Imaginary Numbers

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Galatea

Beloeuie, France


Sunlight streamed in through the hotel window. Charles William Borgiac lay on his bed, staring at the ceiling. He routinely woke up early, but last night he had been unable to sleep. The resurrection of the deer was still on his mind. As a scientist, he naturally assumes a position of skepticism when it came to such things, and yet the carcass of the deer clearly ran into the woods. At the very least, that part he had witnessed with his own eyes. Whatever caused the bright light, or what had happened inside that impenetrable aura could not be verified, yet the one factor of which he could be absolutely certain is that at the core of the strange experience was Vivienne.

That night they had both been silent the rest of the way to the hotel. Feeling an urgent desire to come to terms with the experience, the professor had remained speechless while the radio played Ella Fitzgerald and Louis Armstrong songs. Vivienne, too, had been more quiet than usual. She felt tired and suddenly sleepy, drained of her normal vivaciousness.

Finding that the ceiling held no more clues to the bizarre situation in which he found himself, Dr. Borgiac got out of bed. His silver chest hair shone in the morning light, and the sun warmed his slender frame. He tried the television, but there was still no power.

While he got ready for the day, he revisited the clues to Vivienne’s mysterious identity. Under hypnosis, she had mentioned she was no Galatea. It was a reference to Greek mythology; however, he couldn’t remember the story exactly. Isabelle would know, she always liked mythology. He considered calling her, but decided against it. He checked his phone anyway, and realised that without power, the battery would be dead within a few hours.

With a fluid motion, he slid the the pressed trousers of his suit off a wooden hanger and stepped into them. To accompany the black suit, he selected a purple shirt. While buttoning it up, his phone vibrated on the counter. It was Isabelle.

“Hello?” There was a flurry of activity on the other end, the hustle-bustle of a news room, rushing to get the scoop on the blackout.

“Charles!” Isabelle spoke fast, but he could tell she was trying her best to conceal a worried tone. “Are you okay?”

“Isabelle,” he said warmly, “yes, of course. How nice of you to call. I was just thinking about you!”

“I heard about your lab. What happened?”

“My lab? I’m not sure I know what you mean?” A pause. She sighed into the microphone.

“Listen,” her tone of concern was replaced by a steely cold voice, “I’m not trying to use you to get a story. I was genuinely concerned. I saw the report of the animal that escaped, and I was worried that you were injured. The police said that they found blood and a torn shirt at the scene.” She covered the receiver with her hand while she issued commands to some invisible person in the news room. When she returned, her voice was once again warm and calm. “Charles, where are you?”

“I’m in France actually. Outside Beloeuie, in Normandy. Why? What happened to my lab?”

Mon dieu! You really don’t know.” A rough voice barked loudly on the other side. “Sorry, Charlie, I have to go. Hope you’re doing all right. Things are hectic here with the blackout. Talk soon. Ta ta.” Then she hung up before he could reply.

Alarmed, the professor called his lab. There was no answer. Then he called Marius: also no answer. He was about to call Gagnon, but the battery on his phone died, so instead he flipped his tie around his neck acrobatically, added the vest and jacket, polished his glasses, and combed his hair. Then, ready for the day, he stepped out and knocks on Vivienne’s door.

She opened it with a smile.

“Bonjour!” she said, and waved him to come in. The bed was neatly made.

“Bonjour, my dear,” he said and studied her. She was wearing a dress with a tight black top and a skirt made from flowing cerulean fabric that added the illusion that she is standing in a draft.

“Where did you get that?” He asked curiously.

“Oh. Well, I woke up in the middle of the night. So I walked around the hotel. Some nice people invited me to a party. The man is a fashion designer, and he gave this to me. What do you think?”

“You look beautiful,” he said. “But he just gave it to you?”

“Oh yes. They were all very nice. I asked them about Joan of Arc and he told me that she wore men’s clothes, and that I shouldn’t worship her. They told me in France women like to wear dresses and nice shoes.”

“Well, it’s partially true. But Joan is a hero, you know. She is the patron saint of France. And she wore mens clothing in a time when women didn’t have rights.” She sat on the bed, looking demure in the natural light. “I think it’s fine for you to look up to her.”

“Well, good. I like her a lot.” She smiled, cocked her head to one side, then added, “And if it’s okay for Joan to hear voices, then it’s okay for me too, right?”

The professor frowned. “Do you hear voices, Vivienne? What are you talking about?”

“Yes, sometimes.”

“What kind of voices?”

“It’s just one, actually. An old man. Usually he tells me to come to him. Do you think it’s God?” The professor considered it. He looked out the window, then back at the girl, who was sitting in the sunlight.

“I’m really not sure. Personally, I don’t believe God can be represented in human form.” He sighed. “Honestly, I really can’t even tell if I believe He exists, but after what I saw last night, I’m skeptical of my own skepticism. I need to think it over, Vivienne.”

She leapt off the bed, and with a big smile, locked her arm into his. “Well, don’t worry too much, Professor. It worked out for Joan, I’m sure it’ll work out for me.” Then she guided him towards the mirror. “We both look stylish today! I’m happy I’m finally out of the hospital gown.” Looking at themselves, standing arm-in-arm, it seemed as if they are dressed up for an evening of ballet. In reality, they would be doing much the opposite; instead of going out to a fancy event, they would be going to a bogland just outside the town.

“Impressive.” They made eye contact with their partner’s mirror image. “Vivienne,” he said, “I suppose the man was right. You deserve to wear fashionable clothes. It suits you well.”

“Thank you, William.”

“Shall we go?” He felt awkward standing arm-in-arm with a younger, beautiful girl, and disengaged from her. “Before we lose the light,” he added.

“Let’s!” She skipped out of the room, into the lobby, and past the revolving door, into the tiny city of Beloeuie, where the legend of the girl who fell from Heaven has just continued to grow.

In a new rental car, they headed out into the rural fens at the edge of the arable county land. The road was narrow and almost entirely devoid of life. At last, they passed the final wheat field, surrounding an ancient Gaulish burial mount, constructed with a massive stone post and lintel embedded in the hill. Vivienne stared at it.

“It’s a dolmen,” the professor explained. “The old ones built them: the tribal celts, who lived here before the Romans came. They believed in the earth mother, and their kings and heroes wanted to be near her when they died. Actually, they purposely built their settlements near the marshland, because it provided them with fuel.”

“Oh really?”

“In fact, the marsh also fulfilled a ritualistic purpose. During tough times, the tribe would make a human sacrifice, often a volunteer, who would be buried in the bog, so that the others would have better fortune.”

“That sounds terrible!” Vivienne gasped and covered her mouth with her hand. “How could they kill someone just like that?”

“Yes, it is contentious. In reality, it is a complicated pattern of thought that modern humans might find difficult to understand. However, I should say that the victim was held in high regard, and that they fulfilled a duel purpose in that they alleviated pressure on a strained agricultural system, as well as giving the culture hope.” The professor looked over at Vivienne and saw her concern. “These human sacrifices were altruistic. They were people who were willing to offer their lives for the greater good of their tribes. They went into it willingly, and, in some sense, they were rewarded with eternal life.”

“What do you mean? They didn’t really die?”

“Well, they died.” She looked aghast, and when he noticed her expression, he quickly added, “However, in being buried in the bogs, their bodies were preserved perfectly. Scientists sometimes find two-thousand year old bodies complete with their ritualistic diadems, leather clothes, and neolithic tools. In essence, they are time-travellers.”

“Dead time-travellers.”

“It’s not that uncommon for some animals to show that kind of self-sacrifice. Perhaps it’s a social adaptation to put the good of the community before your own. Now, I’m not saying that humans are altruistic, but occasionally people are willing to put themselves at risk, so that their tribe can prosper.”

“It sounds better when you put it like that, but I still don’t like the idea of killing.”

“I know. But, my dear, I can assure you that human sacrifice is a thing of the past.” The GPS device in the car’s dashboard showed that they were nearing the site. “Well, we are almost here. Are you ready to go for a walk?”

“I’m always ready for a walk, my dear.” She seemed jubilant, and wide-eyed.

“My dear?” He smiled, and raised one eyebrow.

“I’m just trying it on,” she laughed. “You always say it to me.”

She walked ahead of him. The professor’s shiny shoes stepped deep into the bog, pulling up chunks of peat. Vivienne’s new boots were also covered in mud, but she walked undisturbed at an even pace, following a game trail. He wished he had brought another pair of shoes, or clothing that was not a suit, but however much he tried he cannot form an image of himself in hiking gear. Nor can he remember where he put his hiking boots, boots that he had worn only once on an alpine climb organized by Marius when he first arrived in Switzerland.

“Come on, William. It’s right up there,” she said pointing to a vast open area, a softer region where even tree roots didn’t grow.

“Yes, yes! I’m coming.” He trudged through the mud, the sleeves of his pressed suit dirty halfway up the calfs. “I didn’t realise it was this far off the hiking trails.”

When he arrived, she had found the site. It was a soft, peaty flood plain surrounded by deer tracks, which followed the more solid ridges around the fen. One of the first things he noticed was the disturbed ground, perfectly preserved, where Vivienne had rolled over and dragged herself out of the peaty marsh towards the more solid ground.

He found her standing next to an impression in the ground, the exact place where she had landed. It was an inverse imprint of her own naked body.

“So this is where you landed?”

“Yes.”

“It looks like a perfect mould.”

“What do you mean?”

“Well, a mould is a negative space, used to produce a positive. We use it in art to make statues, in metal-smithing to make jewelry, and in industry to make machine parts.”

“Hmmm… It looks like the animals avoid walking through here,” she said, placing both hands on her hips. The yellow sun was high in the sky, and a cool early autumn breeze blew clouds across the blue. “Professor, what did you think we would find here?”

“I’m not sure. I always return to the origin of a problem if my previous methods could not provide a solution.” He looked around, holding the sleeves of his trousers as he stepped into deeper mud. “If we look around, we can determine if any other objects joined you in your descent. Perhaps a clue.”

They surveyed the area, but the only unusual thing they found was a large rectangular peat quarry dug by the locals thirty meters away. Locals must still have been burning peat locally in furnaces. Next to the pit was a wheelbarrow, and spade left in a pile of clay.

The professor found Vivienne standing next to the pit, holding a handful of clay in her right hand. She was squeezing it, so that the dirt extruded between her fingers.

“What are you thinking?” He asked as he approached. “You seem pensive.”

“Well, to be honest, I want to cover the impression I left in the dirt.” The professor considered this. He looked at the dirt in her hands. It was the same colour as her skin.

“Very well. I suppose that this little voyage amounted to nothing. I’m sorry, my dear, I had expected to find something more.”

“Oh, it’s no problem.” The corner of her mouth coiled up on one side. “I’m borrowing this tool,” she said, and started piling clay into the wheelbarrow.

“Can I help?” He asked, but realised that she was determined to cover up this one part of her own story. Perhaps she believed that by erasing this imprint, she was filling a gap that kept her from living a normal life. She worked with determination.

When the wheelbarrow was full, she attempted to roll it, but the professor interrupted her. “Allow me,” he said and rolled it to the crash site. She followed behind, holding the spade. At the site, she stood quietly for a moment. To the professor, she looked more serious than he had ever seen her.

“Are you okay?” he asked. She nodded without looking back at him. Then, again she started shovelling dirt into the mould with a quiet zeal. When the imprint was filled up, a form in brown clay lay face down beneath the crust of the bog.

“It looks like a human sacrifice,” she said.

“Is that why you are so quiet?” he asked. She gazed at him, then down at the outline of her own body.

“We should do a ritual, I think. It doesn’t feel right to just leave it here.”

“Very well. Do you have something in mind?”

“Not really.” They stood in silence, like mourners next to a grave.

“Well, shall I say some words? Or do you want to say something. Perhaps it’s better if you said something.” She shook her head, black hair falling over her shoulders, cascading from behind her ear.

“I can’t think of anything.”

“Hmmm…” The professor thought hard about what he could say about a form in the mud. What did it represent to this girl? This shape was all she has of her past, and the bizarre events of the last night have added a further layer of mystery. As he stood there looking over the clay form in the earth, words abandoned him. He was at a loss. The very act of ritualizing an inanimate object seemed absurd to him. But then his entire life was becoming more and more absurd every day. He considered his own feelings of instability, or a world changing without him, of the many unforeseen events that have altered his normally routine life.

“William, do you have a favourite number?”

“In fact, I have several.”

“What are they?”

“One of them is called ‘phi’. It is the number of the golden ratio, which represents beauty and harmony, and is the mathematical form our galaxy takes.”

“Sounds nice,” she said thinking. “What is another one?”

“Lately, I’ve been thinking a lot about the square root of negative one.”

“What does it mean?”

“Well, it is an imaginary number. It is a number that changed the very way Europeans thought. It challenged God and the simple universe.”

“How is it an imaginary number?”

“Oh, that simply means it is a number that cannot be defined in the real world. It is a fantasy number that cannot really exist, but we can understand it. So, I suppose in a way it is like God.”

“Well, I like the idea of a number that can’t exist in the real world.”

“Why do you ask?”

“Since neither of us can think of anything to say, I wonder if maybe you could just write that imaginary number down.”

“You mean like a grave stone?”

“No, no. Nothing died here, silly!” she laughed. The professor smiled.

“Right. So where do you want me to write it?”

“Just use your finger and write it in the clay. Right here,” she said, pointing at the centre of the clay body.

“Very well.” Dr. Borgiac crouched, and with a tiny stick, wrote the check mark-like root sign and squiggled the number -1 beneath it. When he stood up, there was a tremendous crack of thunder and a boundless rumbling that rolled across the heavens. The professor looked up, checking for rain. The sky was orange. He counted: one, two, three, four, five—lightning sundered the sky in half, bathing them in a pure white light. Vivienne looked down at the clay version of herself embedded in the bog. Then there was a faint shaking of the ground, like the rumbling thunder had occurred in the jello-y earth.

The professor fell backwards into the mud.

“Look!” Vivienne said, pointing at the form.

A crackling of electricity danced over the surface of the clay, and suddenly the form stirred. It’s as if the clay was twisting and turning in on itself, manifesting a musculature. The arm rose up from the bog and pushed itself up. A crude version of Vivienne—hairless and flat-backed—rose from the earth. It was silent, stilted, and moved awkwardly, yet it still possessed the fine features of the girl. The doppelgänger cocked its head and stared at Vivianne.

The professor, on his behind, scuttled backwards, afraid of the unfathomable unfolding right in front of his eyes. Jaw dropped open, he was covered in mud. Vivienne extended her hand, and helped the dirt entity up onto its own feet. It stood.

After a few seconds, the clay girl blinked. The dull eyes vitrified, sand heated until it became glass, and immediately it noticed the professor, who was still cowering in the dirt. Then it turned its head to Vivienne, and breathed a deep breath of air, filling its lungs for the first time.

The clay girl struggled to step out of the mud, and Vivienne supported her with an arm around her waist.

Me gno̱rízeis?” Vivienne asked in a highly intoned language. She seemed to be having a one-sided conversation with the creature.“Boreís na me voi̱thí̱seis?” The professor got up out of the dirt, and seeing that the only danger is the damage to his belief system, he approached.

“Vivienne,” he asked, “What’s happening?”

The clay girl stared at Vivienne. Then she stumbled, as she tried to move her arms in a deliberate gesture.

“She needs help. She knows me. We need to help her.”

“She knows you? What language are you speaking?”

“I don’t know. She started using it and I know it too.” Vivienne and her double slowly struggled out of the peat towards the more solid animal trails. The professor extended his hand and the clay construct grasped it. He pulled her up to the trail.

“Where are we going?” he asked. “Where can we go?”

“I’m not sure, William, but I feel a great need to help her, as I’m sure she does me. We are connected to each other.”

“This is all too surreal.” He scratched his head and left muddy fingerprints on his face. “I fear I’ve ventured into delusion.” They pressed on, trying to get out of the marsh, back to the road. It went faster with both of them supporting the heavy clay girl.

“Professor, she is the best clue we have.”

“This is crazy. Impossible. It’s…It’s…” He shook his head.

“She told me to find her.” Vivienne paused, realising that it doesn’t quite make sense. “She also said that we can help each other.”

“I didn’t hear her say anything.”

The clay girl turned her head to Vivienne, and opened her mouth.

Eímai edó̱,” Vivienne replied to her. “Eímai edó̱.”

“What are you saying?” That sounds like a Greek dialect, he thought. She was speaking Greek.

“I’m telling her I am here.”

“Vivienne, ask her how it is possible. How can she exist?” Vivienne translated the professor’s question. He waited quietly, thinking how the roles have been reversed, how he was no longer her conduit to a world of logic, but that she was now his link to an unorthodox world of irrational physics. The creature responded with a rough, guttural sound, and a wheezing. It had no words. It could not speak.

“Um… Well, she said that occasionally science cannot explain things and that the universe cannot be contained in a simple equation. She said that there are things that we know can exist because we can imagine them, but that they can’t always manifest in our world. Sometimes, however, briefly the rules change.”

Skeptical, the professor remained silent, perhaps questioning his own sanity. He revisited the odd events of the last week: the phone calls from his lab, from Isabelle, and his credit card company, the blackout, and then Vivienne, who fell into his life, a girl unbearably beautiful and delicate, a girl who he is compelled to help despite everything else.

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