.ON THE SUBJECT OF LOVE

"This narrative originally appeared as a chapter in Steven M. Rosen's novel, The Moebius Seed, published by Stillpoint Press in 1985.  Illustrations by Paul Covington"
    

Fool! You fool, you!--a senior struggling to make a respectible graduate school, needing every possible course of substance to shore up your transcript for the physicists at Princeton and Yale and here you are, wasting three perfectly serviceable college credits.
    Why am I sitting here doing this?, Arthur Rosenberg asked himself. I sign up for parapsychology and wind up in arts and crafts.
     I should have known, I really should have known...
     Professor Noel Innerman sat in front of his class, close to the first row of students. On the plastic surface hinged to the arm of his desk-chair were several sheets of blank white paper and a roll of cellophane tape. He was working with a pair of scissors. Every student was similarly equipped and engaged in the identical activity. Students and teacher were cutting out ribbons of paper.
When each participant had snipped off two long, narrow sections, Innerman instructed them softly: "We'll start by making an ordinary ring." He lifted one of his strips, brought the ends together, and fastened them. Again he waited.
      After every student had formed the paper ring, Innerman demonstrated the construction of what he called a "Moebius band."
"Bring the ends of the strip together, just as in making the ring. But before taping them, give one of the ends a half twist; turn it through an angle of 180°"
The instructor stood up and repeated the exercise for everyone to see.
      Now all but two members of the class had successfully fashioned a Moebius strip. Innerman went to the aid of the stragglers, then returned to his place and held up both finished products.
"A cylindrical ring and a Moebius band."
"You still have some paper left that's intact. Take an uncut sheet and notice that it has width and length but of course, not much thickness. We'll disregard the thickness entirely, assume it's negligible. Then the paper surface gives a simple model of a two-dimensional space."
      Innerman put down the ring and its twisted counterpart and raised the paper leaf to the class.
     "Naturally, our space isn't like this one, ours is three-dimensional. Which only means that in our world, you can find three directions to measure in. Measuring is observing, observing is experiencing - it' s nothing more."
     Becoming quite animated now, the teacher moved laterally across the front of the room. He was displaying his model with deliberation but also a springy spontaneity that brought the group's attention fully into focus upon it.
     "Can you imagine your experiences confined to a directional space? Suppose you're a 'Flatlander.' You live in an infinitely thin universe. You're stuck in this surface, so you can move your ruler back and forth or measure up and down, but...?"
     "But no more," said a fellow in the second row. "The third direction couldn't be conceived."
     "Like we can't imagine the fourth," the coed in front of him added.
      "Hey, wait !" Innerman cried comically, feigning chagrin. "You stole my fourth dimension! That was my dramatic climax. Forget what Mindy said, class. We have to get back to Flatland."
      He continued over the subsiding laughter. "Actually, the situation isn't what you might expect, not if you go by the model of Flatland we've started with. There are Flatlanders who seem to lead a purely two-dimensional existence. But others are talking about the higher dimension."
      "How do you know that?" a student asked.
       "Come on, Pat, Flatland is us." The comment came from a lanky biology major in the rear. "It's just an analogy."
     "Yeah," Innerman agreed, addressing himself supportively to Pat Loring. "And you know what Mindy said. Give her credit, even though she upstaged me."
     "Because she mentioned the fourth dimension?" asked Pat.
     "Exactly. I don't have a fourth direction to lay my ruler in, but Mindy spoke about it, if only to say that it couldn't be imagined. If her experiences were strictly three-dimensional, could she even begin to talk about the fourth?"
     Innerman said.no more. He hoped the students would draw the next conclusion on their own. But their responses were not forthcoming.
     Gripping the paper at both ends, he pulled it taut to accentuate its level two-dimensionality. "Can this be the final word on what a Flatlander might experience?"
     A moment later, a new voice was heard. A freshman haltingly suggested that the Flatland model must be wrong. His thought was completed by the aspiring biologist. "If Flatlanders can talk about the third dimension, Flatland can't really be completely flat!"
    "Yes. That's the point. But I want to get personal about Flatland." Innerman went to his chair with the blank sheet of paper, sat down and started to draw. "Say I'm a lover...Hot blooded...Very passionate. Look what happens to me in Flatland."
      "Is that love?" Noel asked, raising his voice above the mirth.
      "Let's have a drawing contest. Free lunch for the best pair of  lovers. But if you decide to enter, please go easy on the anatomy. No hard-core porno because I get embarrassed and besides, I'd like to keep my job here."  Innerman distributed paper to the gleeful group. "You'll have about five minutes...It's a game. Be playful. But be serious too, all right? We could make a nice point."
     The class went with him, despite some restiveness and snickering. When the last request for extra time had been honored, he collected the work and examined each submission. It was not before a second perusal of the entire lot that he lifted his selection into view.
"How about this one?"
  "What is it?" someone sardonically commented.
."Everything.my masterpiece is not," replied Noel.
Mindy Harris now observed, "They're not in love with each other, they look like they are each other," and Innerman delightedly applauded her remark.
     "But," he added, "that can't happen in Flatland."
     "Because it would make no sense. I can't be you if I'm me."
..
     Arthur Rosenberg's declaration of "self-evident truth" launched a discussion of logic that led them quickly to 'the first law of Flatland:
   A = A;  A.is not = not-A
     A thing is equal to itself; it cannot be other than what it is.
In terms of space, it cannot be other than where. it is--no person or object can occupy more than a single location at a given time, and matter cannot pass through matter (at least not without making a bloody mess).
     "That's what my picture showed," said Noel. "Matter trying to pass through matter and being frustrated in the attempt. This picture shows something else." He held it before them again, then turned it around for his own reappraisal. "But how can it happen in Flatland? Authentic love isn't possible in Flatland. .Can we occupy each other's space, share identity, interpenetrate?"
       "We can't, but we do." The biology major was emphatic.
     "Thank God we do. I'd go out of my gourd if my love life always resembled the professor's picture."
     "It doesn't have to make logical sense," Mindy interjected.
     "Maybe you can't explain it. But if it happens. to you, you don't have to."
     "Tell us about it, Mindy."
     "It's over your head," she told the heckler who sat behind her.
.
     The next person to reflect on the winning entry was older than the others. She spoke in a tremulous half-whisper, noting that this kind of "love" wasn't limited to sexual relations. She and her husband had been married for twenty-five years and a mental bond had developed between them. Each frequently knew before-hand what the other was going to say or do. They shared each other's thoughts, even shared dreams. What evidence did she have? The evidence of her lived experience. She didn't expect anyone who had not lived it to accept or believe it.
     "Which is just the trouble," retorted Arthur Rosenberg.
     "I haven't lived it, though I'm taking this course. So what should 1 believe? To me, it could be a string of coincidences or a lot of distortion and wishful thinking. When people live together, they learn a lot about each other. They can read the smallest signs and not even know they're doing it.' Can't be love? It doesn't have to be mysterious or illogical." 
     "Mm, but Greta's kind of 'love' is found somewhere else,"
      Noel said. "In the last place you'd expect it, as a matter of fact--in the physicist's laboratory!"
     Noel went to the blackboard.
     "They call it 'non-local behavior.' It never seemed to happen a hundred years ago, when scientists could only study the more or less large-scale world."
     "Didn't they have microscopes then?" a student asked rhetorically.
     "Right. But the cells and crystals that were examined microscopically are unimaginably immense compared to what modern physicists now have under "scrutiny. They're taking apart the stuff the world is made of. Atoms, subatomic particles...and this is where things begin getting bizarre."
     Chalk dots were put on the board, one at each end.
     "Two well-separated subatomic particles; electrons, let's say. Must they be two? Is there any way they could be the same particle?"
     "They could be the same one at two different times," Pat Loring suggested.
     "Okay, but we'll assume that we're seeing an instantaneous picture. "
      "Then how could it be?"
.-
      "By' non-local behavior.'
      "Flatland physicists are tearing out their hair! It seems absurd, but there's no escaping it. Decades of hard thinking and experimenting tell them that before a particle is observed, it must exist in a peculiar state, in effect, be in more than one place at a given time." Innerman pointed from one dot of chalk to the other. "Conventional wisdom says these have to be different entities. Yet the finest minds of the century insist that, under certain circumstances, they're also one and the same."
     "Now you really lost me," said a student near the window, and another closed his notebook and left the room. Mindy Harris appealed to her classmates: "It's like the lovers. You and your lover go into a special space. In that moment, you're sharing identi ties."
     Responding to Mindy, Innerman drew a pair of symbols around the chalk points:
     "'Special space' is right, is very accurate. Particles cannot be intimate in Flatspace."
     "Because A would have to equal not-A," said Paul Flax, the biology student, "which is against the logic of Flatland~"
    There were those in the group who wondered how the new physics could be valid if it were not logical. Flax answered that all logic was not Flatland logic,. and one of his supporters saw the need for a new logic. There was no going back, they agreed.
     "Not after seventy-five years of Einstein, Planck, Heisenberg and the rest," affirmed Innerman.
      "Then why is this class the first we hear of it?" Rosenberg's misgivings drew nods from several other students, but Paul Flax was impatient.
       "Because there's an Establishment, dummy. The vested interests depend on your ignorance."
       "That's paranoid crap."
       "Hold it a second, fellas. It doesn't have to be that sinister. A lag is inevitable--call it inertia, a natural resistance to change. But I think the incubation period is just about over.I'm predicting that soon,a lot of people will start to realize that Flatland isn't really so flat, that genuine love is possible."
     Innerman returned to his desk and transposed the blackboard illustrations onto paper. Then he demonstrated the union of sexual  opposites.- Flatland was folded over on itself:

      "A similar example was given by a Princeton physicist named Wheeler. He showed how 'wickedly intimate' things can get in the microcosm, where space can curve back on itself. Notice something: as soon as I start bending the two-dimensional model, I'm making use of the dimension perpendicular to Flatland--the higher, third dimension. "
     Laying his latest specimen aside, the teacher fished through the pile of papers on the desk and retrieved his first illustration on the subject of love.
     "That's as intimate as lovers can be in a flat world."
     The remedy was now obvious to everyone. Innerman put the suffering twosome out of their misery:

With an unexpected forcefulness, he spoke again: "There's a point to all this paper-folding that I'd underline in red. It has to do with separation and true union. Suppose a rendezvous is planned. The would-be lovers live in distant cities. One must take a plane, the other a train and a bus. As the meeting time draws near, the distance between them is closed and in the final scene, they leap across a sunlit field of flowers and into each other's arms. Nevertheless, if they allow the space they occupy to remain flat, they can't be truly united, they won't come to share identity in a fundamental way--they should have saved themselves the fare "because, in the important sense, they'll be as far apart as they were before they left.
    "There's only one way for meaningful intercourse to occur: by a folding of flat-space through the higher dimension of space.
     The real separation, the real obstacle to communion is not a given distance in flat-space but the inaccessibility of the higher space. And when movement in the higher direction becomes possible, there can be core-to-core communication --love."
     Moments of silence followed the completion of Innerman's thought. The vacuum vias filled at last by a student wanting clarification on the folding of space.  
     "How is it done?"
      Noel sighed. "Not quite like in my paper-folding, huh? Yes, I agree. A giant from another world does not come along and fold our space the way I folded Flatland. It's not that simple. Or maybe, in a way, it's actually simpler, because the 'giant' isn't needed. "
 Innerman was busy again with paper, pencil and scissors.

He sketched a pair of faces in profile, cut them out and laid them on an uncut sheet. "Behold my final rendition of lovers in Flatland."

     "What is it that's thwarting them...? Not the distance between them in the two dimensional surface, is it?"
    "It's the higher dimension,'! a student asserted.
..
     "Right. And if the third dimension is truly the barrier, there's a better way to show it." Noel taped down the feminine cutout, then removed the masculine one and fastened it to the other side of the paper. Holding the sheet above his head, he turned it to and fro to expose the lovelorn figures alternately. "They're on opposite sides of Flatland now. The only way for them to commune is by moving in the higher direction from one side of space to the other...which they cannot do."
       Innerman noticed Pat Loring shaking her head in the negative and invited her to comment.
      "I don't understand why they can't just come around to each other.."
       "You mean leave their surfaces?"
      "I guess they would have to."

     "They could...," Noel peeled the tape from the male profile and lifted it, "...but it wouldn't be natural. See why?"
   Getting no reply, he retaped the profile and hoisted the paper aloft once more.    
     'What is this thing?..Isn't it Flatland?"
     "Yes."
      "And what does Flatland represent?"
     Pat responded tentatively: "Nature?"
     "Yes! For the moment, it's our model. If you believe the model, you can't believe in love."
      Greta Jurgens raised her hand. "Why must I worry about believing and models and nature when love is something I experience?

      "A hard question. Experiencing does beat modelling, if you're not kidding yourself about your experience. Greta, I don't think you are."
      Noel stood beside his desk-chair, gazing at the tangle of drawings, constructions, and paper cuttings, some of which had fallen onto the seat. His face softened in a wistful smile. Now he took the refuse pail and brought it beneath the edge of the desk surface, cocking his open hand as if about to sweep the surface clean. But there the action froze. "You know why I won't do it? Because I buy that sappy old song about the world needing 'love, sweet love,' needing it now, and for everyone, not just for some.
    "But, Greta, a model will .operate. There'll always be a set of assumptions, hidden perhaps, yet working all the time.
Our model does affect our experiences. For the vast majority of people, the range of experiencing is drastically cut down. The others are pariahs as soon as they become too open and honest about themselves."
    "I thought we switched to a different model," a student said, "--weird acting particles and the like." In the ensuing discussion, the students saw that the process had only just begun, but that a real potential exists for new vistas of experience to be unraveled. After all, modelling is experiencing, though of a limited kind. So for many individuals, the first step toward experiencing love might be an intellectual one. 
     "It was for me," said Noel. "At the moment, of course, the logic of love isn't that widely understood. Love is 'supernatural' then. And if you don't reject it, you'll have to imagine mysterious forces operating outside of nature, like a super-dimensional giant folding your world, or imagine that somehow you can detach yourself from your space and leap out into the void.
     "It gets much simpler when the logic is seen, when the model of nature is extended. Actions in or from the 'void' become unnecessary for transforming the space of your experience. The simplified model of space is one in which space can fold or transform itself." The paper with the taped-on profile was again displayed. "But this thing isn't going to fold itself."  And if lovers find themselves on opposite sides of it, there'll be no natural way for them to merge identities, because nature is two-sided in this Flatland model."
-
     Innerman rummaged through his paper jungle and came up with the first construction they had done, the ordinary ring.
     "Here's another two-sided surface."
The students were asked to make a pair of lovers for their own ring models and stand them on opposite sides.
"Like this":
  "The lovers go round and round but can never come together .in a natural way. They might like to fly to each other, to leave the surface of the ring and travel around through the higher dimension. But in this illustration, the ring is their reality, total and exclusive. And it's a   two sided reality; the sides are mathematically segregated from each other. So any thought of leaving one side and travelling to the other has to be a flight of fancy."
     Grinning, Noel put down the ring and squatted beside his desk-chair. He began tidying up. Stray scraps of paper were retrieved from the seat and the floor and deposited in the waste basket. He sorted through the unruly accumulation of drawings next, separating his own work from the contest submissions,
arranging the latter in a neat pile with the winning entry on top. When Innerman finally rose to face the class, he was holding the twisted counterpart of 'the ordinary ring.
     "The peculiar looking Moebius band you made before happens to be a one-sided surface. Mathematicians call it that and that's why it looks so peculiar--opposite sides of the Moebius strip don't conform to normal expectations. Instead of remaining distinct as they do in the ordinary ring, they twist into each other to become one."
     "Sounds like good news for the lovers," commented Paul Flax.
     "You're so right. But try the experiment yourselves."
      They played with the Moebius model for several minutes and were amused and befuddled. Manipulating little paper profiles on that eccentrically shaped surface was an awkward operation. A few students laughingly resigned; others continued the struggle with no definite results. In the end, Arthur Rosenberg was the one to make the point with greatest clarity: "If you send the figures out in opposite directions, they come around to meet each other."
-
"Wonderful!" cried Noel. "Opposites.do attract. The right-facing male and left-facing female get superimposed. They embrace each other, come to share each other's identity. And no supernatural force is needed to fold them together because they interact in a space that--in effect--folds itself. Sublimely romantic, but also realistic. To love, you don't have to leave the Moebius world--you simply follow its natural contour."
     "And you go through a higher dimension?" Rosenberg wanted to know.
Innerman used his last leaf of blank paper to demonstrate.  He laid the untwisted ring edgewise on the sheet and, moving  his pen along the edge, traced out a path:

     "A complete record of a Flatland event," said Noel, raising into open view the circle he had produced. "Following the bottom edge of the ring gives an unbroken orbit in two-dimensional space. Try it with the Moebius band."
     They saw immediately that it could not be done. The reason was obvious. Travelling.along the edge of the Moebius surface means being lifted out of Flatland in the third direction. Still, one fellow couldn't comprehend vlhat all this had to do with parapsychology, the course for which he had registered.
     It has to do with love, explained another; a psychical experience is a kind of love.
     "Yes, genuine love," affirmed Innerman, "not mechanical pretenses. Telepathy is the clearest example, it's an intimate marriage of minds. But every form of psi is a form of love and there's a level of extra-sensory awareness that is the very
essence of love."
    Noel hastily marked a small "X" in the center of the circular Flatland orbit. "Here I am. Isolated. Alone. Woefully alienated. But if I could only deepen my awareness enough, I'd be like this..."
     He crumpled up the paper and compressed it into a ball.
"...at one with my universe, as though I'd swallowed it. Totally connected, not just to one other mind or objective event--with all of it. Call it 'Nirvana' or 'cosmic consciousness.' The name you give the experience isn't important. You have to experience  it. That's love, a joyous, unadulterated kind of love."
The class was quiet for a time. Then Arthur Rosenberg offered his reaction. "Very clever. I'm enjoying myself."
     "But no telepathic flashes and no Nirvana," said Noel, and Arthur nodded wryly. "Because we've only been modeling, working with what's easy for us,- with what we can see with our eyes--the second and third dimensions of space, instead of the fourth."
     "The fourth dimension is Nirvana, then," Mindy Harris observed.
      "Yes, if you experience it totally. Experience the fourth dimension to a lesser extent and it might show up as telepathy or clairvoyance. And I believe those physicists, with their strange little particles, also have the fourth dimension to deal with. "
      Innerman was sensing a certain amount of resistance in the group. "I know. It's hard to take in all at once. But please listen: the fourth dimension is just the part of your experiencing that isn't seeing. All seeing is experiencing, but not all experiencing is seeing--nor hearing, tasting, or touching, for that matter."
     "Or smelling," said Mindy. "Or smelling," Noel said, returning her smile warmly.
     Now he hooked his Moebius specimen onto the end of a pencil and extended it for the class to inspect. "Here. You're seeing the natural way to enter another dimension--by a Moebius-type twist. You can see it because the transition it shows is only from the second dimension to the third, and human seeing is already three-dimensional."
     Pat Loring: "But if I were a Flatlander.. ."
     Paul Flax: "If you were a Flatlander, you'd only see in two dimensions."
     Arthur Rosenberg: "You would never be able to see a Moebius twist. "
     Mindy Harris: "Yet you should be able to experience it.  I mean, if your space isn't really flat, if it does have the Moebius curve."
     A nursing student, entering the discussion for the first time: "Wait though. That kind of experience is rare. Wouldn't it be a rare exception?"
     Mindy: "I don't think it's so rare."
     Paul: "Rare enough--she's got a point. If space has a twist, it's usually lost on us."
     Arthur: "You wouldn't notice the curve if it was very gradual. I'm thinking about traveling in a plane, say from New York to Tokyo. It might seem that you're traveling in level flight the entire time, but actually you've gone a_round the world."
     Paul: "You're not aware of the curve because you're awareness covers only one small section of the great big globe."
     Arthur: "Yes, only one section at a time. Covering a short distance on a large sphere gives the same impression as covering any distance on a flat surface. To notice the curving  of space, you'd have to expand your horizon."
of space, you would have to expand your horizon."
     Innerman vias beaming. "For a change, I'm speechless...well, almost." He pointed with one hand to the other, which now held the Moebius band.
     "You see my thumb and forefinger. They're on opposite sides of the strip. They cover just a small portion of the total length of the surface. At that or any local cross-section, the Moebius strip is, no different from the two-sided ring or flat sheet of paper. Limit the Flatlander's experiencing in that way and the Moebius nature of his world will be hidden from him. But if his horizon is expanded, his awareness stretched along the length of the surface, he will experience opposite sides becoming one side--the twist in the higher direction.
    "And if I--three-dimensional Noel Innerman--wanted to sample the fourth dimension beyond my seeing, that's the way I'd have to stretch my awareness. I'd enter an altered state of consciousness and it would be equivalent to extending myself along our Moebius twist--there has to be a twist at our level.. If love is real, if it's natural and genuine, there has to be a twist."
     Innerman glanced at his watch and was startled. The period had come to an end.   
     As the students were heading for the door, Noel dashed from desk to desk, shoveling paper cuttings into the refuse pail.
..
..