The graduate seminar, "Modern Critical Theories," (Eng. Lit. 674, 3 Cr.) theoretically occupied only Wednesday afternoon, but in fact it stretched into a region where time virtually ceased to run. There was no relief, for with only six of us in the small seminar room, drowsing or nodding into a sweet ten-minute repose now and then was impossible. We were all graduate "section hands," earning our tiny pittances as we pursued will-o-the-wisp doctoral degrees by teaching the vast, sluggish, introductory courses in English Lit and its stunted, bastard child, Rhetoric (whatever Rhetoric actually is).
Yet what we chosen few studied in our ivory tower of scholarship was even more boring and useless than the oversimplifications we droned at the sleeping or whispering frosh. Finally, after more than two hours of an especially confused lecture. I spoke my complaints to Professor Herman Gabriel Stang, an ancient full bull in English Lit and my major professor.
"Dr. Stang," I said as bravely as possible, "may I speak, for once, frankly to you at this seminar?"
Old Stang, his bald pate a ruddy shine under the fluorescents, turned little colorless eyes in my direction. A diamondback rattler, I thought suddenly, would contemplate a lost prairie dog with similar warmth. "Academic freedom, Mr. Pilson, is the foundation stone of this university. Of course you may speak with frankness," he said from wrinkled lips that hardly moved. His large and rimless trifocals reflected the room lights with a shimmer as his head continually shook and gave him the look of a man turning into a huge bee.
"Then, sir," I said, "I wonder if you would comment on the purpose behind all this stuff we're doing, all these so-called critical theories, like structuralism, deconstruction, semiotics. Hell, we can't even get the freshmen to wake up for Mellors plowing Lady Chatterly. If we ever tried to talk semiotics to them, half the class would dislocate their jaws from yawning and the rest would go into coma."
Stang gave us all a frozen grimace and thin Miss Lee, sitting at my left, gave a shiver and took a large gulp of hot coffee. "You see English Literature as mainly cheap, titillating entertainment then, Mr. Pilson?" he said in an arctic voice.
"Not a bit," I answered. "Look, there are plenty of good, useful reasons for reading and studying literature, but hocus-pocus like semiotics and the rest don't relate to any of them. The trouble with English Literature is that it's run out of dissertation topics. I mean, how many more studies of Henry James's letters to his publisher's cousin's landlady can there be?" That was a bold shot, since James was one of old Stang's "men." Miss Lee's almond eyes went slightly wider, and she casually shifted her chair so as to get a bit farther along the table and away from me.
Stang, surprisingly, gave me a considerable smile. "So, since we have buried James under whole forests of dissertation paper, you see us now simply creating new scholarly methods as—What is the new slang word?—a scam to keep old men like myself employed?"
I nodded, also smiling in what I hoped was a steady way. "I couldn'thave stated it any better than you did, Professor," I said. "Anybody can think up more useful literary tools than semiotics in ten minutes. Take the idea of narrative geometry, for example ... "
The room fell silent, and Dr. Stang's face took on a more crafty, yet somehow more human expression. "So, Mr. Pilson, you've been planning an ambuscade for me, a little scene to enliven our labors. Very well, I will be a sport and play the Stan Laurel part. What, Ollie, is narrative geometry?"
Several in the class chuckled in relief at Stang's suddenly jocular tone, and Miss Lee, who was doing her dissertation in film, gave a brief yet grateful laugh.
'It's always been around," I said, shrugging and speaking with the casual assurance of supposedly long acquaintance. "Any narrative has a beginning, middle, and end. Well, that description also defines a one-dimensional line."
Dr. Stang fired off a pitying sneer. "That sounds like the sort of profound triviality that might entrance the scientific community, but what exactly does it say to us about any given literary work?"
"Nothing," I said. "You've got to go to at least two dimensions, to flat graphs. Plenty of the old books dealt with Shakespearean plots in terms of a rising and falling line. One coordinate was the time sequence of the story and the other was something to do with whether the plot was under development or resolution. The method helps you pick out the moment of peak narrative intensity.
"Okay, now let's extend to three-dimensional geometrical systems. An example might be the Arabian Nights stuff. You know, the Thousand and One Nights? What is the geometrical analog to this work? Think of a three-dimensional volume, say a sphere, which represents Sheherezade and her framing story, in which she spins yarns to delay her execution. Inside that sphere and all contained by it are the thousand stories she tells. Think of them as smaller spheres within the frame story-sphere but having various sizes and relationships. Some story-spheres only touch each other and may form chains, stories in which one person and then another spins a yarn, each in turn but all within the same outer reality.
"Sometimes several story-spheres are completely enclosed, each within the next-larger outer one, as when a character in one story offers to tell a fiction, and then a character in that fiction starts on a new narrative with new characters. The point is, this assemblage of intersecting, enclosing and tangent spheres can be seen as a geometrical model of the total work. Probably undetected patterns and strengths in the story groups \could be uncovered by a study of the total figure, but I think you'd need a computer-graphics capability. There are just too many stories to do it by hand on paper."
I stopped the lecture and Dr. Stang, who did not look especially impressed by all this, shrugged. "Well, perhaps, perhaps. But one swallow does not a summer make, Mr. Pilson. I assume you can offer other congruities between geometry and narrative structure?"
"Let's take a geometrical system and then try to imagine its literary counterpart," I said quickly, now waving a
confident hand at him. "A four-dimensional hypercube or tesseract can be projected into our space in the form of a large cube with a smaller one inside and the two connected at their eight corners. The big cube is the solid boundary of the hypercube nearest to our space, the little one inside is the bounding cube farthest away, and the two are connected by six other distorted cubes that stretch away from us into the fourth dimension. You might call that fourth dimension time, and say that the little cube is the same cube as the big one, but now farther off in future time. It's really going to be the same size up there ahead, but we show it smaller to indicate that it's farther off."
I gave Miss Lee a sideways glance, saw a concealed but unmistakeable bewilderment, and plunged ahead anyway. "Okay, instead of time as the fourth dimension let's use something I'll call narrative distance. Take a classic example, the play-within-the-play in Hamlet. Here are two separate three-dimensional realities: the play, Hamlet itself, with old Claudius popping his mental cork when he sees the Hamlet-buggered script acted out, and the shorter, smaller, on-stage murder-of-Gonzago play. But the little play is at a greater narrative distance than Hamlet, both from the real audience and from the Court of Denmark watching it on stage, since it is presented as a created artifact within the 'true' or 'real' drama. So not only is this part of Hamlet modeled by a four-dimensional geometrical object, but the staging assumes the exact projected form of the hypercube, with one small stage located in the middle of the other, larger one. Pirandello did the same sort of thing, as have others."
Professor Stang had been following me closely and his crafty expression now intensified. "Interesting, Mr. Pilson, but it so happens that I know a little about metageometry and related matters. If this literary model is worth anything, shouldn't we be able to perform, in a literary sense, the same manipulations that are possible in four-dimensional, geometrical space? For example, a normal cubical space, when rotated a half-turn in the fourth dimension, produces a mirror-image reversal of three-dimensional objects contained within it."
I knew old Stang cared little for geometries and less for geometers, and had picked up that tidbit at the joint faculty-student science-fiction seminar last term, when we discussed an H.G. Wells story about a chemist whose body was reversed right for left by being flipped over in the fourth dimension. But I nodded with enthusiasm. "Tom Stoppard really did that when he wrote the play, Rosencrantz and Guildenstern Are Dead," I said at once. "That play is Hamlet in mirror-image narrative. The original main characters—Ophelia, Hamlet, his mom and dad—are only seen now and then, while the minor characters in Shakespeare's play are turned into the leads in Stoppard's. Furthermore, when they did the play in New York, they set the staging as though you were looking at the actual Hamlet from the back, from behind the servants' quarters of Elsinore Castle. Rosencrantz and Guildenstern Are Dead can be geometrically modeled as Hamlet after a mirror-image reversal due to a half-rotation in the fourth dimension."
It all sounded slick, but of course Iwas ready, whereas old Stang was taking in the whole thing from scratch, piece by piece, and each piece was a new thing. But he was paying close attention. "Mr. Pilson, this trial balloon you're sending up is bright and gaudy enough, but I doubt it has much lift. The number of serious literary works that match these patterns is few indeed."
"On the contrary," I said firmly, "the concept of one reality lying inside another applies to every literary work. Everything written has at least two, interconnected three-dimensional spaces; the space of the author and the space of his word-constructed work."
I looked around fiercely. "Look! We here, this little discussion between Dr. Stang and myself, our whole university, can only be recorded as words on paper, right? Somebody in another and entirely different three-dimensional space wrote these words, yet both these spaces are totally interconnected, in the same sense that the front and lack spaces of a hypercube are totally connected through the fourth dimension. And they are connected across that new direction I'm calling narrative distance."
I turned a page in my ring binder. "Reversing the location of the two, separate realities along this fourth, or narrative, axis is quite easy," I said, and I began to read aloud to them from a typed page .. .
My daughter looked up from the typescript and shook her head until her long, blonde hair swung like a pendulum. "Hey, Dad, this is heavy stuff! Are you writing popular fiction or apaper for the Journal of Epistemological Thought?"
I shrugged and took a pull on my drink. "It probably won't sell to Penthouse," I said, "but the point is, can you follow it?"
My daughter responded with a thoughtful sip of her gin and tonic and slowly nodded. "Yeh, sort of, I guess. You're saying that since you and I, this conversation, is presented as the author talking about one of his stories with his daughter, we're closer, in this narrative distance sense, to the reader than the people in the seminar story?"
I nodded in an encouraging manner while she bit her lip and stared silently at the ceiling. "Okay," she continued, "then you and I and this conversation are sort of inside the near boundary of a hypercube, the big cube that seems to hold all the others, while the seminar story is inside the little cube that is farther away from reality?"
"Excellent!" I said, applauding with a few hand claps. "But that entire story configuration can undergo a fourth-dimensional rotation giving a reversal along the narrative axis."
My daughter now shook her head with positive motions. "That part I don't understand, and I never saw that Stoppard play you mention in there, either. How can that be done?"
"Easy. This fellow, Pilson, can simply read and represent this account of our discussion of the seminar story as something he wrote to show Professor Stang how two separate realities can be reversed along the narrative-distance axis. Right now, we're nearest to the reader and Pilson and Company are just created, fictional figures that we're dis-
cussing, but if all this stuff I'm saying to you is actually written by Pilson, well, the rotation and reversal occurs and we're suddenly farther out along that axis of narrative distance."
My daughter grinned at that. "Hey, Dad, come on. We really exist." She waved her arms at the room walls. "I mean, it's all really here!"
I smiled back but shook my head. "As Mr. Pilson so astutely noted, that's all just words on paper."
I stopped reading and looked up at Dr. Stang, then said, "I wrote that last week, as a way of showing how this kind of inversion in the fourth, or narrative, dimension can be made, somewhat in the same way that Hamlet diddled with his little play inside the big one to prove a point."
Stang shook his head in angry irritation at my glibness and my obvious preparations. "You're beating me back into a trackless thicket of geometrical balderdash," he said, then turned to sternly face the rest of his class, spread out around the long table. "Well, well. Where are those heartless harpies, usually so eager to pluck the liver out of the tiniest new thought? Ms. Lee, surely you have not bought the snake-oil elixir this dreadful little medicine-show is touting?"
Miss Lee's calm and oval face took on its most serene and impassive expression. "I found the ideas ingenious and challenging," she said firmly, "though I have a weak background in mathematics."
I gave her a quick, tiny smile of thanks. Miss Lee entered each seminar as a skinny, silent lamb, but somehowby the end of our interminable day she was turned into a lion or, more accurately, into a super-cool dragon lady.
Dr. Stang now became petulant and paranoid. "So you're all joining him, eh? Planned it before hand, I suppose? How many of you find this concept of narrative geometry puerile, superficial, and the work of an intellectual charlatan? Raise your hands."
The room remained very still. Stang smiled with the dreadful avidity of a cat holding the best part of a mouse in its fierce mouth. "And how many find it clever, an interesting concept, and probably worthy of further study?"
Six hands went up together and Dr. Stang swallowed his yummy mouse. "Actually," he said in his most benign manner, "I thought it had a certain superficial ingenuity. And scholarship must progress! For our next seminar, in addition to the assigned readings in Piaget, Wittgenstein, Barthes, and Levi-Strauss, each of you five will bring in an essay showing the application of a geometrical concept to a specific literary situation, or the application of a literary situation to a concept of geometry. This will be a cooperative effort. Each will do a different concept. That is, I want five new applications, in addition to any we may discuss here today. Is this all understood?"
A low moan of disgust and dismay swept over the group and a small voice said, "Sir, Thanksgiving is next week."
Stang only snarled irritably. "So what? You have two weeks instead of one to do a decent job. How long does a damned turkey gluttony take, for God's sake, a couple of hours?"
Miss Lee had acknowledged my briefsmile of thanks with a modest relaxation of her almond features and, almost, a nod, but now she turned stiffly to her notes, her expression set in annoyance that my ego trip had probably cost her both sleep and peace of mind. The others around the table gave out the surly grumbles and mutterings of the sort that once surrounded the tumbrels in Paris.
Dr. Stang, though no Tolstoy, was content with only an occasional boot in the face of his serfs. Now he turned to me with almost a Santa Claus look, his voice transformed and avuncular. "Ah yes, Mr. Pilson, a valuable lesson! How readily is the adulation of the multitudes turned to disgust and rejection by the prospect of work. The Geometry of Narrative is like thick, new snow; interesting and rewarding to see from a distance but not so much fun to actually shovel—if I make my various mixed and hidden metaphors clear?"
"Entirely," I said, "but you said five were to do the assignment. Am I to be excluded?"
Stang shook his head. "Not a bit. The others are mere beginners in this new literary science, albeit dedicated and enthusiastic students, as the voting showed. I am therefore allowing them to, let us say, go fishing through Euclid. In your case, I intend to provide a specific and assigned geometrical concept for you to relate to literary works."
I looked at him steadily and drew a deep breath. "Dr. Stang, I'll make you an offer . . . well, more of a wager, I guess."
He nodded warily and I went on. "You pose your geometrical concept and if I can provide the literary counterpart, right here and now, you agreeto let me write the term paper on narrative geometry instead of semiotics. You will be the sole judge."
Stang gave me a dark and grudging nod and some new irritation appeared in his tone. "You have led me to this devil's bargain with skill and daring, Mr. Pilson. Very well, though reluctantly, I agree to your wager. The geometrical system I set for your consideration is the Möebius strip or so-called one-sided surface."
It had been a gamble, but not much of one. My notes on the science-fiction seminar showed that the only two purely geometrical ideas stressed in the stories were four-dimensional Euclidean space and the Möebius band, so I was ready for him. "Here," I said, handing up several sheets from my ring binder, "you can read these. I don't want to hog the spotlight all afternoon, Professor Stang."
My daughter put the manuscript down next to her on the sofa. "Dad, are we farther out in the narrative dimension than the seminar now? If we are, I don't see how I can comment on its story."
I shook my head. "The story is easily rotated and reversed again. After all, there's nothing that prevents me from writing Pilson's dialogue, so that he says he wrote our part. In fact, you've been reading the seminar story yourself, and you know it all came from my typer. I don't see any problem with convincing the reader that this is the outside, or framing, story and the seminar thing is what we're talking about."
"Then," said my daughter, "I think you've got a problem with this new geometrical system, the Möebius strip. The
other examples you used involved solids, spheres inside of spheres and solid boundaries of a hypercube, but this is a surface, a two-dimensional thing."
"As Pilson would explain," I responded, "though I can just as easily do it for him, a Möbius band is a two-dimensional surface, half-twisted in the third dimension, and joined to itself. If you take a three-dimensional, space, say a tube of space, and twist it once in the fourth dimension and then join it to itself, you have a kind of Möbius space. If a person were to traverse that space, two things would happen. They would return to where they started and they would be reversed when they got back, made a mirror-image of themselves. Okay, if a work of fiction can be constructed to logically turn back on itself, to repeat itself, but after the repeat, it has been mirror-imaged, then you have the narrative analogy."
She frowned. "But how can that be done. . . ?" and at that moment several knocks sounded at the front door.
"That must be Frank," said my daughter. "We're going for a pizza and then to the flicks." She jumped up and soon brought a tall, good-looking young man into the room. "This is Frank Pilson, Dad," said my daughter. "He's a Ph.D. student in English Lit."
I shook his hand. "Listen, Mr. Pilson," I said. "You folks have plenty of time. Let me get you a drink and you can read my little story, which might be something right up your alley."
"That's right, Frank," said my daughter, "it's about an English Lit grad seminar," and she handed Pilson the manuscript.
I mixed his drink and set it down nextto him, but he did not take a sip for several minutes, then looked up with a big grin. "Hey, professor, this is great stuff," he said. "Listen, can I get a copy of this? I'd love to try and pull the Geometry of Narrative out of the hat for old man Stang, who runs this completely incomprehensible seminar on useless lit-crit theories."
"You think he wants another useless one?" I asked.
Frank Pilson nodded with enthusiasm. "I'll mousetrap him with it. I can do this stuff. I've read lots more science fiction than Stang, so I'm way ahead on weird geometries."
"I'll send you over a Xerox," I said. "Just don't mention my name to Professor Stang. Since they started cutting off the English Department's legs by attrition and giving us the positions, Dr. Stang has been talking in the faculty senate about a final solution for Engineering and Computer Science. Something involving high levels of radioactivity, nerve gas experiments, and the forced ingestion of PCBs, I think."
Pilson grinned again and nodded. "They sure hate your guts, all right. That must be why they're deconstructing literature. Sort of the trapped fox chewing off its own leg."
My face must have shown puzzlement at this comment, but my daughter spoke with an impatient shake of her head. "Deconstruction, Dad, is some nutty new kind of literary theory. Don't get Frank going on that stuff. He's rabidly against it."
"I like people who are against new
things," I said firmly. "For example,
I positively hate the metric system . . ."
But my daughter was on her feet and
pulling at Frank Pilson's hand. "You two are not going to just sit here and complain about everything. C'mon, Frank, time for pizza."
At this point, return to the beginning of the story, with the words, "The graduate seminar, 'Modern Critical Theories,' (Eng. Lit. 674,3 Cr.) theoretically occupied . . ." and continue reading until you reach the words, spoken by Professor Stang, "Very well, and reluctantly, I agree to your wager. The geometrical system I set for your consideration is the Möbius strip or so-called one-sided surface."
After he read this instruction aloud to us, Dr. Stang peered directly and blankly at me, and I saw that I had finally lost him in my final thicket of narrative geometry. I spoke up in my best exegetical voice.
"Look, the fiction has to loop, since the Möbius space is closed, right? So I write myself into the author's story, get from him the idea, in fact the complete seminar story, of narrative geometry and bring it here to try out on you." I paused and pointed a confident finger at Dr. Stang.
He nodded silently and I went on. "So there are two seminar stories, the one the author wrote and I read when I went to take his daughter on a date, and the one we have all just lived through."
I stared around the table with determination. "But they are the same story! Their congruence completes the Möbius loop in four-space."
Old Stang came right back at me. "And the mirror-image reversal, Mr.
Pilson, as required by the four-dimensional twist in the Möbius space?"
I nodded and grinned in admiration at his quickness. "I instructed you to stop reading before the author's part, the second time around, Dr. Stang. You said then, 'I set for your consideration the Möbius strip . . .' Okay, I've given you a fiction that, as we saw, looped, and you have to admit that at this moment we are much nearer to the reader, in my narrative distance sense, than is the author and his daughter. Yet when the loop was started, when I read the author's story in his home, that part of the fiction was certainly in a nearer narrative space than this one. Now the thing is reversed. My two-narrative fiction has been made a mirror-image of itself."
I let my voice deepen. "Indeed, we may be the first persons to ever traverse a Möbius-space narrative in the entire history of English Literature!"
Professor Stang glanced up at the clock, which showed five-twenty, and when he looked back I saw that he was suddenly tired. He gave me a wan but real smile, which I returned. "I will look forward to your extended disquisition on narrative geometry, Mr. Pilson." He paused and peered with almost a benign grin at the rest of the class. "And to your more modest explorations of this topic."
As we got up to leave he lifted a hand. "Oh, and don't bother about those assigned readings for the next time. Just get your Euclid and show me how Mellors and Lady Chatterly can be understood as similar, even congruent, triangles," and he gave us an almost raffish wink.