Singapore, 2008
“Xièxie,” Allie said as she took the bowl of chilli crab, the first word she’d spoken in the whole interaction, having indicated what she wanted with a mixture of nodding and pointing.
“You’re welcome,” replied the street hawker in English. “Enjoy!”
Allie nodded at her, trying to express in that one gesture a mixture of genuine gratitude, embarrassment at her own halting attempt at Mandarin, and the respect she thought was due to someone of her advanced years.
A lot of things were different here — she’d never really tried seafood before, for crying out loud — but the thing she was finding hardest to get her head round was seeing so many people who she would have thought of as well past retirement age who were still working. She couldn’t help but think of Nana, who’d looked after her for so long. Keeping up with Allie had been exhausting enough for her; it was impossible to imagine her holding down a full time job at the same time.
But then, Allie was getting used to culture shock.
Even Canada, where she’d ended up first, hiking for days to reach the border after she’d translated herself back home to escape the police raid on her and Soph’s little hut, had had differences both blatant and subtle. She hadn’t stayed long though, thanks to the similarities. It might be politer, more apologetic, maybe even genuinely reluctant at times, but the pressure from its southern neighbour and elements of the local population alike was enough to have driven the country far down the anti-mathematical road.
The UN vote that had been forced by the dumbass President — now re-elected for his third term after some hasty political chicanery to avoid the term limit — had at least given Allie a list of possible next destinations. The twenty-odd countries that had walked out were her best hope of finding somewhere to seek asylum, and continue her studies in relative safety.
She’d wound up in New Zealand first, where she’d been almost overwhelmed by its vast emptinesses, but while the math faculty at the University of Auckland had been enthusiastic about offering her a place, the immigration authorities had been nervous of antagonising a nation that was still, on paper, an ally. When they’d started extradition proceedings, she’d made her way out working passage on a cargo ship that had eventually brought her here. A stop in New Guinea had afforded the opportunity to obtain some fake documents, courtesy of Azizi, the closest thing she had to a friend on the crew, who seemingly had “contacts” in every port.
As far as the bureaucracies of the world were concerned, Aletheia Voss had vanished somewhere in New Zealand. The woman who stepped off the boat in Singapore two months later was Australian citizen Allison Johnson — she’d insisted, against Azizi’s earnest advice, on still being able to shorten herself to “Allie”.
She still hadn’t really got to the point of successfully pulling off an Aussie accent, which was part of why she had taken to trying to speak to people in their own languages while she was here. It was a constant challenge, though, to try and keep it all straight in her head — confusing tenses that straight up didn’t exist in English, situations where the exact inflection really mattered. None of it came naturally, none of it could be neatly summed up in an equation that she could see all at once.
She’d managed to get herself permission to audit a few courses at the university, but she’d have to wait until the next academic year to join properly. She wasn’t the only escapee at the university — a whole swath of Europeans, students and academics alike, had made their way here over the last couple of years, after the EEC had summarily shut down all university departments that weren’t willing to redesignate themselves as being devoted solely to Arithmetical Problem Solving. It wasn’t quite as bad as the “Essential Numeracy” she’d been subjected to, but their stories were certainly familiar.
Finishing the last of the crab, she deposited the bowl and headed back to the small apartment she shared with Marie, a French student who had taken pity on her soon after her arrival. Allie was sleeping on the couch but it was a roof over her head and Marie was good company, most of the time.
She found Marie at the cramped desk in the living area, working through a set of problems. Marie had got here in time to enrol properly, but of course that came with homework. Squinting over her shoulder at obviously more and more desperate lines of working that weren’t resolving properly, she said, “Excusez moi?”
“Please, if I have asked you once I have asked you ten thousand times,” Marie said. “Stop massacring the beautiful language of my forefathers.” Then she sighed. “But I assume you’ve spotted something I haven’t?”
“I think back here–” Allie pointed “–you cancelled through by (x-y), but if x equals y–“
Marie put her hand up. Allie knew well enough by now to stop talking immediately and let her figure it out the rest of the way. A minute or so’s scribbling later, she was satisfied. “I got you that book you wanted from the library.”
“Thank you,” Allie said with a wide smile. Since she wasn’t an official student, while she could visit the library, she couldn’t check anything out. Now that Marie had mentioned it, she spotted the book at the bottom of a pile on the corner of the desk. Extracting it carefully so as not to let the others topple as she took it, she said, “I owe you one.”
“But of course you do,” said Marie. “I should have kept count from the beginning of how many times you say that. If I had an accurate account with the Bank of Allison Johnson, I would be owed many hundreds by now, I think.”
“Merci beaucoup,” she said as she took the book, laughing as Marie covered her ears in mock horror at her terrible French accent.
With Marie still working at the desk, Allie took herself into the cramped kitchen area to read. She had read the first chapter or so at the library itself, but she knew there was more to understand.
It had been an off the cuff comment in a lecture that had set her down this path — a passing mention of “the incompleteness theorem” that had made her realise how much there was that she didn’t know she didn’t know. As an auto-didact who’d taught herself out of a high school textbook, she hadn’t had much exposure to the more philosophical ends of the subject.
As she read, she grew increasingly excited. She hadn’t let on to anyone here — not even Marie — about the full extent of her studies, but she’d been feeling that she was brushing up against the limits of what was possible. She’d spent some time on board ship figuring out how her translation abilities worked with moving objects, only to realise that the Earth itself was moving far faster in its orbit round the sun than almost anything on its surface in the relative frame. But there had to be more, she believed, some way to enter that trance-like state and see how everything fit together, not just her own place in the equations.
Gödel’s insights might — perhaps should — have sent Allie into existential despair. If mathematics could never be complete, there were no final answers. But, as she grappled with the unfamiliar concepts, they turned around in her mind into something else — if there were no final answers, there were potentially no limits. If there were always more axioms that couldn’t be decided, then maybe she could decide what they were in the way that suited her.
There were faint echoes in it of Cantor’s diagonalisation argument, something she had encountered previously, and deepened her understanding of infinity.
Almost without realising it, Allie slipped into a trance as she considered the implications. The universe was, fundamentally, a mathematical system, of that she had long been convinced. But what if it was just one of an uncountable infinity of universes, one where the truth of certain axioms allowed her and others like her to access the underlying structure of reality, to perceive, even manipulate it.
She felt her consciousness expand until the chair, the table, the kitchen, the apartment, the city, the whole troubled world, melted into abstractions. She glimpsed, for a moment, what seemed to her a higher plane, a bird’s eye view that was a map not of physical territories but of a conceptual space of infinite dimensions.
“Allie?” When she noticed Marie’s voice, it sounded as though it came from half a universe away. “Où es-tu? Where have you gone?”
Allie focused back down, reconstructing as best she could from the mathematical perspective she was caught in the details of her specific context. As she did so, she realised that there was one crucial thing missing from the description of the kitchen: her physical form.
Hurriedly, almost desperately, she reassembled herself as best she could. She had no way of knowing whether she had put herself back together exactly the same as before, and no way to know how close she had come to the point of no return where she would have been unable to come back.
What had pulled her back was Marie and her obvious concern.
Later, Marie told her that she had appeared out of thin air. But in the moment all she said was, “I think we need to talk.”