Mysterious Mysteries of the Aro Valley (22 page)

They formed an odd procession. Eleanor led them across the patch of weeds to the road. Ann followed, her hands cuffed behind her back. She glanced back at Sophus as if she were about to speak, but shook her head and resumed her trudge up the slope, heading towards the house at the top of the hill.

Sophus carried the front of Steve's bath. Steve was behind him and the archivist took up the rear. Progress was slow. The bath was heavy and the driveway was steep and muddy. Each time they stumbled the bath slipped from their fingers and fell in the mud, and Steve had to brace himself to stop it from sliding back down the hill and dragging him with it. And each time this happened Ann glanced back at Sophus, and Sophus looked at her, and then at Eleanor, and his expression grew grim.

Steve's training as a psychologist told him that something strange was happening. Why was Ann here? Why was she being taken to Gorgon? He decided to investigate. To probe, subtly. He called out, ‘You there, treasurer. Why are you here?'

‘She's not just a treasurer,' Sophus snapped. ‘She's Professor Ann Day. Show some respect.'

‘Who?'

‘You've never heard of Ann Day? The brilliant mathematical philosopher?'

‘No. Should I have?'

Sophus shook his head in disbelief. ‘She's an international superstar of differential topology. The queen of sympleptic geometry.'

‘Not anymore,' Ann interjected, her voice weary. ‘I used to be those things, but I gave it all up. I retired. He's right—I'm nobody now. Just a simple treasurer.'

‘Why did you retire?'

‘She won't tell you,' Sophus said. ‘She won't tell anyone. She was at the highest vertex of the polyhedron of her career, and she stepped down. She said she was done with mathematics forever, then she disappeared.'

Steve asked, ‘Why?'

‘She won't tell you,' Sophus repeated, and Ann bowed her head.

‘How do you know so much about her?'

‘I studied her work when I was a graduate student,' Sophus replied. ‘I read her final, baffling paper on Gaussian curvature in higher dimensional spaces. It was brilliant, but also disturbing. It seemed she was moving towards a final breakthrough. Something that would change everything we think we know about curves. But it also seemed that she was holding something back. She was hiding something, some key insight. And then she announced that her career was over, and she vanished. I decided to find her.

‘I tracked her here, to Te Aro. I moved here to learn from her. But she rejected me. Oh, she gave me a scholarship and a hovel to live in while I finished my thesis, in exchange for my silence. But she refused to discuss her work, or why she abandoned it. Instead she warned me about the peril of new ideas. Her work was dangerous, she claimed. A threat to civilisation. Possibly to all of existence!

‘I was furious with her. What kind of world would we live in if thinkers refused to publicise our ideas simply because they are incredibly dangerous? Little did she know that her refusal to share her insights would lead me to an even greater discovery.

‘One night, after we fought, I went out and walked the streets of Te Aro. That is when I discovered the clues that lead me to the most important discovery in the history of mathematics. The Real City.'

‘The Real City isn't what you think it is,' Ann replied, her voice a wretched mumble.

Steve asked, ‘What is it?'

‘It's an artefact of pure mathematics,' Sophus said. ‘It's a solution to the oldest unsolved problem in philosophy. The problem of mathematical reality. My work on the topology of the City goes beyond anything Ann dreamed of. And we haven't even reached the Spiral yet, which is technically not even a spiral, but a geometric curve called a cardioid.'

Eleanor snorted. She'd listened to their conversation while she led them up the hill towards Gorgon's house, and now she rounded on Sophus. ‘Do you still think the Real City is some kind of geometry problem? An equation you can solve? That if we reach the Spiral you'll be able to publish some meaningless proof? Go ahead and believe that if it makes you happy. But the City is only a means to an end. It and you are part of Gorgon's work to free humanity from the tyranny of the world of forms and change. Once her work is finished and we reach the Spiral, you won't care about mathematics, or philosophy. Everything will be explained, and nothing will be explained. All will be both light and darkness, wisdom and mystery. That is the Real City.'

Then Ann said in a quiet, miserable voice, ‘You're both wrong. The Real City is a trap.'

And she told them her story.

Danyl watched the procession make its way up the hill. The window looking out over the wastes of Threshold was boarded up, but someone had drilled a circle in the board at head height. A spy-hole. Danyl spied through it now, watching as Steve, Sophus and the archivist wrestled with the bathtub. Eleanor turned to address them, and Ann, looking miserable, replied.

What was Ann doing there? Why was she being taken to Gorgon's house? Danyl didn't know, but he knew he had to rescue her. And Steve. But how? The group was guarded. The hillside swarmed with Cartographers. And Steve was still chained to the bathtub. Impossible.

Danyl stepped back from the spy-hole, avoiding the pool of dried blood on the floor. He looked at the bloodsoaked mattress and shivered.

Whose blood was it? Surely it belonged to whoever lay buried in that crude grave on the distant, windswept plateau on the other side of Threshold. The note Danyl had found downstairs mentioned three names: Eleanor, Verity and Simon. Eleanor was still alive. She was right outside, being evil. He didn't know where Verity was, but she was still alive a day ago, and whatever had happened here had clearly happened a while back. Weeks. Months. An air of abandonment hung about the room. That just left Simon, the chemist. Was he dead? Rotting in that grave? Who killed him? Eleanor? Verity? Gorgon?

He looked at the bloodstained page from his book. When Verity and Simon disappeared, they'd taken the only manuscript of Danyl's novel with them. Why? It was bound up in the mystery somehow: DoorWay, the Real City. And where was the rest of it?

He folded up the page and slipped it into his pocket, then rounded the mattress. There was a triangular gap in the edge of the blood pool. Something had sat on the floor here. A medium-sized box.

Just after Verity broke up with him, before he was exiled from the valley, Danyl found an empty vial of DoorWay in the pocket of Verity's old dressing gown. It was circumstantial proof that she'd drugged him with small amounts of the substance while he was writing his novel. Why? Danyl knew the answer now. To test the drug. She'd given him minute traces: not enough to send him to the Real City, just enough to contaminate his book, somehow, which Verity then read looking for proof that DoorWay worked. He remembered Verity's art exhibition: the black cases, the patrons experiencing dizziness and disorientation. Were the photos inside the cases coated with DoorWay? And what of Eleanor's restaurant? Danyl recalled a prominent food critic accusing the Dolphin Café of giving him food poisoning. The seafood noodles, he'd claimed, caused him to pass out and experience vivid hallucinations of an endless, sprawling city. Did that have something to do with all of this?

Danyl suspected that it did. They'd been testing the drug. Clinical trials. And when they had the right dosage they'd stolen Danyl's book, closed down Eleanor's restaurant and disappeared. They came here, bringing a supply of DoorWay with them. They hid here, mapping the Real City and trying to find their way to the Spiral. But something had happened. Simon the biochemist was killed. After that, Gorgon appeared. Her Cartographers lured people to the bookshop and trapped them in the Real City. And Eleanor and Verity helped her, until yesterday, when Verity left that message on Eleanor's phone then vanished.

A shout came from outside the house. Danyl returned to the spy-hole. The procession hadn't moved far. Sophus and the archivist had slipped in the mud and dropped the bath. Ann was talking to Steve and Sophus, and they were trying to pay attention while they wrestled with the mud-stained tub. Eleanor was shouting at them and pointing up the slope to the old house. Its scaffolding gleamed like teeth in the sunlight.

And suddenly Danyl had a plan. He tucked Steve's crowbar into the back of his pants, climbed out the window and lowered himself down. As he kicked around with his foot, trying to find a toehold, an odd thought struck him.

Back when Verity and Danyl were living together, a lunatic had broken into their house and tried to burn it down, all to destroy Danyl's book. According to the lunatic, the book was contaminated and the ideas within it would infect and destroy the universe. Or something like that. It was late at night and there had been a lot of petrol and screaming.

Back then, Danyl hadn't paid much attention to the lunatic but now he wondered. He recalled the deranged screams and he thought about the DoorWay compound and the Real City, and he wondered some more. If Verity had drugged Danyl while he was writing his book, then where did the ideas in his book come from? If they were inspired by DoorWay, and DoorWay led to the Real City, then, logically, the ideas had come from the Real City. But what did that even mean? And, if the ideas in his book came from there, then were the rest of the thoughts that ran through his head contaminated too? The decision to stop his medication, to return to Te Aro, to look for Verity, to rescue Steve? Where did the thoughts that made him do those things come from? Why did he think them? And why was he thinking this now?

His brain buzzed at him impatiently, and he found himself climbing down the side of the townhouse, his thoughts about his own thoughts scattered and abandoned. Maybe his brain was right, Danyl thought: rescue Ann and Steve now, then escape. Think about thinking later.

He let go of the window ledge and landed in the mud.

Ann said, ‘Like most children, I would lie awake at night and wonder about the world. Why did it have three physical dimensions but only one time dimension? What would our lives be like if it were the other way around? If we could move back and forth through time but were stuck travelling in one direction through space? Of course, later, when I went to pre-kindergarten and taught myself to read, I understood that if there were fewer spatial dimensions, then there would be no gravitational forces between masses. Everything we see'—she pointed at Steve—‘would simply drift apart. And if there were more time dimensions then the elementary particles of matter would be too unstable. They'd simply decay into nothing. But that just made things worse. I worried about what would happen if the structure of our reality suddenly changed, and I and my parents and my doll's house and sandpit instantly dissolved into a quantum vacuum.'

‘I worried about the exact same thing,' Sophus said. ‘I guess most kids do.'

‘When I started school,' Ann continued, ‘my teachers took me out of the normal classes and let me study whatever I wanted. Of course, what I wanted was mathematics, and I began to read Lobachevsky.'

‘Ah!' Sophus gave a blissful smile. ‘Lobachevsky!'

This was why Steve hated mathematicians. He liked to think he knew pretty much everything about everything. Oh, sure, there were tiny areas of academic interest where experts knew more than he did about, say, specific species of beetles or ancient Mayan literature, but in general Steve knew everything important. Mathematicians attacked his sense of omniscience. They didn't know any of the things Steve knew, like the fact that humans evolved from cannibalistic apes addicted to eating each other's brains or that Jesus was a woman who moved to India after he died. Instead they viewed history as the grand sweeping progress of mathematical thought, while art and philosophy and empire ebbed and flowed about it. And he disliked the way mathematicians celebrated great thinkers whom Steve had never heard of, like this Lobachevsky guy. So he said, ‘Lobachevsky? Hasn't he been debunked?'

‘Oh, no.' Ann shook her head, visibly shocked by this heresy. ‘Nikolai Lobachevsky was one of the greatest mathematicians of all time. When he was an astronomer at the University of Kazan in Russia, he developed non-Euclidean geometry, and in so doing he challenged one of the most basic intuitions about reality and the way we think about it.

‘Philosophers once believed that Euclid's Axioms were such basic, obvious truths about our universe that we were born with this mathematical model of reality, in which parallel lines remained at a constant distance even if extended to infinity, and that its truth transcended logic or deduction. No one questioned this until Lobachevsky. It's impossible to overstate his influence on Minkowski and Einstein, and because of that lineage we know that the universe isn't the way it seems at all. It's a four-dimensional hyperbola that can only be described using mathematics pioneered by Lobachevsky.

‘I remember sitting in an empty classroom,' Ann continued, ‘and looking up from his equations and staring at the world around me and wondering, What else is wrong? What else about our reality do we think is so self-evident we never question it, but if we did it would reveal amazing new truths about our existence? And how do you make a breakthrough like that?

‘But then, years later when I was a postgraduate student, I read deeper into Lobachevsky's work and found something … disturbing. At the same time as Lobachevsky, a mathematician called János Bolyai, working in Hungary and totally unknown to Lobachevsky, was working on the exact same idea. At first this seemed like an odd coincidence but then I learned that two other mathematicians, Carl Friedrich Gauss and Friedrich Karl Schweikart, also worked on the same idea at the same time, all independently of one another. How could this be? An idea which had remained unthinkable for two thousand years suddenly manifests itself in four minds simultaneously? Impossible, surely. Yet it happened, and reading their four papers I was struck by the notion that I was reading the work of a single author, a unique individual intelligence somehow working through the separate minds of the four mathematicians. But who or what could this author be? Where did mathematical innovation come from? Was all progress in mathematics over the last several thousand years the result of a singular intellect developing its thoughts through a succession of individuals? Why did almost all mathematical discovery all around the world suddenly stop for 800 years, from 300AD to 1100AD? Is it because whatever directed these discoveries was blocked?

‘These questions haunted me. Perhaps our species was merely a tool for the development of mathematics. But who was the developer and what was their goal?

‘At first, all this was just wild supposition. I couldn't publish anything on it. My career would be destroyed. So I set out to prove my theory. I built models charting and predicting mathematical progress throughout history. Again and again I saw previously incomprehensible concepts suddenly manifest themselves through mathematicians, and those ideas proliferated out in the world, giving birth to technologies, systems, new societies. And they weren't limited to mathematics. I also looked for the emergence of certain abstract mathematical structures in songs, paintings, even novels.

‘And I found them. Hundreds of instances throughout history of inexplicable, emergent breakthroughs. But what I really needed was a contemporary example. I wanted to examine the circumstances behind one of these breakthroughs. I wrote computer algorithms that would search songs, books, academic writings, architectural blueprints—all the intellectual outputs of our species—trying to find an outbreak, a radical change in the pattern. Evidence of something incomprehensible. Something alien and new.

‘And after months of searching, I found it. A series of routine articles published in a biochemistry journal fifteen years ago. The author's name was Simon Ogilvy. There was nothing interesting about the papers themselves, but embedded deep within the words and the graphs were radical new ideas in symmetric geometry, ideas that didn't appear within the mathematics community until a decade after Ogilvy published his work.

‘Who was Ogilvy? More importantly, what happened to him? I learned that he'd been fired from his university, but no reason was given publicly. Then his name was mentioned in a police raid on a remote farm near an isolated seaside town. He was suspected of operating a clandestine laboratory. But he vanished just before the raid; the police never caught him. And after that there wasn't a trace of him. Simon Ogilvy, suspected conduit for revolutionary ideas from an alien dimension, had vanished. So I learned about his past. I learned that he grew up here, in the Aro Valley, in a place called Threshold.'

They were at the house now. The scaffolding served as a stairway to the front door. Eleanor went first, then turned to watch as Steve and the Cartographers manoeuvred the bath onto the first plank, and grunted and strained as they lifted it up the makeshift steps, one by one. Sophus frowned; he looked troubled by Ann's words.

They were halfway to the top when the archivist, exhausted and panting, fumbled and dropped the bath. Steve squawked as it fell backwards, dragging him with it back down the steps, until Sophus grabbed the bath by the rim with one hand and clutched at one of the poles with the other, gritting his teeth with the effort. Steve grabbed on to a wooden slat to stop himself from sliding off the side of the scaffold. The structure swayed.

‘We need to rest,' Sophus told Eleanor, once they'd pulled Steve back up and got their breath back.

‘Don't be absurd,' she snapped. ‘We're nearly there. Gorgon awaits.'

‘She can await a while longer,' Sophus replied. He and the archivist wedged the bath between two poles and squatted down on the plank, breathing heavily and rubbing their hands. Sophus nodded at Ann. ‘Finish your story.'

‘There's no time,' Eleanor barked. ‘Gorgon demands—'

‘Gorgon demands? Or you demand?' He turned to Ann again. ‘Finish.'

‘I took leave from my university,' Ann continued, ‘and I travelled to this country, and made my way to Te Aro, where I took a room in a boarding house on Aro Street. I tried to research the past of Simon Ogilvy, this mysterious biochemist, but the people who lived in Te Aro were hard to reason with. I tried to search the town archive but the archivist told me there was a radiation leak, and the archives were closed for a thousand years.' The archivist gave a low, throaty chuckle. Ann went on. ‘After two weeks I made no progress, but I sensed that the key to my search was here, somewhere in the valley. I quit my job and used my savings and the money from my prizes to buy my house. I took a job at the Community Council to meet my living costs, and help me in my quest. But after months of searching I was still no closer to Simon Ogilvy or his connection with another reality. Oh, there were hints. Signs. Snatches of children's songs. Graffiti on fences. I knew there was something here, somewhere. That something had happened in this valley. But what? When? Why?

‘I reread Ogilvy's work. The mathematics in his papers seemed to describe a specific space. A mathematical graph with edges and vertices.'

‘The Real City,' Sophus murmured.

‘I didn't know that then. I designed an equation to measure the constants of that space. In our universe we can measure the ratio of a circle's circumference to its diameter to find the number pi. The Ogilvy-Day equations measure this value in the non-Euclidean geometry of the Real City. What shocked me is that, six months ago, the values in these equations changed.'

‘Impossible,' Sophus protested. ‘They aren't physical values. They're like the properties of a circle, or the sum of angles of a triangle. They're fixed. They can't change.'

‘That's what I thought,' Ann said. ‘It took weeks of investigations followed by three solid days of calculations to understand what had happened. The values changed when someone took the DoorWay compound and entered the Real City. They observed the City, and the act of that observation changed the deep structure of that reality. Not by much; just a little. The Ogilvy-Day constants fluctuated for a few months, then it returned almost to zero. Then, this winter, they shot up. They've been skyrocketing ever since. The more people who observe the Real City, the more the values change. That's why Gorgon and her Cartographers are drugging people and kidnapping them.' She turned to Steve and said, ‘I know you're not a mathematician. But you understand the relationship between pi and Gaussian curvature, right? You're not a moron.'

Steve chose not to respond.

‘If Gorgon traps a few more people in the Real City, this value will reach its maximal rate in a matter of hours.'

‘Then what happens?'

‘I don't know,' Ann admitted. ‘I fear that whatever exists beyond the Real City will cross over into our world. And then—'

Eleanor interjected. ‘That's enough.' She stood on the steps above them, her taser raised. ‘Pick up that bath.'

~

They made their way up the steps. The old house loomed over them. It was old, crumbling. The windows were dirty and the curtains were drawn. Grass sprouted from the gutter running along the roof. An empty doghouse sat at the end of the scaffolding. The cliff behind it ascended into mist. A sharp wind blew up from the slope; the scaffolding trembled with each gust.

Eleanor reached the top of the steps. Ann was behind her but she'd fallen back to exchange whispers with Sophus. Footsteps clattered on wooden slats; the bath chimed as it knocked against the beams. Then Eleanor, Ann, Sophus, the archivist, Steve and the bathtub were at the top of the scaffolding, outside Gorgon's front door.

Eleanor crossed to the front door and knocked. She bade Sophus and the archivist to wait with a flick of her hand. ‘Gorgon comes,' she announced.

Steve cursed. He kicked out his leg, feeling the cuff bite into his ankle. He didn't want to wait and let Gorgon take him. He wanted to struggle. To fight. To win! But his captors were armed with tasers and syringes, and he was handcuffed to a bath. Even Steve had his limitations.

He drummed his fingertips on the scaffolding and looked out over the vast sweep of the Threshold development. The hill fell away in a patchwork of weeds and mud, ending in a row of pine trees. Beyond that was the valley proper. Steve gazed out at it. He loved Te Aro: its dark narrow roads, the gardens with rusting camper vans, the parks filled with sleeping vagrants. Was he seeing it now for the last time? Would he spend the rest of his days in the Real City, a place where rusting vans and vagrants didn't even exist?

Someone jostled him. Steve did not resist. His time was up. But then there was a cry of pain, a flurry of movement. He looked around.

The archivist lay on the planks of the scaffold, twitching. Someone had stunned him! Steve flinched as Sophus pushed past him, heading for Eleanor with his taser humming in his hand. Eleanor turned, eyes wide, and shrank towards the door, waving her syringe to ward Sophus off. ‘What's the meaning of this?' she asked him. ‘Are you betraying Gorgon to side with these heretics?'

‘Ann isn't a heretic,' Sophus replied. ‘She's just questioning the assumptions behind our beliefs.'

Steve said, ‘That's the definition of a heretic.'

‘Shut up, Steve.' Ann pushed past him and began to say something to Eleanor, but she broke off when a blast of wind shook the scaffolding. They all lurched and swayed. When it was still again, Ann said, ‘I just want to talk to Gorgon. Ask her why she's doing this.'

‘Gorgon doesn't answer to you.'

The scaffolding shook again. Eleanor dropped her syringe. She reached for it, but Sophus darted forward and stepped on it. Eleanor reeled back, eyes flashing. She gave each of them a glance of pure hatred and then ran through Gorgon's front door.