begin with some fundamental facts. It is upon these facts that the course on the new geometry is based. If we understand the fundamental facts, then the remainder of the course will follow logically. Without that understanding, I fear we are destined for confusion and uncertainty.’ Mr. Potter knew his facts; things were proved or disproved, true or false, known or unknown.

You were in my geometry class, one of a small group of girls coaxed into sciences and technology, groomed for the new world. The girls sat together, two by two. Your books were neat, your chatter silenced by Mr. Potter’s litany of facts. From my corner of the room your arm made a shifting triangle, your elbow at the apex, cutting an arc across your desk and into the aisle beside you. It was your hand that shot up first for each question, earning an approving nod from Mr. Potter.

Using the facts from Mr. Potter’s geometry book, we calculated all manner of things, the orbits of planets, the true length of a kick at goal, the height of the school flagpole. When we scrambled to our feet at the end of each class, I delayed or hurried my exit so that our paths converged at the door. I stole into your circle of friends to see if there was a common point at which our worlds might meet. When I said you knew all the answers in geometry you said yes, and parallel lines meet at infinity. You had Mary Quant hair, all angles, a straight fringe and sides framing your face. There were others, but when I looked at them I saw only what they lacked.

Every afternoon a group of girls from the Catholic school stood on the steps of the Cathedral. Their brown gym skirts were crisp and prim, pressed into regular pleats, although I noticed that one had an erratic blue stain at the front. It was like the map of some exotic unexplored island. We always thought the girls had been to Mass, or perhaps to confession. The idea that they must confess their sins, their innermost thoughts, to the grey old priest gave me a hard on, and I wondered if the priest got a hard on too. Years later I married one of the Catholic girls. I learned that the nuns had told them to be careful when standing in the sun, that the slant of its rays could catch a girl’s hair and cause boys to become excited. The girls were practising. They wanted to get the position just right, to have the sunlight shatter on their hair, exploding in a burst of color.

On Mondays we had English for first period. Anything was better than geometry or those other subjects that weighed and measured without stopping to admire. We studied Dickens, and the literature of the Industrial Revolution. Mr. Donleavy handed out copies of Hard Times.

‘Read chapters one and two,’ he said. ‘They’re quite short. Then we can have some discussion. No talking now.’ He was glaring at you, and you shot him one of your looks, then he walked around the room, placing the books on the desks, one emphatic thump each.

I opened my copy and studied the jumble of dates stamped on the page stuck to the inside cover. I read the name from last year, then the year before, and the year before that, right back to Lorraine Henderson, 5C2, 1957. When I lifted the page I saw that someone had written ‘Donleavy’s shit stinks’ underneath. When I saw Mr. Donleavy watching, I flicked the page and started reading.

‘Now, what I want is Facts. Teach these boys and girls nothing but Facts. Facts alone are what’s wanted in life. Plant nothing else and root everything else out.’

I checked the cover and the title page. It was Hard Times all right. It seemed there was no escape from the world of facts. Even in the Industrial Revolution they had to learn facts. We read for half an hour. Chapter Two was called "Murdering the Innocents," which sounded promising, but it too was riddled with the language of facts. Then Mr. Donleavy asked you to read the part you liked most. You read the bit about Sissy Jupe, how she fancied a floral carpet, but Mr. Gradgrind, the teacher, told her she wouldn’t want people walking with heavy boots over flowers, and she mustn’t fancy, and then said, ‘Fact, fact, fact.’ You said Mr. Gradgrind didn’t understand what girls liked, that people still didn’t understand what girls liked, and then it was me getting the look and I turned the colour of Sissy Jupe’s carpet.

On Mufti Day, blazers and school ties gave way to a frenzy of fashion. I stayed up late to iron my shirt. It was black, scattered with yellow polka dots, and sharp button-down collars, then my jeans, white with no cuffs. I cleaned my shoes, then cleaned them again, so that the square toes glinted even in the pale light of my bedroom. I took the early bus, with the office workers and railway clerks. I wanted to keep the sweep of my hair in place, free from the shoving, jostling crush of schoolkids.

At the interval I found you just as you came out of your drawing class. You were wearing a vivid pink dress that flared from your hips, littered with daisies. Your arms were pale and smooth, swinging slowly as you walked. You stopped to talk to a boy from the sixth form, dismissing me with a sweep of your arm. His stovepipe jeans tapered almost to the width of his ankles, stopping just short enough to show a glimpse of luminous green. The tips of his winkle pickers pierced the air as he walked. When I saw you together I knew I’d seen a different symmetry. In a clash of equals I might have merited comparison, but here I held a subordinate position.

For the rest of the year I found the maximum distance between us, diverging from any course that might cross yours. Sometimes from a remote vantage I saw you with him, perfect opposites, poised in dynamic tension.

On the last day of school Mr. Potter wished us luck, and said the girls had proved that geometry was not the province only of boys, that girls, too, could calculate angles, plot positions, measure the space enclosed by sides. We each followed our own dreams after that, pushed by whatever we could take from our past, pulled by promises that beckoned us on, tripped by things that got in the way.

My marriage failed, then failed again. I had affairs, the first with a woman whose hair was brown and straight. She wore it long so that it brushed the freckles on her shoulders. Then there was a woman with a mass of winding curls, spiraling helices of gold. Her hair was a dense tangle, profuse and thick, becoming fine and yellow closer to the sun. As each day closed her hair faded into the night. In time I too was absorbed by darkness.

I saw you once at the shopping centre. You were trudging down the aisle of shelves, veering this way and that, a jumble of shapes in your trolley. Oranges, the corners of biscuit packets, a bunch of bananas, tins and boxes. The contour of your chin was lost in a soft curve, the apexes of your breasts rounded into some sort of sweeping parabolae. Your hair was short and sharp, unnaturally black, shot with shards of copper and bronze. I followed a looping trajectory to avoid you, but our trolleys intersected somewhere near the personal care shelf. Our eyes met for a moment and we saw a lost infinity, the meeting point of parallel lives.

Copyright © Tony O'Brien. Title graphic: "Parallelism" Copyright © The Summerset Review 2003.