psychlo never knew they had names. But they do: "Going counterclockwise, the names of these gates are: "Angel"s Gate," "Betrayer"s Gate," "Devil"s Gate," "G.o.d"s Gate," "Heaven"s Gate," "Infernal Gate,"
"Monster"s Gate," "Nightmare Gate," "Quarrel"s Gate," "Regal Gate," and "Traitor"s Gate." Eleven gates, each with a name."
He took a book, "Force Equations" off his shelf. "It doesn"t matter which types of equations in Psychlo higher math. They"re all the same. You mentioned "force equations" so we"ll use those. No difference."
With a dig of his claw, he opened the book to the point where all the equations were summarized and pointed to the top one. "Now you see this "B"? You might think it is a symbol for something in Psychlo mathematics. But there is no "B" that represents anything mathematical except "Betrayer"s."
He pulled the first paper back. "So where that "B" occurs, we see that the letter "B" has a number value of two. So we just have to add or subtract or whatever it says to do to "B," the number two.
"When we get to the second stage of the equation, there is no letter but a Psychlo mathematician knows you must take the second letter of "Betrayer"s," which is "E" and then look up the number value of "E," which is five, and factor the second stage of the equation with five. Now you get the same equation to its third stage and a mathematician knows he has to factor it with the number value of "T" which is twenty. And so on.
"If the letter in the original equation were "l," then we would use its number value and follow right on down with the number values of the letters for "Infernal."
"You always have one of these letters in the first equation, so you always have the gate name. And you have to use it. When they put the equations together, they constructed them backward from the answer so a gate name would fit. Got it?"
Jonnie got it. A code and cipher mathematics!
No wonder nothing ever seemed to balance. This made even the original equations rigged.
And add to that all the complexity of a base-eleven math and you had what would appear to any outsider to be an utter mess.
He was glad he had the recorder running under his lapel. Completely aside from his being no native of Psychlo, the gate names themselves were weird.
"I have to be honest with you," said Soth. "I don"t know where I am getting all this impulse to be honest. But all this will be of limited use to you."
Chapter 6.
Jonnie sat very still. Something else? You mean, he"d gotten all this way and he still wouldn"t attain it? But he didn"t speak. He waited.
Soth fiddled a bit with his papers. He picked up the contract Jonnie had signed and then laid it down again. Obviously he was having qualms about the honesty of accepting it.
"You have to understand how crazy they were on secrecy," he said at length. "Although what I have given you applies to Psychlo math in general, there is another circ.u.mstance. When equations are applied to the calculation of teleportation, you won"t find all the answers in the texts."
Soth sighed. "The government was afraid of a lot of things. Among them was the possibility that Intergalactic Mining employees, out in some far planet, might get ideas or go into business for them selves. So the exact sequence in which you use the force equations is not revealed in the texts and I think there are dummy equations there as well. I could not work you out a console."
Jonnie objected, "The Chamco brothers seemed to be working on it!"
"Oh, the Chamco brothers!" said Soth impatiently. "They might have monkeyed about. They might even have tried. But they wouldn"t know!"
He swept a paw in the general direction of the other Psychlo dormitories. "These clods here," he said with contempt, "could none of them build a console. They would know what I have told you and it would work for other things. But not consoles!"
He looked at the contract longingly.
Then he confronted Jonnie. "There was a special cla.s.s of trainee at mine school. The catrists went over each incoming cla.s.s with the greatest of care, looking for the most brilliant new students. They were quite rare, really. And when found, they trained them lengthily in every branch of mining activity, theory, and practice.
"The imperial government was determined that only one personnel on any planet would be able to build a teleportation console for use in times of emergency or to repair one. So they specially trained this group of students. We used to call them the "brain-brains." They weren"t always the best people to know but the catrists thought they were.
"And as the government and company were so crazy on the subject of secrecy, of course the post to which these "brain-brains" were appointed was that of security officer."
Terl! thought Jonnie.
And almost as if he was reading Jonnie"s thoughts, Soth said, "Terl was a "brain-brain." Darling of the catrists. Trained in every branch of anything. Sly, evil. A true catrist product. Only Terl could have built a firing console from scratch and he"s gone."
Jonnie"s mind was racing. He had all Terl"s work papers! They would tell him the sequence!
And then his hopes were dashed. Soth said, "That also applies to computing motors. Only Terl could have computed out the full circuits for motor consoles."
Jonnie had no such papers.
"They are," said Soth, "quite different, you know. The firing console overrides and gets around the "sames.p.a.ce" principle. The motor runs on the resistance s.p.a.ce puts up to being changed."
Soth was dangling the contract in his claws. "What I have told you about Psychlo math applies to all of it and can be used in solving anything but teleportation."
Jonnie brightened. At least it would apply to the hundreds of thousands of patents. Still, it meant no motors. It condemned him to eventually flying reaction engines. It meant Desperation Defense wouldn"t have an easy conversion to peacetime. Then he recalled something.
"But executives used to repair motor consoles," he said.
Soth sat up. He looked at the contract and then at Jonnie. "You just want the circuit itself? I thought you were interested in the mathematics. Mathematics is a pure subject," he added with the vehemence of any dedicated hobbyist. "But if you want just the circuit..." He was fishing around under books and papers. "Where"s my breathe-gas mask?"
In minutes they were outside and Jonnie was issuing the orders Soth wanted relayed.
A console was to be removed from a plane, one from a ground car and one from a flying platform. And they were to be brought at once to the repair shop without being further tampered with. Mechanics went racing about.
Presently the three consoles were sitting on the floor of the repair shop.
"These are the three different types of consoles for motor drives. All other motor consoles are one or another of these types. Now you will have to give me a hand. I am not as strong as I was once."
Soth closed the door, barring everyone else. He reached up on a shelf and brought down a "poison ore bag." Jonnie had seen them often enough. They were transparent. They had two very tight armholes you could put your hands and arms into. He thought they were used when one sorted out a.r.s.enic compounds used in ore refining.
Soth, with a little help from Jonnie, struggled the ground car console into the bag. Then he stuffed in all the trailing connection wires that had just been severed from the vehicle. He sealed the bag tight. He connected an air hose to the fitting at the bottom and the bag around the console began to inflate.
He picked up a pressure gauge and a tool kit and shoved these through the armholes. Then he put his own arms in and snapped seals around his elbows.
Through the transparent top he watched the pressure gauge he had put in. "One hundred pounds is what you want," he said.
The bag inflated. The gauge went up to one hundred. He checked his elbow seals. The pressure was holding.
Soth picked up a screwdriver from the kit he had put inside and swiftly took out the screws of the top plate.
Jonnie looked on, fascinated. He had done that once with a tank console and it had promptly ceased to work!
But Soth simply took the screws out. He lifted the top of the console, which contained all the b.u.t.tons, completely off and bunched the cables which led to it.
He then looked into the console itself. There were all kinds of components in there, but unlike a rig, it had no insulating board. Soth selected a wire with clips on both ends and fastened it on either side of three components to bypa.s.s them.
"Pressure fuses," said Soth. "The whole inside of one of these consoles is carried at high pressure. If the pressure drops, any one of those three fuses expands and blows! If anyone monkeys with the cover, it lets the atmosphere out very silently. That blows these fuses.
"Except for the fuses and the erase-surge components, every thing else you"re looking at there is garbage. Sensible seeming. But really just garbage. It has nothing to do with the console operation. I have jumped a wire across the fuses. They will blow and I"ll have to replace them. But the wipe mechanism won"t work now. The real circuit is still intact."
Jonnie was wondering where the real circuit was if that vast area of components was just "garbage."
But Soth knew what he was doing. He kicked the pressure hose with a foot and the bag deflated. He withdrew his arms and pulled off the fasteners. The bag fell away.
Soth turned the console over. "These b.u.t.tons would appear to go down, like ordinary keys, and hit the false circuit. But that isn"t how it operates. The whole circuit is in the cover. When you push a b.u.t.ton, it cuts off an internal light path and makes the circuit operate. Each b.u.t.ton works like that."
A totally hidden circuit, done with molecular alignment in the cover plate. And if you fooled with it, it wiped the circuit out. One cover screw loosened and you had no console anymore.
"Where"s some paper?" said Soth. He found a big sheet of it, larger than the console plate. "Where"s some powdered iron?" He found some, the dust-like brown-black powder, almost capable of floating in the air, so fine was it.
Soth dusted the powder on the white paper and spread a thin coat of it. Then, struggling to keep the bunched cables from tangling, he laid the console cover right-side up on the paper.
He took some jump wires, found a battery, and linked the battery to the console amid a flash of sparks. He was fixing it so that the cover and b.u.t.tons would have juice running through it.
Soth exactly positioned the cover on the paper and then rapidly tapped each console b.u.t.ton.
Jonnie suddenly understood what he was doing. He held up a hand to prevent Soth from removing the cover. Jonnie got a metal a.n.a.lysis camera off a shelf, stood up on a stool, and shot a picture straight down.
When Jonnie had finished, Soth gently lifted up the cover.
There on the paper, drawn in magnetically grouped iron filings, was the whole circuit! Activated by pushing the b.u.t.tons, each part of it had grouped the iron filings.
On the removal, a tiny part of it had gotten blurred. But Jonnie had it in the camera. To be sure, he now took another picture of the tiny, thin, brown-black lines.
They had that circuit!
Soth put it all back in the bag, inflated it to a hundred pounds, replaced the blown fuses, checked the plate gasket, and then screwed the console back together.
Two hours later, they had all three types of motor console circuits. They put everything away, called the mechanics, and had the consoles put back in the vehicles and connected.
Jonnie made a test. They all started the motors.