Knot Theory: A Short Story

Mathematical knots are closed loops. Unlike a usual knot, there are no loose ends.

One female Backpacker, slim build, finds her hostel by accident. Maps in guidebooks are always printed upside down and any destination lurks deep in the page binding. Murphy’s Law. Is she in Ireland now, or Scotland? It’s easy to forget these days. She checks the front of her guidebook. She peers through semi-darkness at the door ahead and notices a small, laminated sign. ‘Beds from 13 pounds.’ Groan. The Backpacker mooched down this very lane twenty damp minutes ago. She has managed a closed loop around the old town. Knot happy.

So, this is The Royal Mile. Dusk must come early to Edinburgh. Through its haze of drizzle, this street feels like something out of a Scottish murder mystery. Is Scotland Yard anywhere round here? Should’ve looked it up.

She presses a button and speaks into a circle of holes in the wall. The speaker phone reminds her she is not really a bit part in some gothic horror flick.

“Yeah, we’ve got a bed. Come on down.” The voice is unmistakeably Australian. The Backpacker hears a click and the heavy door swings open. The hinges don’t creak, but she expects them to. Laminated arrows lead her down a warren of corridors. She clomps down a steep staircase, gripping each handrail with fingerless gloves. Weighted down by a tall canvas pack, gravity is not on her side. She is glad to reach the bottom without going head over turkey.

Underground, The Backpacker discovers a décor of primary colours, bulletin boards and phone cubicles. Reception is enhanced by burnt-out light bulbs: a kind of mood lighting peculiar to hostels. Shadows always help to mask grime. She hears the click-click-sink of billiard balls coming from an annex to the left. Laughter emanates from the living room. This kind of snorting hilarity is often heard from cliques of semi-permanent hostel residents who despise fly-by-nights. The Backpacker has seen many hostels just like this one. So why, after three years’ travelling, does she still not feel at ease?

The Backpacker casts a shadow over the front desk. The receptionist has her eyes fixed on Neighbours broadcasting from a bench-top telly. This must be the fellow Aussie. Unused to the climate, the receptionist wears long-sleeved stripy thermals under a Kathmandu tee. Her hair is wrapped in a towel turban. Wet, bleached strands fall out, sticking to her neck. She hasn’t lost her tan yet. She drinks noodles like beer, but from a polystyrene cup. Like every other hostel within cooee, this one must be short on forks.

The receptionist sees a new guest from the corner of her eye. “How many nights you staying?” Two curly, maggot-coloured noodles hang out of her mouth. Clear juice dribbles down her chin. She wipes her mouth with the heel of one palm.

The Backpacker feels a familiar knot in her stomach. She is hungry. “What’s the weekly rate?”

“No discount for long-termers. Soz.”

“I’ll pay for two nights, then.” The Backpacker has not spoken to anyone all day, not since leaving Victoria Station on the 0900 Megabus. Her unfamiliar, husky voice struggles past a lump in her throat. It’s official. The Backpacker is fighting another foreign cold. After three years of this she should have developed immunity to northern hemisphere bugs. But she hasn’t.

“I can stick you in a unisex room for cheaper?” One maggot flies across the desk and lands on a well-thumbed Time Out mag.

The Backpacker is a fellow Aussie but this is the extent of their camaraderie. In any British hostel, Australian guests are the default. They each meet so many young Aussies over here that they feel a bit sorry for the dude left behind.

Would anyone have noticed if Australia sunk into the ocean? The Backpacker thinks that maybe she should call her Dad. It’s been months. Or has it been a year? She’ll call the old man for Christmas. Get a phone first, with some credit on it.

What’s left when you can’t see the knot, not just because there’s no matter there, but because space itself doesn’t extend to where the space used to be?

The receptionist wipes a salty trickle from the corner of her mouth. “Down the hall, second on the left. You’re sleeping on Elvis.”

If the receptionist expects a puzzled look she gets no such reaction from this guest. The personification of beds is a tacky trick favoured by hostels far and wide, as an aid to the drunk and forgetful. Three years of dossing has uncovered common themes: bed bugs, smelly feet, noisy sleepers and laminated labels on bunks, secured by tape. Scotch tape, no doubt. Ha.

The Backpacker hovers in the doorway and scans her temporary abode. Dolly, Kylie, Madonna, Fatboy Slim… Elvis wears his sheet tucked in. His duvet is slick and smooth, his pillow fluffed. The Backpacker puts little faith in ostentatious displays of housekeeping. A tucked-in sheet means nothing. She dare not sniff his bedclothes. She flips over his pillow and hopes the linen dude didn’t do the same.

Elvis is a top bunk. The Backpacker is pleased. Proximity to the ceiling engenders a sense of privacy and gives her a bird’s eye view of the room. Eleven open packs spill across beds. A survey of scattered boots tells her most of them are blokes. Experience tells her at least one of them will be drunk and two of them will snore like billy-o.

The bathrooms are unisex too. An oval mirror covered in white flecks of toothpaste is studded to the wall above the hand basin. The basin is garnished with a scrap of dirty, yellow soap and someone’s haywire toothbrush. The Backpacker catches sight of her own reflection. The overhead bathroom lighting flatters no one; dark eyes disappear into her skull. Her face is waxen white and unfamiliar. The face does not smile back.

In the real world, mirror reflections are no more than mental images. In mathematics, reflections are as real as the objects themselves.

This hostel, like every other she has known, has too few ablutions. Half are in a state of disrepair. One toilet is blocked. Another is occupied. The third will not lock. The door stays shut with the help of one leg extended. This is no place for the inhibited; the bogs lead straight off the living room. The Backpacker gazes at multi-lingual greetings and invitations on the back of the door, drops a load and hears laughter.

She hears another familiar accent: Saffa, or maybe Kiwi: “You’d look badass with mutton chops, babe.”

The Backpacker pulls off reams of point-five ply toilet tissue and imagines a surfie girl reclining across the lap of a twenty-one year old grungy bloke who hasn’t seen a mirror in weeks. She emerges from the toilet and stands for five minutes beneath a lukewarm trickle masquerading as a shower, then appears at the door of the living quarters. Nobody looks up but The Backpacker has imagined right. The surfie Saffa girl strokes a stubbly cheek and kisses the bloke’s grungy neck.

The furniture is a motley collection from every era. Low couches sag under the weight of crammed-in bodies. The group waits for something to begin on a muted television. A cricket match, no doubt. It’s summer back home. Hard to believe.

Some of the somebodies sip from cans. A pair of legs in low-riding denim stands upon a coffee-table. The head has disappeared through a window set high in the wall. He angles his lips onto the footpath outside, but his exhalations catch on the breeze. The living room fills with sweet smoke. Nobody complains. Still, nobody looks up at the newcomer. Non-descript thumpy music drums from a cheap stereo by the fireplace. And there are no spare seats.

In the kitchen, German tourists have gathered around the table. They might speak Dutch. Or Afrikaans. Anyway, The Backpacker is glad for a reason not to converse. The men hold playing cards like Japanese fans. One pumps his fist into the air. The others groan. Two of the party are young women, each as tall as their men. One dishes out stew from a bubbling vat on the stove. The other dishes out instructions. The kitchen smells of trout.

The Backpacker rinses a chipped mug and refills with Edinburgh tap water. Shavings of cabbage block the sink. The Backpacker stares into the plughole. She gulps the water, wincing as its chill stabs her throat. The taste is not bad. It’s better than the soupy bleach-water of Earl’s Court. The water does nothing to make her less hungry. She opens the fridge and sees knotted plastic bags, each announcing its owner’s name and date. A two-litre bottle of milk is almost empty. ‘DO NOT TOUCH’, it warns. ‘I SPAT IN IT, BTW’. The Backpacker grabs the thick-nibbed marker and etches her own message onto the stranger’s milk: ‘SO DID I.’ She takes a swig and lets the creamy milk soothe her throat.

In her bunk room, two Kiwi boys sit cross-legged on the floor. They pore over a free tourist map. They look up and grin.

The Backpacker raises her eyebrows in greeting. She recognises their faces from an Earl’s Court pub. Or maybe not. Maybe Kiwi boys all look the same.

Long hair is bad for nits but works well as a blindfold. The Backpacker masks her eyes with her dark locks to avoid glare from the centre-ceiling bulb. She drifts off with the aid of a cold-and-flu tablet, lulled to sleep by discussions about castles, walking ghost tours, and a circuitous debate about the unlikelihood of afterlife. One of them reckons he’s seen a ghost. He’ll have to embellish his story before it counts as a bone fide travel yarn.

The Backpacker wakes later to rustling and giggling. The light was switched off at eleven, flicked on again at midnight, off again at one and on again at two. A male and female stagger in. Each stifles bursts of laughter. The Backpacker groans and thrusts herself over to face the wall. The couple snigger at the newcomer’s lack of joviality.

She wakes again before dawn to a pair of entwined grunts. She buries her face into the foreign pillow and imagines she’s anywhere else. After all this time of unisex bunk rooms, this backpacker knows she is no voyeur. Hearing a guttural release from an adjacent bunk excites in her the same feeling you get waiting outside a toilet while someone takes a dump. It’s all natural. But then so are cadavers. She’d rather not see one of them either.

The keenest of the tourists rise early and enjoy the only hot showers of the day. A different sort of groan choruses throughout the bunk room as the grumpiest of the sleepers attempt ten more minutes’ shut-eye. The main light flicks on and off. Long zips emit shrieks, struggling to contain dirty washing and collections of fridge magnets.

The Backpacker’s sore throat has metamorphosed into a proper cold. She wakes with a dry mouth and a full nose. Her stash of semi-transparent toilet paper has come to an end. She navigates down the squeaky bunk ladder, gripping cold metal. She waits for a toilet, pinching wet nostrils between two fingers. A dude with after-grog-bog hangs his head in shame as he ducks out of a cubicle. The Backpacker has lost her sense of smell and is glad of it.

Again, she cannot be bothered eating but her stomach growls. Cornflakes and white toast with jam are included in the overnight price. The kitchen is quiet this morning as solemn faces stare into bowls. The pitter-patter from outside means another day of damp touring. A few of the breakfasters travel in pairs, murmuring to each other in foreign whispers. There are plenty of cornflakes but no spoons. One glance into a stubborn cutlery drawer reveals a carving knife, a rusty vegetable peeler and a serving spoon. Hunger dictates use of the serving spoon, too big to fit comfortably inside anyone’s mouth, but sufficient for the job of shovelling in food.

The Backpacker sits at one end of the trestle table, face dwarfed by her eating implement. She suspects a snide remark from two Germans and wishes she could speak their language, surprising them with a witty retort. She dabs at her pink nose with a fresh supply of hostel toilet paper. She always fashions her hair in one long braid over breakfast. This gives her a mildly religious look and people tend to trust that. Or maybe they avoid her, wondering if she’s a bible basher. Fine either way. She secures the end of her braid with the elastic band she keeps on one wrist. A male voice interrupts her thoughts.

“You sleep on Elvis, no?”

The young man has sandy hair, standing up at the front as if he’s been pressing his palm to it. Sitting opposite, he looks far too cheery. Her oversized spoon makes for a good talking point but The Backpacker does not want a discussion about the bloody spoon. She does not want pleasantries, not at this time of the morning, not ever. She grimaces a greeting. This underground warren is overheated.

“You are the girl who slept on top of me last night, no?” He is definitely one of those irritating morning fools, ill-suited to communal living.

The accent is French. One of life’s disparities: when the French speak English their accent is attractive. When English speakers attempt français they only manage to bugger it up. The Backpacker knows this from a trip to Pareeeee. She’s too scared to go again in case the blokes at Heathrow don’t let her back in. But Irritation Phrasebook French may prove handy yet; a butcher’s job upon his mother tongue might shut the ribbeting up for good.

For now she nods. So, this is the bunk mate that came in late, rattled his pack for way too long and then tossed for half an hour. Tossed and turned, that is. With Elvis being an aluminium construction in need of a good squirt with the WD40, The Backpacker knows her bunk mate’s sleeping habits. He breathes heavily through his nose but doesn’t snore.

The Backpacker puts down her spoon, suddenly self-conscious. “Sorry about last night. That useless bunk creaked and shuddered every time I blew my nose.”

“No problem. I too have a cold. Maybe you contracted it from me.” He shrugs, sniffs, and takes a bite of his breakfast. He has come prepared with light, crusty bread of his own, smothered in glistening jam of deep red. That can’t be hostel jam. Hostel jam is smooth and translucent with wood chips for seeds, and comes in tins the size of paint cans.

Perhaps he senses envious eyes fixing upon his bread. “Would you care for a baguette?”

“Aw, nup.” The Backpacker stares into her bowl of soggy cereal.

“The bread will be stale before lunchtime, so…” He passes his spare bread-roll across the table. The golden crust glistens from behind cellophane. The offering looks far more appealing than a bowl full of scabs.

Gracias.” Hang on, that’s Spanish. “Merci beaucoup.”

“Jam of Strawberry?” He produces a cute jar from a paper bag and slides it across the table.

The Germans wipe their mouths and drop dirty dishes in the sink. The Backpacker and her bunk-mate are now alone at one end of their trestle table. They each eat a baguette from one cellophane two-pack. Theirs is a strange kind of intimacy: the kind that comes from sleeping together but alone. They eat in comfortable silence, as if they might have breakfasted this way for years.

A union of several loops is called a link.

He flips through a weighty book which sits flat upon the table. The Backpacker sees upside-down numbers and mathematical symbols: universal language deciphered by few. She has seen many unusual things in hostels: fisticuffs over the TV, arguments over the washing machine, drunks passed out on the stairs. Human turds in the entrance hall. But she has never seen mathematical studies over breakfast.

Perhaps he senses her gaze. “Mathématiques. I came to Edinburgh last week. Next semester I will study for a PhD in knot theory.”

“Not theory? What, then? I didn’t know you could get a doctorate in anything practical.”

Knot theory, like on the shoelace.”

From school The Backpacker vaguely remembers trig and algebra. “I can tell you how to deal with tangles,” she says. “It’s not something you need to work out with a pencil. All you do, right, is you grab it in the middle and wriggle hard with both hands. Works every time.” She waves her crust in the air, animated for the first time in days. Or months.

The Mathematician smiles. He bows his head in submission. “I will try to wriggle hard next time.”

“I’m shit at maths,” The Backpacker says. “Bores the hell out of me. But I’ll tell you what I’ve always wondered, yeah?” The Backpacker produces an iPod from the front pocket of her jeans. “Look at these headphones. Knotted every time. Explain that to me, doc.”

“Ah. That is the second law of thermodynamics. Left to nature, all things turn to merde.”

She knows he is right. You spend your mid-twenties moving from country to country, town to town. But life doesn’t change. Not really. The climate changes. The landscape changes. But sooner or later all things turn to shit. The bag is packed. Fresh start.

“Either that or… knot pixies? Ch’sais pas.

The Backpacker shifts in her seat. She does not usually find strangers attractive, but she likes the width of his face, the way his cheeks taper down towards a sharp chin. The Mathematician could pass for a knot pixie himself. He pulls out a tissue. She likes the way he sneezes into it.

“I have only been here a week,” says the Mathematician, “but I can show to you the vicinity. Do you want to see Edinburgh Castle?”

“Seen one castle, seen ‘em all.”

“Ah. Let’s go for a walk.”

“It’s pissing down with rain.”

“Not pissing. Sprinkling.”

And so The Backpacker follows The Mathematician up the steep staircase and outside, into Old Town. He wears a transparent poncho over his woollen jumper. Droplets decorate his glasses. She wears long boots and a leather jacket. The front zip is broken, but she turns up its collar.

“Where are we going?” she asks. In the hazy daylight, the streets look different. She can’t even remember the route back to the bus station.

“Let’s walk in a circle.” The Mathematician examines a map on his mobile phone. “A circle has a shorter perimeter than a quadrilateral. We’ll see the same sights, yet we will become less wet.”

They walk together. The Mathematician gives names to parts of the architecture. He speculates on the current temperature, tells her which way is north, points out local plant life. The Backpacker wonders if he ever talks about normal things. She tells him her name is Ruby, because she feels like a Ruby today. She tells him about her mother who spies UFOs for NASA in the outback, and about her father, still on compo after injuring his lower back in a circus related incident, October ‘76.

Mathematics is a kind of fiction. We talk as if numbers exist. A statement like 2 + 1 = 3 is just as false as ‘World’s End Close is just inside the Netherbow Gate’, but both are true according to the relevant fictions.

The Mathematician knows that the best view of The Royal Mile is from Arthur’s Seat, an extinct volcano, apparently. At Holyrood Park, the climb to the summit is slippery. The Mathematician offers his hand. She takes it. Her face is wet and her nose is red. He offers her a tissue. He produces a pack of twenty-five from his breast pocket, reaching under his poncho, insisting she take the lot.

From Arthur’s Seat, the roofs of Edinburgh slope off sharply. The buildings are grey and white and terracotta. They both shiver.

It is still drizzling and the hills are deserted. The Backpacker realises that she is alone, once again, with a man she doesn’t know. But she shared a bunk with him last night. What else is there to know about a person? They lean slightly into each other, sheltering from the wind. She watches his face as he looks, through smeared spectacles, into the horizon and she wonders if he’s processing some mathematical equation.

“Would you like a mint?” The Mathematician produces a bag of green and white pearls.

The Backpacker accepts one. “It always pays to take a mint. You never know if it’s a hint.”

The Mathematician examines her face. “I do not know the state of your oral hygiene.”

“Do you want proof, or something?”    

With a mint stored in each cheek, he reminds her of a squirrel that startled her once in St James’s Park.

Whenever she closes her eyes it is a little easier, pressing her lips against those of another. He angles his head to match the gesture. His nose is cold against her cheek. He places one gloved hand on her knee.

Seconds later she is giggling – a private, inward laugh. His smile is small and his eyes confused. Looking away, he rolls the mints around inside his mouth, counting them with his tongue.

“Your mint,” he says. “Before, I had two mints in my mouth. Now I think three.”

The Backpacker composes herself, but a high-pitched snort escapes. “You are a true mathematician, mate.”

“You want it back?” Perhaps he hopes for another kiss.

She shakes her head, stands up, heads back down the grassy slope.

“Are you sure?” He proffers the bag, but she is gone.

After a moment’s confusion, The Mathematician catches her up. He walks behind. When she slides across mud towards gorse he grabs her arm. She regains balance and pulls away.

The Backpacker cannot remember her way back to their hostel. The Mathematician has good spatial IQ. He leads them back to the alleyway.

She stares at the cricket on the TV, seated between two South Africans on the sagging couch.

He says nothing more, and goes to their bunk. He passes his eyes over a biography of Lynryd Skynryd which he found on the communal bookshelf earlier, edged between a 1989 guide to Czechoslovakia and The Holy Bible. Eventually, the Kiwi boys invite The Mathematician in for a round of Black Bitch. He joins them on the floor and wins all seven games by memorising the cards. The boys think he cheats. They conclude, several days later, that it must’ve been The Frog who pinched their phones, eh.

At five twenty-five the next morning, the keenest of the tourists are still asleep. The Backpacker brushes away her blindfold of dark hair, sits up in her bunk and carefully, gently, negotiates her way down the metal, three-rung ladder, cool beneath her feet. Used to shared accommodation, her fingers work silently with zips and domes and drawstrings until at last she is ready to leave.

The overnight receptionist is asleep on the front desk, head in arms, lulled into slumber by lilting Scottish accents on a talk-back radio show turned down low.

The complements of knots can never be the same space.

A sign at the depot tells The Backpacker that she has just arrived in another Scottish town. She is last to leave the bus, descending from the top deck only after checking the overhead racks for forgotten treasure. The driver chucks her a heavy travel pack. It’s one of those bags with straps coming off everywhere and which feels like it’s been packed tight with bricks.

The Backpacker struggles to lift it, grunting with the exertion, almost falling backwards. Even through her leather jacket, its straps dig into her shoulders. She turns away, peers into the dreich. She is free: open-ended, untethered, untied.

This. This is what they call Freedom.

The Backpacker calls it Lonely. Another knot forms like a fist in her gut. 

There are various reasons for leaving fictional characters unnamed. I decided not to name these characters because the experience of backpacking as a lone traveller can be an anonymising, lonely experience with odd moments of personal connection. Even when you meet really cool people it’s still lonely, because you know you’ll never see them again.

When I put this short story through critique I noticed that readers who’d done the whole Backpacking Through Europe thing connected to this story whereas others didn’t so much. Knot Theory is a bifurcating study of a particular setting, though for anyone worried about my story’s impact on Scottish Tourism, it’s an amalgam of hostels, not any one in particular. (I’m not aware of any underground hostels in that part of the world.) My own Year Of Hostels and Backpackers happened in 2006, mostly in London. This story is a snapshot of that time. I will say, though, that some of my most confronting hostel moments happened in Edinburgh!

Header image: AI generated using SDXL at ClipDrop and the prompt: Knolling of backpacker items for a book nerd, concept design, ultra-detailed, octane render, 8k


On paper, things look fine. Sam Dennon recently inherited significant wealth from his uncle. As a respected architect, Sam spends his days thinking about the family needs and rich lives of his clients. But privately? Even his enduring love of amateur astronomy is on the wane. Sam has built a sustainable-architecture display home for himself but hasn’t yet moved into it, preferring to sleep in his cocoon of a campervan. Although they never announced it publicly, Sam’s wife and business partner ended their marriage years ago due to lack of intimacy, leaving Sam with the sense he is irreparably broken.

Now his beloved uncle has died. An intensifying fear manifests as health anxiety, with night terrors from a half-remembered early childhood event. To assuage the loneliness, Sam embarks on a Personal Happiness Project:

1. Get a pet dog

2. Find a friend. Just one. Not too intense.




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