The Mathematrix
I met a strange lady. She made me nervous. She was doing sums. Long complex sums. I wasn't taken in, she didn't make me breakfast, despite her airfryer. It was on a train. How could I not?
Her face was a skull, but her eyes were alive with ill-fitting light and I could not keep mine off her. How old she was, there was no way to tell but it had to be more than eighty. That’s what I thought at first.
Her cheeks were hollows, grottoes, unhallowed pits, and, within her bony structures plain to see beneath liver-spotted skin; transparent, like layers of clingfilm or a bible-paper shroud. Despite the magnetic pull of the skull face other powers were at work here. I tore my gaze free and looked down for something else to see but the only thing on the table between us was hers: a spiral-bound jotter which lay open.
The ticket inspector interrupted. That gave me a chance to turn my attention elsewhere, anywhere except her face, but her right hand grabbed attention back, feverish purpose in its busy whispery mechanical scratchings, impossible to ignore. The Inspector didn’t notice her at all.
Mathematics. That’s what she was writing. I failed at school —at maths —but I recognised a square root symbol. I owned a calculator once and it was the unused button, the orange one. Mathematics skittered out from her propelling pencil and the page filled, neat as an ink-jet printer, her fingers moving in rapid micro-jerks like an overclocked bone robot.
The pencil stopped and clicking started. Twig-fingers; old, ridged nails on purple beds and a spasmodic thumb on the pencil button. She clicked quickly. Quicker. Then slower, deliberate. My eyes flicked up to hers where they were waiting to catch. She blinked once, lids rolling up like a porcelain doll’s and her eyes grew bigger and blacker in their haunted sockets. She stared right back at me now, daring me to look away —which, of course, I did.
On the seat beside her was a large box. An air fryer. With one arm she pulled it closer for protection while the thumb never stopped clicking the pencil. Then she laid the pencil down and her hand moved to a charm on the lower of three silver chains at her neck. Parabolas, each one thinner than the one above, hanging on tea-stain neck skin; taut, not jowly; tight and shiny like shins, like crackled varnish. Clavicles horned up under the mushroom linen of her shirt.
Her silence challenged me and I lost. I coughed up a nerve, smiled nerves and without looking down, rummaged in my bag of nerves. I pulled out the laptop in desperation. “Ask me,” she said, before I could open it.
Ninja CRISPi Pro 7-in-1.
“Sorry?” I pretended at fascination with the airfryer box, mouthing its blurb.
Shock resistant borosilicate glass.
“You’ve been staring, young man. I’m not blind.”
7 Preset modes including Max-Crisp and Re-Crisp!
Her voice! There was some kindness in it, unexpected youthfulness. It was not the flock of bats I had expected from a skull like that.
“I…I didn’t mean to stare. Only…”
“It’s rude to stare. Didn’t your mother tell you that?” She began to scratch at the jotter again.
“She did, yes. But doesn’t every mother say tha-”
“And yet–” She finished a line of symbols, “—still you stared.”
My hand fluttered toward my mouth the way it does, but I fought it. “I was just curious…” I nodded towards her jotter, but again she didn’t let me finish.
“—Something else your mother used to say.” A statement not a question. She pushed her jotter forward and spun it around tapping it, commanding me to read what she had just that second written:
What’s for pudding? Shit with sugar on!
My eyes widened and she laughed, a young laugh; not the laugh a woman as old as her should have had.
Did she know my mother?
“Good heavens no! A calculated guess, shall we say. Close your mouth, you’ll catch a fly. Is that something else she would say? Shall we see?” The pencil whisper-scratched again. “As you will not ask me what you wanted to ask,” she continued, as the pencil disgorged, “let me show you why you should ask. ‘Show don’t tell’. Who was it said that? You fancy yourself a writer; come on, out with it.”
My mouth flapped as I tried to dredge something up from a sludge of self-doubt that she was making deeper. “Ahh…er…was it Chekhov? Something about moonlight…”
She was at it again. The silver pencil glinted with the rhythm of the afternoon sunlight strobing through trees lining the railway embankment. She lifted the pencil from the paper and a fresh page flipped over just as we entered a tunnel. Did it do that by itself? I couldn’t be sure…surely it couldn’t? I wanted to disengage from this, whatever this was - was becoming - even if it meant getting off the train three stops early.
“That would be quite a way to walk.”
In the tunnel gloom I could not see her mouth move. “But you’re young enough and it won’t rain until teatime tomorrow. So that’s nice. But why the hurry? You haven’t asked me yet. There is time. Plenty of time,” she said.
I willed the train to rattle back into the light: the next stop was just beyond the tunnel, and the tunnel was not long. It was not this long. The carriage rocked, the tunnel walls flashed past and the chackety-chack of the train dropped a semi tone and then another and another. At the end of the carriage, the ticket Inspector stood then leaned over to check someone’s ticket, leaned back, leaned in again. Leaned back. Leaned in again. Leaned back…
“Ask,” she said. “It’s inevitable.”
“Why…” my tongue peeled from the roof of my mouth, thick as a lizard “What–”
“-Every time there is a calculus, somebody must know, or it won’t become part of the when. If it doesn’t enter the when, we won’t know whether we’ve been at the when before. Do you see? And whoever asks, they must want to know. Like you.”
At the end of the carriage, the Inspector still swayed, a jolly-faced pendulum rocking to the rhythm of the red stop lamp that flashed past, again and again. Accustomed to the tunnel gloom I could see her eyes reflect that red pulse from their skull pits. The pencil clickety-clicked. The train chackety-chacked. My head shook with so many difficulties.
“Don’t worry; you don’t have to understand. You just have to ask. And if you could write it down, any of it, afterwards, that would be best. Ink is indelible.” She pointed the pencil at me, twirled a circle with it twice then jabbed. “That’s why I like a writer.”
I swallowed dryly, red light pulsed, the conductor swayed, the pencil clicked.
“You do want to, don’t you.” It wasn’t a question; it was the light at the end of the tunnel. I nodded…and asked.
“I hope you don’t mind my asking…are you a mathematician?” It wasn’t that hard once I started to speak and I did want to know now.
“A Mathematrix.”
She rhymed it with ‘geese’ not ‘six’, exaggerated the ‘eese’ at the end of the word and cut out a smile with a serrated edge as she did so. Light swelled into the carriage and the sound from the tracks climbed back up from 33 to 45 as the train emerged from the tunnel and the Inspector walked out of limbo and into the next carriage. She urged me to continue with an eager jiggle of her head
“And what are you… working out?” I struggled for the verb and she corrected me.
“This and that,” she said. “And the word is ‘casting’. One casts mathematics.”
That didn’t sound like a word for maths, but I had failed at maths, hadn’t I. The train was slowing for the station and, to challenge her now? Frightening dogs snapped mad and whimperish at mind-heels. I had to get off. I was going to get off.
“It looks tricky.” I offered. One of her eyebrows crawled up and her hand went to the charm on the thinnest chain. I pointed at the jotter, “The formulas, calculations. Very complicated.”
“A world is a complicated thing, Mr. Stephenson. But everything can be calculated. Everything and anything.”
“Anything?” I looked back over my shoulder, towards the impossibility of the tunnel.
“Allow me to elucidate. Your mother: it’s proven that she liked things scatological: a ‘shit’ here, a ‘shitty’ there.”
She paused.
I was perplexed.
She tutted. “Shithouse, shithead, shitbag, shite. Shithole, shit the bed, shit for brains, shit-eaters, shit off a stick…must I go on?”
She was not wrong about my mother’s vernacular. “‘Shit with sugar on’ was one of her favourites,” I said. “I mean, she never actually made it for dinn-”
“—‘Shitting’ is a perfect example, Mr. Stephenson; as with all equations, what goes in, must come out. What did you eat for your last three meals? Can you recall or shall we see?”
I sat back. She tutted and began to write again, all of a mutter. The charm moved against gravity, anti-clockwise around the lower parabolic necklace chain. Then it hopped across to the one above and carried on. ‘Tick tick tick tick’ it went, link by link. She seemed unaware. I found myself speaking despite my attention being firmly on the charm as it disappeared from view behind her neck.
“A ham and egg sandwich. It had lettuce in–”
“-No need now, the equations are cast.”
I was struggling. The spiders were coming to the corners of my eyes but I hadn’t had a drink since Friday, a full three sober days hence. The charm reappeared on the other side of her neck and tick ticked its way back to where it began. She touched it with affection.
“In two hours and fourteen minutes you will feel the urge to shit and the shit will weigh exactly two hundred and ten grams. A splendid evacuation. Larger than average, if I may say, but indicative of peri-prandial snacking. Which you should seek to avoid, as Mrs Stephenson tells you often.”
“How do you know all this –not the shitting– all the rest…the things my mother says; the ends of my sentences. The snacking…”
“Mathematics.” Her look said you simpleton.
“But how…”
“I’m a mathematrix. It’s what I can do, and so I do it, for all that it takes a toll. I mean…look at me! I’ll sleep for weeks when I get back.”
I did look at her. Was she somehow even more gaunt than before? The train jerked and I realised I had missed the stop, but now I had more to ask.
“The business in the tunnel. I wasn’t–”
“--imagining it? It felt real enough, didn’t it.”
She knew.
“How…?”
“Everything is a calculation,” she said. “Every thing, every where and every when.”
We sat in silence. The train quickened, then slowed for the penultimate stop before home.
“I want to know more, but I don’t know what to ask.”
“You don’t need to underst–.”
“—But I do need to know!” I blurted. “None of it’s right! What are you doing? Here? On this train—MY train— With the mathematics? What!” It was my turn to interrupt. I couldn’t miss my stop and I had to know, had to understand.
“Oh I can’t tell you that. That would ruin everything, if people knew. It’s precisely enough that someone from the when knows that I was there and a calculus was done.”
I rubbed my fingers back and forth, roughly, through my hair. It never helps; it just feels as if it will.
“What about that then,” I asked, pointing at the box beside her.
“This? It’s an air fryer, Martin. It says so on the box.”
I blinked. Confused yet again.
“We have to eat, like anyone does,” she said. “I’m told they’re the latest thing. You can cook a whole chicken, look!” She pointed at the photo of the golden brown chicken inside the Ninja CRISPi on the front of the box. “I also need to test it, for alimentary impacts on the calculus. Two birds, you might say.” she tapped the chicken again.
“The next stop will be Hexham,” said the train tannoy. I gathered my things and stood in the aisle.
“Which stop’s yours then?” I asked.
“I have a little way to go yet. But I’m never late for dinner.” She patted the Ninja CRISPi.
The train squealed to a stop. “Well, that’s me then, I suppose” I said. “It’s been–”
–a pleasure?” She laughed in a way that sounded like she didn’t think it had been. I offered her my hand, but she wrinkled her nose and shook her head. “We really can’t touch you. Now, off you go.”
I hastened towards the vestibule. From behind me I heard her say ‘Write it down. Don’t forget. Oh, and fix the bolt.” I acknowledged her with a raised hand but didn’t look back.
And I did write it all down, as well as I could remember. And it was what I told my wife when she burst into the bathroom unexpectedly to find me shitting on the kitchen scales.
210 grams exactly.



If you encounter a sybil with prophetic powers you must never let her go. Offer her kitchen appliances or fancy calculators with all formulas on them as bribes.
Have you been reading/thinking/dreaming about time travel recently? Asimov's End of Eternity perhaps? Psychohistory - prediction of the future using complex mathematics and all that.
And of course there's a lot of mathematics in astrology, for example.
I think this vignette only seems weird from the narrator's (and therefore most readers') point of view. From the old lady's point of view it's all perfectly sensible and understandable.
She also struck me as having the same sense of mischief as 80 year old me would have, if I ever made it that far.
There was a time, when I was young, when half my best writing was prompted by stuff that happened when I was on trains. I don't really know what trains are like these days, but back then they were wonderful, interesting places.