Battlefield Earth

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 Jo

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 Jo

Chapter 5

"In the first place,” said Soth, after he had made himself more comfortable and taken a small bite of the kerbango Jo

“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.” (Jo

“Oh, I would love to know about the 'undenary' system!” said Jo

“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 Jo

Jo

“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.'

Jo

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 Jo

Nothing ever balanced.

Soth was looking at him very keenly. “I think you are digging for the teleportation formulas.”

Jo

“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.

Jo

“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 Jo

“Money?” said Jo

“A separate dome, access to compound libraries, and tools to experiment with computers. And not to be cross-fired elsewhere!”

“All right,” said Jo

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.”

Jo

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?”

Jo

“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,' 'God'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.”