ALICE IN THE LOOKING GLASS OF ART By John Briggs Western Connecticut State University Published in Lewis Carroll's Lost Quantum Diaries, William Shanley, ed. Werner Locher (Germany), 1999. A strange house, she decided, but after all these curious journeys, as familiar as anyplace. Alice wandered down the hallway into a dark, friendly parlor. Dusty light beams splayed through the gaps in half-drawn curtains. Two walls towered with venerable books. On another wall, behind a piano, glowed a chaotic collection of paintings. A fire snapped and sighed in the hearth. On the mantle over it a fat pussycat dozed in front of a mirror. The cat didn't belong to Alice but it might as well have because when it stood up, arched its back, stretched out its paws and padded off through the glass she climbed onto the mantle and followed it. "I'm always doing odd things all over again," she thought to herself as first her hand and then her arm and then her whole body melted through the silvereen surface, causing her to slide rather precariously off the mantle into a pool of reversal and otherness. She landed with a thud against the Otherside hearth. "Goodness, don't hurt yourself," she heard a reassuringly familiar voice. She immediately recognized the young man bending over her as Rev. Dodgson. He looked just as fervent and shy as the days when he'd entranced her and her sisters with the Wonderland stories under the hayrick in Oxford. It felt like she hadn't seen him for a century or more, though it can't have been that long. "I'm fine, so far I never get really hurt on these adventures you started me on, just confused. Where in the dickens have I landed now, can you tell me?" She stood up and looked around her. On closer view, this room on the Otherside looked entirely different from the parlor reflected in the looking glass above the mantle. Instead of containing stuffed chairs, library books, paintings and a piano, the space was entirely filled with mirrors. Small baroque mirrors, large French Empire mirrors, round Chinese mirrors, mirrors in the shapes of globes and triangles, mirrors stacked upon mirrors, mirrors suspended from mirrors. Even the room's walls were mirrors. So many mirrors she couldn't tell the room's size or shape. But the most the curious thing was that each of the mirrors seemed to be reflecting an object or scene which was no where in sight. In one small hand mirror hanging by a cord from the frame of a full length mirror was a miniature and somehow distorted reflection of the scene in the parlor where she'd begun this new adventure. "Where's that pussycat?" "Oh, the pussycat's from another story," her friend Rev. Dodgson assured her. "I'm sure he'll turn up. Let me introduce you to my colleague here." It was at that point that she realized there was another figure around in the room, a thin, tall no longer young fellow with a mustache. "This is Professor Sggirb?" "Sggirb? It sounds like something that comes out of you when you slip on the ice." "Yes, quite, in a way slipping is Professor Sggirb's specialty. You see, Alice, my dear, you've been hearing from scientists and of course I'm a mathematician, so I've asked Professor Sqqirb to talk to us about art. He advises me that it's slippery subject." "Slippery?" Alice wondered, "I hope you don't mean like a worm." The Professor cleared his throat. She soon realized he had a low voice, barely audible, and she had to strain to piece together what he was saying across gaps of words she couldn't quite make out. "Not exactly like a worm, more like the slip of the tongue or the slip of a thought, or a lost key that has just slipped out of reach. I'm sure you know what I mean. You remember the difficulties you had with theJabberwocky poem the White Knight recited and the one Tweedledee sang, The Walrus and the Carpenter, and the one your friend Rev. Dodgson wrote that you liked so much, The Hunting of the Snark. Just to name three." "It's true, I never did totally fancy the explanations I heard for those poems. There always seemed a lot more to them--or less," Alice said thinking about all the strange creatures she had gotten poetry instruction from over the years. "That's what I mean by art being slippery. Rev. Dodgson here has asked me to show you how that slipperiness might be related to the quantum slipperiness people have been telling you about lately." "I did think Humpty Dumpty's explanation of ''Twas brillig, and the slithy toves' was illuminating, however," Alice continued her thought. "Perhaps we should sit down for a bit," Rev. Dodgson suggested. "Good idea. How about over here," Professor Sggirb said, turning to his right and plunging headlong through the surface of a full length mirror. As the professor walked away on the Otherside, Alice saw that the mirror contained the reflection of a business establishment on a London street. The sign over the door said "Scrooge and Marley." The air fluctuated with snow falling onto the street. Professor Sggirb pulled a skeleton key from his pocket and opened the door. She and Rev. Dodgson followed. Inside the old office, they brushed snow off their clothes. "Don't worry," Sggirb said. "No one toiling away at the moment. I'm sure you recognize where we are." "It's Mr. Dickens' A Christmas Carol. One of my favorite stories." Rev. Dodgson pulled out some chairs, fetched the scuttle and began stoking the coal fire in the grate. "Mr. Scrooge won't like that; coal's expensive," Alice cautioned. "What Scrooge doesn't know about won't hurt him," Rev. Dodgson replied, then laughed, "Or perhaps it will. Wasn't that what the ghosts of Christmases tried to tell him? Anyway, whether Scrooge likes it or not, I have Mr. Dickens' permission as a fellow author to utilize these premises, and he owns the building." "Well, I do think it's rather daring of you, for such an awfully careful man," Alice teased. Dodgson blushed. Meanwhile, Professor Sggirb had alighted on the tall stool behind the tall clerk's desk, presumably Bob Cratchet's. Alice decided that learning about art was rather fun so far, but she couldn't imagine how it fitted into all these scientific peculiarities she'd been learning about lately. "I was just getting to that," Professor Sggirb said as if reading her mind. "Remember your visit to Professor Bohm's universe?" "I certainly do. That one gave me a hair-raising cab ride through New York City. At least I thought it was New York. But, then again, are we really in London now? When you add your imagination to the picture, geography becomes such a muddle." Sggirb continued and Alice had to lean forward in her chair to catch his words. "Professor Bohm was a very brilliant and subtle fellow. He invented several different ways to talk about the quantum world. One of them was the 'quantum potential' idea you heard about on your cab ride. Let me tell you about another. As you know, in Professor Bohm's universe everything is a part of everything, 'enfolded' in everything. One of the images he used to explain how the enfoldment works is the hologram." "Yes, the yellow cab mentioned holograms but I didn't ask him what they are because he was in such a state and the way he drove was upsetting my stomach." "It so happens I have a hologram with me." Sggirb climbed down from the stool and opened a moldy leather suitcase or portmanteau which Alice now realized he'd been lugging since they left the room full of mirrors. As he rummaged around in the valise he reminded Alice of a long-bodied insect with a mustache. Finally he held up a piece of glass. It looked like the surface of a pond where someone had thrown a handful of pebbles, causing overlapping rings that are bumping into each other. "There's a picture here," Sggirb explained. "You have better eyesight than I do. All I see are rings." "Wait a moment." Sggirb spidered around propping the edge of the glass against Cratchet's inkwell and rigging up what he called "my futuristic battery-powered laser." Then he clicked on his laser, using it to aim a beam of light through the glass plate. Magically, a three dimensional image of the White Rabbit peering at his pocketwatch appeared in Rev. Dodgson's lap. "You see, the plate with the rings on it records an interference pattern of light. That pattern enfolds information about what the White Rabbit looked like when a holographic surveillance camera took his picture. Now here's the interesting part." Sggirb wrapped the glass plate in a cloth, took a hammer out of his portmanteau, and tapped the glass, breaking it into several pieces. Then he mounted one of the plate's fragments against the inkwell and shinned the laser beam through it. The image of the White Rabbit appeared again in Rev. Dodgson's lap, though a bit dimmer and from a slightly different angle. "You see," Sggirb explained. "It turns out that information about the whole image of Mr. Rabbit is enfolded on every part of the plate. So in a hologram each part contains the whole. Professor Bohm showed that each quantum particle also contains an image of the whole universe. Remember that in Quantumland a particle is also a wave. So in Professor Bohm's view each particle is an interference pattern containing a record of all the other particles it has met in its lifetime and also all the particles those particles met in their lifetimes." "That's a lot of information. That's even more complicated than all these adventures Rev. Dodgson invents for me to get into." Here Alice shot the Reverend a look that again made him blush. "Remember, also," Sggirb persisted, "that you're totally made up of quantum particles, so you contain that information, too, in billions and billions of varieties." "So I'm like that room full of mirrors." "Yes, in a way. There's a very old saying from one of India's sacred books, The Flower Garland Sutra, which is very much like Professor Bohm's idea. It says, 'In the heaven of Indra, there is said to be a network of pearls, so arranged that if you look at one you see all the others reflected in it. In the same way each object in the world is not merely itself but involves every other object, and in fact is every other object.'" "That last bit sounds a little like chaos and fractals." "Excellent," Sggirb said, "Now you've read my mind. What do you know about fractals?" "Weelll." Alice wrinkled her brow trying to remember what that dynamical fellow named Strange Attractor had shown her. "I remember that chaos is an idea about how things go in the large scale world we live in, while the quantum is about the very small world we can't see. I remember that chaos means systems that are ghastly complicated and unpredictable, such as the weather and waves in the ocean. When weather and waves work away at a coastline for a long time, they crumble it up to make a fractal. With a fractal the small parts look like the bigger parts and also like the whole fractal." "Splendid. I'd say you remembered quite a bit." "Isn't she the most bright and lovely thing," Rev. Dodgson blurted out with such emotion that it gave a brief pause to the conversation. Then Sggirb resumed and Alice had to lean forward to catch the words. "Nature is full of fractals where the small mirrors the large. The shape of a tree is mirrored in its twigs; the shapes of the bronchial tubes and air sacks in your lungs are similar at different scales; even the billows of clouds look similar on the small scales as they do on the large ones. That's because in systems on the edge of chaos--and those are almost all the systems in nature--everything is connected by feedback to everything else. The feedback insures that things in nature show a 'self-similarity.' So all living things from ants to antelopes have a similarity even though in many other respects they're different." "Like the interference pattern of each photon is both different and similar and they're all connected to each other." "Right." "I don't mean to be rude, professor. But what does this have to do with art?" Rev. Dodgson laughed conspiratorially at the impertinence of his creation. Alice gave him a quick look with her wide eyes and he suddenly wished they were alone, or that he were alone in his rooms so he could write her that way. "I'll show you," Sggirb said. "Follow me." He made his way into Scrooge's inner office and opened the door of a tall wooden locker usually filled with certain counting-house forms but in this circumstance containing--the reader has probably guessed it--a mirror. Professor Sggirb stuck his arm straight into the mirror and followed it with his right leg. In an instant he was swallowed up by the pool of silver. Alice and Rev. Dodgson followed behind. Alice felt a peculiar buzz all over as she passed through. On the other side of Scrooge's mirror was what appeared to be a vast museum containing every conceivable variety and type of art: Egyptian sphinxes, Impressionist landscapes, Japanese bird paintings, portraits, Neolithic cave drawings of bison, all kinds of photographs. She recognized some of the paintings as one's she had seen in the dark, friendly parlor where this latest adventure began. "Actually, we're now in a virtual museum," Sggirb explained swinging his arm around like an insect appendage. "We've stepped into cyberspace. I won't bother to explain what that is. But for our purposes it means that replicas of all these artworks can be brought together in the same place and time. The important thing for us is the artworks themselves. That's what we've come to look at. We could examine any of them and find some form of what I want to show you, but let's stop at this one." They gathered in front of a paper scroll about three feet long and 15 inches wide with a figure drawn in ink. The title under it said Man with Umbrella, after kao Ch'i-p'ei (AD 1672?-1734). "What are we here for?" Alice inquired. "To see the fractal and holographic nature of this drawing." "Oh, that's all. I was sure it was to see the quantumchaotical nature of the Reverend's cerebrated codpiece." The Reverend laughed but Sggirb just smiled, not quite clear that she was having him on. Alice looked at the scroll for a while. She liked it immensely, though she didn't see anything particularly chaotic or quantum about it. The man crossing the bridge seemed so actual, even though he was only a drawing. She felt she knew exactly what he was going through. "What we're looking at in a work of art is not exactly the same kind of order we find in fractals and holograms, but it's similar. I call it the order of 'reflectaphors.'" "'Reflectaphors.' That word sounds strange, but I feel like I recognize it." "It's a portmanteau word," Rev. Dodgson exclaimed. "Right," said Sggirb. "It's a word made by blending pieces of other words together. This one is a rather obvious and academical portmanteau compared to yours, Reverend, which are wonderfully poetic. My word's just made out of combining the words 'metaphor' and 'reflection.' But maybe it will help us understand something. Alice, do you see the umbrella the man on the bridge is holding? How would you describe it?" "Humm. I suppose I'd say it's a triangle with a little top knot." "Good. Now, if I were to tell you that there are other shapes like this in the painting, could you find them? You, too, Reverend. But this isn't a game. The other versions of the shape are subtle and they work together to give the painting a mysterious movement and depth." They looked at the drawing a while and then Alice said, "Is that one, the hat on the man's back? It's a bit like a soggy triangle with a topknot." "Goodness," said Rev. Dodgson, "So it is. And if you trace out these rather darker lines from the man's shoulder, down his back and right leg and up to his armpit you have most of another soggy triangle. The little ink spot on the buttox is a variation of the topknot." "And there are triangles in his trouser legs." "And there's a little one under his armpit." They went on for several minutes discovering other implicit variations of the umbrella shape. It was Rev. Dodgson, the mathematician, who noticed that the drawing seemed to contain a tension between Euclidean triangles represented by the umbrella and Riemannian triangles--triangles that have rounded sides because they are drawn on the surface of a sphere. "The hat is a kind of Riemannian triangle," said the Reverend. "Look at the bridge," Alice said, "If we take Rev. Dodgson seriously (but I should never take him too seriously), the top edge is Euclidean and the bottom edge is Riemannian, and the man crossing it is like a big topknot. This is a fun game. It's a great puzzle." Sggirb harumphed and his voice was more audible than usual. "Sorry, as I said, it's not a game. I only wanted to suggest there's an order going on here that looks something like the order of holographic quanta and fractals. Reflectaphors go much deeper." "Why do you call them reflectaphors?" Alice asked. "In a conventional metaphor two things are compared which you ordinarily wouldn't think of joining or juxtaposing. The two things reflect each other but they also go very strangely beyond the reflection because they're also unlike each other." "Such as my portmanteau word, 'slithy' in 'slithy toves'," The Reverend put in. "Exactly. If I remember Humpty Dumpty's explanation correctly 'slithy' is a combination of 'lithe and slimy.' 'Lithe' Dumpty explained, 'means the same as active.' But of course there's much more to it. 'Slithy' sounds like a lot of things. It's meaning is poetic, slippery. You almost know what it means, but you can't pin it down. It seems quite vivid and clear, but it's a mystery, too. So it gives you a little jolt like overturning a rock and finding a bright blue and yellow worm underneath. The purpose of every literary metaphor is the creation of life, or something very much like blue and yellow worms, in all their precise vividness and unknowableness." "Yes, that's it," the Reverend agreed. "That's what I wanted to do when I made Alice." This time the Reverend blushed even before Alice's eyes turned to him. "Puns, portmanteau words, irony, similes, literary characters--all of these juxtapose things which reflect each other in a way that challenges how our mind organizes the world. They clue us in that reality is far richer than our explanations of it. Now, I'd like to recite a reflectaphoric image made by Wallace Stevens, an American poet. He wrote these lines many years after Rev. Dodgson and Alice Liddell, the little girl who was the model for you, were no longer alive." "I'm very sorry to hear that Rev. Dodgson is no longer alive. I suppose that means he's imaginary like me. Which means we can be anything we want now, doesn't it?" "Before you two get carried away, let me give you the lines," Sggirb intervened. The two leaned forward, but the professor's loud voice knocked them back.   Among twenty snowy mountains The only moving thing Was the eye of the blackbird.   "That's breathtaking, said Alice. "Well I can certainly see contrasts. Those mountains are huge and solid and white and unmoving and there are twenty of them. The blackbird's eye is small, quick moving, really black, and it's the only thing living." "And?" "Well, it does seem like something's going on in the picture. I can't tell whether it's something marvelous or ominous or just everyday. There's just a strong impression that something's implied, but I can't say what it is." "So there's a feeling of vivid meaning that's impossible to paraphrase." "It's a kind of is-ness in the picture." "That's it. A great novelist said that in her work she was trying to describe 'moments of being.'" "And being has the mysterious order to it," the Reverend Dodgson assured them. "But so does nonbeing, according to the Buddhists," said Sggirb, sawing the air with his stalk-like arms. "And maybe being and nonbeing, and emptiness and fullness, are like the eye of the blackbird and the twenty snowy mountains. They're both incredibly different and somehow the same." "But what about all those different kinds of triangles in the Chinese drawing?" "I think they are there because the mind is tuning into that mysterious order, the reflectaphoric order, in which different things are the same." "Whose mind, professor?" "The mind of the artist, first, and then our minds as we view the drawing. You're both familiar with Beethoven's Fifth symphony. Remember how the first measures go. Da Da Da Da, Da Da Da Da (lower). Beethoven establishes a pattern in the first measure and then juxtaposes it to the slight variation in the second measure. Then he keeps juxtaposing variations. Each time our mind expects to hear the pattern again, and it does, but we're also continually surprised because of the way the pattern is varied. Even if you've heard the piece many times before you're surprised. Even if you've read the blackbird lines many times before, the reflectaphoric contrasts and the implied similarity keep them moving. Encountering reflectaphors in art is like watching a fish swimming around on the bottom of a pool. There's a pattern there that's varied in a way that's coherent but always surprising because the movement is made by something alive." "So the triangle patterns are reflectaphors that are part of what's making the man on the bridge seem alive." "Yes, it's because of what happens to our minds in the gap." "What gap, professor?" "When you reflectaphorically juxtapose one thing to another, we see the two things are related but we can't fit the connection into our familiar scheme of things. The fact that the items are both simultaneously similar and different creates a gap. The gaps between the terms of reflectaphors put us in touch with that unspeakable order of being (or perhaps it's nonbeing)--the order that permeates everything but is always deeper than what you can say about it" "It's the blackbird's eye in the snowy landscape." "Yes. Juxtaposing that eye to the twenty snowy mountains creates the gap. That's what reflectaphors do. They make gaps. Or maybe they reveal the gaps that exist all over the place in our knowledge about things. Art helps us notice them. But reflectaphors don't always have to have two or more explicit terms to make the gap." Alice looked puzzled. "Look at our man on the bridge. How would you describe the man's facial expression and his attitude as he's crossing the bridge." "I'd say he looks like the wind is blowing and he's hunched over against it." "Maybe he's bent over because he's tired. He looks like a determined fellow," The Reverend said. "I think he looks a bit sour." "Well, I can see that, Alice," the Reverend said, "but he also seems like he's thinking about something he has ahead of him." "Or something he's coming from," Alice said, reversing her position. "And look at all that space on the scroll above him. He looks like one lone individual moving in all the vast space of the universe." "But I think he looks like he's going off to meet people." "Actually he looks like me after a long day of reading my students' math papers." "Or me trying to get through some of these adventures." Sggirb interrupted them. "You see? There are lots of things we could say about the man, and some of them would be logically contradictory. But they wouldn't be contradictory in terms of the picture. Each thing we could say would touch on some aspect, but nothing we could say would ever come close to saying who or what this man on the bridge is. He's a one-term reflectaphor. He's like something or he is something unstated; maybe we could even conclude that in some subtle way he's like or he is everything. He's a mirror. What's he reflecting?" "I'll be turned to soup if I know," Alice said. "A reflection of X," the professor proclaimed with triumphant obscurity. "Between him and what he's reflecting lies the reflectaphoric gap, the unknown, where the truth is." "Professor slipperiness making us slip again," said Rev. Dodgson. "All right," Alice brought in, "but this kind of talk does make things dreamlike, doesn't it?" "Perhaps Alice agrees with Tweedledum's argument," said Dodgson. "What do you mean?" "Don't you remember? You said to Tweedledum, '"If I'm only a sort of thing in his dream, what are you, I should like to know?" "Ditto," said Tweedledum. "Ditto, ditto!" cried Tweedledee."' "Slippery, slippery," one of the three in the museum said, it wasn't clear which one, perhaps all three. "So Ebenezer Scrooge, Captain Ahab, Hamlet and Jane Eyre all found out the world is not just our ideas. It's not just what we think is separating and joining us. The world is Big Reflecting X. That's clear." "But the Big Reflecting X is everywhere if you look. Like William Blake said, isn't the universe in a grain of sand?" "Or the blackbird's eye against twenty snowy mountains." "Or a man with an umbrella crossing a bridge." "Or the Mad Hatter's tea party." "Of course no one ever created a better reflectaphor than when Rev. Dodgson created you. Shall we have a stroll in the garden?" Alice realized now that all the while they'd been talking they were walking past wall after wall of paintings, turning down corridors, a veritable labyrinth, sometimes passing the same paintings again but now they appeared to be in different sizes. She was thoroughly disoriented. Professor Sggirb took an abrupt turn (possibly left, possibly right) and they passed through a large set of glass doors--mirrors, naturally --into an Oriental garden. Here were lovely quiet pools, the gurgling of water, rocks like claws growing out of the earth, gravel along the stepping stones raked up in waves, trees that made her feel in the middle of a windswept landscape except everything stood perfectly still. The arrangement of objects in the garden seemed to reflect the movement of the planets and yet it was made of simple and perfectly ordinary things of Earth. It was an uncanny mixture of the artificial and the natural. "So you see, through their countless varieties of reflectaphors artists discovered the holographic, fractal universe long before scientists did," Sggirb said as if carrying on the previous conversation, "and they discovered something deeper than pattern. They discovered what you can't discover." "But how could they discover what you can't discover?" "They discovered it and undiscovered it and discovered it again all at the same time. That's what reflectaphors do. That's why art is so rich and slippery. That's why writers pluck you--Alice--out of Rev. Dodgson's books to explain new and subtle ideas that have arisen in science. Even as we speak you're here, as slippery as a jabberwocky helping to explain what can't be explained. Mind your feet." She almost tripped on a root. Without her realizing it, they had passed out of the garden into an actual forest. She began noticing now all the self-similar and reflectaphoric forms around her, each wonderfully different from her but reflecting her in some way. How would she describe it? The gall on the huge oak tree was like rough bubbles, like a thought bubbling up in her own mind; the spaces between the boulders were like the feeling of misunderstandings; the fallen twigs and branches were like forgotten memories. As they crunched through the undergrowth, beside the twist of a stream she saw a shinning plant. It looked very odd and dreamlike in the forest setting. On closer examination she saw it was a plant with leaves of different sizes radiating in all directions, in each one a different Alice reflected, except for one which reflected Rev. Dodgson. The Rev. Dodgson in the leaf looked sad. "I realize," he said, "that as much as I want you and strive to make you real, I must also make you unreal because I love you as life." Alice mentally stomped her foot. Plants were always saying things to her, sending her one place or another, and even commenting on her reality about which they knew next to nothing. It was vexing. "So now I see," Rev. Dodgson continued, "that you must go on with your adventures because you're a reflectaphor and others will claim you." This statement, which offended her sense of self and seemed yet another authorial imposition, produced in her the oddest of feelings, as if she didn't exist except as the abstract relationship of looking at the flower and being looked at by readers. She hadn't even felt herself disappear. Well, the truth was she hadn't disappeared. "Perhaps we all are," she heard the Reverend's voice saying somewhere behind her as she felt herself lifted up into the forest, spinning out in a thousand shimmering reflections, journeying through untold minds. She was still holding the plant. In one of its curious leaves was the pussycat climbing down from the limb of a tree. Oh, well. She started after it.