Empire on Ice #42: Imagination

This week! Benzan tries to figure out what imaginary numbers really mean.

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[In a lounge at the ritzy Club Commons Imperiale, Silence is sitting in an armchair in front of a table. The table is empty and she is perfectly still, but her eyes are open and she looks like she's concentrating very hard. Benzan enters.]

Benzan: Silence! I have a math question for you.

[Silence doesn't move her head or eyes from their stiff position, and doesn't appear to acknowledge Benzan's presence at all, but she does answer him.]

Silence: I have an unmathematical answer for you.

Benzan: I've been taking an algebra refresher course in college this quarter, and we're doing quadratic equations. What does it mean when you solve a quadratic equation and you get an imaginary number?

Silence: What?

Benzan: The instructor didn't do a very good job of explaining it. I'm pretty confident about the math itself, but I don't understand what I'm actually doing. I can interpret a real answer, but not an imaginary one.

Silence: Go ask Grieve. I'm busy.

Benzan: You don't look busy.

Silence: I'm playing five-dimensional chess.

Benzan: …

[Benzan looks around. Nobody else is in the lounge, and there is no chessboard.]

Benzan: No you're not. There's no board. No opponent.

Silence: The board can't exist in our space. I'm playing on a projected simulation of it. You wouldn't be able to perceive it without at least a 315 IQ.

Benzan: Well…who are you playing against?

Silence: The Titans.

Benzan: The Greek Titans?

Silence: Yes, in the fifth dimension time and reality have no meaning.

Benzan: All of them?

Silence: Just the second generation. It'll be another five or six of your mortal years before I can take on all of them combined. Now, shoo!

Benzan: All right. Sorry to bother you.

[Exit Benzan.]

[When he's gone, Silence breaks her pose and relaxes, then smiles.]

Silence: Sucker.

[Gaia emerges from behind the curtains.]

Gaia: I thought he'd never leave! Shall we get back to Hacker Chutes and Ladders?

Silence: Yep! As I recall, you landed on Tile 84, so you either have to hack into the Russian defense computers or go down the chute.

Gaia: Shoot.

Silence: Okay, then—

Gaia: No, not that chute! O, drat this English.

*

[Elsewhere in the Club, Grieve is drinking hot chocolate at the milk bar. He looks to be in rough shape. His eyes are freakishly wide open, and red, and his hands are shaking.]

Grieve: Bartender! Another hot chocolate!

Bartender: Don't you think you've had enough?

[Grieve grabs the bartender by her shirt.]

Grieve: I'll tell you when I've had enough!

Bartender: B-but…no one can take that much sugar!

Grieve: Do I look like a mate who cares anymore?!

[Enter Benzan.]

Benzan: Grieve!

Grieve: Begone from here, Benzan. A promising young up-and-comer like yourself has no business seeing humanity at its lowest and uglinest nadir.

Benzan: I'm pretty sure that would be Hitler or something.

Grieve: Get out of here! I don't want you to see me like this!

Benzan: You're tricked out on sugar again, aren't you?

Grieve: No, dammit!

Benzan: We talked about this. I thought you said you were done with the cubes. You promised me!

[Grieve spins around on his barstool, leaps to his feet, and staggers to Benzan, grabbing him by both shoulders.]

Grieve: Promises were made to be broken!

[He runs out of the milk bar screaming.]

Benzan: What happened to him, anyway?

Bartender: His favorite tomato plant died.

Benzan: Aw.

Bartender: Yeah. He's taking it pretty hard. I'm worried he'll go diabetic. Maybe you should go after him.

Benzan: I don't think he'd listen to me. Besides, I need some help with my math homework.

Bartender: I saw Celadon over in the Gentlemates' Laboratory.

Benzan: Great!

*

[The Gentlemates' Laboratory is a very couth place, reminiscent of the best that steampunk and Victorian England have to offer. Celadon is tinkering on what looks to be a teaspoon with a yellow happy sunshine on the stem.]

Benzan: Celadon.

Celadon: Benzan! Quickly! Go over to the green lever by the Jacob's ladder and pull it. Hurry!

[Benzan scurries over and pulls it.]

Celadon: If you hadn't arrived just then there'd have been a static discharge so powerful that I'd have lost hours of work. [He turns around in his chair and smiles.] What a timely arrival!

Benzan: I need your help with my math homework.

Celadon: Not my best suit, but I'll try. What's up?

Benzan: What does it mean to get an imaginary number in the solution to a quadratic equation?

Celadon: Pft! Don't ask me. I never studied that voodoo.

Benzan: Really? But…you're in a laboratory.

Celadon: Benzan…there's science… [He pushes his safety goggles from his forehead down to his eyes.] …and then there's mad science. We don't do math here. We do amperage. You should probably put on an electrical resistance jacket now, or leave.

Benzan: Eh…I guess I'll be going.

*

[Benzan arrives at the Club's world-famous Imperiale Hall of Banquets. He finds Josh and DeLatia having a crème brûlée eat-off. Both Josh and DeLatia look a little queasy, and there are empty ramekins everywhere, with a few uneaten ones still sitting in the center of the table.]

DeLatia: I'm telling you—hic!—no one beats me at my favorite dessert.

Josh: You mean my favorite dessert! *burp*

Benzan: May I interrupt?

DeLatia: Ugh, it's the boy-thing. Don't let him eat my crèmes brûlées.

Josh: Come on, Lilit. Be nice. What can we do for you, Benzan?

Benzan: What does it mean to get an imaginary number in the solution to a quadratic equation?

Josh: Imaginary?! Ha ha hah!

[Josh and DeLatia both laugh.]

DeLatia: It means you can't eat it!

Josh: And if you can't eat it, better off that it stays imaginary!

DeLatia: "Complex" numbers, really. More like "waste of time" numbers!

Josh: Ho ho ho!

Benzan: But I want to understand what an imaginary term actually means, you know?

[A clearly overstuffed, drunk-looking Josh grabs Benzan on the shoulder.]

Josh: Did your math teacher put you up to this, boy?

DeLatia: Tell your math teacher to fuck off!

Josh: Sound advice!

DeLatia: Now, if you'll excuse us, I still have about forty crèmes brûlées to eat!

Josh: You mean I have about forty more crèmes brûlées to eat.

DeLatia: Not on your life.

Josh: We'll just see who lives through the night!

Benzan: …

[Exit Benzan.]

* * *

[Two days later, Benzan finds Silence in a forested oceanside park. She's walking toward a bench near the ocean, where Grieve is sitting. Benzan catches up to her first. She looks as though she's carrying something, but Benzan can't see anything in her arms.]

Silence: 'Lo, Benzan.

Benzan: You know you missed a crème brûlée eat-off the other night?

Silence: You mean Josh and Lilit? They were just in the semifinals to see who would have the honor of losing to me tomorrow night at the Imperial Crème Cram World Cup. [She looks over at him and smiles.] It really is a big cup, you know. I've already bought a new wardrobe two sizes up.

Benzan: Hah. I can't believe I ever thought you might be missing out on a crème brûlée gluttony contest. So…did you win at chess?

Silence: Oh yes. It wasn't even close. Embarrassing, really. But enough about me. What about you? Did you figure out your imaginary number problem?

Benzan: No, and there was a pop quiz and I lost three points because of it.

Silence: Ah, too bad. But look on the bright side. Those three points don't mean anything in the grand scheme of things, but your lack of understanding of complex numbers will last a lifetime!

Benzan: Gee, thanks.

Silence: I'm just kidding. The hard part is understanding what the complex number system means—what it offers that the real number system doesn't. I think the best way to do that is to look at some applications that get a lot easier with complex numbers. Watch this.

[They arrive at the bench, where a bleary-eyed Grieve is staring out at the ocean. He looks pretty depressed. Still acting as though she's carrying something, Silence sits down to Grieve's right, while Benzan for lack of space on the bench stands off to Grieve's left.]

Silence: Good afternoon, Grieve!

Grieve: …

Benzan: Hey Grieve! [Tenderly.] How are you doing?

Grieve: …

Grieve: Benzan…never love anything. It isn't worth it.

Silence: I know it hurts.

Grieve: It was my best tomato plant. So pretty, so innocent. The little vine crawling up toward the sun. Such tasty, sweet tomatoes. The perfect texture, the "pop!" when you bite into them. The smell. Ah…

[Grieve sniffles and clears his throat.]

Grieve: But it's never coming back, is it?

Silence: Usually, no.

Benzan: "Usually"?

Silence: But you're lucky today, Grievey. I happen to have your tomato plant right here.

Grieve: What?

Silence: The very same.

[He looks around at Silence, but there's nothing. Just her.]

Grieve: I don't see anything.

Silence: It's imaginary.

Grieve: Silence, I'm not in the mood.

Silence: Here. Take it.

[She acts as though she's handing something to him, but he doesn't see anything.]

Grieve: What is this all about?

Silence: Go on, take it!

[Grieve sighs and listlessly pretends to take whatever's there.]

Silence: I bet you didn't know this, but it only takes four imaginary copies of something, multiplied together, to make one real version of it.

Grieve: That's not how imaginary numbers—

Silence: And I just happen to have three more!

[She acts as though she's handing him a second tomato plant.]

Grieve: Come on, Silence.

Silence: Take it!

[With annoyance in his face, Grieve pretends to take another imaginary tomato plant.]

Silence: Put those two together first. If three of them touch it won't work. Go ahead.

[Grieve sighs, and pretends to put the two plants together.]

Silence: Great! Now you have negative one of your tomato plant.

Grieve: Wonderful.

Silence: Give it to Benzan.

Grieve: Ugh.

Silence: Go on.

[Grieve sarcastically pretends to hand it to Benzan, who—for lack of anything better to do—pretends to take it.]

Silence: And now I'll give you two more, same as before.

[She proceeds to do so. Grieve accepts them with annoyance and resignation.]

Silence: Now you have another negative one of your tomato plant. Benzan, give him yours.

[Benzan pretends to do so.]

Silence: Careful! You almost dropped it.

Benzan: Sorry.

Grieve: Don't encourage her, boy.

Silence: Now put them together!

[Grieve does so, with much cynicism and reluctance.]

[Then, to everyone's astonishment, a single tomato appears in his lap. There's even just a smidgen of green vine attached to the top. Grieve's and Benzan's astonishment comes as surprise, but Silence's takes the form of confusion. She scratches her head.]

Grieve: What the—

Benzan: !

Silence: That's strange. It's supposed to be the whole plant.

Grieve: How did you…what did you…how…

Benzan: Imaginary numbers are awesome!

[Grieve holds up the tomato and looks at it. He even gingerly smells it.]

Grieve: [Amazed.] It's exactly the same…

[Silence looks at Benzan apologetically.]

Silence: Truly, a dismaying refutation of modern math theory. It wasn't supposed to turn out like that. I'm sorry.

Benzan: …But—

Silence: Benzan, we'd better get down to the Imperial College of Mathematics and invent a new number system right away! The Large Imaginary Collider goes online in just seven days.

Benzan: Why am I coming along?

Silence: It'll be good, seat-of-your-pants learning. The way we used to it in the old days: Titan-style!

[She rises from the bench and beckons Benzan.]

Silence: Grieve, plant the seeds. And good luck.

[Exit Silence and Benzan.]

[Grieve continues to stare at the tomato in wonder.]

Grieve: The seeds……