Imaginary Numbers

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The Master

Under the bean field in Metaponto

They were led from their quarters, which were minimalist rooms that reminded Vivienne of the nuns’ cells in the hospital in Beloeuie. The hostess answered many of the professor’s questions along the way, but avoided talking about their leader, or the central beliefs of their order. She seemed to know an enormous amount about his work in Geneva.

“How do you know so much about my research?” he inquired as they proceed down a long tunnel towards a brightly lit cavern. “I’m surprised that you’re even aware of my latest breakthroughs in abiogenesis. Nothing has been published on that yet.”

“As I said, dottore, we have listeners living in the upper world, gathering information on anything deemed important. In fact,” she said as they entered the great hall, “you are well acquainted with one of them.” The cavern was huge and brightly lit by magnesium lamps, illuminating long stalactites and stalagmites, that formed a balustrade to a winding carved staircase at the periphery of the room. The floor was made of inlaid marble tiles of various colours: squares dissected from corner to corner, forming a pattern of multi-coloured right triangles. In the middle of the room was a horseshoe-shaped table, made of thick wood. Standing in groups inside the hall were toga-clad men and women, and hanging above the table was a banner with a verse written in faded greek letters.

Near the entrance, a man broke from his group and strode towards the professor.

“Dr. Borgiac!” he called out and extended his arms, embracing the befuddled professor. “It’s been too long.”

“Frederik Gagnon? Is it really you?” The professor regarded him for a long time, holding him by his shoulders. “You look so different. Are you are growing a beard?” The man laughed.

“Yes, when in the Sanctum it is forbidden to shave or cut your hair.”

“That’s a funny rule,” Vivienne giggles and touched her own hair. “What about my legs?”

“Frederik is correct,” the hostess spoke up, “we are forbidden to cut any hair, and can only cut our nails on the full moon. Our society has many such laws.”

“And some might seem a bit silly at first, but you get used to them fast,” Gagnon added. “They give life underground a rhythm that you forget when you live with the stars above your head.”

“What’s another rule?” Vivienne asked.

“There are three main ones, and a number of minor protocols that apply in different contexts.” Astraia led them to their seats at the table. “The Major laws are,” she explained, holding up a slender finger for each one, “‘Do not eat meat,’ ‘Never pick up anything someone else has dropped,’ and ‘Beware of beans’.” Vivienne and the professor couldn’t help but laugh.

“So,” the professor said sitting down, “I suppose tonight’s fare will be vegetarian then.”


“And Gagnon, that would explain your own unique diet,” he added. “All those times I told you beans are the protein of a meatless meal were of no use, then.” They both laughed.

“I prefer mushrooms anyway,” Gagnon said. “But Sanctum meals are superb. You will not be disappointed.” Above them from a nook in the darkness, a large bell tolled just once. The sound reverberated through the bodies below. Vivienne placed her hands on her chest to absorb the vibration, and every standing person sat down. They do so in complete silence. When the professor attempted to ask a question, he noticed Astraia holding her finger over her mouth. There was complete silence in the large cavern, hardly any movement, and when he looked around, everyone—including Vivienne—had closed their eyes. In the dark emptiness behind his eyelids, the professor noticed a toneless silence. It was a void he had not been aware of until now, an absence of the modern droning of technology: the b-flat buzz of fluorescent bulbs, the hum of a computer’s spinning disk drive, the constant orchestra of modern life with all its machinery thrumming an invisible chord in the background of our minds. Here all that was absent. With closed eyes, he inhaled and became aware of his own body, and the subtle sounds of fabric rubbing together. Then there was a second gong of the bell—a beautiful tone, which enters him, profoundly affecting him. Immediately he became overwhelmed by emotions, he wanted to cry, but not out of sadness or joy. He was overwhelmed at being part of life itself. The feeling was too much and he opened his eyes, along with everyone else in the room. A tear rolled down his cheek and he dabbed at it quickly with a loose end of his toga, embarrassed.

Above them, the professor heard a slow clicking of wood against stone. Someone was climbing down the staircase, and in the gaps between the stalactites a group of people descended, all of them wearing crimson robes. At the foot of the stairs, a man in red announced something in Greek, and everyone stood up. They waited for an old man in white robes with a hood covering his head to descend, aided by two stewards in red, and by a very old, gnarled wooden cane.

“What did he say?” the professor whispered to Astraia, who was standing next to him.

“He said ‘All hail the wellspring of our order, the immortal Pythagoras.’”

The old man had a long white beard, and despite his impeded mobility, he looked rather healthy. He walked unaided once on the ground and stepped into the middle of the horseshoe table.

“Sons and Daughters,” he said in a heavily accented, raspy English, “today we feast with honored guests. Our order has survived for millennia, we have passed on our wisdom, and helped all life on earth, yet an opportunity like this only crosses our path once every hundred years. Some of you remember the last time we supped with a viable synthemorphos.” He pointed at Astraia with his cane. “Others will recall this moment for years to come. It is with great pleasure that I can, as an old man, sit next to a creature of perfection, and kneel before my very own creation.” The old man, dropped to his knees slowly and painfully. He then lowered his head until it touched the ground—a protracted procedure that could make you sore just looking at it. As he did so, the other people all bowed down as well, leaving Vivienne and the professor once again feeling out of place above the sea of togas. The professor looked at Vivienne, who simply shrugged.

Two men in crimson togas helped the old man up, and guide him to his seat in the middle of the horseshoe, between Vivienne and the professor.

The old man grasped Vivienne’s hand as he sat down. “Κόρη,” he said, “τι είναι το όνομά σας?”

“They have been calling me Vivienne, but I was really hoping you could tell me my real name,” she replied in English. “I can’t remember who I am.”

“Ahhh,” Pythagoras said, “the question of identity.” Once he was seated, he turned to the professor, “One which Professor Borgiac also is concerned with, I’m sure.” He placed his hand on the professor’s arm. “And identity is also at the very core of our society.” He nodded at a man in crimson at the door, who summoned others carrying dishes of food. “I will explain as much as I am able.” The professor’s stomach rumbled, and Vivienne giggled at him. She looked at the man called Pythagoras, who removed his hood, revealing a shiny, bald head rimmed with long white hair. He was in his 80s, maybe older.

“Are you my father?” Vivienne asked.

“In a manner of speaking. However, I only put into place the conditions for your arrival here.”

“Who is my mother? Do I have any brothers or sisters?”

“Vivienne,” he said as they placed a variety of vegetarian fare in front of them: poached pears, couscous, grilled vegetables surrounded by a ring of mushrooms, watercress soup, cakes baked in the shapes of fish, a spinach souffle, and a platter of pickles, “You have no mother. You are a creation made of air and fire.” A man in crimson placed a jug of water in front of them, which Vivienne used to fill her pewter cup. “I know that you will suffer to understand this, but please allow me to explain.”

She cocked her head to listen to the rest.

“Our order was founded thousands of years ago. Initially, I was a man living in Samos, in Anatolia, of the coast of modern day Turkey. A group of us studied nature. We were all trying to determine the basic building block of life, the arche of the universe, what Dr. Borgiac would call ‘the primordial condition’. It all started by guessing that at the heart of it all lies a certain element. Thales claimed it was water, an element that is essential for life, and contained within its nature an ability to assume many forms.

“His pupil Anaximander refuted this, saying that water could not give rise to fire, and thus could not be the arche. He proved that none of the elements could be the arche, since they each had an opposite which could not spring forth from them. Instead, he argued that the arche was the boundless, what we call the aperion. It was an important step forwards. Undoubtedly, he drew inspiration from the ancient myths of Chronos and the yawning abyss. But Anaximander’s æther was different in that it included the infinite timeline of the universe, which also spurred on the idea of immortality. In our society we give him credit and spend much time considering the boundless, despite the fact that it might be incomprehensible to the human mind, which is essentially stuck in time.”

“Yes,” the professor said between a spoonful of souffle, “Astraia showed us the Star Room scarred with the aperion.”

“Excellent. The aperion is something we must consider as scientists and as philosophers. But allow me to continue. Many philosophers struggled with the idea of the principle building block, and after Anaximander their ideas become more abstract. As Greeks, we believed that it must be something simple. You see, we thought that the universe was essentially ordered. Democritus later conceived of the atom, a particle that is physically but not geometrical indivisible, a particle that is indestructible and will always be in motion. Not far off from what we believe today, eh, professor?”

“Not at all. In fact, it’s miraculous that he came up with such an idea before microscopes. But his atoms were closer to modern day molecules than the particles of physics.”

“Indeed. He drew his conclusions from the growth of seeds. You see, a seed will grow a tree that has the same materials as the tree it came from. It’s a rather complicated process, that ultimately provides more mass than is inside the seed itself. The conclusion he came to is that many properties of materials must derive from something inside, that will itself never decay, something that stores for eternity the same inherent, indivisible properties. Much like DNA.”

“Interesting.” The professor said between mouthfuls of savoury cake.

“Yes, he questioned why the world is not in a constant state of decay, and why the same animals, plants, and materials can be created over and over again in the same design. A question, you will come to understand is very important to our order for two reasons.”

“What are those reasons?” Vivienne chipped in.

“The first one deals with immortality, and identity. And since it answers, to some extent, your initial question, I will start there.” He paused to drink some wine, and scooped some fried mushrooms onto his plate. “In this world we live in, there is are limited things and unlimited things. DNA is limited. There are only so many combinations. Which means that, given unlimited time, another identical Professor Borgiac will be born, or another Pythagoras, for that matter. And, if that is the case, will that Pythagoras be the same person as me?”

“I suppose that depends on the society he is born into,” she said.

“Yes, but that is presupposing that identity is personality. Specifically, the socialized personality.”

“Isn’t that what it is?” Vivienne asked.

“It might be. Identity could also be your genetics, or what actions you take in certain conditions. It could be the soul, or how others see you.”

“Ok, I follow,” she said, ignoring the food on her plate.

“What professor Borgiac knows about me, as Pythagoras of Samos is that I formulated the theory of triangles. That’s perhaps what I am most known for, but it is not my greatest achievement.”

“What is your greatest achievement, then?” Vivienne asked.

“Immortality, and the spiritual ideals we live by,” Astraia interjected. “And our order tried to teach this to the world, but we were ostracized and persecuted for it.”

“Astraia, my dear, we should not hold grudges.” The old man smiled at her then added, “However, since you have lived through those terrible times, I can understand your feelings towards the willfully ignorant.”

“I’m sorry,” Dr. Borgiac interrupted, “but would you explain how biological immortality is possible? And if it is, why has modern science not found the method, when, according to you, the ancient Greeks knew it.”

“Apt questions, professor. But you are thinking like a scientist and not a philosopher. Biological immortality is impossible, as you very well know. Time consumes everything in an ongoing march towards the infinite. But we believe that it is the soul that makes up your identity, and perhaps your personal history.

“Professor, are you aware of the idea of metempsychosis?”

“No, I’m afraid not.”

“It may also be called ‘transmigration of the soul’, however there is a nuance lost in that translation. A birth is not a creation of anything new. Just like matter cannot be created or destroyed, nor can the soul.”

“But,” the professor hesitated, “how can you as a scientist believe in the soul?”

“Easily. You believe in the concept of the infinite, do you not?”


“Well, the soul is the embodiment of the infinite, the boundless.” Pythagoras chewed on some food, then continued. “I’m afraid, I might have got ahead of myself in regards to the arche. Around the time I experimented with the pythagorean theorem, we developed notions of squares and roots. My society almost fell apart when I laid the geometrical squares of a right-angle triangle onto a number line. You see, the hypotenuse landed somewhere between two numbers. We were still using the whole number system at that point, and anything in between numbers violated the concept of a simple, understandable universe. I lost many followers, and had to consider that in our ordered world, there might be imaginary numbers, or complex numbers. Numbers such as π or Φ, which go on forever. These are part of the boundless. And I formed a theory about the arche myself. I imagined that the arche is not any one thing, but a ratio between the boundless and the real. That the empirical world we live in is simply created by a mathematical order that joins the limitless to the limited.” The professor stopped chewing to consider this.

“In fact, that theory has become the fundamental belief of my order. We believe that the souls are attached to bodies at birth, and with a formula, you can know not only which souls is which, but you can predict where the souls will travel.”

“For example,” Astraia added, “I have been born many times, most currently as a woman. Last time I was a man, and prior to that, I died as a child before the Pythagoreans could find me. Our ascetic life and our rigorous training as akousmatikoi allow us remember every life in detail. It is in this way that we gather so much knowledge.”

“Well,” the professor said, raising his glass, “I would never have expected a secret society of scientists gathering information through the ages. Not here under a bean field anyway. To the Pythagoreans!” They all drank.

“You jest, but you are a prime candidate, sir. If you are willing.”

“So, what about me?” Vivienne interrupted, much to the relief of the professor. “Who’s soul am I?” Dr. Borgiac mouthed a silent ‘thank you’ to her.

“Ah, yes! I almost forgot. My apologies.” Pythagoras turned to her. “The second part of Democritus’ notion is the question of why all life doesn’t just decay. What is the regenerating factor?”

“Yes, but who am I? I can’t remember my own past. Is there something wrong with my soul then?”

“My dear girl, all life is on a cycle of regeneration. There are epidemics that become pandemics, that kill off large percentages of people on this planet. Every few thousand years, there are mass extinctions events that threaten every living being. Our order is committed to mitigating those terrible circumstances. I am too old at this stage to give you anything except guidance, but in general our society has been fighting entropy. And in specific, we have at you our disposal, the regenerating factor, a creature of such perfection that conditions for your existence must be carefully crafted.”


“Yes, you are a synthemorph, a creation made out of the purest elements. You are life out of nothingness.”

“What do you mean? Am I just another clay girl?”

“As a matter of fact, you are a girl of fire and air. You were created by me to stop the next extinction event.”

“Extinction event!” Dr. Borgiac coughed on his food, but the Master ignored him.

“And what about the clay girl, then? Was she another me?” Vivienne demanded passionately.

“No.” The old man wiped his lips with a napkin, finishing his meal. “She was part of me. When I created you, you manifested outside our veil of observation. You see, I never suspected you would fall to the earth like a comet. Basically, we lost you, and we were trying to find you.” Pythagoras looked past the professor at Astraia. “Just like we sometimes miss the details of reincarnation of our oldest members, we had to work hard to locate you.”

“So you made the clay girl come alive to guide us here?”

“Exactly, I projected myself into your clay impression. I’m glad you returned there, because even Frederik Gagnon couldn’t get in touch with Dr. Borgiac consistently at that time.”

“Astral projection?” the professor asked.

“Indeed. However, it is taxing at my old age. And I only sent part of myself.”

“And Gagnon was surveying us?”

“He was working with you, helping you reach the successful synthesis of life. But yes, he also happened to be in the right place. You see, doctor, we had no idea you would play such an important role in this. That you went to investigate the girl was mere serendipity. And it is ironic that your protégé would be central to this situation.”

“So Gagnon,” the professor asked, “most of our success was actually thanks to you, then?”

“Actually,” he replied, “the Master makes me seem more important that I actually was. In fact, my mission was to observe Marius van Niekerk.”

“Marius?! Why? He’s not even a scientist.”

“Do not underestimate your protégé, doctor.” Men in crimson robes started clearing the table, and others brought a sweet pudding.

“What do you mean?”

“Marius,” the old man explained, “is the agent of destruction.” The professor frowned. “He is a man full of hubris. It is dangerous for someone like him to be so close the the fundamental process of creation.”

“But he was simply representing me at conferences. Until a month ago, he was hardly in the lab at all.”

“You gave him access to your identity. I will let Astraia explain.”

“Master, perhaps it serves us better to explain the details in the Encyclopaedium.”

“Very well, but know this, Dr. Borgiac, Marius might indeed cause the end of life on our planet. He is a danger to us all.”

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