Robert Heinlein - Citizen of the Galaxy

So Sisu accepted a little uranium and a lot of choice meats and luxury foods. Sisu always picked up gourmet delicacies; this time she stocked tons more than the Family could consume, but valuable for swank at the Gathering.

The balance was paid in tritium and deuterium. A hydrogen-isotopes plant is maintained there for Hegemonic ships but it will sell to others. Sisu had last been able to fuel at Jubbul -- Losian ships use a different nuclear reaction.

Thorby was taken dirtside by his Father several times in New Melbourne, the port. The local language is System English, which Krausa understood, but the fraki spoke it with clipped haste and an odd vowel shift; Captain Krausa found it baffling. It did not sound strange to Thorby; it was as if he'd heard it before. So Krausa took him to help out

This day they went out to complete the fuel transaction and sign a waiver required for private sales. The commercial tenders accepted by Sisu had to be certified by the central bank, then be taken to the fuel plant. After papers were stamped and fees paid, the Captain sat and chatted with the director. Krausa could be friendly with a fraki on terms of complete equality, never hinting at the enormous social difference between them.

While they chatted, Thorby worried. The fraki was talking about Woolamurra. "Any cobber with strong arms and enough brain to hold his ears apart can go outback and make a fortune."

"No doubt," agreed the Captain. "I've seen your beef animals. Magnificent"

Thorby agreed. Woolamurra might be short on pavement, arts, and plumbing; the planet was bursting with opportunity. Besides that, it was a pleasant, decent world, comfortably loose. It matched Doctor Mader's recipe: " -- wait until your ship calls at a planet that is democratic, free, and human... then run!"

Life in Sisu had become more pleasant even though he was now conscious of the all-enveloping, personally-restricting quality of life with the Family. He was beginning to enjoy being an actor; it was fun to hold the stage. He had even learned to handle the clinch in a manner to win from Grandmother a smile; furthermore, even though it was play-acting, Loeen was a pleasant armful. She would kiss him and murmur: "My husband! My noble husband! We will roam the Galaxy together."

It gave Thorby goose bumps. He decided that Loeen was a great actress.

They became quite friendly. Loeen was curious about what a firecontrolman did, so under the eye of Great Aunt Tora, Thorby showed her the computer room. She looked prettily confused. "Just what is n-space? Length, breadth, and thickness are all you see... how about these other dimensions?"

"By logic. You see four dimensions... those three, and time. Oh, you can't see a year, but you can measure it."

"Yes, but how can logic --"

"Easy as can be. What is a point? A location in space. But suppose there isn't any space, not even the four ordinary dimensions. No space. Is a point conceivable?"

"Well, I'm thinking about one."

"Not without thinking about space. If you think about a point, you think about it somewhere. If you have a line, you can imagine a point somewhere on it. But a point is just a location and if there isn't anywhere for it to be located, it's nothing. Follow me?"

Great Aunt Tora interrupted. "Could you children continue this in the lounge? My feet hurt."

"Sorry, Great Aunt Will you take my arm?"

Back in the lounge Thorby said, "Did you soak up that about a point needing a line to hold it?"

"Uh, I think so. Take away its location and it isn't there at all."

"Think about a line. If it isn't in a surface, does it exist?"

"Uh, that's harder."

"If you get past that, you've got it A line is an ordered sequence of points. But where does the order come from? From being in a surface. It a line isn't held by a surface, then it could collapse into itself. It hasn't any width. You wouldn't even know it had collapsed... nothing to compare it with. But every point would be just as close to every other point, no 'ordered sequence.' Chaos. Still with me?"

"Maybe."

"A point needs a line. A line needs a surface. A surface has to be part of solid space, or its structure vanishes. And a solid needs hyperspace to hold it... and so on up. Each dimension demands one higher, or geometry ceases to exist. The universe ceases to exist." He slapped the table. "But it's here, so we know that multi-space still functions... even though we can't see it, any more than we can see a passing second."

"But where does it all stop?"

"It can't. Endless dimensions."

She shivered. "It scares me."

"Don't worry. Even the Chief Engineer only has to fret about the first dozen dimensions. And -- look, you know we turn inside out when the ship goes irrational. Can you feel it?"

"No. And I'm not sure I believe it."

"It doesn't matter, because we aren't equipped to feel it. It can happen while eating soup and you never spill a drop, even though the soup turns inside out, too. So far as we are concerned it's just a mathematical concept, like the square root of minus one -- which we tangle with when we pass speed-of-light It's that way with all multi-dimensionality. You don't have to feel it, see it, understand it; you just have to work logical symbols about it. But it's real, if 'real' means anything. Nobody has ever seen an electron. Nor a thought. You can't see a thought, you can't measure, weigh, nor taste it -- but thoughts are the most real things in the Galaxy." Thorby was quoting Baslim.

She looked at him admiringly. "You must be awfully brainy, Thorby. 'Nobody ever saw a thought.' I like that."

Thorby graciously accepted the praise.

When he went to his bunkie, he found Fritz reading in bed. Thorby was feeling the warm glow that comes from giving the word to an eager mind. "Hi, Fritz! Studying? Or wasting your youth?"

"Hi. Studying. Studying art."

Thorby glanced over. "Don't let Grandmother catch you.

"Got to have something to trade those confounded slugs next time we touch Finster." Woolamurra was "civilization'; the bachelors had replenished their art. "You look as if you had squeezed a bonus out of a Losian. What clicks?"

"Oh, just talking with Loeen. I was introducing her to n-space... and darn if she didn't catch on fast."

Fritz looked judicial. "Yes, she's bright" He added, "When is Grandmother posting the banns?"

"What are you talking about!"

"No banns?"

"Don't be silly."

"Mmm... you find her good company. Bright, too. Want to know how bright?"

"Well?"

"So bright that she taught in El Nido's school. Her specialty was math. Multi-dimensional geometry, in fact."

"I don't believe it!"

"Happens I transcribed her record. But ask her."

"I shall! Why isn't she teaching math here?"

"Ask Grandmother. Thorby, my skinny and retarded brother -- I think you were dropped on your head. But, sorry as you are, I love you for the fumbling grace with which you wipe drool off your chin. Want a hint from an older and wiser head?"

"Go ahead. You will anyhow."

"Thanks. Loeen is a fine girl and it might be fun to solve equations with her for life. But I hate to see a man leap into a sale before he checks the market. If you just hold off through this next jump, you'll find that the People have several young girls. Several thousand."

"I'm not looking for a wife!"

"Tut, tut! It's a man's duty. But wait for the Gathering, and we'll shop. Now shut up, I want to study art."

"Who's talking?"

Thorby did not ask Loeen what she had done in El Nido, but it did open his eyes to the fact that he was playing the leading role in a courtship without having known it. It scared him. Doctor Mader's words haunted his sleep " -- before Grandmother decides to marry you to someone... if you wait that long -- you're lost!"