M = Math Professor, E = English Professor

 

M: "How's your IPA?"

E: "Not bad."

M: "So...are your classes going okay?"

E: "Well, yes and no. Are you finding that these students think differently than we did? It's like they take everything literally."

M: "No sense of poetry or metaphor, you mean?"

E: "Yeah, maybe I'm just a lousy teacher, but I'm having a hard time getting across the idea to these kids that all enjoyment of things like movies and novels depends on one uniquely human ability, and that is the willing suspension of disbelief."

M: "But they don't get it. Yeah, I see the same thing with the math students. I'm not talking about literary stuff, of course. But...for instance, the idea of imaginary numbers."

E: "Ha, yeah, I don't get that either."

M: "Well, it was hard for me at first too. I mean, if it's a number, it's real, right? But, as you say, if you apply a willing suspension of disbelief, you can see that there are two realms: real numbers and imaginary numbers."

E: "Um, really?"

M: "Well, if we say real numbers are like nonfiction, then imaginary numbers are like fiction. Two realms, both actually real, but different in character. That's not exactly an accurate analogy, but maybe it helps.”

E: “Hmm....”

M: “More correctly, geometrically, we might say that real numbers are on the x axis, horizontal, and imaginary numbers are on the y axis, vertical."

E: "Uh-oh, geometry."

M: "Well, it's visual, it helps."

 

E: "But what's the point? Why do we need imaginary numbers? Now I sound like my students."

M: "See, the imaginary unit is the square root of negative one. Technically, it doesn't exist—because to square any real number always gives a positive number. But some algebraic equations need this impossible concept in order to be solved."

E: "Uh-oh, algebra."

M: "Yeah, people don’t like it. But it works. It's part of why we're an advanced society."

E: "But are we? I don't think so."

M: "Well, technologically we are. Philosophically, ethically, not as much, maybe." E: "Moral cavemen. Ugh."

M: "Well, I have to disagree. Sure, there's a lot of ugliness, we have a long way to go, but actually we've made a huge amount of progress. Ethically, morally, I mean. I doubt we can really imagine how brutal life was in the early days of the species. Indiscriminate murder everywhere."

E: "You say we're technologically advanced, but I even wonder about that. I mean we certainly think we are. But maybe that's just hubris."

M: "Maybe. You think I'm overly positive about humans in general?"

E: "Well...I guess maybe I need another beer. Not really looking forward to my Comp 101 lecture tonight."

M: “I get it. But I wanted to extend the metaphor. I was just saying—"

E: “Wait—earlier you said somebody about the square root of negative one.”

M: “Yeah, that would be equivalent to one in real numbers.”

E: “Okay, it made me remember something. Hang on, I have it right here....”

M: “You brought a book with you?”

E: “Sure—I mean, it fits my role, doesn’t it? A good prop. Maybe you should carry a calculator.”

M: “Nope. C’mon, stay in character.”

E: “Okay, here it is...the Irish writer Flann O’Brien has one of his characters say ‘God is the root of minus one.’”

 

M: “Interesting. I guess he means God is impossible. But necessary to humans.”

E: “But then he goes on to say, ‘He is too great a profundity to be compassed by human cerebration.’”

M: “Cerebration, eh?”

E: “Well, he’s a Joycean type. So maybe it’s sort of a Catholic view of God: not impossible, just beyond our understanding.”

M: “Hmm, okay. My colleagues would probably say those are the same thing.” E: “Reductionists?”

M: "Materialists. I reserve judgment on the subject. But anyway, I was telling you about imaginary numbers—."

E: “Uh-oh, there’s more?”

M: "Don't let me bore you!"

E: "No, no, just joking. How’s your wife?”

M: “Why do you ask that?”

E: “Well, you know, we’re supposed to be friends, I thought it would seem natural.” M: “Nah, let’s stick to shop talk. Stay out of the weeds.”

E: “If you say so.”

M: “I do.”

E: “Well, okay, I guess I like to learn math. Sometimes. You were saying...?”

M: "Okay, say there's a technological problem, computer design or something, that really needs the square root of a negative number in order to be solved, then we can get there by simply accepting that i exists. Even if it doesn't. In other words, like you said, by suspending our disbelief."

E: "I?"

M: "Yeah, you." E: "Me?"

M: "Kidding. "i"—lower case i—is the symbol that represents the square root of negative one. Which allows us to get into the whole realm of complex numbers, by multiplying a real number by i."

 

E: "So, wait...the first person singular pronoun that we all use so often, to talk about ourselves, describes something that doesn't actually exist. Hmm, that's a little spooky."

M: "You've jumped the category rails."

E: "Okay, I know. But...yes, I think I get the idea. I like it, but I have to say I empathize with your students."

M: "Or, how about this: it's a mirror. Imaginary numbers mirror real numbers. Negative 2 times negative 2 equals positive 4. But negative 2i times negative 2i equals negative 4."

E: "So...here I am—the real me—looking into a mirror at a backwards world and the guy in there is the imaginary I. Okay, I can work with that. Could be part of a good story."

M: "Well, category shift again. It's too bad these numbers are called "imaginary"—it's misleading. Descartes was actually being derogatory toward the whole idea when he called them that, but it stuck."

E: "Odd...Descartes proposed mind and body as separate realms but couldn't buy the idea of two kinds of numbers? You'd think he'd understand it as mental numbers and physical numbers."

M: "All numbers are mental."

E: "Except that if I had bought two beers a few minutes ago, it would've cost me twice as much as one beer. Actual dollars."

M: "Counting is not the same as numbers.”

E: “As Shakespeare said, I am ill at these numbers.”

M: “Maybe not as ill as you think.”

E: "Okay, back to Descartes. So he thought imaginary numbers was a silly idea. But if we just called fiction 'imaginary stories' it wouldn't seem derogatory. Would it?”

M: “Well—”

E: “Don't answer. I know some people think fiction is a silly idea too."

M: "I don't. I read novels sometimes."

E: "You know, there are studies that show that a lot of fiction reading is correlated with higher empathy. Is it causal? I don't know, but it could be."

M: "Makes sense."

 

E: "Yes. More politicians should read it. Transform their minds."

M: "I can agree with that. You know, this is a damn good stout. We should come here again some time."

E: "Okay, we'll plan on it. Off the clock. So...is that enough dialogue?” M: “No, we may need more. What else ya got?”

E: “Well, I was just thinking about that x-y axis thing you said. In the land of mythology and symbols, we could be entering Christian philosophy here: the meaning of the cross, etc. Atonement, redemption.”

M: “Okay.”

E: “Or, more generically, many wisdom traditions suggest that the vertical plane is where spiritual progress or transformation happens, while the horizontal plane is the mundane—the earthly or material world, without transcendence. So in your geometry, imaginary numbers are related to the realm of spirit."

M: "I don't really go there, but I see the parallels. Or rather, the non-parallels, the intersections."

E: "Ha, right."

M: "Speaking of transformations, here's another thought...by working through certain equations that start with imaginary numbers, you can bring the solution fully into the real numbers realm. Nothing becomes something, so to speak."

E: "Wow. Maybe that's like writing a novel: mere thoughts become actual words on a page. Imagination becomes reality. No, wait...not exactly. More like a description of reality. No...there I go again: jumping category rails, as you say."

M: "Look at quantum theory—the stuff about wave functions, or how a subatomic particle is really just a wave of probability until it's observed. Then it collapses into a physical particle. So a wave is not exactly reality as we think of it, it's just potential. And wave behavior can't be accurately described mathematically without using imaginary numbers. So the unreal is embedded in reality at the deepest level."

E: "I'm sure these ideas must be in science fiction these days, but that's not what I read. At least not since Ray Bradbury long ago. Some of my students are probably ahead of me on these topics. You know, I teach the literary classics, but my guilty pleasure is good old twentieth-century crime fiction."

M: "Ha, why am I not surprised?"

E: "Well... okay. Done with your beer?"

 

M: "Almost."

E: "Whadya think? Is this enough? A good rehearsal?"

M: "Seemed like an excellent improv. Definitely more convincing than last time."

E: “Yeah, the captain would be impressed.”

M: “What, are you bucking for a promotion or something?”

E: “No, but....”

M: “I don't really care if the captain’s impressed. I just want to do it right so we can take down this bunch of over-educated degenerate creeps who are preying on....”

E: “Our future generations.”

M: “Right. You got your phone charged up and ready to record?”

E: “Yep. You got your piece?”

M: “In my waistband.”

E: “Loaded?”

M: “Of course, gimme a break. But I don’t think I’ll need it. We’ll do fine.”

E: "Especially you. Damn, you've done some study."

M: "Well, I never thought I'd be undercover as a frickin' math professor.”

E: “Or me as an English professor. Ha!”

M: “But nothing is ever as you expect, right?"

E: "Right. You ready to go? It's time."

M: "Time... I could talk about that for a while too. You know what Einstein said about relativity...."

E: "No. Save it for the rendezvous, man, we gotta go. Back to reality."