“Anyway, members of this mob of cutthroats began to call themselves 'catrist.' That means 'mental doctor.' So the people became 'Psychlos' or 'brains' and the 'catrist' or 'mental doctor' was the real, hidden government. They taught all the children. They inspected every citizen. They suppressed religion. They told people how to think.
“Oh, I was stupid. There's no excuse for what I did.” He fell silent. “But this catrist was raising so much row! I should not blame my mother. I should never have blamed her.” He paused again and drew a long breath. “It just blurted out. I said, 'They are not animals!' "
He shuddered and after a while said, “So that began my exile. Now you know.”
What Jonnie now knew was that that mob of frauds was stark staring insane.
“Well,” said Soth, coming out of his despondency, “if that isn't why you're here, why are you? An old ruin like me has nothing to offer.”
Jonnie decided to dive in. “You obviously know mathematics.”
Suspicion clouded Soth's already rheumy gaze. “How did you know my hobby was mathematics? It isn't in my record. I paid a female clerk five hundred credits once to see it and I know.” The mystery of it threw him. Then he solved it. "Ah!" he swept his paw down the bookshelves. “My books!” Then he clouded over again. “But they're mostly outer-language books and very few people can read them. A lot of the races are even dead! Come,” he pleaded, “tell me why you're here!”
“I want you to teach me about Psychlo mathematics,” said Jonnie.
There was a sudden tension in Soth. He seemed to become confused. Then it seemed to clear away. “Nobody has asked me to teach them anything for a hundred thirty years. You're an alien race, but what does it matter? There are hardly any Psychlos left. What do you want to know?”
The tension slid out of Jonnie. He'd made it!
Chapter 5
"In the first place,” said Soth, after he had made himself more comfortable and taken a small bite of the kerbango Jonnie had produced, “there are an awful lot of different kinds of mathematics– different races, you know. I sort of kept my interest in life by collecting them.
“There have been existing systems for lots of different whole numbers.
There's the 'binary system' like the Chatovarians use: it has only two numerals in it, one and zero; that's so they can use them in computers, in which the electric current pulse, or the direction of magnetization of an element, has one of two values. One value corresponds to the numeral zero; the other to numeral one. Any number in any system can be translated to the binary system using only zero and one. Unwieldy for beings, but understandable for the computers.
“Then there's a system based on the integer three, an entirely different one based on four, another on five, another on six, another on seven, still another on eight, yet another on nine and so on. There's even been one on twenty and one on sixty.
“For paper computation the best system is called the 'decimal' system, based on ten.” (Jonnie knew about this from man-books.) "Psychlo mathematics are based on eleven; some people call this the 'undenary' system. It 's difficult so I won't try to teach you that.”
“Oh, I would love to know about the 'undenary' system!” said Jonnie. His use of the words 'love to know' gave him a twinge of conscience. He hated this confused mess!
“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, nobody 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!"[4]
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